Tabitha wants to hang a painting in a gallery. The painting and frame must have an area of 58 square feet. The painting is 7 feet wide by 8 feet long. Which quadratic equation can be used to determine the thickness of the frame, x?

Answers

Answer 1

Answer: The quadratic equation would be;
x2+15x-2=0

Working:
Assuming the area around the painting i.e the frame, has a uniform thickness, then;
Length of painting and frame = 8+x
Breadth of painting and frame= 7+x

The area from above step gives;
A= LxW
A= (8+x)(7+x)
On expanding, 56+8x+7x+x2
On simplifying,
56+15x+x2. This should be equal to 58.
58=x2+15x+56
Taking 58 to the other side,
x2+15x-2=0

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What Is 17/4 [fraction] as a mixed or a whole number please answer

Answers

so lets see the biggest counting number that has a factor of four, yet is less than 17 so
16 is divisible by 4 and less than 17 so
16/4 +1/4=17/4
16/4=4 so
4 and 1/4
1/4=.25 so
4.25

So, (as apologiabiology's brother)

We find out how many whole 4's would fit in 17. We get 4 4's with a remainder of 1.

So, 17/4 = 4 1/4 (four and one-fourth)

P.S. 17/4 cannot be written as a whole number without fractions.

A cylindrical swimming pool has a diameter of 18 feet and a height of 4 feet. About how many liters of water are needed to fill the swimming pool 85% of its total volume? Round your answer to the nearest whole number. (1 ft³ ≈ 28.3 L) To the nearest whole number of liters.

Answers

Final answer:

To fill a cylindrical swimming pool with a diameter of 18 feet and a height of 4 feet 85% full, you'll need approximately 24462 liters of water.

Explanation:

To determine how many liters of water are needed to fill the swimming pool to 85% of its total volume, we first need to calculate the total volume of the cylindrical pool. The formula to calculate the volume of a cylinder is V=πr²h were r is the radius (half of the diameter) and h is the height. Therefore, the pool's total volume in cubic feet is V=π*9²*4 ≈ 1018 ft³. However, the student only wants to fill the swimming pool up to 85%, so we multiply this total volume by 0.85 to get approximately 865 ft³.

Since 1 ft³ ≈ 28.3 L, we can calculate the needed volume in liters by multiplying the 865 ft³ by 28.3 to obtain approximately 24462 liters of water. Round to the nearest whole number, so about 24462 liters of water are needed to fill the swimming pool es up to 85% of its volume.

Learn more about Cylindrical Volume Calculation

#SPJ12

Find the measure of the exterior angle.

Answers

Answer:

1) 128°

2) 126°

3) 108°

Question one:

The square in the corner means 90°. If you add the interior angles of any triangle together, you get 180. in this case, x is in exterior angle, so you subtract it from 180 to get the interior angle.

38 + 90 + (180-x) = 180

38 + 90 + 180 - x = 180

38 + 90 + 180 - 180 - x = 0

38 + 90 + 180 - 180 = x

128 = x

Question two:

again, adding all the interior angles makes 180°. use this to make the equation.

3x + (5x-6) + 90 = 180

3x + 5x - 6 = 90

8x = 96

x = 12.

x isn't the answer the question wants, however. if you look at the drawing, the angle that's supplementary to 5x-6 is the exterior angle. so,

180 - (5x-6) = the answer

180 - 5x + 6 = the answer

substitute x for 12

180 - 60 + 6 = the answer

126 = x

Question three

again, adding all the interior angles together makes 180°.

(a + 10) + 44 + (180-2a) = 180

a + 10 + 44 + 180 - 2a = 180

-a + 234 = 180

234 - 180 = a

54 = a

however, the question is looking for the exterior angle, not a. in this case, the exterior angle is 2a, so just multiply 54 by 2.

x = 108

Angle 1 and angle 2 are a linear pair. Measure of angle 1 = x-36, and measure of angle 2 = x+84. Find the measure of each angle.

Answers

angle1 + angle2 = 180°(because they are a linear pair)
or, (x-36) + (x+84) = 180
or, x - 36 + x + 84 = 180
or, 2x + 48 = 180
or, 2x = 180 - 48
or, 2x = 132
or, x = 132/2
therefore, x = 66
angle1 = (x - 36) = 66-36 = 30°
angle2 = (x+84) = 66+ 84 =150°

linear pair means supplementary so
x-36+x+84=180
2x+48=180
2x=132
x=66
Therefore angle 1 is 30 while angle 2 is 150

How To Solve The Equation 3(x-6)=10x+3 ?

Answers

3(x-6)=10x+3

Expand the left side:

3x-18 = 10x + 3

Subtract 3x from each side:

-18 = 7x + 3

Subtract 3 from each side:

-21 = 7x

Divide each side by 7 :

-3 = x

$3(x-6)=10x+3\n 3x-18=10x+3\n 7x=-21\n x=-3$