A 45-45-90 right triangle is formed when a square is cut in half diagonally. This forms two such right triangles, where the sides are in a specific ratio, with the length of the hypotenuse being root 2 times the length of each leg.
Explanation:A 45-45-90 right triangle is formed when a square is cut in half. This is because when you draw a diagonal on a square, the angles it forms with the sides are all 45 degrees, and the angles at the vertices remain 90 degrees. Therefore, it forms two 45-45-90 right triangles.
In a 45-45-90 triangle, the sides are in a specific ratio. The length of the hypotenuse is root 2 times the length of each leg, which are equal in measure because it is an isosceles triangle. These properties are unique to 45-45-90 right triangles.
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A dress that costs x dollars is on sale for 30% off. Write an expression to represent the sale price, in dollars, of the dress.
The expression to represent the sale price, in dollars, of the dress is x - 0.3x dollars
Solution:Given that dress that costs "x" dollars is on sale for 30% off
To find: expression to represent the sale price, in dollars, of the dress
Let the original price of dress is "x"
It is on sale for 30% offer. Which means 30 % of "x" is offer price
Sales price means the price of dress after offer
So the sales price is written as original price - offer price
Sales price = original price - offer price
Sales price = x - 30 % of x
On simplification we get,
[tex]\text {Sales price }=x-\frac{30}{100} \times x=x-0.3 x[/tex]
Thus the sales price of dress is x - 0.3x dollars
All of the following are equivalent except _____.
-5(x - 1)
-5x + 5
5 - 5x
(5 - 5)x
Please explain how you got your answer, thanks
(5 - 5)x because it equals -5x+5x which is 0
all the others equal -5x +5
Answer:
(5-5)x
when you distribute the x here it becomes 5x-5x which is 0 this is the only problem that equals 0
Is the product of square root of 16 and 4/7 rational or irrational
The square root of 16 is rational 4.
The ratio of 4 and 7 is rational 0.5714285714285
The product is hence rational.
The product of the square root of 16 and 4/7 (which equals 16/7) is rational.
What are rational and irrational numbers?Rational numbers can be expressed as fractions of integers, while irrational numbers cannot be expressed as fractions and have non-repeating, non-terminating decimal expansions.
The square root of 16 is 4, and 4/7 is a rational number. When you multiply a rational number (4/7) by an integer (4), the result remains rational.
Calculation: √16 * 4/7 = 4 * 4/7
= 16/7
16/7 is the product which is a rational number.
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HELP:Sarah, who is 19 feet away from Justin, has a ball in her hand. Sarah throws the ball away from Justin at a speed of 5 feet per second. It takes the ball 4 seconds to reach a third friend, Brandon. When the ball reaches Brandon, how far away is it from Justin?
Answer:
Justin is 1 feet far away from Brandon
Step-by-step explanation:
As shown in the diagram, we let the distance between Justin and Brandon be x
[tex]Speed = \frac{distance}{time} [/tex]
from the question
the total time taken by the ball to reach Brandson=4s
Also the total distance is travelled by the ball=19+x
while the average speed=5ft/s
By substitution we obtain
[tex]5 = \frac{19 + x}{4} [/tex]
[tex] \implies4 \times 5 = 19 + x[/tex]
[tex]\implies20=19 + x[/tex]
[tex]\implies20 - 19 = x[/tex]
x=1 feet
The ball is 39 feet away from Justin. The ball, thrown by Sarah at 5 feet per second away from Justin, reaches Brandon in 4 seconds at a distance of 39 feet from Justin.
We need to understand the direction and speed of Sarah's throw relative to the distance between Sarah, Justin, and Brandon.
Sarah throws the ball away from Justin at a speed of 5 feet per second for 4 seconds. The formula to calculate the distance covered by the ball is:
Distance = Speed × TimeSo, Distance = 5 feet/second × 4 seconds = 20 feetThe ball travels 20 feet away from Sarah. Since Sarah is already 19 feet away from Justin, we need to add this distance to determine how far the ball is from Justin:
Distance from Justin = Sarah's Distance from Justin + Distance Traveled by the BallDistance from Justin = 19 feet + 20 feet = 39 feetHence, the ball is 39 feet away from Justin when it reaches Brandon.
Identify the equation of the linear function through the points (- 2,- 7) and (1,2). Then state the rate of change of the function. What is the equation of the linear function?
A. y = 3x - 1
B. y = - 3x - 1
C. y = 3x + 1
D. y = -3x + 1
The rate of change is ( ? ).
Answer:
The equation of line is y = 3 x - 1 , i.e option A .
The rate of change = m = 3
Step-by-step explanation:
Given as :
The points are
([tex]x_1[/tex],[tex]y_1[/tex] ) = (- 2, -7)
([tex]x_2[/tex],[tex]y_2[/tex] ) = (1 , 2)
Let The slope = m
Now, The slope is calculated in points form
So, Slope = [tex]\dfrac{y_2-y_1}{x_2-x_1}[/tex]
I.e m = [tex]\dfrac{2-(-7)}{1-(-2)}[/tex]
or, m = [tex]\dfrac{9}{3}[/tex]
I.e m = 3
So, The slope of points = m = 3
I,e Rate of change = m = 3
Now, the equation of line in slope - point form can be written as
y -[tex]y_1[/tex] = m ( x - [tex]x_1[/tex])
where m is the slope of line
i.e y - (-7) = ( 3 ) × ( x - (-2) )
or, y + 7 = 3 × (x + 2)
∴ y + 7 = 3 x + 6
Or, y = 3 x + 6 - 7
Or, y = 3 x - 1
So, The equation of line is y = 3 x - 1
Hence, The equation of line is y = 3 x - 1 , i.e option A .
And The rate of change = m = 3 Answer
Mathematics MH help ty
When multiplying (or dividing) both sides of an inequality by a negative number, the inequality symbol must be reversed/flipped, regardless of how many steps taken when solving the inequality.
If you were to multiply (or divide) by a positive number, then you would not have to reverse/flip the inequality symbol.
The question in the image is incomplete, so I cannot provide a true/false answer, but this information should be what you need to easily choose an answer.
Let me know if you need any clarifications and happy studying~
Answer:
False
Step-by-step explanation:
only flip symbol when dividing by a negative number
Times the sum of a number and two is less than seven times the number
Answer:
[tex]x >\frac{3}{2}[/tex]
Step-by-step explanation:
The complete question is
Three times the sum of a number and two is less than seven times the number. Find the number
Let
x -----> the number
we know that
The linear equation that represent this problem is
[tex]3(x+2) < 7x[/tex]
Solve for x
Apply distributive property left side
[tex]3x+6 < 7x[/tex]
Subtract 3x both sides
[tex]6 < 7x-3x[/tex]
[tex]6 < 4x[/tex]
Divide by 4 both sides
[tex]\frac{6}{4}< x[/tex]
Simplify
[tex]\frac{3}{2}< x[/tex]
Rewrite
[tex]x >\frac{3}{2}[/tex]
D/3+10=14 solve the equation
Answer: d = 12
Step-by-step explanation: First isolate d/3 by subtracting 10 from both sides of the equation. That gives you d/3 = 4.
From here, since d is being divided by 5, multiply both sides of the equation by 5 so d = 12.
The population of Bumpton increased by 10% from 1980 to 1990 and decreased by 10% from 1990 to 2000. What is the net percent change in the population of Bumpton from 1980 to 2000?
Answer:
10-10=10+10 its the same it will increase and decrease the increased level
Find the minimum or maximum value off
x^2 + 6x +11
Answer:
The minimum is the point (-3,2)
Step-by-step explanation:
we have
[tex]x^{2} +6x+11[/tex]
This is a vertical parabola open upward (because the leading coefficient is positive)
The vertex is a minimum
Convert the equation in vertex form
Complete the square
[tex]f(x)=(x^{2} +6x+3^2)+11-3^2[/tex]
[tex]f(x)=(x^{2} +6x+9)+11-9[/tex]
[tex]f(x)=(x^{2} +6x+9)+2[/tex]
Rewrite as perfect squares
[tex]f(x)=(x+3)^{2}+2[/tex] ----> equation in vertex form
The vertex is the point (-3,2)
therefore
The minimum is the point (-3,2)
FIND THE DISTANCE....Brainlest and extra points.
Answer:BC=11.77 mi
Step-by-step explanation:
cosα=5.71mi/AC
cos61°=5.71mi/AC
0.485=5.71mi/AC
AC=11.77mi
Answer:
BC=10.28
Step-by-step explanation:
Question: 3 of 20
Mark for Review
Instructions
Review Test
Stop Test
Sean ears $300 in a regular work week. A regular work week for Sean consists of 5 work days with 8 hours a day. How much money
does Sean eam each hour?
Answer:
Sean earns $7.5 in each hour.
Step-by-step explanation:
Given:
Money earned by Sean = $300
Number of hours worked in a day = 8 hrs
Number of days of work in a week = 5
We need to find Money earned in each hour.
First we will find Total hours work in a week.
Total hours work in a week is equal to Number of hours worked in a day multiplied by number of days work in a week.
Framing in equation form we get;
Total hours worked in a week = [tex]8\times5 = 40\ hrs[/tex]
Now we will find money earned for each hour.
Money earned each hour will be calculated by Dividing Total Money earned in a week by Total number of hours worked in a week.
Framing in equation form we get;
Money earned each hour = [tex]\frac{300}{40} = \$7.5[/tex]
Hence Sean earns $7.5 in each hour.
teddy brings snacks and ice cream while they wait for santa to arrive on christmas eve if the ice cream has 1250 calories for 5 servings what is the unit rate
Answer:
The unit rate is 250 calories per servings.
Step-by-step explanation:
Given:
The ice cream has 1250 calories for 5 servings.
Now, to find the unit rate.
So, by using unitary method:
If the 5 servings of ice cream has 1250 calories.
Then, to get the calories in 1 servings we divide number of calories by the number of servings:
= [tex]Number\ of\ calories \div number\ of\ servings[/tex]
[tex]=1250\ calories\div 5\ servings[/tex]
[tex]=250\ calories.[/tex]
Thus, in 1 servings there are 250 calories.
Therefore, the unit rate is 250 calories per servings.
Jack puts 2 photos on each of 7 pages of his photo album. How many photos does he use? Complete the jumps on the number lineby adding arrows.
Answer:
14
Step-by-step explanation:
If Jack puts 2 photos per page and there are 7 pages 2x7=14 or 2+2+2+2+2+2+2=14 on a number line it would jump two lines each time.
The number of photos that he uses to fill the photo album will be 14.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
It is also known as the product. If the object n is given to m times then we just simply multiply them.
Jack puts 2 photos on each of the 7 pages of his photo album.
Then the number of photos that he uses will be given by the multiplication of the numbers 2 and 7.
⇒ 2 x 7
⇒ 14
Thus, the number of photos that he uses will be 14.
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There are 4 red and 6 green marbles in a jar. What is the probability of drawing two green marbles, with replacement?
2/5
9/25
3/5
4/25
Select EACH correct answer
Answer:
[tex]\frac{9}{25}[/tex]
Step-by-step explanation:
Number of red balls = 4
Number of green balls = 6
Total number of balls = 6+4 =10
Probability of drawing a green marble is given as
⇒ [tex]\frac{Number\ of\ green\ balls}{Total\ number\ of\ balls}[/tex]
⇒ [tex]\frac{6}{10}[/tex]
The ball is replaced after drawing.
Probability of drawing a green ball a second time will be:
⇒ [tex]\frac{Number\ of\ green\ balls}{Total\ number\ of\ balls}[/tex]
⇒ [tex]\frac{6}{10}[/tex]
Thus, probability of drawing 2 green balls with replacement can be given as:
⇒ (Probability of drawing a green marble) [tex]\times[/tex] (Probability of drawing a green ball a second time)
⇒ [tex]\frac{6}{10}\times\frac{6}{10}[/tex]
⇒ [tex]\frac{36}{100}[/tex]
Simplifying fraction by dividing numerator and denominator by their GCF.
⇒ [tex]\frac{36\div 4}{100\div 4}[/tex]
⇒ [tex]\frac{9}{25}[/tex] (Answer)
a games room charges a $13 entrance fee, plus $2.35 per hour of play time. Annie Marie has $29.45. how long can she play in the games room? a) Choose a variable and write an inequality for this problem
Answer:
a) The Inequality representing this problem is [tex]13+2.35x\leq 29.45[/tex].
b) Annie Marie can play maximum of 7 hours.
Step-by-step explanation:
Given:
Entry fee charge of game room = $13
Cost of hourly playtime = $2.35 per hour
Total Money Annie Marie has = $29.45
We need to find number of hours she can play with this amount.
Let number of hours she will play be 'x'.
No we know that Total Money she has should be less than or equal to sum of Entry fee charge of game room and Cost of hourly playtime multiplied by number of hours she can play.
Framing in equation form we get;
[tex]13+2.35x\leq 29.45[/tex]
Hence The Inequality representing this problem is [tex]13+2.35x\leq 29.45[/tex].
On Solving this equation we get;
Subtracting both side by 13 we get;
[tex]13+2.35x-13\leq 29.45-13\\\\2.35x\leq 16.45[/tex]
Now dividing both side by 2.35 using division property of Inequality we get;
[tex]\frac{2.35x}{2.35}\leq \frac{16.45}{2.35}\\\\x\leq 7 \ hrs.[/tex]
Hence Annie Marie can play maximum of 7 hours.
The difference between 2 times x and y is less than or equal to 1
Answer:
???
Step-by-step explanation:
Answer:
Step-by-step explanation:
2 times x -------> 2x
The difference between 2 times x and y is 2x - y
The difference between 2 times x and y is less than or equal to 1:
2x - y<= 1
If d , e, and f are midpoints of the sides of ABC, find the perimeter of ABC.
The perimeter of a triangle with midpoints d, e, and f on each side is twice the sum of segments d, e, and f. However, without specific numerical values for d, e, and f, the exact numerical measurement for the perimeter of triangle ABC cannot be determined.
Explanation:The question is referring to a specific characteristic of geometry known as the midpoint. The midpoints, in this case d, e, and f, divide each side of the triangle into two equal parts. The side length of ABC is equal to double the sum of segments d, e, and f since they represent the half lengths of the sides.
However, please note that without any additional information or numeric representation, we cannot compute the exact numerical measurement of the perimeter of triangle ABC.
To illustrate, if we were given that the lengths d, e, and f were respectively 5 units, 6 units, and 7 units, we would calculate the perimeter of triangle ABC by adding the lengths of d, e, and f and multiplying the sum by 2.
In such a scenario: Perimeter of ABC = 2 * (d + e + f) = 2 * (5 units + 6 units + 7 units) = 2 * 18 units = 36 units.
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at Sam's sandwich shop, toni ate 3/4 of a medium sandwich, Becky ate 3/4 of a small sandwich, and Mary jo ate 6/8 of a medium sandwich. explain why toni and Mary jo ate the same amount of sandwich, but toni and Becky ate different amounts
Answer:
Here's what I get
Step-by-step explanation:
Let's assume that the sandwiches are circular (because I couldn't find a good rectangular fraction maker.
Toni ate ¾ of a medium sandwich (Figure below).
Mary Jo ate ⁶/₈ of a medium sandwich.
Mary Jo ate the same amount as Toni, because ¾ = ⁶/₈
Becky ate ¾ of a small sandwich and Toni ate ¾ of a medium sandwich.
Becky ate less than Toni, because ¾ of a small amount is less than ¾ of a large amount.
What is 2 5/10 x 3/4
Answer: 1.87500 or 15/8 simplified 1 7/8
Step-by-step explanation:
Answer:
1 7/8
Step-by-step explanation:
So you want to make 2 5/10 into a improper fraction which is 25/10. so 25/10*3/4 you need to do cross cancel but you can't cross cancel so the answer is just going to be 15/8 which is also 1 7/8 hope this helps ;))
The Chinstrap Penguin about 68.58 centimeters tall whilethe Emperor penguin is 1.143 meters tall. How many centimeters taller is theEmperor penguin than the chinstrap pengin
Answer:
45.72 cm
Step-by-step explanation:
Given: Height of the Chinstrap Penguin= 68.58 cm
Height of the Emperor penguin= 1.143 meter
Lets calculate the height of Emperor penguin in centimeter.
Remember, 1 meter = 100 centimeter
∴ Converting the unit of height of Emperor penguin.
[tex]1.143\times 100= 114.3\ cm[/tex]
∴ Height of Emperor penguin is 114.3 cm.
Now, comparing the height of Chinstrap penguin and Emperor penguin´s height.
[tex]114.3\ cm - 68.58\ cm= 45.72\ cm[/tex]
∴ The Emperor penguin is 45.72 cm taller than Chinstrap penguin.
Slove for x: -2.863.98 - 0.8y = -2.86
Answer:The answer is Zero:(0)
Step-by-step explanation:
Answer:
y=0.067825
Step-by-step explanation:
4x/2+11x-20=0
Solve for quadratic formula
Answer:
I think -4 and 1.25
Step-by-step explanation:
. (6.03) Which of the following best describes the expression 6(y + 3)? (4 points) The product of two constant factors six and three plus a variable The sum of two constant factors six and three plus a variable The product of a constant factor of six and a factor with the sum of two terms The sum of a constant factor of three and a factor with the product of two terms
Answer:
B The sum of two constant factors six and three plus a variable
Step-by-step explanation:
In parallelogram LMNO, MP = 21 m, LP = (y + 3) m, NP = (3y – 1) m, and
OP = (2x – 1) m.
Parallelogram L M N O is shown. Diagonals are drawn from point M to point O and from point L to point N and intersect at point P.
What are the values of x and y?
Answer:
x = 11 m
y = 2 m
Step-by-step explanation:
The given figure is parallelogram, with MP = 21 m, LP = (y + 3) m, NP = (3y – 1) m, and OP = (2x – 1) m
It is property of parallelogram that, the diagonals bisect each other.
Thus, from above,
MP = OP and LP = PN
Thus,
[tex]2x-1 = 21[/tex]
[tex]2x = 22[/tex]
[tex]x = 11[/tex]
and,
[tex]y+3 = 3y-1[/tex]
[tex]2y = 4[/tex]
[tex]y = 2[/tex]
Thus, x = 11 m and y = 2 m
Answer:
D. x = 11 m, y = 2 m
Step-by-step explanation:
On a recent survey, 40% of those surveyed indicated that they preferred walking to running. If 540 people preferred walking, how many people were surveyed
Answer:
The Total number of people were surveyed is 1,350 people.
Step-by-step explanation:
Given as :
The total number of people who preferred walking = 540 people
The percentage of people who preferred walking to running = 40% of the total people
Let The Total number of people were surveyed = n people
Now, According to question
The total number of people who preferred walking = 40% of the total number of people were surveyed
Or, 40% of n = 540
Or, [tex]\dfrac{40}{100}[/tex] × n = 540
Or, n = [tex]\frac{540\times 100}{40}[/tex]
∴ n = 1350
So,Total number of people were surveyed = n = 1350 people
Hence,The Total number of people were surveyed is 1,350 people. Answer
Arc are subtends a central angle measuring 3pi/5 radians . What fraction of the circumference is this arc?
Answer:
The arc is 3/10 of the circumference
Step-by-step explanation:
we know that
The complete circumference subtends a central angle of 2π radians
so
using proportion
Find out what fraction of the circumference represent an arc with a central angle of 3pi/5 radians
[tex]\frac{1}{2\pi}=\frac{x}{(3\pi/5)}\\\\x=\frac{(3\pi/5)}{2\pi}\\\\x=\frac{3}{10}[/tex]
A square on a coordinate plane has one vertex at (2.5,33) and a perimeter of 14 units. If all of the vertices are located in Quadrant I, what are the coordinates of the other 3 vertices? Please show how you solved this in a step-by-step order.
Answer:
A(2.5,36.5)
D(6,36.5)
and
C(6,33)
Use the following figure to answer the question.
∠ 2 and ∠ 4 are adjacent angles.
True
False
Answer:
False, they are opposite angles
Step-by-step explanation:
Answer:
False
Step-by-step explanation:
this is what i maked on my work
someone solve this equation much appreciated!
Answer:
[tex]\frac{2A}{h} = b[/tex]
Step-by-step explanation:
this can be done by simple manipulation .in the given equation, A is the subject.so, by the above statement you can understand the meaning of making something as a subject.given equation: A = 1/2 bhmultiply both the sides by 2,2A = bh
divide both the sides by h,[tex]\frac{2A}{h} = b[/tex]
so, the required form is : [tex]\frac{2A}{h} = b[/tex]