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3 years ago

6 am

Mathematics

1 answer:

Roman55 [17]3 years ago

7 0

Answer:

$A=376.99\ cm^2$

Step-by-step explanation:

We need to find the lateral surface area of the cylinder of radius 6 cm and height of 10 cm.

We need to find the lateral surface area of the cylinder. The formula for the lateral surface area of a cylinder is given by :

$A=2\pi rh\\\\A=2\pi \times 6\times 10\\A=376.99\ cm^2$

So, the lateral surface area of the cylinder is $376.99\ cm^2$ .

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Logan genetically engineered a new type of fir tree and a new type of pine tree. The combined height of one fir tree and one pin

Snowcat [4.5K]

Let f be the height of the fir trees
Let p be the height of the pine trees

We know from the problem that
f + p = 21 and 4f = 24 + p
rearrange the 2nd equation to get p = 4f - 24 and substitute into the other equation

so...
f + 4f - 24 = 21
5f - 24 = 21
5f = 45
f = 9 - height of the fir tree

substitute back into the 1st equation
9 + p = 21
p = 12 - height of the pine tree

8 0

3 years ago

Select all of the points that are solutions to the system of linear inequalities that is listed below 10x + 4y < 12 8x -3y &g

liberstina [14]

Answer:

(3, -8) and (2, -10)

Step-by-step explanation:

Given

$10x + 4y < 12$

$8x - 3y > 20$

Required

Select the true coordinate points in (3, -8) (2, 5) (-5, 1) (10, 3) (2, -10)

(3, -8)

x = 3 and y = -8

$10x + 4y < 12$

$10 * 3 + 4 * -8 < 12$

$30 - 32 < 12$

$-2 < 12$ --- True

$8x - 3y > 20$

$8 * 3 - 3 * -8> 20$

$24 +24> 20$

$48> 20$ --- True

(2, 5)

x = 2 and y = 5

$10x + 4y < 12$

$10 * 2 + 4 * 5 < 12$

$20 + 20 < 12$

$40 < 12$ --- False (No need to check the other inequality)

(-5, 1)

x = -5 and y = 1

$10x + 4y < 12$

$10 * -5 + 4 * 1 < 12$

$-46 < 12$ --- True

$8x - 3y > 20$

$8 * -5 - 3 * 1 > 20$

$-43 > 20$ --- False

(10, 3)

x = 10 and y = 3

$10x + 4y < 12$

$10 * 10 + 4 * 3 < 12$

$112 < 12$ --- False (No need to check the other inequality)

(2, -10)

x = 2 and y = -10

$10x + 4y < 12$

$10 * 2 + 4 * -10 < 12$

$-20 < 12$ --- True

$8x - 3y > 20$

$8 * 2 - 3 * -10 > 20$

$46 > 20$ --- True

Hence, the solution to the inequalities are:

(3, -8) and (2, -10)

4 0

3 years ago

Tom and his best friend are going to join a gym. Tom saw that Platinum gym has a sale with a one time fee of $90 and a monthly f

worty [1.4K]

Answer:

Part 1:

For Platinum Gym:

90 + 30x

For Super Fit Gym:

200 + 20x

Part 2: $270

Part 3: $320

Part 4: 11 months

Part 5: See explanation below

Step-by-step explanation:

Part 1:

Let "x" be the number of months:

For Platinum Gym:

90 + 30x

For Super Fit Gym:

200 + 20x

Part 2:

We put x = 6 in platinum gym's equation and get our answer.

90 + 30x

90 + 30(6)

90 + 180

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Part 3:

We put x = 6 into super fit's equation and get our answer.

200 + 20x

200 + 20(6)

200 + 120

=$320

Part 4:

To find the number of months for both gyms to cost same, we need to equate both equations and solve for x:

90 + 30x = 200 + 20x

10x = 110

x = 11

So 11 months

Part 5:

We know for 11 months, they will cost same. Let's check for 10 months and 12 months.

In 10 months:

Platinum = 90 + 30(10) = 390

Super Fit = 200 + 20(10) = 400

In 12 months:

Platinum = 90 + 30(12) = 450

Super Fit = 200 + 20(12) = 440

Thus, we can see that Platinum Gym is a better deal if you want to get membership for months less than 11 and Super Fit is a better deal if you want to get membership for months greater than 11.

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3 years ago

The circumference of a circle is 12 inches. What is the radius

IceJOKER [234]

Greetings!

"The circumference of a circle is 12 inches. What is the radius?"...

We can use the formula to find the circumference of circle to solve this:
 $2 \pi r$

Input the information we know:
 $2 \pi r=12$

Solve for r, using the properties of equality:

Simplify.
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Divide both sides by 6.28
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Simplify.
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The radius is 1.91cm long.

Hope this helps.
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3 years ago

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iren [92.7K]

Answer:

y = 6x - 47

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Step-by-step explanation:

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3 years ago