Solve the inequality. Draw a number line representing the solution- -5x + 12 >7

Based in the diagram which statement is true

Charra [1.4K]

Answer:

14. congruent means "THE SAME" so it will be "A" because there all the same letter.

15. D

7 0

2 years ago

Fundamental theorem of calculus <img src="https://tex.z-dn.net/?f=g%28s%29%3D%5Cint%5Climits%5Es_6%20%7B%28t-t%5E4%29%5E6%7D

mr_godi [17]

Answer:

$\displaystyle g'(s) = (s-s^4)^6$

Step-by-step explanation:

The Fundamental Theorem of Calculus states that:
$\displaystyle \frac{d}{dx}\left[ \int_a^x f(t)\, dt \right] = f(x)$

Where a is some constant.

We can let:
$\displaystyle g(t) = (t-t^4)^6$

By substitution:

$\displaystyle g(s) = \int_6^s g(t)\, dt$

Taking the derivative of both sides results in:
$\displaystyle g'(s) = \frac{d}{ds}\left[ \int_6^s g(t)\, dt\right]$

Hence, by the Fundamental Theorem:

$\displaystyle \begin{aligned} g'(s) & = g(s) \\ \\ & = (s-s^4)^6\end{aligned}$

3 0

1 year ago

Please anyone answer me

ollegr [7]

Let's divide the shaded region into two areas:

area 1: x = 0 ---> x = 2

ares 2: x = 2 ---> x = 4

In area 1, we need to find the area under g(x) = x and in area 2, we need to find the area between g(x) = x and f(x) = (x - 2)^2. Now let's set up the integrals needed to find the areas.

Area 1:

$A\frac{}{1} = ∫g(x)dx = ∫xdx = \frac{1}{2} {x}^{2} | \frac{2}{0} = 2$

Area 2:

$A\frac{}{2} = ∫(g(x) - f(x))dx$

$= ∫(x - {(x - 2)}^{2} )dx$

$= ∫( - {x}^{2} + 5x - 4)dx$

$= ( - \frac{1}{3}{x}^{3} + \frac{5}{2} {x}^{2} - 4x) | \frac{4}{2}$

$= 2.67 - ( - 0.67) = 3.34$

Therefore, the area of the shaded portion of the graph is

A = A1 + A2 = 5.34

3 0

3 years ago

The length of a rectangle is (x+5) and the width is (x+2). The area of the rectangle is 70 square feet. What is the length of th

vaieri [72.5K]

Answer:

The length of the rectangle is 30 feet.

Step-by-step explanation:

Because the equation for area is length times width, you would have to set the two equations to seventy and multiply them.

(x+5) (x+2) = 70

2x + 10 = 70

Then, you would have to subtract ten from both sides, cancelling it from the left side.

 2x = 60

Then do the opposite and divide sixty by two, therefore getting a length of thirty feet.

7 0

3 years ago

900 wind turbines produce 800,500 kilowatts of energy per hour if a total of 32,725,550 kilowatts of energy is produced how much

Brrunno [24]

Answer:

$41\ hours$

Step-by-step explanation:

we know that

Using proportion

$\frac{1}{800,500}\frac{hour}{kw}=\frac{x}{32,725,550}\frac{hours}{kw}\\ \\x=32,725,550/800,500\\ \\x=40.88\ hours$

Round to the nearest whole number

$40.88\ hours=41\ hours$

7 0

3 years ago