Complete the synthetic division to find the quotient of 3x^3-25x^2+12x-32 and x-8

[tex]\implies {\blue {\boxed {\boxed {\purple {\sf { \frac{ - 21}{10} \:(or) \: - 2 \frac{1}{10} }}}}}}[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]

[tex] \frac{8}{ - 5} + ( \frac{ - 1}{2} )[/tex]

[tex] \\= \frac{ - 8}{5} - \frac{1}{2} [/tex]

Since the denominators are unequal, we find the L.C.M (lowest common multiple) for both denominators.

The L. C. M for 5 and 2 is 10.

Now, multiply the L.C.M. with both numerator & denominator.

[tex]\\ = \frac{ - 8 \times 2}{5 \times 2} - \frac{1 \times 5}{2 \times 5} [/tex]

[tex] \\= \frac{ - 16}{10} - \frac{5}{10} [/tex]

Now that the denominators are equal, we can subtract the numerators.

[tex] \\= \frac{ - 16 - 5}{10} [/tex]

[tex] \\= \frac{ - 21}{10} [/tex]

[tex] \\= - 2 \frac{1}{10} [/tex]

[tex]\large\mathfrak{{\pmb{\underline{\orange{Mystique35 }}{\orange{♨}}}}}[/tex]

Answer:

-21/10

Step-by-step explanation:

-8/5. + -1/2

2(-8/5) + (-1/2)5

-16/10 - 5/10

-21/10

Evaluate using a suitable identity:  (997)³

991026973

Given:

(997)³

To solve this using an appropriate identity;

i. Rewrite by splitting the value in bracket (997) into a difference of two numbers. i.e

(997)³ = (1000 - 3)³

ii. Use the appropriate identity

Since the split from (i) above gave a cube of the difference of two numbers,  we can apply the following identity for finding the cube of the difference of two numbers;

(a - b)³ = a³ - b³ - 3ab(a - b)

In this case;

a = 1000

b = 3

(iii) Substitute the values of a and b into the identity equation and solve;

(1000 - 3)³ = 1000³ - 3³ - 3(1000)(3)(1000 - 3)

(1000 - 3)³ = 1000000000 - 27 - 9000(997)

(1000 - 3)³ = 1000000000 - 27 - 8973000

(1000 - 3)³ = 991026973

Therefore,

(997)³ = 991026973

Given:

Two rectangles are similar.

Length of first rectangle = 18 cm

Width of first rectangle = 6 cm

Width of second rectangle = 2 cm

To find:

The length of the second rectangle.

Solution:

We know that the corresponding sides of similar triangles are proportional. So,

[tex]\dfrac{\text{Length of first rectangle}}{\text{Width of first rectangle}}=\dfrac{\text{Length of second rectangle}}{\text{Width of second rectangle}}[/tex]

Let x be the length of the second rectangle. Then,

[tex]\dfrac{18}{6}=\dfrac{x}{2}[/tex]

[tex]3=\dfrac{x}{2}[/tex]

[tex]3\times 2=x[/tex]

[tex]6=x[/tex]

Therefore, the length of the second rectangle is 6 cm.

Answer:

3 hours

Step-by-step explanation:

Let Tamar did the job for x hours,

Since, her charges for 1 hour = $ 8,

⇒  Her charge for x hours = 8x,

Also, the bus fare = $ 6,

hence, her total charge = Bus fare + Her charges for x hours

= 6 + 8x,

If the total charge is at least $30,

⇒ 6 + 8x ≥ 30

⇒ 8x ≥ 24

⇒ x ≥ 3

Thus, the minimum number of hours for a babysitting job she would accept = 3 hours

Hope this helps and if it does, don't be afraid to give my answer a "Thanks" and maybe a Brainliest if it's correct?  

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Answer:

D

Step-by-step explanation:

We can start by taking a look at the x and y intercepts. When x=0, y=3. Plugging this into each function,

5 * 3^(0) = 5

3 * 5^(0) = 3

5 * (1/3)^(0) = 5

3 * (1/5) ^ (0) = 3

Therefore, our answer must be either B or D. Then, although y=0 isn't given on the graph, based on where the graph is heading, we can say that y is getting smaller as x gets larger. For a big number, such as 100, we know that

3 * 5^(100) is something big and 3 * (1/5) ^ (100) is something small*. Therefore, as y must get small, not big, as x gets larger, D is our answer.

* We know that this is something small because anything less than 1 to the power of something greater than 1 makes it smaller. For example, 0.5² is 0.25, which is smaller than 0.5

Answer:

If the shape of end face has n sides

Then, in total, there are n+2 faces

Using that formula

Faces in 20-sided polygon = n+2 = 20+2 = 22

Step-by-step explanation:

Pls vote as brainliest

Answer:

nine $5 bills and twenty-eight $10 bills

Step-by-step explanation:

f = # of five dollar bills

t = # of ten dollar bills

system of equations:

t + f = 37

10t + 5f = 325

solve the first equation for 't' to get:

t = 37-f

substitute '37-f' to 't' in second equation to get:

10(37-f) + 5f = 325

370 - 10f + 5f = 325

-5f = -45

f = 9

t + 9 = 37

t = 28

Answer: y=40

Step-by-step explanation: 70-30=40

Answer:

2

Step-by-step explanation:

When the point on the x-axis is on -3, the point on the y-axis is 2. Therefore, f(-3) is equal to 2.

If this helps please mark as brainliest

Answer:

8900000 * 10^-3

Step-by-step explanation:

(8.9*10^-3)/(10^-6)

(8.9*10^-3)/(1/1000000)

8.9*10^-3* 1000000

8900000 * 10^-3

Answer: 2^-3 = 1/8

2^-1 = 1/2

you have to multiply 2^-3 by 4 to get to 2^-1

Step-by-step explanation:

Answer:

PQ = 46

Step-by-step explanation:

The midsegment ST is half the length of the third side PQ , that is

ST = [tex]\frac{1}{2}[/tex] PQ , so

5x - 22 = [tex]\frac{1}{2}[/tex] (3x + 19) ← multiply both sides by 2 to clear the fraction

10x - 44 = 3x + 19 ( subtract 3x from both sides )

7x - 44 = 19 ( add 44 to both sides )

7x = 63 ( divide both sides by 7 )

x = 9

Then

PQ = 3x + 19 = 3(9) + 19 = 27 + 19 = 46

Answer:

Step-by-step explanation:

According to exponent rules, when we multiply two power with the same base we ADD the exponents.

[tex]c^{6}*c^{4} = c^{6+4} = c^{10}[/tex]

The transformations that could map ABC to A"B"C" are: (d) a dilation and a rotation

From the figure, we have the following highlights:

The above highlights mean that:

The transformations that could map ABC to A"B"C" are dilation and rotation

Hence, option (d) is true

Read more about transformations at:

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Answer:

x+2x+90 =180

3x =180

x =60

x=2y

2y=60

y=30

2y +z =180

z =180-60

. z =120

Answer:

39.52

Step-by-step explanation:

Answer:

Table multiplication:

7.6 times

5.2 =

15.2

38.0

—-

39.52

Answer:

The average rate of change in that interval is 1.99

Step-by-step explanation:

Here we have that the difference quotient for g(x) is:

[tex]\frac{6^{x + h} - 3 - 6^x + 3}{h}[/tex]

Remember that for a general function f(x), the difference quotient is:

[tex]\frac{f(x + h) - f(x)}{h}[/tex]

So if we look at the difference quotient for g(x), we can conclude that:

[tex]g(x) = 6^x - 3[/tex]

Also remember that the average rate of change in an interval (a, b) is just:

[tex]\frac{g(b) - g(a)}{b - a}[/tex]

So here we want the average rate of change of g(x) in the interval from x = -2 to x = 1, this is:

[tex]R = \frac{(6^1 - 3) - (6^{-2} - 3)}{1 - (-2)} = \frac{6 - 6^{-2}}{3} = 1.99[/tex]

The average rate of change in that interval is 1.99

Answer:

12

Step-by-step explanation:

Length of the radius of the circle is equals to 6units.

" Length of the arc is defined as the distance between two point as a part of the circumference of the given curve."

Formula used

Length of the arc = rθ

r = radius of the circle

θ = central angle

Radius = [tex]\frac{diameter}{2}[/tex]

According to the question,

Given,

Diameter = AB

Length of the arc = 6pi

Here central angle formed with diameter 'θ' = 180°

                                                                     = [tex]\pi[/tex]

Substitute the value in the length of the arc formula we get,

   [tex]6\pi = r \pi[/tex]

⇒ [tex]r = 6units[/tex]

Hence, length of the radius of the circle is equals to 6units.

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Answer:

angle IGH = 50 degree

Step-by-step explanation:

triangle GHI is an isosceles triangle because it's two sides are equal.

if angle I is 50 degree then angle G is also 50 degree becasue in isosceles triangle the base angles are equal.

Answer:

(f+g)(x) = 60x + 400

Step-by-step explanation:

Given :

Amount in account A:

f(x) = 20x + 100

Amount in account B :

g(x) = 40x + 300

Total amount in Account A and B:

f(x) + g(x) = (20x + 100) + (40x + 300)

(f+g)(x) = (20x + 40x) + (100 + 300)

(f+g)(x) = 60x + 400

Answer:

Top right

Step-by-step explanation:

First, we have "h is increasing on the interval (3, +∞)." This means that h must be increasing for all values 3 and higher. This is shown on the top left, top right, and bottom right graphs because when x goes up on each of them, the function increases as well. However, for the bottom left graph, this is not shown because as x goes from 3 to 4, the function decreases.

Next, the statement given is "h(4)=2". This means that when the x value is 4, the y value is equal to 2. This is true for the top left and top right pictures. However, for the bottom right, as the x value is 4 on the x axis, the corresponding y value is 1, not 2.

This leaves us with the top left and top right. The final characteristic given is "The domain of h is [3, +∞). This means that the x values of said function only go from 3 to infinity. As the top left graph has values of x below 3, this leaves the top right graph as h

Answer:

$5.50

Step-by-step explanation:

5+6= 11

11/2

Answer:

False

Step-by-step explanation:

If angle 2 and angle 5 are equal in length, then what we have is that the two lines are not parallel

For the two lines to be parallel, these two angles should be supplementary

what this mean is that these two angles should add up to give 180 degrees

Answer:

Cori could be 35 years old.

Livy could be 8 years old

Step-by-step explanation:

Given

[tex]C + L \ge 43[/tex]

[tex]C - 4L \ge 3[/tex]

Required

Possible values of C and L

Make C the subject in: [tex]C - 4L \ge 3[/tex]

[tex]C \ge 3 + 4L[/tex]

Substitute for C in [tex]C + L \ge 43[/tex]

[tex]3 + 4L + L \ge 43[/tex]

[tex]3 + 5L \ge 43[/tex]

Collect like terms

[tex]5L \ge 43-3[/tex]

[tex]5L \ge 40[/tex]

Solve for L

[tex]L \ge 8[/tex]

Solve for C

[tex]C \ge 3 + 4L[/tex]

[tex]C \ge 3 + 4 * 8[/tex]

[tex]C \ge 35[/tex]

Answer:

D

Step-by-step explanation:

higher amount then the rest

Respuesta:

Ingresos = 9500

Ingresos = 8573,75

Explicación paso a paso:

La ecuacion:

Yo = 10000 (0,95) ^ (0,2) p

p = monto gastado en publicidad

Los ingresos totales cuando no hay gastos:

p = 0

Yo = 10000 (0,95) ^ (0,2) * 0

Yo = 10000 (0,95) ^ 0

Yo = 10000 (0,95)

Yo = 9500

Si el gasto mensual de la promoción es de $ 15

p = $ 15

Yo = 10000 (0,95) ^ (0,2) * 15

Yo = 10000 (0,95) ^ 3

Yo = 10000 (0,857375)

Yo = 8573,75

Answer:

angle = 67°

Step-by-step explanation:

let

a = angle in degrees

(90-a) = complement

given

a = 2(90-a)+21

Solve for a

a = 180 - 2a + 21

3a = 201

a = 67°