What’s the slope between (4,5) and (1,2)

The width of a container is 5 feet less than its height. Its length is 1 foot longer than its height. The volume of the containe

juin [17]

The height of container is 8 feet

Solution:

Let "w" be the width of container

Let "l" be the length of container

Let "h" be the height of container

The width of a container is 5 feet less than its height

Therefore,

width = height - 5

w = h - 5 ------ eqn 1

Its length is 1 foot longer than its height

length = 1 + height

l = 1 + h ---------- eqn 2

The volume of container is given as:

$v = length \times width \times height$

Given that volume of the container is 216 cubic feet

$216 = l \times w \times h$

Substitute eqn 1 and eqn 2 in above formula

$216 = (1 + h) \times (h-5) \times h\\\\216 = (h+h^2)(h-5)\\\\216 = h^2-5h+h^3-5h^2\\\\216 = h^3-4h^2-5h\\\\h^3-4h^2-5h-216 = 0$

Solve by factoring

$(h-8)(h^2+4h+27) = 0$

Use the zero factor principle

If ab = 0 then a = 0 or b = 0 ( or both a = 0 and b = 0)

Therefore,

$h - 8 = 0\\\\h = 8$

Also,

$h^2+4h+27 = 0$

Solve by quadratic equation formula

$\text {For a quadratic equation } a x^{2}+b x+c=0, \text { where } a \neq 0\\\\x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$

$\mathrm{For\:} a=1,\:b=4,\:c=27:\quad h=\frac{-4\pm \sqrt{4^2-4\cdot \:1\cdot \:27}}{2\cdot \:1}$

$h = \frac{-4+\sqrt{4^2-4\cdot \:1\cdot \:27}}{2}=\frac{-4+\sqrt{92}i}{2}$

Therefore, on solving we get,

$h=-2+\sqrt{23}i,\:h=-2-\sqrt{23}i$

Thus solutions of "h" are:

h = 8

$h=-2+\sqrt{23}i,\:h=-2-\sqrt{23}i$

"h" cannot be a imaginary value

Thus the solution is h = 8

Thus the height of container is 8 feet

8 0

3 years ago

Coffee with sugar and milk added to it can contain up to calories. To consume a maximum of 600 mg if caffeine per day, how many

Marina CMI [18]

We know there is 330 mg of caffeine per 16-ounce serving. So if we want 8-ounce servings:
330 mg : 2 = 165 mg
Also we have to consume a maximum of 600 mg.
165 mg * 3 = 495 mg < 600 mg
165 mg * 4 = 660 mg > 600 mg
Answer: Someone could drink 3 full 8-ounce servings in a day and still stay below the limit.

8 0

3 years ago

Read 2 more answers

Pls help easy i thinkk

soldi70 [24.7K]

Answer:

1 1/2 miles

Step-by-step explanation:

if running 1 lap around a track is 1/2 miles then all we have to do is add it up

so we know that 1/2 miles is one lap

so if he runs two laps we would have run 1 mile

now that we know that he would have ran 1 mile in 2 laps then all we have to do it just add 1 more 1/2 mile in which would give u the answer of 1 1/2 miles or 1.5 miles

4 0

1 year ago

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I need help with this one too

natali 33 [55]

Hey there! :)

Answer:

y = 11.

Step-by-step explanation:

Set both of the equations equal:

5x - 9 = x² - 3x + 7

Rearrange the equation:

0 = x² - 3x - 5x + 9 + 7

Combine like terms:

0 = x² - 8x + 16

Factor:

0 = (x -4)²

Solve for x:

0 = x - 4

x = 4.

Plug this into an equation to solve for 'y':

y = 5(4) - 9

y = 20 - 9

y = 11.

3 0

2 years ago

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Johnny bought an oil painting originally priced at $80 but on sale for for 50% off. After 10% sales tax, what was the total cost

Alecsey [184]

Answer:

$44

Step-by-step explanation:

Original price = $80

Discount on sale = 50%

Discounted price = (1 - 50%) * original price

Discounted price = 0.5 * $80 = $40

Sales tax = 10%

Sales tax amount = 0.1 * $40 = $4

Total cost = discounted price + sales tax amount

Total cost = $40 + $4 = $44

5 0

2 years ago