There are 20 baby devils in 2013 on Maria Island

in 2014 200 % where born

the number of baby devils born in 2014 can be gotten by

20 -------- 100

x -----------200

by proper analysis x = (200 x 20)/100 = 4000/100 = 40

**40 baby devils were born in 2014**

Use the given conditions to write an equation for the line in point-slope form and general form. Passing through (8,-4) and perpendicular to the line whose equation is x-6y-5=0

**Answer:**

y + 4 = -6 (x - 8)

**Step-by-step explanation:**

Change the equation to the slope intercept form for a line

x - 6y 5 = 0 Add 5 to both sides

x - 6y = 5 Subtract x from both sides

-6y = -x + 5 Divide both sides by -6

y = [tex]\frac{1}{6}[/tex] c - [tex]\frac{5}{-6}[/tex] Your slope is [tex]\frac{1}{6}[/tex]

A perpendicular slope is the opposite reciprocal of [tex]\frac{1}{6}[/tex], that would be -6

y - [tex]y_{1}[/tex] = m( x - [tex]x_{1}[/tex]) Plug is -4 for [tex]y_{1}[/tex] and 8 for [tex]y_{1}[/tex]

y - -4) -6(x-8)

y + 4= -6 (x -8)

What is the product of

(5+2i) and (-3 - 4i)?

**Answer:**

-7 - 26i

**Step-by-step explanation:**

(5+2i)(-3 - 4i)

take this and distribute them to each other

-15 -20i -6i -8i^2

then combine like terms

-15**-26i**-8i^2

i^2 is always equal to -1, so replace i^2 with -1 in the problem

-15-26i**-8(-1)**

now solve

-15-26i+8

now combine like terms and you have your answer

**-7-26i**

3. An automatic machine inserts mixed vegetables into a plastic bag. Past experience revealed that some packages were underweight and some were overweight, but most of them had satisfactory weight.

What is the probability of selecting four packages that are underweight?

If an automatic machine inserts mixed vegetables into a plastic bag. the **probability **of selecting four packages that are **underweight** is: 0.000000390625

Probability can be defined as the **tendency **or likelihood that an event will happen.

We would be making use of **multiplication **rule to determine the probabiliy that four packages are underweight.

Given :

Underweight = 2.5 % or 0.025

Hence,

Now let find the probability that P (all four underweight) :

P(all four underweight) = ( 0.025 ) ( 0.025 ) ( 0.025 ) ( 0.025 )

P(all four underweight) = 0.000000390625

Therefore we can conclude that the **probability **is 0.000000390625.

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Which of the expressions are equivalent to the one below? Check all thatapply.5•(3 + 7)A. 5•(7+3)B. 5.3 + 5.7C. (5.3) +7D. (3+7)5

Concept

To solve the question you will use the associative property.

a . ( b + c ) = a . b + a . c

The expressions that is equivalent to 5 .(3 + 7) = 5 . 3 + 5 . 7 , ( 3 + 7 ) 5 , 5 . (

Fi

A company prices its tornado insurance using the following assumptions:

• In any calendar year, there can be at most one tornado.

• In any calendar year, the probability of a tornado is 0.09.

• The number of tornadoes in any calendar year is independent of the number of tornados in any other calendar year.

Using the company's assumptions, calculate the probability that there are fewer than 2 tornadoes in a 14-year period.Round your answer to 4 decimals.

The **probability **that there are fewer than **3 tornadoes** in a 14-year period is** 0.992333**

Let x = number of tornados

n = 14

p = 0.03

There are just two **outcomes** that can occur in these independent, fixed trials, and the success probability is 0.03

Consequently, we may determine the probability using the** binomial distribution.**

Here we want to find ** P( X < 3) = P( X < = 3-1) = P(X <=2)**

Using Excel:

P( X <=2) = "=**BINOMDIST**(2,14,0.03,1)" = 0.992333

Be aware that the default Excel command to find** binomial probabilities **that are less than or equal is "=BINOMDIST(x, n, p, 1)"

Therefore**, 0.9923333 percent **of the time there won't be more than **3 tornadoes **in a 14-year period.

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Find the area of

8 in

3 in

10 in

4.5

**Answer:**

**Step-by-step explanation:**

square kilometre (km 2): 1,000,000 hectare: 10,000

Unit: Area in m 2 square meter: SI Unit

There exist more distinctions and classifications for different types of

trapezoids, but their areas are still calculated in the same manner using the

following equation: area = b 1 + b 2 2 × h where b1 and b2 are the bases. h is the height, or perpendicular distance between the bases The Farmer and his Daughter – Ramping Endeavors

y+ 4X=0 linear or nonlinear

**Answer:**

linear

**Step-by-step explanation:**

y+4x=0

-4x -4x

=y=-4x+0

it is in the y=mx+b form so it is linear

The number of classified documents has increased approximately linear from 8.2 million documents in 2001 to 17. 4 million documents in 2005. let in be the number of documents in millions labeled as classified in the year that is years since 2000 find the equation of the linear model to describe the data

Knowing that

- The number of classified documents has increased linearly.

- In 2001 there were 8.2 million documents.

- In 2005 there were 17.4 million documents.

- The variable "n" represents the number of documents (in millions) labeled as classified.

- The variable "t" represents the number of years since 2000.

The Slope-Intercept Form of the equation of a line is:

[tex]y=mx+b[/tex]Where "m" is the slope and "b" is the y-intercept.

The slope of a line can be found using this formula:

[tex]m=\frac{y_2-y_1_{}}{x_2-x_1}[/tex]Where these two points are on the line:

[tex](x_1,y_1),(x_2,y_2)[/tex]In this case, you know these two points:

[tex](1,8.2),(5,17.4)[/tex]Then, you can substitute values into the formula and find the slope of the line:

[tex]m=\frac{17.4-8.2}{5-1}=\frac{9.2}{4}=2.3[/tex]Now you know that the form of the equation is:

[tex]n=2.3t+b[/tex]In order to find "b", you need to:

- Choose one of the points on the line:

[tex]\mleft(1,8.2\mright)[/tex]- Identify the value of each variable. Notice that:

[tex]\begin{gathered} n=8.2 \\ t=2001 \end{gathered}[/tex]- Substitute those values of "n" and "t", and the slope into the equation:

[tex]8.2=2.3(1)+b[/tex]- Solve for "b":

[tex]\begin{gathered} 8.2=2.3+b \\ 8.2-2.3=b \\ b=5.9 \end{gathered}[/tex]Therefore the equation of the Linear Model is:

[tex]n=2.3t+5.9[/tex]Hence, **the answer is: Option D.**

The function is defined by h(x) = (4 + x)/(- 3 + 3x) Find h(4x) .

Given h(x), find h(4x) as shown below

[tex]h(4x)=\frac{4+(4x)}{-3+3(4x)}=\frac{4+4x}{-3+12x}[/tex]Thus, the expanded form of h(4x) is (4+4x)/(-3+12x)7.02 is what percent of 67.5?

312% of what is 39?

7.02 is 10.4% of 67.5

312% of 12.5 is 39

Explanation:

7.02/67.5 is 0.104 which is 10.4 as a percent.

100x39=3900, 3900/312 is 12.5

Hope this helped!

312% of 12.5 is 39

Explanation:

7.02/67.5 is 0.104 which is 10.4 as a percent.

100x39=3900, 3900/312 is 12.5

Hope this helped!

The functions f(x) and g(x) are shown on the graph.

f(x) = |x|

What is g(x)?

10

f(x) = x

-5

107

-5

-10

g(x) = ?

~XAX

K

**Answer:**

what graph?

**Step-by-step explanation:**

By the knowledge on **absolute values**, functional theory and rigid transformations and given that the** function** f(x) = |x|, the function g(x) = f(x - 4) is equal to |x - 4|.

In mathematics, the **absolute value** or modulus of a real number x, denoted |x|, is the non-negative value of x without regard to its sign. Namely, {\displaystyle |x|=x} if x is a positive number, and {\displaystyle |x|=-x} if x is negative, and {\displaystyle |0|=0}.

here, we have,

According to the image attached herein,

the** function** f(x) is an **absolute value **and the function g(x) results from translating f(x) in +x direction, representing a kind of rigid transformation as Pythagorean distance at every point of th**e function** is conserved.

There, we can define the function g(x) as follows:

g(x) = f(x - k), for k > 0 (1)

By the knowledge on **absolute values**, functional theory and rigid transformations

and given that

the** function** f(x) = |x|, the function g(x) = f(x - 4) is equal to |x - 4|.

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This graph shows the height in inches, `h`, of a bamboo plant `t` months after it has been planted.

Write an equation that describes the relationship between `t` and `h`.

Drag the movable point to trace along the line if that helps you with your thinking.

The **graph** that shows the **relationship** between the **height** of the bamboo and **months **planted is given as h = 5t + 10

Given that the graph shows the **relationship** between the** height** (h) of a bamboo plant after **months** it has been planted.

Let us assume that h is plotted on the **vertical axis** and months (t) is planted on the** horizontal axis**.

If the** graph **passes through the points (0, 0) and (2, 10), hence:

h - 10 = [(10 - 0)/(2 - 0)](t - 0)

h - 10 = 5(t)

h = 5t + 10

The **graph** is given as h = 5t + 10

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A radar unit is used to measure speeds of a car on a motorway. Speeds are normal distributed with a mean of 90 km an hour and a standard deviation of 10 km an hour. What is the probability that a car picked at random is traveling out more than 100 km an hour

let x is the random variable that represents the speed of car.

[tex]\begin{gathered} \mu(\operatorname{mean})=90 \\ \sigma=10 \end{gathered}[/tex]probability that x is higher than 100 :

[tex]P(x>100)[/tex]for x=100:

[tex]\begin{gathered} z=\frac{x-\mu}{\sigma} \\ z=\frac{100-90}{10} \\ z=1 \end{gathered}[/tex]so,

[tex]p(x>100)=p(z=1)[/tex]probability =total area - area of the left of (z=1)

[tex]\begin{gathered} \text{probability}=1-0.8413 \\ p(x>100)=0.1587 \end{gathered}[/tex]and the area of the left of z=1 is 0.8413 (from normal distribution)

Tell how many tens & onesWrite the number and the word name

Every column have 7 bricks

There are 8 columns,

Then there are

8x7 = 56 bricks + another 7 bricks = 63 bricks

Divide now 63 between 10

63/10 = 6 tens + 3 ones

ANSWER IS

6 TENS 3 ONES

For a standard normal distribution, find:P(z > 1.74)

Solution

Using Z score calculator

**P(x>Z) = 0.04093**

What’s the correct answer answer asap for brainlist

**Answer:**

B. radio stations stopped advertising

**Answer:**

As televisions became more affordable and advertisers flocked to the new medium, radio stations had to quickly adapt to the changing field. Stations stopped using live in-studio performances, instead playing less expensive recordings.

**Step-by-step explanation:**

In the 1950s, television surpassed radio as the most popular broadcast medium, and commercial radio programming shifted to narrower formats of news, talk, sports and music. Religious broadcasters, listener-supported public radio and college stations provide their own distinctive formats.

Solve these problems.

The **solutions** will be (x-2)(x+1), (3x+5)(5x+2) and (x+1)(x-1) respectively using **factorization**.

A number or other **mathematical** object is factorized or factored in **mathematics** by writing it as the product of numerous **factors**, typically smaller or simpler things of the same kind.

18) 8x³-8x²-16x = 0

Taking 8x common we get,

8x(x²-x-2) = 0

x²-x-2 = 0×8x

x²-(2-1)x-2 = 0

x²-2x+x-2 = 0

x(x-2)+1(x-2) = 0

(x-2)(x+1) = 0

Hence, the **factors** are (x-2)(x+1).

19) 15x³+31x²+10x = 0

Taking x as common as we get,

x(15x²+31x+10) = 0

**Factorize** 15x²+31x+10=0

15x²+(25+6)x+10=0

15x²+25x+6x+10=0

5x(3x+5)+2(3x+5)=0

(3x+5)(5x+2)=0

Hence the **factors** are (3x+5)(5x+2).

20) x³-x=0

Taking x as common as we get,

x(x²-1)=0

x²-1=0

(x+1)(x-1)=0

Hence the factors are (x+1)(x-1).

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Use the graph of the function to estimate the intervals on which the function is increasing or decreasing. (Enter your answers using interval notation.)

The **intervals **on which the **graph **is **increasing** at (-∞, 0) U (3.5, ∞). On the other hand, the graph is **decreasing** at (0, 3.5)

A **graph **can be defined as a pictorial representation or a **diagram **that represents data or **values**.

Increased or decreased **functions **are two categories of functions. Consequently, a **function **increases when the y-values grow, while a function decreases when the y-**values **decrease.

The **graph **indicates the y-values **increase **in the x-**intervals **from -∞ to 0 and from 3.5 to ∞. You can express that a **function **is **increasing **in the following ways using **interval notation**: (-∞, 0) U (3.5, ∞).

The graph, on the other hand, is **decreasing**: (0, 3.5)

Hence, the **intervals **on which the **graph **is **increasing** at (-∞, 0) U (3.5, ∞). On the other hand, the graph is **decreasing** at (0, 3.5)

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Yvonne wants to use a dissection argument to justify the formula for the area of a circle. She dissects the circle into congruent sectors and reassembles the sectors as a parallelogram-like figure. The diagram below shows the arrangement for a circle dissected into 8 sectors. M Height Base Yvonne knows that as the number of sectors of the circle increases, the reassembled figure becomes closer and closer to an actual parallelogram so that it can be used to determine the area of the circle. Determine the value of each characteristic of the parallelogram in the table below. Select the best value for each characteristic.base of the parallelogram height of the parallelogram area of the parallelogram

Each sector is formed like a triangle with a circle base. The sum of all the bases should be equal to half the length of the circle's circumference, this is calculated with the following expression:

[tex]\text{base}=\frac{2\pi r}{2}=\pi r[/tex]This is the base of the parallelogram.

The height of each triangle is the radius of the circle, therefore:

[tex]\text{height}=r[/tex]The area of the parallelogram is the product of the base and the height.

[tex]\text{Area =}\pi r^2[/tex]So the base is pi*r;

The height is r;

The area is pi*r².

Describe two different ways to translate a figure that result in the same image. Justify your answer.

The ways to translate the **figure** include:

It doesn't change its **orientation**.

It also doesn't change its **size** or shape.

When a **geometric** figure glides up, down, left, or right on the coordinate plane, this is referred to as translation. The figure changes its **location** but not its orientation. It also retains its size and shape. When you translate a figure, you slide it left or right, up or down.

When you **translate** a figure, you slide it left or right, up or down. This indicates that the coordinates for the figure's vertices will vary on the coordinate plane. To graph a, make the same **modification** at each point. The variations in coordinates of a reflection can be used to identify it.

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Find the value of x in the given right triangle. 12. x = [?] 62° х Enter your answer as a decimal rounded to the nearest tenth. Enter

EXPLANATION

Let's see the facts:

We can use the Law of Cosines to calculate the unknown value:

[tex]\cos \alpha\text{ = }\frac{\text{Adjacent cathetus}}{\text{Hypothenuse}}[/tex]Replacing terms:

[tex]\cos 62\text{ = }\frac{x}{12}[/tex]Isolating x:

[tex]x\text{ = 12}\cdot\cos 62\text{ = 6}[/tex]**Answer is x=6.**

Express Your Answer As A Polynomial In Standard Form.

f(x)= x-7

g(x)= 3x^2-7x-10

Find (f o g)(x)

Look at photo

According to the solving the **Polynomial Standard Form** of the given equation is :

3x^2-7x-17.

What isWhen expressing a **polynomial** in its **standard** **form**, the greatest degree of terms are written first, followed by the next degree, and so on. When x is the variable and ai are **coefficients**, the polynomial has the conventional form f(x) = anxn + an-1xn-1 + an-2xn-2 +... + a1x + a0.

f(x)= x-7

g(x)= 3x^2-7x-10

f(x)= x-7 by substituting in the value of g into f.

f(3x^2-7x-10) = (3x^2-7x-10)-7

= 3x^2-7x-17

According to the solving the slandered form of the given equation is :

3x^2-7x-17

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Simplify the expression.

the expression negative one eighth j plus two thirds minus the expression five thirds j plus nine twelfths

negative 37 over 24 times j minus 17 over 12

negative 37 over 24 times j plus 17 over 12

43 over 24 times j plus 1 over 12

negative 43 over 24 times j plus negative 1 over 12

The **value **of the **expression **after simplify will be,

''negative 43 over 24 times j plus negative 1 over 12.''

**Option D** is true.

**What is mathematical expression?**

**Expression in math** is defined as the collection of the **numbers**, **variables **and **functions **by using operations like addition, subtraction, multiplication, and division.

Given that;

The **expression **is;

''The expression negative one eighth j plus two thirds minus the expression five thirds j plus nine twelfths.''

Now, We can write the **expression** in** mathematical form **as;

⇒ (- 1/8 j + 2/3) - (5/3 j + 9/12)

Solve the **expression **as;

⇒ - 1/8 j + 2/3 - 5/3 j - 9/12

⇒ - 1/8 j - 5/3 j + 2/3 - 9/12

⇒ j (-1/8 - 5/3) + 2/3 - 3/4

⇒ j (- 3 - 40)/24 + (8 - 9)/12

⇒ j (-43/24) + (- 1/12 )

This can be written as;

''negative 43 over 24 times j plus negative 1 over 12''

Therefore, The **value **of the **expression **after simplify will be,

''negative 43 over 24 times j plus negative 1 over 12.''

**Option D** is true.

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Simplify these thing below please. I am stuck again... Thank you

[tex]9\sqrt{56 x^7 y^{12}}\qquad \begin{cases} 56=7\cdot 2\cdot 2\cdot 2\\ \qquad 7\cdot 2^2 \cdot 2\\ \qquad 2^2\cdot 14\\ x^7=x^{(3)(2)+1}\\ \qquad (x^3)^2\cdot x^1\\ y^{12}=y^{(6)(2)}\\ \qquad (y^6)^2 \end{cases}\hspace{5em} \begin{array}{llll} 9\sqrt{2^2(14)(x^3)^2 x (y^6)^2} \\\\\\ 9(2)(x^3)(y^6)\sqrt{14x} \\\\\\ {\Large \begin{array}{llll} 18x^3y^6\sqrt{14x} \end{array}} \end{array}[/tex]

**Answer:**

[tex]\textsf{1.} \quad 18\;x^3\;y^{6}\sqrt{14x}[/tex]

[tex]\textsf{2.} \quad -8\sqrt{2}[/tex]

**Step-by-step explanation:**

Given expression:

[tex]9\sqrt{56x^7y^{12}}[/tex]

[tex]\textsf{Apply radical rule} \quad \sqrt{ab}=\sqrt{a}\sqrt{b}:[/tex]

[tex]\implies 9\sqrt{56}\sqrt{x^7}\sqrt{y^{12}}[/tex]

Rewrite 56 as 4·14:

[tex]\implies 9\sqrt{4 \cdot 14}\sqrt{x^7}\sqrt{y^{12}}[/tex]

[tex]\textsf{Apply radical rule} \quad \sqrt{ab}=\sqrt{a}\sqrt{b}:[/tex]

[tex]\implies 9\sqrt{4}\sqrt{14}\sqrt{x^7}\sqrt{y^{12}}[/tex]

Rewrite 4 as 2²:

[tex]\implies 9\sqrt{2^2}\sqrt{14}\sqrt{x^7}\sqrt{y^{12}}[/tex]

Simplify:

[tex]\implies 9\cdot 2\sqrt{14}\sqrt{x^7}\sqrt{y^{12}}[/tex]

[tex]\implies 18\sqrt{14}\sqrt{x^7}\sqrt{y^{12}}[/tex]

[tex]\textsf{Apply exponent rule} \quad \sqrt{a}=a^{\frac{1}{2}}:[/tex]

[tex]\implies 18\sqrt{14}\;(x^7)^{\frac{1}{2}}\;(y^{12})^{\frac{1}{2}}[/tex]

[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:[/tex]

[tex]\implies 18\sqrt{14}\;x^{\frac{7}{2}}\;y^{\frac{12}{2}}[/tex]

[tex]\implies 18\sqrt{14}\;x^{\frac{7}{2}}\;y^6[/tex]

Rewrite ⁷/₂ as 3 + ¹/₂

[tex]\implies 18\sqrt{14}\;x^{(3+\frac{1}{2})}\;y^{6}[/tex]

[tex]\textsf{Apply exponent rule} \quad a^{b+c}= a^b \cdot a^c:[/tex]

[tex]\implies 18\sqrt{14}\;x^3 \; x^{\frac{1}{2}}\;y^{6}[/tex]

[tex]\textsf{Apply exponent rule} \quad a^{\frac{1}{2}}=\sqrt{a}:[/tex]

[tex]\implies 18\sqrt{14}\;x^3 \; \sqrt{x}\;y^{6}[/tex]

Rearrange:

[tex]\implies 18\;x^3\;y^{6}\sqrt{14x}[/tex]

Question 2Given expression:

[tex]7\sqrt{32}-6\sqrt{72}[/tex]

Rewrite 32 as 16·2 and 72 as 36·2:

[tex]\implies 7\sqrt{16 \cdot 2}-6\sqrt{36 \cdot 2}[/tex]

[tex]\textsf{Apply radical rule} \quad \sqrt{ab}=\sqrt{a}\sqrt{b}:[/tex]

[tex]\implies 7\sqrt{16}\sqrt{2}-6\sqrt{36}\sqrt{2}[/tex]

Rewrite 16 as 4² and 36 as 6²:

[tex]\implies 7\sqrt{4^2}\sqrt{2}-6\sqrt{6^2}\sqrt{2}[/tex]

[tex]\textsf{Apply radical rule} \quad \sqrt{a^2}=a, \quad a \geq 0:[/tex]

[tex]\implies 7 \cdot 4\sqrt{2}-6\cdot 6\sqrt{2}[/tex]

Simplify:

[tex]\implies 28\sqrt{2}-36\sqrt{2}[/tex]

[tex]\implies -8\sqrt{2}[/tex]

What is the equation of the line that passes through the point (5, 0) and has a slope of 6/5?

**Answer:**

[tex]y=\frac{6}{5}(x-5)[/tex]

**Step-by-step explanation:**

Use point-slope form.

Nolan is deciding between two truck rental companies. Company A charges an initialfee of $90 for the rental plus $2 per mile driven. Company B charges an initial fee of$50 for the rental plus $3 per mile driven. Let A represent the amount Company Awould charge if Nolan drives I miles, and let B represent the amount Company Bwould charge if Nolan drives a miles. Write an equation for each situation, in termsof 2, and determine the number miles driven, , that would make the cost of eachcompany the same.

first we writte the information they are giving to us:

For company A:

initial fee = $90

rent per mile = $2

For combany B:

initial fee = $50

rent per mile = $3

Now for company A the equation that represent the charge in one mile will be: (where n is the number of miles)

[tex]\begin{gathered} A=90+2(n) \\ A=90+2(1) \\ A=90 \end{gathered}[/tex]And for company B:

[tex]\begin{gathered} B=50+3n \\ B=50+3(1) \\ B=53 \end{gathered}[/tex]Now to determine the number miles driven, that would make the cost of each company the same, we have to make A = B

[tex]\begin{gathered} A=B \\ 90+2n=50+3n \\ \end{gathered}[/tex]and finaly we can solve for n

[tex]\begin{gathered} 90-50=3n-2n \\ 40=n \end{gathered}[/tex]so if they drive for 40 miles the will pay the same

If f(x)=rootx-3 and g(x)=1-x^2, then what do you notice about the domaine of (f•g)(x)

The **domain** will be** x ≥ 3** for f(x)=√x-3 and g(x)=1-x².

In case a** function **f gives a way to effectively create a single value y utilizing for that reason a value for x at that point that chosen x-value is said to have a place to the **domain of f**. there are some conditions to be checked such as ** denominators** cannot equal 0, **radicands** of even roots can't have a negative value,** logarithms **can as it was being taken of positive values. Since we are given that f[tex]\sqrt{x-3}[/tex] and g(x)=1-x², for g(x) since it's a** polynomial function** its domain had to be real numbers, whereas for f(x) is all positive and real numbers.

for the given condition ** (f•g)(x)**

=> (f•g)(x)= f(x)*g(x)

=> (f•g)(x) = √(x-3) * (1 - x²)

=>(f•g)(x) = √(x-3)-x²(√x-3)

So the domain for (f•g)(x) will be all **positive real numbers ** x≥3 x ∈ [3,∞)

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Kylie shoots an arrow during an archery lesson at camp. The height of the arrow can be modeled by the equation ℎ = −8t(2t−6), where ℎ is the height in feet of the arrow and t is the time in seconds. How long is the arrow in the air?

The arrow will be in the **air** for 3 **seconds** after 3 seconds the arrow hit the **target**.

Any **equation** of the form [tex]\rm ax^2+bx+c=0[/tex] where x is **variable** and a, b, and c are any **real** numbers where a ≠ 0 is called a **quadratic** equation.

As we know, the **formula **for the roots of the** quadratic **equation is given by:

[tex]\rm x = \dfrac{-b \pm\sqrt{b^2-4ac}}{2a}[/tex]

The **equation**:

h = −8t(2t−6)

To find the **total **number of seconds the **arrow **will be in the air:

Plug h = 0

−8t(2t−6) = 0

t(2t−6) = 0

t = 0 or t = 6/2

t = 0 or t = 3 seconds

Thus, the arrow will be in the **air** for 3 **seconds** after 3 seconds the arrow hit the **target**.

Learn more about **quadratic equations** here:

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You put together allowance money and head toward a distant planet forsome routine experiments on alien life forms. You abduct 12 aliens from thestrange planet, and you capture the internal body temperature of each(harmlessly of course). That data is presented above. Does this species ofaliens have an average internal body temperature less than that of the humanaverage of 98.6°F?

Solution

The mean of the internal body temperature of the 12 abducted aliens is given by;

[tex]\frac{96.8+98.3+97.6+98.5+97.5+97.5+98.5+65.6+95.4+98+97.4}{12}=87.14<98.6[/tex]Simplify by finding the product of the polynomials below. Then Identify the degree of your answer. When typing your answer use the carrot key ^ (press shift and 6) to indicate an exponent. Type your terms in descending order and do not put any spaces between your characters. (8n-4)(n^2+9) This simplifies to: AnswerThe degree of our simplified answer is: Answer

**Answer**

[tex]\begin{gathered} \text{ Question 1:} \\ 8n^3-4n^2+72n-36 \\ \\ \text{Qusetion 2:} \\ \text{THE DEGREE OF THE POLYNOMIAL IS 3} \end{gathered}[/tex]

**SOLUTION**

**Problem Statement**

The question gives us an expression to simplify and we are to simplify by finding the product. We are also asked to find the degree of the polynomial as well

**Method**

We simply need to expand the bracket to solve this question. But the degree of the polynomial is gotten by assessing which term in the final expression has the highest power. If the expression has a term with its highest power being 3, then the degree of the polynomial is 3.

With this information, let us begin solving.

**Implementation**

1. Expanding the expression:

Expanding the polynomial, we have:

[tex]\begin{gathered} (8n-4)(n^2+9) \\ \text{ Using the FOIL method,} \\ F=8n(n^2)=8n^3 \\ O=8n(9)=72n \\ I=-4(n^2)=-4n^2 \\ L=-4(9)=-36 \\ \\ \therefore(8n-4)(n^2+9)=8n^2+72n-4n^2-36 \\ \\ \text{ Remember, we are asked to write this result in descending order of terms. Thus, we have that:} \\ 8n^3-4n^2+72n-36 \end{gathered}[/tex]2. Degree of the polynomial:

From the above result, we can see that the highest degree of n in all the terms is 3, **therefore, the degree of the polynomial is 3**

**Final answer**

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