This trapezoid represents the base of a right prism that has a surface area of 1280 square feet. The sum of the lengths of the legs of the trapezoid is 52 feet. What is the height of the prism? Enter your answer in the box.

Answer:

2

Step-by-step explanation:

1 ⅚ + ⅙ = 1 6/6, also known as, 2

Answer:

Yes

Step-by-step explanation:

Because it has 4 sides and 4 x 2 = 8

Answer:

Step-by-step explanation:

top = 120sq m

middle = 17sq cm

bottom = 102 sq feet

Answer:

Parallelogram

Step-by-step explanation:

Instead of one pair of parallel sides like in a trapezoid, a parallelogram has two pairs of opposite sides (for example a rectangle)

Answer:

Just give me the questions and ill do it

Step-by-step explanation:

Answer:

(-3, 0) and (1, 0)

(0, 4)

Step-by-step explanation:

x-intercept is the point where y = 0.

y-intercept is the point where x = 0.

or points ...

f(x) = y = -4×|x + 1| + 8

let's start with the y-intercept (x = 0)

y = -4×1 + 8 = -4 + 8 = 4

the y-intercept point (only 1 point) is (0, 4).

for x = 0 the absolute value function contains 0+1. and that is always +1.

the x-intercept(s) :

0 = -4×|x + 1| + 8 (dividing by -4)

0 = |x + 1| - 2

|x + 1| = 2

because of the absolute value we have 2 possibilities :

+(x + 1) = 2

x + 1 = 2

x = 1

and

-(x + 1) = 2

-x - 1 = 2

-x = 3

x = -3

so the points of x-intercept are (-3, 0) and (1, 0)

Replace x with π/2 - x to get the equivalent integral

[tex]\displaystyle \int_{-\frac\pi2}^{\frac\pi2} \cos(\cot(x) - \tan(x)) \, dx[/tex]

but the integrand is even, so this is really just

[tex]\displaystyle 2 \int_0^{\frac\pi2} \cos(\cot(x) - \tan(x)) \, dx[/tex]

Substitute x = 1/2 arccot(u/2), which transforms the integral to

[tex]\displaystyle 2 \int_{-\infty}^\infty \frac{\cos(u)}{u^2+4} \, du[/tex]

There are lots of ways to compute this. What I did was to consider the complex contour integral

[tex]\displaystyle \int_\gamma \frac{e^{iz}}{z^2+4} \, dz[/tex]

where γ is a semicircle in the complex plane with its diameter joining (-R, 0) and (R, 0) on the real axis. A bound for the integral over the arc of the circle is estimated to be

[tex]\displaystyle \left|\int_{z=Re^{i0}}^{z=Re^{i\pi}} f(z) \, dz\right| \le \frac{\pi R}{|R^2-4|}[/tex]

which vanishes as R goes to ∞. Then by the residue theorem, we have in the limit

[tex]\displaystyle \int_{-\infty}^\infty \frac{\cos(x)}{x^2+4} \, dx = 2\pi i {} \mathrm{Res}\left(\frac{e^{iz}}{z^2+4},z=2i\right) = \frac\pi{2e^2}[/tex]

and it follows that

[tex]\displaystyle \int_0^\pi \cos(\cot(x)-\tan(x)) \, dx = \boxed{\frac\pi{e^2}}[/tex]

Finding the p-value of the test using the z-distribution, as we are working with a proportion, it is found that this was a significant difference for levels of significance of 0.02 and lower.

At the null hypothesis, we test if the proportion is of 50.3%, hence:

[tex]H_0: p = 0.503[/tex]

We have a two-tailed test, hence at the alternative hypothesis we test if the proportion is different, that is:

[tex]H_1: p \neq 0.503[/tex]

The test statistic is given by:

[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]

In which:

In this problem, the parameters are:

[tex]n = 300, \overline{p} = \frac{171}{300} = 0.57, p = 0.503[/tex]

Hence:

[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]

[tex]z = \frac{0.57 - 0.503}{\sqrt{\frac{0.503(0.497)}{300}}}[/tex]

[tex]z = 2.32[/tex]

Considering a two-tailed test, using a z-distribution calculator, the p-value is of 0.0203. Hence this was a significant difference for levels of significance of 0.02 and lower.

More can be learned about the z-distribution at https://brainly.com/question/26454209

it's interpreted as 28 - 21 = 7

Answer:

Area is 30cm^2 if thats what your asking

Step-by-step explanation:

Answer:

X = 5

Step-by-step explanation:

You need to use the Pythagorean theory to solve this question.

[tex] {13}^{2} = {x}^{2} + {(x + 7)}^{2} [/tex]

[tex]169 = {x}^{2} + ( {x}^{2} + 14x + 49)[/tex]

[tex]169 = 2 {x}^{2} + 14x + 49[/tex]

[tex]0 = 2 {x}^{2} + 14x + 49 - 169[/tex]

[tex]0 = 2 {x}^{2} + 14x - 120[/tex]

Now simply the equation by dividing everything by 2.

[tex]0 = {x}^{2} + 7x - 60[/tex]

[tex]0 = (x - 5)(x + 12)[/tex]

Now, you can find the possible solutions by setting each bracket to 0.

[tex]0 = x - 5[/tex]

[tex]5 = x[/tex]

OR

[tex]0 = x + 12[/tex]

[tex] - 12 = x[/tex]

However, a measurement on a triangle cannot be negative. Therefore, we can ignore -12 and say that the answer is x = 5.

Answer:

The answer is g(x) = 10x + 15

Step-by-step explanation:

Here, If we assume the value of x is 1 we get,

g(x) = 10x + 15

g(1) = 10(1) + 15

g(1) = 10 + 15

g(1) = 35

Here, We get the answer 35.

Now,

f(x) = 2•3ˣ

f(1) = 2•3¹

f(1) = 2•3

f(1) = 6

Here, We get the answer 6.

Now,

h(1) = 5x² + x + 10

h(1) = 5(1)² + 1 + 10

h(1) = + 5 + 1 + 10

h(1) = + 16

Thus, The answer is g(x) = 10x + 15.

-TheUnknownScientist 72

Answer:

6.46 seconds

Step-by-step explanation:

[tex] - 16 {t}^{2} + 65t + 248 = 0[/tex]

[tex]t = 6.46[/tex]

Answer:

Step-by-step explanation:

The amount of interest earned in one year is the product of the interest rate and the amount invested at that rate. The total interest earned is the sum of the amounts of interest earned on each investment.

Let x represent the lower interest rate. Then the higher rate is x+0.03 and the total interest earned is ...

  1100x +1300(x+0.03) = 255

  2400x +39 = 255 . . . simplify

  2400x = 216 . . . . . . subtract 39

  x = 216/2400 = 0.09 = 9% . . . . divide by the coefficient of x

Rosa invested $1100 at 9%, and $1300 at 12%.

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{5\% of 78}}{\left( \cfrac{5}{100} \right)78}\implies 3.9[/tex]

The expression for the simplified total gas used is 1.43x.

let the gas used on the way to camp "x"

Then the gas used on the way back can be calculated as follows:

360 / 420 × 0.5 × x

To calculate the total fuel used, We need to add this to the 'x' used on the way.

Therefore,

total gas used = x + 360 / 420 × 0.5 × x = x + 0.43x = 1.43x

learn more on expression here: https://brainly.com/question/1462980

Answer:

so first you want to mulitply the 5,5,5.8, and 8 together to get 1160 then take away 464 from 1160 to get 696. then you add all of the numbers up to get 719.8 ten subtract .75 from that and you get 719.05. then take the cubic feet and get 200 then taky away 200 from 719.05 and get 519.05 then do that again

Step-by-step explanation:

219.05

Answer:

vertex is a point where two sides meet

Answer:

Step-by-step explanation:

Prove by multiplication

Similarly

So the expression is 5873/8

Now

We can prove the given statement to multiplication

Multiply with 8

And

Yes

We see 5873 lies between 5600 and 6400 hence the quotient is greater than 700 but less than 800

Step-by-step explanation:

I think the answer is x=70

Answer:

Step-by-step explanation:

The angle containing y and 63 are vertically opposite. They are equal.

y + 23 = 63                   Subtract 23 from both sides

y +23-23 = 63 - 23

Answer y = 40

Step-by-step explanation:

Answer: 78 /5 = 15.6 = 16 taxis. Step-by-step explanation: I HOPE THIS WILL HELP YOU AND MARK IT AS BRAINLIEST ANSWER PLEASE.

Answer:

  7/3

Step-by-step explanation:

To write the ratio with no units. we need to have both parts of the ratio in the same units. That way the units cancel.

__

  6 weeks : 18 days = (6×7) days : (6×3) days = 7 : 3

The ratio as a fraction is ...

  (6 weeks)/(18 days) = 7/3

Step-by-step explanation:

this is the answer for you

The functions f(4x-3)≥f(2-x^2) and f(5-x^2)≥f(3x-5) are quadratic functions

The values of the inequalities are -5 ≤ x ≤ 1 and -5 ≤ x ≤ 2

Inequality 1: f(4x - 3) ≥ f(2 - x^2), Df = (-8 , 4)

The function increases at (-8,4).

So, we have:

4x - 3 ≥ 2 - x^2

Rewrite as:

x^2 + 4x - 2 - 3 ≥ 0

Evaluate the like terms

x^2 + 4x - 5 ≥ 0

Expand

x^2 + 5x - x - 5 ≥ 0

Factorize the expression

x(x + 5) - 1(x + 5) ≥ 0

Factor out x + 5

(x - 1)(x + 5) ≥ 0

Solve for x

x ≥ 1 or x ≥ -5

Rewrite as:

-5 ≤ x ≤ 1

Inequality 2: f(5 - x^2) ≥ f(3x - 5), Df=(-∞,4)

The function decreases at (-∞,4).

So, we have:

5 - x^2 ≥ 3x - 5

Rewrite as:

x^2 + 3x - 5 - 5 ≤ 0

Evaluate the like terms

x^2 + 3x - 10 ≤ 0

Expand

x^2 + 5x - 2x - 10 ≤ 0

Factorize the expression

x(x + 5) - 2(x + 5) ≤ 0

Factor out x + 5

(x - 2)(x + 5) ≤ 0

Solve for x

x ≤ 2 or x ≤ -5

Rewrite as:

-5 ≤ x ≤ 2

Hence, the values of the inequalities are -5 ≤ x ≤ 1 and -5 ≤ x ≤ 2

Read more about inequalities at:

https://brainly.com/question/11234618

Answer:

C) 11.1

Step-by-step explanation:

7.4 -(-3.7)

- and - make +

7.4 + 3.7 = 11.1

Answer:

(- 3, 1 )

Step-by-step explanation:

2x - 2y = - 8 → (1)

x + 2y = - 1 → (2)

adding the 2 equations term by term will eliminate y

3x + 0 = - 9

3x = - 9 ( divide both sides by 3 )

x = - 3

substitute x = - 3 into either of the 2 equations and solve for y

substituting into (2)

- 3 + 2y = - 1 ( add 3 to both sides )

2y = 2 ( divide both sides by 2 )

y = 1

solution is (- 3, 1 )

Answer:

(–3, 1)

Step-by-step explanation:

Step 1: Solve for x

2x – 2y = –8 -----------(1)

x + 2y = –1. -------------(2)

⇒2x + x| -2y + 2y |= -8 -1

⇒3x = -9

⇒3x/3 = -9/3

⇒x = -3

Step 2; Solve for y

x + 2y = –1

(-3) + 2y = -1

-3 + 2y + 3 = -1 + 3

2y = 2

2y/2 = 2/2

y = 1

So, ( x,y) ⇒(-3,1)

19.6 gallons

Explanation: