Mathematics College

## Answers

**Answer 1**

SOLUTION:

Step 1:

In this question, we are given the following:

Step 2:

**The details of the solution are as follows:**

[tex]\begin{gathered} Given\text{ the function,} \\ f(x)\text{ = x}^3-20x^2\text{ + 123 x - 216} \\ Using\text{ Rational Root theorem, we have that:} \\ f(x)\text{ =}\frac{x^3-20\text{ x}^2+\text{ 123x - 216}}{x-\text{ 3}}=\text{ x}^2-\text{ 17 x + 72} \\ Now,\text{ factorizing x}^2-17x\text{ + 72 , we have that:} \\ \end{gathered}[/tex][tex]\begin{gathered} x^2\text{ -17 x+ 72 = \lparen x- 8 \rparen \lparen x - 9 \rparen} \\ Hence,\text{ we can see that:} \\ x^3-20x^2+\text{ 123 x - 216 = \lparen x- 3\rparen \lparen x - 8 \rparen \lparen x - 9 \rparen} \\ Hence,\text{ we have zero imaginary roots and 3 real roots} \end{gathered}[/tex]

**CONCLUSION:**

**The final answer is:**

[tex]zero\text{ imaginary , 3 real roots \lparen OPTION A \rparen}[/tex]

## Related Questions

please gelp with the attached picture if my algebra 1 hw

### Answers

Answer:

The y-intercept = (0, 12621)

Explanation:

The **initial population**, P₀ = 12,621

**Rate of increase**, r = 6% = 6/100

r = 0.06

The **number of years after the first census** = x

The population after x years is given as:

[tex]\begin{gathered} P=P_0(1+r)^x \\ P=12621(1+0.06)^x \\ P=12621(1.06)^x \end{gathered}[/tex]

**The graph that represents the above illustration is shown below**

**The y-intercept is found by setting x = 0, and finding the corresponding value of P**

[tex]\begin{gathered} P=12621(1.06)^x \\ P=12621(1.06)^0 \\ P=12621 \end{gathered}[/tex]

**The y-intercept = (0, 12621)**

Find the sales tax on an appliance costing $272.26 if the tax rate is 5.2%.The sales tax is $_(Round to the nearest cent.)

### Answers

To determine the sales tax, we have to compute the 5.2% of 272.26. To determine the x% of y, we use the following expression:

[tex]y*\frac{x}{100}.[/tex]

Therefore, the 5.2% of 272.26 is:

[tex]272.26*\frac{5.2}{100}.[/tex]

Simplifying the above result, we get:

[tex]sales\text{ tax}\approx14.16.[/tex]

Answer: $14.16

I’m not sure what to put for this question some help would be great

### Answers

If the point **(x, y) is rotated around the origin by 90 degrees counterclockwise**, then **its image will be (-y, x)**

We just change the sign of y-coordinate and switch the 2 coordinates

From the given figure we can see

The coordinates of point **P are (4, 2)**

Since the triangle will rotate around the origin by 90 degrees counterclockwise

Then **change the sign of the y-coordinate to be -2**, and **switch x and y coordinates**

The image of P is P', then

**P' = (-2, 4)**

**The answers are**

**P = (4, 2)**

**P' = (-2, 4)**

23. ABCD is a rectangle. If m21-5x and m22 - 8x -1, find x, m<1, and m<2.ABEDm

### Answers

If ABCD is a rectangle, each of its four angles at the vertex is a right angle.

Then the angle at D is a right angle (measure of 90 degrees).

The right angle is divided in two angles, <1 and <2, by the diagonal, so <1 and <2 are complementary.

Then, we can write:

[tex]\begin{gathered} m\angle D=m\angle1+m\angle2=90\degree \\ (5x)+(8x-1)=90 \\ 13x-1=90 \\ 13x=90+1 \\ 13x=91 \\ x=\frac{91}{13} \\ x=7 \end{gathered}[/tex]

Then, with the value of x we can calculate m<1 and m<2:

[tex]\begin{gathered} m\angle1=5x=5\cdot7=35\degree \\ m\angle2=8x-1=8\cdot7-1=56-1=55\degree \end{gathered}[/tex]

**Answer:**

**x = 7**

**m<1 = 35º**

**m<2 = 55º**

Hi tutor, Please explain the connection between the derivative of a constant, and the slope of a tangent, of a function.If possible, can you please use a diagram too to help explain? , I just needed clarification on whether the answer is that they’re both zero or otherwise

### Answers

The derivative of a constant is zero

, the only condition to have a slope of zero is when the function is a constant and a constant function has no tangent.

**Hence, the answer is Otherwise.**

A boat is heading towards a lighthouse who’s beacon-light is 132 feet above the water. the boat’s crew Measure the angle of elevation to the beacon, 5 degrees. what is the ships horizontal distance from the lighthouse and the shore? round your answer to the nearest tenth of a foot

### Answers

The right angle triangle representing this scenario is shown below

A represents the beacon light

AB is the ship'e horizontal distance from the lighthouse

Taking angle A which is the angle of elevation as the reference angle,

opposite side = BC = 132

adjacent side = AB

To find AB, we would apply the tangent trigonomeric ratio which is expressed as

Tan # = opposite side/adjacent side

Therefore,

Tan 5 = 132/AB

ABtan5 = 132

AB = 132/tan5

AB = 1508.8

**The ship's horizontal distance from the lighthouse and the shore is 1508.8 feet**

Toby eats tacos every 5 days. Toby also drinks horchata every 6 days. If Toby has horchata and tacos today how many days will he have too wait to enjoy his favorite treats on the same day again?

### Answers

We are given the following information

Toby eats tacos every **5 days**.

Toby also drinks horchata every **6 days**.

If Toby has horchata and tacos today how many days will he have to wait to enjoy his favorite treats on the same day again?

We need to find the least common multiple (LCM) of 5 and 6 days.

Multiples of 5 = 5, 10, 15, 20, 25, **30**

Multiples of 6 = 6, 12, 18, 24, **30**

As you can see, the least common multiple (LCM) of 5 and 6 is **30**

Therefore, Toby has to wait for **30 days **to enjoy his favorite treats on the same day again.

which numbers of stars and total points could be used as the missing values in a table

### Answers

First, we find the constant of proportionality

[tex]k=\frac{y_2-y_1_{}}{x_2-x_1}[/tex]

Let's replace the points (8,12) and (10,15).

[tex]k=\frac{15-12}{10-8}=\frac{3}{2}=1.5[/tex]

This means that 1 star is equivalent to 1.5 total points.

So, observe that 2 stars get 3 total points. 16 stars get 24 points. And, 12 stars get 18 points.

Hence, A, C, and D are correct.

Review the equation, then complete the following. f(x) = 2x + 5 , g(x) = (2 - 5)/2 1. Graph the functions f(x) and g(x) on the same coordinate plane. You may use technology to create the graph of the functions or submit a handwritten graph. 2 In two or more complete sentences, explain how to use the graphs of f(x) and g(x) to prove that the functions are Inverses of each other.

### Answers

**See graph and explanation below**

Explanation:

[tex]\begin{gathered} f\mleft(x\mright)=2x-5 \\ g\mleft(x\mright)\text{ = }\frac{x\text{ - 5}}{2} \end{gathered}[/tex]

**Plotting both graphs:**

To prove the functions are inverse of each other:

At any coordinate, the value of x (input) of one function is the the value of y (output ) of the second function and vice versa. The value of x (input) of second function is the the value of y (output ) of the First function.

**for f(x): when x = -2.5, y = 0**

**for g(x): when x = 0, y = -2.5**

**for f(x): when x = 0, y = 5**

**for g(x): when x = 5, y = 0**

what is the equation in standard form y= -3x - 4

### Answers

**The standard form of equation of a line is expressed as y = mx+c** where;

m is the slope of the line

c is the intercept

Given the equation of the line y = -3x - 4

you can see that the equation given is already in its standard form with -3 as the slope and -4 a the intercept.

**Hence the standard form of the equation is still ****y = -3x - 4**

3) y = 3x+1 A) Domain: x 2-1 Range: y so B) Domain: x 2-1 Range: y20 C) Domain: x 21 Range: y = 0 D) Domain: { All real numbers. Range: {All real numbers.

### Answers

Given:

[tex]y=\sqrt[]{x+1}[/tex]

Let's determine the domain and the range of the function.

The domain is the set of all possible values of x. It is also called the input.

The range is the set of possible values of y. It is also called the output.

• To find the domain, set the values in the radicand greater than or equal to zero and solve for x:

x + 1 ≥ 0

Subtract both sides by 1:

x + 1 - 1 ≥ 0 - 1

x ≥ -1

**Therefore, the domain is all possible values greater or equal to -1:**

** x ≥ -1**

To find the range, input the lowest value of the domain which is -1 and evaluate for y:

[tex]\begin{gathered} y\ge\sqrt[]{-1+1} \\ \\ y\ge\sqrt[]{0} \\ \\ y\ge0 \end{gathered}[/tex]

Therefore, the range of the function is all integers positive interges including zero.

The graph is attached below:

**ANSWER:**

**C) Domain: x ≥ -1**

** Range: y ≥ 0**

What is the value of the expression 268.75 2.5

### Answers

[tex]\frac{268.75}{2.5}=107.5[/tex]

Given the point A (-8 , 1) and point B (-2 , 4), find the following.A. Find the slope of line ABB. Write the equation of a line in point-slope form for ABC. Write the equation of a line in slope-intercept form for AB

### Answers

First, find the slope (m):

Apply the formula:

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

Given the points:

(x1,y1) = (-8,1)

(x2,y2)= (-2.4)

m= 4-1 / -2-(-8) = 3 / 6 =** 1/2**

Slope intercept form:

y=mx+b

Where:

m= slope = 1/2

b= y-intercept

So far:

y = 1/2x + b

Replace (x,y) with any point , for example (-8,1), and solve for b

1 = 1/2 (-8) + b

1 = -4 + b

1+4= b

b= 5

Slope intercept form:

**y= 1/2x + 5**

point slope form:

y-y1 = m ( x- x1 )

**y- 1 = m ( x + 8 ) **

Evaluate 4x^2 – 3xy if x=-3 and y=-2

### Answers

We have the following:

[tex]4x^2-3xy[/tex]

replacing, x=-3 and y=-2:

[tex]\begin{gathered} 4\cdot(-3)^2-3\cdot(-3)\cdot(-2) \\ 4\cdot9-18 \\ 36-18=18 \end{gathered}[/tex]

The answer is 18.

In this figure above, line l is parallel to m, segment BD is perpendicular to line m, and segment AC and segment BD intersect at E. What is the length of segment AC?

### Answers

step 1

In the right triangle ADE

Apply Pythagorean Theorem

Find AE

AE^2=AD^2+DE^2

substitute the given values

AE^2=12^2+5^2

AE^2=169

AE=13 units

step 2

In this problem triangle ADE and triangle CBE are similar

that means ----> the ratio of its corresponding sides is proportional

so

AE/EC=DE/EB

substitute the given values

13/EC=5/1

EC=13/5

EC=2.6 units

step 3

Find AC

AC=AE+EC

AC=13+2.6=15.6 units

therefore'

AC=15.6 units

Justin’s Local Market has the freshest watermelons. The cost is determined based on the number of pounds purchased which is detailed in the table below.

### Answers

**Answer:**

**1.4 $/pound**

**Explanation:**

The rate of change of the cost of water melon is expressed as;

Rate of change = C2-C1/p2-p1

Using the coordinates (C, p)

(0,0) and (0.35, 0.25)

Rate of change = 0.35-0/0.25-0

Rate of change = 0.35/0.25

Rate of change = 1.4 $/pound

**Hence the rate of change of watermelon is 1.4 $/pound**

the pitch of the roof is its slope. find the pitch.

### Answers

Let's draw a rough drawing of what's needed to be solved.

*x* is the pitch of the roof and we need to solve for x.

This is a right triangle so we can use the Pythgaorean Theorem to solve it.

It states that in a right triangle, the Sum of the Squares of its legs is equal to the square of its Hypotenuse.

The hypotenuse is x

The legs are 16 and 14

Thus, we can write:

[tex]\begin{gathered} x^2=14^2+16^2 \\ x^2=452 \\ x=\sqrt[]{452} \\ x=\sqrt[]{4}\sqrt[]{113} \\ x=2\sqrt[]{113} \end{gathered}[/tex]

Which angles are vertical angles and, therefore, congruent? de A\B EF C/D G H O ZA and ZD O ZA and ZG O ZA and ZE O ZA and ZF

### Answers

The vewrtical angles are < A and < D

Write the fraction as a percent. Round to the nearest tenth of a percent if necessary.7/11A) 63.6%B) 57.8%C) 6.4%D) 110%

### Answers

To express a fraction as a percent, divide the numerator by the denominator, then multiply by 100.

7 / 11 = 0.636

0.636 x 100 = 63.6 %

**Answer:**

**A) 63.6 %**

If the length and width of a rectangle each change by a factor of nine, what happens to the area of the rectangle?

### Answers

Answer:

The area of the rectangle changes by the factor of

[tex]9^2[/tex]

Explanation:

Let** l** and **w** represent the length and width of the rectangle respectively.

The area is

** A = lw**

If these change by a factor of nine, then we have:

**9l** and** 9w**

The area, which is the product of the length and width becomes:

[tex]\begin{gathered} A=9l\times9w \\ =9^2lw \\ =9^2A \end{gathered}[/tex]

Find the sale price when the original price is $64.00 and the discount rate is 12%.

### Answers

SOLUTION:

Step 1:

In this question, we are given the following:

Find the sale price when the original price is $64.00

and the discount rate is 12%.

Step 2:

Recall that the discount rate is 12% and the original price is $ 64.00

Then, we have that:

[tex]\begin{gathered} 12\text{ \% of \$ 64.00} \\ =\frac{12}{100}X\text{ \$ 64.00} \\ =\frac{768}{100} \\ Discount=\text{ \$ 7.68} \end{gathered}[/tex]

Next,

We need to find the sale price =

[tex]\begin{gathered} \text{Original price - Discount price} \\ =\text{ \$ 64.00 - \$ 7. 68} \\ =\text{ \$ 56.32} \end{gathered}[/tex]

If three tacos and two drinks cost $13.00, and four tacos and one drink costs $15.25, how much does a taco cost?

### Answers

**Answer: 3.5**

**Step-by-step explanation:**

**3x+2y=13**

**4x+y=15.25**

**System of equations**

**I solved using elimination but there are other methods**

**3x+2y=13**

**-8x-2y=-30.5**

**The y cancels out**

**3x=13**

**-8x=-30.5**

**=**

**-5x= -17.5**

**Solve**

**x=3.5**

**Answer:**

$3.50

**Step-by-step explanation:**

Which of the following option represent the measure of arc ra?

### Answers

Explanation:

An arc measure is an angle the arc makes at the center of a circle

From the given question, we will have to apply the intersecting chord theorem

If two chords intersect in the interior of a circle, then the measure of each angle is one half the sum of the

measures of the arcs intercepted by the angle and its vertical angle.

[tex]\begin{gathered} In\text{ our case} \\ m

Thus

[tex]\begin{gathered} 71.4=\frac{1}{2}(65.6^0+mRA) \\ \\ mRA=2\times71.4-65.6^0 \\ mRA=77.2^0 \end{gathered}[/tex]

Thus, the answer is **77.2** degrees

use the multiplication equality to solve for the unknown. A video game system and several games are sold for 632.dollar . The cost of the games is 3 times as much as the cost of the system. Find the cost of the system and the cost of the game

### Answers

The multiplication property of equality states that when we multiply both sides of an equation by the same number, the two sides remain equal.

We have that the videogame system and games cost $632. And the cost of the games is 3 times as much as the cost of the system. Then we have the following expressions:

[tex]\begin{gathered} VS+G=632 \\ G=3\cdot VS \end{gathered}[/tex]

Where, VS = Videogame system and G = games.

We plug in 3*VS in the first equation to get:

[tex]VS+3\cdot VS=632[/tex]

And we solve for VS, to find the cost of the videogame system:

[tex]4\cdot VS=632[/tex]

We use the multiplication property of equality here, and multiply both sides of the equation by 1/4:

[tex]\begin{gathered} 4\cdot VS\cdot\frac{1}{4}=632\cdot\frac{1}{4} \\ VS=158 \end{gathered}[/tex]

**The cost of the videogame system is $158**. Now we can find the cost of the games, replacing VS in the first equation:

[tex]\begin{gathered} VS+G=632 \\ 158+G=632 \\ G=632-158=474 \end{gathered}[/tex]

**Games cost $474.**

I'm not sure what I suppose to being doing, I don't understand it. I know it has something to do with the rectangle box above the number lines, but I'm having problems tbhnm

### Answers

SOLUTION:

Step 1:

In this question, we are given the following:

**Step 2:**

**The details of the solution are as follows:**

Sample size: 12

Median: 66

Minimum: 60

Maximum: 70

First quartile: 63.5

Third quartile: 67.5

Interquartile Range: 4

Outliers: none

Please can someone help me with this 2 part question

### Answers

Solution

Step 1:

Write the matrix:

[tex]\begin{gathered} X\text{ = }\begin{bmatrix}{6} & {a} \\ {-2} & {-5}\end{bmatrix} \\ I\text{ = }\begin{bmatrix}{1} & {0} \\ {0} & {1}\end{bmatrix} \end{gathered}[/tex]

Step 2:

Find the inverse of X.

[tex]X^{-1}\text{ = }\frac{Adjoint}{Determinant}[/tex]

Step 3:

Find the determinant

[tex]\begin{gathered} Determinant\text{ of X = }\begin{bmatrix}{6} & {a} \\ {-2} & {-5}\end{bmatrix} \\ Co-factor\text{ of X = }\begin{bmatrix}{-5} & {2} \\ {-a} & {6}\end{bmatrix} \\ Adjoint\text{ is the transpose of the co-factor of X} \\ Adj\text{oint = }\begin{bmatrix}{-5} & {-a} \\ {2} & {6}\end{bmatrix} \\ Deterninant\text{ = 2a - 30} \end{gathered}[/tex]

Step 4:

[tex]\begin{gathered} X\text{ - }X^{-1}\text{ = I} \\ \\ \begin{bmatrix}{6} & {a} \\ {-2} & {-5}\end{bmatrix}\text{ - }\frac{\begin{bmatrix}{-5} & {-a} \\ {2} & {6}\end{bmatrix}}{2a\text{ - 30}}\text{ = }\begin{bmatrix}{1} & {0} \\ {0} & {1}\end{bmatrix} \\ \begin{bmatrix}{6} & {a} \\ {-2} & {-5}\end{bmatrix}\text{ - }\begin{bmatrix}{\frac{-5}{2a-30}} & {\frac{-a}{2a-30}} \\ {\frac{2}{2a-30}} & {\frac{6}{2a-30}}\end{bmatrix}\text{= }\begin{bmatrix}{1} & {0} \\ {0} & {1}\end{bmatrix} \\ \begin{bmatrix}{6\text{ + }\frac{5}{2a-30}} & {a\text{ + }\frac{a}{2a\text{ - 30}}} \\ {-2\text{ -}\frac{2}{2a\text{ - 30}}} & {-5-\text{ }\frac{6}{2a\text{ - 30}}}\end{bmatrix}\text{ = }\begin{bmatrix}{1} & {0} \\ {0} & {1}\end{bmatrix} \end{gathered}[/tex]

Step 5;

Write equations

[tex]\begin{gathered} \text{ 6 + }\frac{5}{2a\text{ - 30 }}\text{ = 1} \\ \frac{6(2a\text{ - 30\rparen + 5}}{2a\text{ - 30}}\text{ = 1} \\ \frac{6(2a\text{ -30\rparen + 5}}{2a\text{ - 30}}\text{ = 1} \\ 12a\text{ - 180 + 5 = 2a - 30} \\ 12a\text{ - 2a = 175 - 30} \\ 10a\text{ = 145} \\ \text{a = }\frac{145}{10} \\ \text{a = }\frac{29}{2} \end{gathered}[/tex]

Final answer

[tex]\begin{gathered} i)\text{ }X^{-1}\text{ = }\frac{1}{2a\text{ - 30}}\begin{bmatrix}{-5} & {-a} \\ {2} & {6}\end{bmatrix} \\ ii)\text{ }a\text{ = }\frac{29}{2}\text{ or 14.5} \end{gathered}[/tex]

Sadie invested $89,000 in an account paying an interest rate of 9 5/8% compounded daily. Robert invested $89,000 in an account paying an interest rate of 10 1/4% compounded monthly. After 16 years, how much more money would Robert have in his account than Sadie, to the nearest dollar?

### Answers

Robert will have $40,561.53 **more **than Sadie.

**What is Compound Interest?**

**Compound interest**, also called "compounding interest," is the interest on the initial **investment **as well as the accrued interest on that **investment**.

Given that Sadie and Robert **invested **$89000 on different rates 77/8% and 41/4% respectively.

Formula for CI = P( 1 + \dfrac{r}{n}^{nt} )

Using this, we get Sadie's total **amount **= $415,064.26 and Robert's total **amount **= $455,625.79

Hence, Robert will have $40,561.53 **more **than Sadie.

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write a compound inequality for each solution 1. students are to present a persuasive speech in English class. the guidelines state that the speech must be at least 7 minutes but not to exceed 12 minutes.2. children and senior citizens receive a discount on tickets at the movie theater. to receive a discount, a person must be under 10 years old, or 65 years or older.3. the scores on the last estranged from 65% to 100%

### Answers

Let x represent the number of minutes.

The guidelines state that the speech must be at least 7 minutes but not to exceed 12 minutes. This means that x must be greater than or equal to 7 minutes but x must be lesser than or equal to 12 minutes.

The representation would be

[tex]\begin{gathered} x\text{ }\ge7\text{ } \\ x\text{ }\leq12 \\ The\text{ compound inequatity would be} \\ 7\text{ }\leq x\leq12 \end{gathered}[/tex]

the table above gives the annual ales (in billions of dollars) of Pepsico, which operates two major businesses: beverages (including Pepsi) and snack foods. The table shows Pepsico ales in billions of dollars for the 11 years.A) What was the change of annual ales between the first year, 2010, and the 2015 year?B) What is the average rate of change in sales for the 2015 years beginning in 2010?billion dollars per year

### Answers

**Answer:**

**A) 5.92 billion dollars**

**B) 1.184 billion dollars per year**

**Explanation:**

Part A)

The change in annual sales between 2010 and 2015 is calculated as the difference between the sales of 2015 and 2010. So, taking into account the table, we get:

59.42 - 53.5 = 5.92 billions of dollars

Because 59.42 billion are sales in 2015 and 53.5 billion are sales in 2010.

Therefore, the answer is 5.92 billion dollars

Part B)

The average rate of changes in sales from 2010 to 2015 is equal to the change in the annual sales divided by the number of years, so it is calculated as

[tex]\frac{59.42-53.5}{2015-2010}=\frac{5.92}{5}=1.184[/tex]

Therefore, the average rate of change is 1.184 billion dollars per year.

A company is selling toothpicks. It costs $0.03 to produce each toothpick and a fixed cost of $100 a month for the company. If the company is selling toothpicks for $0.05 each, how many toothpicks must they sell a month in order to break-even?

### Answers

5,000 toothpicks must be sold in order to **break even**.

How many toothpicks sell?

Numerous aspects of business and finance make use of **break-even points**. It is the production level where total production revenue and total production costs are equal in accounting terms. The break-even point in investing is the point at which the purchase price is equal to the market price.

Here, let's assume that m toothpicks must be sold to break even = m

So, for m toothpicks, Total cost = Total Earnings

Currently, the price to produce 1 toothpick is $0.03

So, cost of production of m toothpicks = m x ( cost of 1 toothpick)

= $(0.03 m)

Also, fixed month cost = $100

So, Total cost of production = $100 + $0.03 m .... (1)

Again, the selling cost of 1 toothpick = $0.05

So, selling cost of m toothpicks = m ( cost of 1 toothpick) = $(0.05 m) ..(2)

From (1) and (2)

100 + 0.03 m = (0.05 m)

⇒ 100 = 0.02 m

or, m = 100/0.02

⇒ m = 5000

Therefore 5,000 **toothpicks **must be sold in order to break even.

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Aaron is buying some fruit at grocery store the score reads 4 3/4 pounds what is the decimal equivalent of this mixed number Anticipated consumer demand in a restaurant for free-range steaks next month can be modeled by a normal random variable with mean of 1,000 pounds and a standard deviation of 110 pounds. a. what is the probability that demand will exceed 800 pounds? b. what is the probability that demand will be between 900 and 1,100 pounds? c. the probability is 0.15 that demand will be more than how many pounds? To determine the number of deer in a game preserve, a conservationist catches450 deer, tags them and lets them loose. Later, 494 deer are caught; 247 of themare tagged. How many deer are in the preserve? _____ deer are in the preserve The polynomial P(x) = 5x^3 + 2x^2 - 4x has ____ local maxima and minima a compound is found to be 51.38% carbon, 8.64% hydrogen, and 39.97% nitrogen. it has a molecular molar mass of 140,22 g/mol 1. How many hours is 3,500 minutes? (Remember your answer need to have the correct amount of significant figures and the correct units written).2. Two-Step Conversion:How many grams is 45.0 lbs? (Remember your answer need to have the correct amount of significant figures and the correct units written).(1 Kg = 2.2 lbs)3. Three-Step Conversion:How many cm is 4.0 mi? (Remember your answer need to have the correct amount of significant figures and the correct units written).(1 mi = 5280 ft, 1 in=2.54 cm) (hint: cm -> in -> ft -> mi) an electrician charges a set field for every house call and then charges an hourly rate depending on how long the job take let C represent the total cost of the visit when the electrician spent T hours at the house working. A graph of C is shown below. Write an equation for C then State the slope of the graph and determine its interpretation in the context of the problem Find the slope-intercept form of the line that passes through the point (3, -6) and is parallel tothe line 4x-2y = -3. find the slope of the lineI really need help with these two What is the x-intercept of: 3y+x=6? Find the probability of getting 6 or more girls in 8 births. What are the coordinates of the midpoint of AB?- 1](-1,-)(--) Write the equation of the line that passes through the given points: (1, -2); (- 3,7) (Hint: use the formula m = (y_2-y_1) / (x_2-x_1), y = mx + b)a) Y= 1x-2 b) y=-3x+7 c) y= - 9/4 x+ 1/4Escriba la ecuacin de la lnea que pasa por los puntos dado: (1,-2) ;(-3,7) (Sugerencia: usar la formula m=(y_2-y_1)/(x_2-x_1 ) , y=mx +b) a) Y= 1x-2 b) y=-3x+7 c) y= - 9/4 x+ 1/4 What are at least 3 ways that the united states imposes its will in other countries around the world. Purple hibiscusChapter 10Page. 188ff: (ff= and following pages) What happens when Papa arrives? Whats his reaction? Whats his first question? How does Ifeoma react? Question Help please!To find simple interest, you multiply the principal (in dollars), the interest rate (as a decimal), andthe time in years. The equation 24 = 400.0.0154 shows how to find the simple interest for acertain account after 4 years. What is the interest rate (as a percent)? How much is the simpleinterest? What is the principal?What is the interest rate (as a percent)?OA. 24%OB. 1.5%OC. 400%OD. 0.015%Click to select your answer and then click Check Answer.Clear AllCheck And2 pansremainingQuestion 2Review progressBackof 9Next which of the following represents the difference of the polynomial below? (x^4+8x^3+9x^2)-(5x^4+4x^3+2x^2)A. 5x^4+12x^3+11x^2B.-4x^4+12x^3+11x^2C.4x^4+4x^3+7x^2D.-4x^4+4x^3+7x^2 You bought 7 pencils for $2.45. Your friend bought 9 pencils for $3.15. Write an equation in POINT-SLOPE Form to model the total bill (y) in terms of the number of pencils purchased (x). The regression equation y=-0.428x+111.73 approximates the percent of people in anaudience who finish watching a documentary, y, given the length of the film inminutes, x.What is the best prediction for the percent of people in an audience who will finishwatching a documentary that is 47 minutes long? (Round your answer to thehundredths place) Give the center and radius in each of the following circles.Circle a