Part 3: Solve a real-world problem using a cube root function.
Once Isabel rented the warehouse space, she decided to post ads on several social media sites to advertise her online bookstore. Let x represent the number of months the ads have been posted. Isabel finds that the function below describes the number of books sold as a function of the number of months her ads have been posted.
f(x) = 1000 + 1000
⦁ How many books were sold after 8 months? (3 points)



⦁ Graph the function. (10 points)

EXPLANATION

Let's see the facts:

Plan A --> $35 + $0.25/minute

Plan B --> $20 + $0.5/minute

Let's call "x" to the number of minutes that a person could talk.

Here we have two equations as follows:

(1) 35 + 0.25x

(2) 20 + 0.5x

Where x represents the number of minutes a person talks on the phone.

We need to equal both equations in order to obtain the same cost.

35 + 0.25x = 20 + 0.5x

Now, we need to solve this equality as shown as follows:

-Subtracting -35 to both sides:

35 + 0.25x -35 = 20 + 0.5x -35

-Adding similar terms:

0.25x = 0.5x - 15

-Subtracting -0.5x to both sides:

0.25x - 0.5x = -15

-Adding similar terms:

-0.25x = -15

-Dividing both sides by -0.25:

x = -15/-0.25

-Simplifying:

x= 60 minutes

So, when a person talks for 60 minutes the cost of both plans is the same.

Answer:

All of them work.

Step-by-step explanation:

An invertible function can be tested for by the horizontal line test. An function is not invertible is a horizontal line drawn anywhere crosses two or more points. A straight line is an invertible function as long as the slope is not equal to 0. With that, let's check A. From x = -6 to -4, the horizontal line test does not cross two points anywhere. A works. Let's check B. B also works because it passes the horizontal line test. C also works.

The area of the square is 16 square inches.

The area of a square is calculated by multiplying a side by itself.

In this case, the side S is replaced by 4 in, then:

Answer:

Step-by-step explanation:

Starting from tan x, you can find sec x, because of the trigonometric identity 1 + tan2 x = sec2 x.

1 + (-4/3)2 = 1 + 16/9 = 25/9 = sec2 x.

So sec x = ±√(25/9) = ±5/3.  But since x is in Quadrant II, sec x has to be negative.  That's because sec x has the same sign as cos x, because sec x = 1 / cos x.  We know that cos x is negative is Quadrant II, therefore so is sec x.  So sec x = -5/3.

Since sec x and cos x are reciprocals of each other, cos x = 1/sec x = -3/5.

Now use the identity sin2 x + cos2 x = 1, to find sin x:

sin2 x + (-3/5)2 = 1

sin2 x + 9/25 = 1

sin2 x = 16/25

sin x = ±4/5

Again, we know that sin x is positive in Quadrant II, so sin x = 4/5.

Now that we know sin x and cos x, we can use the double angle formulas to find sin 2x and cos 2x.

sin 2x = 2 sin x cos x = 2 (4/5) (-3/5) = -24/25

cos 2x = cos2 x - sin 2 x = (-3/5)2 - (4/5)2 = 9/25 - 16/25 = -7/25

Finally use the identity tan x = sin x / cos x to find tan 2x:

tan 2x = sin 2x / cos 2x = (-24/25) / (-7/25) = -24/-7 = 24/7

She cannot afford to buy the car with monthly instalments of $350. She needs to make a downpayment of $856.44 to afford the car

The total amount of the car loan = 13456.44

Number of instalments = 36 monthly payments

Affordable installment per month = $350

EMI: A fixed payment is made by a borrower to a lender at a specific time each month, known as an equated monthly instalment (EMI). The loan is repaid in full over a predetermined period of time by making equal monthly payments to the principal and interest.

Total payment that can be made using the instalments = Monthly instalments * Number of instalments

= 350*36

Total payment that can be made using the instalments = 12600

The amount remaining after paying instalments = 13456.44 - 12600

= 856.44

Downpayment required = $856.44

Learn more about loans:

https://brainly.com/question/11794123

#SPJ1

Answer:

first one is 80

Step-by-step explanation:

i did it

The total area for the parallelogram-shaped tiles Felix needs to buy exists 80cm² at the price of $40.

In calculating the area of a parallelogram, the base exists multiplied by the height, in an exact way as computing the area of a rectangle.

Given that, the base of one parallelogram-shaped tile exists 4cm with a height of 2 cm.

Area of one parallelogram shaped tile = 4cm × 2cm

Area of one parallelogram-shaped tile = 8cm²

Total area for the 5black and 5white tiles = 10 × 8cm²

Total area for the 5black and 5white tiles = 80cm²

Therefore, Felix must buy a total area of 80cm² of 10 parallelogram-shaped tiles.

To learn more about the area of parallelograms refer to:

brainly.com/question/970600

#SPJ2

Answer:

The answer is -23/2 or -11.5

Step-by-step explanation:

h(t) = -16t^2+h^0

object falls untill height becomes 0, so h(t) =0, h^0 = 18.9feet

0 = -16t^2 + 18.9

-18.9= -16t^2

-18.9/-16 = -16t^2/-16

t^2=1.18125

ANSWER= OPTION B

a. The linear Equations :

3x + (x+42)= 90

⇒4x +42 =90

b. ∠ 1 = 36° and ∠2 =54°

Systems of equations can be solved using one of three techniques: graphing, substitution, or elimination. Simply plot the provided equations on a graph and locate the point(s) where they all cross to solve a problem by graphing. You may find the values of the variables you are working for by finding the coordinate of this point.

here

4x+42 = 90 ⇒ x=12

∠1 =4 x 12=36 and ∠2 = 12+42=54

To learn more about :  Linear equation.

Ref : https://brainly.com/question/2030026

#SPJ13

The amount of money should be invested to obtain interest of amount 50000$ is 34,000$(approximately)

The practice of adding interest to the principal amount of a loan or deposit is known as compound interest, sometimes known as interest on principal and interest. Reinvesting interest, or adding it to the lent capital rather than paying it out or seeking repayment from the borrower, results in interest being received on the principal amount plus interest collected previously.

[tex]{\displaystyle A=P\left(1+{\frac {r}{n}}\right)^{nt}}[/tex]

Where,A is the total sum.

P equals the initial principal amount.

The nominal yearly interest rate is r.

The compounding frequency is n.

t is the total amount of time that the interest is charged (expressed using the same time units as r, usually years).

The final value less the beginning investment yields the entire compound interest.

On substituting the values we get that initial investment of approximately 34000$

To learn more about compound interest visit:

https://brainly.com/question/14295570

#SPJ13

The probability of a horse winning a race is

The probability of the horse losing will be calculated as

By substituting the value, we will have

The formula used to calculate the odds of winning is given below as

By substituting the values, we will have

Hence,

The odds of winning = 1 : 24

2=-8-x Equation

x=-10

Explanation

Step 1

the scale is in balance, that indicates that the weights to the right and left are equal

Let

left side=2 squares of 1 each

then

left side=2

Step 2

rigth side=8 times (1) plus -x

rigth side=(8*-1)-x

rigth side=-8-x

Step 3

finally

Step 4

finally solve equation (1) for x

I hope this helps you

As we can see, there are 8 parts in our circle but 4 parts belong to wedge 2 and 5. Then, the probability of landing on 4 or 6 is given by

because part 4 and part 5 are disjoint sets. Since there are 8 parts in our circle, we have

which gives

which corresponds to option B

The tanker has been filling the reservoir for 0.0288 minutes or 1.728 seconds as the rate of filling is 1212 gallons per minute using the estimation concept.

As per the question statement, A tanker truck fills the gas station’s reservoir at the rate of 1212 gallons per minute and the reservoir was empty and it is now 35 gallons full. We are supposed to find out for how long has the tanker been filling the reservoir. We will use the concept of estimation.

Rate of filling gas = 1212 gallons per minute

i.e., 1212 gallon of gas taken 1 minute for transfer.

1 gallon of gas will take = (1/1212) minutes

Hence 35 gallons of gas will take = (1/1212)*35 minutes = 0.0288 min.

So, the  tanker has been filling the reservoir for 0.0288 minutes or 1.728 seconds as the rate of filling is 1212 gallons per minute.

To learn more about Estimation click on the link given below:

https://brainly.com/question/28338974

#SPJ1

Answer:

54 x 5

Step-by-step explanation:

the first figure out the brackets, then multiply by 5.

plss mark me as brainlist

Answer:

the answer is 6 ^ 15 you are very welcom

The cost for 1 liter of premimum gasolinz is 1. 182 times greater

A ratio can be described as the ordered pair of numbers, like x and y, written in the form of a rational numbers, x/y with the denominator greater than zero.

It is also described as the number of times a number or element would contain another one.

It is also known to compare two quantities, elements or numbers.

From the information given, we have that;

To determine the value, we have;

Cost of 1 liter of 25 liters in permimum gasoline/Cost of 1 liter of 25 liters in regular gasoline

substitute the values

$69.73/ $58.98

Find the quotient

1. 182

Hence, the value is 1. 182

Learn more about ratio here:

https://brainly.com/question/2784798

#SPJ1

EXPLANATION

Let's see the facts:

The angles of symmetry in point A is 60 degrees because the plane in point A is divided in 6 parts, so dividing 360° by 6 give us 60°. The same reasoning applies for the point B dividing it by 3 parts.

The angles of symmetry in point B is 120 degrees.

Answer:

The expression is given below as

Concept:

We will have to explain the options so we can figure out what the final answer is

Sum:

The result is obtained by adding numbers

Quotient:

a quotient is a quantity produced by the division of two numbers.

Product:

A product is the result of multiplication,

Factor:

factor, in mathematics, a number or algebraic expression that divides another number or expression evenly—i.e., with no remainder.

Step 1:

We will then have to deal with the parenthesis

We will then have to multiply 7 by 16 before adding to 10

Hence,

7 in the expression above represents a factor because after adding 3 and 13, you would need to multiply 2 and 5. Then, you will multiply 7 and 16 which shows that 7 in the expression above represents a factor. 7 is a factor common to both 3 and 16

Therefore,

The final answer is OPTION A

to find the slope of a line select the two points given.

in this case the point to the left will be (-4,-1) and the one to the right will be (3,1)

use the formula of the slope to calculate

replace the points into the formula

the slope of the line will be 2/7

Answer:

242.

Step-by-step explanation:

Basically, you have to put the 2 numbers "1936" and "8" down. After you put the 2 numbers down, you have to figure out how many times 8 goes into 19 which is 2 times.

You put the 2 above the 1 in 1936. After you put the 2 up there, you have to figure out 2 x 8 which is 16. You have to put the 16 below the 19 and subtract 19 by 16 which is 3.

After you finish that equation, you must bring the 3 down next to the 3 you wrote down on 19 - 16. The number turns into 33 and you have to figure out how many times 8 goes into 33 which is 4 times. You put the 4 next to the 2 above and then do 4 x 8 which is 32. You do 33 - 32 which is 1.

You bring the 6 down in 1936. It turns into a 16. You now have to figure out how many times 8 goes into 16 which is 2 times. You put 2 next to the 2 and the 4 above and that turns the number into 242.

You then have to do 2 x 8 which is 16 and put 16 under the 16 from 33 - 32. That'll make an equation which is 16 - 16 which is 0. There is no remainder and all the numbers were added above so 242 is your answer.

Hopefully, this has helped, tried my best!

=================================

Long Division - Solution and Process    

=================================

We are given the Divisor 8 and the Dividend 1,936.

     242  ← Our Final Solution

8 | 1936

     16

     ___

       33

       32

      ____

          16

           16

            0

The quotient of the given problem would be 242 with a remainder of 0, or simply 242.

Hope this helps!

During a basketball game, you made 11 shots of either 2 or 3 points. You scored a

total of 25 points. How many shots of each point value did you make?

Let

x -----> number of shots of 2 points

y -----> number of shots of 3 points

we have that

x+y=11

x=11-y -----> equation A

and

2x+3y=25 -----> equation B

substitute equation A in equation B

2(11-y)+3y=25

solve for y

22-2y+3y=25

y=25-22

y=3

Find the value of x

x=11-3

x=8

therefore

Answer:

{48, 55,73}

Explanation:

To determine if any three side lengths can form a right triangle, we check if it satisfies the Pythagorean Theorem.

Therefore, the side lengths that could form a right triangle are {48, 55,73}.

You have to find a line perpedicular to the line y=1/2x-3 that passes through the point (-5,2)

Given one line, to find another one perpedicular to it, you have to keep in mind that the slope of the perpedicular line is the negative inverse of the slope of the first one, that is:

Let the given line be:

And the perpendicular line

The slope of the perpendicular line will be:

So for the line

The slope is

For the perpedicular line it will be:

Now that the slope of the perpendicular is determined, use the point slope form to find the equation of the perpedicular line:

Replace the with m=-2 and (-5,2)

The equation perpendicular to

is

Now you can draw both lines:

The length of AC is given by AE + EC

According to the Pythagorean Theorem, we know that:

AE² = AD² - ED²

AE² = 5² - 3²

AE² = 25 - 9

AE² = 16

AE = 4

EC² = DC² + ED²

Since DC = BC, we have:

EC² = BC² + ED²

EC² = 45 - 9

EC² = 36

EC = 6

Therefore, AC = 4 + 6 = 10

Answer: D. 10

Answer:

  (d)  Isosceles right

Step-by-step explanation:

You want to know the classification of a triangle with angles 45°-45°-90°.

The largest angle is 90°, a right angle. Any triangle containing a right angle is a right triangle.

Two of the angles have the same measure. This means the triangle is an isosceles triangle.

The triangle is classified as an isosceles right triangle.

__

Additional comment

A triangle whose largest angle is less than 90° is an acute triangle. If the largest angle is greater than 90°, it is an obtuse triangle.

If no sides are the same length, the triangle is scalene. If two sides are the same length, the triangle is isosceles. If all three sides are the same length, it is an equilateral triangle.

Larger angles are opposite longer sides, so if angles are the same, their opposite sides are the same.

It can be worthwhile to remember that the side length ratios in an isosceles right triangle are 1 : 1 : √2.

Given:

Set U: {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20}

Set P: {2, 3, 5 7, 9, 11, 13, 17, 19}

Questin 7.

Complement of set P.

The complement of set P will be the set that contains the elements present in set U but not in P.

Hence, we have:

ANSWER:

P' = {1, 4, 6, 8, 10, 12, 14, 15, 16, 18, 20}

To make things easier to understand, let's see this figure, which represents the given situation:

According to this diagram, to find x, which is the length of the side of the triangle, we can use pythagorean theorem, this way: