Which represents a quadratic functionWhich represents a quadratic function? f(x) = 2x3 + 2x2 – 4 f(x) = –7x2 – x + 2 f(x) = –3x + 2 f(x) = 0x2 + 3x – 3

The length of the pond is 77.4 inches, and the width of the pond is 38.7 inches.

In geometry, a rectangular prism can be defined as a 3-dimensional solid shape that has six faces that are rectangles. A rectangular prism is also a cuboid.

Let,a be the length of the pond and b be the width of the pond.

The volume of the pond is;

[tex]\rm Volume \ of \ the \ pond= Area\ of\ the\ base\times deep\\\\Area\ of\ the\ base=\dfrac{Volume \ of \ the \ pond}{base}\\\\Area\ of\ the\ base=\dfrac{72000}{24}\\\\Area\ of\ the\ base=3000 in^2[/tex]

The length of the pond is two times its width.

a = 2b

The area of the base = a × b

3000 = ab

ab = 3000

Substitute the value of a in equation 2

[tex]\rm ab=3000\\\\2b \times b = 3000\\\\b^2=\dfrac{3000}{2}\\\\b^2=1500\\\\b=38.7[/tex]

Substitute the value of b in equation 1

[tex]\rm a=2b\\\\a=2 \times 38.7\\\\a=77.4[/tex]

Hence, the length of the pond is 77.4 inches, and the width of the pond is 38.7 inches.

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The width of the pond is approximately 38.7 inches and the length is approximately 77.4 inches.

To find the length and width of the pond, we can use the formula for the volume of a rectangular prism: length × width × depth. We are given that the depth is 24 inches and the volume is 72,000 cubic inches.

Let's denote the width as w.

Since the length is two times the width, we can express the width as w and the length as 2w.

Therefore, the equation for the volume becomes:

2w × w × 24 = 72,000

48w^2 = 72,000

w^2 = 1,500

w ≈ 38.7

Therefore, the width is approximately 38.7 inches and the length is approximately 77.4 inches.

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Answer:

The side length of the square Kevin cuts is slightly less than the length the instructor required

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The total cost to tile a rectangular floor measuring 231 feet by 37 feet, with tile costing $14 per square foot, will be $119,658.

To find the cost of tiling a rectangular floor, first, calculate the area of the floor which is the length times the width. In this case, the rectangle is 231 feet by 37 feet so its area is 231 x 37 = 8,547 square feet.

With the tile costing $14 per square foot, the total cost will be the area of the floor times the cost per square foot. This can be calculated by multiplying 8,547 square feet x $14 per square foot = $119,658.

Therefore, the total cost to tile the rectangular floor will be $119,658.

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Answer:

step 3

Step-by-step explanation:

took test

The number of hours if they worked the job together will be 2 hours.

A ratio is a collection of ordered integers a and b represented as a/b, with b never equaling zero. A proportionate expression is one in which two items are equal.

One maid can clean the house in 3 hours. Another maid can do the job in 6 hours.

We know that work and time are inversely proportional to each other.

Let T be the total time taken. Then the equation will be

1/T = 1/3 + 1/6

1/T = (2 + 1) / 6

1/T = 3 / 6

T = 6 / 3

T = 2

The number of hours if they worked the job together will be 2 hours.

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The equation of the straight line whose x - intercept = 8 and

y - intercept = - 2 is y = x/4 - 2.

The slope - intercept form of a straight line is -

y = mx + c

Given is the equation of the line whose x-intercept is 8 and y-intercept is -2.

The given intercepts are -

x - intercept = 8

y - intercept = - 2

Then, the coordinates of the points through which the line passes are -

(0, -2) and (8, 0)

The slope of this line will be -

m = 0 - (- 2)/8 - 0

m = 2/8

m = 1/4

So the equation of the straight line will be -

y = x/4 - 2

Therefore, the equation of the straight line whose x - intercept = 8 and

y - intercept = - 2 is y = x/4 - 2.

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The width of the lawn surrounding the garden is 2 yards.

Let's denote the width of the lawn as "w" yards.

The dimensions of the garden are 40 yards by 35 yards. Including the lawn, the dimensions become:

Length: 40 + 2w yards

Width: 35 + 2w yards

The area of the rectangle including the garden and the lawn is:

(40 + 2w) × (35 + 2w) square yards

The area of the garden itself is:

40 × 35 = 1400 square yards

The area of the lawn alone is:

Total area - Area of the garden = 316 square yards

Therefore:

(40 + 2w) × (35 + 2w) - 1400 = 316

Expand the left side of the equation:

= (40 + 2w)(35 + 2w)

= 40 × 35 + 40 × 2w + 35 × 2w + 2w × 2w

= 1400 + 80w + 70w + 4w²

= 1400 + 150w + 4w²

Set up the equation:

= 1400 + 150w + 4w² - 1400 = 316

= 150w + 4w² = 316

Rearranging the equation:

4w² + 150w - 316 = 0

Solve this quadratic equation using the quadratic formula:

w = (-b ± √(b² - 4ac)) / 2a

Here, a = 4, b = 150, and c = -316

Calculate the discriminant:

= b² - 4ac

= 150² - 4 × 4 × (-316)

= 22500 + 5056

= 27556

√27556 ≈ 166

Therefore:

w = (-150 ± 166) / 8

This gives two potential solutions:

w = (16 / 8) = 2

w = (-316 / 8) (not valid as width cannot be negative)

Saving to easily access the money when needed is the situation would a savings account be the best investment to earn interest

Investment is traditionally defined as the commitment of resources to achieve later benefits

An investment  can be regarded as asset or item that is been gotten so as to generate income or appreciation.

It should be noted that appreciation serves as increase in the value of an asset over time.

To earn interest, it will be best to use savings account so that there could be easy access to the  money when needed.

Hence, saving to easily access the money when needed is the situation would a savings account be the best investment to earn interest

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Information Technology and Engineering

Mathematics is also a branch of Science. A person who is good in mathematics can take the analytical view of anything and convert ideas into practical form by using mathematical models. There are a lot of applications that can be used for converting analog models into digital models by using mathematics. So all of these models require mathematical backgrounds and engineers are the people who bring ideas to reality. The same is applied on IT field too.

To find Damien's mean bowling score, we add up his scores and divide by the number of games played. The mean bowling score is 78.

To calculate Damien's mean bowling score, we need to find the sum of all his scores and divide it by the total number of games played. Damien's scores are 82, 83, 65, 84, and 76.

Adding these scores together we get: 82 + 83 + 65 + 84 + 76 = 390.

Then, divide the sum by the total number of games played: 390 ÷ 5 = 78.

Therefore, Damien's mean bowling score is 78.

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Final answer:

To find the side length of the smaller square, we take the square root of the larger square's area (400 sq inches) to get 20 inches, then halve it to align with the 1:2 scale factor of the sides for a correct length of 10 inches.

Explanation:

To solve this problem, we first acknowledge that the ratio of the areas of the two squares is 1:4. Since area is a function of the side length squared, we look for a scale factor of the side length that when squared will give us this ratio. In this case, the scale factor is 1:2, meaning the side length of the smaller square is half that of the larger square.

The area of the larger square is given as 400 square inches. To find the side length, we take the square root of the area, which is 20 inches. Therefore, the side length of the smaller square is half of this, which is 10 inches. However, given that the statement seems to expect an 8-inch side for the larger square, there might be a misunderstanding in the problem, assuming that area scales directly with side length rather than its square. Nonetheless, based on area and scale factor, the correct side length is 10 inches.

Answer with Step-by-step explanation:

We know that volume of a cylinder with radius r and height h is:

πr²h

and  volume of cone with radius r and height h is:

πr²h/3

Volume of cone=Volume of cylinder/3 < Volume of cylinder

Volume of cylinder=84π in² where π=3.14

Volume of cone=84π/3 in²

                          = 84(3.14)/3 in²

Hence, correct options are:

The volume of the cone is 1/3 the volume of the cylinder.

The volume of the cone is less than the volume of the cylinder.

The expression 84(3.14)/3 finds the volume of the cone.

the answer is: A, C, and D

Answer:

-4-23i

Step-by-step explanation:

Above answer didn't quite understand what the question was asking. It's asking to SUBTRACT 8+7i from 4-16i. So it would be written like this:

(4-16i) - (8+7i).

Simplify it from there and you'd get -4-23i

To subtract 8 + 7i from 4 - 16i, subtract the real parts and the imaginary parts separately, resulting in -4 - 23i.

To subtract 8 + 7i from 4 − 16i, you treat the real and imaginary parts separately.

Subtract the real parts: 4 − 8 = −4.

Subtract the imaginary parts: (−16i) − (7i) = −16i − 7i = −23i.

Combine the results to get the final answer: −4 − 23i.

Therefore, subtracting 8 + 7i from 4 − 16i gives −4 − 23i.

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The double lathe milk with 2 percent fat concentration, is made by

considering the concentration and amount of each constituent.

The amount of each type of milk to be used in the [tex]\dfrac{1}{3}[/tex] pint of double lathe

are;

Reasons:

Let x represent the amount of the milk that contains 1 percent fat in the

volume of the 2 percent fat milk.

Therefore, we have;

The amount of the 4 percent fat milk to be used = [tex]\dfrac{1}{3} - x[/tex]

[tex]Amount \ of \ fat = \dfrac{1}{100} \times x + \dfrac{4}{100} \times \left (\dfrac{1}{3} - x\right) = \dfrac{2}{100} \times \dfrac{1}{3} = \dfrac{2}{300}[/tex]

[tex]\dfrac{1}{100} \times x + \dfrac{4}{100} \times \left (\dfrac{1}{3} - x\right) = \dfrac{4 - 9 \cdot x}{300} = \dfrac{2}{300}[/tex]

Therefore;

4 - 9·x = 2

4 - 2 = 9·x

[tex]x = \dfrac{2}{9}[/tex]

The amount of the 1 percent fat milk to be used for the double lathe, x = [tex]\dfrac{2}{9}[/tex]

of a pint.

The amount of the 4 percent fat milk to be used for the double lathe = [tex]\dfrac{1}{3} - x[/tex]

Therefore;

The mount of the 4 percent fat milk = [tex]\dfrac{1}{3} - \dfrac{2}{9} =\dfrac{1}{9}[/tex]

The amount of the 4 percent fat milk to be used for the double lathe = [tex]\dfrac{1}{9}[/tex]

pint.

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