Use the function below to answer the question.

[tex]f(x)=x^3+7x^2+16x+12=(x+2)(x+2)(x+3)[/tex]

What is the multiplicity of the root -3 ?

l - lenght

w - width

l - w = 5 → l = 5 + w

26 m - perimeter

l + l + w + w = 2l + 2w - perimeter

substitute l = 5 + w:

2(5 + w) + 2w = (2)(5) + (2)(w) + 2w = 10 + 2w + 2w = 10 + 4w

The equation:

10 + 4w = 26     subtract 10 from both sides

4w = 16    divide both sides by 4

w = 6

Answer: 15

Step-by-step explanation:

 Boys  :  Girls

    3x   +   1x    = 60

4x = 60

 x = 15

Girls (1x) = 1(15) = 15

Answer:

The answer is 15

Answer:

88%

Step-by-step explanation:

if she got 3 problems wrong, so she got (25-3)=22problems correct,

22/25=x/100,x=88

The percent of the questions did she get correct will be 88%.

The quantity of anything is stated as though it were a fraction of a hundred.

Kimberly got 3 problems wrong on a test of 25 questions.

Then the number of the correct question will be

⇒ 25 – 3

⇒ 22

Then the percent of the questions did she get correct will be

⇒ (22 / 25) x 100

⇒ 0.88 x 100

⇒ 88%

More about the percentage link is given below.

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Answer:

The required simplest form is: [tex]\frac{2}{5}[/tex]

Step-by-step explanation:

We have been given Kyle has 125 marbles.

And 50 out of total 125 are red and rest of them are other colours

that means other colour marble are 125-50=75

we need to find ratio of the number of red marbles to the total of marbles  

The rat io is: [tex]\frac{50}{125}=\frac{2}{5}[/tex]

The required simplest form is: [tex]\frac{2}{5}[/tex]

Answer:

Step-by-step explanation:

2/5

Answer:

Find tan θ if sec θ = (sqrt26)/5 and sin θ < 0 = tan θ = -1/5

Step-by-step explanation:

cos θ = 5/√26  

opposite side = s  

s^2 = 26-25 = 1  

s = -1  

tan θ = -1/5

Answer:

arc ≈ 25.13 feet

Step-by-step explanation:

arc length = circumference × fraction of circle

= 2 πr × [tex]\frac{\frac{4\pi }{3} }{2\pi }[/tex] ← cancel 2π

= 6 × [tex]\frac{4\pi }{3}[/tex] = 8π ≈ 25.13 feet

Answer: he has 3000

Step-by-step explanation: just multiply 600 by 5

Answer:

120

Step-by-step explanation:

all you do is 600 x 1/5

but u have to turn 1/5 into a decimal which is .20

so 600 x .20= 120

Answer:

convenience sample

Step-by-step explanation:

Answer: Convenience Sample

Step-by-step explanation: Biased sample–Parts of the population are favored over others. She only asked people in her office

Answer:

It would be 90 because if there are 15 soccer people on the team and there are 6 in the packets then each would get 1 and if you multiply 15 times 6 you will get 90.

So the answer would be 90

Answer:

90

Step-by-step explanation:

just do 15x6

The largest possible value for (a.bc + 0.d) is (10.56).

The largest possible value for (a.bc + 0.d) when (a), (b), (c), and (d) are replaced by four different digits from 1 to 9, inclusive, can be found by selecting the largest digits for (a), (b), and (c), and the smallest digit for (d).

This results in the number (9.86 + 0.7), which equals (10.56).

Therefore, the largest possible value for (a.bc + 0.d) is (10.56).

Complete question:

If a,b,c,d are replaced by four different digits from 1 to 9, inclusive, then what's the largest possible value for a.bc + 0.d ?

Answer:

18.91 percent

Step-by-step explanation:

Percent error equation:     Difference       or    Difference/Actual

                                            Actual

The difference is the greater amount minus the smaller.

111 - 89 = 22

The actual is 111.

Now divide 22/111.

22/111 = 0.189 repeating

0.189 repeating = about 18.91 percent

Hence, the option (A) is the correct answer i.e., The graph of [tex]g(x + 1)[/tex]is the graph of [tex]g(x)[/tex] shifted right one unit.

What is the function?

Functions are often defined by a formula that describes a combination of arithmetic operations and previously defined functions; such a formula allows computing the value of the function from the value of any element of the domain.

As per the given information option (A) is correct because it will shift to the right side by one unit when the function of [tex]g(x)[/tex] is [tex]g(x+1)[/tex].

For example:-

[tex]x=2[/tex]

So,

[tex]g(2)\\g(2+1)[/tex]

Hence, the option (A) is the correct answer i.e., The graph of [tex]g(x + 1)[/tex]is the graph of [tex]g(x)[/tex] shifted right one unit.

To know more about the functions

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Final answer:

The true statement for the graphs of all functions g(x) is that the graph of g(x + 1) is the graph of g(x) shifted left by 1 unit.

Explanation:

When considering the transformation of the graph of a function g(x) to g(x + 1), we are applying a horizontal shift to the graph. According to the principles of graph transformation, when we add a positive constant to the input of a function, every point on the graph shifts left by that amount. Therefore, the graph of g(x + 1) is the same as the graph of g(x), shifted to the left by 1 unit. This corresponds to the option C, which states that adding 1 to the input of the function shifts the graph to the left by 1 unit.

Answer:

The triangles are similar, because the angles are congruent and the sides are proportional.

Step-by-step explanation:

The first step to see if the triangles are similar is to see if the angles are the same.

The third angle in the large triangle is

30 + 65+ unknown = 180

95 + unknown = 180

Subtract 95 from each side

unknown = 180-95

unknown = 85

So the angles are the same.

Lets check the ratio of the the sides

14            10

------ = ----------

7                5    

Both simplify to 2/1  so the ratio's are the same.

The triangles are similar because the angles are congruent and the sides are proportional.

Melanie drove a total of 500 miles over three days. To determine how many miles she drove each day, we divided total miles by total days. This gives us 166.67 miles or 166 2/3 miles as a mixed number.

The subject of the provided question is related to simple division. Here, Melanie has traveled 500 miles in total over the course of three days, and she drove the same distance each day. Mathematically speaking, to find out how many miles Melanie drove each day, we need to divide the total distance by the number of days. Hence, we divide 500 miles by 3 days.

This comes out to be 166.67 miles, which is the decimal format of the distance traveled by Melanie each day. However, the question asks for the answer to be written as a mixed number. Therefore, 166.67 miles can be expressed as 166 2/3 miles per day, as a mixed number. This is calculated by expressing the decimal .67 as a fraction.

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Answer:

35 + 5h = m

Step-by-step explanation:

Add 1,1.5,1.25,2.5, and 3 to get D, or 9 and 1/4.

Answer:

9 and 1/4 hope this helps!!!!!

Answer:

Number of​ restaurant-purchased meals eaten in a​ restaurant = 70

Number of​ restaurant-purchased meals eaten in a​ car = 22

Number of​ restaurant-purchased meals eaten in a​ home = 60

Step-by-step explanation:

Let the number of people that will eat in a restaurant be R.

Let the number of people that will eat in a car be C.

Let the number of people that will eat in a home be H.

From the information given in the problem we have,

R+C+H = 152 ____equation (1)

C+H-R = 12 ____equation (2)

R = H+10 ____equation (3)

1) Plugging in R=H+10 from equation 3 into the equation 2, we get

C+H-R=12

=> C+H-(H+10)=12

=> C+H-H-10=12

2) Cancelling out +H and -H, we get

C-10=12

3) Add 10 to both sides

C-10+10=12+10

4) Cancelling out -10 and +10, we get

C=22

5) Plugin C=22 in equation 1, we have

R+C+H = 152

=> R+22+H=152

Subtract 22 from both sides,

R+22+H-22=152-22

Cancelling out +22 and -22 from the left side, we get

R+H=130 ____let it be equation (4)

6) Plugin C=22 in equation 2, we have

C+H-R = 12

22+H-R = 12

Subtracting 22 from both the sides, we get

22+H-R-22 = 12-22

Cancelling out +22 and -22 from the left side,

H-R = -10 ____let it be equation (5)

7) Adding equation 4 and equation 5, we get

(R+H)+(H-R) = 130 + (-10)

=> R+H+H-R = 130-10

8) Cancelling out R and -R from the left side, we get

2H = 120

9) Dividing both sides by 2, we get

[tex]\frac{2H}{2} = \frac{120}{2}[/tex]

10) Cancelling out the 2's from the left side, we have

H=60

11) Plugging in C=22 and H=60 in the equation 1, we have

R+C+H = 152

=> R+22+60=152

=> R + 82 = 152

12) Subtracting 82 from both the sides, we get

R + 82 -82 = 152 -82

13) Cancelling out +82 and -82 from the left side, we get

R = 70

So, C=22, H=60, R=70

Answer:

Two real solutions

Step-by-step explanation:

z=-1.45

z=0.45

Answer:

ANSWER: Two real solutions

Step-by-step explanation:

its z=-1.45

its z=0.45

Answer:

46%  of Xander's friends prefer to stay home on Friday nights.

Step-by-step explanation:

Formula

[tex]Percentage = \frac{Part\ value\times 100}{Total\ value}[/tex]

As given

[tex]\frac{23}{50}\ of\ Zanders\ friends\ prefer\ to\ stay\ home\ on\ Friday\ night.[/tex]

i.e

Zanders friends prefer to stay home on Friday night = 23

Total numbers of Zanders friends are 50.

Part value = 23

Total value = 50

Put in the formula

[tex]Percentage = \frac{23\times 100}{50}[/tex]

[tex]Percentage = \frac{2300}{50}[/tex]

Percentage = 46%

Therefore 46%  of Xander's friends prefer to stay home on Friday nights.

Answer:

wasdd ada

Step-by-step explanation:

Answer:

the bacteria's population is 120

Step-by-step explanation:

Answer:

After 40 hrs it is 213.333 bacterias

Approximately 213 bacterias

Step-by-step explanation:

Initial population of bacteria is 40

And it doubles every 15 hrs

If 15 hrs is double

1 hrs is 0.13333

Then 10 hrs is 1.3333

So the first 15 hrs

It multiplies to 40*2= 80

The second 15 hrs it multiplies by 80*2=160

The next 10 hrs it multiplies by

160*1.33333= 213.333

Answer:

1) [tex]2s+s\leq18[/tex]

2) 6 years old

Step-by-step explanation:

Let Hannah's age be [tex]h[/tex] and her sister's age be [tex]s[/tex]

It means [tex]h=2s[/tex]

It means the sum is LESS THAN or EQUAL TO 18. So we can write:

[tex]h+s\leq18[/tex]

1. We can substitute first equation into second equation to get our desired inequality of the situation. Thus,

[tex]h+s\leq18\\2s+s\leq18[/tex]

2. To find MAXIMUM age of Hannah's sister, let's further simplify the inequality from number 1. So,

[tex]2s+s\leq18\\3s\leq18\\s\leq\frac{18}{3}\\s\leq6[/tex]

Hence, Hannah's sister's age is LESS THAN OR EQUAL TO 6. So maximum age of her sister is 6.

Answer:

f(t) = 451,400(0.968)^t

Step-by-step explanation:

Exponential Decay Function:

y = b (1-r) ^t

where

f(t)= 451,400 ( 1 - 0.032) ^t

f(t) = 451,400 (0.968) ^t

Answer:

This was the correct answer, I even provided proof from my own test. Hope this helps!

Step-by-step explanation:

Answer:

C. 2x^2 - 85 / 13

Answer:

(x, y) = (- 3, - 2)

Step-by-step explanation:

given the 2 equations

5x + 7y = - 29 → (1)

y = x + 1 → (2)

substitute y = x + 1 into (1)

5x + 7(x + 1) = - 29 ( distribute and simplify left side )

5x + 7x + 7 = - 29

12x + 7 = - 29 ( subtract 7 from both sides )

12x = - 36 ( divide both sides by 12 )

x = - 3

substitute x = - 3 into (2)

y = - 3 + 1 = - 2

solution is (- 3, - 2 )

Answer:

(-3,-2)

Step-by-step explanation:

4.42×10^34 molecules/min

Multiply the various factors, along with the unit conversion (60 s/min).

... (3.35×10^25 molecules/L) × (2.2×10^7 L/s) × (60 s/min)

... = (3.35×2.2×60)×10^(25+7) molecules/min

... = 442.2×10^32 molecules/min

... ≈ 4.42×10^34 molecules/min

_____

Comment on scientific notation problems

Your scientific or graphing calculator will allow you to enter and display numbers in scientific notation.

Answer:

The solution to the system would be (3, -1)

Step-by-step explanation:

You can find the solution to this system by using the elimination method. To do that, start by multiplying the top equation by -5 and then adding it through.

-5x + 20y = -35

5x + 9y = 6

-----------------

29y = -29

y = -1

Now that we have the value of y, we can plug it into either equation and find the x value.

x - 4y = 7

x - 4(-1) = 7

x + 4 = 7

x = 3

Final answer:

The solution to the given system of equations is the ordered pair (3, -1).

Explanation:

To find the solution to the system of equations, we can use the method of substitution or elimination. Let's use the method of substitution.

1. Solve the first equation for x:

x = 7 + 4y

2. Substitute this value of x into the second equation:

5(7 + 4y) + 9y = 6

3. Simplify and solve for y:

35 + 20y + 9y = 6

29y = -29

y = -1

4. Substitute the value of y back into the first equation to find x:

x = 7 + 4(-1)

x = 3

Therefore, the solution to the system is the ordered pair (3, -1).

Answer:

A.  F(x) = x^3+9x^2+27x+27

Step-by-step explanation:

I am not 100% sure but I think this is right.

I found the root for this equation: x=-3

Hope this helps!

Answer:

The correct option is D.

Step-by-step explanation:

In option A,

The given function is

[tex]F(x)=x^3+9x^2+27x+27[/tex]

[tex]F(x)=x^3+3(3)x^2+3(3^2)x+3^3[/tex]

[tex]F(x)=(x+3)^3[/tex]              [tex][\because (a+b)^3=a^3+3a^2b+3ab^2+b^3][/tex]

Equate the function equal to zero, to find the roots.

[tex](x+3)(x-3)(x-3)=0\Rigtharrow x=-3[/tex]

The real root of this function is -3 with multiplicity 3. It means this function has 3 real roots.

In option B,

The given function is

[tex]F(x)=x^3+3x^2-9x-27[/tex]

[tex]F(x)=x^2(x+3)-9(x-3)[/tex]

[tex]F(x)=(x^2-9)(x+3)[/tex]

[tex]F(x)=(x+3)(x-3)(x+3)[/tex]         [tex][\because a^2-b^2=(a+b)(a-b)][/tex]

Equate the function equal to zero, to find the roots.

[tex](x+3)(x-3)(x+3)=0\Rigtharrow x=-3,3,-3[/tex]

Therefore, this function has 3 real roots.

In option C,

The given function is

[tex]F(x)=x^3-9x^2+27x-27[/tex]

[tex]F(x)=x^3-3(3)x^2+3(3^2)x-3^3[/tex]

[tex]F(x)=(x-3)^3[/tex]              [tex][\because (a-b)^3=a^3-3a^2b+3ab^2-b^3][/tex]

Equate the function equal to zero, to find the roots.

[tex](x-3)(x-3)(x-3)=0\Rigtharrow x=3[/tex]

The real root of this function is 3 with multiplicity 3. It means this function has 3 real roots.

In option D,

[tex]F(x)=x^3+3x^2+9x+27[/tex]

[tex]F(x)=x^2(x+3)+9(x+3)[/tex]

[tex]F(x)=(x+3)(x^2+9)[/tex]

Equate the function equal to zero, to find the roots.

[tex](x+3)(x^2+9)=0[/tex]

[tex]x+3=0\Rightarrow x=-3[/tex]

[tex]x^2+9=0\Rightarrow x^2=-9\Rightarrow x=\pm 3i(Imaginary)[/tex]

The roots of this functions are -3, 3i and -3i. Since this function has exactly one real root, therefore option D is correct.

Answer: (A) 10

Step-by-step explanation:

                Value       Quantity     =  TOTAL Value

dimes:        .10            Q + 5        =    .10(Q = 5)

quarters:    .25               Q           =      .25Q

Dimes + Quarters = $4.00

.10(Q + 5) + .25Q = 4.00

.10Q + .50 + .25Q = 4.00

           .50 + .35Q = 4.00

                    .35Q = 3.50

                          Q = 10

Quarters = 10

Dimes = Q + 5

           = 10 + 5

           = 15

Answer: Option A, she has 10 quarters.

Step-by-step explanation:

We have quarters of $0.25 and dimes of $0.10

We have 5 more dimes than quarters and a total of $4.00

How many quarters Ms. Kincaid has?

Q is the number of quarters and D the number of dimes.

We have the system of equations:

D = Q + 5

Q*$0.25 + D*$0.10 = $4.00

First, we can replace the first equation into the second and solve it for Q.

Q*$0.25 + (5 + Q)*$0.10 = $4.00

Q*($0.25 + $0.10) + $0.50 = Q*($0.35) + $0.50  = $4.00

Q = (4.00 - 0.50)/0.35 = 3.50/0.35 = 10

So she has 10 quarters.

The correct option is A.