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3 years ago

What positive value of x makes the following equation true: 125 = x^3? Explain

Mathematics

1 answer:

alina1380 [7]3 years ago

4 0

Answer: The correct answer is x=5

Step-by-step explanation:

x=2−5−−75=2−5−5i3=−2.5000−4.3301i

x=2−5+−75=2−5+5i3=−2.5000+4.3301i

x=5

Hoped I helped

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Myra won the hurdles event for the seventh graders. She completed the race in 22.8 seconds and knocked down 1 hurdle. Byron won

gregori [183]

Answer:

Myra: 24.8s (winner) Byron: 26.3s

Step-by-step explanation:

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2 years ago

(a) Derive an equation of the line passing through the points A(0, 545) and B(4, 726). (Let t be the independent variable and y

a_sh-v [17]

Answer:

The equation of the line is $y=45.25t+545$

Step-by-step explanation:

The general for of a line is:

$y=mt+n$ (1)

where:

$m$ is the slope of the line and $m$ is the intercept with the axis of the dependent variable, $y$ in this case.

In order to obtain the value of the slope ( $m$ ) we can use the corresponding slope formula:

$m=\frac{y_{2}-y_1 }{t_2-t_1}$ (2)

where $t_1, t_2, y_1$ and $y_2$ are the corresponding coordinates of the given points. In this case:

$t_1=0\\t_2=4\\y_1=545\\y_2=726\\$

Substituting these values in equation (2) we obtain:

$m=\frac{726-545}{4-0}=\frac{181}{4}=45.25\\m=45.25$

Hence, the line equation is now:

$y=45.25t+n$ (3)

Now to obtain the value of $n$ you can follow two options:

You can substitute one of your points, $A$ or $B$ , in equation (3). In this way, you will obtain an equation where the variable is $n$

Note that for this question, it is easier to select point A because of having the independent variable equals to zero $t=0$ . Hence, substituting point A in equation (3):

$45.25*0+n=545\\n=545$

Therefore, the line equation is: $y=45.25t+545$

The second option to find $n$ is to think of the meaning of the intercept. The intercept of a line is defined as the point in which the line crosses the axis of the dependent variable, which also means that the value of the independent variable for this point is zero. From this, we could have automatically said that $n$ is equal to $545$ .

See the attachment for a plot of the line.

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3 years ago

The ratio of the length to the width of a rectangle is 5:4. The length of the rectangle is 60 inches. What is the width?

Firlakuza [10]

$\huge\boxed{\text{48 inches}}$

We know that $\frac{\text{length}}{\text{width}} = \frac{60}{\text{width}} = \frac{5}{4}$ .

Solve using cross multiplication of the last two fractions. I will use $w$ to represent the width of the rectangle. $60*4=w*5$

Multiply. $240=5w$

Divide both sides of the equation by $5$ . $\boxed{48}=w$

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