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Irina18 [472]
3 years ago
5

Write as many equations as possible that could represent the relationship between the ages of the two children in each family de

scribed. Be prepared to explain what each part of your equation represents. In Family A, the youngest child is 7 years younger than the oldest, who is 18​
Mathematics
1 answer:
Daniel [21]3 years ago
4 0

Answer:

Step-by-step explanation:

a) Here we have:

"In Family A, the youngest child is 7 years younger than the oldest, who is 18"

Let's define:

Y = age of the youngest child.

O = age of the oldest child.

Then we know that:

Y = O - 7

O = 18

Then we can replace the second equation into the first one:

Y = 18 - 7 = 11.

b) Here we have:

"In Family B, the middle child is 5 years older than the youngest child."

Let's define:

Y = age of the youngest child.

M = age of the middle child.

Here we have only one equation:

M = Y + 5.

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This a pretty typical right triangle trig problem; the first step is to figure out what we have and what we want in relation to an acute angle in the problem.

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31 = FG is <em>adjacent </em>to F.

x = GE is <em>opposite </em>to F.

OK, we have an opposite and adjacent; that tells us we need to use the tangent of F.  Let's write it:

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Solving,

x = 31 tan 23°

I hate the calculator part.  I used to love that part.

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Ilia_Sergeevich [38]
D is answer.
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The change in y is the difference of the two y coordinates (it doesn't matter the order): -1 - (-4) = 3

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ANSWER

P-G = 11{w}^{4} - 5 {w}^{2}  {z}^{2}   - 4z^{4}

EXPLANATION

The given polynomials are:

G =  - 3 {w}^{4}  + 2 {w}^{2}  {z}^{2}  + 5z^{4}

and

P = 8 {w}^{4}   - 3{w}^{2}  {z}^{2}  + z^{4}

We want to subtract these two polynomials.

P-G = 8 {w}^{4}   - 3{w}^{2}  {z}^{2}  + z^{4}  - (- 3 {w}^{4}  + 2 {w}^{2}  {z}^{2}  + 5z^{4} )

Expand the right hand side to obtain:

P-G = 8 {w}^{4}   - 3{w}^{2}  {z}^{2}  + z^{4}   + 3 {w}^{4}   -  2 {w}^{2}  {z}^{2}   -  5z^{4}

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P-G = 8 {w}^{4}  + 3 {w}^{4}- 3{w}^{2}  {z}^{2} -  2 {w}^{2}  {z}^{2}   -  5z^{4} + z^{4}

Combine the similar terms to get:

P-G = 11{w}^{4} - 5 {w}^{2}  {z}^{2}   - 4z^{4}

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