If the polynomial x5 − 105 can be split as the product of the polynomials
x − 10 and a, what is a?

Answers

Answer 1

To answer this item, all that needs to be done is dividing the mathematical expression of x⁵ - 10⁵, our dividend, by x - 10, which is our divisor.

The mathematical expression that can be used in order to properly express the given scenario is,
x⁵ - 10⁵ = (x - 10)(a)

The value of a, as stated above, can be calculated by the equation,
a = (x⁵ -10⁵) / (x - 10)

There are two ways to solve the problem: synthetic division and the long way. Each of which will yield the same answer. Simplifying the value of a will give us a final answer of,
a = x⁴ + 10x³ + 100x² + 1000x

Answer 2

the value of a is

[tex]$ a = \frac{9845}{x - 10} $[/tex].

To find a, we can use polynomial long division or synthetic division to divide [tex]$ x^5 - 105 $[/tex] by [tex]$ x - 10 $[/tex]. The remainder should be zero if [tex]$ x - 10 $[/tex] is a factor of [tex]$ x^5 - 105 $[/tex].

Let's perform polynomial long division:

____________________________

x - 10 | x^5 + 0x^4 + 0x^3 + 0x^2 + 0x - 105

- (x^5 - 10x^4)

____________________________

10x^4 + 0x^3 + 0x^2 + 0x - 105

- (10x^4 - 100x^3)

____________________________

100x^3 + 0x^2 + 0x - 105

- (100x^3 - 1000x^2)

___________________________

1000x^2 + 0x - 105

- (1000x^2 - 10000x)

___________________________

995x - 105

- (995x - 9950)

___________________________

9845

```

Since the remainder is a constant term, it's clear that [tex]$ x - 10 $[/tex] is a factor of [tex]$ x^5 - 105 $[/tex]. So, [tex]$ a = \frac{9845}{x - 10} $[/tex].

Therefore, [tex]$ a = \frac{9845}{x - 10} $[/tex].

Related Questions

I NEED THIS QUICK

Alvin’s first step in solving the given system of equations is to multiply the first equation by 2 and the second equation by –3. Which linear combination of Alvin’s system of equations reveals the number of solutions to the system?
9x + 4y = 36
6x + 2.5y = 24

Answers

After multiplying by the given coefficients and adding, the new equation obtained is:
8y - 7.5y = 0

after doing the calculations the answer is:
y = 0
x = 4

Because the two equations formed were independent, they had one solution

Answer:

its C

Step-by-step explanation:

a telephone pole casts a shadow that is 34 m long. find the height of the telephone pole if a statue that is 36cm tall casts a shadow 77cm long

Answers

This is the concept of proportionality, the length of the pole will be given by:
[length of the post]/[length of the shadow]=[length of the statue]/[length of the shadow of statue]
thus;
suppose the length of the pole is x m
thus;
x/34=36/77
x=36/77*34
x=15.8 m
the answer is 15.9 m

if a number is tripled , it equals the product of four and the number diminished by two. find the number

Answers

so basically, translating it to algebra:

3x = 4(x-2)
3x = 4x - 8
flip the like terms to the other sides so they become similar;

8 = 4x -3x
8 = x

And the number is 8!

A perfect circle figure has four lines of symmetry. True or false?

Answers

True, because the lines can be drawn from all directions of the circle, therefore that must be at least 4 lines of symmetry

A person died leaving behind inheritance of Rs. 300000. Distribute the amount among 4 sons and 3 daughters so that each son gets double of what a daughter gets. Find the share of each when a debt of Rs. 80,000 was also to be paid.

Answers

s=2d

4s+3d=300000-80000

4s+3d=220000, now using s=2d in this equation you get:

4(2d)+3d=220000

8d+3d=220000

11d=220000

d=20000

So each daughter gets 20000 and each son gets 40000.

The inheritance problem deals with distributing Rs. 300,000 among 4 sons and 3 daughters after a Rs. 80,000 debt is paid. Using algebra and ratios, it is determined that each daughter receives Rs. 20,000 while each son receives Rs. 40,000.

The situation given is that a person dies leaving behind an inheritance of Rs. 300,000, which must be divided among 4 sons and 3 daughters such that each son receives double what each daughter gets. Additionally, a debt of Rs. 80,000 is to be taken out of the inheritance before distribution.

First, we need to consider the debt. Subtracting the debt from the total inheritance, we have:

Total inheritance after debt = Rs. 300,000 - Rs. 80,000 = Rs. 220,000

Now, let's assume each daughter gets x amount. Therefore, each son gets 2x the amount. We can set up the equation accounting for all sons and daughters:

3x (daughters' shares) + 4(2x) (sons' shares) = Rs. 220,000

Simplifying:

3x + 8x = Rs. 220,000

11x = Rs. 220,000

x = Rs. 20,000 (share of each daughter)

Consequently, the share of each son will be double that of a daughter, which is:

2x = 2(Rs. 20,000) = Rs. 40,000 (share of each son)

George plays basketball in a week-long camp. On Day 2, he scored 8 points. On day 4, he scored 12 points. Explain how to measure his average rate of change

Answers

you got the avg of two days((8+12)\2=10)so you can guess that its around 70 in a week.
avg rate of change is x+2=y

Two mechanics worked on a car. the first mechanic worked for 5 hours, and the second mechanic worked for 15 hours. together they charged a total of $1450 . what was the rate charged per hour by each mechanic if the sum of the two rates was $160 per hour

Answers

the first mechanic = a
the second mechanic = b

the first mechanic works for 4 hours = 4 * a
the second mechanic works for 15 hours = 15 * b
total charged = t

t = 4a + 15b

sum of their rates:
a + b = 160
b = 160 - a

t = 4a + 15b
1450 = 4a + 15 * (160 - a)
1450 = 4a + 2400 - 15a

now let's make the formula easier.

15a - 4a = 2400 - 1450
11a = 950

a = 86.36
b = 160 - 86.36 = 73.64

Find the equation of the quadratic function with zeros -1 and 1 and vertex at (0, -4).

Answers

since the vertex is at 0,-4 and the zeros are above it, we'll use a vertical parabola equation, namely with the dependent variable to be the "y".

bear in mind that, a zeor or solution of say -1 and 1, simply means x-intercepts at -1, 0 and 1,0.

[tex]\bf \qquad \textit{parabola vertex form}\\\\ \begin{array}{llll} \boxed{y=a(x-{{ h}})^2+{{ k}}}\\\\ x=a(y-{{ k}})^2+{{ h}} \end{array} \qquad\qquad vertex\ ({{ h}},{{ k}})\\\\ -------------------------------\\\\ vertex\ (0,-4)\ \begin{cases} h=0\\ k=-4 \end{cases}\implies y=a(x-0)^2-4\implies y=ax^2-4 \\\\\\ \textit{we also know that } \begin{cases} y=0\\ x=-1 \end{cases}\implies 0=a(-1-0)^2-4 \\\\\\ 0=a(-1)^2-4\implies \boxed{4=a}\qquad thus\implies \boxed{y=4x^2-4}[/tex]

Erica purchased adult and youth tickets for a movie. She bought x adult tickets for $7 each and y youth tickets for $5. Write an expression that can be used to show the total cost, C, of all tickets.

Answers

7x plus 5y equals C(cost)

Answer:

7x + 5y = C

Step-by-step explanation:

X is the number of people buying an adult ticket

Y is the number of people buying a youth ticket

Using this we can find C, cost

1. How many ways can you arrange the letters in the word MOMMY
A. 20
B. 25
C. 60
D. 120

2. A bag of marbles has 3 red, 2 blue and 5 white marbles in it. What is the probability of reaching in and selecting a white marble ?

Answers

1. [tex]\frac{5!}{3!} [/tex] which is further simplified to [tex]5*4[/tex] which is 20.

2. [tex] \frac{5}{5+3+2}= \frac{5}{10}= \frac{1}{2} [/tex]

HELP ASAP 30 POINTS

Evaluate f(3) for the piecewise function: f(x) = Which value represents f(3)?
–11
8
12.5
16

Answers

Answer:

-11

Step-by-step explanation:

A scale model of a human heart is 198 inches long. The scale is 34 to 1. How many inches long is the actual heart? Round your answer to the nearest whole number.

Answers

would be 198 / 34 = 5.82 = 6 inches to nearest whole number.

jill traveled to the ferry office and back. the trip there took 5 hours and the trip back took 4 hours. she averaged 65 mph on the return trip. find the average speed of the trip there

Answers

We know from physics class that the formula for distance of a linear motion is given as:

d = v t

Where,

d = distance travelled

v = average velocity

t = time it took to reach the destination

Since the distance going to the office and back is just similar, therefore we can simply equate the two:

v1 t1 = v2 t2

Where 1 signifies going to the office and 2 signifies going back from the office. Therefore this yields to:

v1 * 5 hours = 65 mph * 4 hours

v1 = 52 mph

Answer: The average speed going to the office is 52 mph.

The average speed of Jill's trip to the ferry office was 52 mph, calculated by dividing the distance of 260 miles by the time of 5 hours.

To find the average speed of the trip there, we need to know the distance Jill traveled to the ferry office. Since she averaged 65 mph on the return trip which took 4 hours, the distance is calculated as speed x time, which equals 260 miles (65 mph x 4 hours).

The distance to the ferry office is the same as the distance back, so Jill also traveled 260 miles on the trip there. Given that the trip there took 5 hours, we can find the average speed by dividing the distance by the time. The average speed is 260 miles / 5 hours, which equals 52 mph.

Find the value of each variable for the right triangles. Make sure all answers are in reduced radical form. Show your work.

Answers

By the Pythagorean theorem:

#1
[tex]t= \sqrt{13^2-12^2}= \sqrt{169-144}= \sqrt{25}=5 [/tex]

#2
[tex]a= \sqrt{12^2-9^2}= \sqrt{144-81}= \sqrt{63}= \sqrt{9*7}=3 \sqrt{7} [/tex]

#3
[tex]x= \sqrt{6^2+9^2}= \sqrt{36+81}= \sqrt{117}= \sqrt{9*13}=3 \sqrt{13} [/tex]

Answer:

i) t = 5

ii) a = 3√7

iii) x =3√13

Step-by-step explanation:

We have right triangles.

Know the two sides of the triangle and need to find the third missing side.

In order to find the third side of the right triangle, we use pythagoras theorem.

It is,

(Hypotenuse)² = (base)² + (height)²

13² = 12² + t²

169 = 144 + t²

t² = 25

t = 5.

ii)

12² = 9² + a²

144 = 81 + a²

144 - 81 = a²

a² = 63

a = √63

iii)

x² = 9² + 6²

x² = 81 + 36

x² = 117

x = √117

x = 3√13

A bag contains 20 candies: 3 cherry, 4 orange, 7 lemon, and 6 grape. if two candies are selected simultaneously, what is the probability that they are both the same flavor?

Answers

the answer is shown below

What is the product of any integer and –1?

Answers

Since negative 1 is negative, we multiply by 1 and make it negative. Therefore, if the integer is x, the product of that and negative 1 is -1*x=-x

Solve each system of equations by using elimination.

7)2t-u=17
3t+u=8

8)2j-k=3
3j+k==2

9)3c-2d=2
3c+4d=50

Answers

7. 5t= 25. 3(5)+u=8
t= 5. 15+u=8
u=-7

8. 5j= 5. 3(1)+ k= 2
j=1. k= -1

9. 6c - 4d= 4. 3(6)+4d= 50
3c +4d= 50. 18 + 4d= 50

9c = 54. 4d= 32
d= 8
c = 6

what is the sum of 27 and 5 times a number is 187

Answers

27+5x=187
5x=160
x=32
.

The value of a $225,000 house increases at a rate of 3.5% each year. Use a graph to predict the value of the house in 8 years.
A) ≈ $276,582
B) ≈ $286,263
C) ≈ $306,652
D) ≈ $296,282

Answers

The growth function is
V (t)=V0 (1+r)^t
V (t) ?
V0 225000
R 0.035
T 8 years

V (8)=225,000×(1+0.035)^(8)
V (8)=296,282

The value of the house in 8 years. (D) ≈ $296,282

How to predict the value?

The given parameters are:

Initial value, a = $225,000

Rate, r = 3.5%

The scenario is an illustration of an exponential growth function.

So, we have:

V(x) = a * (1 + r)^x

Substitute known values

V(x) = 225000 * (1 + 3.5%)^x

This gives

V(x) = 225000 * (1.035)^x

Next, we plot the graph of V(x)

See attachment

From the attached graph

V(x) = $296,282

Read more about exponential functions at:

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How many hours is from 9:00am to 6:00 pm?

Answers

9 am to 6 pm is a 9 hour difference. hope this helps

What is the length of the side opposite the 30° angle? HELP

Answers

the answer is B
√3 times as long as the side opposite the 30 degree so the side opposite the 30 degree angle is 5/√3 inches long.

Determine the slope of a line that makes an angle of 5pi/4 radians with the x-axis.

Answers

check the picture.

π radians is the angle 180 degrees, so π/4 radians is 180°/4=45°.

to construct the angle [tex]5 \frac{ \pi}{4} [/tex] we can proceed as shown in the figure, that is, we open an angle equal to 5 half right angles.

We see that the line making the angle 5pi/4 is the same line making the angle pi/4 radians, that is 45 degrees.

A line making the angle 45 degrees with the x axis, has slope equal to 1.

Remark, we have considered a line passing through the origin, as it represents all other lines making 5pi/4 radians.

Answer: slopi=1

Triangle END is translated using the rule (x, y) → (x − 4, y − 1) to create triangle E'N'D'. If a line segment is drawn from point E to point E' and from point N to point N', which statement would best describe the line segments drawn? (1 point

Answers

Here are the choices for this problem:
They are parallel and congruent.
They are perpendicular to each other.
They share the same midpoints.
They create diameters of concentric circles.

The transformation that is done is a translation. Which means that the coordinates will be translated or moved in the coordinate plane without changing the size and the orientation of the image. If is a line was drawn from E to E' and another line was drawn from N to N', the two lines would be parallel and congruent since the translation done to E is the same to that of N.

The answer is
They are parallel and congruent.

This answer is right!!!!! They are parallel and congruent.

Write the sum using summation notation, assuming the suggested pattern continues.

-1 + 2 + 5 + 8 + ... + 44

A) summation of negative three times n from n equals zero to fifteen
B) summation of the quantity negative one plus three n from n equals zero to fifteen
C)summation of negative three times n from n equals zero to infinity
D) summation of the quantity negative one plus three n from n equals zero to infinity

Answers

The answer is C. Summation of negative three times n from n equals zero to infinity

Find the value of x if B is between A and C, AB = 4x – 9, BC = 3x + 5 and AC = 17.

Answers

If A,B and C lie on the same line:

4x- 9 + 3x+5 = 17

7x = 21

x = 3

AB + BC = AC
4x - 9 + 3x + 5 = 17
7x - 4 = 17
add 4 to both sides
7x = 21
divide both sides by 7
x = 3

The area of a rectangle is 33 m2 , and the length of the rectangle is 5 m less than double the width. find the dimensions of the rectangle.

Answers

By definition, a rectangle is a quadrilateral (4-sided polygon) containing two sets of equal and parallel sides called the length and the width. For determining the area of a rectangle, you simply have to multiply length times width. In this problem, let L be the length and W be the width. Then, we formulate the two independent formulas: formula for area, and formula relating L and W

A = LW = 33
L = 2W-5

Substituting the second equation to the first,

A = 33 = (2W - 5)W
33 = 2W² - 5W
2W² - 5W -33 = 0
W = 5.5 and -3

Since the equation is quadratic, there are two possible roots: 5.5 and -3. However, we can only use the positive value. Thus, W=5.5 m. Consequently,

L = 2(5.5)-5
L = 6 m

Therefore, the dimensions of the rectangle is 6 m by 5.5 m.

The tip of a 15-inch wiper blade wipes a path that is 36 inches long. What is the angle of rotation of the blade in radians to the nearest tenth?
2.4 radians
1.2 radians
2.8 radians
0.4 radians

Answers

The length of the arc is a fraction of the circumference of the circle depending on the length of the radius and the intercepted angle. This can be calculated through the equation,

L = (2πr) x (θ /360)

where L is the length of arc, r is the radius, and θ is the intercepted angle in terms of degrees.

Substituting the known values to the equation,

36 = (2π)(15) x (θ / 360)

We translate the equation to find the value of θ,

θ = (36)(360) / 2π(15)

The value of θ is equal to 137.51°.

This can be coverted to radians through the equation below,

θ (in radians) = 137.51° x (2π rad / 360°) = 2.4 rad

What is the graph of the function f(x) = the quantity of x squared plus 3 x plus 5, all over x plus 2

Answers

Answer:

Your answer is in the picture below

The graph approaches x=−2 asymptotically, has no x-intercepts, and the y-intercept of the graph is the point (0, 5).

Attached graph.

The graph of the function f(x) = (x² + 3x + 5 )/(x+ 2) is a parabola that is shifted to the left by 2 units.

The parabola is similar to the graph of the function y = x², but it is narrower because the denominator of the fraction is x + 2.

The graph also has a hole at the point (-2, 5), which is the point where the denominator of the fraction is 0.

Attached graph.

Here are the steps on how to sketch the graph of the function:

Sketch the graph of the function y = x².

Shift the graph to the left by 2 units.

Add a hole at the point (-2, 5).

The attached figure shows the graph of the function f(x) = (x² + 3x + 5 )/(x+ 2):

The graph of the function has the following features,

The domain of the function is all real numbers except for -2.

The range of the function is all real numbers except for 5.

The function has a minimum point at (-4, 1).

The function has a hole at the point (-2, 5).

learn more about graph here

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PLEASE HELP!!!! If a function, f(x) is shifted to the left four units, what will the transformed function look like?

Answers

If you shift f(x) to the left four units, then the coordinate axis effectively moves four units to the right. This "four units to the right" movement for the axis means that every x is replaced with x+4.

So that means f(x) turns into f(x+4)

For example, say we had the function f(x) = 5x^2 + 10x
Shifting f(x) four units to the left leads to
f(x) = 5x^2 + 10x
f(x+4) = 5(x+4)^2 + 10(x+4) ... notice the replacements in bold
f(x+4) = 5(x^2+8x+16) + 10(x+4)
f(x+4) = 5x^2 + 40x + 80 + 10x + 40
f(x+4) = 5x^2 + 50x + 120

Find the greatest common factor for the group of numbers. 12 , 28 , 24

Answers

Final answer:

The greatest common factor (GCF) of the numbers 12, 28, and 24 is found by identifying the smallest powers of their common prime factors, which are 2 and 3. Multiplying these together, 2 squared times 3, gives us the GCF of 12.

Explanation:

To find the greatest common factor (GCF) of the numbers 12, 28, and 24, we break each number down into its prime factors:

28 = 2 x 2 x 7

The smallest power of 3 that is common is just 3.

Therefore, the GCF of 12, 28 and 24 is 22 x 3 = 4 x 3 = 12.

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If the polynomial x5 − 105 can be split as the product of the polynomials x − 10 and a, what is a?

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If the polynomial x5 − 105 can be split as the product of the polynomials
x − 10 and a, what is a?