Find a polynomial function of degree 4 with the zeros -3 (multiplicity 2) and 3 (multiplicity 2), whose graph passes through the point (-4,245).

The value of f(5) is 0 in the function f(x) = x⁴ - 7x³ + 2x² + 40x

A relation is a function if it has only One y-value for each x-value.

The given function is f(x) = x⁴ - 7x³ + 2x² + 40x and given x-5 such that x=5

We need to find the value of f(5)

Plug x=5 in the above function

f(x) = x⁴ - 7x³ + 2x² + 40x

f(5) = 5⁴ - 7(5)³ + 2(5)² + 40(5)

=625-875+50+200

=0

Hence, the value of f(5) is 0 in the function f(x) = x⁴ - 7x³ + 2x² + 40x

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Complete question is below

f(x) = x⁴ - 7x³ + 2x² + 40x and given x-5 find value of f(5)

Answer: 35/6 or 5 and 5/6

Step-by-step explanation:

Answer:

35/6

Step-by-step explanation:

In the equation, the number 5,000 represents the initial value of the motorcycle. The value of the motorcycle is increasing at a rate of 3% per year.

Exponential functions are functions where the independent variable, x is in the exponent.

The given exponential equation is,

V = 5,000 (1.03)^t

Here V represents the value of the motorcycle in t years.

When t = 0,

V = 5000 (1.03)⁰ = 5000

So 5000 represents the initial value of the motorcycle.

V = 5,000 (1 + 0.03)^t

At t = 0, V = 5000

At t = 1, V = 5000 (1.03)¹ = 5150

At t = 2, V = 5000 (1.03)² = 5304.5

So the value of the motorcycle is increasing.

The rate is 0.03 or 3%.

Hence, 5,000 represents the initial value of the motorcycle and the value of the motorcycle is increasing at a rate of 3% per year.

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The sales tax on the Bluray disc player is $17.60.

What is percentage ?

Percentage can be defined as product of ratio of given value, total value and hundred.

To calculate the sales tax on the Bluray disc player, we need to add the state tax and county tax to the sale price of the player.

First, we can calculate the amount of the state tax. The state tax rate is 4%, which can be expressed as a decimal by dividing by 100:

State tax rate = 4% = 0.04

To find the amount of state tax, we can multiply the sale price by the state tax rate:

State tax = 0.04 x $219.99 = $8.80

Next, we can calculate the amount of the county tax. The county tax rate is also 4%, so we can use the same method as above to find the county tax:

County tax rate = 4% = 0.04

County tax = 0.04 x $219.99 = $8.80

Now, we can find the total sales tax by adding the state tax and county tax:

Total sales tax = State tax + County tax

= $8.80 + $8.80

= $17.60

Therefore, the sales tax on the Bluray disc player is $17.60.

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Answer:

Step-by-step explanation:

a

Answer: Let's assume that the marked price of the watch is M.

The discount amount would be 20% of M, which can be calculated as:

0.2 * M = 0.2M

The selling price after the discount would be:

M - 0.2M = 0.8M

The VAT amount would be 13% of the selling price after the discount, which can be calculated as:

0.13 * 0.8M = 0.104M

Now, as the discount amount is Rs.192 more than the VAT amount, we can write an equation:

0.2M = 0.104M + 192

0.096M = 192

M = 192 / 0.096 = 2000

So, the marked price of the watch is Rs.2000 and the selling price after the discount and VAT is 0.8M = 0.8 * 2000 = 1600.

Step-by-step explanation:

Answer:B

Step-by-step explanation:

area of triangle is (10*11)/2=55

area of semicircle is

[tex]d=2r\\r=10/2=5\\s=\pi r^{2} /2=25\pi /2=39.25\\39.25+55=94.25[/tex]

Answer:

120°

Step-by-step explanation:

360 / 12

30 X (5-1)

30 X 4= 120°

Answer:

Rafael and Lucy's credit for retirement plan contributions is $570.

Step-by-step explanation:

The Saver's Credit is a tax credit for low and moderate-income taxpayers who make contributions to a retirement plan. The credit is worth between 10% and 50% of the taxpayer's contributions, up to a maximum credit of $1,000 ($2,000 for married taxpayers filing jointly).

To determine the credit amount, we need to calculate the taxpayers' adjusted gross income (AGI) and their credit rate.

For the tax year in question, the AGI is $40,500 and the contribution limit is $2,850 per person. The total contribution amount is $2,850 x 2 = $5,700.

The credit rate is determined by the taxpayer's AGI and filing status, as follows:

For AGI up to $19,750 for married taxpayers filing jointly, the credit rate is 50%.

For AGI between $19,750 and $32,000 for married taxpayers filing jointly, the credit rate is 20%.

For AGI between $32,000 and $40,000 for married taxpayers filing jointly, the credit rate is 10%.

For AGI above $40,000 for married taxpayers filing jointly, the credit is not available.

Since the taxpayers' AGI is $40,500, the credit rate is 10%. The credit amount is calculated as follows:

Credit amount = Credit rate x Contribution amount

Credit amount = 10% x $5,700 = $570

So, Rafael and Lucy's credit for retirement plan contributions is $570.

Answer:

Step-by-step explanation:

THE ANSWER TO YOUR QUESTION IS C.

Answer:a=-2

b=5

Step-by-step explanation:

[tex]\frac{a}{b} =\frac{\frac{-1}{4} }{\frac{5}{8} } \\\frac{a}{b} =\frac{-1}{4}*\frac{8}{5}\\\frac{a}{b}=-2/5[/tex]

Answer: 75%

Step-by-step explanation: To calculate,

(0.1 x 100) + (0.3 x 80) + (0.2 x 95) + (0.4 x 75) = 83%

The demand function of the question is expressed as;

D(q) = -²/₅₀₀₀q + 14.6

The formula to find the slope between two coordinates is;

m = (y2 - y1)/(x2 - x1)

The coordinates we are given are;

(28000, 9) and (33000, 7)

Thus;

Slope; m = (7 - 9)/(33000 - 28000)

m = -2/5000

Now, the equation of a line in point slope form is;

y - y1 = m(x - x1)

Where (x1, y1) is (28000, 9)

y - 9 = (-2/5000)(x - 28000)

y - 9 = -²/₅₀₀₀x + 5.6

y = -²/₅₀₀₀x + 14.6

This can be rewritten as a demand function; D(q) = -²/₅₀₀₀q + 14.6

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Answer:

the answer to this question is 936

Step-by-step explanation:

[tex] \frac{ \tan( \alpha ) }{1 + \sec( \alpha ) } = - \cot( \alpha ) + \csc( \alpha ) [/tex]

Multiply by 1-sec(a)

[tex] \frac{ \tan( \alpha ) (1 - \sec( \alpha ) }{(1 + \sec( \alpha ) )(1 - \sec( \alpha ) )} [/tex]

[tex] \frac{ \tan( \alpha ) - \tan( \alpha ) \sec( \alpha ) }{1 - \sec {}^{2} ( \alpha ) } [/tex]

[tex] \frac{ \tan( \alpha ) }{1 - \sec {}^{2} ( \\ \alpha ) } - \frac{ \tan( \alpha ) \sec( \alpha ) }{1 - \sec {}^{2} ( \alpha ) } [/tex]

[tex] \frac{ \tan( \alpha ) }{ - \tan {}^{2} ( \alpha ) } + \frac{ \tan( \alpha ) \sec( \alpha ) }{ \tan {}^{2} ( \alpha ) } [/tex]

[tex] - \frac{1}{ \tan( \alpha ) } + \frac{ \sec( \alpha ) }{ \tan( \alpha ) } [/tex]

[tex] - \cot( \alpha ) + \frac{ \frac{1}{ \cos( \alpha ) } }{ \frac{ \sin( \alpha ) }{ \cos( \alpha ) } } [/tex]

[tex] - \cot( \alpha ) + \frac{1}{ \sin( \alpha ) } [/tex]

[tex] - \cot( \alpha ) + \csc( \alpha ) [/tex]

Answer:

0

Step-by-step explanation:

surface of ocean = sea level = elevation of zero

The number of containers needed is given as follows:

3 containers.

The number of containers needed is obtained applying the proportions in the context of this problem.

She has 2 cups, hence the number of fluid ounces that she has is given as follows:

16 fluid ounces.

Each container holds a total of 6 fluid ounces, hence the number of containers needed is given as follows:

16/6 = 3 containers.

(rounding up).

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Answer: The answer to your problem is choice b

The volume of the parallelopiped is 4

We have to solve this with the use of matrix system in math

PQ, PR, PS where

P(-3, 3, 2), Q(-1, 6, 5), R(-4, 2, 1), S(3, 1, 4)

we have to find

Q - P

(-1, 6, 5) - (-3, 3, 2)

= (2, 3, 3)

R - P

R(-4, 2, 1) - (-3, 3, 2)

= ( -1 , -1, -1)

S - P

S(3, 1, 4) - (-3, 3, 2)

= (6 , -2, 2)

we would have [tex]\left[\begin{array}{ccc}2&3&3\\-1&-1&-1\\6&-2&2\end{array}\right][/tex]

the determinant of the matrix is the volume

2[(-1 * 2) - 3[(-1x2)-(6x-1)] + 3[(-1x-2) -(6 x -1)]

= -8 - 12 + 24

= 4

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The solution of the expression 3h(n) + 2g(n) will be 2n³ -8n +16.

Expression in maths is defined as the relation of numbers variables and functions by using mathematical signs like addition, subtraction, multiplication, and division.

Given that the two values are h(n) =4n+2 and g(n)= n³ +5 - 2n. The value of the expression 3h(n) + 2g(n) will be calculated as:-

E = 3h(n) + 2g(n)

E = 3 ( 4n+2 ) + 2 (n³ +5 - 2n)

E = 12n + 6 + 2n³ + 10 -4n

E = 2n³ + 8n + 6

Therefore, the answer to the equation 3h(n) + 2g(n) is 2n3 -8n +16.

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By using the composition of functions, we can find valid decompositions of c(x) using f(x) = [tex](x+1)^{1/3}.[/tex] and g(x) = x²

A function is a rule that takes an input value and produces an output value.

One way to do this is to use the composition of functions. The composition of two functions f(x) and g(x) is denoted as f(g(x)). This means that we first apply g(x) to the input, and then apply f(x) to the output of g(x). In other words, we first evaluate g(x), and then plug that result into f(x) to get the final output.

Using this concept, let's look at the first set of functions. We are given

=> c(x) = f ◦ g (x) = (x²) f(x) = [tex](x+1)^{1/3}.[/tex]

This means that c(x) is the composition of two functions, f(x) and g(x). We can see that g(x) = x², and f(x) = [tex](x+1)^{1/3}.[/tex] This is a valid decomposition of c(x).

Similarly, in the second set of functions, we have

=> c(x) = f ◦ g (x) = [tex](x+1)^{1/3}[/tex] g(x) = x² + 1.

This means that c(x) is the composition of two functions, f(x) and g(x). We can see that g(x) = x² + 1, and [tex](x+1)^{1/3}.[/tex] This is also a valid decomposition of c(x).

In the third set of functions, we have

=> c(x) = f ◦ g (x) = [tex](x+1)^{1/3}[/tex] g(x) = x + 1, and f(x) = [tex](x^2)^{1/3}=x^{2/3}[/tex]

This is another valid decomposition of c(x).

Finally, in the fourth set of functions, we have

=> c(x) = f ◦ g (x) = x² g(x) = [tex](x+1)^{1/3}[/tex], and f(x) = [tex]x^{2/3}[/tex].

This is yet another valid decomposition of c(x).

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Answer:

$475

Step-by-step explanation:

x = former rent

2x - 200 = 750

2x = 750 + 200 = 950

x = 950/2 = 475

The start point the graph of a function of this form is (h, k)

From the question, we have the following parameters that can be used in our computation:

f(x) = a√(x - h) + k

The domain is given as

x ≥ h

This means that the initial x value is h

From the question, we have the following parameters that can be used in our computation:

f(h) = a√(h - h) + k

Evaluate

f(h) = k

Hence, teh initial point is (h, k)

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Answer:

x = 32

Step-by-step explanation:

First we would move the x's to the left and the numbers to the right. When doing so they switch from being positive to negative or from negative to positive.

3/4x = 27-3

Now we would try to simplify it as much as we can. Here I would make 3/4 a decimal and subtract 37-3

0.75x = 24

Now we can divide 24 by 0.75 to find x

x = 32

x = 32.

[tex]\frac{3}{4} x+3=27[/tex]

[tex]\frac{3}{4} x+3-3=27-3\\ \\\frac{3}{4} x+3-3=27-3\\ \\\frac{3}{4} x=24[/tex]

[tex]\frac{\frac{3}{4} x}{\frac{3}{4}} =\frac{24}{\frac{3}{4}}\\ \\x=24*\frac{4}{3}\\ \\x=\frac{24*4}{3} \\ \\x=\frac{96}{3} \\\\x=32[/tex]

If "32" is our correct answer, then substituting it by variable "x" on the original equation should make the equation return the same number on both sides of the equal (=) symbol. Let's test it!

[tex]\frac{3}{4} (32)+3=27\\ \\\frac{3*32}{4}+3=27\\ \\\frac{96}{4}+3=27\\ \\24+3=27\\ \\27=27[/tex]

That's correct!

x = 32.

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Guido can choose his Jolly Rancher in 78,125 different ways over the course of a week.

Guido chooses one sweet per day from a selection of five options; there are a total of five possible selections for a single day. Since there are seven days in a week, the sum of the ways Guido can choose candy over the course of a week equals the sum of the methods for each day.

Using the multiplication principle of counting

Total number of ways = 5 x 5 x 5 x 5 x 5 x 5 x 5

Simplifying this expression gives:

Total number of ways = 5^7

Using a calculator or by hand, we can compute:

Total number of ways = 78,125

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Answer:if their corresponding sides are proportional.

Step-by-step explanation:

The equation y² - y²x = 6  can be describe as a function of x as:

y = √(6/(x - x)).

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

y² - y²x = 6

Taking y² as common.

y²(1 - x) = 6

Divide both sides with (1 - x).

y² = 6/(1 - x)

Square root on both sides.

y = √(6/(x - x))

This is a function of x.

Thus,

y = √(6/(x - x)) is a function of x.

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