Quadrilateral MATH is dilated by a scale factor of 2.5 centered at (1, 1) to create quadrilateral M’ A’T” H’
Answers
M' A'T" H' is (1,1) and (2.5) equals 3.6 to form a quadrilateral. A two-dimensional shape with four sides, four vertices, and four angles is referred to as a quadrilateral.
What is meant by scale factor of quadrilateral?The scale factor is the ratio of one figure's side length to the other figure's corresponding side length.The scale factor of a shape refers to the amount by which it is increased or shrunk. It is applied when a 2D shape, such as a circle, triangle, square, or rectangle, needs to be made larger. The scale factor is the ratio of one figure's side length to the other figure's corresponding side length. A scale factor is the amount by which an object is multiplied to produce a second object of different size but with the same appearance. Just a larger or smaller version of the original is created, not an exact copy.Let the scale factor of quadrilateral is center at 2.5 at (1, 1) then
(1,1) and (2.5) equals 3.6
(1,1) + (2.5) = 3.6
Therefore, the statement exists true about the dilation is
B. [tex]$\overline{A^{\prime} T^{\prime}}$[/tex] will overlap [tex]$\overline{A T}$[/tex]
C.[tex]$\overline{M^{\prime} A^{\prime}}$[/tex] will overlap [tex]$\overline{M A}$[/tex]
D. The slope of [tex]$\overline{H T}$[/tex] is equal to the slope of [tex]$\overline{\bar{H}^{\prime} T^{\prime}}$[/tex]
The complete question is :
Show the graph below
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Final Answer:
The dilated quadrilateral MATH with a scale factor of 2.5 centered at (1, 1) transforms into the quadrilateral M’A’T’H’.
Explanation:
Quadrilateral MATH is dilated by a scale factor of 2.5 centered at (1, 1). The dilation process involves multiplying the coordinates of each vertex (M, A, T, H) by the scale factor. Let's denote the original coordinates as (x, y), and the new coordinates as (x', y').
1. For point M (x_M, y_M):
- x'_M = 2.5 * (x_M - 1) + 1
- y'_M = 2.5 * (y_M - 1) + 1
2. Similarly, for points A, T, and H:
- x'_A = 2.5 * (x_A - 1) + 1
- y'_A = 2.5 * (y_A - 1) + 1
- x'_T = 2.5 * (x_T - 1) + 1
- y'_T = 2.5 * (y_T - 1) + 1
- x'_H = 2.5 * (x_H - 1) + 1
- y'_H = 2.5 * (y_H - 1) + 1
These formulas calculate the new coordinates for each point after the dilation. The resulting coordinates (x', y') form the vertices of the dilated quadrilateral M’A’T’H’. The center of dilation, (1, 1), is crucial in determining how each point is transformed. The scale factor of 2.5 indicates that the new coordinates are 2.5 times the distance from the center for each point. The final quadrilateral M’A’T’H’ is an enlarged version of the original MATH, maintaining the same shape but with all dimensions multiplied by the scale factor.
Related Questions
What is the answer to linear equation: 9t = -3
Answers
Answer:
-3
Step-by-step explanation:
Anything that is negative multiplied by a negative is a positive so knowing this, you can multiply -3*-3=9 or divide 9/-3=-3
Hope this helps
<> Anna <>
Answer:
The answer to linear equation 9t=-3 is t = - (1/3)
Step-by-step explanation:
9t=-3
Solving for t: Dividing both sides of the equation by 9:
9t/9=-3/9
t=-(3/9)
Simplifying the fraction on the right side of the equation dividing the numerator and denominator by 3:
t = - (3/3) / (9/3)
t = - (1/3)
Out of 75 students, 15 are on the student council. What percent of the students are NOT on the student council?
Answers
Answer: 80%
15 are on the council, so 75-15 = 60 are not on the council. Therefore, 60/75 = 0.80 = 80% of the students aren't on the council.
An alternative way to find this answer is to compute 15/75 = 0.20 = 20% showing that 20% of the students are on the council, so 100% - 20% = 80% are not on the council.
To find the percent of students not on the student council, subtract the number of students on the council from the total number of students and calculate the percentage.
Explanation:To find out what percent of the students are NOT on the student council, we need to subtract the number of students who are on the student council from the total number of students and then calculate the percentage.
Number of students on the student council: 15
Total number of students: 75
Number of students NOT on the student council: 75 - 15 = 60
Percentage of students NOT on the student council: (60/75) * 100 = 80%
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write an equation of the line that passes through (2,-5) and is parallel to the line 2y=3x+10
Answers
Answer:
y=3/2+5
Step-by-step explanation:
Answer:
[tex]\frac{3}{2}x^{2} +5x-21[/tex]
Step-by-step explanation:
put into y=mx+b form
x+1/3=5 6/9
A. 1/3
B. 1 8/9
C. 4 1/3
D. 5 1/3
Answers
x=
D) 5 1/3
Simplify 5 6/9 to 5 2/3. Subtract 1/3 from both sides and you are left with x=5 1/3
what the simplified of 2/3 dived by 2/9
Answers
Answer:
3
Step-by-step explanation:
Divide [tex]\dfrac{2}{3}[/tex] by [tex]\dfrac{2}{9}:[/tex]
[tex]\dfrac{2}{3}:\dfrac{2}{9}=\dfrac{2}{3}\cdot \dfrac{9}{2}=\dfrac{2\cdot9}{3\cdot 2}=\dfrac{9}{3}=3.[/tex]
1/2 x 4 + 1/2 x Z
A. 4(1/2 + Z)
B. Z(1/2 x 4)
C. 1/2 x (4 + 1/2) x Z
D. 1/2(4 + Z)
Answers
Answer:
D. 1/2(4 + Z)
Step-by-step explanation:
1/2 x 4 + 1/2 x Z
We can factor out a 1/2 since it is in both terms
1/2 (4+z)
[tex]\dfrac{1}2{\times4+\dfrac{1}{2}\times z=\boxed{\dfrac{1}{2}}\times4+\boxed{\dfrac{1}{2}}\times z=\boxed{\dfrac{1}{2}}\times(4+z)}\\\\Answer:\ \boxed{D.\ \dfrac{1}{2}(4+z)}[/tex]
solve for x in the triangle
Answers
tan(angle) = opposite/adjacent
tan(37) = x/14
14*tan(37) = x
x = 14*tan(37)
x = 10.5497567
x = 10.5
Answer: 10.5
Please help with this word problem
Answers
Charlie guesses that his dog weighs 34.5 pounds. The dog actually weighs 32.7 pounds.
What is the percent error in Charlie’s guess, to the nearest tenth of a percent?
A: 0.05%
B: 0.5%
C: 5.2%
D: 5.5%
Answers
Answer:
d 5.5
Step-by-step explanation:
Answer:
D: 5.5%
Step-by-step explanation:
For the figures below, assume they are made of semicircles, quarter circles and squares. For each shape, find the area and perimeter. Give your answer as a completely simplified exact value in terms of π (no approximations).
Answers
Answer:
Part a) The area of the figure is [tex]\frac{9}{2}(4+\pi )\ cm^{2}[/tex]
Part b) The perimeter of the figure is [tex]3(2+2\sqrt{2}+ \pi)\ cm[/tex]
Step-by-step explanation:
Step 1
Find the area of the figure
In this problem we have that
The figure ABC is the half of a square and the other figure is a semicircle
Find the area of the figure ABC
we have
[tex]AB=6\ cm, BC=6\ cm[/tex]
The area of the half square ABC is equal to find the area of triangle ABC
so
[tex]A1=\frac{1}{2}*6*6=18\ cm^{2}[/tex]
Find the area of the semicircle
The area of the semicircle is equal to
[tex]A2=\pi r^{2}/2[/tex]
we have that
[tex]r=6/2=3\ cm[/tex]
substitute
[tex]A2=\pi (3)^{2}/2[/tex]
[tex]A2=(9/2) \pi\ cm^{2}[/tex]
The area of the figure is equal to
[tex]18\ cm^{2}+(9/2) \pi\ cm^{2}= \frac{9}{2}(4+\pi )\ cm^{2}[/tex]
Step 2
Find the perimeter of the figure
The perimeter of the figure is equal to
[tex]P=AB+AC+length\ CB[/tex]
we have
[tex]AB=6\ cm[/tex]
Applying Pythagoras theorem
[tex]AC=\sqrt{6^{2}+6^{2}}\\AC=6\sqrt{2}\ cm[/tex]
Remember that
the circumference of a semicircle is equal to
[tex]C=\frac{1}{2}2\pi r=\pi r[/tex]
[tex]r=6/2=3\ cm[/tex]
[tex]C=\pi(3)[/tex]
[tex]C=3 \pi\ cm[/tex]
The perimeter of the figure is equal to
[tex]P=6\ cm+6\sqrt{2}\ cm+3 \pi\ cm[/tex]
Simplify
[tex]P=3(2+2\sqrt{2}+ \pi)\ cm[/tex]
the function c=1.50(n-2)+5.50
Answers
Answer:
c =1.50n +2.50
Step-by-step explanation:
c=1.50(n-2)+5.50
The first step is to distribute the 1.5
c= 1.50*n -1.50*2 + 5.50
c = 1.50n - 3.0 +5.50
Now we need to combine like terms
c =1.50n +2.50
Jake sold 36 tickets at the school fair, and Jeanne sold 15 tickets. What is the ratio in simpilest form, of the number of tickets Jeanne sold to the number of tickets Jake sold.
Answers
Answer:
12:5
Step-by-step explanation:
We want to find the ratio of Jeanne's tickets to Jake's tickets
Jeanne's tickets: Jake's tickets
15:36
We can simplify this ratio by dividing each side by 3
15/3:36/3
5:12
Answer:
Step-by-step explanation:
15:36
simplifies to
5:12
Jeanne: Jake
A rescue helicopter is used to help victims who fell in a ditch. The helicopter begins at sea level, which is an elevation of 0 feet. It then travels down for 100 seconds at a speed of 10.5 feet per second. It then travels directly up for 150 seconds at a speed of 5.2 feet per second. After this 250 second period, how much time, in seconds, will it take for the rescue helicopter to travel back to sea level at the helicopter's maximum speed of 15.8 feet per second?
Answers
Answer:
17 seconds
Step-by-step explanation:
The rescue helicopter travels down for 100 seconds at a speed of 10.5 feet per second.
So, the distance it covered = 100(10.5) = 1050 feet.
It then travels directly up for 150 seconds at a speed 5.2 feet per second.
So, the distance = 150(5.2) = 780 feet
Now, the distance from sea level = 1050 - 780 = 270 feet.
It will reach this distance with a maximum speed of 15.8 feet per second.
Hence, the time required to reach this distance = [tex]\frac{distance}{speed}[/tex]
= [tex]\frac{270}{15.8}[/tex]
≈ 17 seconds
1/8 of pizza costs 2 dollars. In an hour, 6 1/4 pizzas were sold. How much money was made at the food booth in that hour
Answers
Answer:
$12.50
Step-by-step explanation:
1) Mutliply 6 with 2
6*2= 12
2) multiply 1/4 with 2
1/4 * 2 =1/2
3) add 12 and 1/2
12+1/2 = 12.50
By converting the mixed number of pizzas sold to an improper fraction and multiplying by the price per whole pizza, we find the food booth made $100 in one hour from selling pizzas.
To determine how much money was made at the food booth in the given hour, we need to calculate the total sale of pizzas. Since 1/8 of a pizza costs $2, an entire pizza would cost 8 times that amount, which is $16 per pizza. It was stated that 6 1/4 pizzas were sold in that hour. To find the total, we multiply the price per pizza by the number of pizzas sold.
First, convert the mixed number 6 1/4 to an improper fraction to simplify the calculation: 6 1/4 is the same as (6 × 4 + 1) / 4, which is 25/4. Then, multiply the cost per pizza, which is $16, by the number of pizzas sold, which is represented by the fraction 25/4.
The equation for total money made is then $16 × {25}/ {4} = $100.
So, the food booth made $100 in that hour from selling pizzas.
The candy machine in the bookstore has five rows to choose from with six items in each row. Currently, there are seven items that are sold out. If Ari randomly pushed a button, what is the probability he will select an item that is already sold out?
Answers
Answer:
23.3%
Step-by-step explanation:
so 5 by 6 is 30
so to find the fraction or desimal or persent u need to put 7/30
and that would be .23 reapeating then time it by 100 to get
23.3% ps the 3 is reapeating
Final answer:
The probability that Ari will select a sold-out item is 7/30 or approximately 23.33%.
Explanation:
The question asks about the probability that Ari will select an item that is already sold out from a candy machine with a certain configuration and number of sold-out items. To calculate this probability, we need to know the total number of items in the machine and how many are sold out.
There are five rows with six items each, giving a total of 30 items. With seven items sold out, there are 30 - 7 = 23 items available for purchase. The probability of selecting a sold-out item is the number of sold-out items divided by the total number of items. In this case, it's 7/30, which simplifies to 7/30.
So, if Ari randomly pushes a button on the candy machine, the probability that he will select an item that is already sold out is 7/30, or approximately 23.33%.
Solve for X
8^3x-10 =4^6x-27
Thanks in advance!
Answers
[tex]8^{3x-10}=4^{6x-27}\\\\(2^3)^{3x-10}=(2^2)^{6x-27}\qquad\text{use}\ (a^n)^m=a^{nm}\\\\2^{3(3x-10)}=2^{2(6x-27)}\qquad\text{use distributive property}\\\\2^{(3)(3x)+(3)(-10)}=2^{(2)(6x)+(2)(-27)}\\\\2^{9x-30}=2^{12x-54}\iff9x-30=12x-54\qquad\text{add 30 to both sides}\\\\9x=12x-24\qquad\text{subtract 12x from both sides}\\\\-3x=-24\qquad\text{divide both sides by (-3)}\\\\\boxed{x=8}[/tex]
A local amusement park charges $21.50 per daily adult ticket and $14.75 per daily child's ticket. A group of 12 people paid $204.00 for tickets. Which system of equations could be used to find x, the number of adult tickets purchased, and y, the number of children's tickets purchased
Answers
Answer:
[tex]x+y=12[/tex]
[tex]21.50x+14.75y=204[/tex]
Step-by-step explanation:
Let x be the number of adult tickets and y be the number of children's tickets.
We are given that there are total 12 people. Therefore, we can set:
[tex]x+y=12[/tex]
Moreover, we are given that an adult ticket costs $21.50 and a child's ticket costs $14.75, therefore, cost of x adult tickets will be [tex]21.50x[/tex] and cost of y children's ticket will be [tex]14.75y[/tex]. We can form the second equation by setting the total cost of tickets as:
[tex]21.50x+14.75y=204[/tex]
Therefore, the required system of equations that could be used to find x and y will be:
[tex]x+y=12[/tex]
[tex]21.50x+14.75y=204[/tex]
Answer:
[tex]x+y = 12[/tex]
[tex]21.50x+14.75y=204.00[/tex]
Step-by-step explanation:
Given :
A local amusement park charges $21.50 per daily adult ticket and $14.75 per daily child's ticket.
Group of 12 people paid $204.00 for tickets.
To Find : System of equations could be used to find x, the number of adult tickets purchased, and y, the number of children's tickets purchased.
Solution :
Since group contains 12 people so no. of tickets are 12 .
Let out of 12 people no. of adults's tickets are x.
Let out of 12 people no. of children's ticket are y .
⇒[tex]x+y = 12[/tex]
Since charge of one adult ticket = $21.50
So, charge of x adult tickets = $21.50 x
Since charge of one child ticket = $14.75
So, charge of y children tickets =$14.75 y
And we are given that total amount paid by these 12 people = $204.00
Thus [tex]21.50x+14.75y=204.00[/tex]
Hence , System of equations could be used to find x, the number of adult tickets purchased, and y, the number of children's tickets purchased:
[tex]x+y = 12[/tex]
[tex]21.50x+14.75y=204.00[/tex]
six more than seven times a number is less than three times the number decreased by fourteen. FInd the numbers that make this true
Answers
Answer:
find below
Step-by-step explanation:
7x-6 = 3x-14
4x = -8
x = -2
-2*7-6 = -14-6 = -20
-2*3-14 = -6-14 = -20
Write as a fraction in lowest terms:
0.126126125= a/b
Answers
Answer:
a= 14
b= 111
just took it
need help with these questions. show work to plzzzz
Answers
[tex]2.\\k(x)=2x^2-3\sqrt{x}\\\\k(9)\to\text{put the value of x = 9 to the equation of the function:}\\\\k(9)=2(9)^2-3\sqrt9=2(81)-3(3)=162-9=153\to\boxed{(4)}\\\\3.\\3(x^2+2x-3)-4(4x^2-7x+5)\qquad\text{use distributive property}\\\\=(3)(x^2)+(3)(2x)+(3)(-3)+(-4)(4x^2)+(-4)(-7x)+(-4)(5)\\\\=3x^2+6x-9-16x^2+28x-20\qquad\text{combine like terms}\\\\=(3x^2-16x^2)+(6x+28x)+(-9-20)\\\\=-13x^2+34x-29\to\boxed{(2)}[/tex]
[tex]4.\\p(x)=x^2-2x-24\\\\x^2-2x-24=0\\\\x^2+4x-6x-24=0\\\\x(x+4)-6(x+4)=0\\\\(x+4)(x-6)=0\iff x+4=0\ \vee\ x-6=0\\\\x=-4\ \vee\ x=6\to\boxed{(3)}[/tex]
The results for a survey of 130 students who were selected randomly are listed below:
•70 students have a cell phone plan with company X
•32 students have a cell phone plan with company Y
•28 students do not have a cell phone
The total population of students was 390. Based on the data, what is the best approximation for the total number of students who have a cell phone plan with company X?
A) 210
B) 96
C) 84
D) 724
Answers
Answer:
A) 210
Step-by-step explanation:
The percentage of students who have a cell phone plan with company x is student with plan x over total.The total is 130
P(x) = 70/130
The number of students with cell phone company x is found by multiplying the total number of students times the percentage of students with company x
Students with company x = total * P(x)
= 390 * 70/130
= 210
Answer:
A) 210
Step-by-step explanation:
70 students have company X, out of the sample size 130. This forms the fraction 70/130.
n students have company X, out of the population 390. The n is simply a placeholder for a number. This forms the fraction n/390
Equate the two fractions, cross multiply, then divide both sides by 130 to solve for n
Doing all that gives us the following
70/130 = n/390
70*390 = 130*n ..... cross multiply
27300 = 130n
130n = 27300
130n/130 = 27300/130 ...... divide both sides by 130
n = 210
Out of the entire population, the best approximation to the number of students who have company X is 210 people.
Find the value of x so that the line m is parallel to line I.
Answers
Here's why:
If these two lines are parallel, it means those 2 angles, (3x+11)° and (4x-21)°, are equal. So to find X, you need to set the equation
[tex]3x + 11 = 4x - 21 \\ x - 21 = 11 \\ x = 32[/tex]
If you want to check if it's the right answer, you can go back to those two angles, and if you put 32 instead of X, you'll get two identical numbers (that is 107°)
Which inequality is true? A. |-15| > |-19| B. |-16| < |13| C. |-15| > |12| D. |12| < |-8| E. |-19| > |-20|
Answers
The modulus or absolute value function of a real number x is the non-negative value of x without regard to its sign.
The only correct option is C. because 15 is indeed greater than 12.
Options A., B., D. and E. are wrong.
Answer: C
Step-by-step explanation: |-15| is 15. |12| is 12. 15 is greater then 12.
Tessa drew a scale drawing of the elementary school. She used the scale 1 centimeter : 7 meters. The school yard is 7 centimeters in the drawing. How wide is the actual school yard?
Answers
Answer:
see below PLEASE GIVE BRAINLIEST
Step-by-step explanation:
If 1cm = 7m
then:
7c = 49m
Which is an example of dealer incentives? A. Sun car dealers pay $18,000 to Galaxy car manufacturers for a car worth $20,000. B. Sun car dealers pay $21,000 to Galaxy car manufacturers for a car worth $20,000. C. Sun car dealers pay $20,000 to Galaxy car manufacturers for a car worth $20,000.
Answers
Answer: A. Sun car dealers pay $18,000 to Galaxy car manufacturers for a car worth $20,000.
Step-by-step explanation:
Hi, "dealer incentives" for this case mean that a car dealer pays a reduced price for a car. This incentive allows the car dealer to make a profit.
To be an example of dealer incentive the option must state that the car dealer makes a profit.
So, with this information analyzed the correct option is A."Sun car dealers pay $18,000 to Galaxy car manufacturers for a car worth $20,000" because this option states that the Sun car dealers make a profit of $2000.
Feel free to ask for more if it´s necessary or if you did not understand something.
Find the value of y when x = 4 in the equation 4x - 2 = y + 5 Show your work help
Answers
Then multiply 4 times 4
Subtract 2
Then subtract 5 from both sides
16-2=y+5
14=y+5
9=y
Saheel has $20,000 property damage insurance and $5,000 comprehensive and collision insurance with a $500 deductible. One evening he slides on a patch of ice and hits a parked car, causing $4,500 worth of damage. The accident causes $1,750 of damage to his own car. How much will the insurance pay to fix both cars?
Answers
Answer:
$5750
Step-by-step explanation:
Property damage insurance = $20,000
Comprehensive insurance = $5,000
Deductible = $500
Amount of Property damage caused by him by hitting a parked car = $4,500
Amount of Damage caused to his own car = $1,750
Since, the property damage of $4500 is within the property damage insurance limit of $20,000 and own damage of $1,750 is also within the comprehensive insurance limit of $5000, he'll be paid the entire amount excluding the compulsory deductible of $500.
So,
The amount paid by the insurance company to fix both cars = 4500+1750 - 500
= 6250 - 500
= $5750
The insurance will cover a total of $5,750 for the damages caused by Saheel's accident. It will completely cover the $4,500 worth of damage to the parked car that he hit, and will cover $1,250 of the $1,750 damage to his own car after the deductible.
Explanation:In this case, Saheel has coverage for both property damage ($20,000) and comprehensive and collision insurance ($5,000 with a $500 deductible). When he slid on ice and hit a parked car, causing $4,500 worth of damage, his property damage insurance will cover this cost since it is under the $20,000 limit.
As for the $1,750 damage to his own car, his comprehensive and collision insurance can cover this after he pays the $500 deductible. So, his insurance will pay $1,250 ($1,750 - $500 deductible) towards the repair of his own car.
Therefore, the total money that the insurance company will pay to fix both cars would be $5,750 ($4,500 for the parked car's damages and $1,250 for Saheel's car damages after deductible).
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Please help
The tape diagram
Answers
On a map, the distance between Jacksonville, FL and Tallahassee, FL is about 8 inches. According to the scale, 1 inch represents 20 miles. About how far apart are the two cities?
Answers
Answer: 160 miles
Step-by-step explanation:
Because if each inch is 20 miles then you multiply 20 times 8. You multiply by 8 because that how far they live from each other in inch but you want to know miles so you multiply the I with 20 and get 160 miles
refurbished phone 30% off now only 78£ how much was the phone before
Answers
Answer:
120 pounds
-hope this helps
Answer:
£111.43
Step-by-step explanation:
100% represents the original cost of the phone
30% off is then (100 - 30) = 70% of the original cost
divide the cost by 70 to find 1% then multiply by 100 for original cost
original cost = [tex]\frac{78}{70}[/tex] × 100 = £111.43