Three roots of a fifth degree polynomial function f(x) are -2,2 and 4 + i which statement describes the number and nature of all roots for this function?

Answer:

b.the graph of g(x) is the graph of f(x) compressed vertically

Step-by-step explanation:

The given functions are

[tex]f(x)=x^2[/tex]

and

[tex]g(x)=\frac{2}{5}x^2[/tex]

This is a transformation in the form

[tex]y=a*f(x)[/tex] where [tex]a=\frac{2}{5}[/tex]

Since 0<a<1, the graph of f(x) is compressed vertically by a factor of

[tex]\frac{2}{5}[/tex]

A function assigns the value of each element of one set to the other specific element of another set. The correct option is B.

A function assigns the value of each element of one set to the other specific element of another set.

When the graph of the two function f(x) and g(x) is plotted, then it can be observed that the graph of g(x) is the graph of f(x) compressed vertically.

Hence, the correct option is B.

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Answer:

y = 2x

Step-by-step explanation:

Given that y varies directly as x then the equation relating them is

y = kx ← k is the constant of variation

To find k use the condition y = 12 when x = 6

k = [tex]\frac{y}{x}[/tex] = [tex]\frac{12}{6}[/tex] = 2, hence

y = 2x ← equation of variation

Replace x with 3 and solve for Y.

If y equals 8 in both equations, then it is a solution.

y = -5(3) +1 = -15+1 = -14

-14 does not equal 8 , so it is not a solution.

No because -5• 3 +1 does not equal 8 makings it impossible for it to work for that equation. Then 3•3-2 doesn’t equal 8 either so (3,8) is not a solution for these equations

Answer:

C. It represents the product of two rational numbers and its equivalent to a rational number.

Step-by-step explanation:

5 is a natural number, a real number and a rational number.

[tex]\frac{1}{4}[/tex] is a real number and a rational number.

The product of 5 × [tex]\frac{1}{4}[/tex] = 1.25 which is also a rational number in addition to being a real number.

Answer:

The correct answer is option C.  

Step-by-step explanation:

It s given that 5 * 1/4

To find the correct answer

The given expression is 5 * 1/4

Here 5 is a rational number and 1/4 is a rational number

5 * 1/4 = 5/4

The number 5/4 is a rational number.

5/4 represents the product of two rational numbers and is equivalent to a rational number.

Therefore the correct answer is option C

Answer:

[tex]4\pi[/tex]

or

12.57

Step-by-step explanation:

I have a circular piece of fabric I am going to make a tablecloth. The radius of the fabric is 2 meters. What is the area of the tablecloth I can make

Essentially, you are attempting to find the area of a circle with a radius of 2 meters.

The formula for an area of a circle is [tex]\pi r^2[/tex], or pi times radius squared.

Plugging in 2 meters as your radius, that gets your answer to be [tex]4\pi[/tex], or 12.57 in decimal.

Answer:

997

From right to left, the place values are, ones, tens, hundreds, thousands, etc.

The number with '7 ones', '9 tens', and '9 hundreds' is written as 997 in numeral form, by combining the values of each digit based on their place value.

When writing the number that consists of '7 ones', '9 tens', and '9 hundreds', we are dealing with a three-digit number where each place value represents a power of 10. To construct the number, we consider the value each digit represents:

The '9 hundreds' means 9 × 100 (which is 900).

The '9 tens' means 9 × 10 (which is 90).

The '7 ones' means 7 × 1 (which is 7).

Adding these values together, we have 900 (hundreds) + 90 (tens) + 7 (ones), which equals 997. This is the decimal representation of the number expressed by the student.

Therefore, the number 7 ones 9 tens 9 hundreds written in numeral form is 997.

Answer:

Step-by-step explanation:

abs(x)>0

This statement is false because what happens when x = 0? For all other instances, the statement is true, but not for 0.

Zero is not greater than itself.

Answer:

4200 divided by 10

Step-by-step explanation:

To make 4200 a multiple of ten after dividing it by a multiple of ten, we first find the number of 5's in 4200 to see how many 10's go into 4200. Since 4200 = 6*7*2*2*5*5, we see that there are 2 fives. This means that there are two tens too. Since we have to keep 4200 a multiple of ten after dividing it by another 10. So the only possible way to do that is dividing 4200 by 10.

Dividing 4200 by the power of 10, 100, results in the quotient 42, which is also a multiple of 10. This is achieved by moving the decimal point two places to the left in the number 4200 due to the two zeros in the power of 10.

In this mathematics problem, you are asked to divide 4200 by a multiple of 10 such that the result, or quotient, is also a multiple of 10. The key to this problem lies in understanding the concept of dividing by powers of 10.

When you divide a number by a power of 10, you move the decimal point to the left by as many places as there are zeros in the power of 10. So if you wanted to divide 4200 by a multiple of 10 so that the result is also a multiple of 10, you might choose 100 (10^2) as your divisor. Why? Because there are two zeros in the power of 10, which means you move the decimal point two places to the left in the number 4200.

So when you divide 4200 by 100, you get 42 which is a multiple of 10. Therefore, 4200 divided by a multiple of 10 (100 in this case) gives a quotient (42) that is also a multiple of 10.

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Answer:

IT would be 6 because 10 X 6 = 60 just take away the 0

Step-by-step explanation:

Answer:

900 feet / 5,280 = 0.1704545... miles

8 seconds / 3,600 = 0.0022222222 hours

0.1704545 miles / 0.0022222222 hours = 76.704525767 miles per hour

The car is well over the speed limit

Step-by-step explanation:

73 divided by 8967:

0.0081409613

91 divided by 8743:

0.01040832666

37 divided by 86322:

0.00042862769

The z-score for 2,500 g is –2.According to the empirical rule, 95% of babies have a birth weight of between 2,500 g and 4,500 g.5% of babies have a birth weight of less than 2,500 g or greater than 4,500 g.Normal distributions are symmetric, so 2.5% of babies weigh less than 2,500g.

2.5% of babies weigh less than 2,500g.

Empirical rule states that for a normal distribution, 68% of the values are within 1 standard deviation from the mean, 95% of the values are within 2 standard deviation from the mean and 99.7% are within 3 standard deviation from the mean.

Given that mean (μ) = 3,500 g and a standard deviation of σ = 500 g.

Hence 2.5% of babies weigh less than 2,500g.

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Answer:

hmmm

Step-by-step explanation:

hmmm

the answer after simplify is:

[tex] \frac{ 9{x}^{5} {y}^{16} }{45 {x}^{5} {y}^{4} } = \frac{ {y}^{12} }{5} [/tex]

Answer:

[tex]\large\boxed{\dfrac{1}{5}y^{12}}[/tex]

Step-by-step explanation:

[tex]\text{Use}\ \dfrac{a^n}{a^m}=a^{n-m}\\\\\dfrac{9x^5y^{16}}{45x^5y^4}=\dfrac{9\!\!\!\!\diagup^1}{45\!\!\!\!\!\diagup_5}x^{5-5}y^{16-4}=\dfrac{1}{5}y^{12}[/tex]

Answer:

11877

Step-by-step explanation:

11100 * 7% = 777

11100 + 777 = 11877

When you multiply by 7%, you get the amount of additional tax. You add this to the original amount to get the answer.

Answer:

A,C,D

Step-by-step explanation:

Answer:

The following are the correct statements regarding mathematics in the Egyptian, Chinese, and Babylonian cultures:

A - Both Egyptian and Chinese number systems use base 10.

C - All three cultures had unique symbolism to represent their numbers(Earlier symbols were used to depict things)

D - There are two primary sources for ancient Egyptian mathematics(The primary sources are the Rhind Papyrus and the Moscow Papyrus)

Answer:

option D

8√2

Step-by-step explanation:

Given in the question a right angle triangle,

hypotenuse = x

height = 8

We can use trigonometry identity to solve x

we know that,

sinФ = opposite / hypotenuse

sin(45) = 8 / x

x = 8 / sin(45)

x = 8√2

[tex] \frac{27}{30} \times 100\% \\ = 90\%[/tex]

Approximately 90 percent voted for her

Answer:

180i^2 - 20j^2

Step-by-step explanation:

u.v

(12i+4j) . (15i-5j)

12i(15i-5j) + 4j(15i-5j)

180i square -60ij + 60ij-20j square

180i^2 - 20j^2

The value of the dot product of the two vectors is u · v = -160.

The product of vectors can refer to several different operations, including the dot product, cross product, and scalar multiplication.

Dot Product:

The dot product of two vectors u and v is a scalar given by the formula:

u · v = ||u|| ||v|| cos θ

We have,

To find the dot product of two vectors, we need to multiply their corresponding components and add up the results:

u · v

= (12i + 4j) · (15i - 5j)

= 12i · 15i + 12i · (-5j) + 4j · 15i + 4j · (-5j)

= 180i^2 - 60ij + 60ij - 20j² [since i² = j² = -1]

= 180(-1) - 20(-1) [since ij = ji = 0]

= -160

Therefore,

The value of the dot product of the two vectors is u · v = -160.

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Answer:

1

Step-by-step explanation:

sec(x)*cos(x) + cos(x)-1/(sec(x))

We know that sex(x) = 1/(cos(x))

substitute it in our expression.

1/(cos(x)) * cos(x) + cos(x) - 1/(1/cos(x)) = 1+cos(x) - cos (x)= 1

ANSWER

A. 1

EXPLANATION

The given trigonometric expression is

[tex] \sec(x) \cos(x) + \cos(x) - \frac{1}{ \sec(x) } [/tex]

Recall and use the following reciprocal identities.

[tex] \frac{1}{ \sec(x) } = \cos(x) [/tex]

and

[tex] \sec(x) = \frac{1}{ \cos(x) } [/tex]

When we apply these identities, we get

[tex] \frac{1}{ \cos(x) } \times \cos(x) + \cos(x) - \cos(x) [/tex]

This simplifies to:

[tex]1 + 0 = 1[/tex]

The correct choice is A

Answer:

47 is greater than or equal to 5x+10y

Step-by-step explanation:

you can't spend more than $47 but you can spend less than or equal to that amount.

Answer:5x+10y=47

Step-by-step explanation:

 Given

$47 money needed to spend

Each cassette tape cost $5

and each CD cost $10

Given no of cassette be x and no of CD be y

Thus cost of x cassette is 5x

cost of Y CD's 10y

Total cost=5x+10y

5x+10y=47

Answer: The length and width are 20 square centimeters and 8 square centimeters

Explain: 20:8 can be reduced to 5:2 as a ratio. 20 times 8 equals 160.

Answer:

Step-by-step explanation:

l - length

w - width

length and width are in a ratio of 5:2

[tex]\dfrac{l}{w}=\dfrac{5}{2}[/tex]           cross multiply

[tex]2l=5w[/tex]          divide both sides by 2

[tex]l=\dfrac{5w}{2}[/tex]

the area is 160cm²

[tex]lw=160[/tex]

We have the system of equations:

[tex]\left\{\begin{array}{ccc}l=\dfrac{5w}{2}&(1)\\lw=160&(2)\end{array}\right[/tex]

Substitute (1) to (2):

[tex]\left(\dfrac{5w}{2}\right)(w)=160\\\\\dfrac{5w^2}{2}=160\qquad\text{multiply both sides by 2}\\\\5w^2=320\qquad\text{divide both sides by 5}\\\\w^2=64\to w=\sqrt{64}\\\\w=8[/tex]

Put the value of w to (1):

[tex]l=\dfrac{(5)(8)}{2}=\dfrac{40}{2}=20[/tex]

Answer:

The new equation is y= (x-3)

Step-by-step explanation: we know that   the point (1, 1) is moved to (4,1).

So, the rule of the translation is: [tex](x,y) -----> (x+3, y)[/tex]

that means  the translation is 3 units to the right

Answer:

[tex]y=|x-3|[/tex]

Step-by-step explanation:

The parent absolute function is

[tex]y=|x|[/tex]

The graph of y= |x| is translated so that the point (1, 1) is moved to (4,1). It means the rule of translation is

[tex](x,y)\rightarrow (x+3,y)[/tex]

it means the graph of y=|x| translated 3 units right. So, the new vertex of the function is (3,0).

The vertex form of an absolute function is

[tex]y=|x-h|+k[/tex]

The new vertex of the function is (3,0). Substitute h=3 and k=0 in the above equation.

[tex]y=|x-3|+0[/tex]

[tex]y=|x-3|[/tex]

Therefore, the required equation is y=|x-3|.

Answer:

2t blocks

Step-by-step explanation:

We measure these distances from Jim's house.

The school is t blocks from Jim's house.  Twice that is 2t blocks.  Thus, the library is 2t blocks from Jim's house.

the answer is 10 units

[tex]distance = \sqrt{(9 - 1) ^{2} + (9 - 3) {}^{2} } \\ = \sqrt{ {8}^{2} + {6}^{2} } \\ = 10[/tex]

The distance between points (1, 3) and (9, 9) will be 10 units so option (b) will be correct.

A pair of numbers that employ the horizontal and vertical distinctions from the two reference axes to represent a point's placement on a coordinate plane. typically expressed by the x-value and y-value pairs (x,y).

For instance, in this case (5,3), 5 will represent the x and 3 the y.

(9,0) is another illustration, where 9 stands for x and 0 for y.

Coordinates are always written in the form of small brackets the first term will be x and the second term will be y.

The distance between two points (x₁,y₁) and (x₂,y₂) is given by

[tex]d = \sqrt {\left( {x_1 - x_2 } \right)^2 + \left( {y_1 - y_2 } \right)^2 }[/tex]

So,

Distance between (1, 3) and (9, 9)

[tex]d = \sqrt {\left( {1- 9 } \right)^2 + \left( {3 -9 } \right)^2 }[/tex]

d = √(64 + 36) = 10 units.

Hence, The distance between points (1, 3) and (9, 9) will be 10 units

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Answer:

x=−0.825789

Step-by-step explanation:

x=(−6x3−4x−6)/x

Step 1: Multiply both sides by x.

x2=−6x3−4x−6

x2−(−6x3−4x−6)=−6x3−4x−6−(−6x3−4x−6)(Subtract -6x^3-4x-6 from both sides)

6x3+x2+4x+6=0

(Use cubic formula)

x=−0.825789

Answer:

- 3

Step-by-step explanation:

Substitute x = - 6 into the expression

[tex]\frac{(-6)^2-6}{-6-4}[/tex]

= [tex]\frac{36-6}{-10}[/tex] = [tex]\frac{30}{-10}[/tex] = - 3

Answer:

$100

Step-by-step explanation:

To find out how much money Gayle initially had, we solved the two equations provided by the problem: G + 20 = 2(J + 20) and J + 20 = G + 20 - 50. Solving these equations, it was found that Gayle initially had $90.

The question is asking us to figure out how much money Gayle had before their mother gave them each $20. Let's denote the amount of money Jerry initially had as J and the amount of money Gayle initially had as G. According to the problem, after the mother gave them $20 each, Gayle had twice the amount of Jerry's, which mathematically translates to G + 20 = 2(J + 20). Likewise, Jerry had $50 less than Gayle, which can be written as J + 20 = G + 20 - 50. Thus we are given a system of two equations that we can solve simultaneously.

Both equations can be simplified to G = 2J + 20 and J = G - 50. By substituting J = G - 50 in the first equation, we can solve for G to get G = 2(G - 50) + 20 which further simplifies to G = $90. Thus, Gayle initially had $90.

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Answer: D

Step-by-step explanation:

That is a small sample out of the entire school

The answer is B)Two rectangular pyramids joined at two congruent lateral faces

Answer:

Option B. is the answer.

Step-by-step explanation:

As you can see from the figure attached, Rectangular pyramid has five faces. Four triangular and one rectangular face.

In this question we have to find the a composite figure which has eight triangular faces.

Therefore, by adding two rectangular pyramids by common rectangular base we can get the composite figure with eight triangular faces.

Option B. will be the answer.

Answer:

Sample response: Use the slope formula three times: once for the first pair of points, then for the second pair of points, then for one point from each pair. If all three slopes are the same, then all the points lie on the same line.

Which did you include in your response:

The way in which a person can accurately determine whether two known pairs of points are on the same line is:

One of the ways through which a person can accurately determine whether two known points are on the same line when using a linear graph is to make use of the slope formula.

With this in mind, we can see that this slope formula is used to find the different pair of points on the graph to check if they all lie on the same line.

In conclusion, we can come to the determination that:

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