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3 years ago

Which table represents a direct variation function?

Mathematics

2 answers:

leonid [27]3 years ago

8 0

3 i think it might be

konstantin123 [22]3 years ago

3 0

Answer:

The correct option is 3.

Step-by-step explanation:

A function is direct variation function if

$y\propto x$

$y=kx$

where, k is the constant of proportionality.

It means the value of y is k times of x. Only table 3 represents a direct variation function because each value of y is -2 times of x.

$y=-2x$

At x=-5,

$y=-2(-5)=10$

At x=-4,

$y=-2(-4)=8$

At x=-3,

$y=-2(-3)=6$

At x=-2,

$y=-2(-2)=4$

At x=-1,

$y=-2(-1)=2$

Therefore the correct option is 3.

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Use the following information for problems 1 – 3. Suppose you sign a contract for an annual salary of $50,000 with a guaranteed

erik [133]

Initial salary = $50,000 .

Rate of raise = 5% each year.

Therefore, each next year salary would be 105% that is 1.05 times.

5% of 50,000 = 0.05 × 50000 = 2500.

Therefore raise is $2500 each year.

According to geometric sequence first term 50000 and common ratio 1.05.

Applying geometric sequence formula

$a_n = ar^{n-1}$

1) $a_n = 50000(1.05)^{n-1}$

2) In order to find salary in 5 years we need to plug n=5, we get

$a_5 = 50000(1.05)^{5-1}= 50000(1.05)^4$

= 50000(1.21550625)

3) In order to find the total salary in 10 years we need to apply sum of 10 terms formula of a geometric sequence.

$S_n = \frac{a(1-r^n}{1-r}$

Plugging n=10, a = 50000 and r= 1.05.

$S_10 = \frac{50000(1-(1.05)^{10}}{1-1.05}$

$S_10 = \frac{50000(0.050)^{10}}{0.05}$

= 628894.62678.

<h3>Therefore , you will have earned $ 628894.62678 in total salary by the end of your 10th year.</h3>

7 0

3 years ago

What is the solution to this system of linear equations?

alexandr1967 [171]

Answer:

A. (-1 , 3)

Step-by-step explanation:

2x + y = 1

plus 3x - y = -6

------------------------------

5x = -5

x = -1

y = 1 - (2*-1) = 3

3 0

3 years ago

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Beatrice buys a dishwasher for her new house. The price of the dishwasher is D dollars, and she pays an additional 2% tax.

Lubov Fominskaja [6]

The answers are as follows:
Box 1) D
Box 2) .02D
Box 3) D + .02D

7 0

3 years ago

Read 2 more answers

Find the perimeter of the following triangle.

pashok25 [27]

Hello!

To find the perimeter of the triangle, we need to find the length of all the sides using the <u>distance formula</u>.

The distance formula is: $d =\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$ .

First, we can find the distance between the points (-3, -1) and (2, -1). The point (-3, -1) can be assigned to $(x_{1},y_{1})$ , and (2, -1) is assigned to $(x_{2},y_{2})$ . Then, substitute the values into the formula.

$d =\sqrt{(2 - (-3))^{2}+ (-1 - (-1))^{2}}$

$d =\sqrt{5^{2}+0^{2}}$

$d =\sqrt{25} = 5$

The distance between the points (-3, -1) and (2, -1) is 5 units.

Secondly, we need to find the distance between the points (2, 3) and (2, -1). Assign those points to $(x_{1},y_{1})$ and $(x_{2},y_{2})$ , then substitute it into the formula.

$d =\sqrt{(2 - 2)^{2}+ (-1 - 3)^{2}}$

$d =\sqrt{0^{2}+(-4)^{2}}$

$d =\sqrt{16} = 4$

The distance between the two points (2, 3) and (2, -1) is 4 units.

Finally, we use the distance formula again to find the distance between the points (-3, -1) and (2, 3). Remember the assign the ordered pairs to $(x_{1},y_{1})$ and $(x_{2},y_{2})$ and substitute!

$d =\sqrt{(2 -(-3))^{2}+ (3 - (-1))^{2}}$