6c3c² +d³ for c = 5 and d = 3

We need to know about roots of a quadratic equation to solve the problem. The quadratic equation is [tex]x^{2} -3x-40=0[/tex]

Quadratic equation is an equation with the highest degree of the variable being 2. A quadratic equation has two roots. The two roots can be real and different or real and equal or imaginary. The roots of a quadratic equation can be found using factorization method. The roots of a quadratic equation can be used to find the quadratic equation itself. Here in this question we have two points (-5,0) and (8,0). These points lie on the x-axis hence we can say that they are the two roots of the equation and the quadratic equation is in terms of x since it cuts the x-axis. Hence we can say that the two roots of the equation are -5 and 8.

For a quadratic equation [tex]ax^{2} +bx+c=0[/tex] let us say that the roots are α and β

α+β=-b/a

αβ=c/a

Here α and β are -5 and 8

-5+8=-b/a ⇒b/a=-3

c/a=-5 x 8=-40

The quadratic equation is given by [tex]x^{2} +\frac{b}{a} x+\frac{c}{a} =0[/tex] which is [tex]x^{2} -3x-40=0[/tex]

Therefore we found the quadratic equation using the two points given, the equation is [tex]x^{2} -3x-40=0[/tex]

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64.00336 × 10⁵  is the solution of the Expression .

What in mathematics is a linear equation?

=(48*7) +65 ×10⁵

=((40+8) *7) +65 × 10⁵

=(280+56)+65 ×10⁵

=336+65 × 10⁵

=.336*10^3+65 × 10⁵

=.00336*10^5+65 × 10⁵

=(.00336+65) × 10⁵

= 64.00336 × 10⁵

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The total price that Cheyenne must pay if he gets his haircut and beard shaved $60.89

A sales tax is one that applies to the purchase of goods and services for consumers and to the sale of goods and services for businesses. It's a type of consumption tax, meaning it taxes people for spending money.

The formula for calculating the sales tax on a good or service is: selling price x sales tax rate, and when calculating the total cost of a purchase, the formula is:

total sale amount = selling price + sales tax.

Given that

spot cost = $20

shave cost =  $25

state sales tax = 8.25%

tips = 25%.

find out  the total price that Cheyenne pay.

total selling price = spot + shave cost

total selling price = $20 + $25

total selling price = $45

we know that

sales tax = selling price x sales tax rate

sales tax = $45 x 8.25%

sales tax = $45 x 8.25 / 100

sales tax = $3.7125.

Cost with sales tax = $45 + $3.7125

Cost with sales tax = $48.7125

Tip is calculated on total bill

Tip Total: $ 12.18

Total (Bill + Tip): $ 60.89

hence , total amount of $ 60.89 is that Cheyenne must pay if he gets his haircut and beard shaved with the bill and tip.

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The required irrational number is 13 / 16 among the options given. Option D is correct.

Given that,
To determine the irrational number among the number given.

Rational numbers are numbers that can be structured in the form of the fraction of integers. Eg- 5/6, 2/3, etc.

here,

49² = is rational number
34 ² = rational number
9 / 2 = rational number
13 / 16 = irrational number

Thus, the required irrational number is 13 / 16 among the options given. Option D is correct.

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Answer:c

Step-by-step explanation:

c

The statement that best describes the expression p-1(x) is (c) the amount for x grams

The equation of the function is given as

P(n) = 0.2n + 5.3

(a) which statement best describes (p^-1) (x)?

The function is given as

P(n) = 0.2n + 5.3

This means that the inverse of the function is represented as p-1(n)

Hence, the statement that best describes the expression p-1(x) is (c) the amount for x grams

(b) The function p^-1 (x)

We have

P(n) = 0.2n + 5.3

Rewrite as

y= 0.2x + 5.3

Swap x and y

x = 0.2y + 5.3

Make y the subject

y = 5x - 26.5

Express as inverse function

p^-1(x) = 5x - 26.5

(c) The value of p^-1 (6.6)

We have

p^-1(x) = 5x - 26.5

This gives

p^-1(6.6) = 5 x 6.6 - 26.5

Evaluate

p^-1(6.6) = 6.5

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The solution to the expression is  7r - 8

The expression is given as

-r + 6 + 8r - 14

Collect the like terms in the above expression

So, we have

-r + 8r + 6  - 14

Evaluate the like terms in the above expression

7r - 8

Hence, the solution to the expression is  7r - 8

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[tex]\textit{internal division of a segment using a fraction}\\\\ A(\stackrel{x_1}{-3}~,~\stackrel{y_1}{-8})\qquad B(\stackrel{x_2}{10}~,~\stackrel{y_2}{5})~\hspace{8em} \frac{7}{10}\textit{ of the way from A to B} \\\\[-0.35em] ~\dotfill\\\\ (\stackrel{x_2}{10}-\stackrel{x_1}{(-3)}~~,~~ \stackrel{y_2}{5}-\stackrel{y_1}{(-8)})\qquad \implies \qquad \stackrel{\stackrel{\textit{component form of}}{\textit{segment AB}}}{\left( 13 ~~,~~ 13 \right)} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\left( \stackrel{x_1}{-3}~~+~~\frac{7}{10}(13)~~,~~\stackrel{y_1}{-8}~~+~~\frac{7}{10}(13) \right)\implies \left(-3+\cfrac{91}{10}~~,~~-8+\cfrac{91}{10} \right) \\\\\\ \left( \cfrac{-30+91}{10}~~,~~\cfrac{-80+91}{10} \right)\implies \left(\cfrac{61}{10}~~,~~\cfrac{11}{10} \right)\implies \left(6\frac{1}{10} ~~,~~1\frac{1}{10} \right)[/tex]

Answer:

B & C

Step-by-step explanation:

a rate has to have an incline or decline. A&D are set amounts.

Answer:

Step-by-step explanation:

Answer:

y=-4x+0

Step-by-step explanation:

Slope form is y=mx+b

m is the slope, and b is the y intercept. If the line must pass through (0,0) then the y intercept would be zero.

This give you y=mx+0

Now to find the slope you need a perpendicular line to the previous line. This would mean you have to swap 1/4 which is the previous lines slope.

1/4 is a positive so make it a negative, -1/4

Now flip -1/4 to make is -4/1 which also equals -4

Now with the slope -4 and y-intercept 0, you know you equation

y=-4x+0

Answer:

x < 0

Step-by-step explanation:

We are given this inequality:

3x + 4 < 4

And we want to solve it.

Solving inequalities is very similar to solving equations. We want to isolate the variable (in this case, x) on one side, while leaving the numbers on the other side.

To start, we can subtract 4 from both sides.

3x + 4 < 4

    -4     -4

__________________

3x < 0

Now, we have the numbers on one side and the variable on the other, but we aren't done yet, as we want to solve for the value of x, or 1x, not the value of 3x.

So, we'll need to divide both sides by 3.

3x < 0

÷3   ÷3

___________

x < 0

The answer is x < 0.

Answer:

45/8

Step-by-step explanation:

Answer:

See attached graphs Graph1, Graph2 and Graph3 and detailed explanation below

Step-by-step explanation:

The process for plotting and shading are essentially the same but with different inequalities

To plot any line

To determine area to shade

Choose a point on either side of the line from the graph. See if the corresponding (x,y) values satisfy the inequality. If they do, then that's the area to shade. If not, shade the other area

1. Inequality y > -3x - 2

The line equation is y = -3x -2

Let's choose x = 0. Then y = -3(0) -2 = -2. So one point is (0, -2)

Choose another value for x, say x = 1

y = -3(1) - 2 = -3-2 = -5. So another point is (1,-5).

Draw a straight line through both points (see attached Graph1)

Determining area to shade

Choose a point on the graph on one side of the line. Let's choose (1,2). So x = 1 and y = 2. Does this satisfy the inequality y = -3x -2? Let's see

Is 2 > -3(1) - 2 ?

2 > -3-2 ?

2 > -5 ? YES since a positive number is greater than a negative number. So the area containing (1,2) should be shaded as shown in Graph 1

2. Inequality 4x + 5y ≤ 20

Line equation is  4x + 5y =20

Convert to a function of x as follows

Choose two values of x and find corresponding y values to get the coordinates of two points

Plug x = 0 into line equation ==> y = 4- 4x/5

==> y = 4 - 4(0)/5 = 4

==> (0, 4) is one point

Choose another value of x, say 5(this is a convenient value since we are dividing by 5)

==> y = 4- 4(5)/5 = 4-4 = 0

==> (5, 0) is another point

Draw straight line through (0,4) and (5,0)

To determine area to shade let's choose a point on the graph. (0,0) is a convenient point.  Do the values of x=0 and y=0 satisfy the inequality
4x + 5y ≤ 20?

Plugging in x = 0 and y = 0 gives us

4(0) + 5(0) = 0 and 0 is indeed ≤ 20

So the inequality is satisfied at (0,0)

Shade the region on the side of the line where (0,0) is (see Graph2)

3. Inequality y > -4

The line equation is y = -4

Since this equation does not involve x, the line plot will be a horizontal line at y = -4 for all x values

Simply draw a horizontal line which crosses the y axis at y = -4

To determine which area to shade, choose a point. Use (0,0)

Does y = 0 satisfy the inequality y > -4?

0 > -4 so indeed the point (0,0) satisfies the inequality. Just shade the area on the side of the line which contains (0,0). This will be the region above the line y = -4 See Graph3

Hope that helps :)

The least cost per unit of peanut butter is $0.095 for 20 ounces for ​$1.90 therefore option (B) will be correct.

Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.,

Division = divide any two numbers or variable called division.

Given the four options of jars;

1) 16 ounces for ​$1.70

Cost per ounces = 1.70/16 = $0.10625

2) 20 ounces for ​$1.90

Cost per ounces = 1.90/20 = $0.095

3) 26 ounces for ​$3.33

Cost per ounce = 3.33/26 = $0.128

The least cost per ounce is $0.095 for 20 ounces for ​$1.90.

Hence "The least cost per unit of peanut butter is $0.095 for 20 ounces for ​$1.90".

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Jenna paid a total interest of $4810 (13% of the cost of the car) for the car.

Suppose there is initial amount as P.

The interest, or say charge on it is applied annually as 'C' amount.

Taking how much percent of P is C, we get:

[tex]APR = \dfrac{C}{P} \times 100[/tex]

WE have been given that Jenna bought a new car for $37,000 and paid a 10% down payment and financed the remaining balance for 72 months with an APR of 6.5%

Assuming that she makes monthly payments, to determine the total interest Jenna pays over the life of the loan.

The cost = $37,000

Time = 72 months

APR = 6.5%

Then;

Interest = (37,000 x 6.5 x 2) /100

= $4810

Percentage of interest paid = (4810/37,000 ) x 100

= 13%

Therefore, Jenna paid a total interest of $4810 (13% of the cost of the car) for the car.

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Answer:50.63

Step-by-step explanation: line them up on top of each other and multiply 9 by all them and if its over 10 put the 2nd digit the the next number.

Answer:

Either 40 or 80, depending on whether you worded the question correctly or not.

Step-by-step explanation:

If you mean he has gone 80 miles:

velocity is distance per time, so 80miles/2hours = 40 miles/hour

If you mean he is going 80mph, then the answer is in the question, 80 miles/hour and the distance he has traveled is in miles, therefore you need to multiply by hours, i.e., 80*2=160 miles.

Answer:

y=6

Step-by-step explanation:

15y-16y=-6     subtract (15y-16y=-1y or -y)

-y=-6         Divide each side by -1 in order to make the -y a positive number.

y=6  

You didn't really clarify what you were looking for in your question, but I answered according to what I thought you were talking about. I hope this helps you. If not, reply to me with what you were looking for and I will edit my answer to meet your requirements.

No student took both calculus and physics out of the 30 students.

Given that, total number of students are 30. Out of which 18 took calculus and 12 took physics. Then, we have to calculate how many took both calculus and physics. So, by using venn diagram we have,

Total number of students = 30

Students who took calculus = P(A) = 18

Students who took physics = P(B) = 12

Students who took both calculus and physics = P(A∩B) = x

Students who took only physics = P(B)-x = (12-x)

Students who took only calculus = P(A)-x = (18-x)

From venn diagram, we get

(18-x)+x+(12-x) = 30

18-x+x+12-x = 30

⇒ x = 0

∴ P(A∩B) = 0

Therefore, No student took both physics and calculus.

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The representation of x^pi in base e is e^xln3.

An exponential function is a the kind of mathematical function that involves exponents.

       f (x) = aˣ

where x is a variable and an is a constant known as the function's base.

        f (x) = eˣ

When the exponent in this component increases by one, the function's value increases by a factor of e.

When the exponent is reduced by one, the value of the function is reduced by the same factor (it is divided by e ).

        f ( x ) = 10ˣ

Now, for the given function.

3x=e^ln3^x

= e^xln3

Therefore, the base e representation of the expression is e^xln3.

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-45 represents a loss of 45 yards (integers include negative numbers)

Answer:

60/3 - 40

Step-by-step explanation:

Answer: 60/3 -40

Step-by-step explanation:

Step-by-step explanation:

y-intersec is (0,y)

sub x=0 in 3x-2y=15

3*0-2y=15

0-2y=15

y=-15/2

The loss percentage of cloth is 12.5%.

Stock of cloth = Rs. 1,60,000

worth of destroyed cloth = Rs. 20,000

A percentage is a number or ratio that can be expressed as a fraction of 100. It is denoted by the symbol %.

Percentage = Value/ Total value × 100%

Loss percentage = Loss/Total value × 100%

So, the loss percentage of cloth = 20,000/1,60,000 ×100%

                                                   = 0.125 × 100%

                                                   = 12.5%.

The approximate rate of change of the function is 224.95

The rate of change of the given function is expressed according to the equation below;

f'(x) = f(b)- f(a)/b-a

Given the interval [-4, 3]

a = -4

b = 3

f(a) = 9(-4)⁴ + 7/(-4)²

f(-4) = 2304+ 7/16

f(-4) = 2304.4375

f(b) = 9(3)⁴ + 7/(3)²

f(3) = 729 + 7/9

f(3) = 729.7778

Substitute to have:

f'(x) = 729.7778-2304.4375/3+4

f'(x) = 1574.65/7

f'(x) = 224.95

Hence the approximate rate of change of the function is 224.95

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