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3 years ago

If 3 + 4(2x - 1) = 23, then 2x - 2 equals: 2468

Mathematics

1 answer:

Anarel [89]3 years ago

7 0

Answer:

Step-by-step explanation:

3 + 4(2x - 1) = 23

4(2x - 1) = 20

8x - 4 = 20

8x = 24

x = 3

---------

2(3) - 2

6 - 2

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Consider this sphere inside the cylinder. Which statements are true? Check all that apply. NEED HELP ASAP

-Dominant- [34]

Option A: The height of the cylinder is equal to the diameter of the sphere.

Option C: The radius of the sphere is half the height of the cylinder.

Option E: The volume of the sphere is two-thirds the volume of the cylinder.

Solution:

The sphere is inside the cylinder.

Let r be the radius of the sphere.

Option A: The height of the cylinder is equal to the diameter of the sphere.

The sphere is fully occupied the cylinder.

If we draw the vertical line through enter of the sphere, which is equal to the height of cylinder.That is h = d. It is true.

Option B: The height of the cylinder is two times the diameter of the sphere.

That is h = 2d. From the above option, we know that h = d.

So, it is not true.

Option C: The radius of the sphere is half the height of the cylinder.

we know that diameter = 2 × radius (d = 2r)

From option A, we have h = d.

Substitute d = 2r, we get

⇒ h = 2r

Divide by 2 on both sides, we get

$$\Rightarrow \frac{h}{2}=r$

Therefore, it is true.

Option D: The diameter of the sphere is equal to the radius of the cylinder.

It is not true, because diameters of both cylinder and sphere are equal.

Option E: The volume of the sphere is two-thirds the volume of the cylinder.

Radius of cylinder and sphere = r

Height of cylinder h = 2r (by option C)

Volume of cylinder = Volume of sphere

$$\Rightarrow \pi r^2 h = \frac{4}{3} \pi r^3$ (formula)

$$\Rightarrow \pi r^2 (2r) = \frac{2\times2}{3} \pi r^3$

$$\Rightarrow 2 \pi r^3= \frac{2}{3} \times 2\pi r^3$

Hence it is true.

Option A, option C and option E are true.

6 0

4 years ago

Read 2 more answers

The revenue, in dollars, of a company that makes toy cars can be modeled by the polynomial 3x2 + 4x – 60. The cost, in dollars,

Tems11 [23]

For this case we have the following quadratic functions:

Revenue: $3x ^ 2 + 4x - 60$

Cost: $3x ^ 2 - x + 200$

Then, we observe that the profit is given by the following mathematical relationship:

$Profit = Revenue - Cost$

Substituting values we have:

$Profit = (3x ^ 2 + 4x - 60) - (3x ^ 2 - x + 200)$

Making the corresponding calculations we have:

$Profit = x ^ 2 (3-3) + x (4 + 1) + (-60-200)\\Profit = 5x - 260$

Answer:

An expression that represents the profit is:

$Profit = 5x - 260$

4 0

3 years ago

Read 2 more answers

John opens a savings account with $1,000 that compounds interest daily. The APR at the time John deposits the account is 3.5%. H

3241004551 [841]

$\bf \qquad \qquad \textit{Annual Yield Formula}
\\\\
\qquad \qquad \left(1+\frac{r}{n}\right)^{n}-1
\\\\
\begin{cases}
r=rate\to 3.5\%\to \frac{3.5}{100}\to &0.035\\
n=
\begin{array}{llll}
\textit{times it compounds per year}\\
\textit{daily, so in a year is 365}
\end{array}\to &365
\end{cases}
\\\\\\
\left(1+\frac{0.035}{365}\right)^{365}-1$

you'll get a decimal format, just multiply it times 100, to get the % format

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3 years ago

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Shawn planned to run 4.2 miles every day, but yesterday he only had time to run 0.2 of that distance. How far did Shawn run yest

Fynjy0 [20]

Answer:

That would be 4.0

Step-by-step explanation:

if you have 4.2 take away 0.2 that would be 4.0

4.2

0.2

-__

4.0

Hope this helped regards

4 0

3 years ago

If h(x) = 4x – 3 and p(x) = x2 – 3x, find p(-3)<br><br> 18<br> 0<br> -3

navik [9.2K]

Answer: p(-3)=18

Step-by-step explanation:

To find p(-3), you plug -3 into p(x) and solve.

p(-3)=(-3)²-3(-3) [exponent]

p(-3)=9-3(-3) [multiply]

p(-3)=9+9 [add]

p(-3)=18

Now we found that p(-3)=18.

7 0

3 years ago

*If 3 + 4(2x - 1) = 23, then 2x - 2 equals: *​2468

If 3 + 4(2x - 1) = 23, then 2x - 2 equals: 2468