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3 years ago

What is the algebraic solution to the function 2x+3=83

Mathematics

2 answers:

spin [16.1K]3 years ago

6 0

Answer:

x = 40

Step-by-step explanation:

Solve for x

2x + 3 = 83 Subtract 3 from both sides

2x = 80 Divide 2 on both sides

x = 40

The algebraic solution to the function is x = 40

nirvana33 [79]3 years ago

3 0

3-83= 80
80 divided by 2 is 40
the answer is 40

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Translate this phrase into an algebraic expression.

Alekssandra [29.7K]

4/x+10

(4 divided by x + 10)

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3 years ago

What is the volume of the cylinder?

Anna007 [38]

Answer:

B. 2010.62 ft³

Step-by-step explanation:

The formula for the volume of a cylinder is ...

V = πr²h . . . . . where r is the radius and h is the height

Filling in the numbers and doing the arithmetic, we get ...

V = π(8 ft)²(10 ft) = 640π ft³ ≈ 2010.6193 ft³ ≈ 2010.62 ft³

The volume of the cylinder is about 2010.62 ft³.

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3 years ago

Find the area of following rhombuses. Round your answers to the nearest tenth if necessary.

polet [3.4K]

Answer:

$Area =55.4ft^2$

Step-by-step explanation:

Given

The attached rhombus

Required

The area

First, calculate the length of half the vertical diagonal (x).

Length x is represented as the adjacent to 60 degrees

So, we have:

$\tan(60) = \frac{4\sqrt 3}{x}$

Solve for x

$x = \frac{4\sqrt 3}{\tan(60)}$

$\tan(60) = \sqrt 3$

So:

$x = \frac{4\sqrt 3}{\sqrt 3}$

$x = 4$

At this point, we have established that the rhombus is made up 4 triangles of the following dimensions

$Base = 4\sqrt 3$

$Height = 4$

So, the area of the rhombus is 4 times the area of 1 triangle

$Area = 4 * \frac{1}{2} * Base * Height$

$Area = 4 * \frac{1}{2} * 4\sqrt 3 * 4$

$Area =2 * 4\sqrt 3 * 4$

$Area =55.4ft^2$

7 0

3 years ago

4TH TIME ASKING THIS!!! Please help me! Someone pleaseeee. I need the correct answers. I don’t want to fail

Alexeev081 [22]

Answer:

The functions are inverses; f(g(x)) = x ⇒ answer D

$h^{-1}(x)=\sqrt{\frac{x+1}{3}}$ ⇒ answer D

Step-by-step explanation:

* Lets explain how to find the inverse of a function

- Let f(x) = y

- Exchange x and y

- Solve to find the new y

- The new y = $f^{-1}(x)$

* Lets use these steps to solve the problems

∵ $f(x)=\sqrt{x-3}$

∵ f(x) = y

∴ $y=\sqrt{x-3}$

- Exchange x and y

∴ $x=\sqrt{y-3}$

- Square the two sides

∴ x² = y - 3

- Add 3 to both sides

∴ x² + 3 = y

- Change y by $f^{-1}(x)$

∴ $f^{-1}(x)=x^{2}+3$

∵ g(x) = x² + 3

∴ $f^{-1}(x)=g(x)$

∴ The functions are inverses to each other

* Now lets find f(g(x))

- To find f(g(x)) substitute x in f(x) by g(x)

∵ $f(x)=\sqrt{x-3}$

∵ g(x) = x² + 3

∴ $f(g(x))=\sqrt{(x^{2}+3)-3}=\sqrt{x^{2}+3-3}=\sqrt{x^{2}}=x$

∴ f(g(x)) = x

∴ The functions are inverses; f(g(x)) = x

* Lets find the inverse of h(x)

∵ h(x) = 3x² - 1 where x ≥ 0

- Let h(x) = y

∴ y = 3x² - 1

- Exchange x and y

∴ x = 3y² - 1

- Add 1 to both sides

∴ x + 1 = 3y²

- Divide both sides by 3

∴ $\frac{x + 1}{3}=y^{2}$

- Take √ for both sides

∴ ± $\sqrt{\frac{x+1}{3}}=y$

∵ x ≥ 0

∴ We will chose the positive value of the square root

∴ $\sqrt{\frac{x+1}{3}}=y$

- replace y by $h^{-1}(x)$

∴ $h^{-1}(x)=\sqrt{\frac{x+1}{3}}$

4 0

3 years ago

Jenn went shopping and spent $112. She bought a book for $24 and CD's that cost $8 each. What equation would you use to find out

slavikrds [6]

I would use the equation
24 + 8x = 112

let x = the amount of CDs she bought.

Hope this helps!!

3 0

3 years ago