Determine the equation of the graph and select the correct answer below.

The root(s) of f (x) are

6 with multiplicity 2

-2 with multiplicity 2.

What is the solution to an equation?

In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.

We are given to find the roots of the following polynomial function :

f (x) = (x- 6)²(x + 2)²

We know that

the roots of a polynomial f(x) are given by the equation f(x) = 0.

Therefore, the roots of the given polynomial are given by

(x- 6)² =0 => x =6,6

(x + 2)² =0 , x =-2, -2

Thus, the required roots are

6 with multiplicity 2 and -2 with multiplicity 2.

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So the different number has a 4 with a value of 40.

What is Algebraic expression ?

Algebraic expression can be defined as combination of variables and constants.

To solve this problem, we need to first identify the place value of the digit 4 in the given number.

The digit 4 is in the hundreds place in the number 431.67, so its value is 4 x 100 = 400.

According to the problem statement, the 4 in the different number represents a value which is one-tenth of the value of the 4 in 431.67. Therefore, the value of the 4 in the different number is:

400/10 = 40

To determine the value of the different number, we need to look at the other digits in the number. Since we don't have any information about the other digits, we cannot determine the value of the different number. The answer is that the value of the different number cannot be determined with the information given.

Therefore, So the different number has a 4 with a value of 40.

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Answer:

A. 4(12)

C. 36+12

E. (9+3) +(9+3) +(9+3) +(9+3)

Step-by-step explanation:

\(4(9+3)=48\)

\(4*9=36\\4*3=12\)

           \(48\)

\(4*12=48\)

\(36+12=48\)

\((9+3) +(9+3) +(9+3) +(9+3)\\12+12+12+12\)

=48

Answer + Step-by-step explanation:

Check the illustration that I provided .

Answer:

a. lines intersecting at a single point

b. one solution

Step-by-step explanation:

a. The equations can be rewritten as:

y = -5x+23 and y = -1/6x+1

Comparing the equations with standard equation: y=mx+c, where m is the gradient of the line formed by the linear equation.

Since the gradient of the lines are different then the lines cannot be parallel and will intersent at one point.

b. The equation will have one solution as below.

The equations can be rewritten as:

5x+y=23

5x+30y=30

Subtracting both equation will result in,

29y=7

=> y=7/29

Hence x= 660/29

Answer:

25,200

Step-by-step explanation:

Increase in population per year =8%=((100+8)*10,000)/100=10,800. So,there will be an increment of 800 people to the population every year. =>after twenty years,the total population=10,000+19*(800)=25,200.

Answer:

10800

Step-by-step explanation:

10000+8%=10800

hope this helps:)

Answer:

B) (1/2, -8)

Step-by-step explanation:

(1, -6) and (0, -10)

Midpoint formula:

((x1+x2)/2, (y1+y2)/2)

Solving for x:

(x1+x2)/2

(1 + 0)/2

1/2

Solving for y:

(y1+y2)/2

(-6-10)/2

(-16)/2

-8

Answer:

Step-by-step explanation:

A regular hexagon is made up of six triangles having a height of 8.7cm and a base of 10cm. So the area of the hexagon is 6 times the area of one of the triangles. Since the area of a triangle is bh/2 we have

A=6(8.7)10/2

A=261cm^2

Answer:

261 cm²

Step-by-step explanation:

The area of the hexagon is 6 times the area of one of the triangles. The area of a triangle is base × height ÷ 2.

A = 6(8.7)10 ÷ 2

A = 261 cm²

Answer:

800 books

problem solving steps：

adults:60%

young people:5%

children=100%-60%-5%

=35%

35%=280 books

1%=280÷35

=8

100%=800

so,there are 800 books

Answer:

7

Step-by-step explanation:

PEMDAS

First we do the parenthesis, then we multiply and then we subtract (left to right)

= (2+2) * 3 - 1 - 4

= 4 * 3 - 1 -4

= 12 - 1 -4

= 12

Answer:

add wtwo numbers x by 3? I am sorry don't understand question

Step-by-step explanation:

Answer:

1/560

Step-by-step explanation:

So the x input which is the top row the numbers increase by 1 so that is your top number of your slope (rate of change)

And your bottom row increases by 560 so that is your bottom number of your slope

So your rate of change is 1/560

How do I know where to get these numbers?

Well if you take the first 2 numbers from the top row (in your case 1 and 2) and subtract them from each other (2-1=1) you get your first number. Then you do the same for the bottom (in your case 560 and 1120) subtract them (1120-560=560) and get your bottom....If needed you can simplify your fraction but sometimes your slope can come out as a whole number instead of a fraction but in your case you have a fraction.

That is where you get 1/560

Hope this helped!

Answer: 63.7 + (-26) = 37.7

Answer:

AB = 14.0 cm

Step-by-step explanation:

Pythagora's Theorem

In a right triangle with a hypotenuse of length H and legs of lengths L and W, then it's satisfied the equation:

\(H^2 = L^2+W^2\)

The diagram shows a wedge ABCDEF and it's required to calculate the length of the side AB.

Note the triangle FCB is right at C, where side length is the hypotenuse:

\(BF^2=13^2+6^2\)

\(BF^2=169+36=205\)

Triangle ABF is right at B and 20 cm is the hypotenuse, thus:

\(20^2 =AB^2+BF^2\)

Solving for AB:

\(AB^2=20^2-BF^2\)

\(AB^2=20^2-205\)

\(AB^2=400-205=195\)

\(AB=\sqrt{195}\)

AB = 14.0 cm

Answer:

The answer is 275 students.

Step-by-step explanation:

In 75 students, 33 students attend.

So the ratio is 33/75.

so multiply with 625.

625 x 33/75 = 275

Answer:

x = 3 , y = 1

Step-by-step explanation:

2x + y = 7

3x + y = 8

solution

2x + y = 7-----------(1)

3x - y = 8------------(2)

from equation 1

2x + y = 7

y = 7 - 2x-------------(3)

substitute equation 3 into equation 2

3x - y = 8

3x - (7 - 2x) = 8

3x - 7 + 2x = 8

3x + 2x = 8 + 7

5x = 15

divide through by the coefficient of x

5x/5 = 15/5

x = 3

to find y

substitute x into equation 1

2x + y = 7

2(3) + y = 7

6 + y = 7

y = 7 - 6

y = 1

A variable is defined as the alphabetic character that expresses the unknown value or unknown number. It can be changed according to the operations performed.

In this experiment,

Each side of the shower is sprayed with lemonade juice to determine whether it has any changes in the cleanliness of the shower. So each side of the shower with lemon juice is an independent variable.

This dependent variable is a variable that can measure Lemonade a manipulated variable or independent variable has any effect on it, such as whether lemonade juice cleans the slime off of the side or not.

A control is something that remains unchanged to assess the condition or impact which has not changed or may be contrasted to it. In the this scenario, the water spray is under command.

The experiment concludes drinking lemonade seems to not influence the cleaning of slime inside the shower.

Thus, slime is constant.

Hence,

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Answer:

AC = 12

Step-by-step explanation:

If BC is parallel to DE then ∠D ≅ ∠B and ∠E ≅ ∠C. Therefore

ΔABC is similar to ΔADE.

The sides of smaller triangle are in proportion with sides of bigger triangle.

Therefore we have the equation:

AC/AE = AB/AD

Substitute the given numbers:

x/x+15 =8/18

18x= 8(x+15)

18x = 8x+120

10x = 120

x = 12

AC=12

We have been given graph of function \(y=f(x)\). We are asked to find the value of \(f^{-1}(6)\) from the graph of  \(y=f(x)\).

We know that to find an inverse function is a function that reverses another function. A function f(x) gives an output of y, when we input some value of x. The inverse of f(x) will give the same value of x from value of y.

So to find inverse of a function we need to switch all x and y values.

We can see that \(f(4)=6\), so to to find value of  \(f^{-1}(6)\), we have to switch x and y values.

After switching x and y values, we will get:

\(f^{-1}(6)=4\)

Therefore, \(f^{-1}(6)=4\).

Answer:

4

Step-by-step explanation:

To find the greatest common factor (GCF), I like to split it up into two steps:

1. Find the greatest common factor of the coefficients.

2. Find the greatest common factor of the variables and any exponents.

For starters, we will find the GCF of 14 and 18.

List the factors of 14:

1, 2, 7, 14

List the factors of 18:

1, 2, 3, 6, 9, 18

Now, find the factor that is the largest of the two: 2.

The GCF of 14 and 18 is 2.

Now, find the GCF of t² and t⁴.

Factors of t²: t, t²

Factors of t⁴: t, t², t⁴

The GCF of t² and t⁴ is t².

Now, put them together: 2t².

The GCF of 14t⁴ and 18t² is 2t².

Pressure is force per unit area. If the block is sitting at rest on the surface, it applies a pressure of mg/A, where mg is the block's weight and A is the area of the face that makes contact with the surface.

The smaller the value of A, the larger the pressure. So the highest pressure the block can exert is achieved when it's resting on the face with the smallest dimensions.

If the block is a cube with side length 95 cm, then the pressure exerted by each face is the same.

Answer:382.5

Step-by-step explanation: 45 x 8.5 = 382.5

Answer: it will take approximately 14.62 years for the initial investment to double at an interest rate of 4.75% per year, compounded continuously.

Step-by-step explanation: Given an investment of $2000 at a continuously compounded interest rate of 4.75%, the balance in the account can be calculated using the following mathematical expression after t years:

The aforementioned equation, A = P * e^(rt), denotes the relationship between the accrued amount (A) and the principal amount (P), compounded continuously at a fixed annual rate of interest (r) over a specific time period (t), as governed by the mathematical constant "e."

In the context of financial calculations, the symbol 'P' denotes the initial capital investment. The interest rate, represented by the variable 'r', is expressed in the form of a decimal. Additionally, 'e' is the mathematical constant, roughly equivalent to 2.71828. Finally, 't' refers to the duration of the investment, measured in years.

In order to determine the duration of time required for the investment to achieve a twofold increase, it is necessary to solve the corresponding equation:

The equation expressed as 2P = P * e^(rt) can be restated more formally as follows. Given a principal investment amount represented by P and a rate of return indicated by r, compounded over time t, the equation can be expressed as the product of P and the exponential function of e^(rt), yielding twice the initial investment amount.

The variable 2P represents the monetary value acquired through doubling the initial investment.

Upon division of both sides by P, the resulting expression is as follows:

The equation 2 equals the exponential function of the base e raised to the power of the product of r and t.

By applying the natural logarithm function to both expressions, the resultant outcome is:

The natural logarithm of 2 can be represented as rt, where r denotes the logarithmic base and t denotes the logarithm of the argument, in accordance with the conventions of academic mathematical writing.

Upon resolving for the variable t, an outcome is yielded:

The mathematical expression t = ln(2) / r can be written in a formal academic style as follows: The equation determines the relationship between time t and the rate of decay r, where t is equal to the natural logarithm of 2 divided by r.

Upon substitution of the provided values, the resultant output is:

The calculated value of the variable t, representing the length of time in years, is approximately equal to 14.62 years, obtained through the algebraic manipulation of the natural logarithmic function of 2 divided by the constant value of 0.0475.

Answer:

\(\displaystyle 64-32\sqrt{2}+\frac{32\sqrt{2}}{3}\approx3.66\)

Step-by-step explanation:

\(\displaystyle \iint_R(3x-y)\,dA\\\\=\int^\frac{\pi}{2}_\frac{\pi}{4}\int^4_0(3r\cos\theta-r\sin\theta)\,r\,dr\,d\theta\\\\=\int^\frac{\pi}{2}_\frac{\pi}{4}\int^4_0(3r^2\cos\theta-r^2\sin\theta)\,dr\,d\theta\\\\=\int^\frac{\pi}{2}_\frac{\pi}{4}\int^4_0r^2(3\cos\theta-\sin\theta)\,dr\,d\theta\\\\=\int^\frac{\pi}{2}_\frac{\pi}{4}\frac{64}{3}(3\cos\theta-\sin\theta)\,d\theta\\\\=\int^\frac{\pi}{2}_\frac{\pi}{4}\biggr(64\cos\theta-\frac{64}{3}\sin\theta\biggr)\,d\theta\)

\(\displaystyle =\biggr(64\sin\theta+\frac{64}{3}\cos\theta\biggr)\biggr|^\frac{\pi}{2}_\frac{\pi}{4}\\\\=\biggr(64\sin\frac{\pi}{2}+\frac{64}{3}\cos\frac{\pi}{2}\biggr)-\biggr(64\sin\frac{\pi}{4}+\frac{64}{3}\cos\frac{\pi}{4}\biggr)\\\\=64-\biggr(64\cdot{\frac{\sqrt{2}}{2}}+\frac{64}{3}\cdot{\frac{\sqrt{2}}{2}}\biggr)\\\\=64-32\sqrt{2}+\frac{32\sqrt{2}}{3}\biggr\\\\\approx3.66\)

Answer:

is there a question for this problem if there is try your best

Answer:

D

Because you have to find out what they could all equal up to

Answer:

d

Step-by-step explanation:

Answer: 31 passengers are in each car.

Step-by-step explanation:

You divide:

403 ÷ 13 = 31

31 Passengers are in each chair.

I hope I helped you with this question. Have a great day!

Answer:

9

Step-by-step explanation:

length*width

3*3=9

Answer:

hi there is that something you can block

Answer:

14.48=11.99+y

or

y=14.48-11.98

Step-by-step explanation:

it should be one of these (the variable might be different)

y is the price of the drink