Answer:
X=5
Step-by-step explanation:
[tex]5x - 1 = 3x + 9 \\ 5x - 3x = 9 + 1 \\ 2x = 10 \\ x = 5[/tex]
5x-1=3x+9
collect like terms
5x-3x=9+1
2x=10
divide both sides by 2
x=5
Triangle ABC was dilated and translated to form similar triangle A’B’C’.
What is the scale factor of the dilation?
A. 1/5
B. 2/5
C. 5/2
D. 5/1
The scale factor for the transformation of the pre-image ABC to A'B'C' shown in the figure is 5/2
How to estimate the scale factor of the dilation
From the question, we have the following parameters that can be used in our computation:
The transformation of the pre-image ABC to A'B'C'
By definition, the scale factor is simply the ratio of sides of two corresponding figures
So, the scale factor (S) would be:
S = A'B'C'/ABC
The actual measurements are given as
ABC = 2
A'B'C' = 5
Substitute the known values into the equation
S = 5/2
Hence, the estimated scale factor is 5/2
In a certain Algebra 2 class of 23 students, 11 of them play basketball and 13 of them play baseball. There are 8 students who play neither sport. What is the probability that a student chosen randomly from the class plays both basketball and baseball?
Answer:
9/23
Step-by-step explanation:
Students who play at least 1 sport = 23-8
= 15
Students playing both sports = (11+13)-15
= 24-15
= 9
Probability = 9/23
Alternatively,
A venn diagram could be drawn
The probability that a student chosen randomly from the class plays both basketball and baseball is 39%.
First step
Either (or both) sports =(23 - 8)=15 students play
Both=[11 basketball and 13 baseball)-15]= 9 must play both
Second step
Probability=9/23
Probability=0.39 or 39%
Therefore the probability that a student chosen randomly from the class plays both basketball and baseball is 39%.
Learn more about probability here:https://brainly.com/question/24756209
Twenty-eight athletes participate in a 100-meter race. The time of each athlete is measured during the qualification round. The average time is 11 seconds. The 8 athletes with the fastest time qualified for the final. The average time of these 8 athletes is 10.5 seconds. Calculate the average time of the 20 athletes who did not qualify for the final.
The average time of the 20 athletes who did not qualify for the final is 11.2 seconds .
Step-by-step explanation:
Here we have , Twenty-eight athletes participate in a 100-meter race. The time of each athlete is measured during the qualification round. The average time is 11 seconds. The 8 athletes with the fastest time qualified for the final. The average time of these 8 athletes is 10.5 seconds. Let's have equations for this:
[tex]\frac{x_1+x_2+.....+x_2_8}{28} = 11[/tex] where [tex]x_1, x_2, ....., x_2_8[/tex] are athletes
⇒ [tex]x_1 + x_2 + .. + x_2_8 = 11(28)= 308[/tex]
⇒ [tex](x_1 + x_2 + .. + x_8 )+ (x_9+x_1_0+...+x_2_8) = 308[/tex]
⇒ [tex](\frac{x_1 + x_2 + .. + x_8}{8} )(8)+ (\frac{x_9+x_1_0+...+x_2_8}{20} )(20) = 308[/tex]
⇒ [tex]10.5(8)+m(20) = 308[/tex] , where m is average time of the 20 athletes who did not qualify for the final.
⇒ [tex]84+m(20) = 308[/tex]
⇒ [tex]20m= 224[/tex]
⇒ [tex]m=11.2[/tex]
∴ The average time of the 20 athletes who did not qualify for the final is 11.2 seconds .
Katie has a loan balance of $5,000 with a 15% APR. She will take 3 years to pay it off, making her monthly payments $201.39. How much is she paying in interest over the 3 years?
A.) $2,250
B.) $4,250
C.) $604.17
D.) $750
Answer:
a
Step-by-step explanation:
Answer:
$2250
Step-by-step explanation:
First we calculate total payment made by her in 3 years time. This can be done by multiplying monthly payments by 36 months (3 years time). Then we deduct the same by the loan balance required to pay off. The difference of both is the interest paid over the three years. As done below
Total Payment = 201.39 x 36 = 7,250.04
Interest Paid = 7,250.04 - 5,000 = 2,250.04
Rounding off to whole number that is $2,250
- Which mathematical expression represents "add 6, 9, and 24 and then divide by 3"?
A. (6 + 9 + 24) = 3
B. 6 + 9 + 24-3
C.3 = (6 + 9 + 24)
D. 3 = 6 + 9 + 24
Answer:
(6 + 9 + 24)/3
Step-by-step explanation:
First, you must add 6, 9, and 24.
6 + 9 + 24
Now you need to divide that sum by 3.
You must use parentheses to show the sum being divided by 3.
(6 + 9 + 24)/3
None of your expressions contain a division sign, so there is no answer contained in the choices. Did you use the equal sign to mean a division sign?
Two movie tickets and 3 snacks are $24. Three movies tickets and 4 snacks are $35. How much is a movie ticket and how much is a snack.
Answer: A movie ticket is $9 while a snack is $2
Step-by-step explanation: We shall let a movie ticket be m while a snack is s. So, from the clues given, if two movie tickets and three snacks cost $24, we can write it as the following expression;
2m + 3s = 24
Also if three movie tickets and four snacks cost $35, we can as well write another expression as follows;
3m + 4s = 35.
Now we have a pair of simultaneous equations which are
2m + 3s = 24 ----------(1)
3m + 4s = 35 ----------(2)
We shall solve this by using the elimination method, since none of the variables has a coefficient of 1. We'll start by multiplying equation (1) by 3 and multiplying equation (2) by 2 (so as to eliminate the m variable)
2m + 3s = 24 -------- x3
3m + 4s = 35 ---------x2
We now arrive at the following
6m + 9s = 72--------(3)
6m + 8s = 70--------(4)
Subtract equation (4) from equation (3) and we arrive at
s = 2
Having determined that s equals 2 we can now substitute for the value of a into equation (1)
2m + 3s = 24
2m + 3(2) = 24
2m + 6 = 24
Subtract 6 from both sides of the equation
2m + 6 - 6 = 24 - 6
2m = 18
Divide both sides of the equation by 2
m= 9
Therefore one movie ticket costs $9 while one snack costs $2
find a common factor for 3y^3+2y^2 and 6y^4+4y^3
Answer:
[tex]3y + 2 [/tex]
Step-by-step explanation:
We want to find a common factor for
[tex]3 {y}^{3} + 2 {y}^{2} [/tex]
and
[tex]6 {y}^{4} + 4 {y}^{3} [/tex]
We factor each of them to get;
[tex]3 {y}^{3} + 2 {y}^{2} = {y}^{2} (3y + 2)[/tex]
and
[tex]6 {y}^{4} + 4 {y}^{3} = 2 {y}^{3} (3y + 2)[/tex]
We can observe now that;
The factor common to both expression is
[tex]3y + 2[/tex]
The car owned by a person is part of his or her
a investment assets
b. liquid assets
C. long term assets
d. use assets
Please select the best answer from the choices provided
Answer: answer is B, long term asset
Step-by-step explanation:
This is because cars are depreciated over time. It is therefore reported under the long term asset in a balance sheet.
Select the correct answer.
If ΔABC and ΔGEF are congruent by the ASA criterion, which pair of angles must be congruent?
A.
∠ACB and ∠FEG
B.
∠CAB and ∠GEF
C.
∠CAB and ∠EGF
D.
∠ABC and ∠GFE
Answer:
<A=<G
so <CAB=<EGF
Step-by-step explanation:
Answer:
B.
∠CAB and ∠GEF
if the polygon shown below is a regular nonagon,what is the value of x
Answer:
[tex]x=40^o[/tex]
Step-by-step explanation:
the picture of the question in the attached figure
step 1
Find the measure of the interior angle of a regular nonagon
The formula to calculate the measure of the interior angle in any polygon is given by
[tex]\frac{(n-2)180^o}{n}[/tex]
where
n is the number of sides
In this problem we have
n=9 sides
substitute
[tex]\frac{(9-2)180^o}{9}=140^o[/tex]
step 2
Find the value of x
Remember that
The sum of the interior angle and the exterior angle in any vertex of the polygon must be equal to 180 degrees
so
[tex]x+140^o=180^o[/tex]
solve for x
[tex]x=180^o-140^o=40^o[/tex]
Write -5.8 as a mixed number in simplest form
Answer:
[tex]-5 \frac{4}{5}[/tex]
Step-by-step explanation:
That's the answer
Answer:
I guess the answer would be -5 and 4/5.
Hope this helps!
A square and a regular hexagon have side of the same length. The perimeter of the square increased by 48 units will be equal to the perimeter of the hexagon. What is the x, the length of the side of the hexagon or square
The length of the side of the hexagon or square is 24 units.
Step-by-step explanation:
It is given that, a square and a regular hexagon have side of the same length.
The length is not given in the problem. So, let us assume the length of the side of hexagon or square as 'x'.
The additional information given is that, the perimeter of the square increased by 48 units will be equal to the perimeter of the hexagon.
The perimeter of the square = 4 × length of the side.Then, the perimeter of the square increased by 48 units = (4x + 48).The perimeter of the hexagon = 6 × length of the side.Therefore, the perimeter of the hexagon = 6x.To calculate the length x of square and hexagon :
Comparing both the perimeters of square and hexagon,
⇒ (4x + 48) = 6x
⇒ 48 = 6x-4x
⇒ 2x = 48
⇒ x = 48/2
⇒ x = 24 units.
The length of the side of the hexagon or square is 24 units.
Quiz
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Eli is buying a townhouse that costs $276,650. He has $28,000 in savings and earns $4,475 a month. Eli would like to spend no
more than 30% of his income on his mortgage payment. Which loan option would you recommend to Eli?
a 30 year FHA, 3.5% down at a fixed rate of 6.5%
b. 30 year fixed, 5% down at a fixed rate of 6.25%
c. 30 year fixed, 6.5% down at a fixed rate of 5.75%
d. 30 year fixed, 10% down at a fixed rate of 5%
Please select the best answer from the choices provided
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Mark this and return
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Answer: D. 30 year fixed, 10% down at a fixed rate of 5%
Step-by-step explanation:
The total cost of the house is $276,650.
He has in his savings $28,000
10% of $276,650 = $27,665. This will cover for the down payment.
His monthly income is $4,475 and he will like to spend 30% of it on his mortgage = $4,475* 30%= $1,342.50.
From the bal of mortgage =
$276,650 - $27,665 = $248,985
$248,985/ (30*12) = $691.625 $248,985* 5% /12= $1037.45
Total monthly repayment = $1037.45+ 691.63= $1729.08
Answer:
b. 30 year fixed, 5% down at a fixed rate of 6.25%
Step-by-step explanation:
Jerome found another feather that made the difference between the longest and shortest feather 1 3/4 inches what could be the length of the new father explain
Answer:
By assuming that shortest feather has a length of 1/4 inches, the length of the longest feather is 2 inches.
Step-by-step explanation:
A mathematical translation of the statement of the problem is:
[tex]x - y = \frac{7}{4}[/tex]
Where x, y represent the lengths of the longest and shortest feathers, respectively. Let assume that length of the shortest feather is 1/4 inches. Then, the length of the longest feather is:
[tex]x = y + \frac{7}{4}[/tex]
[tex]x = 2[/tex]
By assuming that shortest feather has a length of 1/4 inches, the length of the longest feather is 2 inches.
The length of the new feather that made the difference between the longest and shortest feathers is 1 3/4 inches.
Explanation:The question is asking for the possible length of the new feather that made the difference between the longest and shortest feathers. We know that the difference between these feathers is 1 3/4 inches.
To find the length of the new feather, we need to consider the lengths of the longest and shortest feathers.
Let's say the length of the shortest feather is x inches. Then, the length of the longest feather would be x + 1 3/4 inches. So, the equation would be: (x + 1 3/4) - x = 1 3/4 inches.
Simplifying the equation, we get: 1 3/4 = 1 3/4 inches.
Therefore, the length of the new feather is 1 3/4 inches.
Employees of a discount appliance store receive an additional 20% off of the lowest price on an item.
an employee purchases a dishwasher during a 15% off sale, how much will he pay if the dishwasher
originally cost $450?
A. $280.90
B. $287
C. $292.50
D. $306
E. $333.89
Answer:
D. $306.
Step-by-step explanation:
If the dishwasher originally cost $450, then after applying 15% off, its price will be 100% - 15% = 85% of the original price:
[tex]\dfrac{85\%}{100\%} *\$450[/tex]
[tex]0.85*\$450 = \$382.5[/tex]
Thus, during the 15% off sale, the dishwasher will cost $382.5.
Now, the employees of the discount appliance store receive an additional 20% off; therefore, the price of the dishwasher will be 100% - 20% = 80% of $382.5:
[tex]\dfrac{80\%}{100\%} *\$382.5[/tex]
[tex]0.8*\$382.5=\$306[/tex]
Therefore, the employee will purchase the dishwasher at a price of $306, which is choice D.
Final answer:
The employee will pay $306 for the dishwasher, which corresponds to answer choice D.
Explanation:
The subject of this question is Mathematics, and it pertains to the calculation of cumulative discounts on an item. The question is designed to test the student's understanding of how to apply successive percentage discounts to an original price.
Original price of the dishwasher: $450
15% off sale discount: 0.15 × $450 = $67.50
Price after sale discount: $450 - $67.50 = $382.50
Employees receive an additional 20% off the lowest price: 0.20 × $382.50 = $76.50
Price after employee discount: $382.50 - $76.50 = $306
Therefore, the employee will pay $306 for the dishwasher, which corresponds to answer choice D.
Yeah I’m not good at this
For the given triangle, x = 5.1 cm and y = 6.1 cm.
Step-by-step explanation:
Step 1:
In the given triangle, the angle is 50°. It is given that the opposite side has a length of y cm and the adjacent side has a length of y cm. The hypotenuse of the triangle measures 8 cm.
To determine the length of the opposite side of the triangle, we use the sin of the given angle.
To determine the length of the adjacent side of the triangle, we use the cos of the given angle.
[tex]sin \theta = \frac{oppositeside}{hypotenuse} , cos \theta = \frac{adjacentside}{hypotenuse}.[/tex]
Step 2:
In the given triangle,
The length of the opposite side = y cm,
The length of the adjacent side = x cm,
The length of the hypotenuse = 8 cm,
The angle of the triangle = 50°.
[tex]sin \theta = \frac{oppositeside}{hypotenuse} , sin 50 = \frac{y}{8}.[/tex]
[tex]y = 0.7660 (8) = 6.128.[/tex]
[tex]cos \theta = \frac{adjacentside}{hypotenuse} , cos 50 = \frac{x}{8}.[/tex]
[tex]x = 0.6427 (8) = 5.1416.[/tex]
So x = 5.1416 cm and y = 6.128 cm. Rounding these off to one decimal place, we get x = 5.1 cm and y = 6.1 cm.
Solve: 2x + 3 = 11 SHOW WORK
Answer:
X=4
Step-by-step explanation:
2x+3=11
Substrate 3 from both sides
2x=11-3
2x=8
Divide both sides by 2
X=4
The value of X is 4.
please see the attached picture for full solution
Hope it helps
HELPPP PLEASE
A cone-shaped tent has a diameter of 12 ft and a height of 6 ft. What is the approximate volume of the tent? Question 2 options: 226 ft3 679 ft3 905 ft3 2714 ft3
The volume of the tent is option A) 226 ft³
Step-by-step explanation:
The given data are,
A cone-shaped tent has a diameter of 12 ft.The height of the cone is 6 ft.To find the volume of the tent :
The volume of the tent can be found using the formula for volume of the cone, since the tent is in the shape of a cone.
Volume of the cone = (1/3)πr²h
where, r is the radius of the cone. The diameter is given as 12 ft. Therefore, to find the radius = diameter /2 = 12/2 = 6 ft.
The radius, r = 6 ft.
The height h of the cone is h= 6 ft.
Volume of the cone = (1/3)× 3.14× 6²× 6.
⇒ (1/3)× 3.14× 216
⇒ 678.24 / 3
⇒ 226.08 (which is approximately 226)
⇒ 226 cubic. ft
Therefore, the volume of the tent is option A) 226 ft³
Use the relationships between the angles to solve for x (most brainliest fastest answer)
Answer:
100 degrees
Step-by-step explanation:
A straight line pretty much means you have 180 degrees.
180 - 115 = 65
A triangle has 180 degrees
x = 180 - 15 - 65 = 100
pls help fast!!
1. factorize(l-x²)
2. simplify:9³×125×27×t⁻⁴/3⁻²×4⁴×5³×(t⁻⁴)³
Answer:
Step-by-step explanation:
Four consecutive integers add up to 378
Answer:
The numbers are 93, 94, 95 and 96
Step-by-step explanation:
Four consecutive integers add up to 378.
Let the first number be x
Second number will be x+1
Third number will be x+2
And the fourth number will be x+3
These four numbers add up to 378
Which means, we add them up
x + (x+1) + (x+2) + (x+3)=378
x+x+1+x+2+x+3= 378
Collect like terms
4x+6=378
4x= 378-6
4x=372
Divide both sides by 4
x=378/4
x=93
The first number is 93
The second number is x+1 = 93+1= 94
The third number is x+2= 93+2= 95
The fourth number is x+3= 93+3=96
Add up the four numbers
93+94+95+96 = 378
I need help figuring this out I’m so confused
Answer:
just do the steps accordingly
Step-by-step explanation:
asdv
Hey there! Welcome to Brainly!
When solving equations for a variable, our goal is to get the variable all by itself on one side of the equation to show what it equals.
In your case, there are two variables, but there is no need to worry! Just pretend like C is another number; you are still solving for x.
So, how do we isolate the x? What we need to do is use inverse operations. If you were to say that x+1=20, how would you figure out what x is? Well, you have to get rid of the one next to the x. We need to subtract this one. But, if we subtract the one, we have to do it to the other side of the equation as well so that it balances it out. This leaves us with x=19.
Now, let's figure out your problem. You have a few more steps. When solving bigger equations, you first undo the constants (terms without a variable) and then the coefficients (numbers with variables attached).
So, the first thing we need to do is add 20 to both sides to cancel out the subtracting on x's side.
C+20=25x-20+20
C+20=25x
Now, we need to divide both sides by 25 to completely isolate the x.
(C+20)÷25=x
In algebra, it is customary to put the x on the left side of the equation, so we will just flip it around.
x=(C+20)÷25
We can further simplify this because the 20 in the numerator and 25 in the denominator are not in simplest form.
[tex]\frac{C+20}{25} =\frac{C+4}{5}[/tex]
Given this information, you should be able to put the steps in order accordingly.
I hope this helps! Have a great day!
what has to be added to the sum of 5/8 and 8/5 to get 3
Answer:
31/40 has to be added to the sum of 5/8 and 8/5 to get 3.
Step-by-step explanation:
Solve this equation: 5/8 + 8/5 + f = 3, where f is the number that has to be added to the sum of 5/8 and 8/5.
The LCD of 5/8 and 8/5 is 40; thus, 5/8 + 8/5 = 25/40 + 64/40 = 89/40.
Then 89/40 + f = 120/40 (where 120/40 is equivalent to 3).
Subtracting 89/40 from both sides yields the desired result:
f = (120 - 89)/40 = 31/40
31/40 has to be added to the sum of 5/8 and 8/5 to get 3.
Answer:
[tex]\frac{31}{40}[/tex]
Step-by-step explanation:
let the unknown be x
[tex]\frac{5}{8} + \frac{8}{5} + x =3[/tex]
[tex]\frac{25+64+40x}{40} = 3[/tex]
cross multiply
25 + 64 + 40x = 3 × 40
89 + 40x = 120
collect like terms
40x = 120 - 89
40x = 31
divide both sides by 40
x = [tex]\frac{31}{40}[/tex]
therefore, [tex]\frac{31}{40}[/tex] has to be added to the sum of 5/8 and 8/5 to get 3
Convert the length as indicated What is 2600 cm= ft
Answer:
85.30184
Step-by-step explanation:
1ft........30.48cm
x .........2600cm
x=2600×1/30.48=85.30ft
Answer: 85.30ft
6⁴×6⁴ as a single power
Answer:
6^16
Step-by-step explanation:
4 x 4 = 16
Answer:
Step-by-step explanation:
if bases are equal then powers are added during multiplication.
x^a×x^b×x^c=x^{a+b+c}
here [tex]6^4 \times 6^4=6^{4+4}=6^8[/tex]
Maria has an annual income of
$32,000. If she saves 8% of her
income, how much money does
she save?
Answer:
17,810.58
Step-by-step explanation:
A = $ 17,810.58
A = P + I where
P (principal) = $ 10,000.00
I (interest) = $ 7,810.58
Step-by-step explanation:
we can write it in %form:
100% of the total income Annual income= $32,000 (given in question)
1%=$320. (divide both sides by 100 to solve by 1%)
8%=$320×8
(multiply by 8 both side to get money saved)
8%= *$2,560*
find the value of x
Answer:
x = 20
Step-by-step explanation:
When a line is on two lines, it means they are congruent. This means they have the same value.
6. Two-thirds of a number is equal to 20. What is
the number?
What is the value of x in the solution to this system of equation
y + 2x = -1
y= x+4
x
+
4
The value of x is 1 in the solution to this system of equation.
Step-by-step explanation:
The system of equation are :
2x+y = -1 ---------(1)
x-y = 4 ---------(2)
Adding the equations (1) and (2),
2x+y = -1
x - y = 4
3x = 3
⇒ 3x = 3
⇒ x=3/3
⇒ x = 1
x - 8 + (-8x) - 15 when x = -9
Answer:
40
Step-by-step explanation:
Plug x=-9 in. -9-8+(-9×(-8)) -15=-17+72-15=-17+72-15=40. I hope this helped!
Answer:
40
Step-by-step explanation:
72-32=40