divide (x3−8x2+2)÷(x−3)

The values of the function are-

For the given function;

f(x) = x - 3

g(x) =(x - 3)/(x - 9)

Part a: Value of (f/g)(x)

For the finding the value of  (f/g)(x) simply divide the function g(x) by f(x).

(f/g)(x) = (x - 3)/ [(x - 3)/(x - 9)]

As, (x -3) will get cancelled.

(f/g)(x) = x - 9

Part b: Domain of (f/g)(x)

(f/g)(x) = x - 9

As, the resultant function is a polynomial function, thus the domain of the function is all real numbers.

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If the midpoint of ST is (6, -7) then its distance from S and T must be the same!

The distance from point T (0,5 ) to (6, -7) is from the Pythagorean theorem:

which is

In this question, we are given a line. The standard equation of line is:

y = mx + b

Here, m is the slope, that is the difference of y values over the x values.

m = (y2 - y1) / (x2 - x1)

b is the y-intercept, where the value of x is zero.

If we see the line, x = 0, when y = -4. Hence, the y-intercept = b = -4

Also,

(x1, y1) = (0, -4)

(x2, y2) = (-4, 4)

m = [4 - (-4)]/ [-4 - 0]

m = 8/-4

m = -2

Hence, the equation of given line is

y = -2x - 4

The rule is: two lines are perpendicular if their slopes are negative reciprocal of each other.

In other words, two lines with slope m1 and m2 are perpendicular if

m1 = -1/m2

Now, the slope (m1) of the given line is -2. Hence, the slope (m2) of the perpendicular line would be m2 = 1/-(-2) = 1/2

Now, just put this value, we get

Y = 1/2 x - 4

As there is no solution closer to this one, I believe the 2nd answer Y = 1/2x + 3 would be correct.

Step 1: Write out the values

For Cougars

Total Points = 84

Number of 1 point shot = 0

Number of 3 and 2 points shots = 38

Step 2: Write out the system of equations

Since there are x number of two-point shots, then the total number of points from the two-point shots is 2x

Also, there are y number of three-point shots, then the total number of points from the three-point shots is 3y

Hence, the total number of points is 2x + 3y

Therefore,

Step 3: Solve the system of equation simultaneously

x + y = 38 ------ equation 1

2x + 3y = 84 ------ equation 2

Using the elimination method to eliminate x

Multiply equation 1 by 2 to get a new equation

2x + 2y = 76 ------ equation 3

Step 4: combine equation 2 and 3 and solve simultaneously

2x + 3y = 84------- equation 2

2x + 2y = 76 ------ equation 3

Subtract equation 3 from 2

Answer:

The constant is 5 and the variation is known as the slope of the equation which is the rate of change of y with respect to x. In other words how much does y change when x changes by 1 unit

Step-by-step explanation:

Solution

for this case we can see that for

Figure 0 = 6 tiles

Figure 1 = 7 tiles

Figure 2 = 8 tiles

Figure 3= 9 tiles

Figure 4 = 10 tiles

Figure 5= 11 tiles

Then the table would be given by:

Figure number (x) 0 1 2 3 4 5 x

Number of tiles (y) 6 7 8 9 10 11 6+x

And the line should be like this:

Two workers in a holiday boutique are filling stockings with small gifts and candy.

Katie has already filled 3 stockings and will continue to fill them at a rate of 1 stocking per hour.

3 + x

Peter, who just arrived to help, can fill 4 stockings per hour.

4 x

At some point, Peter will catch up with Katie and they will have completed the same number of stockings.

3 + x = 4x

3 = 4x -x

3 x =3

x = 3/3

x =1 hour How long will that take?

How many stockings will each worker have filled by then?

Katie = 3 + 1 = 4

Peter = 4 x 1 = 4

The local salesman has to sell $19564.3 in a month if he needed to have a monthly income of $2200.

The monthly salary will be the sum of the fixed part or base salary and the commission part.

The base salary of the local salesman is $925.

The salesman commission part is 7% on all sales over $1350.

Let x be the total amount of sales, and x must be greater than $1350.

Then,

The amount of sales over $1350 is x - 1350.

He earns 7% on that amount, so the commission part is 7% of (x - 1350),

or 0.07( x - 1350 ).

So,

monthly salary = fixed part + commission part

monthly salary = 925 + 0.07( x - 1350)

925 + 0.07(x - 1350) = 2200

0.07(x - 1350) = 1275

0.07x - 94.5 = 1275

0.07x = 1369.5

x = 19564.3

He would have to sell $19564.3 in a month if he needed to have a monthly income of $2200.

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The answer is y=3(x+3)

Answer:6.67x10^2

Step-by-step explanation:

For the given functions, it is found that:

1) The inverse is: [tex]f^{-1}(x) = \frac{4x^2}{9} + 1[/tex]

2) f(a) = f(b) if, and only if, a = b, hence the function is one-to-one.

3) The composite of these two functions is different of x, hence the two functions are not inverses.

The function is defined by:

[tex]y = 3\frac{\sqrt{x - 1}}{2}[/tex]

To find the inverse, we exchange x and y on the original function and then isolate y, hence:

[tex]x = 3\frac{\sqrt{y - 1}}{2}[/tex]

[tex]3\sqrt{y - 1} = 2x[/tex]

[tex]\sqrt{y - 1} = \frac{2x}{3}[/tex]

[tex](\sqrt{y-1})^2 = \left(\frac{2x}{3}\right)^2[/tex]

[tex]y - 1 = \frac{4x^2}{9}[/tex]

[tex]y = \frac{4x^2}{9} + 1[/tex]

[tex]f^{-1}(x) = \frac{4x^2}{9} + 1[/tex]

To show that the function is one-to-one, we need to show that f(a) = f(b) if, and only if, a = b, then:

Equaling the functions:

-2/(2a - 1) =  -2/(2b - 1).

Applying cross multiplication:

-2(2b - 1) = -2(2a - 1)

2b - 1 = 2a - 1

2b = 2a

b = a.

Hence the function is one-to-one.

The functions will be inverses if the composition of the functions result in x, hence:

f(g(x)) = f(x/3 + 5) = 3(x/3 + 5) - 5 = x + 15 - 5 = x + 10.

Hence the functions are not inverses.

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Which two transformations preserve the side lengths and angles of the preimage:

Rotations and reflections both preserve a polygon's side lengths. Dilations and translations both preserve a polygon's angle measures.

A reflection across line will preserve the angles

A dilation by a factor of 4 will preserve the both

Hence the correct answer is Option A and D

Answer:

1: a translation to the right

2: a reflection across line m

Step-by-step explanation:

Answer

a° = 58°

b° = 48°

c° = 74°

d° = 122°

Explanation

To answer this, we need to first know

- what alternate angles are.

- that the sum of angles in a triangle is 180°.

- The sum of angles on a straight line is 180°.

Alternate angles are angles that are in opposite positions relative to a transversal intersecting two lines. If the two lines are parallel to each other, then alternate angles are equal.

We can see that

a° = 58°

b° = 48°

Then, for c°,

48° + 58° + c° = 180° (Sim of angles in a triangle is 180°)

106° + c° = 180°

c° = 180° - 106°

c° = 74°

Then, for d°,

58° + d° = 180° (Sum of angles on a stright line is 180°)

d° = 180° - 58°

d° = 122°

Hope this Helps!!!

Answer: D and C are the other rotations

Step-by-step explanation: A is mirrored

1) We know that the sum of the interior angles within a triangle is 180º

So we can state that :

∠X = 80º , ∠V=32º and ∠W = 180º-(80+32), ∠W=68º

2) The area of a triangle can be found by the Heron formula, but before that, we need to find out the other legs. Let's sketch this and use the Law of Sines:

The Law of Sines:

Now let's proceed to find the length of side x:

Now we can add the three sides and find out the Perimeter:

2p: 722.26 +388.65 +680

2p=1790.91

And the semi perimeter is p =2p/2, p =895.455.

2.2) Finally we can find out the area using the Heron Formula:

3) Hence, the area is 130,060 cm²

Answer:

x = -12

Step-by-step explanation:

these two angles are same side interior angles. These two angles will add up to 180.
so we have the equation:

(x + 142) + (x + 62) = 180

Now just simplify:

(x + 142) + (x + 62) = 180

___-142_________-142

x + (x + 62) = 38

_____-62___-62

x + x = -24

2x = -24

-24/2 = -12

Therefore, x = -12

The Solution:

Given:

We are required to simplify.

Therefore, the correct answer is:

the division of fractions follows the stes

Applying this into the expression given

simplify the coefficients by decomposing 9 into a product and cancelling the common factors

simplify

In the denominators there is a difference of squares that can be rewriten as a product, in which by definition the difference of square is described as

In the denominator of the expression we can see that a is squared and that 81 has an exact root which is 9, reason why we can write this as a difference of squares, it should look like this:

simplify the expression

distribute the 3

Using the normal distribution, it is found that:

a) 95.99% of Tiger's drives travel at least 290 yards.

b) 44.40% of Tiger's drives travel between 305 and 325 yards.

c) If the z-scores do not show on table A, they represent too low or too high values, with probabilities very close to either 0 or 1.

The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is given by the following rule:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation for the length of Tiger Woods's swings are given as follows:

[tex]\mu = 304, \sigma = 8[/tex]

The proportion of golf swings that are at least 290 years is one subtracted by the p-value of Z when X = 290, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Z = (290 - 304)/8

Z = -1.75

Z = -1.75 has a p-value of 0.0401.

1 - 0.0401 = 0.9599.

Hence the percentage is of 95.99%.

The proportion of golf swings that are between 325 yards and 305 yards is the p-value of Z when X = 325 subtracted by the p-value of Z when X = 305, hence:

X = 325:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Z = (325 - 304)/8

Z = 2.63

Z = 2.63 has a p-value of 0.9957.

X = 305:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Z = (305 - 304)/8

Z = 0.13

Z = 0.13 has a p-value of 0.5517.

0.9957 - 0.5517 = 0.4440.

Hence the percentage is of 44.40%.

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The Solution:

Let the present value of the investment be represented with P.

We shall use the formula below:

Substituting these values in the formula above, we get

So,

Thus, the present value of the investment that will yield $7000 at the end of 5 years is $5189.61 (or 518961 cents )

Therefore, the correct answer is $5189.61 (or 518961 cents )

The relative frequency is the percentage of a count over the total count.

To get the relative frequency, here are the steps:

1. Get the total count.

2. Divide each frequency or count by 654.

For example, the frequency between 10 - 13.9 km/h is 4 players.

Hence, the relative frequency for the first class interval is 0.0061.

Moving on to the next interval 14 - 17.9 km/h. x = 8 players

Moving on to the next interval 18-21.9 km/h. x = 20 players

Moving on to the 4th interval 22 - 25.9 km/h . x = 74 players

At 5th interval 26 - 29.9 km/h, x = 336 players.

Finally, at the last interval 30 - 33.9 km/h, x = 212 players.

Completing the table, we have:

Answer: $31.50 for the four brushes after using the coupon

Step-by-step explanation:

$10.50 (Amount for EACH brush) * 0.75 (coupon 25% off)  = $7.875 (Amount for each after coupon)

$7.875* 4 brushes = $31.5

or

$10.50 (regular price) * 4 brushes = $42 (4 brushes at regular price)

$42 * 0.75(25% coupon) =$ 31.5

Answer:

0.91

Step-by-step explanation:

If the order of choice is relevant, use permutation. We have to choose 5 objects in a total of 9:

Obs: Initially we have 9 objects, you choose one, then we have 8, you choose another, then you have 7..... (this is the reasoning)

If the order of choice is not relevant, use a combination. This can be done by the equation above:

Obs: It is a combination of 9 elements chosen 5 by 5.

Given the a point and a slope

point coordinate ( -2 , -2 )

Slope (m) = 4

Step 1: Write the formula for the point-slope equation

Step 2: Identify the x and y values

Step 3: substitute the values in the point-slope equation formula

Hence, the equation of the line is y = 4x+6

Let the number be x:

So intepreting the word problem into words we will have:

Simplifying further, we will have:

Cross multiply:

Answer:

A

Step-by-step explanation:

Adding 8 to both sides,

[tex]4|x|=0 \\ \\ |x|=0 \\ \\ x=0[/tex]

50 x 600= 30,000 which has more zeros than 50 and 600 combined

The given values the equation evaluate is:

f(2) = 15,

f(x+8) = x² + 25x + 129,

f(-x) = x² - 9x - 7

x ax2 + bx + c = 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. a 0. Since it is a second-order quadratic equation, which is ensured by the algebraic fundamental theorem, it must have at least one solution. The solution might be straightforward or difficult.

f(x) = x² + 9x− 7

a) At, f(2)

f(2) = (2)² + 9(2) - 7

f(2) = 4 + 18 - 7

f(2) = 15

b) At, f(x+8)

f(x+8) = (x + 8)² + 9(x + 8) - 7

f(x+8) = x² + 8² + 16x + 9x + 72 - 7

f(x+8) = x² + 64 + 25x + 72 - 7

f(x+8) = x² + 25x + 129

c) At,  f(-x)

f(-x) = (-x)² + 9(-x) - 7

f(-x) = x² - 9x - 7

Hence,

The given values the equation evaluate is:

f(2) = 15,

f(x+8) = x² + 25x + 129,

f(-x) = x² - 9x - 7

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Answer:

-11

Step-by-step explanation:

7y=-84

7y=-84/7 you have to divide the whole equation by 7 to get rid of the 7 in fron of the y

y=-11

Answer:

7y = -84

y = -84/7

y = -12

Final answer after checking will be the following:-

7(-12) = -84