Use the Rational Zeros Theorem to write a list of all possible rational zeros of the function. f(x) = 2x3 + 8x2 + 7x - 8

Answer:

3 * (4x - 8) = 60

x = 7

Step-by-step explanation:

First you have to find out what is being done first.

Three times the quantity eight less than 4 times a number is 60.

x = a number

3 *

- 8

4 * x

= 60

The first thing to do is 4 times a number.

4 * x = 4x

Then minus 8.

4x - 8

Then multiply by 3.

3 * (4x - 8) = 60

Now divide both sides by 3

4x - 8 = 20

Add 8 to both sides

4x = 28

Divide both sides by 4

x = 7

Answer:

7

Step-by-step explanation:

let number = x

"4 times a number" = 4x

"eight less than 4 times a number" = eight less than 4x = (4x - 8)

"Three times the quantity eight less than 4 times a number"

= 3 times (4x - 8) = 3(4x-8)

Given that the expression = 60

3(4x-8) = 60

(4x-8) = 20

4x  = 20 + 8

x = 28 / 4

x = 7

Answer:

  6

Step-by-step explanation:

The denominator cannot be zero, so x cannot be 6.

Answer:

value of a = 6

value of b = 3

value of c = 64

value of d= 64

Step-by-step explanation:

1. Apply the quotient of powers:

(-2)^a / 4^b

In the given expression:

[tex]4^5(-2)^9/4^8(-2)^3[/tex]

We know if we have the same base then the powers are subtracting if the bases are in numerator and denominator

i.e [tex]a^m/a^n = a^{m-n}[/tex]

Solving:

[tex]=(-2)^{9-3}/4^{-5+8}\\=(-2)^6/4^3[/tex]

So, the value of a = 6

and the value of b = 3

2. Evaluate Powers

c/d

We have

[tex](-2)^6/4^3[/tex]

Solving:

When power is even negative sign changes into plus sign

64/64

So value of c = 64

and value of d= 64

Answer:

a=6

b=3

c=64

d=64

Step-by-step explanation:

Answer:

Step-by-step explanation:

See below for a graph.

___

Choices B, C, E can be eliminated on the basis that neither x nor g(x) can be negative. The domain of f(x) is x>0; the range of g(x) is x≥0.

Answer:

just so you can give the other guy brainly

Step-by-step explanation:

Answer:

  (b)  line symmetry only

Step-by-step explanation:

This question asks you to identify any applicable form of symmetry the given figure may have.

For plane figures, three kinds of symmetry are defined:

A figure is symmetrical about a point if that point is a midpoint between every point on the figure and a corresponding point on the figure.

A figure is symmetrical about a line if that line is the perpendicular bisector of the segment between any point on the figure and a corresponding point on the figure.

A figure has rotational symmetry if it can be rotated about a center and be congruent to itself. The number of different rotational angles for which this is true is the degree of the rotational symmetry.

There is no point within the bounds of the figure that matches the definition of the center of symmetry about a point.

A vertical line through the center of the figure will serve as a line of symmetry. Each point on the left side of the line corresponds to a point on the right side of the line at the same distance. So, the figure has symmetry about a line.

There is no angle other than 360° through which the figure can be rotated to map to itself. It has no rotational symmetry.

Answer:

B.3

Step-by-step explanation:

If you divide 36 by 12 or 27 by 9 or 21 by 7, you get 3, which means that triangle ABC is 3 times as large as triangle XYZ.

For this case it is observed that the measures of the small triangle are smaller than those of the large triangle, so we have to use a division scale factor. We have to:

[tex]xy = \frac {AB} {3} = \frac {27} {3} = 9\\yz = \frac {BC} {3} = \frac {36} {3} = 12\\xz = \frac {AC} {3} = \frac {21} {3} = 7[/tex]

It is observed that the factor used was [tex]\frac {1} {3}.[/tex]

ANswer:

Option D

Hello There!

The answer would be "C"

For every 10 pieces of candy Simone buys, she pays $1.

By looking at the the graph, you can see that is is moving up at a constant rate each time so each time Simone buys 10 more pieces of candy, the price increases.

Answer:

C

Step-by-step explanation:

Simply match up the values for each choice and see which one fits the graph

A) for every hour, the graph shows an increae in $10 not $20 (Not valid)

B) For every 10 swimmers, the graph shows an increase in 1 lifeguard not 2 (not valid)

C) for 10 pieces of candy, there is an increase in $1 (VALID!!)

D) for every 2 km, the graph shows and increase in 20 min, not 30 min (not valid)

Hence only C fits the graph

Answer:

y=mx+b

x=5

Step-by-step explanation:

[tex]x=5[/tex]

This is the equation for the line, because both points match this equation.  It is a vertical line, since the [tex]x[/tex] is the same for both of them, and it is equal to [tex]5[/tex] both times.

You can then double check your answer by graphing.  If you graph [tex]x=5[/tex], then both points, you can see that they both fall on the line, as shown in the attached graph.

That picture doesn't have anything to do with the problem.

Snail went right, into positive numbers, frog went left, negative numbers.  Their distance is the absolute difference.

d = | 2 - 4(-3) | = | 14 | = 14

Answer: 14

Answer:

4. 158

Step-by-step explanation:

First let's make things a little simpler and put these arcs in terms of x.  We know that the degree measure around the outside of a circle, regardless of its size, is 360.  So let's say that arc BC is x.  That means that arc BDC is 360 - x.  This is because arc BC + arc BDC = 360.  Substituting in our x's we have:

x + 360 - x = 360 and

360 = 360.  (That's just the proof that putting in our x's as we did does in fact work!)

Following the formula then, we have

[tex]22=\frac{1}{2}(360-x-x)[/tex] and

[tex]22=\frac{1}{2}(360-2x)[/tex]

Multiply both sides by 2 to get rid of the fraction and get

44 = 360 - 2x

Subtract 360 rom both sides to get

-316 = -2x

Divide both sides by -2 to get that x = 158

Since we are looking for arc BC and we designated arc BC as our x, that means that arc BC = 158.

[tex]arc=\frac{\pi\theta}{360}(d)[/tex]

There is no any option, but the question is answerable. The length of an arc of a circumference is a fraction of that circumference. Recall that a circumference measures 360 degrees. Suppose you have an arc whose central angle [tex]\theta[/tex] degrees, then the arc of a circumference can be found as:

[tex]\boxed{arc=\frac{\pi\theta}{360}(d)} \\ \\ Where: \\ \\ \theta: \ central \ angle \\ \\ d: \ diameter \ of \ the \ circle[/tex]

So in this case, the expression:

[tex]\frac{\pi\theta}{360}[/tex]

represents the fraction we are talking about.

The equation that gives the length of an arc is s = θ * r, where s is the distance traveled along the circular path, θ is the angle of rotation, and r is the radius of curvature.

The equation that gives the length of an arc is given by:

Length of Arc (s) = θ * r

Where:

For example, if the angle of rotation is 45 degrees and the radius is 5 units, the length of the arc would be:

s = (45 degrees) * (5 units) = 225 degrees * units

https://brainly.com/question/32035879

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Answer:

4 m so, A.

Step-by-step explanation:

Area = side x altitude then,

Your altitude = area/side

which =40/12.5= 4 m  

Hope my answer has helped you!

Answer: A. 4 m

Step-by-step explanation:

We know that a rhombus is a kind of parallelogram.

Area of parallelogram = (Altitude ) x ( Base)

Thus , Area of rhombus = (Altitude ) x ( Base)

As per given , Base =  2.5 meters

Area of rhombus = 10 square meters

Substitute all values in formula , we get

[tex]10=(\text{Altitude})\times2.5\\\\\Rightarrow\ \text{Altitude}=\dfrac{10}{2.5}=4[/tex]

Hence, the altitude of a rhombus is 4 m.

Thus , the correct answer is A. 4 m ,

Answer:

(3x² - 2)(x² + 5)

Step-by-step explanation:

Given

3[tex]x^{4}[/tex] - 2x² + 15x² - 10

Factor the first/second and third/fourth terms

= x²(3x² - 2) + 5(3x² - 2) ← factor out (3x² - 2) from each term

= (3x² - 2)(x² + 5)

Answer:

[tex](x^2+5)(3x^2-2)[/tex]

Step-by-step explanation:

The polynomial is

[tex]3x^4-2x^2+15x^2-10[/tex]

You can group the first and third term and the second and last term

[tex]3x^4+15x^2-2x^2-10[/tex]

Factorize each pair

[tex]3x^4+15x^2-2x^2-10[/tex]

[tex]3x^2(x^2+5)-2(x^2+5)[/tex]

Finally, you can factor the [tex](x^2+5)[/tex] and obtain

[tex](x^2+5)(3x^2-2)[/tex]

Then, the answer is (x2 + 5)(3x2 – 2)

Answer:

y = [tex]\frac{3}{2}[/tex] x + 4

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here m = [tex]\frac{3}{2}[/tex], hence

y = [tex]\frac{3}{2}[/tex] x + c ← is the partial equation

To find c substitute (- 4, - 2) into the partial equation

- 2 = - 6 + c ⇒ c = - 2 + 6 = 4

y = [tex]\frac{3}{2}[/tex] x + 4

Answer:

difference

Step-by-step explanation:

When you're subtracting two (or more) numbers, you're looking to see how far apart they are.  You're looking for their difference.

The result of a subtraction is the difference between the numbers involved in the operation.

When you're adding two numbers up, you're creating a sum.

When you're multiplying two numbers together, you have a product.

When you're dividing two numbers, you have a quotient.

The answer is B, C, and D. Like terms are terms with all the same variable, so 5x and -x are like terms.

C is correct. If we add -x to 5x, we get 4x. The other numbers remain unchanged because they have no like terms.

D is correct. Applying the rule of like terms, which is that like terms are numbers with the same variable, only add together numbers with the same variable.

Hope this helps!

Answer:

Options B, C, and D.

Step-by-step explanation:

We have to simplify the given expression given (5x + 3y + (-x) + 6z).

We will use the process as given below.

1) We will identify the like terms, we have to add or subtract.

2) Like terms are those, which have the same variable of the same degree.

3) We get the simplified expression by combining the same terms.

5x + 3y + (-x) + 6z = 4x + 3y + 6z

Therefore, Options B, C and D will be the correct options.

Answer:

Option D x=4

Step-by-step explanation:

we have

[tex]f(x)=\frac{1}{x-3}+1[/tex]

[tex]g(x)=2\sqrt{x-3}[/tex]

Solve the system by graphing

Remember that the solution of the system of equations (f(x)=g(x)) is the x-coordinate of the intersection point both graphs

The intersection point is (4,2)

therefore

x=4

see the attached figure

[tex]\int_{0}^{2}sin(x^{2})dx \approx 1units^2[/tex]

First of all, the graph of the function [tex]f(x)=sin(x^2)[/tex] is shown in the first figure below. We need to calculate the area under the curve which is in fact the definite integral. From calculus, we know that [tex]f(x)=sin(x^2)[/tex] is non integrable, that is, it doesn't have a primitive,  so we must use calculator to evaluate [tex]\int_{0}^{2}sin(x^{2})dx[/tex]. To do so, calculator uses the Taylor Series, so:

[tex]sin(x^{2})=\sum_{n=-\infty}^{+\infty}\frac{(-1)^{n}}{(2n+1)!}x^{4n+2}$[/tex]

You an use a calculator or any program online, and the result will be:

[tex]\int_{0}^{2}sin(x^{2})dx=0.804units^2[/tex]

Since the problem asks for rounding the result to the nearest integer, then we have:

[tex]\boxed{\int_{0}^{2}sin(x^{2})dx \approx 1units^2}[/tex]

The area is the one in yellow in the second figure.

The value of the integral is approximately 0.8380, rounded to the nearest integer, is 1.

Evaluating the given integral involves using numerical methods since the antiderivative of sin(x²) doesn't have a simple closed-form expression in terms of elementary functions. One common numerical method is to use numerical integration techniques like Simpson's rule or the trapezoidal rule.

Let's approximate the integral using Simpson's rule with n=4 subintervals.

The interval of integration is [0, 2].

The width of each sub-interval is (2 - 0)/n = (2 - 0) / 4 = 0.5

The endpoints of the sub-intervals are:

x₀ = 0,

x₁ = 0 + 0.5 = 0.5,

x₂ = 0 + 2(0.5) = 1.0

x₃ = 0 + 3(0.5) = 1.5

x₄ = 0 + 4(0.5) = 2.0

Evaluate the function at these points:

f(x₀) = sin(0²) = 0

f(x₁) = sin(0.5²) = 0.2474

f(x₁) = sin(1²) = 0.8415

f(x₃) = sin(1.5²) = 0.7781

f(x₄) = sin(2²) = -0.7568

Apply Simpson's rule:

[tex]\int_{0}^{2} \sin(x^2) \, dx \approx \frac{h}{3} \left( f(x_0) + 4 \sum_{i \text{ odd}} f(x_i) + 2 \sum_{i \text{ even, } i \neq 0, n} f(x_i) + f(x_n) \right)\\ = \frac{0.5}{3} \left( f(x_0) + 4f(x_1) + 2f(x_2) + 4f(x_3) + f(x_4) \right)\\ = \frac{0.5}{3} \left( 0 + 4(0.2474) + 2(0.8415) + 4(0.7781) + (-0.7568) \right) \\ = \frac{0.5}{3} \left( 0 + 0.9896 + 1.6830 + 3.1124 - 0.7568 \right) \\ = \frac{0.5}{3} \left( 5.0282 \right)\\ =0.8380[/tex]

Thus, the value of the given integral is approximately 0.8380.

Round the result to the nearest integer, which is 1.

Complete question:

Use your calculator to evaluate [tex]\int_{0}^{2} \sin(x^2) dx[/tex]. Give your answer to the nearest integer.

Answer:

[tex]g^2-4g-21=(g-7)(g+3)[/tex]

Step-by-step explanation:

To complete the left side of the equation, we need to bring it to the form

[tex](g-a)(g+b)[/tex]

expanding this expression we get:

[tex]g^2+bg-ag-ab[/tex]

[tex]g^2+(b-a)g-ab[/tex]

Thus we have

[tex]g^2-4g-21=g^2+(b-a)g-ab[/tex]

from here we see that for both sides of the equation to be equal, it must be that

[tex]b-a=-4[/tex]

[tex]-ab=-21[/tex].

Getting rid of the negative signs we get:

[tex]a-b=4[/tex]

[tex]ab=21[/tex]

At this point we can either guess the solution to this system (that's how you usually solve these types of problems) or solve for [tex]a[/tex] and [tex]b[/tex] systematically.

The solutions to this set are [tex]a=7[/tex] and [tex]b=3[/tex]. (you have to guess on this—it's easier)

Therefore, we have

[tex](g-a)(g+b)=(g-7)(g+3)[/tex]

which completes our equation

[tex]\boxed{ g^2-4g-21=(g-7)(g+3)}[/tex]

Answer: -7 and +3

did the assignment

Answer:

C there is no mode

Step-by-step explanation:

The mode is the number that appears most often.  Since there is no number that appears more than once, there is no mode

Answer:

B.  

help reduce total interest charges

Step-by-step explanation:

Assuming there are no prepayment penalties, paying more than your monthly car payment can help reduce total interest charges

Answer:

x=15

Step-by-step explanation:

We know that a right angle is 90 degrees. When we subtract the 30 from 90, we get 60 degrees as the other, smaller angle. Then, we divide 60 by 4 to get 15. This mean x equals 15.

Answer:

  -2p² -11p -35

Step-by-step explanation:

-2(p +4)² -3 +5p = -2(p² +8p +16) -3 +5p

  = -2p² -16p -32 -3 +5p

  = -2p² -11p -35

Answer:

–2p2 – 11p – 35

Step-by-step explanation:

Answer:

A(n)=130+13(n-1) ; 86

Step-by-step explanation:

Here is the sequence

130,143,156,169.......

the first term denoted by a is 130 and the common difference denoted by d is second term minus first term

143 - 130 = 13

Hence a=130 and d = 13

Now we have to evaluate to 13th term.

The formula for nth term of any Arithmetic Sequence is

A(n) = a+(n-1)d

Hence substituting the values of a ,and d  get

A(n)=130+13(n-1)

To find the 13th term , put n = 13

A(13)=130+13*(13-1)

      = 130+13*12

      = 130+156

A(13) = 286

Answer:

Irrational because it is not a terminating or repeating decimal.

Step-by-step explanation:

Final answer:

The square root of 35 is an irrational number because it cannot be expressed as a fraction or a terminating/repeating decimal.

Explanation:

The best description for the real number square root of 35 is irrational, because it is not a terminating or repeating decimal. In general, an irrational number cannot be expressed as a quotient of two integers.

For example, let's approximate the square root of 35. We can use a calculator to find that the square root of 35 is approximately 5.91607978309961. This decimal representation goes on indefinitely without repeating or terminating, confirming that it is irrational.

Therefore, the square root of 35 is an irrational number because it cannot be expressed as a fraction or a terminating/repeating decimal.

Answer:

The new area is 4 times the original area

Step-by-step explanation:

we know that

The area of a rectangle is equal to

[tex]A=bh[/tex]

where

b is the base

h is the height

If the height is multiplied by 4

then

the new area is equal to

[tex]A=(b)(4h)[/tex]

[tex]A=4bh[/tex]

therefore

The new area is 4 times the original area

Answer:

3+2x<30

Step-by-step explanation:

3 represents that Emily is 3 years older than 2x

2x represents twice Mary's age

<30 represents that it's always less than 30

Answer:

The compound inequality is [tex]0<x<9[/tex]

Step-by-step explanation:

Consider the provided information.

It is given that Emily is three years older than twice her sister Mary's age.

Let x represent Mary's age.

Then the age of Emily is: 2x+3

The sum of their ages is less than 30.

This can be written as:

[tex]2x+3+x<30[/tex]

[tex]3x+3<30[/tex]

[tex]3x<27[/tex]

[tex]x<9[/tex]

As we know the age can't be a negative number.

Therefore, the age of Mary must be a positive number greater than 0.

Thus, the compound inequality is [tex]0<x<9[/tex]

1. First, let us find the probability that the first card is a diamond.

Now, since we are given that there are four suits and there are, assumably, an equal number of cards in each suit, we can say that the probability of choosing a diamond card is 1/4. We can also write this out as such, where D = Diamond:

Pr(D) = no. of diamond cards / total number of cards

There are 52 cards in a deck, and 13 cards of each suit, thus:

Pr(D) = 13/52 = 1/4

2. Now we need to calculate the probability of not choosing a diamond as the second card.

In many cases, when given a problem that requires you to find the probability of something not happening, it may be easier to set it out as such:

Pr(A') = 1 - Pr(A)

ie. Pr(A not happening, or not A) = 1 - Pr(A happening, or A)

This works because the total probability is always 1 (100%), and it makes sense that to find the probability of A not happening, we take the total probability and subtract the probability of A actually happening.

Thus, given that we have already calculated that the probability of choosing a Diamond is 1/4, we can now set this out as such:

Pr(D') = 1 - Pr(D)

Pr(D') = 1 - 1/4

Pr(D') = 3/4

3. Now we come to the final step. To find the probability of something and then something else happening, we must multiply the two probabilities together. Thus, given that Pr(D) = 1/4 and Pr(D') = 3/4, we get:

Pr(D)*Pr(D') = (1/4)*(3/4)

= 3/16

Thus, the probability of choosing a diamond as the first card and then not choosing a diamond as the second card is 3/16.

The first card is a diamond and the second card is not a diamond when drawing cards with replacement from a standard deck is 3/16.

The subject of this question is probability, a topic in Mathematics, specifically dealing with the calculation of the likelihood of certain outcomes when drawing cards from a deck. To find the probability that the first card is a diamond and the second card is not a diamond when each card is replaced after being drawn, we must consider two independent events. The probability of drawing a diamond card from a standard deck of 52 cards is 1/4, since there are 13 diamonds out of 52 cards. Because the card is replaced, the probability that the second card is not a diamond remains the same as for any single draw where the desired outcome is not a diamond, which is 39/52 or 3/4. Thus, the combined probability of both events happening in sequence (first drawing a diamond, then drawing a non-diamond) is determined by multiplying the probabilities of individual events: (1/4) × (3/4) = 3/16.

Answer:

4/3

Step-by-step explanation:

The exponential form is (3x+4)^4=4096

Take the fourth of both sides:

3x+4=plus or mins 8

3x+4=8          or 3x+4=-8

So

3x=4            or    3x=-12

x=4/3          or     x=-4 (this sound won't work because 3x+4 becomes neg)

So only sol 4/3.

The solution to log3x-2 4096 = 4 is x = 4.493409.

The solution to log3x-2 4096 = 4 is x = 4.493409 after isolating the logarithmic term and converting the equation to exponential form.

To solve the equation log3(x-2) = 4096, we first isolate the logarithmic term by adding 2 to both sides, resulting in log3x = 4098. Next, we rewrite the equation in exponential form as 3^4098 = x, which simplifies to x = 4.493409. Therefore, the solution to the equation log3x-2 4096 = 4 is x = 4.493409.

Answer:

Rational numbers are decimals that can't be turned into fractions and irational numbers are decimal numbers that can be turned into Fraction.

Step-by-step explanation:

Example Pi 3.14 can be 22/7