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3 years ago

The sum of a number and 20 is no more than the sum of the square of the number and 9.

2 answers:

8 0

The answer is A because the phrase " no more than" stands for the symbol "less than or equal to", and "the sum of the square if the number and 9" stands for the number squared and then added to nine (x + 9)2.

Olegator [25]3 years ago

8 0

Answer:

Option A is correct

$x+20 \leq x^2+9$

Step-by-step explanation:

Let the number be x.

As per the statement:

The sum of a number and 20 is no more than the sum of the square of the number and 9.

"sum of a number and 20" translated to x + 20

"no more than" means $\leq$

"sum of the square of the number and 9" translated to $x^2+9$

then;

$x+20 \leq x^2+9$

Therefore, the following inequalities can be used to determine this unknown number is, $x+20 \leq x^2+9$

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2 years ago

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The curves y = √x and y=(2-x) and the Cartesian axes form two distinct regions in the first quadrant. Find the volumes of rotati

makkiz [27]

Answer:

Step-by-step explanation:

If you graph there would be two different regions. The first one would be

$y = \sqrt{x} \,\,\,\,, 0\leq x \leq 1 \\$

And the second one would be

$y = 2-x \,\,\,\,\,, 1 \leq x \leq 2$ .

If you rotate the first region around the "y" axis you get that

$A_1 = 2\pi \int\limits_{0}^{1} x\sqrt{x} dx = \frac{4\pi}{5} = 2.51$

And if you rotate the second region around the "y" axis you get that

$A_2 = 2\pi \int\limits_{1}^{2} x(2-x) dx = \frac{4\pi}{3} = 4.188$

And the sum would be 2.51+4.188 = 6.698

If you revolve just the outer curve you get

If you rotate the first region around the x axis you get that

$A_1 =\pi \int\limits_{0}^{1} ( \sqrt{x})^2 dx = \frac{\pi}{2} = 1.5708$

And if you rotate the second region around the x axis you get that

$A_2 = \pi \int\limits_{1}^{2} (2-x)^2 dx = \frac{\pi}{3} = 1.0472$

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3 years ago

Write the equation of the line parallel to the given line and through the given

zloy xaker [14]

Answer:

y-2x -8

Step-by-step explanation:

your jus gonna right it back because it's parallel which means it's the same thing.

6 0

3 years ago

Find the exact value of csc ø, if cos ø= 1/9; 180° less ø less than 270°

Iteru [2.4K]

Answer:

The answer to your question is: the first option - 9/ $\sqrt{80}$

Step-by-step explanation:

Process

cosФ = adjacent side / hypotenuse

-1/9 = adjacent side / hypotenuse

adjacent side = -1 hypotenuse = 9

c² = a² + b²

b² = c² - a²

b² = 81 - 1

b = $\sqrt{80} \\$ b = opposite side

But b is negative because we are in the third quadrant.

b = - $\sqrt{80}$

Finally csc Ф = hypotenuse / opposite side

csc Ф = - 9 / $\sqrt{80}$

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2 years ago