If you pay the credit card company 292.68 each month in order to pay off your credit card, and it takes you 51 months to pay it off, what is the total cost of the credit card loan?​

For the given polynomial function,

f(x) = (x + 2)² (x - 4) (x + 1)

The roots of f(x) is -2 with multiplicity 2 , 4 with multiplicity 1 and -1 with multiplicity 1.

So, correct option is option(A).

Roots of a polynomial is defined as the values of a variable(i.e x) for which the given polynomial is equal to zero. If "a" is the root of the polynomial q(x), then q(a) = 0.

We have given that,

f(x) = (x + 2)² (x - 4) (x + 1)

we have find out all roots of f(x) .

The roots of polynomial function are the values of x which gives f(x) = 0 so,

( x + 2)²(x - 4) (x + 1) = 0

product of three factors equal to zero implies that either one , two or all are equal to zero

mathematically, ( x+2)² = 0 or (x - 4) = 0 or

(x + 1)=0

Now, ( x+2)² = 0 gives x= -2 with multiplicity 2 because power of factor 2 .

similarly, (x - 4) = 0 , gives x = 4 with multiplicity 1

(x + 1) = 0 => x = -1 with multiplicity 1

So, we got all the three roots of given f(x) i.e -2, 4, -1..

To learn more about Roots of polynomial function, refer:

https://brainly.com/question/2833285

#SPJ4

Complete question:

Which of the following describes the roots of the polynomial function f(x) = (x + 2)^2 (x - 4) (x + 1)?

a) -2 with multiplicity 2, 4 with multiplicity 1, -1 with multiplicity 1,

b)-2 with multiplicity 3, 4 with multiplicity 2, and -1 with multiplicity 1

c) 2 with multiplicity 2, -4 with multiplicity 1, and 1 with multiplicity 1

d)2 with multiplicity 3, -4 with multiplicity 2, and 1 with multiplicity 4

Based on the information given, we can conclude that RM = 2, but we cannot determine the lengths of the other sides of the quadrilaterals without further information.

Given that quadrilateral YFGT can be mapped onto quadrilateral MKNR by a translation, we can use the information to determine the length of RM.

A translation is a transformation that moves every point of a figure by the same distance and in the same direction. In this case, the translation is such that the corresponding sides of the quadrilaterals are parallel.

Since TY = 2, and the translation moves every point by the same distance, we can conclude that the distance between the corresponding points R and M is also 2 units.

Therefore, RM = 2.

By the properties of a translation, corresponding sides of the two quadrilaterals are congruent. Hence, side YG of quadrilateral YFGT is congruent to side MK of quadrilateral MKNR, and side GT is congruent to NR. However, the given information does not provide any additional details or measurements to determine the lengths of these sides.

For more such questions on quadrilaterals

https://brainly.com/question/27991573

#SPJ8

PA BRAINLIEST

The fare for a 500-mile trip is 164.

The equation provided in the question is known as a linear equation. A linear equation is an equation that has a single variable that is raised to the power of one.

The general form of a linear equation is:

y = mx + b

Where:

In the equation used to calculate the fare, y=0.28x+24, 0.28 is the variable cost and 24 is the fixed cost.

Cost of a 500-mile trip = y=0.28(500) +24

y = 140 + 24

y = 164

To learn more about linear functions, please check: https://brainly.com/question/26434260

#SPJ1

The function f(x) = sin⁻¹x, x ≠ π/4 and sinx, x = π/4 is continuous on[-1, π/4) ∪ (π/4, 1]. There is a removable discontinuity at x = π/4

A function is said to be continuous if there are no breaks or jumps in the functions

Conditions for continuity of a function

Now, for the given function f(x) = sin⁻¹x, x ≠ π/4 and sinx, x = π/4

We need to determine the interval of continuity, We proceed as follows.

Since f(x) = sin⁻¹x, x ≠ π/4 , we know that the minimum value of x is - 1 and its maximum value is 1.

So, x must lie in the interval (-1, 1) for x ≠ π/4,

Now, when x = π/4 f(x) = sinx. We know that x = π/4 lies in the interval (-1, 1).

But we know that f(x) = sinx at x = π/4. So, there is a removable discontinuity at x = π/4.

So, from the left, f(x) is continuous on the interval [-1, π/4) and  from the right, f(x) is continuous on the interval (π/4, 1]

So, combining both intervals, we have f(x) is continous on the interval [-1, π/4) ∪ (π/4, 1] and since f(x) = sinx at x = π/4, there is a removable discontinuity at x = π/4

So, the function f(x) is continuous on[-1, π/4) ∪ (π/4, 1]. There is a removable discontinuity at x = π/4

Learn more about continuity of a function here:

https://brainly.com/question/28830920

#SPJ1

Answer:

$70.31

Step-by-step explanation:

Hope this helps

Answer:

$117.19

Step-by-step explanation:

93.75 * .25 =23.4375

23.4375+93.75 = $117.1875

(rounded:$117.19)

Here is the graph for this solution

Answer:

C & D

Step-by-step explanation:

A. p = 29

B. p= 29

C. p = 0

D. p = 0

E. p = 29

________

Answer:

Let x be the number of additional outfits.

5 + x < 11

Answer:

The lines of symmetry in the wheel is infinite.

Explanation:

Since there are an infinite number of lines through the center, a circle has an infinite number of lines of symmetry.

Answer:

c

Step-by-step explanation:

Answer:

A. Yes, the points have no pattern.

Step-by-step explanation:

just did it on edge and got 100%

The definite integral which represents the area of the region in the fourth quadrant enclosed by r = 10 - cos is A = 210π - 80/8

Given:

the area of the region in the fourth quadrant enclosed by r = 10 - cos

we know that:

A = (limit a to b)∫ r²/2 dθ

we know that area of first quadrant = area of fourth quadrant (by symmetry)

A = (limit θ=0 to π/2)∫ (1-cosθ)²/2 dθ

= (limit θ=3π/2 to 2π)∫ (1-cosθ)²/2 dθ

A = 1/2(limit 0 to π/2)∫ (100 - 20cosθ + cos²θ)dθ

A = 1/2 (limit 0 to π/2)∫ (100 - 20cosθ + 1/2 + cos2θ/2)dθ

= 1/2 (limit 0 to π/2) ∫ (201/2 - 20cosθ + cos2θ/2)dθ

= 1/2 ( 201/2 θ- 20sinθ + sin2θ/4) limit π/2 to 0

= 1/2 ( 201π/4 - 20 + 0)

= 1/2 ( 210π - 80/4)

Hence we get the required answer.

Learn more about Definite Integral here:

brainly.com/question/22008756

#SPJ4

Answer:

To find f(-8), we need to substitute -8 for x in the expression for f(x) and evaluate:

f(-8) = 3(-8)² + 9(-8) - 16

Simplifying this expression, we get:

f(-8) = 3(64) - 72 - 16

f(-8) = 192 - 72 - 16

f(-8) = 104

Therefore, f(-8) = 104 when f(x) = 3x² + 9x - 16.

Learn more about Graphing Functions here:

https://brainly.com/question/23945486

#SPJ5

Based on the constant first differences and the zero second differences, we can conclude that the given relation is linear.

To determine if the given relation is linear or quadratic, we can examine the finite differences of the y-values.

First differences:

The first differences are calculated by subtracting each consecutive y-value:

6 - 8 = -2

4 - 6 = -2

2 - 4 = -2

0 - 2 = -2

-2 - 0 = -2

-4 - (-2) = -2

Since the first differences are constant (-2), it suggests that the relation could be linear.

Second differences:

The second differences are calculated by taking the difference between consecutive first differences:

-2 - (-2) = 0

-2 - (-2) = 0

-2 - (-2) = 0

-2 - (-2) = 0

The second differences are all zero, indicating that the relation is not quadratic.

In a quadratic relation, the second differences would be constant.

Hence, based on the constant first differences and the zero second differences, we can conclude that the given relation is linear.

To learn more on Linear Equation:

https://brainly.com/question/10413253

#SPJ1

Answer:

\(\dfrac{240}{4} =60\)

\(\dfrac{1800}{3}=600\)

Step-by-step explanation:

1.  The result should by a 2 digit number.

So, I fix a two digit number first, say 60.

Then, I multiplied it by some random integer, say 4 and got 240.

Now, 240 is my dividend and 4 is my divisor.

My division problem is:

\(\dfrac{240}{4} =60\)

2.  The result should be a 3 digit number.

So, I fix a three digit number first, say 600.

Then, I multiplied it by some random integer, say 3 and got 1800.

Now, 1800 is my dividend and 3 is my divisor.

My division problem is:

\(\dfrac{1800}{3}=600\)

The central angle measure, x, for the Baseball slice in the circle graph is 50.4 degrees.

Given that, a survey was conducted in which 2400 people were asked to name their favorite sport to watch and the table below shows their answers: Sport percentage of people are:

Football 29%

Soccer 9%

Baseball 14%

Basketball 8%

Hockey 8%

Other 32%

We need to find the central angle measure, x, for the Baseball slice in the circle graph.

For this, we need to use the formula that gives the central angle measure in degrees for a sector of a circle:

Central angle measure = (Percentage/100) × 360°

Now, using the above formula, we can calculate the central angle measure for each sport as shown below:

Football: (29/100) × 360° = 104.4°

Soccer: (9/100) × 360° = 32.4°

Baseball: (14/100) × 360° = 50.4°

Basketball: (8/100) × 360° = 28.8°

Hockey: (8/100) × 360° = 28.8°

Other: (32/100) × 360° = 115.2°

The sum of all central angle measures should be 360°, which is the measure of a full circle.

So we can check if the calculations are correct: 104.4° + 32.4° + 50.4° + 28.8° + 28.8° + 115.2° = 360°

We see that the sum is indeed 360°, so the calculations are correct. The central angle measure for the Baseball slice is 50.4°.

Therefore, the central angle measure, x, for the Baseball slice in the circle graph is 50.4 degrees.

For more such questions on central angle, click on:

https://brainly.com/question/10945528

#SPJ8

The tangent of the smaller acute angle in a right triangle is tanФ = 0.42.

We know a right-angled triangle has three sides they are -: Hypotenuse,

Opposite and Adjacent.

We can remember SOH CAH TOA which is,

sin = opposite/hypotenuse, cos = adjecen/hypotenuse and

tan = opposite/adjacent.

Given, A right triangle with side lengths 5, 12, and 13.

tanФ = 5/12.

tanФ = 0.42.

Ф = tan⁻¹(0.42).

Ф = 22.8°.

learn more about trig ratios here :

https://brainly.com/question/14977354

#SPJ1

The probability Julian chooses a blue hat is 1/3.

Probability refers to the branch of math which deals with finding out the likelihood of the occurrence of an event.

Total hat is:

= 25+20+40+30+25+1

= 150.

There are a total of 150 hats to choose from.

The number of blue hats to choose from is:

= 40 + 10

= 50.

The probability that Julian chooses a blue hat is:

= 50/150

= 1/3

= 0.33 or 33.33%.

Read more about probability

brainly.com/question/24756209

#SPJ1

Garage B is more cost-effective for any parking duration exceeding 2 hours.

When comparing Garage A and Garage B based on their pricing structure, it's important to consider both the flat fee and the hourly rate to determine which option is more cost-effective.

Garage A charges a flat fee of $5, regardless of the duration of parking, and an additional $2 for every hour parked. This pricing structure benefits those who need to park for shorter durations, as the flat fee is relatively low.

However, for longer parking durations, the hourly charge can accumulate significantly, making it less favorable for extended stays.

On the other hand, Garage B follows a different approach by charging a rate of $4.50 per hour with no flat fee. This pricing structure is more suitable for those who require shorter parking times, as they only pay for the exact duration of their stay. In such cases, Garage B would likely be more cost-effective compared to Garage A.

However, for longer stays, Garage A might offer better value. For example, if someone needs to park for 6 hours, Garage A would charge $17 ($5 flat fee + 6 hours * $2/hour) while Garage B would charge $27 ($4.50/hour * 6 hours). In this scenario, Garage A would be the more affordable option.

Ultimately, the choice between Garage A and Garage B depends on the individual's specific parking needs. If the stay is anticipated to be short, Garage B's hourly rate is preferable.

However, for longer durations, Garage A's combination of a flat fee and hourly rate may result in lower overall costs. It's essential to consider the anticipated length of stay to make an informed decision.

For more question on cost visit:

https://brainly.com/question/2292799

#SPJ8

The interest is 16% compounded semi-annually, is Rs. 121,179.10.

To determine how much money needs to be deposited now to provide a payment of Rs. 15,000 at the end of each half year for 10 years, we will use the formula for the present value of an annuity.

Present value of an annuity = (Payment amount x (1 - (1 + r)^-n))/rWhere:r = interest rate per compounding periodn = number of compounding periodsPayment amount = Rs. 15,000n = 10 x 2 = 20 (since there are 2 half years in a year and the payments are made for 10 years)

So, we have:r = 16%/2 = 8% (since the interest is compounded semi-annually)Payment amount = Rs. 15,000Using the above formula, we can calculate the present value of the annuity as follows:

Present value of annuity = (15000 x (1 - (1 + 0.08)^-20))/0.08 = Rs. 121,179.10Therefore, the amount that needs to be deposited now to provide payment of Rs. 15,000 at the end of each half year for 10 years, if the interest is 16% compounded semi-annually, is Rs. 121,179.10.

For more such questions on semi-annually

https://brainly.com/question/30573341

#SPJ8

to be honest i dont know all you said was ratio and some colored rings i dont know what im supposed to to that

Answer:

15:8 or 4:15 or 3:15

Step-by-step explanation:

The slope of the line passing through the points (-6, 1) and (8, -7) is -4/7.

Slope is simply expressed as change in y over the change in x.

Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given the data in the question;

Point A: ( -6,1 )

x₁ = -6

y₁ = 1

Point B: ( 8,-7 )

x₂ = 8

y₂ = -7

Now, plug the given x and y values into the slope formula above and simplify:

\(Slope\ m = \frac{y_2 - y_1}{x_2 - x_1} \\\\Slope\ m = \frac{-7 - 1}{8 - (-6)} \\\\Slope\ m = \frac{-7 - 1}{8 + 6} \\\\Slope\ m = \frac{-8}{14} \\\\Slope\ m = -\frac{4}{7}\)

Therefore, the slope of the line is -4/7.

Learn more about slope formula here: brainly.com/question/24578307

#SPJ1

The equivalent expression of \(\sqrt{\frac{128x^5y^6}{2x^7y^5}}\) is \(\frac{8\sqrt y}{x}\)

The expression is given as:

\(\sqrt{\frac{128x^5y^6}{2x^7y^5}}\)

Divide 128 by 2

\(\sqrt{\frac{64x^5y^6}{x^7y^5}}\)

Apply the law of indices to the variables

\(\sqrt{\frac{64y^{6-5}}{x^{7-5}}}\)

Evaluate the differences

\(\sqrt{\frac{64y}{x^2}}\)

Take the square root of 64

\(8\sqrt{\frac{y}{x^2}}\)

Take the square root of x^2

\(\frac{8\sqrt y}{x}\)

Hence, the equivalent expression of \(\sqrt{\frac{128x^5y^6}{2x^7y^5}}\) is \(\frac{8\sqrt y}{x}\)

Read more about equivalent expression at:

https://brainly.com/question/2972832

#SPJ1

Answer:

Part a [5522.3511 ; 5727.8488]

Part b. The p-value is 0.050115.

The H0 is rejected and concluded that the true mean life of a biomedical device is greater than 5500.

Step-by-step explanation:

The 95 % confidence interval for the mean of the population is given by

∝= 1- 0.95= 0.05

υ= n-1= 15-1= 14

x`± t ∝() s / √n

5625.1 ± { t (0.05) (14)} 226.1 / √15

5625.1 ± 1.76 * 226.1/3.8729

5625.1 ± 102.7488

[5522.3511 ; 5727.8488]

Part b

State the null and the alternate hypothesis

H0: u= 5500  against the claim Ha: u > 5500

the test statistic

t= x`- u/ s/ √n

t= 5625.1-5500/226.1 / √15

t=2.143

The p-value is 0.050115.

The result is not significant at p < 0.05.

The H0 is rejected and concluded that the true mean life of a biomedical device is greater than 5500.

Answer:

She would no reach her goal.

Step-by-step explanation:

Given the triangle ABC, you can identify that the coordinates of its vertices are:

You know that it is reflected over the following line:

Notice that it has the form of a horizontal line. It intersects the y-axis at this point:

Knowing that you can graph the line. See the picture below:

By definition, when a figure is reflected over a line, the points of the Image (the figure obtained after the transformation) and the points of the Pre-Image (the original figure), have the same distance from the line of reflection.

Notice that:

- Point A is 3 units away from the line of reflection.

- Point B is 1 unit away from the line.

- Point C is 3 units away from the line.

See the picture attached:T

Therefore, the points of the Image will have this distance from the line of reflection:

- Point A' will be 3 units away from the line of reflection.

- Point B' will be 1 unit away from the line.

- Point C' will be 3 units away from the line.

Answer:

B.$53,000

Step-by-step explanation:

i hope that helps

The answer choice which sin(x + y) - sin(x - y) simplifies to is; 2(cos x)(sin y).

It follows from the task content that the expression given in the task content can be simplified by trigonometric identities as follows;

sin(x + y) - sin(x - y) = sinxcosy + cosxsiny - (sinxcosy -cosxsiny)

= 2cosxsiny.

Read more on trigonometric identities;

https://brainly.com/question/7331447

#SPJ1

The correct equation to calculate c is (c) 56 + 38 + c = 180

From the question, the given parameter is the triangle

The angles in the triangle are represented as

c, 56 and 38

The sum of angles in a triangle is 180 degrees

Mathematically, this statement can be represented as

Sum of angles in a triangle = 180 degrees

Substitute the known values in the above equation, so, we have the following representation

c + 56 + 38 = 180

Hence, the equation is (c)

Read more about triangles at

https://brainly.com/question/14285697

#SPJ1

The rent per unit should be $8,354.22 to generate a Net Operating Income (NOI) of $100,000, given the vacancy rate and operating expenses.

The operating expenses are costs that must be deducted from the gross operating income to arrive at the net operating income.

The operating expenses do not include some period expenses, which are indirect costs.

                                                                                            Total

Rent per unit (per month) = $696.19 ($8,354.22/12)   $150,376

Vacancy Rate (5% of Potential Gross Income)                   7,519

Effective Gross Income                                                $142,857

Operating Expenses (30% of Effective Gross Income) 42,857

Net Operating Income (NOI)                                      $100,000

Number of Units 18

Gross operating income = net operating income + operating expenses

Operating expenses = 30% of effective gross income

Net operating income = 70% of effective gross income (100 - 30%)

= $100,000

Effective Gross Income (100%) = $142,857 ($100,000 ÷ 70%)

Vacancy rate = 5% of potential gross income

Effective Gross Income = 95% (100 - 5)

Potential gross income = $150,376 ($142,857 ÷ 95%)

Number of units = 18

Rent per unit = $8,354.22 ($150,376/18)

Rent per month = $696.19 ($8,354.22 ÷ 12)

Thus, a rent of $8,354.22 per unit can generate a Net operating income of $100,000.

Learn more about the net operating income at https://brainly.com/question/26206936

#SPJ1