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The area of a triangle is one half the base and times the height. If the area of the triangle is 16 square inches and the vase i

sergij07 [2.7K]

Step-by-step explanation:

so, yes, the area of a triangle is

baseline × height / 2

so, we have here

16 = 8 × height / 2 = 4 × height

height = 16/4 = 4 in.

8 0

2 years ago

Derivative of<br><img src="https://tex.z-dn.net/?f=%20%5Cfrac%7B%20%7B3x%7D%5E%7B2%7D%20-%202x%20-%201%20%7D%7B%20%7Bx%7D%5E%7B2

Anastaziya [24]

Answer:

$\displaystyle \frac{dy}{dx} = \frac{2x + 2}{x^3}$

Step-by-step explanation:

we would like to figure out the derivative of the following:

$\displaystyle \frac{ { 3x }^{2} - 2x - 1 }{ {x}^{2} }$

to do so, let,

$\displaystyle y = \frac{ { 3x }^{2} - 2x - 1 }{ {x}^{2} }$

By simplifying we acquire:

$\displaystyle y = 3 - \frac{2}{x} - \frac{1}{ {x}^{2} }$

use law of exponent which yields:

$\displaystyle y = 3 - 2 {x}^{ - 1} - { {x}^{ - 2} }$

take derivative in both sides:

$\displaystyle \frac{dy}{dx} = \frac{d}{dx} (3 - 2 {x}^{ - 1} - { {x}^{ - 2} } )$

use sum derivation rule which yields:

$\rm\displaystyle \frac{dy}{dx} = \frac{d}{dx} 3 - \frac{d}{dx} 2 {x}^{ - 1} - \frac{d}{dx} {x}^{ - 2}$

By constant derivation we acquire:

$\rm\displaystyle \frac{dy}{dx} = 0 - \frac{d}{dx} 2 {x}^{ - 1} - \frac{d}{dx} {x}^{ - 2}$

use exponent rule of derivation which yields:

$\rm\displaystyle \frac{dy}{dx} = 0 - ( - 2 {x}^{ - 1 -1} ) - ( - 2 {x}^{ - 2 - 1} )$

simplify exponent:

$\rm\displaystyle \frac{dy}{dx} = 0 - ( - 2 {x}^{ -2} ) - ( - 2 {x}^{ - 3} )$

two negatives make positive so,

$\displaystyle \frac{dy}{dx} = 2 {x}^{ -2} + 2 {x}^{ - 3}$

<h3>further simplification if needed:</h3>

by law of exponent we acquire:

$\displaystyle \frac{dy}{dx} = \frac{2 }{x^2}+ \frac{2}{x^3}$

simplify addition:

$\displaystyle \frac{dy}{dx} = \frac{2x + 2}{x^3}$

and we are done!

5 0

3 years ago

Explain when a relation is also a function

nordsb [41]

Answer:

A relation is a function if the x-values map to only one y-value. In other words, if a relation is one-to-one or many-to-one it is a function.

Step-by-step explanation:

4 0

3 years ago

Owen used these steps to solve the equation 4x+7=1+2(2x+3). Which choice describes the meaning of his result, 7=7?

ivanzaharov [21]

Answer:

Option D. All values of x make the equation true

Step-by-step explanation:

<u><em>The options of the question are</em></u>

a.The result is not correct because Step 2 has an error.

b.The solution is x=7.

c.No values of x make the equation true.

d.All values of x make the equation true

we have the equation

$4x+7=1+2(2x+3)$

solve for x

Apply distributive property right side

$4x+7=1+4x+6$

Combine like terms

$4x+7=4x+7$

subtract 4x both sides

$7=7$

The equation has infinity solutions

.All values of x make the equation true

6 0

3 years ago

Find x and y. Please help this is on a test!!!

ozzi

To find the x-intercepts algebraically, we let y = 0 y=0 y=0 in the equation and then solve for values of x. In the same manner, to find for y-intercepts algebraically, we let x = 0 x=0 x=0 in the equation and then solve for y.

6 0

3 years ago

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