is 144 a perfect square or not
Answers
Answer: Yes
Step-by-step explanation: 144 is a perfect square. In other words, it's possible to find a whole number that can be multiplied by itself that gives us 144.
In this case, we multiply 12 by 12 or 12² to get 144 which means 144 is a perfect square. Also, it's on our perfect square list which I will attach below.
Related Questions
Word problem for distributive property
Answers
Answer:
To build a computer, you need to buy a motherboard for 120 dollars, a CPU for 100 dollars, RAM memory for 45 dollars, storage for 30 dollars, a case for 15 dollars, and a power supply for 50 dollars. What is the cost of building 10 computers? Hope this helps, if so then please mark brainliest.
The distributive property allows for the distribution of multiplication over addition within an expression and is key in algebra and vector operations.
The distributive property is a fundamental algebraic property used in mathematics, especially when dealing with expressions containing variables and constants. This property allows one to distribute multiplication over addition within an expression, helping simplify and solve equations. For example, using the distributive law, the expression A(A + B) can be expanded to AA + AB. Due to the idempotency theorem, which states that A times A is equal to A (AA = A), the result simplifies to A + AB = A. Furthermore, the distributive property is also a key concept in vector operations, such as the cross product, and is critical for proving various mathematical axioms and properties, such as the associative and commutative laws.
Find the solution of this system of equations
8x - 5y = -8
-7x - 5y = 82
Answers
Answer:
x=-6, y=-8. (-6, -8).
Step-by-step explanation:
8x-5y=-8
-7x-5y=82
---------------
-(8x-5y)=-(-8)
-7x-5y=82
---------------------
-8x+5y=8
-7x-5y=82
---------------
-15x=90
x=90/-15
x=-6
8(-6)-5y=-8
-48-5y=-8
5y=-48-(-8)
5y=-48+8
5y=-40
y=-40/5
y=-8
What is the solution for x in the equation?
1/2-x+3/2=x-4
Answers
Answer:
3Step-by-step explanation:
The solution for x in that equation is 3.
The solution to the equation 1/2 - x + 3/2 = x - 4 is x = 3. This solution was found by simplifying and solving the equation step-by-step.
Explanation:You're trying to solve an equation for x. The equation given is 1/2 - x + 3/2 = x - 4.
First, combine similar terms on each side of the equation. So, this becomes -x + 2 = x - 4.
Next, add x to both sides to get 2 = 2x - 4.
Then, add 4 to both sides to isolate x on one side, you will get 2x = 6.
Finally, divide both sides by 2 to determine the value of x. So, x = 3.
Learn more about Solving equations here:https://brainly.com/question/14410653
#SPJ2
A Mathematics competition consists of 30 multiple-choice questions. A
correct answer is awarded 4 marks while 1 mark is deducted for a wrong
answer. No marks will be awarded or deducted for questions not attempted.
A student skipped 3 questions and had a score of more than 44. Find the
minimum number of correct answers obtained.
Answers
Answer:
16
Step-by-step explanation:
let "x" be the number of correct questions and 37-x be the wrong questions,
4x-1(37-x)=44
4x-37+x=44
5x=81
x=16.2
hence,16 is the answer
The minimum number of correct answers obtained is 17.
In this mathematics competition, each correct answer is awarded 4 marks, while a wrong answer incurs a deduction of 1 mark. If a question is not attempted, no marks are awarded or deducted.
Let's use "c" to represent the number of correct answers and "w" to represent the number of wrong answers. Since there are 30 multiple-choice questions in total, we can express the number of attempted questions as c + w = 30.
Now, we know that the student skipped 3 questions, so the number of attempted questions is 30 - 3 = 27. Since no marks are awarded or deducted for questions not attempted, the number of correct answers will be c = 27 - w.
Next, let's consider the score of the student. Each correct answer earns 4 marks, and each wrong answer incurs a deduction of 1 mark. So, the total score can be expressed as 4c - w.
The problem states that the score is more than 44. Therefore, we have the inequality 4c - w > 44.
Now, we need to find the minimum value of "c" that satisfies this inequality. To do this, let's substitute c = 27 - w into the inequality:
4(27 - w) - w > 44
Simplify the equation:
108 - 4w - w > 44
Combine like terms:
108 - 5w > 44
Now, isolate "w" by moving constants to the other side:
-5w > 44 - 108
-5w > -64
Finally, divide both sides by -5 (remember to reverse the inequality when dividing by a negative number):
w < 64/5
w < 12.8
Since "w" represents the number of wrong answers, it must be a whole number. The largest integer less than 12.8 is 12, so the minimum number of wrong answers is 12.
Now, let's find the corresponding value of "c":
c = 27 - w
c = 27 - 12
c = 15
So, the minimum number of correct answers obtained is 15. However, the question asks for the minimum number of correct answers to achieve a score *more than* 44. Let's check the score:
4c - w = 4 * 15 - 12 = 48 - 12 = 36
The student's score is 36, which is less than 44, meaning they need more correct answers to exceed 44.
Let's try c = 16:
4c - w = 4 * 16 - 12 = 64 - 12 = 52
Now, the student's score is 52, which is greater than 44. Thus, the minimum number of correct answers obtained is 16.
However, the question states that the student *skipped* 3 questions, meaning they did not attempt them. So, we need to subtract these skipped questions from the total:
Total attempted questions = c + w = 16 + 12 = 28
Skipped questions = 3
Total questions = Total attempted questions + Skipped questions = 28 + 3 = 31
Since there are only 30 questions in the competition, the maximum number of attempted questions should be 30. Therefore, the minimum number of correct answers obtained is 16 - 3 = 13.
But remember, the question asks for the minimum number of correct answers obtained, so we need to find the smallest possible number of correct answers. Since the student skipped 3 questions, the actual number of attempted questions must be 27.
Let's try c = 17:
4c - w = 4 * 17 - 12 = 68 - 12 = 56
The student's score is 56, which is greater than 44. Therefore, the minimum number of correct answers obtained is 17.
In conclusion, the minimum number of correct answers obtained is 17.
To know more about Inequality here
https://brainly.com/question/24156113
#SPJ2
An angle measures 14.8° less than the measure of its complementary angle. What is the measure of each angle?
and
Answers
Answer:
The larger angle is 52. 4
The smaller angle is 37. 6
Step-by-step explanation:
The equation is:
(x-14. 8)+x=90
x+x-14. 8=90
2x=90+14. 8
2x=104. 8
x=52. 4
The value for the larger angle is x
and x =52. 4
The value for the smaller angle is x-14. 8
and x-14. 8=52.4-14.8
=37.6
Verification
(x-14.8)+ x=90
(52.4-14.8)+52.4=90
37.6+52.4=90
90=90
The smaller angle measures 37.6° and its complementary angle measures 52.4°. These measures satisfy the condition that one angle is 14.8° less than the measure of its complementary angle, and both angles sum to 90°.
Explanation:To determine the measure of each angle when one angle is 14.8° less than its complementary angle, we need to set up an equation.
Complementary angles add up to 90°.
Let's denote the smaller angle as x, so the complementary angle is x + 14.8°. The equation becomes:
x + (x + 14.8°) = 90°
Combining like terms, we have:
2x + 14.8° = 90°
Subtracting 14.8° from both sides:
2x = 90° - 14.8°
2x = 75.2°
Dividing both sides by 2 to solve for x:
x = 75.2° / 2
x = 37.6°
So the smaller angle measures 37.6° and the complementary angle measures x + 14.8° = 37.6° + 14.8° = 52.4°.
A cuboid with a volume of 924cm^3 has dimensions
4cm,(x+1)cm and (x+11)cm
Clearly show that x^2+12x-220=0
Solve the equation by factorising,make sure you show your factorisation.
State both values of x on the same line
Finally,find the dimensions of the cuboid,writing all three on one line
Answers
The values of x are -22 and 10
The dimensions are 4 cm , 11 cm , 21 cm
Step-by-step explanation:
The given is:
A cuboid with a volume of 924 cm³It has dimensions 4 cm , (x + 1) cm and (x + 11) cmWe want to show that x² + 12x - 220 = 0, and solve the equation to find its dimensions
The volume of a cuboid is the product of its three dimensions
∵ The dimensions of the cuboid are 4 , (x + 1) , (x + 11)
∴ Its volume = 4(x + 1)(x + 11)
- Multiply the two brackets and then multiply the product by 4
∵ (x + 1)(x + 11) = (x)(x) +(x)(11) + (1)(x) + (1)(11)
∴ (x + 1)(x + 11) = x² + 11x + x + 11 ⇒ add like terms
∴ (x + 1)(x + 11) = x² + 12x + 11
∴ Its volume = 4(x² + 12x + 11)
∴ Its volume = 4x² + 48x + 44
∵ The volume of the cuboid = 924 cm³
- Equate the expression of the volume by 924
∴ 4x² + 48x + 44 = 924
- Subtract 924 from both sides
∴ 4x² + 48x - 880 = 0
- Simplify it by dividing all terms by 4
∴ x² + 12x - 220 = 0
Now let us factorize it into two factors
∵ x² = x × x
∵ 220 = 22 × 10
∵ 22(x) - 10(x) = 12x ⇒ the middle term
∴ x² + 12x - 220 = (x + 22)(x - 10)
∴ (x + 22)(x - 10) = 0
- Equate each factor by 0 to find x
∵ x + 22 = 0 ⇒ subtract 22 from both sides
∴ x = -22
∵ x - 10 = 0 ⇒ add 10 to both sides
∴ x = 10
∴ The values of x are -22 and 10
We can not use x = -22 because there is no negative dimensions, then we will use x = 10
∵ The dimensions are 4 , (x + 1) , (x + 11)
∵ x = 10
∴ The dimensions are 4 , (10 + 1) , (10 + 11)
∴ The dimensions are 4 cm , 11 cm , 21 cm
Learn more:
You can learn more about the factorization in brainly.com/question/7932185
#LearnwithBrainly
Answer: Showed that: [tex]x^2+12x-220=0[/tex].
Both values of x are -22 and 10.
The dimensions are: 4 cm, 11 cm, 21 cm.
The given dimensions are 4cm,(x + 1)cm and (x + 11)cm.
So the volume is = [tex]4(x+1)(x+11)[/tex].
Given that volume= 924 [tex]cm^3[/tex].
Equating the volumes we get:
[tex]4(x+1)(x+11)=924\\4(x^2+12x+11)=924\\x^2+12x+11=\frac{924}{4}\\ x^2+12x+11=231\\x^2+12x+11-231=0\\x^2+12x-220=0\\[/tex]
Then we factor and solve the equation:
[tex]x^2+12x-220=0\\x^2+22x-10x-220=0\\x(x+22)-10(x+22)=0\\(x+22)(x-10)=0\\x=-22,10\\[/tex]
Since x can not be negative, so x = 10.
So the dimensions are: 4 cm, (x + 1) = (10 + 1) = 11 cm, (x + 11) = (10 + 11) = 21 cm.
Learn more: https://brainly.com/question/16955358
Your class has 18 students. Exactly 23
2
3
of them say that, out of all their subjects, they like science the most. Which model shows 23
2
3
of 18 circled?
Answers
Answer:
Sample model as the picture attached, which shows 2/3 of 18 are circled.
Step-by-step explanation:
Here is the correct question: Your class has 18 students. Exactly 2/3
of them say that, out of all their subjects, they like science the most. Which model shows 2/3 of 18 circled?
Given: Total number of student is 18.
2/3 of the total students like science the most.
Now, calculating the number students like the science the most.
∴ Number of students who like the science most= [tex]\frac{2}{3} \times 18= 12 \ students[/tex]
12 students like the science most out of total students.
Sample model are shown in the picture attached, where out of 18 students only 12 are inside the circle to show they like science the most.
The statements below can be used to prove that the triangles are similar.
On a coordinate plane, right triangles A B C and X Y Z are shown. Y Z is 3 units long and B C is 6 units long.
StartFraction A B Over X Y EndFraction = StartFraction 4 Over 2 EndFraction
?
StartFraction A C Over X Z EndFraction = StartFraction StartRoot 52 EndRoot Over StartRoot 13 EndRoot EndFraction
△ABC ~ △XYZ by the SSS similarity theorem.
Which mathematical statement is missing?
StartFraction Y Z Over B C = StartFraction 6 Over 3 EndFraction
∠B ≅ ∠Y
StartFraction B C Over Y Z EndFraction = StartFraction 6 Over 3 EndFraction
∠B ≅ ∠Z
Answers
Answer:
BC/YZ=6/3
Step-by-step explanation:
Doing the quiz rn
The similarities of triangles can be proved using SSS theorem.
The missing mathematical statement is: [tex]\mathbf{\frac{BC}{YZ} = \frac 63}[/tex]
Because the similarities of both triangles is being proved using SSS, then only the sides would be compared
Sides AB, AC, XY and XZ have already been compared.
So, the missing mathematical statement is the ratio of sides BC and YZ
From the question, we have:
[tex]\mathbf{BC = 6}[/tex]
[tex]\mathbf{YZ = 3}[/tex]
So, the missing statement is:
[tex]\mathbf{\frac{BC}{YZ} = \frac 63}[/tex]
Read more about similarities of triangles at:
https://brainly.com/question/14926756
Hue is arranging chairs.She can form 6 rows of a given length with 3 chairs left over,or 8 rows of that same length if she gets 11 more chairs.Write and solve an equation to find how many chairs are in that row length
Answers
Answer:
There are 7 chairs in each row length.
Step-by-step explanation:
Let number of chairs in 1 row be 'x'.
Let total number of chairs be 'y'.
Given:
Hue can form 6 rows of a given length with 3 chairs left over.
It means that Total number of chairs is equal to chairs in 1 rows multiplied by number of rows which is 6 plus number of chairs which is left which is 3.
Framing in equation form we get.
[tex]y=6x+3 \ \ \ \ \ equation \ 1[/tex]
Also Given:
Hue can form 8 rows of that same length if she gets 11 more chairs.
It means that Total number of chairs is equal to chairs in 1 rows multiplied by number of rows which is 8 minus number of chairs which is required more which is 11.
Framing in equation form we get.
[tex]y=8x-11 \ \ \ \ \ equation \ 2[/tex]
From equation 1 and equation 2 we can say that L.H.S is same.
So according to law of transitivity we get;
[tex]6x+3=8x-11[/tex]
Combining like terms we get;
[tex]8x-6x=11+3[/tex]
Using Subtraction and Addition property we get;
[tex]2x=14[/tex]
Now Using Division Property we will divide both side by 2.
[tex]\frac{2x}{2}=\frac{14}{2}\\\\x=7[/tex]
Hence there are 7 chairs in each row length.
By setting up the equations as described, we find that each row has 7 chairs.
Explanation:The subject of the question is a mathematical problem involving the concept of solving linear equations. Let's denote the number of chairs in a row as x. According to the problem, Hue can form 6 rows with 3 chairs leftover. So the total number of chairs she has is 6x + 3. Also, if she gets 11 more chairs, she can form 8 rows of the same length. So, in that case, the total number of chairs would be 8x. So we can write the equation 6x + 3 + 11 = 8x.
This equation simplifies to 14 = 2x. Therefore, x = 7. That is, each row has 7 chairs.
Learn more about Solving Linear Equations here:https://brainly.com/question/11897796
#SPJ11
The St. Louis Cardinals play 160 games in a season. So far, they have won 50 games. How many more games must they win in order to win at least 68% of all games for the season?
Answers
Answer:
More wins required = 59 wins
Step-by-step explanation:
Given:-
Total numbers of games played = 160.
Total games won = 50.
Total win percentage required = 68 %
Now,
Total percentage of games won = [tex]\frac{50}{160} \times 100[/tex]
Total percentage of games won = 0.312 [tex]\times[/tex]100
Total percentage of games won =31.25% ------------(equation 1)
Balance percentage of wins required = total win percentage required - total percentage of games won
Balance percentage of wins required = 68 - 31.25 -----(from equation 1)
Balance percentage of wins required = 36.75%
More wins required = [tex]\frac{Balance\ percentage\ of\ win\ required}{100} \times 160[/tex]
More wins required =[tex]\frac{36.75}{100}\times 160[/tex]
More wins required = 0.368 [tex]\times[/tex] 160
More wins required =58.88
More wins required = 59 wins --------------(rounded value)
St. Louis Cardinals need to win 59 more games to achieve at least a 68% winning percentage for the season.
To determine how many more games the St. Louis Cardinals must win in order to achieve at least a 68% winning percentage for the season, let's go through the calculations step by step.
Total Games: The Cardinals play a total of 160 games in a season.
Current Wins: The Cardinals have currently won 50 games.
Winning Percentage Goal: We want the Cardinals to win at least 68% of their games.
The formula to calculate the winning percentage is:
[tex]\text{Winning Percentage} = \frac{\text{Wins}}{\text{Total Games}} \times 100\%[/tex]
Therefore, the number of wins needed to achieve at least a 68% winning percentage can be calculated as follows:
[tex]\text{Wins Needed} = 0.68 \times 160 = 108.8 \text{ (approximately 109 games)}[/tex]
Calculating Additional Wins Needed: To find out how many more games the Cardinals need to win, we'll subtract the current wins from the wins needed:
[tex]\text{Additional Wins Needed} = \text{Wins Needed} - \text{Current Wins}[/tex]
[tex]\text{Additional Wins Needed} = 109 - 50 = 59[/tex]
the roof of a farm silo is the shape of a hemisphere and is made of sheet tin. if the diameter of the silo is 126.5 feet, how much sheet tin is needed to make the roof?
Answers
The amount of sheet tin needed to make the roof of the farm silo is approximately 25132.74125 square feet.
Explanation:The roof of the farm silo is in the shape of a hemisphere, which means it is like half of a sphere. The diameter of the silo is given as 126.5 feet. To find the amount of sheet tin needed to make the roof, we need to calculate the surface area of the hemisphere.
The surface area of a hemisphere can be calculated using the formula: SA = 2πr^2, where SA is the surface area and r is the radius of the hemisphere.
Since the diameter is given, we can find the radius by dividing the diameter by 2. So, the radius is 126.5/2 = 63.25 feet. Plugging this value into the formula, we get:
SA = 2π(63.25^2)
Using a calculator to find the surface area, we get:
SA ≈ 2π(4005.0625) ≈ 25132.74125 square feet
Therefore, approximately 25132.74125 square feet of sheet tin is needed to make the roof of the farm silo.
Learn more about Surface area of a hemispherehttps://brainly.com/question/14314143
#SPJ12
The amount of sheet tin needed to make the roof of a farm silo, in the shape of a hemisphere, with a diameter of 126.5 feet is approximately 25,132.741 square feet.
Explanation:To calculate the sheet tin needed to make the roof of a farm silo shaped like a hemisphere, we need to find the hemisphere's surface area. The surface area of a hemisphere is given by the formula 2πr2, where r is the radius of the hemisphere.
The diameter of the silo provided is 126.5 feet, meaning the radius, r, would be half of the diameter, or 63.25 feet.
Now, substitute 63.25 feet into the formula:
2 * π * (63.25)2 = 2 * π * 3996.0625.
The total sheet tin needed to make the roof is approximately 25,132.741 square feet.
Learn more about the Surface Area of the Hemisphere here:https://brainly.com/question/24316529
#SPJ12
There are 12 men who may be elected to the council. If there are only 5 members of the council, how many different combination of council members are possible?
Answers
Answer:
252 different combinations
Step-by-step explanation:
There are 12 men who may be elected to the council. If there are only 5 members of the council (the order doesn't matter), then there are
[tex]C^{10}_5\\ \\=\dfrac{10!}{5!(10-5)!}\\ \\=\dfrac{10!}{5!\cdot 5!}\\ \\=\dfrac{5!\cdot 6\cdot 7\cdot 8\cdot 9\cdot 10}{5!\cdot 5!}\\ \\=\dfrac{6\cdot 7\cdot 8\cdot 9\cdot10}{1\cdot 2\cdot 3\cdot 4\cdot 5}\\ \\=7\cdot 4\cdot 9\\ \\=252[/tex]
different combinations of council members.
Select all that apply.
Which was an Indo-European group?
Hittites
Aryans
Portuguese
Egyptians
Sumerians
Answers
Answer:
Hittites, Aryans, Portuguese.
Step-by-step explanation:
I just know for a fact. These are the correct answers.
Simplify the expression
Answers
Answer:
A)
Step-by-step explanation:
1. Similar figures have the same ____ but not necessarily the same ____.
Answer it.
Answers
Answer:
shape and size
Step-by-step explanation:
we know that
If two figures are similar, then its corresponding sides are proportional and its corresponding angles are congruent
Similar figures have the same shape but not necessarily the same size
10 to the zero power time 10
Answers
Answer:
10
Step-by-step explanation:
10^0=1
1*10=10
For the school play, the advance tickets cost $3, while tickets at the door cost $5. Thirty more tickets were sold at door in advance, and $2630 was collected. How many of each kind of ticket was sold?
Answers
Answer:
310 tickets were sold in advance before school pay and 340 door tickets were sold in advance.
Step-by-step explanation:
Given:
Let number of tickets sold in advance be 'x'.
Cost of advance ticket = $3
Cost of door tickets = $5
Also given:
Thirty more tickets were sold at door in advance
Hence number of door tickets sold = [tex]x+30[/tex]
Total Money Collected = $2630
Now we can say that Total Money Collected is equal to sum of number of tickets sold in advance multiplied by Cost of advance ticket and number of door tickets sold multiplied by Cost of door tickets.
Framing in equation form we get;
[tex]3x+(x+30)5=2630[/tex]
Solving the equation to find the value of x we get;
[tex]3x+5x+150=2630[/tex]
Combining the like terms we get;
[tex]3x+5x=2630-150\\\\8x= 2480[/tex]
Now Dividing 8 on both side using division property we get;
[tex]\frac{8x}{8} =\frac{2480}{8}\\ \\x=310[/tex]
Substituting the value of x to find number of door tickets been sold.
number of door tickets sold = [tex]x+30=310+30 =340[/tex]
Hence, 310 tickets were sold in advance before school pay and 340 door tickets were sold in advance.
How do you know what angles they are talking about when they say some like ∠OCA ∠CAO ∠OAB
Answers
Answer:
You would know what people would say by saying that because they mean that you were to match up the letters into a shape in that order
Step-by-step explanation:
Hopefully this helps, give me a brainliest
Answer:
The given angles are
[tex]\angle BOA\\\angle AOC[/tex]
When we write down angles, we have different notations to do it.
In this case, we have angles with three letter, each one indicates a specific element.
The first letter indicate the initial point where the angle starts, for example, [tex]\angle BOA[/tex], beginas at point B, the middle letter indicates the vertex where the angle is at, so [tex]\angle BOA[/tex] indicates is at vertex O, at last, the third letter A indicates the final point where the angle goes.
Having said that, [tex]\angle BOA[/tex] is the opening from point B, then goes to vertex O and finally goes to point A, in the image attached you can see this angle highlighted.
Using the same reasoning, we have that [tex]\angle AOC[/tex] starts at points A, goes to vertex O, and ends at point C. Refer to the image attached.
Carlos has saved 19.80. Shaq saved 5/6 of the amount that Carlos saved. Deontae
saved 4 times as much as Shaq. What is the total saved amount of all three
Answers
Answer:
$102.30
Step-by-step explanation:
Carlos: 19.80
Shag: 19.80 x 5/6 = 16.5
Deontae: 16.5 x 4 = 66.0
Total: 19.80 + 16.50 + 66.00 = 102.30
The total amount saved by Carlos, Shaq, and Deontae is $102.30.
Explanation:To find the total amount saved by Carlos, Shaq, and Deontae, we first need to understand how much each of them saved individually. Carlos saved $19.80. Shaq saved 5/6 of the amount that Carlos saved, which we can calculate as (5/6) * $19.80 = $16.50. Deontae saved 4 times as much as Shaq, which we can calculate as 4 * $16.50 = $66. Finally, we add all these amounts together to get the total saved amount.
So, the total saved amount of all three is $19.80 (Carlos) + $16.50 (Shaq) + $66 (Deontae) = $102.30
Learn more about Total savings here:https://brainly.com/question/33132528
#SPJ3
Evan was carrying forward a balance of $300 from the previous month. His annual interest rate is 30%. Use computation to determine the interest charged for this month
Answers
Answer:
The interest charged for this month is $7.5
Step-by-step explanation:
Given:
Principal = $300
Interest = 30%
Time = 1 month
To Find:
The interest charged for this month = ?
Solution:
we know that the interest charged = [tex]principal \times \text {Interest rate} \times time[/tex]
1 month can also be written as [tex]\frac{1}{12}[/tex]
Substituting the values,
interest charged:
=> [tex] 300 \times 30% \times \frac{1}{12}[/tex]
=> [tex] 300 \times \frac{30}{100} \times \frac{1}{12}[/tex]
=> [tex] 300 \times \frac{3}{120}[/tex]
=>[tex] \frac{900}{120}[/tex]
=>[tex] \frac{30}{4}[/tex]
=>[tex] \frac{15}{2}[/tex]
=> 7.5
I WILL GOVE BRAINLIEST PLEASE PLEASE HELPPP
Answers
Answer:
(5) ∠ FEH ≅ ∠ GHE : CPCTC
(6) ∠ FEH and ∠ GHE are supplementary : Consecutive angles of a parallelogram are supplementary.
(7) m∠ FEH = 90° : Congruent supplementary angles are right angles.
(8) EFGH is a rectangle : Definition of a rectangle.
Step-by-step explanation:
Given:
Quadrilateral EFGH is a parallelogram.
[tex]\overline{EG}\cong \overline{HF}[/tex]
Statements Reasons
1. EFGH is a parallelogram. Given
[tex]\overline{EG}\cong \overline{HF}[/tex]
2. [tex]\overline{EF}\cong \overline{GH}[/tex] If a quadrilateral is a parallelogram, then the opposite sides are congruent
3. [tex]\overline{EH}\cong \overline{EH}[/tex] Reflexive property of Congruence.
4. Δ EFH ≅ Δ HGE SSS Triangle Congruence Postulate.
Now, when two triangles are congruent by SSS, their corresponding angles are also congruent by CPCTC.
(5) ∠ FEH ≅ ∠ GHE CPCTC
Also, for a parallelogram, the same side angles sum is 180 degrees. ∠ FEH and ∠ GHE are supplementary as their sum is 180°.
(6) ∠ FEH and ∠ GHE are supplementary Consecutive angles of a parallelogram are supplementary.
Now, from statement (5), ∠ FEH ≅ ∠ GHE, so the supplementary pair are congruent. Therefore, each angle is equal to 90°.
Let ∠ FEH = ∠ GHE = [tex]x[/tex]. Then,
[tex]x+x=180\\2x=180\\x=\frac{180}{2}=90\°[/tex]
Therefore, ∠ FEH = ∠ GHE = 90°
(7) m∠ FEH = 90° Congruent supplementary angles are right angles.
Now, for a parallelogram with congruent diagonals, if any two consecutive angles are 90 degree each, then the remaining angles are also 90 degrees.
Now, if a parallelogram has all its angles equal to 90°, then the parallelogram is a rectangle from the definition of a rectangle.
(8) EFGH is a rectangle Definition of a rectangle.
Pete’s return from selling his investment is $22,000. He had purchased the investment at a cost of $20,000. What is Pete’s return on investment? A. 0.1% B. 1.1% C. 10% D. 100% E. 110%
Answers
Answer:
Option C
10%
Step-by-step explanation:
Given information
Cost of investment=$20000
Selling price=$22000
Profit=Selling price-Cost of investment=22000-20000=2000
Return on investment=profit/cost of investment
[tex]RoI=\frac {2000\times 100}{20000}=10%[/tex]
The amount of money on a property or good sold is known as ROI. Pete’s return on investment is 10%
Return on investmentThe amount of money on a property or good sold is known as ROI.
Given the following
Cost price = $20000
Selling price = $22000
ROI = SP-CP/CP * 100
%ROI = 2000/20000 * 100
%ROI = 1/10 * 100
%ROI = 10%
Hence Pete’s return on investment is 10%
Learn more on ROI here: https://brainly.com/question/15726451
#SPJ2
Write the equation in slope intercept form. y + 6 = -3( x - 4)
Answers
Answer:
y = -3x + 6
Step-by-step explanation:
Distribute -
y + 6 = -3x + 12
Subtract 6 from both sides, final answer
y = -3x + 6
Final answer:
The equation y + 6 = -3(x - 4) in slope-intercept form is y = -3x + 6, where the slope is -3 and the y-intercept is 6.
Explanation:
To write the equation y + 6 = -3(x - 4) in slope-intercept form, which is y = mx + b, we need to solve the equation for y. First, distribute the -3 to both terms within the parentheses: y + 6 = -3x + 12. Next, subtract 6 from both sides to isolate y: y = -3x + (12 - 6). Simplifying the equation, we get y = -3x + 6. Thus, the slope-intercept form of the equation is y = -3x + 6, where the slope (m) is -3 and the y-intercept (b) is 6.
Which of the following equals 8 when you evaluate f(2) ? Select all that apply
A) f(x)=2x+1
B) f(x)=3x-2
C) f(x)=x(5x-2)
D) f(x)=3x-2x+4
E) f(x)=|x-8|+2
Answers
Answer:
E) [tex]f(x)=|x-8|+2[/tex]
Step-by-step explanation:
We will check each of the given choices by finding [tex]f(2)[/tex] of the given functions.
In order to find [tex]f(2)[/tex], we plugin [tex]x=2[/tex] in the function.
A) [tex]f(x)=2x+1[/tex]
[tex]f(2)=2(2)+1[/tex]
[tex]f(2)=4+1[/tex]
[tex]f(2)=5[/tex]
B) [tex]f(x)=3x-2[/tex]
[tex]f(2)=3(2)-2[/tex]
[tex]f(2)=6-2[/tex]
[tex]f(2)=4[/tex]
C) [tex]f(x)=x(5x-2)[/tex]
[tex]f(2)=2(5(2)-2)[/tex]
[tex]f(2)=2(10-2)[/tex]
[tex]f(2)=2(8)[/tex]
[tex]f(2)=16[/tex]
D) [tex]f(x)=3x-2x+4[/tex]
[tex]f(2)=3(2)-2(2)+4[/tex]
[tex]f(2)=6-4+4[/tex]
[tex]f(2)=6[/tex]
E) [tex]f(x)=|x-8|+2[/tex]
[tex]f(2)=|2-8|+2[/tex]
[tex]f(2)=|-6|+2[/tex]
[tex]f(2)=6+2[/tex] [Since absolute value of any number is positive]
[tex]f(2)=8[/tex]
So, the function in E has value =8 for [tex]f(2)[/tex]
On a scale drawing, A school is 1.6 feet tall. The scale factor is 1/22 (A fraction). Find the height of the school. Please help!
Answers
Answer:
35.2
Step-by-step explanation:
1/22=1.6/?
Cross multiply: 1.6*22=35.2
Toby divided 59.50 by 6.8, as shown. But he forgot to put a decimal point in the answer. Complete the sentence below
Answers
Answer:
The decimal point should be placed between the digits 8 and 7 because the quotient should be greater than 56 ÷ 7 and less than 63 ÷ 7.
Step-by-step explanation:
The division of the number 59.50 by 6.8 is equal to 8.75.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
The division is one of the four basic operations of arithmetic, which are the methods by which numbers are combined to form new numbers. Addition, subtraction, and multiplication are the other operations.
Given that the number 59.50 is divided by the number 6.8. The division will be done as below,
Division = 59.50/6.8
Division = 8.75
To know more about an expression follow
https://brainly.com/question/24976972
#SPJ3
How does h(x)=-2x+5 change over the interval from x=1 to x=2?
Answers
As the rate of change of function is negative from x=1 to x=2, the function decreases at this interval.
Step-by-step explanation:
We have to find the rate of change of the function
The rate of change of function is given by:
[tex]Rate\ of\ change = \frac{h(b)-h(a)}{b-a}[/tex]
Given function is:
[tex]h(x) = -2x+5[/tex]
Here
a =1
b = 2
So,
[tex]h(2) = -2(2) +5\\= -4+5\\= 1\\h(1) = -2(1) +5\\= -2+5\\= 3[/tex]
Putting the values in the formula
[tex]Rate\ of\ change = \frac{1-3}{2-1} = -2[/tex]
As the rate of change of function is negative from x=1 to x=2, the function decreases at this interval.
Keywords: Functions, rate of change
Learn more about functions at:
brainly.com/question/9323337brainly.com/question/9381080#LearnwithBrainly
If s store is selling boxes of pudding at 3 for $0.99,how much would 12 boxes cost
Answers
Answer:
The cost price of 12 boxes of pudding is $3.96
Step-by-step explanation:
Given as :
The quantity of pudding boxes = 3
The cost price for 3 boxes = $0.99
Again ,
The quantity of pudding boxes = 12
Let The cost price for 12 boxes = $x
Now, According to question
Using Unitary method
∵ The cost price of 3 boxes of pudding = $0.99
or,The cost price of 1 boxes of pudding = [tex]\dfrac{0.99}{3}[/tex] = $0.33
∴The cost price of 12 boxes of pudding =$0.33 × 12
I.e x =$3.96
So,The cost price of 12 boxes of pudding = x =$3.96
Hence,The cost price of 12 boxes of pudding is $3.96 Answer
8(2x-6)=96 solve the equation
Answers
Answer:
x=9
Step-by-step explanation:
8(2x-6)=96
2x-6=96/8
2x-6=12
2x=12+6
2x=18
x=18/2
x=9
Hello, thanks for usin Brainly. :)
Let's solve by using distributive property.
8(2x-6)=96
16x-6=96
16x-48=96
+48 +48
16x = 144
x = 9
First, what we did was do 8 x 2 & 6 x 8.
Then, we got 16x-6=96.
We want to get X by itself, therefore we need to get rid of -48, so we 48 to all of our terms.
Then our equation should look like 16x = 144.
Divide and get 9!
Therefore, x = 9.
Wait, how can we be sure?
Let's check our answer.
Let's allow our x value to be 9.
Now, our equation should look like:
8(2(9)-6=96
Follow the PEMDAS rule.
8(18-6)=96
8(12)=96
8 times 12 is 96.
96 = 96 Done!
Therefore, we know our answer is correct.
Can someone pls help
Answers
Answer:
square so all sides are equal
bc^2+mc^2=bm^2
16x^2+4x^2=20x^2=2root5x
nd^2+dm^2=nm^2
x^2+4x^2=5x2=root5x
then:-
1/2*b*h=1/2*2root5x*root5x
=1/2*10x^2=5x^2
==================================
Work Shown:
ND = x
AN = 3x
MD = 2x
MC = 2x
BC = 4x
AB = 4x
-------
P = Area of square ABCD
P = (AB)^2
P = (4x)^2
P = 16x^2
-------
Q = Area of triangle ABN
Q = (1/2)*base*height
Q = (1/2)*AN*AB
Q = (1/2)*3x*4x
Q = 6x^2
-------
R = Area of triangle MBC
R = (1/2)*base*height
R = (1/2)*BC*MC
R = (1/2)*4x*2x
R = 4x^2
-------
S = Area of triangle MND
S = (1/2)*base*height
S = (1/2)*ND*MD
S = (1/2)*x*2x
S = x^2
-------
T = Area of triangle BMN
T = P - Q - R - S
T = 16x^2 - 6x^2 - 4x^2 - x^2
T = 5x^2
-------
An alternative method is to use the pythagorean theorem to find the lengths of BM and MN. Then you can directly compute the area of triangle BMN. You should find that BM = sqrt(20)*x and MN = sqrt(5)*x.