Find the zeros of the function and state the multiplicities.
k(x)=15x³-48x²-48x
If there is more than one answer, separate them with commas. Select "None" if applicable.
Part: 0/2
Part 1 of 2
Zero(s) of k:

Answers

Answer 1

The zeroes of the function k(x)=15x³-48x²-48x are 0, 4 and -4/5.

The function provided is a cubic polynomial.

There will be three zeroes in total for the function k(x).

K(x) = 15x³-48x²-48x

If we put x = 0,

We can see that k(x) becomes zero,

So we can say that 0 is a solutions for this function,

Now,

K(x) = x(15x²-48x-48)

Solving 15x²-48x-48 seperately using quadratic formula,

a = 15

b = -48

c = -48

x = (-b+√D)/D and (-b-√D)/D

D = b²-4ac.

D = (-48)²-4(15)(-48)

D= 5184.

√D = 72

putting all the values to find x,

x = (-(-48)+72)/30 and (-(-48)+72)/30

x = 4 and -4/5.

our function becomes,

k(x) = x(x-4)(x+4/5)

so the zeroes are 0, 4, -4/5.

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Related Questions

The second angle of a triangle is 10 more than the first angle. The third angle is three times the first. Find the three angles.
First angle:
Second angle:
Third angle:

Answers

Answer:

First, let one angle be a variable (eg: x) so that you can form expressions and solve.

Let the first angle be x°.

Then we can form expressions for the second and third angles using the information given.

First angle = x°

Second angle = (x + 10)°

Third angle = (3x)°

Since sum of angles in a triangle is 180°, we can form an equation.

x + (x + 10) + 3x = 180

Simplify and solve for x.

5x + 10 = 180

5x = 170

x = 34

Substitute x into the expressions to find the angles.

First angle = 34°

Second angle = 34 + 10

= 44°

Third angle = 3(34)

= 102°

3. Allison Separates 23 stickers into 4 4 equal piles. How many stickers does she have left over?​

Answers

She has 3 left over. 23/4=5.777 this is not an even/valid awnser. So you round down!

A is shaped like a rectangle whose perimeter is 378ft . The length is 8 times as long as the width. Find the length and the width.

Answers

The length and width of the rectangle with a perimeter of 378ft are 168ft and 21ft respectively.

What is the length and the width of the rectangle?

The formula used in calculating the perimeter of a rectangle is expressed as;

P = 2( l + w )

Where l is length and w is width.

Given the data in the question;

Let 'x' represent the width of the rectangle.

Width of the rectangle w = xLength of the rectangle l = 8xPerimeter P = 378ft

Plug the given values into perimeter formula and solve for x .

P = 2( l + w )

378 = 2( 8x + x )

378 = 2( 9x )

378 = 18x

18x = 378

x = 378/18

x = 21

Now, we find the length and width of the rectangle.

Width of the rectangle w = x = 21ft

Length of the rectangle l = 8x = 8( 21 ) = 168ft

Therefore, the width of the rectangle is 21ft while its length is 168ft.

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The difference of the ages of a father and his son is 25 years.Fifteen years ago.the father was six times of his son's age. Find their present ages.

Answers

Present age of father is 48 years and that of son is 23 years.

Let the age of father be x years

And the son's age be y years

According to the question,

x - y = 25 -----------1

15 Years ago, x= 6( y - 15 )

x= 6y - 90 -------------2

Substituting value of x from equation 2 in equation 1, we get

6y - 90 - y = 25

5y -90 = 25

5y = 25+90

5y= 115

y= 23

Therefore son's age is 23 years and from equation 1 we get x= 25+y = 25+23 = 48 years. So father's age is 48 years.

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Use the table to answer the question. 2 6 10 12 10 30 50 60 Simplify each ratio in the table to prove that all the ratios are equivalent. (2 points) 210= , 630= , 1050= , 1260=

Answers

The expression given relating to the take all have an equivalent ratio of 1:5.

How to express the ratio?

It should be noted that ratio is simply used to show the comparison between two or or more things.

In this case, in the table, the ratio given will be illustrated as:

2/10 = 1/5 = 1:5

6/30 = 1/5 = 1:5

10/50 = 1/5 = 1:5

12/60 = 1/5 = 1:5

In this case, it should be noted that for every number that was illustrated, we have an equivalent value of 1:5. Therefore, this explains that it's an equivalent ratio.

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Solve for all values of x:
√8x + 1 = √2x + 5

Answers

Step-by-step explanation:

[tex] \sqrt{8} x - \sqrt{2} x = 4[/tex]

[tex]x( \sqrt{8} - \sqrt{2} ) = 4[/tex]

[tex]x = \frac{4}{ \sqrt{8} - \sqrt{2} } [/tex]

the second term could be positive or negative

therefore

x=2.83 or

=-2.83

which is the square root of 8 - and positive

A serving of rice is 5/6 of a cup. How many servings are there in a 3 1/3 cup bag of rice?

Answers

Answer:

there are 7 severeings of rice

the value of a share of stock on the stock market decreased by 15%. If it used to be worth $55.55, what is it worth now? Round to the nearest hundredth.

Answers

The worth of the share after a 15% fall will be $47.21.

What is the percentage?

The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.

Given that the value of a share of stock on the stock market decreased by 15%. If it used to be worth $55.55.

The value of the share after 15% fall will be calculated as:-

Decreased amount = 55.55 - ( 55.55 x ( 15 / 100)

Decreased amount = $47.21

Therefore, the worth of the share after a 15% fall will be $47.21.

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I'm trying to find out if {(6,0), (-9,5), (1,-5), (0,0)} is a function or not

Answers

A technical definition of a function is: a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.

In this case, it would be a function

Each Saturday 8 workers mow the park
lawn. When all 8 workers are there, it takes
them 6 hours to complete the job. Last
Saturday three of the workers had the flu.
How many hours did it take the remaining workers
to complete the job?
A. 9 and %
B. 2 and 14
C. 12 and 18
D. 6 and 2

Answers

I think it’s answer A.

20PTS
Please help answer quickly

Answers

Answer:

second option

HURRY
TIME REMAINING
57:30
What are the solutions to –24x – 24 = x3 + 8x2?

Negative 1, negative 3 + i StartRoot 3 EndRoot, negative 3 minus i StartRoot 3 EndRoot.
1, 3 + i StartRoot 3 EndRoot, 3 minus i StartRoot 3 EndRoot.
2, 3 + i StartRoot 3 EndRoot, 3 minus i StartRoot 3 EndRoot.
Negative 2, negative 3 + i StartRoot 3 EndRoot, negative 3 minus i StartRoot 3 EndRoot.

Answers

Answer:

Negative 2, negative 3 + i StartRoot 3 EndRoot, negative 3 minus i StartRoot 3 EndRoot.

Step-by-step explanation:

So basically that whole last section you had your answer should look like this:

Volunteers are preparing identical backpacks for refugees. There are 32 maps and 24 dictionaries to use for the backpacks. What is the greatest number of backpacks they can prepare using all of the maps and dictionaries?​

Answers

Considering the definition of greatest common divisor, the greatest number of backpacks volunteers can prepare using all of the maps and dictionaries is 8.

Definition of greatest common divisor

Considering that a divisor can be formally defined as that number that is contained in another exactly n times, the greatest common divisor is the largest number by which two or more numbers can be divided. That is, the greatest common factor is the highest number by which a set of numbers can be divided, resulting in a whole number.

To calculate the greatest common factor, the following steps must be followed:

Decompose each number into prime factors. [The prime factors of an integer are the exact divisors of that integer, that is, they have only two divisors: one and themselves]Then point out the common factors.In each of the common factors, choose the factor with the smallest exponent.Multiply the chosen factors.

Greatest number of backpacks prepared

In this case, you must calculate the greatest common factor as follows:

Decomposition of 32: 2⁵Decomposition of 24: 2³×3

2 is the factor common to both numbers, with 3 being the smallest exponent found. Then the greatest common divisor is calculated as:

Greatest common divisor= 2³

Greatest common divisor= 8

This means that they can prepare 8 backpacks.

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What the area of the sphere if it's volume is 3x +1 cm³​

Answers

Answer:

[tex]{ \tt{volume = \frac{4}{3} \pi {r}^{3} }} \\ \\ { \tt{v = \frac{4}{3} \pi {r}^{3} }} \\ \\ { \tt{area = \frac{dv}{dr} = 4\pi {r}^{2} }} \\ \\ { \tt{area = \frac{d(3x + 1)}{dx} }} \\ \\ { \tt{area = 3 \: {cm}^{2} }}[/tex]

If EGF & EGH, EF = 6a, and EH = a + 55, what is the value of a?

Answers

Answer:

a=11

Step-by-step explanation:

If both triangles have two sides E and G the same then thethird side F and H must be equal

EF=EH

6a=55+a

5a=55

a=11

Please help I’ll mark you as brainliest if correct!!

Answers

Answer:The answer is 8

Step-by-step explanation:

21-13

Write the equation that is parallel to 2x+y =4 going through the point (-1,3)

Answers

Answer:

  2x +y = 1

Step-by-step explanation:

You want the equation of a line parallel to 2x+y=4 through point (-1, 3).

Parallel line

A parallel line will have the same slope, which is a function of the ratio of the x- and y-coefficients. Hence, the equation of the parallel line can use the same coefficients. It will have a constant suitable for the given point.

  given: 2x +y = 4

  parallel: 2x +y = c

  through point (-1, 3): 2x +y = 2(-1) +(3) = 1

The equation of the parallel line is 2x+y = 1.

Determine the more basic function that has been shifted reflected stretched or compressed what does

Answers

[tex]f(x)=\sqrt{x}[/tex]

Explanation

The graph of a function f is the set of all points in the plane of the form (x, f(x)).

Step 1

iven

[tex]g(x)=-2\sqrt{x-1}+4[/tex]

g(x) is a transformation of the function f(x)we have a root in the function, note that the variable x is inside the root, so we can conclude the basic function is

square tooroot

Step 2

rove

ow, lets's check the transformation of f(x)

[tex]f(x)=\sqrt{x}[/tex]

a)1 was subtracted form the argument of the fucnction

[tex]\begin{gathered} f(x)=\sqrt{x} \\ f^{\prime}(x)=\sqrt{x-1} \end{gathered}[/tex]

when you subtract a number b form the argument of the function you are shifting the function b units to the rigth

so

he function was shifteed 1 unit to rigth

) the resulting function was multiplied by 2-

[tex]\begin{gathered} f^{\prime}(x)=\sqrt{x-1}\text{ *-2} \\ f^{\prime}^{\prime}(x)=-2\sqrt{x-1} \end{gathered}[/tex]

when you multplie by a negavitve constant you are reflecting the funciton acrros x-axis, and is is stretched vertically.

so

he funcition was reflected across x-axis an strtched vertically by a factor of 2

c) 4 was added to the function

[tex]\begin{gathered} f^{\prime\prime}(x)=-2\sqrt{x-1} \\ g(x)=-2\sqrt{x-1}+4 \end{gathered}[/tex]

when you add a constant b to any function, the graph will be shifted b units up,so

he functinon was shifted 4 units up

hrerefore, we can conclude the answer is

[tex]f(x)=\sqrt{x}[/tex]

I hope this helps you

Each question on a multiple choice exam has four choices. One of the choices is the correct answer, worth five points another choice is wrong but still carries partial credit of 1 point and other two choices are worth 0 points. If the student picks answers at random, what is the expected value of his or her score for a problem?

Answers

If a student picks randomly then the expected value of his or her score for a problem is 1.5.

Each question on a multiple-choice exam has four choices.

One of the choices is correct, worth four points.

Another choice is wrong but carries partial credit for one point.

The other two choices are wrong and worth a negative one point.

Each has a probability of getting selected is 0.25.

[tex]0.25*5+0.25*1+0.25*0+0.25*0[/tex]

[tex]1.25+0.25[/tex]

[tex]1.5[/tex]

What is the expected value?

The expected value denotes potential. The occurrence of a random event is the subject. Its fundamental notion is that something is probable to occur.

Actually, the anticipated value may be viewed as the mean of a random variable. This indicates that the anticipated value is the average of all the values acquired if a probability experiment were repeated again while keeping track of the outcomes. The anticipated value of a game of chance is what you should expect to occur over the long run of several trials.

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The new bookkeeper at Karlin Construction Company was asked to write off two accounts totaling $1,610 that had been determined to be uncollectible. Accordingly, he debited Accounts Receivable for $1,6

10 and credited Bad Debt Expense for the same amount.

Answers

The thing that is wrong with the bookkeeper’s entry assuming Karlin uses the allowance method is that the company uses allowance method and thus the write-off entry would not be to bad debt account.

How yo illustrate the information?

It should be noted that because the business is using the allowance approach in this instance, the write-off entry would not be to the account for bad debts. To write off an account, a debit must be made to a separate account that is kept as an allowance for dubious accounts.

Since the receivables would not be collected, the accounts receivable account would be credited. In this case,the write off isn't appropriately illustrated in the account.

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The new bookkeeper at Karlin Construction Company was asked to write off two accounts totaling $1,610 that had been determined to be uncollectible. Accordingly, he debited Accounts Receivable for $1,610 and credited Bad Debt Expense for the same amount.

Determine what was wrong with the bookkeeper’s entry assuming Karlin uses the allowance method.

HELP PLEASE WILL GIVE BRAINLIEST!!! I NEED HELP

Answers

Answer: y = -x + 3

Step-by-step explanation:

y = mx + b

We need to find the slope of the equation first.

Change in y: 7 - 0 = 7

Change in x: -4 - 3 = -7

Slope = Change in y / Change in x

slope = 7 / -7 = -1

Now, plug the slope into the equation to find b.

0 = -1(3) + b

b = 3

or 7 = -1(-4) + b

b = 3

in the pic.............

Answers

Given -

a = 2.5 cm

b = 3.6 cm

∠A = 43°

To Find -

Remaining angles and sides =?

Step-by-Step Explanation -

We will start by drawing the diagram:

Now, we know

By, sine rule:

[tex]\begin{gathered} \frac{\sin A}{a}\text{ =}\frac{\sin B}{b}=\frac{\sin C}{c} \\ \\ =\text{ }\frac{\sin43}{2.5}\text{ = }\frac{\sin C}{3.6} \\ \\ =\text{ }\sin C\text{ = }\frac{3.6\times\sin44}{2.5} \\ \\ =\text{ }\sin C\text{ = 0.9820} \\ \\ C\text{ = }\sin^{-1}(0.9820) \\ \\ C\text{ = 79} \\ \end{gathered}[/tex]

Now, we know N

A + B + C = 180 c°°

43 + B + 79° = 180°°

B = 180° - 799 - 43°°

B = 58°

Now, Side b =

[tex]\begin{gathered} \frac{\sin A}{a}\text{ = }\frac{\sin B}{b} \\ \\ \frac{\sin43}{2.5}\text{ = }\frac{\sin58°}{b} \\ \\ b\text{ = }\frac{2.5\times\sin58°}{\sin43°} \\ \\ b\text{ = 3.1} \end{gathered}[/tex]

Final Answer -

∠B = 58B°

∠C = 797°

Side, b = 3.1 cm

Factor 15cd − 45c ^2d.

3c ^2d(5 − 15)
5cd(3 − 15c ^2d)
3cd(5 − 15c)
5cd(3 − 45c ^2d)

Answers

3/2d

DIFFERENTIATE W.R.T. D

3

2

≈0.666666667

Solve each related rate problem.6) Oil spilling from a ruptured tanker spreads in a circle on the surface of the ocean. Theradius of the spill increases at a rate of 4 m/min. How fast is the area of the spillincreasing when the radius is 7 m?A) 63 m²/min B) 54rt m®/min C) 5211 m²/min D) 560 m²/min7) A spherical balloon is inflated so that its radius increases at a rate of 2 cm/sec. How fast

Answers

6.

We know area of circle is

[tex]\pi r^2[/tex]

Radius increases at a rate of 4.

So, we can write:

[tex]\frac{dr}{dt}=4[/tex]

We want rate of change of area. Thus,

[tex]\begin{gathered} A=\pi r^2 \\ dA=2\pi\text{rdr} \\ \frac{dA}{dt}=2\pi r\frac{dr}{dt} \end{gathered}[/tex]

We want dA/dt at r = 7, so substituting all that we know:

[tex]\begin{gathered} \frac{dA}{dt}=2\pi r\frac{dr}{dt} \\ \frac{dA}{\text{dt}}=2\pi(7)(4) \\ =56\pi \end{gathered}[/tex]

The correct answer: 56*pi m^2/min

Please answer I give Brainliest

Answers

Answer:

hmmm

Step-by-step explanation:

what does the j, k, m, and l stand for?

Which property of multiplication is (ab)c = a(bc)

Answers

Answer: The Associative Property

Step-by-step explanation:

Example:

[tex]a * (b * c) = (a * b) *c[/tex]

[tex]2 *(4 * 5) = (2 * 4) * 5[/tex]

linear inequality: y>-2x-3

Answers

Answer:

The graph depicting inequality y > -2x - 3 is C

You thought you had finished 35 pages, but you actually read 32 Pages. What was your percent error?

Answers

[tex]\frac{35-32}{32} \times 100=\frac{75}{8}=9.375\%[/tex]

Answer:

9.375%

Step-by-step explanation:

Percentage Error formula

[tex]\textsf{Percentage error}=\sf \left|\dfrac{estimated\:value\:-actual\:value}{actual\:value} \right| \times 100\%[/tex]

Given:

Estimated value = 35 pagesActual value = 32 pages

Substitute the given values into the formula:

[tex]\begin{aligned}\implies \textsf{Percentage error}&= \left|\dfrac{35-32}{32} \right| \times 100\%\\\\&=\left|\dfrac{3}{32} \right| \times 100\%\\\\&=0.09375 \times 100\%\\\\&=9.375\%\end{aligned}[/tex]

Therefore, the percentage error was 9.375%.

5x-4=-3x+12
What is the answer

Answers

The answer is x = 2

I have attached a picture with the work

Match the following.

Answers

The match of the given equations and choices of the properties of equality are;

If a = b and b = c then a = c ; Transitive Property

If a = b then a ÷ c = b ÷ c; Division property of =

a = a; Reflexive property

If x + a = b and x = c then c + a = b; Substitution Property

If a = b then a + c = b + c; Addition Property of =

If a = b then ac = bc; Multiplication Property of =

If a•b = a•c then a•c = a•b Symmetric Property

a•(b + c) = a•b + a•c; Distributive property

If a = b then a - c = b - c; Subtraction Property of =

What are the properties of equality?

Properties of equality includes; addition, subtraction, transitive, reflexive, and symmetric properties of equality

Transitive Property

The transitive property of equality can be stated as follows; If two variables are each equal to a third variable, then the two variables are equal to each other.

Therefore; a = b and b = c then a = c represents the transitive property

Division property of equality

The division property states that both sides of an equation remain equal, following a division of both sides by the same non zero number

Therefore;

If a = b then a ÷ c = b ÷ c; represents the division property of equality

Reflexive property

The reflexive property of equality states that a measure or number is always equal to itself

Therefore;

a = a represents the reflexive property

Substitution Property

Substitution property indicates that if two variables are equal, then one can replace the other in an equation and the results will remain the same

Therefore;

If x + a = b and x = c then c + a = b; represents the substitution property

Addition and Subtraction Property of Equality

The statement of the addition (and subtraction) property of equality is that both sides of an equation remain equal following the addition or subtraction of the same amount from both sides the same

Therefore;

If a = b then a + c = b + c; represents the addition property of equality

If a = b then a - c = b - c; represents the subtraction property of equality

Multiplication Property of Equality

This states that both sides of an equation remain equal following the multiplication of both sides by the same value

Symmetric Property

The symmetric property states that two sides of an equation remain equal when their relative positions are interchanged

Distributive Property

This states that two sides of an equation remain equal following a distribution with multiplication over addition or subtraction.

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