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3 years ago

If the function f(x) = -1/2x - 7 were graphed, which of the following would be true?

Mathematics

1 answer:

Fittoniya [83]3 years ago

5 0

ANSWER

D. As the x-values increase, the y-values would decrease

EXPLANATION

The given function is
$y = - \frac{1}{2} x - 7$

The slope of this function is
$m = - \frac{1}{2}$

Since the slope is negative, there is a negative or an inverse relationship between x and y.

As the values of x increases, the values of y decreases.

Also, as the values of x decreases, the values of y increases.

The first option is not true because as x is becoming bigger and bigger negatively, y will become positive.

For instance, when
$x = - 40$
$y = - \frac{1}{2} ( - 40) - 7$

This implies that,

$y = 20 - 7 = 13$

Options B is obviously not true because the function has a negative relationship between x and y.

Option C is also false because, x can be positive since it is the independent variable.

See graph

Therefore, the correct answer is option D.

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Marta_Voda [28]

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3 years ago

Use the pythagoren theorem to solve x

defon

Well the equation is (A^2)+(B^2)=(C^2)

A= x
B= 2x
C will always be the longest side because it is the Hypotenuse = 25

So if you plug in those numbers into the equation...

(x^2) + (2x^2) = (25^2)

x^2 + 4x^2 = 625

Combine like terms

5x^2 = 625

Divide by five to both sides

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Then Square root,

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3 0

4 years ago

"Data from the World Health Organization in 2013 were used to predict the life expectancy of men in a country from the life expe

marshall27 [118]

Answer:

The predicted life expectancy of men in a country in which the life expectancy of women is 70 years is 65.33 years.

Step-by-step explanation:

The least square regression line is used to predict the value of the dependent variable from an independent variable.

The general form of a least square regression line is:

$\hat y=\alpha +\beta x$

Here,

y = dependent variable

x = independent variable

α = intercept

β = slope

The regression line to predict the life expectancy of men in a country from the life expectancy of women in that country is:

$\hat y=3.73 +0.88 x$

Compute the life expectancy of men in a country in which the life expectancy of women is 70 years as follows:

$\hat y=3.73 +0.88 x$

$=3.73 +(0.88\times 70)\\=3.73+61.6\\=65.33$

Thus, the predicted life expectancy of men in a country in which the life expectancy of women is 70 years is 65.33 years.

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4 years ago

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Bess [88]

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$z(t)=x(t)^2+4y(t)^2+1$

$z(t)=\cos^2t+4\sin^2t+1$

$z(t)=3\sin^2t+2$

Then $z(t)$ has critical points where

$\dfrac{\mathrm dz}{\mathrm dt}=6\sin t\cos t=3\sin2t=0$

$\implies\sin2t=0\implies2t=n\pi\implies t=\dfrac{n\pi}2$

where $n$ is any integer.

$z(t)$ is increasing wherever $\sin2t>0$ , which happens for

$\dfrac{2n\pi}2$

$\boxed{n\pi$

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3 years ago

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loris [4]

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3 0

3 years ago