Can someone please help me with these questions? Greatly appreciated!

What is the inverse of the function f(x) = 2x + 1?

Rasek [7]

X= - 1/2 , To find x- intercept zero , substitute f (x) = 0 , then just solve the equation for X , Hope this helped

5 0

3 years ago

Sarah saved $12.75 every week for a number of weeks, w. She received an additional $25 during the last week in which she saved m

Umnica [9.8K]

Answer:

12.75w + 25 = 114.25

w = 7

Step-by-step explanation:

since sarah is receiving 12.75 each week for a number of weeks, w (we don't know its value yet) we know that first part of the equation: that 12.75 is the coefficient next to w. Then we have the extra 25, so we know that adding 12.75w and 25 would give us sarah's total amount, which is 114.25.

to find out what w represents, we have to solve for it. solving for w means isolating it on one side. so, what we can do first is subtract 25 from both sides. that would then make the equation:

12.75w = 89.25

now, we have only one step left to isolating w, and that's to get 12.75 on the other side somehow. since we're multiplying 12.75 with w, and we're applying additive inverse properties, meaning the opposite of what is happening to cancel it out on the side it's in, we would divide 12.75 on both sides. in the left, 12.75 would cancel out, and in the right, we would divide 89.25 by 12.75. the quotient is 7.

now there's nothing left to take out to isolate w, so we have:

w = 7

sarah saved up for 7 weeks.

3 0

3 years ago

Can someone help with this I don’t understand

Karo-lina-s [1.5K]

Answer: see below

Step-by-step explanation:

3x-12=7x+8 ⇔ given

-12=4x+8 ⇔ addition property of equality

-20=4x ⇔ subtraction property of equality

x=-5 ⇔ division property of equality

-----------------------

5(x-1)=4x+13 ⇔ given

5x-5=4x+13 ⇔ distributive property

x-5=13 ⇔ subtraction property of equality

x=18 ⇔ addition property of equality

3 0

3 years ago

Find the amount of empty space within a cylinder containing three solid spheres, where each sphere has a radius of 3 cm. (Volume

aalyn [17]

Answer : The correct option is, (A) $54\pi cm^3$

Step-by-step explanation :

First we have to calculate the volume of cylinder.

Formula used:

Volume of cylinder = $\pi r^2h$

where,

r = radius = 3 cm

h = height = 18 cm (We are assuming that 3 solid spheres stacked to each other = 3 × diameter of each sphere = 3 × 2 × 3 = 18)

Volume of cylinder = $\pi (3cm)^2\times (18cm)$

Volume of cylinder = $162\pi cm^3$

Now we have to calculate the volume of 3 solid spheres.

Formula used:

Volume of 3 spheres = $3\times \frac{4}{3}\pi r^3$

Volume of 3 spheres = $4\pi r^3$

Volume of 3 spheres = $4\pi (3)^3$

Volume of 3 spheres = $108\pi cm^3$

Now we have to calculate the amount of empty space within a cylinder.

Amount of empty space within a cylinder = Volume of cylinder - Volume of 3 spheres

Amount of empty space within a cylinder = $162\pi cm^3-108\pi cm^3$

Amount of empty space within a cylinder = $54\pi cm^3$

Therefore, the amount of empty space within a cylinder is, $54\pi cm^3$

5 0

3 years ago

the ratio of cars to trucks on the parking lot is 2:3 there are 24 trucks on the lot what is the total number of vehicles on the

SVEN [57.7K]

x=16

Explanation

the ratio is 2:3

it means for every 2 cars, there are 3 trucks

Now, it the total of trucks is 24,the proportion must be the same, so

Step 1

Let

x represents the number of cars for 24 trucks

$\frac{\text{2 cars}}{3\text{ trucks}}=\frac{x}{24\text{ trucks}}$

Step 2

solve for x

$\begin{gathered} \frac{\text{2 cars}}{3\text{ trucks}}=\frac{x}{24\text{ trucks}} \\ 2\cdot24=3\cdot x \\ x=\frac{2\cdot24}{3} \\ x=\frac{48}{3} \\ x=16 \end{gathered}$

Hence, the answer is 16

4 0

1 year ago