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3 years ago

A transformation of ΔDEF results in ΔD'E'F'.

Mathematics

2 answers:

sladkih [1.3K]3 years ago

6 0

Answer:

Rotation

Step-by-step explanation:

A transformation of a triangle can be either dilation or reflection or rotation or a translation.

Dilation happens when a symmetric figure is formed with scale factor other than 1. But here both triangles have same side length. Hence no dilation

Reflection happens when it is reflected over a line as we see in a mirror. But here the two triangles are not looking as images on a line. Hence no reflection

Rotation is keeping the same shape but rotating through a certain angle. Here DEF is rotated without disturbing its shape or size through a certain angle. Hence rotation is right

Translation is not right because there is no vertical or horizontal shift to get new triangle.

EastWind [94]3 years ago

6 0

Answer:

Step-by-step explanation:

The transformation is a rotation.

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(3x + 5)º (6x + 13)°

Zigmanuir [339]

Answer: 18x2 + 69x + 65

Step-by-step explanation:

(3x + 5) (~6x + 13)

1. 3x(6x + 13) + 5(6x + 13)

2. 18x2 + 39x + 5(6x + 13)

3. 18x2 + 39x + 30 + 65

4. 18x2 + 69 + 65

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2 years ago

Fill in the y-value for each box in the t-chart using the equation below !?

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2 years ago

Which equation is y = –6x^2 + 3x + 2 rewritten in vertex form? y = negative 6 (x minus 1) squared + 8 y = negative 6 (x + one-fo

mart [117]

Answer:

$y = -6(x - \frac{1}{2})^2 -\frac{7}{2}$

Step-by-step explanation:

Given:

$y = -6x^2 + 3x + 2$

Required

Rewrite in vertex form

The vertex form of an equation is in form of: $y = a(x - h)^2+ k$

Solving: $y = -6x^2 + 3x + 2$

Subtract 2 from both sides

$y - 2 = -6x^2 + 3x + 2 - 2$

$y - 2 = -6x^2 + 3x$

Factorize expression on the right hand side by dividing through by the coefficient of x²

$y - 2 = -6(x^2 + \frac{3x}{-6})$

$y - 2 = -6(x^2 - \frac{3x}{6})$

$y - 2 = -6(x^2 - \frac{x}{2})$

Get a perfect square of coefficient of x; then add to both sides

------------------------------------------------------------------------------------

Rough work

The coefficient of x is $\frac{-1}{2}$

It's square is $(\frac{-1}{2})^2 = \frac{1}{4}$

Adding inside the bracket of $-6(x^2 - \frac{x}{2})$ to give: $-6(x^2 - \frac{x}{2} + \frac{1}{4})$

To balance the equation, the same expression must be added to the other side of the equation;

Equivalent expression is: $-6(\frac{1}{4})$

------------------------------------------------------------------------------------

The expression becomes

$y - 2 -6(\frac{1}{4})= -6(x^2 - \frac{x}{2} + \frac{1}{4})$

$y - 2 -\frac{6}{4}= -6(x^2 - \frac{x}{2} + \frac{1}{4})$

$y - 2 -\frac{3}{2}= -6(x^2 - \frac{x}{2} + \frac{1}{4})$

Factorize the expression on the right hand side

$y - 2 -\frac{3}{2}= -6(x - \frac{1}{2})^2$

$y - (2 +\frac{3}{2})= -6(x - \frac{1}{2})^2$

$y - (\frac{4+3}{2})= -6(x - \frac{1}{2})^2$

$y - (\frac{7}{2})= -6(x - \frac{1}{2})^2$

$y +\frac{7}{2} = -6(x - \frac{1}{2})^2$

Make y the subject of formula

$y = -6(x - \frac{1}{2})^2 -\frac{7}{2}$

Solved

7 0

3 years ago

Read 2 more answers

A survey was taken of 100 potential voters, asking them which candidate they would vote for in a local election. The results are

In-s [12.5K]

Candidate X won 63 out of the 100 "votes" of the poll participants.

So candidate X won 63% of the votes in the poll.

This means that candidate X is expected to win the elections by a percentage close to 63%.

63% of the voters is (63/100)*5000=63*50=3150 voters

Answer: 3150

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2 years ago

Need help on geometry please right answer only I’m giving out 40 points

Juliette [100K]

Answer: first option 392.699 square feet.

Explanation:

1) The shape of the sidewalk is an ring with exterior radius equal to the radious of the fountain + 5 feet and inner radius equal to the radius of the fountain.

2) The area of such ring is equal to the area of the outer circle less the area of the inner circle (the fountain)

Area of a circle = π × r²

Area of the outer circle: π (10ft + 5 ft)² = π (15 ft)² = 225 π ft²

Area of the inner circle = π (10ft)² = 100 π ft²

Area of the ring (sidewald) = 225π ft² - 100π ft² = 125π ft² = 392.699 ft²

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3 years ago

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