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3 years ago

PLEASE I NEED HELP I DONT UNDERSTAND HOW TO DO ILL GIVW MORE IF RIGHT

Mathematics

1 answer:

ASHA 777 [7]3 years ago

8 0

Answer: Choice D

$\frac{9\sqrt{2}}{2}$

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Explanation:

We have a 45-45-90 triangle. If x is the leg length, then y = x*sqrt(2) is the hypotenuse.

Solving for y gets us $x= \frac{y}{\sqrt{2}} = \frac{y\sqrt{2}}{2}$

In this case, y = 9 is the hypotenuse which then leads to choice D.

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Another way to find the answer is to use the pythagorean theorem

a = x and b = x are the two congruent legs

c = 9 is the hypotenuse

Solving a^2+b^2 = c^2, aka x^2+x^2 = 9^2, will lead to $x = \frac{9\sqrt{2}}{2}$

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Sebastian bought x gallons of gas at a price of $2.91 per gallon at his local gas station. When he paid for the gas, Sebastian a

rjkz [21]

Answer:

Sebastian spent $40.40 at the gas station.

Step-by-step explanation:

First let's find how much the gas cost.

So it's $2.91 a gallon, and Sebastian fills 10 gallons of gas, so we multiply.

10 * 2.91 = $29.10

Then we add on the $11.40 from the granola bars and the box of tissues.

$29.10 + $11.40 = $40.50

So the final price should be $40.40. Sebastian spent $40.40 at the gas station.

4 0

3 years ago

Find the slope, distance and midpoint between

Dovator [93]

Answer:

Slope- 4

Distance- 12.4

Midpoint- (6,8)

Step-by-step explanation:

Slope- $\frac{y2-y1}{x2-x1}$

$\frac{2-14}{4-7} =\frac{-12}{-3}=4$

Distance- $d = \sqrt{(x_2 - x_1)^2 + (y_2-y_1)^2}$

$d = \sqrt{(4 - 7)^2 + (2-14)^2}$

$d = \sqrt{-3^2 + -12^2}$ $d = \sqrt{144+9}=\sqrt{153}$

$\sqrt{153} = 12.4$

Midpoint- $\frac{x1+x2}{2} ,\frac{y1+y2}{2}$

$\frac{7+4}{2} =\frac{12}{2} = 6=x$

$\frac{14+2}{2} = \frac{16}{2} = 8 = y$

(6,8)

6 0

3 years ago

Please help will receive brainliest

Luden [163]

Answer:

5 m

Step-by-step explanation:

The perimeter is the sum of the lengths of the four sides. Opposite sides have the same length, so it is twice the sum of the lengths of adjacent sides.

The sum of adjacent sides is (32 m)/2 = 16 m. If one of them is 11 m long, the other is ...

16 m - 11 m = 5 m

The "missing" side is 5 m long.

6 0

3 years ago

Which of the following represents the additive inverse of 41?

inna [77]

Answer:

<em>Correct answer is C. -41</em>

Step-by-step explanation:

Theory:

Number + Additive inverse = 0

Therefore, Addictive inverse of 41 is

Additive inverse + 41 = 0

Additive inverse = -41

Correct answer is C. -41

7 0

4 years ago

Read 2 more answers

I have calculus problems that I need help with.

aleksklad [387]

a. Note that $f(x)=x^ne^{-2x}$ is continuous for all $x$ . If $f(x)$ attains a maximum at $x=3$ , then $f'(3) = 0$ . Compute the derivative of $f$ .

$f'(x) = nx^{n-1} e^{-2x} - 2x^n e^{-2x}$

Evaluate this at $x=3$ and solve for $n$ .

$n\cdot3^{n-1} e^{-6} - 2\cdot3^n e^{-6} = 0$

$n\cdot3^{n-1} = 2\cdot3^n$

$\dfrac n2 = \dfrac{3^n}{3^{n-1}}$

$\dfrac n2 = 3 \implies \boxed{n=6}$

To ensure that a maximum is reached for this value of $n$ , we need to check the sign of the second derivative at this critical point.

$f(x) = x^6 e^{-2x} \\\\ \implies f'(x) = 6x^5 e^{-2x} - 2x^6 e^{-2x} \\\\ \implies f''(x) = 30x^4 e^{-2x} - 24x^5 e^{-2x} + 4x^6 e^{-2x} \\\\ \implies f''(3) = -\dfrac{486}{e^6} < 0$

The second derivative at $x=3$ is negative, which indicate the function is concave downward, which in turn means that $f(3)$ is indeed a (local) maximum.

b. When $n=4$ , we have derivatives

$f(x) = x^4 e^{-2x} \\\\ \implies f'(x) = 4x^3 e^{-2x} - 2x^4 e^{-2x} \\\\ \implies f''(x) = 12x^2 e^{-2x} - 16x^3e^{-2x} + 4x^4e^{-2x}$

Inflection points can occur where the second derivative vanishes.

$12x^2 e^{-2x} - 16x^3 e^{-2x} + 4x^4 e^{-2x} = 0$

$12x^2 - 16x^3 + 4x^4 = 0$

$4x^2 (3 - 4x + x^2) = 0$

$4x^2 (x - 3) (x - 1) = 0$

Then we have three possible inflection points when $x=0$ , $x=1$ , or $x=3$ .

To decide which are actually inflection points, check the sign of $f''$ in each of the intervals $(-\infty,0)$ , $(0, 1)$ , $(1, 3)$ , and $(3,\infty)$ . It's enough to check the sign of any test value of $x$ from each interval.