The expression (a + 1)x^3 + (2 – 3a)x^2 – (3a – 1)x +
2a – 13 has a factor x – 3. Find the value of a and
hence find the other two factors of the expression.​

SOLUTION:

Step 1:

In this question, we are given the following:

Step 2:

From the question,

We have that:

The values of each composite function are:

a) -1

b) -1

c) 2

d) 0

e) 2

f) -4

We have,

These are composite functions.

It is written as:

(f o g) (x) = f (g(x))

Now,

From the table, the values for each function f and g at specific values x are taken.

a.

(f o g)(1)

f(g(1)) = f(0) = -1

b.

(f o g) (-1)

f(g(-1)) = f(0) = -1

c.

(g o f) (-1)

g(f(-1)) = g(-2) = 2

d.

(g o f) (0)

g(f(0)) = g(-1) = 0

e.

(g o g) (-2)

g(g(-2)) = g(2) = 2

f.

(f o f) (-1)

f(f(-1)) = f(-2) = -4

Thus,

The values of each composite function are:

-1, -1, 2, 0, 2, and -4.

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Answer:

5/8.

Step-by-step explanation:

we first have to find the total amount of marbles in the bag by adding the blue and green marbles.

15 + 25 = 40

40 is the total.

to get the fraction of green marbles, we do 25 over the total number of marbles,

that is....... 25/40.....then we simplify the fraction by dividing both the numerator and the denominator with a common divisor, which will be 5.

25 ÷ 5 = 5

40 ÷ 5 = 8

hence..... 5/8.

An infinite geometric series is one in which each term is equal to the preceding term multiplied by a fixed non-zero number, known as the common ratio.

The first term is called a1, and the common ratio is represented by r.In this particular question, we are required to find the value of a1 and r for an infinite geometric series. The partial sum S2 will also need to be found.For a geometric sequence that is infinite, the formula for the partial sum, Sn, is:Sn = a1 / (1-r), where a1 is the first term and r is the common ratio.To solve for a1, it is necessary to know two other variables: the common ratio r and the value of the first term a1. S2 is the sum of the first two terms, so: S2 = a1 + arTo find S2, we must first determine a1 and r. a1 is the first term in the sequence, and r is the common ratio. We can obtain both a1 and r by dividing the second term by the first term.The formula is:r = (ar/a1) = a2/a1 Substitute the value of r and a1 into the formula for S2 to obtain the result: S2 = a1 + ar = a1 + a1r = a1(1+r) Therefore, the value of a1 is a constant number that will appear in the series, and the common ratio, r, will be multiplied by this number to obtain the next value in the series.

So, a1 is the first term, and r is the common ratio of the infinite geometric series. S2, the sum of the first two terms, is found by using the formula S2 = a1 + ar where a1 is the first term and r is the common ratio.

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The flow speed u in the Skykomish River with a bottom slope of 0.002 and constant depth with a Manning number of n can be determined using the Manning Equation. The equation is given as Q = (1/n) * (A/R)^2/3 * S^(1/2) where Q = Flow Rate A = Cross-sectional area of the river R = Hydraulic radius S = Bottom slope of the river n = Manning number

Explanation:

The Manning number is a measure of the roughness of the river bed and sides. The value of n depends on the characteristics of the river channel such as the size of sediment, vegetation, and other obstructions. It can be estimated from tables or charts that relate n to the type of channel and other factors.

Substituting the values given in the problem:Q = uA, where u is the flow speed of the river and is what we need to find out. Rearranging the Manning equation to solve for u, we get:u = (1/n) * (A/R)^2/3 * S^(1/2)Therefore, the flow speed u in the Skykomish River can be calculated using the Manning Equation.

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Oil spilling from a ruptured tanker spreads in a circle on the surface of the ocean. The

radius of the spill increases at a rate of 4 m/min. How fast is the area of the spill

increasing when the radius is 7 m?

Area of a circle = Pi r^2

A = Pi (7)^2 = Pi (49) =

Answer:

the figure A was rotated 145° over the origin(0,0), and flipped over the x-axis, and for last it was moved 4 to the right and 1 down (x+4,y-1)

Answer:

a

Step-by-step explanation:

Answer:

y=mx+b is the form in which these equations are. B represents the y intercept and M is the slope

currently to find slope we need to get y alone on the left side of the equation for all the answers:

A.y-4=3(x-2) -----> y-4=3x-6 (i also distributed) ----> y=3x-2

B.  y+4=-3(x+2)----> y+4=-3x-6 -------> y=-3x-10

C. y-2=-3(x-4) --------> y-2=-3x+12 ------> y=-3x+14

D. y-4= -3( x-2) --------> y-4= -3x+6 ---------> y=-3x+10

All of these equations except A have a slope of -3 so A is already out and to find which one is valid we need to plug in the point (2, 4) for each of the equations

B. 4=-3(2)-10 ------> 4=-6-10----> 4=-16- not valid

C. 4 =-3(2)+14 ----->  4=-6+14------>4=8 not valid

D. 4=-3(2)+10 ----->4=-6+10 ------> 4=4 - Valid

Only D is correct

Step-by-step explanation:

The pair of 1st line is vertical opposite angle and 2nd one is adjacent angles.

What is vertical opposite angle ?

When 2 lines meet one another, then the other angles, shaped thanks to intersection ar known as vertical angles or vertically opposite angles. A try of vertically opposite angles ar continuously adequate to one another. Also, a angle and its adjacent angle are supplementary angles, i.e., they add up to a hundred and eighty degrees.

Main body:

1st pair of line intersect each other , so ∠1 = ∠2 by using vertical opposite angle.

2nd pair of line also intersect each other , so ∠3 ,∠4 are adjacent angles.

Hence ,pair of 1st line is vertical opposite angle and 2nd one is adjacent angles.

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Answer:

4. D

5. D

Step-by-step explanation:

To subtract Matrices, subtract the numbers that are in the same position.

You can only add or subtract Matrices that have the same order.

Here, both Matrix X and Y, are 2 by 2 matrices.

So let's subtract

\(5 - 6 = - 1\)

\( - 4 - ( - 1) = - 3\)

\(3 - ( - 7) = 10\)

\( - 2 - 4 = - 6\)

The Matrix that matches that is D so the answer to 4 is D.

5. We do the same thing above, but we multiply by 2 first.

\(5 - 2(6 ) = - 7\)

\( - 4 - 2( - 1) = - 2\)

\(3 - 2( - 7) = 17\)

\( - 2 - 2( 4) = - 10\)

The answer here is D as well.

Answer:

8 3/4 is a mixed number

Step-by-step explanation:

I don know how to explain

To find the value of 1 (y) when y = -3/5, we substitute the value of y into the expression 1 (y).

In mathematical notation, 1 (y) means the reciprocal or multiplicative inverse of y. The reciprocal of a number is obtained by dividing 1 by that number.

Therefore, to find 1 (y) when y = -3/5, we calculate:

1 (y) = 1 / y

Substituting y = -3/5:

1 (y) = 1 / (-3/5)

To divide by a fraction, we multiply by its reciprocal:

1 (y) = 1 * (5/(-3))

Multiplying the numerators and denominators:

1 (y) = (5/(-3))

Simplifying the fraction:

1 (y) = -5/3

Therefore, 1 (y) is equal to -5/3 when y = -3/5.

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Answer:

30, root 3 over 2 or the third option

I did it on my quiz :)

But basically it is 30, root 3 over 2 because sin and cos are complements to one another.

Trigonometric Identities are equalities that utilize trigonometry functions and hold true for all variables in the equation. The correct option is C; 30°, (√3)/2.

Trigonometric Identities are equalities that utilize trigonometry functions and hold true for all variables in the equation. There are several trigonometric identities relating to the side length and angle of a triangle.

Given that sin(60°) is (√3)/2. Therefore, the value of cos can be written as,

sin(60°) = (√3)/2

cos(90° - 60°) = (√3)/2 {Cos(90° - x) = Sin(x)}

cos 30° = (√3)/2

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Answer:

a. v

Step-by-step explanation:

Given

\(3v - 8\)

Required

Identify the variable

Literary, variable means things that change in values;

Going by this definition, we have that:

3 -> This is not a variable because its value will always be 3

v -> This is a variable because its value can change once its value changes, the result of the expression will also change

- -> This is not a variable; it is an arithmetic operator to subtract

8 -> This is not a variable because its value will always be 8

Take for instance

\(v = 2\)

\(3v - 8 = 3 * 2 - 8 = 6 - 8 = -2\)

When \(v =5\)

\(3v - 8 = 3 * 5 - 8 = 15 - 8 = 7\)

Notice that there's a difference in both results;

This is as a result of v being a variable

Answer:

\(→12 {x}^{3} + 4 {x}^{2} + 3x + 1 \\ = 4 {x}^{2} (3x + 1) + 1(3x + 1) \\ = \boxed{(3x + 1)(4 {x}^{2} + 1)}✓\)

Answer:

Step-by-step explanation:

The angle bisector of a triangle divides the opposite side in 2 segments that are proportional to the other 2 sides of the triangle. Namely:

\(\frac{15}{18}=\frac{w}{30}\) and cross multiply.

18w = 450 so

w = 25

Answer:

Which of the given mathematical sentens are quadratic equation?

Answer:

The third answer, y = 4x + 1

Step-by-step explanation:

Let's take the pair x = 2, and y = 9.

We know what x is, and what the result, y, is now.

Let's plug x into the third equation, y = 4x + 1

y = 4 * 2 + 1

y = 8 + 1

y = 9

We already know that y = 9, so this equation is correct.

Hope this helps!

(Let me know if you want to know why it's not any of the others.)

Given:

The scores on a standardized test are normally distributed with a mean of 115 and standard deviation of 10.

Required:

What test score is 0.8 standard deviations below the mean?

Explanation:

Answer:

answered the question.

Answer:

44

Step-by-step explanation:

Isosceles triangles have two angles that are equal.  If the two equal angles are 68

We have  68, 68, and an unknown angle x

They add to 180

68+68+x = 180

136+x=180

x =180-136

x =44

The probability that the 5th ball drawn is red and the 8th ball drawn is blue is 45/196 or approximately 0.2307.

What is probability ?

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1.

The probability of drawing a red ball on the 5th draw is the number of red balls divided by the total number of balls in the bin, which is 5/14. The probability of drawing a blue ball on the 8th draw is the number of blue balls divided by the total number of balls in the bin, which is 9/14.

The probability of both events happening is the product of the individual probabilities:

P(red on 5th draw and blue on 8th draw) = (5/14) * (9/14) = 45/196

So, the probability that the 5th ball drawn is red and the 8th ball drawn is blue is 45/196 or approximately 0.2307.

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The probability that the 5th ball drawn is red and the 8th ball drawn is blue is 45/196 or approximately 0.2307.

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1.

The probability of drawing a red ball on the 5th draw is the number of red balls divided by the total number of balls in the bin, which is 5/14. The probability of drawing a blue ball on the 8th draw is the number of blue balls divided by the total number of balls in the bin, which is 9/14.

The probability of both events happening is the product of the individual probabilities:

P(red on 5th draw and blue on 8th draw) = (5/14) * (9/14) = 45/196

So, the probability that the 5th ball drawn is red and the 8th ball drawn is blue is 45/196 or approximately 0.2307.

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Answer:

$330

Step-by-step explanation:

$3 times 60 students = $180

$5 times 30 adults = $150

$180 + $150 = $330

Answer:

Step-by-step explanation:

you would find your answer by multiplying the amount of students/adults by how much each ticket costs

60 x $3 = $180

30 x $5 = $150

$180 + $150 = $330

Answer:

B (Y, N, N)

Step-by-step explanation:

a) y = 1/3x, so each value satisfies it. This is true.

b) If "a" is "Y" then b has to be no

c) 1 * 11 = 11

2 * 2 = 22

3 * 5 = 15

The last equation does not follow the rules for the previous two equations, so it is no.

Thus, the answer is B (Y, N, N)

Answer:

\((f+g)(x)=x^2-2x-35\)

Step-by-step explanation:

So we have the two functions:

\(f(x)=x^2-3x-40\text{ and } g(x)=x+5\)

And we want to find (f+g)(x). This is the same as:

\((f+g)(x)=f(x)+g(x)\)

Substitute:

\(=(x^2-3x-40)+(x+5)\)

Combine like terms:

\(=x^2+(-3x+x)+(-40+5)\)

Add:

\(=x^2-2x-35\)

And we're done!

The tree diagram illustrates the probabilities associated with different combinations of weather patterns and seasons of the year. The tree diagram is a visual representation that presents the probabilities of various outcomes resulting from the combination of weather patterns and seasons of the year.

It is a useful tool for understanding the likelihood of specific events occurring based on different factors.

The diagram is structured hierarchically, with the weather patterns forming the first level and the seasons of the year forming the second level. Each branch represents a specific combination, and the probability associated with that combination is indicated on the branch.

By analyzing the diagram, one can observe how the probabilities change depending on the weather patterns and seasons. For instance, certain weather patterns may be more prevalent during specific seasons, resulting in higher probabilities for certain combinations.

Overall, the tree diagram serves as a visual aid to comprehend the probabilities associated with simple events combining weather patterns and seasons of the year, enabling a better understanding of the likelihood of different outcomes based on these factors.

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Answer:

y = 1

Step-by-step explanation:

y is inversely proportion to x means that ,

y ∝ 1/x or ,

\(y\ \alpha\ \frac{1}{x}\)

When we remove the proportionality sign we get,

\(y=k(\frac{1}{x})\\y=\frac{k}{x} \\\)

now we know the point is (2 , 3) which means it corresponds to (x , y) which furthermore means y=3 when x=2,

so we insert these values and get the value of k.

\(y=\frac{k}{x} \\\\3=\frac{k}{2}\\\\6=k\\\)

now the equation becomes,

\(y=\frac{6}{x}\)

now we need to find y when x is 6 so just replace x with 6

\(y=\frac{6}{x}\\\\y=\frac{6}{6} \\\\y=1\)

so we get the value of y is 1

To draw a triangle with a side length of 4 inches between angles of 50° and 65°, we can follow these steps:Step 1: Draw a line segment AB of length 4 inches using a ruler.

Step 2: At point A, draw an angle of 50° using a protractor. Step 3: At point B, draw an angle of 65° using a protractor. Step 4: Join points A and B to form the third side of the triangle. The final triangle will have a side length of 4 inches and angles between 50° and 65°.

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Answer:

x=25⁰

y=25⁰

Step-by-step explanation:

ABC+BAC+ACB = 180⁰

65⁰+90⁰+y = 180⁰

y = 180⁰-155⁰

y = 25⁰

In triangle ABD,

ABD+ADB+BAD = 180⁰

65⁰+90⁰+x = 180⁰

x = 180⁰-155⁰

x = 25⁰