#3 Solve and graph the inequality: -4+x<-9

What is the exponential expression 24^1/3

guapka [62]

Answer:

2.884499

Step-by-step explanation:

3 0

3 years ago

A cone has radius 9 and a height 12. A frustum of this cone has height 4.

Anettt [7]

Answer:

Part A)

The lower base has a radius of 9 units, and the upper base has a radius of 6 units.

Part B)

5 units.

Part C)

75π or about 235.62 square units.

Step-by-step explanation:

Please refer to the figure below.

The cone has a radius of 9 units and a total height of 12 units.

A frustum of the cone has a height of 4 units.

Part A)

The lower radius of the frustum will simply be 9 units.

For the upper radius, we will use the properties of similar triangles. We will compare the smaller upper triangle to the overall larger triangle. This yields:

$\displaystyle \frac{12}{8}=\frac{9}{x}$

Solve for x. Simplify:

$\displaystyle \frac{3}{2}=\frac{9}{x}$

Cross-multiply:

$18=3x\Rightarrow x=6$

The upper base has a radius of 6 units.

Part B)

We can first find the total slant height of the entire cone. By using the Pythagorean Theorem, this yields that the total slant height is:

$SH^2=12^2+9^2$

Simplify:

$SH^2=225\Rightarrow SH=15\text{ units}$

Now, find the slant height of the upper cone:

$(SH_\text{cone})^2=8^2+6^2=100$

So:

$SH_\text{cone}=10$

Then the slant height of the frustum will be the cone subtracted from the total. Thus:

$SH_{\text{frustum}}=15-10=5\text{ units}$

Part C)

We can first find the lateral area of the entire cone. The lateral area is given by:

$LA=\pi r\ell$

The lateral area of the entire cone will be:

$LA=\pi (9)(15)=135\pi$

The lateral area of the upper cone will be:

$LA_\text{cone}=\pi(6)(10)=60\pi$

Then the lateral area of the frustum is:

$LA_\text{frustum}=135\pi-60\pi =75\pi\text{ units}^2\approx235.62\text{ units}^2$

5 0

3 years ago

Which graph shows that ice cream sales increase when temperatures increase

fenix001 [56]

Answer:

.hh

Step-by-step explanation:

jj

5 0

3 years ago

Read 2 more answers

In Las Vegas, Nevada, stores charge a 4.6% state sales tax and a 3.65% county sales tax. Keven is buying a handbag priced at 220

marshall27 [118]

Keven paid a sales tax of $ 18.15 for handbag purchase

Solution:

Given that stores charge a 4.6% state sales tax and a 3.65% county sales tax

Keven is buying a handbag priced at 220 before tax

To find: Sales tax paid by Keven

Sales tax amount = state sales tax amount + country sales tax amount

Finding state sales tax amount:

stores charge a 4.6% state sales tax which means 4.6 % of $ 220

state sales tax amount = 4.6 % of 220

$\text{ state sales tax amount }= \frac{4.6}{100} \times 220$

$\text{ state sales tax amount }= 0.046 \times 220 = 10.12$

Thus state sales tax amount is $ 10.12

Finding country sales tax amount:

Store charges a 3.65% of country sales tax which means 3.65% of $ 220

Country sales tax = 3.65 % of 220

$\text{ Country sales tax } = \frac{3.65}{100} \times 220\\\\\text{ Country sales tax } = 0.0365 \times 220 = 8.03$

Thus country sales tax = $ 8.03

Now let us add both amount to get total tax paid by Keven

Sales tax amount = state sales tax amount + country sales tax amount

Sales tax amount = $ 10.12 + $ 8.03 = $ 18.15

Therefore Keven paid a sales tax of $ 18.15 for handbag purchase

4 0

3 years ago

Find all the real zeros of the function f(x) = 2x3 - 19x2 + 38x + 24 given that x-4 is a factor.

iris [78.8K]

Answer:

Zeroes: x=4, x=-1/2, and x=6

Step-by-step explanation:

Use Synthetic Division where x-4=0 to find another factor:

4 | 2 -19 +38 +24

___8_-44_-24

2 -11 -6 | 0

So far, your two factors are x-4 and 2x^2-11x-6.

We can actually factor 2x^2-11x-6 into (2x+1)(x-6), so we have three factors which are (x-4), (2x+1), and (x-6)!

By the Zero Product Property, x=4, x=-1/2, and x=6 are your zeroes.

8 0

3 years ago