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3 years ago

Which set of transformations has been performed on triangle ABC to form triangle A’B’C’?

Mathematics

2 answers:

Mice21 [21]3 years ago

8 0

The answer is D, dilation by a scale factor of 2 followed by reflection about the y- axis.

pashok25 [27]3 years ago

8 0

Answer:

D. Dilation by a scale factor of 2 followed by reflection about the y-axis

Step-by-step explanation:

The pre image or original triangle ABC is first enlarged by a scale factor of 2. Means its each side is multiplies by 2 or we can say that each side in the new triangle A'B'C' has become 2 times the pre image.

Then afterwards, it is reflected over to y axis. When you reflect a point across the line y = x, the x-coordinate and y-coordinate change places. The new image is just the opposite image of the pre image but its enlarged.

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Derive the equation of the parabola with a focus at (6, 2) and a directrix of y = 1

geniusboy [140]

Answer:

Step-by-step explanation:

eq. of directrix is y-1=0

let (x,y) be any point the parabola.

then\sqrt{ (x-6)^2+(y-2)^2}=\frac{y-1}{(-1)*2}

squaring

x²-12x+36+y²-4y+4=y²-2y+1

x²-12 x+40-1=4y-2y

2y=x²-12x+39=x²-12x+36+3

(x-6)²=2y-3

5 0

3 years ago

Distance between parallel lines y=3x+10 and y=3x-20

Alecsey [184]

1. Take an arbitrary point that lies on the first line y=3x+10. Let x=0, then y=10 and point has coordinates (0,10).

2. Use formula $d=\dfrac{|Ax_0+By_0+C|}{\sqrt{A^2+B^2}}$ to find the distance from point $(x_0,y_0)$ to the line Ax+By+C=0.

The second line has equation y=3x-20, that is 3x-y-20=0. By the previous formula the distance from the point (0,10) to the line 3x-y-20=0 is:

$d=\dfrac{|3\cdot 0-10-20|}{\sqrt{3^2+(-1)^2}}=\dfrac{30}{\sqrt{10}}=3\sqrt{10}$ .

3. Since lines y=3x+10 and y=3x-20 are parallel, then the distance between these lines are the same as the distance from an arbitrary point from the first line to the second line.

Answer: $d=3\sqrt{10}$ .

4 0

3 years ago

What is a reasonable estimate for the problem ? -3/2 multiply by ( -5 1/4 )

Nat2105 [25]

= -3/2 * -5 1/4
convert 5 1/4 to improper fraction

= -3/2 * -21/4
multiply numerators; multiply denominators

= (-3*-21)/(2*4)
multiply in parentheses

= 63/8
convert back to mixed number

= 7 7/8

ANSWER: Since the exact answer is the mixed number 7 7/8, a reasonable estimate is 8.

Hope this helps! :)

5 0

3 years ago

Read 2 more answers

Mr.Eastman drew triangle JKL,with a height of 12 inches and a base of 12 inches, and triangle XLZ, with a height of 8 inches and

34kurt

Answer:

Step-by-step explanation:

Area of triangle = 1/2 × Base × Height

Mr.Eastman drew triangle JKL,with a height of 12 inches and a base of 12 inches

Area of JKL = 1/2 × 12 inches × 12 inches

= 72 Square inches

triangle XLZ, with a height of 8 inches and a base of 16 inches. Which triangle has the greater area?

5 0

3 years ago

Joshua invested $750 in an account paying an interest rate of

Maslowich

Due to the difference in the interest rate and the quarterly compounding, Joshua will have $212.24 more than Josiah.
Step-by-step explanation:
Giving the following information:
Joshua:
Initial investment (PV)= $750
Interest rate (i)= 0.0341/4= 0.008525
Number of periods (n)= 18*4= 72 quarters
Josiah:
Initial investment (PV)= $750
Interest rate (i)= 0.0285
Number of periods (n)= 18 years
To calculate the future value of each one, we need to use the following formula:
FV= PV*(1 + i)^n
Joshua:
FV= 750*(1.008525^72)
FV= $1,381.98
Josiah:
FV= 750*(1.0285^18)
FV= $1,169.74
Due to the difference in the interest rate and the quarterly compounding, Joshua will have $212.24 more than Josiah.

5 0

2 years ago