Determine the multiplicity of the roots of the function k(x) = x(x + 2)3(x + 4)2(x − 5)4. 0 has multiplicity −2 has multiplicity −4 has multiplicity 5 has multiplicity

Answer:

12%

Step-by-step explanation:

3/25 x 100 = 12

Answer:12%

Step-by-step explanation:

3/25 * 100 ☺

Answer:

For triangle VZX, VZ and ZX are perpendicular to each other.

This is because, perpendicular sides intersect to make a right angle.

Hope this helps,

♥A.W.E.S.W.A.N.♥

Final answer:

John can afford a maximum of 13 help sessions with his $170 budget for the year, after accounting for the $25.50 annual fee and the $10.50 per session charge.

Explanation:

To find the maximum number of help sessions John can use within his budget, we need to set up a simple algebraic equation. The total cost for the online help service consists of an annual fee plus the charge per help session. The equation to represent this situation will be:

Total Cost = Annual Fee + (Charge per Session × Number of Sessions)

We know the Annual Fee is $25.50, the Charge per Session is $10.50, and John's budget, or the Total Cost, is $170.

Let's denote the Number of Sessions as 'x'. The equation therefore becomes:

$170 = $25.50 + ($10.50 × x)

Subtracting the annual fee from both sides gives us:

$170 - $25.50 = $10.50 × x

$144.50 = $10.50 × x

Dividing both sides by $10.50 gives us the number of sessions John can afford:

x = $144.50 / $10.50

x = 13.7619...

Since John can't have a fraction of a session, we round down to the nearest whole number. John can afford a maximum of 13 help sessions within his budget of $170 for the year.

Answer:

The line which has slope 1/3 is a shallow line.

The line which has slope 2 is a steep line.

Both are increasing.

Step-by-step explanation:

Compare the lines by finding the slope between each pair of points.

Using the slope formula, substitute the points.

[tex]m = \frac{y_2-y_1}{x_2-x_1} = \frac{4-2}{6-0} = \frac{2}{6} = \frac{1}{3}[/tex]

[tex]m = \frac{y_2-y_1}{x_2-x_1} = \frac{7-1}{5-2} = \frac{6}{3} = 2[/tex]

The line which has slope 1/3 is a shallow line.

The line which has slope 2 is a steep line.

Answer:  option B.

Step-by-step explanation:

You can apply the elimination method:

- Multiply the first equation by -7 and the second equation by 3.

- Add both equations to cancel out the variable y.

- Solve for x

[tex]\left \{ {{(-7)9x+3y=(-39)(-7)} \atop {(3)(4x+7y)=(-57)(3)}} \right.\\\\\left \{ {{-63x-21y=273} \atop {12x+21y=-171}} \right.\\-------\\-51x=102\\x=-2[/tex]

- Substitute x=-2 into any of the original equations ans solve for y. Then:

[tex]9(-2)+3y=-39\\-18+3y=-39\\3y=-21\\y=-7[/tex]

The answer is:

B.

[tex]x=-2\\y=-7[/tex]

Solving the system of equations by elimination, we have:

[tex]\left \{ {{9x+3y=-39} \atop {4x+7y=-57}} \right.[/tex]

Then, multiplying the second equation by [tex]-\frac{9}{4}[/tex]

So,

[tex]\left \{ {{9x+3y=-39} \atop {4x*(-\frac{9}{4}) +7y*(-\frac{9}{4}) =-57*(-\frac{9}{4})}} \right\\\\\left \{ {{9x+3y=-39} \atop {-9x-\frac{63}{4}y=\frac{513}{4} }} \right\\\\-\frac{51}{4}y=\frac{357}{4}\\\\y=\frac{357}{4}*(-\frac{4}{51})=-\frac{1428}{204}=-7[/tex]

Then, substituting y=-7 into the first equation (also, we could substitute it into the first equation) we have:

[tex]9x+3(-7)=-39\\9x-21=-39\\9x=-39+21\\9x=-18\\x=\frac{-18}{9}=-2[/tex]

So, the solutions for the system of equations are:

[tex]x=-2\\y=-7[/tex]

Have a nice day!

Shade in 9 boxes

12÷4= 3 (This is 1 fourth)

3×3=9 (This is 3 fourths)

From the said figure, 9 out of the 12 pieces of the figure are shaded

The figure is cut into 12 equal pieces, and 3/4 of the figure is shaded. To find out how many pieces are shaded, we need to calculate 3/4 of 12.

To do this, we can multiply 3/4 by 12:

3/4 * 12 = 36/4 = 9.

So, 9 out of the 12 pieces are shaded.

To visualize this, imagine a circle divided into 12 equal slices. If you shade 3/4 of the circle, you will shade 9 out of the 12 slices.

Therefore, 9 out of the 12 pieces of the figure are shaded

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Answer:

G(12) = 15

Step-by-step explanation:

When doing g(x) equations, all you do is substitute the value inside the parentheses to x in the equation.

So you get 3/4(12) + 6.

Then simplify to get g(12) = 15

Answer:

The area of the octagon is [tex]173.8\ in^{2}[/tex]

Step-by-step explanation:

we know that

The area of a regular octagon is equal to the area of eight isosceles triangle

The base of each isosceles triangle is equal to the length side of the regular octagon

The vertex angle of each isosceles triangle is equal to

[tex]360\°/8=45\°[/tex]

The area of each isosceles triangle is equal to

[tex]A=\frac{1}{2}bh[/tex]

where

b is the length side of the regular octagon

h is the height of each isosceles triangle

Find the length side of the regular octagon b

The perimeter of a octagon is equal to

[tex]P=8b[/tex]

[tex]P=48\ in[/tex]

so

[tex]48=8b[/tex]

[tex]b=6\ in[/tex]

Find the height of each isosceles triangle h

[tex]tan(45\°/2)=(b/2)/h[/tex]

[tex]h=(b/2)/tan(45\°/2)[/tex]

substitute the values

[tex]h=(6/2)/tan(22.5\°)=7.24\ in[/tex]

Find the area of the octagon

[tex]A=8[\frac{1}{2}bh][/tex]

[tex]A=8[\frac{1}{2}(6)(7.24)]=173.8\ in^{2}[/tex]

➷ This will make sense once you see the formula:

volume = length x width x height

As it is a cube, all lengths are the same

Substitute the values in:

volume = 14 x 14 x 14

Exponents are when you multiply a value by itself

For example, 2 x 2 can be written as [tex]2^{2}[/tex]

In this case, the answer would be option 1. [tex]14^{3}[/tex]

➶ Hope This Helps You!

➶ Good Luck (:

➶ Have A Great Day ^-^

↬ ʜᴀɴɴᴀʜ ♡

Answer:

14 x 14 x 14

Step-by-step explanation:

Answer:

50 miles per day

Step-by-step explanation:

Answer:

Step-by-step explanation:

35 per day

Answer:

"All the powers have a value of 1 because the exponent is 0"

Step-by-step explanation:

To answer this, we need to recall the property that "ANYTHING to the power 0 is ALWAYS equal to 1" (except 0^0).

Here, we see that the base of all of the 4 choices are integers (and NOT ZERO) and all of them are raised to 0th power. So all of them are EQUAL TO 1.

Hence, the correct answer is "All the powers have a value of 1 because the exponent is 0"

Answer:

All the powers have a value of 1 because the exponent is 0

Step-by-step explanation:

Answer: 4 inches x 7 inches

Step-by-step explanation: Knowing that the formula for the area is length times width, 4 x 7 = 28 square inches. The perimeter of the rectangle with 2 sides that are 4 inches and 2 sides that are 7 inches is 22 inches. (2 x 4) + (2x7) = 8 + 14 = 22 inches.

The dimensions of the note card are length = 4 inches and width = 7 inches or length = 7 inches and width = 4 inches.

Let l be the length of the rectangular note card and w be its width.

Since the area of the rectangular note card is 28 square inches, we have that

lw = 28 (1)(the area of a rectangle).

Also, the perimeter of the rectangular note card is 22 inches. We have that

2(l + w) = 22 (2) (perimeter of a rectangle)

So, l + w = 11 (3)

From (3), l = 11 - w.

Substituting l into (1), we have

(11 - w)w = 28

11w - w² = 28

re-arranging, we have

w² - 11w + 28 = 0

Factorizing, we have

w² - 7w - 4w + 28 = 0

w(w - 7)- 4(w - 7) = 0

(w - 7)(w - 4) = 0

w - 7 = 0 or w - 4 = 0

w = 7 or w = 4

Since l = 11 - w,

substituting w = 7 into l, we have

l = 11 - 7 = 4 inches

substituting w = 4 into l, we have

l = 11 - 4 = 7 inches.

So, we have l = 4 and w =  7 or l = 7 and w = 4

So, the dimensions of the note card are length = 4 inches and width = 7 inches or length = 7 inches and width = 4 inches.

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Answer:

See attached picture.

Step-by-step explanation:

If you graph the system, you will find a region of solutions which are shaded. The point must be within the darkest shaded portion where each equation overlaps. This means it is a solution to both. Choose a point form your list in this region.

See attached picture.

Answer: ITS (0,5)

Step-by-step explanation:

i just did the algebra nation!!!

Answer:

Step-by-step explanation:

[tex]-2x^2-9=-107\qquad\text{add 9 to both sides}\\\\-2x^2-9+9=-107+9\\\\-2x^2=-98\qquad\text{divide both sides by (-2)}\\\\\dfrac{-2x^2}{-2}=\dfrac{-98}{-2}\\\\x^2=49\to x=\pm\sqrt{49}\\\\x=-7\ \vee\ x=7[/tex]

Answer: Normally C/C++

Step-by-step explanation:

The Arduino platform uses a language that is based on the C++ programming language. Despite some simplifications and extensions to better interact with Arduino hardware, those who are familiar with C++ will find similarities in Arduino.

The Arduino language is based on the C++ programming language. Although the materials provided mention Python, Scheme, and Modula-3, none of these are directly related to the Arduino language. The Arduino language includes many functions and libraries common in C++, which means that if you are familiar with C++, you will find it easier to understand and use Arduino.

However, note that Arduino is also slightly different from standard C++ as it includes some simplifications and extensions to make it easier to work with the Arduino hardware.

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Answer:

$14

Step-by-step explanation:

This should be simple, if ray earns $11 more, than hunter earns $25-$11, or $14

To find out how much Hunter earns, we subtract the $11 that Ray earns extra from Ray's total earning of $25, resulting in Hunter earning $14.

The student has asked a question regarding how much Hunter earns if Ray earns $25 which is $11 more than Hunter. To solve this, we subtract $11 from Ray's earnings to find Hunter's earnings:

Therefore, Hunter earns $14.

Answer:

D. 75%

Step-by-step explanation:

Percent of full retail price = 8+(1/2)(8)+(3/4)(8)/24

This simplifies to 0.75, which is equivalent to 75 percent.

$24 is full retail price so by dividing the amount Gia paid by it, you can find the percent of the full retail price.

Gia paid 75% of the full retail price for the three movie tickets.

To calculate the percent of the full retail price that Gia paid for the three tickets, we need to determine the total amount Gia paid and the full retail price for the three tickets.

Gia's $8.00 ticket is the regular retail price, so she paid the full price for her ticket. Her daughter's ticket is half-priced, which is $8.00 divided by 2, equaling $4.00. Her mother's ticket has a 25% discount, so she paid 75% of the full price, which is $8.00 multiplied by 0.75, equaling $6.00.

The total amount Gia paid is $8.00 + $4.00 + $6.00 = $18.00. The full retail price for the three tickets is $8.00 + $8.00 + $8.00 = $24.00. Therefore, Gia paid $18.00/$24.00 = 0.75, which is 75%, of the full retail price.

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A. ability to access cash value

hope this helps!!

Answer:

Part A) The function written in vertex form is [tex]f(x)=15(x+2)^{2}-79[/tex]

Part B) The vertex of the function is the point [tex](-2,-79)[/tex]

Step-by-step explanation:

Part A) Write the function in vertex form

we know that

The equation of a vertical parabola in vertex form is equal to

[tex]y=a(x-h)^{2}+k[/tex]

where

(h,k) is the vertex of the parabola

In this problem we have

[tex]f(x)=15x^{2}+60x-19[/tex]

Convert to vertex form

Group terms that contain the same variable, and move the constant to the opposite side of the equation

[tex]f(x)+19=15x^{2}+60x[/tex]

Factor the leading coefficient

[tex]f(x)+19=15(x^{2}+4x)[/tex]

Complete the square. Remember to balance the equation by adding the same constants to each side

[tex]f(x)+19+60=15(x^{2}+4x+4)[/tex]

[tex]f(x)+79=15(x^{2}+4x+4)[/tex]

Rewrite as perfect squares

[tex]f(x)+79=15(x+2)^{2}[/tex]

[tex]f(x)=15(x+2)^{2}-79[/tex] -----> function in vertex form

Part B) Name the vertex for the function

we have

[tex]f(x)=15(x+2)^{2}-79[/tex]

The vertex of the function is the point [tex](-2,-79)[/tex]

The parabola open upward, so the vertex is a minimum

see the attached figure to better understand the problem

4p + 7 = 3 + 4 + 4p

subtract 4p on both sides

7=7

since the equation equals it is infinite many solutions or...

all real numbers

Answer:

Infinite solutions!!

Step-by-step explanation:

4p + 7 = 3 + 4 + 4p

7 = 3 + 4

7 = 7

the domain, is the values for "x", namely the values used up over the x-axis.

the arrowheads on the lines, indicate the graph continues, upwards and to the sides, so it keeps on going to infinity.

however, let's notice that the values between -3 and 5, are not used up, those are not part of the graph, and therefore, are not part of the domain, however -3 and 5 ARE part of it, whilst all numbers between them are not.

using interval notation

( -∞ , -3 ]  ∪ [ 5 , +∞ )

it's notable that the ∞ signs have a parentheses, reason being, is a number we never touch because we don't know what the last number is :).

Answer:

x = -3

Step-by-step explanation:

Substitute the values m = 1 and from the points into the slope formula. Then solve for x.

[tex]m = \frac{y_2-y_1}{x_2-x_1}\\\\1 = \frac{1--6}{4-x}\\\\1 = \frac{7}{4-x}\\\\4-x = 7\\\\-3 = x[/tex]

ans 4th. ∆dcj =∆yam

Answer:

6x - 7y = -11

Step-by-step explanation:

To write the equation of a line when given two points, calculate the slope and substitute it into the point slope form of a line. From this form of the equation, you can simplify and convert to the standard form.

First, find the slope using the formula.

[tex]m = \frac{y_2-y_1}{x_2-x_1} =\frac{2--1}{\frac{1}{2} --3} =\frac{3}{\frac{7}{2}} = \frac{6}{7}/tex]

Substitute m = 6/7 and the point (-3,-1) into the point slope form [tex](y-y_1) = m(x-x_1)[/tex].

[tex]y--1=\frac{6}{7}(x--3)\\y + 1 = \frac{6}{7}(x+3)\\7y + 7 = 6(x + 3)\\7y + 7 = 6x + 18\\-6x + 7y + 7 = 18\\-6x + 7y = 11\\6x - 7y = -11[/tex]

To convert to standard form, multiply the equation by 7. This means each term is multiplied by 7 to clear the denominator. Then multiply using the distributive property. You will now need to move terms across the equal sign. Begin by subtracting 6x from both sides. Then subtract 7 from both side. Lastly, multiply the equation by -1 since the leading coefficient in standard form cannot be negative.

Answer:

65°

Step-by-step explanation:

<3 + <6 = 180  because they are same side interior angles

115 + <6 = 180

Subtract 115 from each side

115-115 +<6 = 180 -115

<6 = 65

Well according to my calculations its 110.

The real numbers between -4 and 6 are -3, -2, -1, 0, 1, 2, 3, 4, and 5.

The question asks for all real numbers between -4 and 6. In this case, the numbers between -4 and 6 are -3, -2, -1, 0, 1, 2, 3, 4, and 5.

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Answer:

8,if it broke some tiny thing from that it will fail but if it not broke it will be heavy then the broke one. the one that do not broke is the heavy one.

Step-by-step explanation:

Answer:10/16 (can simplify I think)

Step-by-step explanation: First you do 10+6 to find out the total of all the marbles which is 16. There are 10 blacks so you do 10/16 AS you wanna find out the probability of getting the black.

Answer:

62.5%

Step-by-step explanation:

First you add up all the marbles and then divide 100 into the sum of all of the marbles and then you times it by the black marbles to find the percent

100/(6+10)*10=%

X is 7 and y is 7 square root of 3.

Answer:

x = 7 and y = 7√3

Step-by-step explanation:

Let's review, and then apply, the definition of "cosine."

cos Ф = adjacent side / hypotenuse.

Here, x is the adjacent side, Ф is the angle and is 60°, and 14 represents the length of the hypotenuse.  cos Ф = adjacent side / hypotenuse becomes:

adjacent side = hypotenuse * cos Ф.

Here, Ф = 60° and cos Ф = cos 60° = 1/2.  Therefore,

in this case, x = 14(1/2), or 7.

Applying the definition of sine:

sin Ф = opp / hyp.  In this case, sin Ф = sin 60° = y/14, so that

y = 14 sin 60°, or y = 14(√3 / 2) = 7√3.

In summary, x = 7 and y = 7√3.