Just need reassurance in my answer. not sure if I got it right

The complete question is;

The polynomial P(x) = 5x²(x − 1)³(x + 9) has degree ____. It has zeros 0, 1, and ____. The zero 0 has multiplicity ____ , and the zero 1 has multiplicity ____

Answer:

A) degree = 6

B) -9 is also a zero of the polynomial

C) 0 has multiplicity of 2

1 has multiplicity of 3

Step-by-step explanation:

A) To find the degree of the polynomial, we will first have to identify each term [term is for example (x - 1)³]. Thus, to find the degree of each term we will add the exponents.

The terms are;

5x², (x - 1)³, (x + 9)

The exponents are, 2, 3 and 1 respectively.

Thus, degree = 2 + 3 + 1 = 6

B) A zero of a polynomial is the value of x that causes the polynomial function to equal 0.

Since 0 and 1 are zeros, looking at the polynomial P(x) = 5x²(x − 1)³(x + 9), we can tell that when the term which when x = 0 makes the polynomial 0 is 5x².

Similarly, the term which when x = 1 makes the polynomial 0 is (x - 1)³

Thus,we are left with the term (x + 9)

So for the polynomial to be zero, (x + 9) = 0

Thus,x = -9

So -9 is a zero of the polynomial

C) The zero 0 is from the term 5x².

Thus,the multiplicity is the highest power of x which is 2.

The zero 1 is from the term (x - 1)³. Thus, the multiplicity is the highest power of x which is 3

Answer:

I'm pretty sure that's true.

Answer:

Step-by-step explanation:

x+y=14

y=14-x

2x+3y=32, using y=14-x we have

2x+3(14-x)=32

2x+42-3x=32

-x+42=32

-x=-10

x=10, and since y=14-x

y=14-10=4

So Amelia made 10 two-pointers and 4 three-pointers.

Let's assume that John buys x boxes of Cereal A and y boxes of Cereal B. Then, we can write the following system of inequalities based on the nutrient and calorie requirements:

10x + 5y ≥ 500 (minimum 500 units of vitamins)

5x + 10y ≥ 600 (minimum 600 units of minerals)

15x + 15y ≥ 1200 (minimum 1200 calories)

We want to minimize the cost, which is given by:

0.5x + 0.4y

This is a linear programming problem, which we can solve using a graphical method. First, we can rewrite the inequalities as equations:

10x + 5y = 500

5x + 10y = 600

15x + 15y = 1200

Then, we can plot these lines on a graph and shade the feasible region (i.e., the region that satisfies all three inequalities). The feasible region is the area below the lines and to the right of the y-axis.

Next, we can calculate the value of the cost function at each corner point of the feasible region:

Corner point A: (20, 40) -> Cost = 20

Corner point B: (40, 25) -> Cost = 25

Corner point C: (60, 0) -> Cost = 30

Therefore, the minimum cost is $20, which occurs when John buys 20 boxes of Cereal A and 40 boxes of Cereal B.

Answer: Half of them are even and half of them are odd.

Step-by-step explanation:

The even numbers are 6, 12, 18, 24, and 30. An even number is defined as a number that is divisible by 2, meaning it has no remainder when divided by 2. For example, 6 divided by 2 equals 3 with no remainder, so 6 is even.

The odd numbers are 3, 9, 15, 21, and 27. An odd number is defined as a number that is not divisible by 2, meaning it has a remainder of 1 when divided by 2. For example, 9 divided by 2 equals 4 with a remainder of 1, so 9 is odd.

Therefore, out of the given numbers, half of them are even and half of them are odd.

________________________________________________________

If Jane took 30 min to drive her boat upstream to water-ski at her favorite spot. her boat speed in still water is;3 km/h.

Let's x represent the  Jane's boat speed in still water

Upstream, her speed was x - 2 km/h.

Downstream, her speed was x + 2 km/h.

Let's d represent the distance between the start and end point

Let the  time it takes to cover d at a speed of x - 2 km/h=  30 min.

Let the  time it takes to cover d at a speed of x + 2 km/h=  10 min.

So we have:

d / (x - 2) = 30 min and

d / (x + 2) = 10 min.

Multiplying both sides of each equation

d * x - 2d = 30 * (x - 2)

d * x + 2d = 10 * (x + 2).

Adding the two equations and solve for x

2d * x = 40 * x + 20

20 * x = 40 * x + 20

20 * x = 60 * x

x= 3 km/h

Therefore Jane's boat speed in still water is 3 km/h.

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Answer:

Step-by-step explanation:

you

60 +14*number of weeks

sister

120+10*number of weeks

let x be the number of weeks until they have the same amount of money

60+14x = 120+10x ; isolate like terms

14x -10x = 120-60

4x = 60; divide both sides by 4

x= 15 weeks

120+10*15 = 120+ 150 = $270 will be the amount they will have the same

Answer:

-2z+4>=-4

-2z>=-8

z>=4

The average rate of change of the given function from x equals -7 to x equals 2 is calculated as: B. 101/90.

If we are given a function, f(x), to find the average rate of change of the function within the interval from a to b, the formula to use is:

Average rate of change = f(b) - f(a) / b - a.

Given the table that represents  function, we have the following:

a = -7

b = 2

f(a) = f(-7) = -2.7

f(b) = f(2) = 7.4

Plug in the values into the formula:

Average rate of change = (7.4 - (-2.7)) / (2 - (-7))

= (7.4 + 2.7) / 2 + 7)

= 10.1 / 9

= 101/90

Therefore, the average rate of change is: B. 101/90.

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Step-by-step explanation:

i think 16b+a+10 is the answer

The number she'd have is:

Explanation:

First, let's see which number is in the tens place and which number is in the ones place (the units place).

In the number 548, the place value of 5 is hundreds, the place value of 4 is tens, and the place value of 8 is ones (or units).

So if Sera adds two to the units, she'll have 10. But, since we can't write the number as 5410 (that would be a totally different number), we just write 0 in the units place, and shift 1 to the tens place, which gives us :

550

That's not all, since we also add 1 to the tens:

560

The third term (a3) of the sequence is -8, the fourth term (a4) is 35, and the fifth term (a5) is -183. These values are obtained by applying the given formula recursively and substituting the previous terms accordingly. The calculations follow a specific pattern and are derived using the provided formula.

The sequence is defined by the following formula:

a1 = 1, a2 = 3,

and

an = (-1)nan - 1 + an - 2 for n ≥ 3.

To find the third term (a3), we substitute n = 3 into the formula:

a3 = (-1)(3)(a3 - 1) + a3 - 2.

Next, we simplify the equation:

a3 = -3(a2) + a1.

Since we know a1 = 1 and a2 = 3, we substitute these values into the equation:

a3 = -3(3) + 1.

Simplifying further:

a3 = -9 + 1.

Therefore, the third term (a3) is equal to -8.

To find the fourth term (a4), we substitute n = 4 into the formula:

a4 = (-1)(4)(a4 - 1) + a4 - 2.

Simplifying the equation:

a4 = -4(a3) + a2.

Since we know a2 = 3 and a3 = -8, we substitute these values into the equation:

a4 = -4(-8) + 3.

Simplifying further:

a4 = 32 + 3.

Therefore, the fourth term (a4) is equal to 35.

To find the fifth term (a5), we substitute n = 5 into the formula:

a5 = (-1)(5)(a5 - 1) + a5 - 2.

Simplifying the equation:

a5 = -5(a4) + a3.

Since we know a4 = 35 and a3 = -8, we substitute these values into the equation:

a5 = -5(35) + (-8).

Simplifying further:

a5 = -175 - 8.

Therefore, the fifth term (a5) is equal to -183.

In summary, the third term (a3) is -8, the fourth term (a4) is 35, and the fifth term (a5) is -183.

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The measure of the angle s 50. 2 degrees

To determine the angle, we need to know the different trigonometric identities.

These trigonometric identities are;

From the information given, we have that;

The ratios of the identities are;

cos θ = adjacent/hypotenuse

tan θ = opposite/adjacent

sin θ = opposite/hypotenuse

Then, we have that;

cos A = 16/25

divide the values

cos A = 0. 64

Find the inverse

A = 50. 2 degrees

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Answer:

solution:

Here,7+4-2-8=13-9

or, 9-B=4

or, -B=4-9

or-B=-5

*B= 5

Answer:

Function f is translated to the right 2 units, and then up 1 unit to obtain function g.

To see this, note that g(x) = (x+1)³ - 2 = (x-(-1))³ - 2. Comparing this to f(x) = (x-2)³, we see that replacing x with x+3 in f(x) gives g(x) = (x+3-2)³ = (x+1)³, so this transformation moves the graph of f(x) three units to the left. Then, adding the constant -2 to f(x) translates the graph down 2 units. Finally, adding the constant 2 to the result of the previous step translates the graph up 2 units, so the graph of g(x) is obtained by first translating the graph of f(x) to the right 2 units, and then translating it up 1 unit. Therefore, the correct answers are:

Function f is translated to the right 2 units.

Function f is translated up 1 unit.

Function f is translated to the right 2 units, and then up 1 unit to obtain function g.

To see this, note that g(x) = √x - 2 + 1 = f(x-2) + 1. This means that the graph of g(x) is obtained by translating the graph of f(x) to the right 2 units, and then translating it up 1 unit. Therefore, the correct answers are:

Function f is translated to the right 2 units.

Function f is translated up 1 unit.

Step-by-step explanation:

Answer:

d = 126, z = 28

Step-by-step explanation:

The angle with the variable is diagonal from the 105 degree angle. In this case, that means that they are equivalent. So, 105+21 = 126. d = 126 :)

Answer:

simple interest=$97.50.

compound interest= $100.668

Step-by-step explanation:

Given:

Principal (P) = $750

Rate (R) = 6.5% (in decimal form, 0.065)

Time (T) = 2 years

Simple Interest = Principal*Rate*Time

Using the formula, the simple interest is calculated as follows:

Simple Interest = $750*0.065*2 = $97.50

Therefore, the simple interest for $750 with a 6.5% interest rate over 2 years is $97.50.

Again:

Compound Interest = Principal*(1 + Rate)^(Time)-Principal

Using the same values as above, the compound interest can be calculated as follows:

Compound Interest = $750*(1+0.065)^(2)-$750

= $750*1.065^2 -$750

= $750 × 1.134225 - $750

= $850.66875-$750

= $100.668

Therefore, the compound interest for $750 with a 6.5% interest rate over 2 years is $100.668

The set of side measurement could be used to form a triangle is option(4) 7, 12 and 18

If the sides of the triangles are a, b and c. There will be three condition

a + b > c

b + c > a

c + a > b

We have to check these condition

Part 1

The sides are 3, 5 and 7

3 + 5 > 11

8 < 11

It does not form a triangle

Part 2

The sides are 4, 18 and 23

4+18 >23

22 < 23

It does not form a triangle

Part 3

The sides are 5, 9 and 14

5+9 > 14

14 = 14

It does not form a triangle

Part 4

The sides are 7, 12 and 18

7+12 > 18

19 > 18

12 + 18 > 7

30 > 7

7+18 > 12

25 > 12

It forms a triangle

Hence, the set of side measurement could be used to form a triangle is option(4) 7, 12 and 18

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Answer:

I think your good but just in case check part C on first page also check 3c and 2.

Step-by-step explanation:

The electrical resistance varies directly as the square of the voltage and inversely as the electric power, and the equation that relates them isR ∝ V²/PR = kV²/PR = V²/P. This relationship can be used to calculate the electrical resistance of the wire or component for any given voltage and power.

The electrical resistance is the measure of the difficulty in passing electric current through a wire or an electrical component. It depends on various factors, such as the material, dimensions, and temperature of the wire.The given statement says that the electrical resistance varies directly as the square of the voltage and inversely as the electric power.

In mathematical terms, this relationship can be expressed as R ∝ V²/PR = kV²/P where R is the electrical resistance, V is the voltage, P is the electric power, and k is the constant of proportionality. The constant k depends on the material, dimensions, and temperature of the wire or component.

The given statement implies that the constant k is the same for the given wire or component, and it is not affected by the voltage or the power.To find the value of k, we can use the given values of V, P, and R.

According to the statement, if the voltage is 20 volts and the electric power is 5 watts, then the electrical resistance is 80 ohms. Therefore,R = kV²/PR = k(20²)/5R = 400k/5R = 80 ohms

Substituting the value of R in the equation, we get80 = 400k/5k = (80 x 5)/400k = 1. Therefore, the equation that relates the electrical resistance, voltage, and power isR = V²/PThe constant of proportionality k is 1 for the given wire or component.

Therefore, the electrical resistance varies directly as the square of the voltage and inversely as the electric power, and the equation that relates them isR ∝ V²/PR = kV²/PR = V²/P. This relationship can be used to calculate the electrical resistance of the wire or component for any given voltage and power.

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The distance between the two points is

d = √( -2-x)² + (3 -y)² OR d = √ (x+2)² + (y-3)².

Distance between two points is the length of the line segment that connects the two points in a plane.

The distance between two points is expressed as;

d = √ (X-x )² + (Y-y)²

X = -2

x = x

Y = 3

y = y

Therefore the distance between the two points is

d = √( -2-x)² + (3 -y)²

or it can also be written in this form

d = √ x-(-2)² + (y-3)²

d = √ x+2)² + (y-3)²

therefore the model of the distance between the two points can be

d = √( -2-x)² + (3 -y)² OR d = √ (x+2)² + (y-3)².

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The tangent of the angle is tan(θ) = -0.5

From the question, we have the following parameters that can be used in our computation:

(-10, -5)

This means that

(x, y) = (-10, -5)

In other words,

x = -10 and y = -5

The trigonometry tan(θ) is then calculated as

tan(θ) = y/x

Substitute the known values in the above equation, so, we have the following representation

tan(θ) = -5/-10

Evaluate the quotient

tan(θ) = -0.5

Hence, the value of tan(θ) is -0.5

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Y is 1/3x +5 an equation of the line that passes through point P.

The slope of the new line will be equal to (1/3) = 1/3because perpendicular lines have slopes that are the negative reciprocals of one another.

X and Y are represented by X and Y, (x,y) is the pair of coordinates for the point, and m is the slope in this equation, which reads: Y - y = m(X-x).

Y-4 = 1/3(X-1), which leads to Y = 1/3X +1 +4 and Y = 1/3X +5.

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The distance to second base is approximately 127.28 feet. Round to the nearest hundredth

Since the angle is 45 degrees, the other side of the right triangle are equal, hence we have two sides of 90 ft to be used to find the hypotenuse

Using Pythagoras theorem given by the  the formula

hypotenuse² = opposite² + adjacent²

plugging the values as in the problem

let x be the required distance

x² = 90² + 90²

x² = 16200

x = √16200

x = 90√2

x = 127.28 ft (to the nearest hundredth)

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You have to find 4 consecutive integers whose sum is 270.

Let "x" represent the first integer.

The next one can be expressed as (x+1)

The third one can be expressed as (x+2)

The fourth one can be expressed as (x+3)

The sum of these integers must be 270 so that:

From this expression, you can determine the value of x:

- First, order the like terms together and simplify:

-Second, subtract 6 to both sides of the equal sign to pass the term to the right side of the expression:

-Third, divide both sides by 4 to determine the value of x:

Now that you know the value of the first integer, you can determine the other three:

The four consecutive integers that sum 270 are 66, 67, 68, and 69. (option b)

Answer:

A

Step-by-step explanation:

ita a bc i know its I did this before

Answer:

54

Step-by-step explanation:

27 is half of what number?

27 x 2 = 54

:)

Answer:

135

Step-by-step explanation:

27 x 0.5 = 135

Hope it helps!!!!!