the rational roots of a polynomial function F(x) can be written in the form p/q,
where p is a factor of the constant term of the polynomial, and q is a factor of the leading coefficient

TRUE OR FALSE??

Answer:

B its is B that is the most ansewrablea .

Step-by-step explanation:

Answer:

112=4.5p+40

16

Step-by-step explanation:

Answer:

800 miles apart

Step-by-step explanation:

0.75a+0.75b=200

0.25(a+b)=200

a+b=800 miles apart

In order for the sine and cosine to be equal, the angles must be complementary

sin (7x-15) = cos (3x+5)

7x-15+3x+5 =90 (because sum of both angles a and b must be 90)

10x -10 = 90

10x = 100

x =10

One angle = 7x-15= 7*10-15 = 70-15 =55

Other angle = 3x +5 = 3*10+5 = 30+5 = 35

Since B is less than A, A = 55 degrees and B = 35 degrees

Since we need B, B = 35 degrees

The distance from the building to the base of the ladder, when the ladder makes an angle of 70 degrees with the ground and the ladder is 25 feet long, can be calculated using the cosine function. The calculated distance is approximately 8.6 feet.

To calculate the distance from the building to the base of the ladder, we have to use the trigonometric function cosine given the information in the problem. The cosine of an angle in a right triangle is defined as the adjacent (which is the distance we wish to find) over the hypotenuse (which is given as 25 feet).

Therefore, we write the equation as follows:

cos(70) = Adjacent/25

To find the 'Adjacent', we rearrange the equation:

Adjacent = 25*cos(70)

When you perform the calculation, you get Approximately 8.6 feet as the distance from the building to the base of the ladder.

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The base of the ladder is approximately 8.5 feet from the building. This is determined using trigonometry and the cosine of the ladder's angle of elevation.

This is a trigonometry problem where we have to find the base of the triangle formed by the ladder, the ground, and the distance from the building. The question gives us the length of the ladder (hypotenuse in the right triangle) and the angle of elevation. We can thus use cosine of the angle (base/hypotenuse) to find the base.

We know that Cosine of 70° is equal to the (base / Hypotenuse). And in the present case, the hypotenuse is given to be 25 ft.

Therefore, calculation will be as follow:

Base = Cosine (70°) * Hypotenuse.

Base = Cosine (70°) * 25 ft.

After calculating, this gives a base length of approximately 8.5 feet. So, the base of the ladder is approximately 8.5 feet from the building.

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Composite functions involve combining more than one functions

The value of 2f(x) - 3g(x) is [tex]2x^2 -2x-+ 10[/tex]

We have:

[tex]f(x) = x^2 + 2x - 1[/tex]

[tex]g(x) =2x - 4[/tex]

The value of 2f(x) - 3g(x) is calculated as follows:

[tex]2f(x) - 3g(x) = 2 \times f(x) -3 \times g(x)[/tex]

Substitute the values of f(x) and g(x)

[tex]2f(x) - 3g(x) = 2 \times (x^2 + 2x -1) -3 \times (2x - 4)[/tex]

Open brackets

[tex]2f(x) - 3g(x) = 2x^2 + 4x -2 -6x + 12[/tex]

Collect like terms

[tex]2f(x) - 3g(x) = 2x^2 + 4x -6x-2 + 12[/tex]

[tex]2f(x) - 3g(x) = 2x^2 -2x-+ 10[/tex]

Hence, the value of 2f(x) - 3g(x) is [tex]2x^2 -2x-+ 10[/tex]

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Answer:

B

Step-by-step explanation:

Im assuming.

Answer:

The ratio of green paint to white paint is A. [tex]\pi:(4-\pi)[/tex]

Step-by-step explanation:

To find the ratio of green paint to white paint we need to divide the surface that will be painted green by the surface that will be painted white.

In the graph we can see 4 equal circles. Let be ''R'' the radius of the circles.

We can also see a square. The side of the square is 4R (because the length of the side is 4 times the radius of any circle).

The surface of a circle which radius is ''R'' is equal to :

[tex]\pi .R^{2}[/tex]

The surface inside this 4 circles is equal to :

[tex]4.\pi .R^{2}[/tex]

The surface [tex]4.\pi .R^{2}[/tex] will be painted green.

The surface outside the circles is equal to [tex]4.\pi .R^{2}[/tex] subtracted to the area of the square.

The area of the square is :

[tex](4R)^{2}=16R^{2}[/tex] ⇒

[tex]16R^{2}-4.\pi.R^{2}[/tex] is the surface that will be painted white.

If we make the division between the surfaces :

[tex]\frac{GreenSurface}{WhiteSurface}[/tex] ⇒

[tex]\frac{4.\pi .R^{2}}{16R^{2}-4.\pi .R^{2}}[/tex]

[tex]\frac{(4R^{2}).\pi}{(4R^{2}).(4-\pi)}=\frac{\pi}{4-\pi}[/tex]

We find that the ratio of green paint to white paint is [tex]\pi:(4-\pi)[/tex]

Answer:  0.275

To get 11/40 converted to decimal, you simply divide 11 by 40. Then you get 0.275

The correct answer is C.) There are 9 pieces of data that are greater than the median. The statement that is NOT TRUE is C.) There are 9 pieces of data that are greater than the median.

To understand why option C is not true, let's review some basic concepts about quartiles and the median in a set of data:

- 3 pieces of data are less than Q1.

- 3 pieces of data are in the first quartile (Q1).

- 6 pieces of data are between Q1 and Q3 (the interquartile range, IQR).

- 3 pieces of data are in the third quartile (Q3).

- Including the median itself, 4 pieces of data are greater than or equal to the median.

This breakdown correctly accounts for all 12 pieces of data. As a result, the statement that is NOT TRUE is indeed option C:

C.) There are 9 pieces of data that are greater than the median.

Since there are 4 pieces of data that are greater than or equal to the median, option C, which asserts there are 9 such pieces, is false. The correct understanding aligns with your analysis of quartiles and the median in this dataset.

3

Applying Distribution Law, we multiply 3 with 6 and 2.

So, 3 * ( 6 -2 ) = ( 3* 6 ) - ( 3 * 2)

so, '?' = 3

A pyramid is the correct answer

In order to find the zeros in a quadratic in vertex form, you need to follow a number of steps. They have been outlined for you along with a sample problem.

y = (x - 2)^2 - 16

After getting the original form, you can place a 0 in for y. In is where the graph will cross the x-axis, so it is where you will find both of your zeros.

0 = (x - 2)^2 - 16

Now take the constant and add it to both sides. In this equation, -16 is your constant. So, we'll add 16 to both sides to begin to solve.

16= (x - 2)^2

Now we can take the square root of both sides. After we do so, we take both the positive and negative version of what we get. This is because both 4 and -4 squared is equal to 16.

+/-4 = x - 2

Now we add 2 to both sides to get us what is left of x.

2 +/- 4 = x

Now that we have a final form such as this, we can separate and get two answers for our two zeros.

2 + 4 = 6

2 - 4 = -2

Alyssa must design a fence within a 140 ft perimeter to keep out deer and rabbits, requiring heights and depths appropriate for each animal. She may use a combination of high electric fencing for deer and buried hardware cloth for rabbits, being mindful of her perimeter constraint.

The student, Alyssa, needs to build a fence around her garden and requires the length to be at least 50 ft with a total available perimeter of 140 ft. To keep deer and rabbits out, she might consider different fence designs.

For preventing deer from entering, it's suggested to use electric fencing at least 8-10 feet tall or two parallel fences that are about 4 feet high and spaced 3 feet apart.

For rabbits, a two-foot high fence made of hardware cloth or chicken wire should be used, extended at least five inches below the ground. This will discourage rabbits from digging under the fence and protect the garden effectively.

Since Alyssa has a limited amount of fencing material, she will need to calculate the perimeter carefully to maximize the enclosed area while keeping within the 140 ft limitation. She might use lengths of sides that meet her minimum requirement and stay within her total available perimeter.

Set the situation up as a system of linear equations based on the information provided in the problem. Then, solve the system to get the number of each type of vehicle that the company can buy.

To solve this problem, let's set it up as a system of linear equations. This is a mathematics problem involving problem-solving and linear equations.

Let's denote v as the number of vans, s as the number of small trucks, and l as the number of large trucks.

We know that the total money spent should equal $15 million, and we can express this as:

(35,000v) + (70,000s) + (60,000l) = 15,000,000

We also know that the number of vans is twice the number of small trucks, so we can express this as:

v = 2s

We know also that the total number of vehicles is 310, so we have:

"v + s + l = 310"

Solving these three equations will give us the number of vans, small trucks, and large trucks that the company can buy.

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