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3 years ago

11

Help please! my teacher wants us to show how we got our answer

1 answer:

Mila [183]3 years ago

3 0

Direct variation is when $\dfrac{y}{x}$ is the same for each coordinate.

Indirect variation is when x · y is the same for each coordinate.

11. Answer: Direct Variation

<u>Step-by-step explanation:</u>

$\begin {array}{c||c|c|c|c|c}x&12&18&23&29&34\\y&132&198&253&319&374\\\\\dfrac{y}{x}&\dfrac{132}{12}=11&\dfrac{198}{18}=11&\dfrac{253}{23}=11&\dfrac{319}{29}=11&\dfrac{374}{34}=11\\\end{array} \\\\\\\text{The coordinates x and y show a direct variation.}$

12. Answer: Indirect Variation

<u>Step-by-step explanation:</u>

$\begin {array}{c||c|c|c|c|c}x&4&6&8&8.4&12\\y&21&14&10.5&10&7\\x\cdot y&4\cdot 21=84&6\cdot 14=84&8\cdot 10.5=84&8.4\cdot 10=84&12\cdot 7=84\\\end{array} \\\\\\\text{The coordinates x and y show an indirect variation.}$

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You invested $10,000 into two accounts: one that has a simple 3% interest, the other with 2.5% interest. If your total interest

artcher [175]

Answer:

3300 was on 3% and 6700 on 2,5%

Step-by-step explanation:

We can say that 'a' represents the price that will go on 3% interest and 'b' 2,5% interest.

Therefore;

a + b = 10 000

And

0,03a + 0,025b = 283.5 (0,03 means 3% etc)

You can move 'b' to the other side to leave 'a' on the LHS

0,03a = 283.5 - 0,025b - - > (divide both sides by 0,03)

a=9450 - 0,8333b

Substitute this equation as 'a' in the first equation to get:

9450 - 0,8333b + b = 10 000 (move 9450 to the RHS to leave values with b on the LHS)

-0,8333b + b = 10 000 - 9450

0,1666b = 550 (divide both sides by 0,1666)

b = 3,300

Therefore 'a' will be :

a= 10 000 - 3 300

a = 6700

I hope this helps.

4 0

3 years ago

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fiasKO [112]

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3 years ago

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SpyIntel [72]

Given:

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$f(x)=x^2$

$g(x)=\left(\dfrac{1}{3}x\right)^2$

To find:

The statement that best compares the graph of g(x) with the graph of f(x).

Solution:

The horizontal stretch is defined as:

$g(x)=f(kx)$ ...(i)

If $0$ , the function f(x) is horizontally stretched by factor $\dfrac{1}{k}$ .

If $k>1$ , the function f(x) is horizontally compressed by factor $\dfrac{1}{k}$ .

We have,

$f(x)=x^2$

$g(x)=\left(\dfrac{1}{3}x\right)^2$

Using these functions, we get

$g(x)=f\left(\dfrac{1}{3}x\right)$ ...(ii)

On comparing (i) and (ii), we get

$k=\dfrac{1}{3}$

Since $0$ , the function f(x) is horizontally stretched by factor $\dfrac{1}{\frac{1}{3}}=3$ .

Hence, the correct option is D.

5 0

3 years ago

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monitta

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