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2 years ago

Evaluate the following when x = 3 2x+ 5(x)

Mathematics

1 answer:

Nina [5.8K]2 years ago

4 0

Hi!

I can help you with joy!

Evaluate:

$\fbox{2x+5x}$ when $\fbox{x=3}$

First, add x's:

$\rm{7x}$

Now, plug in the value of x (3)

$\rm{7(3)$

Multiply:`

$\rm{21}$ (Answer)

Hope it helps!

Ask me if you have any doubts.

Enjoy Your Day/Night! :)

<em>Answered by</em>

<em>~</em>Silent~

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3. A prop for the theater club’s play is constructed as a cone topped with a half-sphere. What is the volume of the prop? Round

Mariana [72]

The volume of the prop is calculated to be 2,712.96 cubic inches.

<u>Step-by-step explanation:</u>

Step 1:

The prop consists of a cone and a half-sphere on top. We will have to calculate the volumes of the cone and the half-sphere separately and then add them to obtain the total volume.

Step 2:

The volume of a cone is determined by multiplying $\frac{1}{3}$ with π, the square of the radius (r²) and height (h). Here we substitute π as 3.14. The radius is 9 inches and the height is 14 inches.

The volume of the cone : $V=\pi r^{2} \frac{h}{3}$ = $3.14 \times 9^{2} \times \frac{14}{3}$ = 1,186.92 cubic inches.

Step 3:

The area of a half-sphere is half of a full sphere. The volume of a sphere is given by multiplying $\frac{4}{3}$ with π and the cube of the radius (r³).

Here the radius is 9 inches. We take π as 3.14.

The volume of a full sphere = $V=\frac{4}{3} \pi r^{3}$ = $\frac{4}{3} \times 3.14 \times 9^{3}$ = 3,052.08 cubic inches.

The volume of the half-sphere = $\frac{3,052.08}{2}$ = 1,526.04 cubic inches.

Step 4:

The total volume = The volume of the cone + The volume of the half sphere,

The total volume = 1,186.92 + 1,526.04 = 2,712.96 cubic inches.

5 0

3 years ago

Please help! If you can answer both that would be great, thank you!!!

Levart [38]

I cant see the numerators on the numbers on the top one but the last one is 53/60.

7 0

3 years ago

Use the variable x to write the phrase in symbols.

Rudik [331]

Answer:

155 + $x^{3}$ + 14

Step-by-step explanation:

The variable x would represent the number/value we don't know, and in this case, we don't know what number is raised to the third power. This being said, x would represent that number.

The question, although worded a bit confusingly, asks to add 155, the number (x) to the exponent of 3, and 14. Mathematically, this would be 155 + $x^{3}$ + 14.

6 0

3 years ago

Exercise 3.5. For each of the following functions determine the inverse image of T = {x ∈ R : 0 ≤ [x^2 − 25}.

masya89 [10]

a. The inverse image of f(x) is f⁻¹(x) = ∛(x/3)

b. The inverse image of g(x) is $g^{-1}(x) = e^{x}$

c. The inverse image of <u>h</u>(x) is h⁻¹(x) = x + 9

<h3 /><h3>The domain of T</h3>

Since T = {x ∈ R : 0 ≤ [x^2 − 25} ⇒ x² - 25 ≥ 0

⇒ x² ≥ 25

⇒ x ≥ ±5

⇒ -5 ≤ x ≤ 5.

<h3>Inverse image of f(x)</h3>

The inverse image of f(x) is f⁻¹(x) = ∛(x/3)

f : R → R defined by f(x) = 3x³

Let f(x) = y.

So, y = 3x³

Dividing through by 3, we have

y/3 = x³

Taking cube root of both sides, we have

x = ∛(y/3)

Replacing y with x we have

y = ∛(x/3)

Replacing y with f⁻¹(x), we have

So, the inverse image of f(x) is f⁻¹(x) = ∛(x/3)

<h3>Inverse image of g(x)</h3>

The inverse image of g(x) is $g^{-1}(x) = e^{x}$

g : R+ → R defined by g(x) = ln(x).

Let g(x) = y

y = ln(x)

Taking exponents of both sides, we have

$e^{y} = e^{lnx} \\e^{y} = x$

Replacing x with y, we have

$y = e^{x}$

Replacing y with g⁻¹(x), we have

So, the inverse image of g(x) is $g^{-1}(x) = e^{x}$

<h3>Inverse image of h(x)</h3>

The inverse image of <u>h</u>(x) is h⁻¹(x) = x + 9

h : R → R defined by h(x) = x − 9

Let y = h(x)

y = x - 9

Adding 9 to both sides, we have

y + 9 = x

Replacing x with y, we have

x + 9 = y

Replacing y with h⁻¹(x), we have

So, the inverse image of <u>h</u>(x) is h⁻¹(x) = x + 9

Learn more about inverse image of a function here:

brainly.com/question/9028678

5 0

2 years ago

What is the greatest common factor for 28,42,56

mixer [17]

14 is the largest factor

3 0

3 years ago