Lyndsey’s advertising firm is working on a project for one of its customers. Lyndsey is asked to move a figure in the advertisement. The new figure must be similar to the old figure. The change is shown in the graph. Write a series of transformations that Lyndsey can use to move the old figure to the new figure. Explain why the figures are similar. *
Answers
Answer:
Step-by-step explanation:
Since, old figure is the dilated form of the new figure.
For the dilation of the old figure to new by a scale factor 's',
s = [tex]\frac{\text{Side length of the new figure}}{\text{Side length of the old figure}}[/tex] = [tex]\frac{2}{4}=\frac{1}{2}[/tex]
Rule for the dilation of a point by a scale factor 'k',
(x, y) → k(x, y)
→ (kx, ky)
If the vertices of the old triangle are dilated by a scale factor of [tex]\frac{1}{2}[/tex],
Coordinates of the dilated triangle of the old triangle will be,
A(3, 4) → A'([tex]\frac{3}{2}[/tex], 2)
B(3, 8) → B'([tex]\frac{3}{2}[/tex], 4)
C(5, 4) → C'([tex]\frac{5}{2}[/tex], 2)
Now these points are rotated by an angle of 90° counterclockwise about the origin,
Rule for the rotation is,
(x, y) → (-y, x)
[tex]A'(\frac{3}{2},2)[/tex] → A"(-2, [tex]\frac{3}{2}[/tex])
B'([tex]\frac{3}{2}[/tex], 4) → B"(-4,
C'([tex]\frac{5}{2}[/tex], 2) → C"(-2,
Further these points have been reflected across x-axis,
A"(-2, [tex]\frac{3}{2}[/tex]) → P(-2, -[tex]\frac{3}{2}[/tex])
B"(-4, [tex]\frac{3}{2}[/tex]) → Q(-4, -[tex]\frac{3}{2}[/tex])
C"(-2, [tex]\frac{5}{2}[/tex]) → R(-2, -[tex]\frac{5}{2}[/tex])
Therefore, old triangle is dilated by a scale factor of [tex]\frac{1}{2}[/tex], followed by rotation of 90° counterclockwise about the origin and then reflected across x-axis to form the new triangle.
Related Questions
1) Solve the equation 6= 1/4z -1 z=
Answers
Answer:
z=28
Step-by-step explanation:
first, add one to each side to eliminate the negative one. you'll get:
7= [tex]\frac{1}{4}[/tex]z
now, to get rid of the 1/4, multiply both sides by 4.
(7x4)=(1/4z)4
simplify to get 28=z.
hope this helps!
the correct answer is z=28
Draw a figure in which ∠1 and ∠2 are acute vertical angles, ∠3 is a right angle adjacent to ∠2, and the sum of the measure of ∠1 and the measure of ∠4 is 180°.
Answers
Answer:
654321
Step-by-step explanation:
Claire bought five toy boxes. Each toy box is in the shape of a cube. The total volume of the five toy boxes when placed in a row is 2,600 cubic inches. Claire thinks she will need about 40 inches of floor length for the toy boxes and Lucy thinks she will need about 45 inches of floor length for the toy boxes.
Answers
Answer:
Please find the answer in the explanation.
Step-by-step explanation:
Given that Each toy box is in the shape of a cube. The total volume of the five toy boxes when placed in a row is 2,600 cubic inches.
If Claire thinks she will need about 40 inches of floor length for the toy boxes and Lucy thinks she will need about 45 inches of floor length for the toy boxes, one of them must be right.
Since Volume = L × B × h
Substitute the volume value and the length into the formula to know the area of the box. This must be in whole number and not in decimal number.
Area = 2600 / 40
Area = 65 square inches. For Claire.
Then for Lucy, we get:
Area = 2600 / 45
Area = 57.7778 square inches
We can therefore conclude that Claire is correct.
A store has 2 packs of paper for $3.52. How much would it cost if you were to buy 4 packs of paper
Answers
Answer:
7.04?
Just multiply 3.52 by two...
can you help me solve this (x+5)(x+3)=0
Answers
Answer:
x= -3, x=-5
Step-by-step explanation:
Answer:
x = -3 or -5
Step-by-step explanation:
This is a quadratic equation, meaning that the solutions (x-values) will occur when the parabola intersects the x-axis
For now, all you have to do is isolate each mini expression, because you can divide each side by either parenthesis (since it's multiplication)
(x+5)(x+3) = 0 (x+5)(x+3) = 0
divide by (x+5) divide by (x+3)
x+3 = 0 x+5 = 0
subtract 3 subtract 5
x = -3 x = -5
Keep in mind that the parabola intersects the axis at BOTH (-3, 0) and (-5, 0)
Therefore, both answers (must be together unless question says otherwise) can be the value of x
x = -3 OR -5
I need help on this question
Answers
Answer:
1.0 x [tex]10^{6}[/tex]
Step-by-step explanation:
Answer:
1.0*10^-6!!!
Step-by-step explanation:
So soft ball bags are on clearance for an additional 30% off the sales price Finley finds one size:it was originally $70.00,but is marked down to $50.00. How much will the bat cost Finley on clearance?
Answers
Answer:
$35
Step-by-step explanation:
50 * 30% = 15$ discount
50 - 15 = 35$ cost
30% discount is additional so based off sales price
Evaluate 7 + q if q = -2
Answers
Answer:
5
Step-by-step explanation:
7-2=5
Answer:
5
Step-by-step explanation:
7 + q if q = -2
7 + (-2)
7 - 2
5
One triangle has angles that measures 45 degrees and 83 degrees. Another triangle has angles that measure 45 degrees and 42 degrees Are the triangles similar? How do you know?
Answers
Answer:
The two triangles are not similar
Step-by-step explanation:
Similar triangles have equal corresponding angles and proportion sides
Ex: If Δ ABC is similar to ΔXYZ, then
m∠A = m∠X, m∠B = m∠Y, m∠C = m∠Z[tex]\frac{AB}{XY}=\frac{BC}{YZ}=\frac{AC}{XZ}[/tex]In the given question
∵ One triangle has angles that measure 45° and 83°
→ Find the measure of the 3rd angle
∵ The sum of the measures of the angles of a triangle is 180°
∴ The measure of the 3rd angle = 180° - 45° - 83°
∴ The measure of the 3rd angle = 52°
∴ The measures of the angles of this triangle are 45°, 83°, 52°
∵ Another triangle has angles that measure 45° and 42°
→ Find the measure of the 3rd angle
∴ The measure of the 3rd angle = 180° - 45° - 42°
∴ The measure of the 3rd angle = 93°
∴ The measures of the angles of this triangle are 45°, 93°, 42°
∵ The two triangles have different measures of 2 angles
→ That means their corresponding angles are not equal
∴ The two triangles are not similar
Help me out please need them by tomorrow, answer any question you know just put the number so I can know what question you answered.
Answers
Answer:
7. 69
Step-by-step explanation:
6x+3(x-7) when x=10
6(10)+3(10)-21
60+30-21
90-21
69
Answer: (7.) the answer is 69
Step-by-step explanation:
The best way to remember this is PEMDAS ("Please Excuse My Dear Aunt Sally)
Parenthesis, Exponent , Multiplication, Division, Addition, Subtraction (this is the order that you should work your problem)
6x+3(x-7) lets see where there is a parenthesis first (x-7), we're going to plug in 10 where x is listed >> (10-7)= 3
The problem now reads 6x+3(3)
We do not have exponents, so we move to see if there is multiplication
6x>> we're going to replace x with 10 to read 6*10 = 60
The other multiplication is 3(3) which = 9
your problem now reads : 60+9
There are no division so we move to Addition
60+9= 69
There are no subtractions so you are now done with your problem and left with the answer 69
Write 4.5 as a mixed number and an improper fraction
Write your answer in simplest form
Answers
Answer:
9/2 and mixed number: 4 1/2
Step-by-step explanation:
Answer:
Mixed number: [tex]4\frac{1}{2}[/tex]Improper fraction: [tex]\frac{9}{2}[/tex]I hope this helps!
5 1/4 divided by 1/8
Answers
Answer:
42
Step-by-step explanation:
Answer:
the answer is 42
Step-by-step explanation:
becuase in decimal 5.25 divided by .125 is 42
5 irrational number
Answers
Answer: 5 is rational because it can be a fraction or ratio.
Answer:
√5 Unlike √9, you cannot simplify √5 .
Step-by-step explanation:
2. What is the equation in point-slope form of the line tha passes through the point
(1, -1) and has a slope of 4?
Answers
Y(sub1)=-1
m=4
Since the slope is given use y-y(sub1)=m(x-x(sub1))
y-(-1)=4(x-(1))
y+1=4(x-1) in point-slope form
y+1=4x-4
Subtract 1 on both sides
y=4x-5 in slope-intercept form
Find a point-slope form for the line with slope 5 and passing through the point (-6,- 4).
Answer y+4=1/5(x+6)
Answers
Answer: 2x+y=20 (A)
Step-by-step explanation:
Which compound inequality can be represented by the graph below?
A. x 9
D. 5 < x ≤ 9
Answers
Answer:
[tex]5 > x \leq 9[/tex]
Step-by-step explanation:
It would be [tex]5 > x \leq 9[/tex]. The reason why, is because according to graph, there is a open circle (open circle signifies as [tex]<[/tex] or [tex]>[/tex], depending on what sign) on [tex]5[/tex], pointing to the right side of the number line and there is a closed circle (closed circle signifies as [tex]\leq[/tex] or [tex]\geq[/tex], depending on what sign) on [tex]9[/tex] pointing to the left side of the number line.
Select the given points in the coordinate plane that lie on the graph of the linear equation 4x - y = 3.
1.(-1,-7) 2.(0,3) 3.(3/4,0) 4.(1,1) 5.(2,5) 6.(4,-1)
Answers
Answer:
HERE IS YOUR ANSWER
Step-by-step explanation:
The standard form of a linear equation is
Ax+By=C,A,B≠0Ax+By=C,A,B≠0
Before you can graph a linear equation in its standard form you first have to solve the equation for y.
2y−4x=82y−4x=8
2y−4x+4x=8+4x2y−4x+4x=8+4x
2y=4x+82y=4x+8
2y2=4x2+822y2=4x2+82
y=2x+4
(-1, -7), (3/4, 0),(1,1),(2,5) are the points in the coordinate plane that lie on the graph of the linear equation 4x - y = 3.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The given points in the coordinate plane that lie on the graph of the linear equation 4x - y = 3.
For (-1,-7)
4(-1)-(-7)=3
3=3
So the point (-1, -7) lie on the line.
(0,3)
4(0)-3=3
-3=3
the point (0,3) does not lie on the line.
For point (3/4, 0)
4(3/4)-0=3
3=3
the point (3/4,0) lie on the line.
For point (1,1)
4-1=3
3=3
The point (1,1) lie on the line.
For point (2,5)
8-5=3
3=3
The point (2,5) lie on the line.
For point (4,-1)
16+1=3
17=3
For point (4,-1) does not lie on the line.
Hence, (-1, -7), (3/4, 0),(1,1),(2,5) are the points in the coordinate plane that lie on the graph of the linear equation 4x - y = 3.
To learn more on Equation:
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Factor by grouping
3x^2-11x+10
Answers
Answer: (x - 2)(3x - 5)
Step-by-step explanation:
I'm using the berry method to factor, so first, I multiply 3 times 10 to get 30. Now I have to figure out what two numbers, when multiplied together, yield 30 and when are added together, give me -11. Those two numbers are -6 and -5. The equation now becomes (3x -6)(3x -5). Reducing the first binomial: (3x - 6)/3 = (x - 2)
the solution is (x - 2)(3x - 5), and we can check this by multiplying it out, which gives us our starting number, meaning it's correct.
Gina is hiking from the top of a mountain. In 24 minutes, she walks down the mountainside to a location 1,524 feet from the top of the mountain. If she walks at about the same pace, express ginas average Change in alititude per minute?
Answers
Answer: 63.5 alt/min
Step-by-step explanation: 1,524/24.
The change in altitude per minute is 63.5 alt/ min
What is unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Given:
In 24 minutes = 1524 feet
So, the average Change in altitude per minute
=1524/24
= 63.5 alt/ min
hence, change in altitude per minute is 63.5 alt/ min.
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the jones family road trip covers 3640 miles and they visit 9 states. what is the average mileage per state?
Answers
Answer:
About 404.4444444445
Step-by-step explanation:
Answer:
404 miles per state
Step-by-step explanation:
First, let's write an equation.
For every 9 states, they covered 3640 miles. So our equation would look like this:
9s=3640 (s= number of states)
Second, let's get s by itself. To do this, divide 9 on both sides/
s=404.44444....
HELPP please ??? I’ll appreciate it a lot .
Answers
Answer: [tex]\sqrt{41}[/tex]
On a keyboard you would type sqrt(41)
===========================================
Work Shown:
[tex]\text{point L} = (x_1, y_1) = (2,-1)\\\\\text{point N} = (x_2, y_2) = (7,-5)\\\\[/tex]
[tex]d = \text{distance from L to N}\\\\d = \sqrt{ (x_1-x_2)^2 + (y_1-y_2)^2 } \ \text{ ... distance formula}\\\\d = \sqrt{ (2-7)^2 + (-1-(-5))^2 }\\\\d = \sqrt{ (2-7)^2 + (-1+5)^2 }\\\\d = \sqrt{ (-5)^2 + (4)^2 }\\\\d = \sqrt{ 25 + 16 }\\\\d = \sqrt{ 41 }\\\\[/tex]
----------
A slight alternative is to plot the point M(2,-5) to form right triangle LMN. The 90 degree angle is at point M.
The legs are of length LM = 4 and MN = 5, which are found by subtracting the x coordinates together and the y coordinates together (or you can count the spaces). From there, use the Pythagorean theorem to get the hypotenuse LN.
The distance formula is an altered version of the Pythagorean theorem.
Answer:
The distance between the two points provided is: [tex]\sqrt{41}[/tex]
Step-by-step explanation:
First thing is to evaluate what the distance formula is:
d = [tex]\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2} }[/tex]
Then substitute the points provided:
d = [tex]\sqrt{(7-2)^{2}+(-5-(-1)^{2} }[/tex]
(The double negative between -5 and -1 will make the -1 a positive 1). (1)
d = [tex]\sqrt{(5)^{2}+(6)^{2} }[/tex]
Now the exponents:
d = [tex]\sqrt{25+36}[/tex]
Second to last, you must add:
d = [tex]\sqrt{41}[/tex]
If needed ± should be added in front of the radical.
The points are the same as the ones that were given.
If josiah skateboards from his house to school 4 miles away. It takes him 20 minutes.
If josiahs speed, in miles per minute, is constant, what is the constant of proportionality?
Answers
The constant of proportionality is 0.2
The constant of proportionality for Josiah's speed is 0.2 miles per minute.
To find the constant of proportionality, we can use the formula:
constant of proportionality = distance / time
In this case, we have the distance Josiah skateboards from his house to school is 4 miles, and it takes him 20 minutes.
So, the constant of proportionality is:
4 miles / 20 minutes = 0.2 miles/minute
Therefore, the constant of proportionality for Josiah's speed is 0.2 miles per minute. This means that he skateboards at a constant rate of 0.2 miles per minute from his house to school.
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find the slope of the line through each pair of points for questions 21 to 39
Answers
Answer:
23,24,26,27 sorry if you get it wrong
Absolute value of -23/7
Answers
Mark is working with the quadratic function y= x2 - 10x + 7. Determine the number and type of roots for the equation using the discriminant.
Answers
72
Which does not represent a rational number? A)3/2 B)√7 C)16 D)0.29 with a repeat bar
Answers
pretty sure it’s D
hope that helps
a professional organizer charged a $45 consultation fee, plus $20 per hour. write an equation to represent the total cost for hiring the organizer. define your variables.
Answers
Answer: y=20x+45
Step-by-step explanation:
y=total cost to hire the organizer
x=number of hours you are hiring the organizer
I need help with number 4 plz answer it
Answers
write 0.49 as a fraction
Answers
Answer:
49/100
Step-by-step explanation:
Answer:
49/100
Step-by-step explanation: .49 you imagine that the decimal is a 1 and the numbers after it are 0's so there are 2 digits so 100
Simplify this please. Will give brainliest for the correct answer. Please explain too.
5(x+3)−5x
Thanks
Answers
Answer:
15
Step-by-step explanation:
First, you must distribute 5 to (x + 3)
5(x + 3) - 5x
5x + 15 - 5x
5x - 5x +15
(You can typically say 0x + 15, as a representation to show there are no more x values, but it is bet not to show any if there are none left)
(5x - 5x will cancel out, leaving only 15)
= 15