Given the polynomial equation: x^3-7x^2-x+7=0

1. Make a list of possible rational roots

2. Test the possible roots until you find one that produces a reminder of 0. Show your work.

3. Write the resulting quadratic function.

4. Factor or use the quadratic formula to find the final 2 roots.

The simple interest owned for the use of the money is $2625.

What is Simple Interest?

Simple interest is a quick and simple way to figure out how much money has accrued interest. Interest is always applied to the original principal amount and is calculated at the same rate for each period of time. Any bank where we deposit money will pay us interest on that amount. Simple interest is one of many forms of interest that banks charge. Now, let's first clarify what a loan is before delving further into the idea of simple interest. A loan is a sum of money that someone borrows from a bank or other financial institution to cover expenses. Home loans, auto loans, student loans, and personal loans are a few instances of loans.

In the given question we have:

Principal amount  = ​7000$​,

Rate of interest r​ = ​7.5%,

Time t​ =  15 months;

So, applying the formula to calculate simple Interest:

S.I = [tex]\frac{PRT}{100}[/tex]

S.I = [tex]\frac{7000 \times 7.5 \times 15}{ 12 \times 100}[/tex]

S. I =  $2625;

Hence, The Simple Interest owed for the use of the money.  is $ 2625.

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Ji-Min will spend a total of $235.62 to fence or cover the area of the circular window.

What is the area of the a circle?

The area of circle is equal to pi times square of its radius, i.e. πr². To find the area of circle we have to know the radius or diameter of the circle.

Let's find the area of the circle first;

radius = diameter / 2

radius = 5 / 2

radius = 2.5ft

The area of the circle is;

A = πr²

A = π * 5²

A = 25π

A = 78.54ft²

For every square foot, the glass cost $3, this implies that 3 * 78.54 will be the total cost to cover the window.

cost = 3 * 78.54 = $235.62

She will spend $235.62 to fence the window

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If she decides to use double strength glass costing $ 3 per square foot. the total cost for the glass is $58.88.

Given data:

Diameter = 5ft

Glass costing = $3 per square foot

Hence,

Let the radius be 5/2 feet

Area = π × (5/2)²

Area = 25π /4 ft²

So,

Total cost = ( π × 25 /4 × $3)

Total cost = $58.875

Total cost = $58.88

Therefore $58.88 is the total cost.

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The set of side measurements that could be used to form a right triangle is

This gotten by  Pythagoras theorem, with the formula stated as

hypotenuse² = opposite² + adjacent²

plugging the values as in the problem

50² = (√18)² + (√32)²

50² = 18 + 32

50² = 50 - incorrect

(√50)² = 6² + (√14)²

50 = 36 + 14

50 = 50 - correct

20² = 8² + 4²

400 = 64 + 16

400 = 80 - incorrect

6² = 5² + 4²

36 = 25 + 16

36 = 41 - incorrect

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Answer:

[tex] \huge{ \bold{y = - 43x - 25}}[/tex]

Step-by-step explanation:

Equation of a line in slope-intercept form is given by

[tex]y = mx + c[/tex]

where

m is the slope

c is the y intercept

From the question

m = - 43

In order to find c we substitute the point (0,−25) into the equation y = mx + c

That's

[tex] - 25 = - 43(0) + c \\ - 25 = 0 + c \\ c = - 25[/tex]

We now substitute m and c into the equation

We have the final answer as

[tex] \bold{y = - 43x - 25}[/tex]

Hope this helps you

The zeros of the function f(x) = x⁴− x² − 2 are  ±√2 or x = ±i option third positive or negative square root of 2,  ±i is correct.

What is a complex number?

It is defined as the number which can be written as x+iy where x is the real number or real part of the complex number and y is the imaginary part of the complex number and i is the iota which is nothing but a square root of -1.

We have a function:

f(x) =  x⁴− x² − 2

Assume u = x²

f(x) = u² - u - 2

(u + 1)(u - 2)

(x² + 1)(x² - 2)

x² = -1

x = √1

x² = 2

x = √2

x = ±√2  or  x² = -1 ⇒ x = ±i

Thus, the zeros of the function f(x) = x⁴− x² − 2 are  ±√2 or x = ±i option third positive or negative square root of 2,  ±i is correct.

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Answer:

x^25

Step-by-step explanation:

The simplified expression is x²⁵.

Given is an expression (x⁵)⁵, we need to simplify the expression.

To simplify the expression (x⁵)⁵, we need to apply the exponentiation rules.

The exponent outside the parentheses should be distributed to each term inside the parentheses.

In this case, the exponent outside is 5, and the term inside the parentheses is x⁵.

To distribute the exponent, we multiply the exponents together.

Applying the rule, we get:

(x⁵)⁵ = x⁵⁽⁵⁾ = x²⁵

Therefore, the simplified expression is x²⁵.

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Answer:

slope = (1/3)

Step-by-step explanation:

(-8, 2), (-11, 3)

(x₁, y₁)   (x₂, y₂)

m = slope

        y₂ - y₁          3 - 2              1              1

m = ------------ = -------------- = ----------- = -------

        x₂ - x₁         -11 - (-8)       -11 + 8        3

I hope this helps!

Answer:

z=38

Step-by-step explanation:

Using the fact that angles on a straight line add to 180°, the interior angles of the triangle are 86°, (180-3z)°, and (180-4z)°.

Angles in a triangle add to 180°, so:

[tex]86+180-3z+180-4z=180 \\ \\ 86-3z+180-4z=0 \\ \\ 266-7z=0 \\ \\ 7z=266 \\ \\ z=38[/tex]

The polynomial function that has the degree of 5 is written as f(x) = 2x⁵ + 26x⁴ + 128x³ + 296x² + 320x + 128

Polynomial function:

The equations formed with variables, exponents and coefficients are known as the polynomial equations. And it can have different exponents, where the higher one is called the degree of the equation.

Given,

Here we have the following things,

Degree = 5

Root of multiplicity 2 is x = -4

Root of multiplicity 1 at x = -1

Root of multiplicity 2 at x = -2

y-intercept of (0, 128)

Here we need to find the polynomial equation of the function.

According to the given roots of multiplicity, we have the factors of the polynomials are,

=> (x + 4)² (x + 1) (x + 2)²

So, the general form of the polynomial function can be written as,

=> f(x) = A (x + 4)² (x + 1) (x + 2)²

In order to find the 5 degree polynomial function, we have to calculate the value of A.

To Find the value of A, we have to apply the y - intercept point on the equation then we get,

=> 128 = A (0 + 4)² (0 + 1) (0 + 2)²

=> 128 = A (4)² (1) (2)²

=> 128 = A (16 x 1 x 4)

=> 128 = 64A

=> A = 2

Now, the polynomial function is written as,

=> f(x) = 2 (x + 4)² (x + 1) (x + 2)²

When we expand this one then we get,

=> f(x) =2 [x⁵ + 13x⁴ + 64x³ + 148x² + 160x + 64]

Therefore, the resulting polynomial function is,

=> f(x) = 2x⁵ + 26x⁴ + 128x³ + 296x² + 320x + 128

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Answer: 5 is the ancer

Step-by-step explanation:!

The slope for the following question is = 4.

acc to our question-

hence the value of slope=4

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The total cost of the shoe after tax is $79.50

From the question, we are to determine the total cost of the shoes after tax.

From the given information,

Jason bought new shoes priced at $75

and

The sales tax is 6%

The total cost of the shoe = Price of the shoe + Sales tax

Sales tax = 6% of $75

Sales tax = 0.06 × $75

Sales tax = $4.50

Thus,

Total cost of the shoe = $75 + $4.50

Total cost of the shoe = $79.50

Hence, the total cost is $79.50

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Answer:

$205.6

Step-by-step explanation:

20.56hours × $10/hour = $205.6

The fractions have a LCD of 84 is option C, 2/21,1/4,1/3.

Given:

3/14,1/42,1/6

= 3/14 + 1/42 + 1/6

= 9+42+7 / 42

The LCD  is 42 not 84.

2/84,1/16,1/42

= 6+21+8 / 336

The LCD  is 336 not 84

2/21,1/4,1/3

= 8+21+28 / 84

The LCD is 84

2/3,1/6,1/7

= 28+7+6 / 42

The LCD is 42 not 84

Therefore the fractions have a LCD of 84 is option C, 2/21,1/4,1/3.

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Answer:

[tex]\textsf{C)} \quad \dfrac{2}{21}, \dfrac{1}{4}, \dfrac{1}{3}[/tex]

Step-by-step explanation:

The least common denominator (LCD) is the smallest number that is exactly divisible by each denominator of a set of fractions.

To find the LCD of a set of fractions, reduce the fractions to their smallest equivalent, list the multiples of each denominator, then locate the smallest common number.

[tex]\textsf{A)} \quad \dfrac{3}{14}, \dfrac{1}{42}, \dfrac{1}{6}[/tex]

Multiples of 14:  14, 28, 42, 56, 70, 84, 98, ...

Multiples of 42:  42, 84, 126, 168, 210, ...

Multiples of 6:  6, 12, 18, 24, 30, 36, 42, 48, ...

Therefore, the LCD is 42.

[tex]\textsf{B)} \quad \dfrac{2}{84}, \dfrac{1}{16}, \dfrac{1}{42}=\dfrac{1}{42}, \dfrac{1}{16}, \dfrac{1}{42}[/tex]

Multiples of 42:  42, 84, 126, 168, 210, 252, 294, 336, ...

Multiples of 16:  16, 32, 48, 64, 80, 96, 112, ... , 336, ...

Therefore, the LCD is 336.

[tex]\textsf{C)} \quad \dfrac{2}{21}, \dfrac{1}{4}, \dfrac{1}{3}[/tex]

Multiples of 21:  21, 42, 63, 84, 105, 126, 147, ...

Multiples of 4:  4, 8, 12, 16, 20, 24, 28, ... , 84, 88, ...

Multiples of 3:  3, 6, 9, 12, 15, 18, 21, ... , 84, 87, ...

Therefore, the LCD is 84.

[tex]\textsf{D)} \quad \dfrac{2}{3}, \dfrac{1}{6}, \dfrac{1}{7}[/tex]

Multiples of 3:  3, 6, 9, 12, 15, 18, 21, ... , 42, 45, ...

Multiples of 6:  6, 12, 18, 24, 30, 36, 42, 48, ...

Multiples of 7:  7, 14, 21, 28, 35, 42, 49, 56, ...

Therefore, the LCD is 42.

The expression that represents the quotient of given model is x + 5

The correct answer is an option (C)

In this question, we have been given a synthetic division of x^2 + 5x and x

We need to find the quotient.

    x  + 1  + 1 + 1 + 1 + 1        

x) x^2    x   x   x   x   x

 - x^2                                  

    0      x

         -  x                            

            0   x

             -  x                    

                  0  x

                  -  x                

                      0    x

                       -    x            

                             0  x

                             -    x      

                                   0

Therefore, the expression that represents the quotient of given model is x + 5

The correct answer is an option (C)

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The selling price of the two washing machies are

I will buy the first because it has a lower selling price

The question is a percentage problem

The first washing machine has a mark down by ​40%

= 40 percent

= 40 / 100

= 0.4

marked down factor = 1 - 0.4 = 0.6

selling price of the first machine = 550 * 0.6 = 330

the second washing machine has mark down of 30%

30% = 0.3

marked down factor = 1 - 0.3 = 0.7

selling price of the second washing machine at first mark down

= 550 * 0.7 = 385

marked down again

10% = 0.1

the  factor here is = 1 - 0.1 = 0.9

selling price of the second washing machine at second mark down

= 385 * 0.9 = 346.5

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Answer:

y-intercept (0,-3)

x-intercept (3,0)

Step-by-step explanation:

Let x = 0

-y =3

y = -3

(0,-3)

Let y = 0

x = 3

(3,0)

Answer:

[tex]s \approx \$182.14[/tex]

[tex]c \approx \$435.72[/tex]

Step-by-step explanation:

Set up a system of equations, where s is the cost of a sheep and c is the cost of a cow:

[tex]4s + 2c = \$ 1660[/tex],  [tex]3s + 5c = \$ 2925[/tex]

First, isolate c in the first equation.

[tex]4s + 2c = \$ 1660[/tex]

[tex]2c = \$ 1660 - 4s[/tex]

[tex]c = \$ 840 - 2s[/tex]

Next, substitute this value into the second equation:

[tex]3s + 5c = \$2925[/tex]

[tex]3s + 5(\$840 - 2s) = \$2925[/tex]

and simplify.

[tex]3s + \$4200 - 10s = \$2925[/tex]

[tex]-7s = -\$1275[/tex]

[tex]7s = \$1275[/tex]

[tex]s \approx \$182.14[/tex]

Finally, plug this value into the first equation to get the value of c:

[tex]4(\$182.14) + 2c = \$1660[/tex]

[tex]2c = \$1600 - \$728.57[/tex]

[tex]c \approx \$435.72[/tex]

So, a sheep costs about $184.14, and a cow costs about $435.72.

Answer:

150

Step-by-step explanation:

I had this on one of my quizzes, hope this helps :D

Answer:

Below

Step-by-step explanation:

x^2 + 32 + 116 = 12x         1st intermediate step: put everything on one side

x^2 -12x + 148 = 0      2nd intermediate step : re-arrange with constant on R

x^2 -12x = -148            3 rd intermediate step : take 1/2 of the 'x' coefficient

                                            square it and add to both sides

x^2 -12x + 36 = -148 + 36    4th intermediate step :   simplify

(x-6)^2  = -112

Answer: hi

Step-by-step explanation:

this is it

77 is 0.7% of 11000

this number is a lot greater than 77.

Let 77 is 0.7% of m

0.7 percent of m = 77

(0.7/100) * m = 77

m = 77 * (100/0.7)

m = 11000

Therefore, 77 is 0.7% of 11000

this number is a lot greater than 77.

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Answer:

At x = 0 and at x = 2 there are points of inflections. In the intervals of

(negative infinity, 0) and (2, positive infinity) it is concave up.

In the intervals of (0, 2) it is concave down.

Step-by-step explanation:

Inflection points are point where h'(x) changes from increasing to decreasing and vise versa.

When a graph is concave up, h'(x) is increasing.

When a graph is concave down, h'(x) is decreasing.

Answer:

f(-2) = 2

Step-by-step explanation:

 -2 is the input/ domain value

It's corresponding value from the graph is 2.

The sales tax rate of the cocktail table is 0.055

A sales tax is a consumption tax imposed by the government on the sale of goods and services

The cocktail table sold for $250 and the sales tax amount was $13.75. The sales tax rate can be calculated as follows:

Sales tax = list price * sales tax rate

Therefore,

sale tax rate = sales tax / list price

sales tax = $13.75

list price = $250

sale tax rate = 13.75 / 250

sales tax rate = 0.055

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The number of highway routes from A to D is 560

Number of highway routes from A to B = 7 highways

Number of highways routes from B to C = 8 highways

Number of highways routes from C to D = 10 highways

Number of routes from A to D = Number of highway routes from A to B × Number of highways routes from B to C × Number of highways routes from C to D

Here we have to use multiplication

Substitute the values in the equation

Number of routes from A to D = 7 × 8 × 10

= 560 highways

Hence, the number of highway routes from A to D is 560

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Answer:They are all the same because 40/100 divided by 10 on both sides is just 4/10 and 4/10 as a decimal is equal to 0.4

Step-by-step explanation:

Answer:

0.4 is the decimal form of [tex]\frac{4}{10}[/tex], which means that 4 ÷ 10 = 0.4, shown below.

If you multiply the numerator and denominator of [tex]\frac{4}{10}[/tex] by 10, you would get [tex]\frac{4*10}{10*10} =\frac{40}{100}[/tex]. This is equal in value to [tex]\frac{4}{10}[/tex] because 40 ÷ 100 = 0.4.

slope= -3/2, y-intercept=8

y=mx+b m is the slope while b is the y-inteecept

The expression of the given statement is  [tex]\frac{2x}{5}[/tex] .

What is algebraic expression?

  When terms are combined using operations like addition, subtraction, multiplication, division, etc., the result is an algebraic expression (or variable expression). Let's look at the formula 5x + 7 as an illustration. Consequently, we can state that 5x + 7 is an illustration of an algebraic statement. Here are some more examples: 5x + 4y + 10

Here the given product of two and a number. Lets us take number as x. Then ,

=> 2*x= 2x

Product of two and a number divided by 5. Then,

=> [tex]\frac{2x}{5}[/tex]

Hence the algebraic expression of the given statement is  [tex]\frac{2x}{5}[/tex] .

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According to the volume of cylinder formula, an aluminum can with a 2 3/5 diameter and 5 1/4 in height are in 27.86 cubic inches.

Volume of Cylinder

The formula to calculate the volume of the cylinder is

Volume of a cylinder = πr²h cubic units.

where

r refers the radius

h refers the height.

Given,

Here we have an aluminum can with a 2 3/5 diameter and 5 1/4 in height and now we have to find the volume in cubic inches.

While we looking into the given question, we know the following values,

Diameter = 2 3/5

When we simplify it, then we get the value of diameter as

d = 13/5 or 2.6

Similarly, the value of height is rewritten as,

h = 5.25

So, based on the formula of volume of cylinder,

We get the value as,

=> V = π x (2.6/2)² x 5.25

Apply the value of π as 3.14, then we get,

=> V = 3.14 x (1.3)² x 5.25

=> V = 16.485 x 1.69

Therefore, the volume in cubic inches is 27.86 cubic inches.

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