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3 years ago

20

Mathematics

1 answer:

elena-s [515]3 years ago

7 0

Answer:

12 in

Step-by-step explanation:

the scale factor of the enlarged frame is found by comparing the widths

original width : enlarged width = 2 : 6 = 1 : 3

That is 3 times the original width , then

enlarged height = 4 × 3 = 12 in

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A computer online service charges one hourly rate for regular use but a higher hourly rate for designated "premium" areas. One c

N76 [4]

Answer: the service charge per hour for premium services is $5.5

the service charge per hour for regular services is $3

Step-by-step explanation:

Let x represent the service charge per hour for premium services.

Let y represent the service charge per hour for regular services.

One customer was charged $38 after spending 2 h in premium areas and 9 regular hours. It means that

2x + 9y = 38- - - - - - - - - - - 1

Another customer spent 3 h in premium areas and 6 regular hours and was charged $34.50. It means that

3x + 6y = 34.5- - - - - - - - - - -2

We would eliminate x by multiplying equation 1 by 3 and equation 2 by 2. It becomes

6x + 27y = 114

6x + 12y = 69

Subtracting, it becomes

15y = 45

y = 45/15

y = 3

Substituting y = 3 into equation 1, it becomes

2x + 9 × 3 = 38

2x + 27 = 38

2x = 38 - 27 = 11

x = 11/2 = 5.5

8 0

3 years ago

Find the lateral area for the pyramid with the equilateral base

likoan [24]

<h3>The lateral area for the pyramid with the equilateral base is 144 square units</h3>

Solution:

The given pyramid has 3 lateral triangular side

The figure is attached below

Base of triangle = 12 unit

Find the perpendicular

By Pythagoras theorem

$hypotenuse^2 = opposite^2 + adjacent^2$

Therefore,

$opposite^2 = 10^2 - 6^2\\\\opposite^2 = 100 - 36\\\\opposite^2 = 64\\\\opposite = 8$

Find the lateral surface area of 1 triangle

$\text{ Area of 1 lateral triangle } = \frac{1}{2} \times opposite \times base$

$\text{ Area of 1 lateral triangle } = \frac{1}{2} \times 8 \times 12\\\\\text{ Area of 1 lateral triangle } = 48$

Thus, lateral surface area of 3 triangle is:

3 x 48 = 144

Thus lateral area for the pyramid with the equilateral base is 144 square units

5 0

3 years ago

What is the volume of a right circular cone if the circumference of the base is 125.6 ft and the height is 75 ft.?

Eddi Din [679]

Answer:

Hence the volume of the cone is 31384.52 cubic feet

Step-by-step explanation:

We must first need to understand how the volume of a cone is calculated.

It is simply calculated by multiplying the base area of the cone by the height, and dividing the result by 3.

This is :

Volume of cone = $\frac{\pi r^2 h}{3}$

we are not given the base area of the cone. However, we are given the circumference from which we can get the radius of the base.

Circumference =

$2 \pi r=125.6ft\\r =125.6/2 \pi=19.99ft$

hence the volume of the cone is

$\frac{\pi (19.99)^2 75}{3}=31384.52ft^{3}$

Hence the volume of the cone is 31384.52 cubic feet

3 0

3 years ago

Holly has $10.00 . she saw a purse in a catalog that was marked 14.95 plus 5% sales tax . how much more did holley need to buy t

vladimir1956 [14]

For this case we will first look for the total cost of the purse.
We then have the following rule of three:
14.95 $ -----> 100%
x -------------> 105%
Clearing x we have:
x = (105/100) * (14.95)
x = 15.6975 $
The amount needed to buy the purse is:
15.6975 - 10 = 5.6975 $
Answer:
holley needs 5.6975 $ to buy the purse

6 0

3 years ago

Sam paid 75 for 15hamburgers what is the unit price of one hamburger

stellarik [79]

The cost of one hamburger is 5

look at the attached picture

Hope it will help you

Good luck on your assignment

5 0

3 years ago

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