Draw the image of \triangle ABC△ABCtriangle, A, B, C under a dilation whose center is PPP and scale factor is \dfrac{1}{3} 3 1 start fraction, 1, divided by, 3, end fraction.
Answers
Dilating the triangle ABC would create another triangle whose size is different from the triangle ABC
How to dilate the triangle?From the complete question, we have the following coordinates:
Point A = (-4,5)Point B = (7,-7)Point C = (-2,2)Point P = (1,-4)Scale factor, k = 1/3The dilation rule across the center P is:
(x, y) --> (1/3x – 1, 1/3y + 4)
So, the coordinates of the image of the triangle are:
A' = (-1/3 * 4 – 1, 1/3 * 5 + 4)
A' = (-7/3, 17/3)
B' = (1/3 * 7 – 1, -1/3 * 7 + 4)
B' = (4/3, 5/3)
C' = (-1/3 * 2 – 1, 1/3 * 2 + 4)
C' = (-5/3, 14/3)
From the above computation, the coordinates of the new triangle is:
A' = (-7/3, 17/3)
B' = (4/3, 5/3)
C' = (-5/3, 14/3)
See attachment for the image of triangle ABC
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Related Questions
Please hurry!!! Thank you to whoever answers this!! Love yaaa
Answers
Answer: The dimensions of the builder's scale drawing is 40 x 32 inches.
Step-by-step explanation:
The scale factor of Karl = 1:12
Dimensions = 10 x 8 inches
Area = 80 square inches
1:12 = 1/12
1/12 = 80/a
a = 80 x 12
a = 960 square inches
So dimensions are 120 x 96 inches
Builders scale factor = 1:3
Actual Length = 120inches
Actual width = 96 inches
Builders drawing length = 120/3
= 40 inches
Builders drawing width = 96/3
= 32 inches
HELP PLEASE ASAP
Which situation can be represented by the equation y = 25x
Question 1 options:
David earned y amount of money at a rate of $25 per x hours.
David earned $25 for one day, which x amount is earned for y number of days.
David earned x amount of money at a rate of $25 per y hours.
David earned $25 for one day, which y amount is earned for x number of days.
Answers
The situation that best represents the equation y = 25x is David earned y amount of money at a rate of $25 per x hours.
Using equations to represent expressionsRate of payment is the amount of money a worker receives after each hour, day or week.
David receives the amount of y as his payment every hour.
He is paid at the rate of $25 every X hours.
Therefore the amount he will receive which is represented as y would be $25 * X hours.
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for 30 POINTS
pls help me rn
this is very urgent
thx in advance
Answers
2- observation
3- observation
4- questionnaire
5- experimentation
6- interview
7- census
8- questionnaire
9- questionnaire
10- experimentation
My apologies if any are wrong! ;-;
A consumer charges a $2,530.16 purchase on a credit card. the card has a daily interest rate of 0.042%. if the balance is paid off at the end of 30 days, how much interest will the consumer pay? a. $0.32 b. $3.19 c. $31.88 d. $318.78
Answers
The total interest consumer pay on the credit card which has a daily interest rate of 0.042% is $32.08.
What is compound interest?Compound interest is the amount charged on the principal amount and the accumulated interest with a fixed rate of interest for a time period.
The formula for the final amount with the compound interest formula can be given as,
[tex]A=P\times\left(1+\dfrac{r}{100}\right)^{t}\\[/tex]
Here, A is the final amount (principal plus interest amount) on the principal amount P of with the rate r of in the time period of t.
In the given problem,
A consumer charges a P, $2,530.16 purchase on a credit card. The card has a daily interest rate r of 0.042%. The balance is paid off at the end of 30 days. Thus the time t is 30.Put these values in the above formula as,
[tex]A=2530.16\times\left(1+\dfrac{0.042}{100}\right)^{30}\\\\A=2562.24[/tex]
The interest amount paid is,
[tex]I=A-P\\I=2562.24-2530.16\\I=32.08[/tex]
Thus, the total interest consumer pay on the credit card which has a daily interest rate of 0.042% is $32.08.
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Answer:
The correct answer is C
Step-by-step explanation:
Find the solution to the equation below.
Answers
Answer:
Answer is G 1.5
Step-by-step explanation:
1. Distribute the 5 to x and 2 by multiplying. and the 7 to the 4 and -x by multiplying
2. carry over the 7x by adding it to 5x. to get x to one side.
3. subtract 10 from both side
4. Divide both side by 12
5. simplify and convert to decimal
The base of a merry-go-round spans an area of about 153.88 square meters What is the radius of
the merry-go-round?
Nysean says the radius of the merry-go-round is 14 meters. Do you agree or disagree? Explain.
Answers
Answer:
Disagree
radius = 7 m
diameter = 14 m
Step-by-step explanation:
Formula
[tex]\sf Area\:of\:a\:circle=\pi r^2[/tex]
Given:
area = 153.88 m²Substitute given value into the formula and solve for r:
[tex]\sf \implies \pi r^2=153.88[/tex]
[tex]\sf \implies r^2=\dfrac{153.88}{\pi}[/tex]
[tex]\sf \implies r=\sqrt{\dfrac{153.88}{\pi}}[/tex]
[tex]\sf \implies r=6.998680253[/tex]
Therefore r ≈ 7 m
So I disagree with Nysean, as from my calculations, the approximate radius of the merry-go-round is 7 m.
Diameter = 2r
⇒ diameter of merry-go-round = 2 x 7 = 14m
So Nysean has actually given the approximate measure of the diameter rather than the radius.
Solve by factoring
3v^2-10v+3=
Answers
[tex]3v^2-10v+3=0\\\\\implies 3v^2 - 9v-v +3=0\\ \\\implies 3v(v-3)-(v-3)=0\\\\\implies (v-3)(3v-1)=0\\\\\implies v = 3,~~v=\dfrac 13[/tex]
The area of a triangle is 115 in2. If the height of the triangle is 7.5 inches, what is the length of its base? Round to the nearest hundredth, if necessary.
Answers
Answer:
30.67 inches
Step-by-step explanation:
Area of a triangle: 1/2 x b x h
115 = 1/2 x b x 7.5
115 = 3.75b
115/3.75 = b
30.66666 = b
30.67 = b
Solve for the unknown value.
x = _____ degrees
Answers
Answer:
x= 89°
Step-by-step explanation:
Let's use the rule of corresponding angles.
x+ 32°= 121° (corr. ∠s)
x= 121° -32°
x= 89°
Write the equation of the line that passes through (9, 5) and (7, 6) in slope-intercept form.
Answers
Answer:
y = -1/2x + 19/2
Step-by-step explanation:
Hi there!
We are given the points (9,5) and (7,6)
We want to write an equation of the line that contains these two points, in slope-intercept form
Slope-intercept form is given as y=mx+b, where m is the slope and b is the y intercept
First, let's find the slope of the line
The formula for the slope (m) calculated from 2 points is [tex]\frac{y_2-y_1}{x_2-x_1}[/tex], where [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] are points
We have everything we need to find the slope, but let's label the values of the points to avoid any confusion.
[tex]x_1=9\\y_1=5\\x_2=7\\y_2=6[/tex]
Now substitute these values into the formula to find the slope
m= [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
m=[tex]\frac{6-5}{7-9}[/tex]
Subtract
m=[tex]\frac{1}{-2}[/tex]
m=-1/2
The slope of the line is -1/2
We can substitute this as m into the formula for slope-intercept form:
y = -1/2x + b
Now we need to find b
As the equation passes through (9, 5) and (7, 6), we can use either one to solve for b
Taking (7, 6) for example:
Substitute 7 as x and 6 as y into the equation
6 = -1/2(7) + b
Multiply
6 = -7/2 + b
Add 7/2 to both sides
19/2 = b
substitute 19/2 as b:
y = -1/2x + 19/2
Hope this helps!
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PLEASE HELP ME ANSWER THIS QUESTION
Answers
Answer:
Scale faction is 4
Step-by-step explanation:
You want to step this up as new/old this is because the shape is increasing in size. 18 times 4 is 72.
find the value of x.
Answers
Answer: 7.2
Step-by-step explanation:
Which equation is true for x = –6 and x = 2? 2x2 – 16x 12 = 0 2x2 8x – 24 = 0 3x2 – 4x – 12 = 0 3x2 12x 36 = 0
Answers
The equation that is true for x = -6 and x= 2 is given by: Option B: 2x^2 +8x -24 = 0
What are those values of the variables called for which an equation is true?Suppose there is an equation given, involving some variables.
Then, those values of the involved variable, for which the equation is true, are called solution of the equation.
For single variable equations, specially for polynomials, these solutions are called the roots of the equation.
How to find the roots of a quadratic equation?Suppose that the given quadratic equation is
[tex]ax^2 + bx + c = 0[/tex]
Then its roots are given as:
[tex]x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]
For this case, the options are all quadratic equations, so we can check all the options to find the roots to see if they match to x = -6 and = 2
Option 1: [tex]2x^2 -16x + 12 = 0[/tex]Then its roots are given as:
[tex]x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a} = \dfrac{-(-16) \pm \sqrt{(-16)^2 - 4(2)(12)}}{2(2)}\\\\x = \dfrac{16 \pm \sqrt{196 - 96}}{4} = \dfrac{16 \pm 10}{4}\\\\x = 26/4, x = 6/4[/tex]
Thus, this equation isn't true for both x = -6 and x= 2
Option 2: [tex]2x^2 +8x -24 = 0[/tex]Then its roots are given as:
[tex]x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a} = \dfrac{-8 \pm \sqrt{(8)^2 - 4(2)(-24)}}{2(2)}\\\\x = \dfrac{-8 \pm \sqrt{64 +192}}{4} = \dfrac{-8 \pm 16}{4}\\\\x = -6, x = 2[/tex]
Thus, this equation is true for both x = -6 and x= 2
Since the question says "Which equation is true", so that means only one option is true.
Thus, the equation that is true for x = -6 and x= 2 is given by: Option B: [tex]2x^2 +8x -24 = 0[/tex]
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Answer:
b
Step-by-step explanation:
edge
What’s the surface area of this tent? length:10.5.
Width:8
height:7
Answers
Answer:
427
Step-by-step explanation:
i could be wrong i used surface area calculator
A password is 4 characters long, consisting of 2 letters and 2 numbers. the password must begin and end with a letter. if numbers can be repeated but letters cannot, how many possibilities are there? a. 65,000 b. 60,840 c. 58,500 d. 52,650 please select the best answer from the choices provided. a b c d
Answers
The question is an illustration of arrangements, and the number of possibilities of the password is 65000
How to determine the number of possibilities?The length of the password is:
Length = 4
If the password begins and ends with a letter and cannot be repeated, then the possibilities are:
First = 26
Last = 25
If the password contains numbers that can be repeated, then the possibilities are:
Number 1 = 10
Number 2 = 10
So, the number of possibilities is:
Possibilities = 26 * 10 * 10 * 25
Evaluate the product
Possibilities = 65000
Hence, there are 65000 possibilities of a 4 character password
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One company makes inflatable swimming pools that come in four sizes of rectangular prisms.
The length of each pool is twice the width and twice the depth.
The depth of each pool is a whole number from 3 to 6 feet.
If the pools are filled all the way to the top, what is the volume of each pool?
Answers
Answer:
Pool 1: 2(3)*3*3= 54 ft^3
pool 2: 2(4)*4*4= 128 ft^3
Pool 3: 2(5)*5*5= 250 ft^3
pool 4: 2(6)*6*6= 432 ft^3
Step-by-step explanation:
length can be modeled by twice the width or twice the depth which means that deapth=width,
both the width and the depth are equal, hence
L= 2x
W=X
x=3,4,5,6 (which are values for depth as well as width)
susbtitute values:
Pool 1: 2(3)*3*3= 54 ft^3
pool 2: 2(4)*4*4= 128 ft^3
Pool 3: 2(5)*5*5= 250 ft^3
pool 4: 2(6)*6*6= 432 ft^3
help A S A P IM STUCK
Answers
Answer:
this is the unit area of: 24
Step-by-step explanation: hope this helps
Choose one answer: A: 13+t=17
B:13t=17
Find the value of t that makes the equation true
Answers
Answer:
a: 13 + t = 17
Step-by-step explanation:
the top is equal to the bottom
the top is 13 and t together but you are not multiplying
thus the answer is 13 + t = 17
Answer:
A, 13+t=17
Step-by-step explanation:
Since you are trying to find the missing part of the diagram and both rows add up to 17, the answer would be A. This is the case because you aren't multiplying 13 over and over to get 17, rather instead you are adding a number to get 17.
if the area of a circle is 154 cm square then find the diameter and circumference
Answers
Answer:
Diameter = 14 cm
Circumference = 44 cm
Step-by-step explanation:
Area of circle = πr²Diameter = 2rCircumference = 2πr = πdπ ≈ 3.142[tex]\pi {r}^{2} = 154 \\ {r}^{2} = \frac{154}{\pi} \\ r = \sqrt{ \frac{154}{\pi} } \: cm[/tex]
[tex]Diameter = 2r \\ = 2 \sqrt{ \frac{154}{3.142} } \\ ≈ 14 \: cm[/tex]
[tex]Circumference = πd \\ = 14\pi \\ = 14 \times 3.142 \\ = 43.988 \\ ≈ 44 \: cm[/tex]
A credit card company is collecting data for their end of the year review. The chart below shows the interest change for the year that they will use to market to new customers.
What is the mean interest change for the year? Group of answer choices
A. 20%
B. 5%
C. 2%
D. 4%
Answers
the answer of the year is 20%
What is the factored form of the function? what are the zeros of the quadratic function?
Answers
Answer:
The factored form of the equation is f(x) = (x - 2)(x + 10), which makes the zeros of the function x = -10 and x = 2.
In order to factor a quadratic like this, you must find factors of the constant (in this case -20). The pairs of factors are listed below.
1 and -20
-1 and 20
2 and -10
-2 and 10
4 and -5
-4 and 5
Now we must pick out the pair that add to the coefficient of x.
1 and -20
-1 and 20
2 and -10
-2 and 10
4 and -5
-4 and 5
Once you've picked out those numbers, you can place each in a parenthesis with x.
f(x) = (x - 2)(x + 10)
Then to find the zeros to the equation, set each parenthesis equal to 0 and solve.
x - 2 = 0
x = 2
x + 10 = 0
x = -10
Step-by-step explanation:
hope this helps:)
true or false if two half planes never intersect, then their system of inqeualities has no solution
Answers
Answer:
True
Step-by-step explanation:
If two of the half planes never intersect, there is no way for the lines to reach each other hence giving no soultion
Answer:
its false
Step-by-step explanation:
Monica made this object from snap cubes. Monica made 9 more objects just like this one. she laid them one next to the other to form a square. Monica said she could use the square to write a percent and a decimal for 6/10 and for 4/10. is she correct?
Answers
The fraction 6/10 and 4/10 can be represented by using the objects laid together to form a square.
What is an equation?
An equation is an expression that shows the relationship between two or more variables and numbers.
The fraction 6/10 and 4/10 can be represented by using the objects laid together to form a square.
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А
. Which phrase represents the
expression 8x + 5?
eight times five plus a number
B five times a number plus eight
Cfive less than a number
multiplied by eight
D a number multiplied by eight
then added to five
Answers
Answer:
D i think a number represents x. not sure
Answer:
8x+5
Assume x is the unknown number.
8x+5 means
8*x = a number multiplied by eight
8x+5 = a number multiplied by eight eight then added to five.
Therefore, the correct option is D.
A softball player has had 8 base hits out of 25 at bats for a current batting average of 8/25 = .320. How many consecutive base hits does she need if she wants to raise her batting average to .400? Explain or show your reasoning.
Answers
Using proportions, it is found that she needs 4 consecutive hits to raise her batting average to .400.
What is a proportion?A proportion is a fraction of a total amount.
Hence, the batting average is given by the number of hits divided by the number of at-bats.
If she gets x consecutive hits, she will have 8 + x hits in 25 + x at-bats, for an average of 0.400, hence:
[tex]0.4 = \frac{8 + x}{25 + x}[/tex]
8 + x = 10 + 0.4x
0.6x = 2
x = 3.33
Rounding up, she needs 4 consecutive hits to raise her batting average to .400.
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Which of the following does not have a value that is greater than 0?
|-11|
-11
|11|
11
Answers
Answer:
-11
Step-by-step explanation:
The | | around a number means the absolute value of that number. The absolute value is the positive value of the number given.
Find the common ratio of the sequence.
1,-1, 1,-1...
Answers
Slope intercept form of x intercept=3 y intercept=-5
Answers
Answer:
[tex]y = \frac{5}{3} x - 5[/tex]
Step-by-step explanation:
To write an equation in the slope-intercept form, we need the slope (which can also be calculated) and at least a coordinate.
What is slope-intercept form?
y= mx +c, where m is the slope and c is the y-interceptWhen the coefficient of y is 1, and all the other terms are on the right-hand side of the equationx- intercept occurs at y= 0 while y-intercept occurs at x= 0. With this information, let's write out the two coordinates given.
(3, 0) and (0, -5)With two coordinates, we can calculate the slope using the equation below.
[tex]\boxed{ slope = \frac{y _{1} - y_2 }{x_1 - x_2} }[/tex]
[tex]slope = \frac{ - 5 - 0}{0 - 3} [/tex]
[tex]slope = \frac{ - 5}{ - 3} [/tex]
[tex]slope = \frac{5}{3} [/tex]
Substitute the value of the slope into m in the equation.
[tex]y = \frac{5}{3} x + c[/tex]
Given that the y-intercept is -5, c= -5.
[tex]y = \frac{5}{3} x - 5[/tex]
Two numbers have a least common multiple of 48 and a greatest common factor of 4?
Answers
Answer:
The numbers are 12 and 4
Step-by-step explanation:
12÷4=3
4÷4=1
12×4=48
Consider two unique parallel lines. What aspects of these
two lines are the same? What aspects of these two lines
would have to be different? Explain your reasoning.
Answers
Answer:
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░░░▌░▄▄▄▐▌▀▀▀░░ This is Bob
▄░▐░░░▄▄░█░▀▀ ░░
▀█▌░░░▄░▀█▀░▀ ░░ Copy And Paste
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Step-by-step explanation: