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3 years ago

Describe how the point-slope formula is useful when writing the equation of a trend line

Mathematics

1 answer:

Hitman42 [59]3 years ago

5 0

Answer:

Trend lines are lines used to approximate the general shape of a scatter plot. A positive trend line tells us the scatter plot has a positive correlation. A negative trend line tells us the scatter plot has a negative correlation.

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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

Match the equation to the graph where n is the Number of Burgers and C is the cost.

Softa [21]

Answer:

How did life during the Industrial Revolution differ in the North and the South?

In what ways did the Industrial Revolution make life better?

How did it make life more difficult? How did life during the Industrial Revolution differ in the North and the South?

In what ways did the Industrial Revolution make life better?

How did it make life more difficult?

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

The function h(x) is given below.

Nutka1998 [239]

Answer:

Step-by-step explanation:

I wish I knew :(

8 0

3 years ago

There will be 58 people at a breakfast and each person will eat 2 eggs. There are 12 eggs in each carton. How many cartons of eg

inna [77]

9.6 if my math is right lol

7 0

3 years ago

The probability that any postcard posted in Portugal on Monday is delivered to the UK within a week is 0.62.

sashaice [31]

Answer:

You can expect at least 9 of her postcards to arrive within a week

To find that, we multiply the number of postcards by the probability

15 x 0.62 = 9.3

Hope this helps

Good Luck

5 0

3 years ago