Some number added to seventeen? Help!

Triangle ABC is reflected across the line y=2x to map onto triangle RST. Select all statements that are true.

Anettt [7]

The reflection transformation in the question is a rigid transformation,

therefore, the image and the preimage are congruent.

The statements that are true are;

AB = RS

∠ABC ~ ∠RST

ΔABC = ΔRST

m∠BAC = m∠SRT

Reasons:

The given parameter are;

Triangle ΔABC is reflected across the line 2·X, to map onto triangle ΔRST

Required:

To select the true statements

Solution:

A reflection is a rigid transformation, therefore, the distance between corresponding points on the image and the preimage are equal.

Therefore;

AB = RS

BC = ST

AC = RT

Given that the image formed by a reflection is congruent to the preimage, we have;

ΔABC ≅ ΔRST

∠ABC ≅ ∠RST

m∠ABC = m∠RST by the definition of congruency

∠BCA ≅ ∠STR

m∠BCA = m∠STR by the definition of congruency

∠BAC ≅ ∠SRT

m∠BAC = m∠SRT by the definition of congruency

Therefore, the true statements are;

AB = RS; Image formed by rigid transformation

∠ABC ~ ∠RST; Definition of similarity

ΔABC = ΔRST; By definition of congruency

m∠BAC = m∠SRT; by the definition of congruency

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Find two equivalent fractions for 2/12

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Ian tosses a bone up in the air for his dog, Spot. The height, h, in feet, that Spot is above the ground at the time t seconds a

kirill115 [55]

Answer:

12 feet per second.

Step-by-step explanation:

Please consider the complete question.

Ian tosses a bone up in the air for his dog, Spot. The height, h, in feet, that Spot is above the ground at the time t seconds after she jumps for the bone can be represented $h(t)=-16t^2+20t$ .

What is Spot's average rate of ascent, in feet per second, from the time she jumps into the air to the time she catches the bone at t=1/2?

We will use average rate of change formula to solve our given problem.

$\text{Average rate of change}=\frac{f(b)-f(a)}{b-a}$

$\text{Average rate of change}=\frac{h(\frac{1}{2})-h(0)}{\frac{1}{2}-0}$

$\text{Average rate of change}=\frac{-16\cdot(\frac{1}{2})^2+20\cdot \frac{1}{2}-(-16\cdot(0)^2+20\cdot (0))}{\frac{1}{2}-0}$

$\text{Average rate of change}=\frac{-16\cdot\frac{1}{4}+10-(0)}{\frac{1}{2}}$

$\text{Average rate of change}=\frac{-4+10}{\frac{1}{2}}$

$\text{Average rate of change}=\frac{6}{\frac{1}{2}}$

$\text{Average rate of change}=\frac{2\cdot 6}{1}$

$\text{Average rate of change}=12$

Therefore, Spot's average rate of ascent is 12 feet per second.

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When finding 433 - 249 using place value. What do you subtract first?

Ksenya-84 [330]

You subtract the ones place, then the tens, and lastly the hundreds place. Your answer will be 184 if you are looking for the answer as well.

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3 years ago

Describe the transformation that takes f(x)=x+1 to g(x) = -x+4. Will Mark Brainliest.

lions [1.4K]

Answer:

Reflection across y axis

Translate up by 3 units

Step-by-step explanation:

Given

$f(x) = x + 1$

$g(x) = -x + 4$

Required

Describe the transformation from f(x) to g(x)

First, take a reflection of f(x) across the y axis.

So f(x) becomes f(-x)

$f(x) = x + 1$ when reflected

$f(-x) = -x +1$

Next, translate f(-x) up by 3 units to give g(x)

$g(x) = f(-x) + k$

Where

$k = 3$

$f(-x) = -x +1$

$g(x) = -x + 1 + 3$

$g(x) = -x + 4$

Hence, the transformation from f(x) to g(x) includes:

Reflection across y axis

Translate up by 3 units

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2 years ago