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2 years ago

Mario travels 180 miles in 2.5 hours. How many miles will he travel in one hour, if the rate is not changed? Explain.

2 answers:

Colt1911 [192]2 years ago

8 0

Your answer is 180/2.5. The rate goes 180 miles in 2.5 hours, so to find the rate, divide 180 by 2.5. You will get 72. The rate is 72 mph, so your answer is 72.

Furkat [3]2 years ago

7 0

I think it’s 40 but I’m not really sure or it’s around 80 sorry

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2 years ago

The sum of two numbers is 9.9, and the sum of the squares of the numbers is 53.21. What are the numbers?

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Answer:

There are two possibilities:

$x_{1} = 3.5$ and $y_{1} = 6.4$

$x_{2} = 6.4$ and $y_{2} = 3.5$

Step-by-step explanation:

Mathematically speaking, the statement is equivalent to this 2-variable non-linear system:

$x + y = 9.9$

$x^{2} + y^{2} = 53.21$

First, $x$ is cleared in the first equation:

$x = 9.9 - y$

Now, the variable is substituted in the second one:

$(9.9-y)^{2} + y^{2} = 53.21$

And some algebra is done in order to simplify the expression:

$98.01-19.8\cdot y +2\cdot y^{2} = 53.21$

$2\cdot y^{2} -19.8\cdot y +44.8 = 0$

Roots are found by means of the General Equation for Second-Order Polynomials:

$y_{1} \approx \frac{32}{5}$ and $y_{2} \approx \frac{7}{2}$

There are two different values for $x$ :

$y = y_{1}$

$x_{1} = 9.9-6.4$

$x_{1} = 3.5$

$y = y_{2}$

$x_{2} = 9.9 - 3.5$

$x_{2} = 6.4$

There are two possibilities:

$x_{1} = 3.5$ and $y_{1} = 6.4$

$x_{2} = 6.4$ and $y_{2} = 3.5$

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ahrayia [7]

-4(x + 1) + 5 = 17

Distribute -4 inside the parentheses.

(-4x - 4) + 5 = 17

Combine like terms (-4 + 5).

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Subtract 1 from both sides.

-4x = 16

Divide both sides by -4.

x = -4

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