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3 years ago

Which table shows input and output values that represent a linear function?

Mathematics

1 answer:

shepuryov [24]3 years ago

4 0

Answer:

Table A

Step-by-step explanation:

In order for it to be a linear relationship, the change in the x values and y values (f(x)) needs to be consistent.

In every table, the x values change the same, so we can focus on the y values.

Notice in table A, the f(x) values go down consistently by 10 for every change in x.

All of the other tables are not consistent.

Therefore, table A is the only linear function.

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PLEASE HELP ME

sineoko [7]

Answer:

C. Exponential

Step-by-step explanation:

If the function is linear, the differences will be equal.

d₁ = y₁ − y₀ = 4.2 − 0.6 = 3.6

d₂ = y₂ − y₁ = 29.4 − 4.2 = 25.2

d₃ = y₃ − y₂ = 205.8 − 29.4 = 176.4

d₄ = y₄ − y₃ = 1440.6 − 205.8 = 1234.8

The differences are not equal, so this is not linear.

If the function is quadratic, the differences of the differences will be equal.

d₂ − d₁ = 25.2 − 3.6 = 21.6

d₃ − d₂ = 176.4 − 25.2 = 151.2

d₄ − d₃ = 1234.8 − 176.4 = 1058.4

The differences of the differences are not equal, so this is not quadratic.

If the function is exponential, the ratios will be equal.

r₁ = y₁ / y₀ = 4.2 / 0.6 = 7

r₂ = y₂ / y₁ = 29.4 / 4.2 = 7

r₃ = y₃ / y₂ = 205.8 / 29.4 = 7

r₄ = y₄ / y₃ = 1440.6 / 205.8 = 7

The ratios are equal, so the function is exponential.

5 0

3 years ago

The length of the rectangle is x cm. The length of a diagonal of the rectangle is 8 crn. The perimeter of the rectangle is 20 cm

klemol [59]

Answer:

$x^2-10x+18=0$

a = -10 and b = 18.

Step-by-step explanation:

Let w represent the width of the rectangle.

We are given that the perimeter of the rectangle is 20 cm, this means that:

$20=2(x + w)$

Let's put w in terms of x. Divide both sides by two:

$10=x+w$

And solve for w:

$w=10-x$

So, the rectangle measures x by (10 - x) cm.

According to the Pythagorean Theorem:

$a^2+b^2=c^2$

a and b are the legs and c is the hypotenuse.

Substitute x for a, w for b, and 8 for c:

$x^2+w^2=8^2$

Simplify and substitute:

$x^2+(10-x)^2=64$

Square:

$x^2+(100-20x+x^2)=64$

Isolate the equation. So:

$2x^2-20x+36=0$

Since the leading coefficient is one, divide both sides by two:

$x^2-10x+18=0$

Therefore, a = -10 and b = 18.

6 0

2 years ago

Express in partial fraction

aksik [14]

Step-by-step explanation:

There is one possible way:

(4x² - 47x + 141)/(x² + 13x + 40) =
(4x² + 4*13x + 4*40 - 47x - 52x - 160 + 141)/(x² + 13x + 40) =
4 - (99x + 19)/(x² + 13x + 40)

No further simplification

8 0

2 years ago

Read 2 more answers

In AGHI, the measure of ZI=90°, the measure of ZG=5°, and IG = 57 feet. Find the

xxTIMURxx [149]

Answer:

The answer is 57.2

This is correct

3 0

2 years ago

What is the slope of this line

kifflom [539]

Answer:

3/4

Step-by-step explanation:

We can find the slope from the two points given

m = (y2-y1)/(x2-x1)

= (1- -2)/(2 - -2)

= (1+2)/(2+2)

= 3/4

8 0

3 years ago