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3 years ago

5

The Olympic-size pool at the recreational center is a right rectangular prism 50m long and 25m wide. The pool contains 3000m3 of

water. How deep is the water in the pool?

1 answer:

Oksana_A [137]3 years ago

3 0

Step-by-step explanation:

50 * 25 = 1250 square meters

3000 / 1250 = 2.4 meters deep

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What are the exact solutions of x2 − 5x − 7 = 0, where x equals negative b plus or minus the square root of b squared minus 4 ti

Marat540 [252]

Answer:

$x = \frac{5 + \sqrt{53}}{2}$ or $x = \frac{5 - \sqrt{53}}{2}$

Step-by-step explanation:

Given

$x^2 - 5x - 7 = 0$

Required

Solve for x using:

$x = \frac{-b \± \sqrt{b^2 - 4ac}}{2a}$

First, we need to identify a, b and c

The general form of a quadratic equation is:

$ax^2 + bx + c = 0$

So, by comparison with $x^2 - 5x - 7 = 0$

$a = 1$ $b = -5$ $c = -7$

Substitute these values of a, b and c in

$x = \frac{-b \± \sqrt{b^2 - 4ac}}{2a}$

$x = \frac{-(-5) \± \sqrt{(-5)^2 - 4 * 1 * -7}}{2 * 1}$

$x = \frac{5 \± \sqrt{25 +28}}{2}$

$x = \frac{5 \± \sqrt{53}}{2}$

Split the expression to two

$x = \frac{5 + \sqrt{53}}{2}$ or $x = \frac{5 - \sqrt{53}}{2}$

To solve further in decimal form, we have

$x = \frac{5 + 7.28}{2}$ or $x = \frac{5 - 7.28}{2}$

$x = \frac{12.28}{2}$ or $x = \frac{-2.28}{2}$

$x = 6.14$ or $x = -1.14$

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3 years ago

A football player is running the length of a 100 yard long football field. For the first part of the field, he runs at a rate of

notka56 [123]

Answer:

$\frac{2}{5}$ th part of the field is covered in the second sprint.

Step-by-step explanation:

A football player is running the length of a 100 yard long football field.

Let player sprints x yards with the speed = 2 yards per second.

So time taken to cover x yards player will take time = $\frac{x}{2}$ seconds

Now rest distance (100 - x) yards when covered with the speed of 4 yards per second, so time taken to cover this distance = $\frac{Distance}{Speed}$

= $\frac{100-x}{4}$ seconds

Now total time taken by the player can be represented by the equation

$\frac{x}{2}+\frac{100-x}{4}=40$

Now we can solve this equation for the value of x.

$\frac{2x+100-x}{4}=40$

x + 100 = 40×4

x + 100 = 160

x = 160 - 100 = 60 yards

And length of the second part will be = 100 - 60 = 40 yards

Now the fraction of the field covered by the player in second sprint will be

= $\frac{40}{100}$

= $\frac{2}{5}$ or 40%

Therefore, $\frac{2}{5}$ th part of the field was covered in second sprint.

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3 years ago

Alex is standing 60 feet from the base of a flagpole. He measures the angle of elevation to the top of the pole as 35º. Vera is

ivanzaharov [21]

Answer:

49.4 degrees

Step-by-step explanation:

In Triangle AXY,

$Tan 35^0=\frac{|XY|}{60} \\|XY|=60*Tan 35^0=42.01\:feet\\$Therefore, Height of the pole=42.01 \:feet$

We want to determine the angle of elevation from the point Vera is standing to the top of the flagpole, which is the angle at V in the diagram.

In Triangle XVY

|VY|=36 feet

$Tan \theta=\frac{|XY|}{|VY|} \\Tan \theta=\frac{42.01}{36}\\ \theta=arctan(\frac{42.01}{36})\\ \theta=49.4^0$

Therefore, the angle of elevation from the point Vera is standing to the top of the flagpole is 49.4 degree to the nearest tenth of a degree.

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4 years ago

The pH of solution A is 2.4, while the pH of solution B is 9.4.

pishuonlain [190]

Answer:

The answer to your question is below

Step-by-step explanation:

pH definition

pH = - log [H⁺]

a) For pH = 2.4, solution A

2.4 = -log[H⁺]

[H⁺] = antilog⁻².⁴

[H⁺] = 0.00398

For pH = 9.4, solution B

[H⁺] = antilog⁻⁹.⁴

[H⁺] = 3.98 x 10⁻¹⁰

b) Divide hydrogen-ion concentration of solution A by hydrogen-ion concentration of solution B.

0.00398 / 3.98 x 10⁻¹⁰

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c) By 7, because 7 is the number of zeros

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3 years ago

Simplify the expression <br> 15+(x+9)+3

Allushta [10]

27 + x is the simplified expression.

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4 years ago

Read 2 more answers