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3 years ago

Distribute property to simplify 4(3x+2)

Mathematics

1 answer:

Julli [10]3 years ago

8 0

Here is the equation:

$4(3x+2)$

Since 4 is next to the parentheses, you have to multiply everything in the parentheses by 4.

First multiply 3x by 4:

$3x \times 4 = 12x$

Now multiply 2 by 4:

$4 \times 2 = 8$

Now add them together:

$12x+8 = 12x +8$

Your answer is 12x + 8

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What is the inverse of the function? f(x) = 1/3x-5

OlgaM077 [116]

Answer:

-1

f (x) = -3(x + 5)

Step-by-step explanation:

1) in f(x) = 1/3x-5, replace f(x)= with y= as follows: y = (1/3)x - 5

2) interchange x and y, obtaining: x = (1/3)y - 5

3) solve this result for y: (1/3)y = -x - 5, or -(x + 5). Next, multiply both sides by 3 to eliminate the fraction (1/3): y = -3(x + 5)

4) replace y with the symbol for "inverse of f(x);

-1

f (x) = -3(x + 5)

5 0

3 years ago

A ladder reaches a window 20 feet above the ground. The foot of the ladder is 4 feet from the wall. Which of the following measu

forsale [732]

Use pythagorians theorem a^2 + b^2 = c^2. 4^+20^ = 20.40 feet. The ladder is 20.40 feet long.

6 0

3 years ago

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Select the curve generated by the parametric equations. Indicate with an arrow the direction in which the curve is traced as t i

bixtya [17]

Answer:

length of the curve = 8

Step-by-step explanation:

Given parametric equations are x = t + sin(t) and y = cos(t) and given interval is

−π ≤ t ≤ π

Given data the arrow the direction in which the curve is traces means

the length of the curve of the given parametric equations.

The formula of length of the curve is

$\int\limits^a_b {\sqrt{\frac{(dx}{dt}) ^{2}+(\frac{dy}{dt}) ^2 } } \, dx$

Given limits values are −π ≤ t ≤ π

x = t + sin(t) ...….. (1)

y = cos(t).......(2)

differentiating equation (1) with respective to 'x'

$\frac{dx}{dt} = 1+cost$

differentiating equation (2) with respective to 'y'

$\frac{dy}{dt} = -sint$

The length of curve is

$\int\limits^\pi_\pi {\sqrt{(1+cost)^{2}+(-sint)^2 } } \, dt$

$\int\limits^\pi_\pi \, {\sqrt{(1+cost)^{2}+2cost+(sint)^2 } } \, dt$

on simplification , we get

here using sin^2(t) +cos^2(t) =1 and after simplification , we get

$\int\limits^\pi_\pi \, {\sqrt{(2+2cost } } \, dt$

$\sqrt{2} \int\limits^\pi_\pi \, {\sqrt{(1+1cost } } \, dt$

again using formula, 1+cost = 2cos^2(t/2)

$\sqrt{2} \int\limits^\pi _\pi {\sqrt{2cos^2\frac{t}{2} } } \, dt$

Taking common $\sqrt{2}$ we get ,

$\sqrt{2}\sqrt{2} \int\limits^\pi _\pi ( {\sqrt{cos^2\frac{t}{2} } } \, dt$

$2(\int\limits^\pi _\pi {cos\frac{t}{2} } \, dt$

$2(\frac{sin(\frac{t}{2} }{\frac{t}{2} } )^{\pi } _{-\pi }$

length of curve = $4(sin(\frac{\pi }{2} )- sin(\frac{-\pi }{2} ))$

length of the curve is = 4(1+1) = 8

conclusion:-

The arrow of the direction or the length of curve = 8

7 0

3 years ago

Solve and simplify 25 x 1/5 (thanks)

sammy [17]

Answer:

Step-by-step explanation:

First let turn 25 into a fraction

$\frac{25}{1}*\frac{1}{5}$

Multiply

$\frac{25}{5}$

Divide/Simplify

$=5$

Answer = 5

[RevyBreeze]

4 0

2 years ago

It cropped out but the 4th option is Z.

Ivahew [28]

Answer:

x and y

Step-by-step explanation:

Remote interior angles are angles that don't share a vertex or corner of a triangle with the exterior angle.

6 0

3 years ago

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