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2 years ago

Find the two numbers whose sum is 29 and whose difference is 15.

Mathematics

1 answer:

yulyashka [42]2 years ago

7 0

Answer:

a = 22

b = 7

Step-by-step explanation:

Let the two numbers be represented as a and b.

a + b = 29

a - b = 15

Using elimination method

Add both equations

2a = 44

Divide both sides by 2 to get a

2a/2 = 44/2

a = 22

Now substitute a = 22 in any of the equations to get b .

Using the first equation, we have

a + b = 29

22 + b = 29

Subtract 22 from both sides of the equation

22 - 22 + b = 29 - 22

b = 7

Therefore the two numbers are 22 and 7

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XYZ has coordinates X(2, 3), Y(1,4), and Z(8,9). A translation maps X to X'(4,7). What are the coordinates for Y' and Z' for thi

Rashid [163]

Answer:

The coordinates are $Y'(x,y) = (3, 8)$ and $Z'(x,y) = (10, 13)$ .

Step-by-step explanation:

First, we have to derive an expression for translation under the assumption that each point of XYZ experiments the same translation. Vectorially speaking, translation from X to X' is defined by:

$X'(x,y) = X(x,y) + T(x,y)$ (1)

Where $T(x,y)$ is the vector translation.

If we know that $X(x,y) = (2,3)$ and $X'(x,y) = (4,7)$ , then the vector translation is:

$T(x,y) = X'(x,y)-X(x,y)$

$T(x,y) = (4,7) - (2,3)$

$T(x,y) = (2, 4)$

Then, we determine the coordinates for Y' and Z':

$Y'(x,y) = Y(x,y) + T(x,y)$

$Y'(x,y) = (1,4) + (2,4)$

$Y'(x,y) = (3, 8)$

$Z'(x,y) = Z(x,y) + T(x,y)$

$Z'(x,y) =(8,9) + (2,4)$

$Z'(x,y) = (10, 13)$

The coordinates are $Y'(x,y) = (3, 8)$ and $Z'(x,y) = (10, 13)$ .

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2 years ago

Find -15(-8) A. 120 B. 80 C. -23 D. -120

podryga [215]

Answer:

Step-by-step explanation:

-15(-8)

=+(15*8)

=120

So, the ans is A

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2 years ago

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liubo4ka [24]

Answer:

5/6 of an hour is 50 minutes.

Step-by-step explanation:

There are 60 minutes in 1 hour

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2 years ago

4. Neelam's annual income is Rs. 288000. Her annual savings amount

Vikki [24]

Answer:

The ratio of her savings to expenditure 1 : 7.

Step-by-step explanation:

Given:

Neelam's annual income is Rs. 288000.

Her annual savings amount to Rs. 36000.

Now, to get the ratio of her savings to her expenditure:

So, we get the expenditure first:

Expenditure = Income - Savings.

Expenditure = 288000 - 36000 = Rs. 252000.

Now, the ratio of savings to expenditure:

$\frac{Savings}{Expenditure} =\frac{36000}{252000}$

$\frac{Savings}{Expenditure} =\frac{1}{7}$

Thus, Savings:Expenditure = 1:7.

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