Solve for x:

Classify the angle. I need this urgently please! Thank you!

Radda [10]

The following is a right angle

If this helped you a Brainliest would be much appreciated!

4 0

3 years ago

Read 2 more answers

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

Solve the quadratic equation.

kondaur [170]

The answer is C. Use the quadratic formula to solve it and you should be just fine!

3 0

3 years ago

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MULTIPLE CHOICE DON'T ASK! THANK YOUFOR HELPING ;)

Tcecarenko [31]

Each side of Pentagon is forming a triangle with third vertices being center of pentagon .

this way we get 5 triangles .

The line drawn from center to the mid point of side of pentagon is perpendicular line , that is height of triangle

ARea of such one triangle =

( 1/2)( side of pentagon )* height of the triangle )

(1/2)( 11.8 )( 8.1) = 47.79 square inch

Area of the pentagon = 5 times area of one such triangle =

5* 47.79 = 238.95

Answer : 238 .95 square inch

5 0

4 years ago

In order to study whether there is a relationship between gender and age at marriage, 50 couples were randomly selected and the

katovenus [111]

Answer:

Part 1) Side by side box-plots

Part 2) Presence of allergies is a Categorical variable

Step-by-step explanation:

Part 1)

Study: "Relationship between gender and age at marriage"

Categorical variable: Gender.

Quantitative variable: Age at marriage.

For this problem side by side box-plots would be a good choice to show relationship between quantitative variable "age at marriage" and categorical variable "gender".

Advantage of using side by side box-plots is that it shows five point summary of the data which are;

1. minimum value

2. Lower quartile

3. Median value

4. Upper quartile

5. Maximum value

Part 2)

Study: "Does Vitamin C level in the breast milk of new mothers reduce the risk of allergies in their breastfed infants?"

Presence of allergies: Either presence of allergies exists or it doesn't, this is simple yes/no therefore, it is a categorical variable.

Levels of vitamin C: Since levels of vitamin C can be measured (in milligrams) and thus have numerical value therefore, it is a quantitative variable.

4 0

4 years ago