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prisoha [69]
3 years ago
15

The vertices of triangle FGH are F(4, 1), G(0, 3), and H(2, -1). After a translation of 6 units left and 2 units down, triangle

FGH becomes triangle F'G'H'. After a translation of 1 unit right and 5 units up, triangle F'G'H' becomes triangle F"G"H". What translation would move triangle FGH to triangle F"G"H" directly? a. 6 units left and 2 units down c. 5 units left and 3 units up b. 1 unit left and 5 units up d. 2 units right and 6 units down Please select the best answer from the choices provided A B C D
Mathematics
1 answer:
Vesna [10]3 years ago
4 0

Answer:

c. 5 units left and 3 units up

Step-by-step explanation:

Transformation is the movement of a point from its initial location to a new location. Types of transformation is translation, rotation, reflection and rotation.

If a point A(x, y) is translated a units right and b units up, the new location is at A'(x+a, y+b), while if a point A(x, y) is translated a units left and b units down, the new location is at A'(x-a, y-b)

The vertices of triangle FGH are F(4, 1), G(0, 3), and H(2, -1). A translation of 6 units left and 2 units down, triangle FGH becomes triangle F'(-2, -1) G'(-6, 1) H'(-4, -3). A translation of 1 unit right and 5 units up, triangle F'G'H' becomes triangle F"(-1, 4) G"(-5, 6) H"(-3, 2)

The translation of FGH to F"G"H" is a translation of (x -5, y + 3), that is 5 units left and 3 units up

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LenKa [72]

Given:

The given sets are:

Set a : 200, 104, 100, 160.

Set b: 270, 400, 483, 300, x.

Mean of set a: mean of set b= 3:8

To find:

The value of x.

Solution:

Formula for mean:

Mean=\dfrac{\text{Sum of observations}}{\text{Number of observation}}

The mean of set of a is:

Mean=\dfrac{200+104+100+160}{4}

Mean=\dfrac{564}{4}

Mean=141

The mean of set of b is:

Mean=\dfrac{270+400+483+300+x}{5}

Mean=\dfrac{1453+x}{5}

Mean=\dfrac{1453+x}{5}

It is given that,

Mean of set a: mean of set b= 3:8

\dfrac{141}{\dfrac{1453+x}{5}}=\dfrac{3}{8}

\dfrac{705}{1453+x}=\dfrac{3}{8}

8\times 705=3\times (1453+x)

5640=4359
+3x

Isolate the variable x.

5640-4359
=3x

1281
=3x

Divide both sides by 3.

\dfrac{1281}{3}
=x

427
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Therefore, the value of x is 427.

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3 years ago
A school needs 25 butterfly breeding kits, and places an order with an educational company. They already have 7 kits, and they r
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A box of cereal states that there are 75 calories in a three fourths 3/4​-cup serving. What is the unit rate for calories per​ c
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Answer:

a) The unit rate for calories per​ cup is 100 calories per cup

b) 200 calories in 2 cups of cereal.

Step-by-step explanation:

A box of cereal states that there are 75 calories in a three fourths 3/4​-cup serving.

a) What is the unit rate for calories per​ cup?

This is calculated as:

3/4 cup = 75 calories

1 cup = x

Cross Multiply

3/4x = 75 calories × 1

x = 75 calories /3/4 cup

x = 75 ÷ 3/4

x = 75 × 4/3

x = 100 calories per cup

The unit rate for calories per​ cup is 100 calories per cup

b) How many calories are there in 2 cups of the​ cereal?

From the above question

3/4 cup = 75 calories

2 cups = x

Cross Multiply

3/4x = 75× 2

x = 150 ÷ 3/4

x = 150 × 4/3

x = 200 calories

There are 200 calories in 2 cups of cereal.

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Jack invested some money in a bank at a fixed rate of interest compounded annually. The equation below shows the value of his in
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Putting the value of x as 3 and 5, we can get the value of his investment after 3 years and 5 years respectively.

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