The root x = 1 has multiplicity 3 for the function f(x) = x³ - x² - x + 1.
Explanation:The statement is true.
A root of a polynomial function has a multiplicity equal to the number of times it appears as a factor in the polynomial. In this case, the root x = 1 appears three times as a factor in the function f(x) = x³ - x² - x + 1. Therefore, it has a multiplicity of 3.
Please i really need help on this one please!!!! :( I need an answer ASAP
Multiply r^2 + 7r + 10 / 3 by 3r - 30 / r^2 - 5r - 50
A. r + 2
B. 7r^2 - 20r - 300 / -5r - 5
C. (r + 5)( r + 2) / (r + 10)
D. 3r + 6 / 2
By factoring and simplifying the given polynomials, we found that the expressions simplify to r + 2. Therefore, the correct answer is option A. This process involves cancelling out common factors from the numerator and the denominator.
Polynomial Multiplication and Simplification
To solve the problem, we need to multiply the given rational expressions and simplify the result. The expressions are:
(r^2 + 7r + 10) / 3 and (3r - 30) / (r^2 - 5r - 50)
First, let's factor the polynomials where possible:
Factor the numerator of the first expression:[tex]r^2 + 7r + 10 = (r + 2)(r + 5)[/tex]Factor the denominator of the second expression: [tex]r^2 - 5r - 50 = (r - 10)(r + 5)[/tex]Now, the problem can be written as:
([tex](r + 2)(r + 5) / 3 ) * ( 3(r - 10) / (r - 10)(r + 5) )[/tex]
Next, we simplify by canceling out the common factors:
[tex]=( (r + 2)(r + 5) / 3 ) * ( 3(r - 10) / (r - 10)(r + 5) )[/tex]
The (r + 5) terms and the (r - 10) terms can be canceled:
[tex]= (r + 2) / 1[/tex]
So, the simplified answer is r + 2,
The correct option is A. r+2
Tammy takes a job after school to earn money to buy a violin. she knows that the more hours she works, the more money she will make.
a. the number of hours tammy works is a function of the amount of money she makes.
b. the amount of money tammy makes is a function of the number of hours she works.
c. tammy's job is a function of her interest in music.
Suppose you have 52 feet of fencing to enclose a rectangular dog pen. The function A = 26x = x2 where x = width, gives you the area of the dog pen in square feet. what width gives you the maximum area? what is the maximum area? round to the nearest tenth if necessary.
maximum area is a square
the side of the square would be 52/4 = 13 feet
area = 13*13 = 169 square feet
Answer:
Width = 13 ft
Maximum Area = 169 ft²
Step-by-step explanation:
Given: A rectangular dog pen whose fencing is 52 feet.
Let length be y and width be x
Fencing = 2(l+b)
52 = 2 (x+y)
x + y = 26
y = 26 - x
Area of rectangular pen = Length x width
= y . x
[tex]A=x(26-x)[/tex]
[tex]A=26x-x^2[/tex]
It is parabolic equation. Maximum/Minimum at vertex.
[tex]x=-\dfrac{b}{2a}[/tex]
where, a=-1, b=26
[tex]x=\dfrac{26}{2}=13[/tex]
Now we put x=13 into A
[tex]A=13(26-13)[/tex]
[tex]A=169[/tex]
Hence, The width is 13 feet and Maximum area is 169 ft²
What shape has 6 sides?
Question 10 options:
pentagon
hexagon
decagon
octagon
Save
A B) hexagon is the shape with 6 sides.
A hexagon is a polygon with six straight sides and six angles. In geometry, hexagons are commonly used in various designs and structures due to their symmetry and stability.
Regular polygon refers to a polygon with equal sides and equal angles, such as a hexagon. Hexagons have the property of being equilateral and equiangular, making them regular polygons.
Six Electron Groups form an octahedron, which is a polyhedron made up of identical equilateral triangles and has six identical vertices, showcasing the connection between the number six and geometric shapes.
Therefore, option B is correct.
Rachelle can walk 2.5 miles in 40 minutes. At this rate, how far can she walk in 1 hour?
The distance travel Rachelle in 1 hour (60 minutes) will be 3.75 miles.
What is speed?The distance covered by the particle or the body in an hour is called speed. It is a scalar quantity. It is the ratio of distance to time.
We know that the speed formula
Speed = Distance/Time
Rachelle can walk 2.5 miles in 40 minutes.
Then the speed will be
Speed = 2.5 / 40
Speed = 0.0625 miles per minute
At this rate, distance travel Rachelle in 1 hour (60 minutes) will be
0.0625 = d / 60
d = 3.75 miles
The distance travel Rachelle in 1 hour (60 minutes) will be 3.75 miles.
More about the speed link is given below.
https://brainly.com/question/7359669
#SPJ5
Susan can run 2 city blocks per minute. she wants to run 60 blocks. how long will it take get to finish if she has already run 18 blocks?
Please help with 3 questions thank you.
1. an angle congruent to a given angle
2. x = 68, y = 75
3. corresponding angles
Angles A and B are complementary. If m/ A= 3x - 8 and m/ B = 5x + 10, whqt is the measure of each angle ? Show your work and explain the steps
1. The measure of angle A is [tex]\(22^\circ\).[/tex]
2. The measure of angle B is[tex]\(68^\circ\).[/tex]
Explanation:To find the measures of angles A and B, we can use the fact that they are complementary, meaning their measures add up to[tex]\(90^\circ\).[/tex]Let's set up an equation using the given information:
[m_A + m_B = 90]
Given that[tex]\(m_A = 3x - 8\)[/tex]and (m_B = 5x + 10), substitute these expressions into the equation:
3x - 8 + 5x + 10 = 9
Combine like terms:
8x + 2 = 90
Subtract 2 from both sides:
8x = 88
Divide by 8:
x = 11
Now that we know the value of (x), we can find the measures of angles A and B:
[tex]\[m_A = 3x - 8 = 3(11) - 8 = 33 - 8 = 25\][/tex]
[tex]\[m_B = 5x + 10 = 5(11) + 10 = 55 + 10 = 65\][/tex]
Therefore, the measure of angle A is \(25^\circ\) and the measure of angle B is [tex]\(65^\circ\).[/tex] To check, we can verify that these angles are indeed complementary:
25 + 65 = 90
So, angles A and B satisfy the condition of being complementary.
While traveling along a highway a driver slows from 24 m/s to 15 m/s in 12 seconds. What is the automobile’s acceleration? (Remember that a negative value indicates slowing down or deceleration)
We are given that:
vi, initial velocity = 24 m/s
v, final velocity = 15 m/s
t, time = 12 s
The formula for acceleration is:
a = (v – vi) / t
a = (15 – 24) / 12
a = - 0.75 m/s^2 (deceleration)
Determine if the lines are parallel, perpendicular, or neither x-3y= 15 and y = -3+4
Answer:
Step-by-step explanation:
Liam is setting up folding chairs for a meeting. If he arranges the chairs in 4 rows of the same length, he has 5 chairs left over. If he arranges the chairs in 2 rows of that same length, he has 17 left over. How many chairs does Liam have?
If Tara spends $219 a month for her car payment and she makes $3200 a month what percent of her monthly income is spent on her car payment
cosx - 4 = sinx -4
(0,2pi)
Find solutions
what is 2.6 repeating as a fraction
cuharra studied Monday and Tuesday for her math test she spent a total of 120 minutes studying. she spend an extra 15 minutes on Tuesday. how long did she study for on Monday and on tuesday
Cuharra studied for 52.5 minutes on Monday and 67.5 minutes on Tuesday.
Explanation:To find out how long Cuharra studied on Monday and Tuesday, we can set up an equation. Let's say C represents the amount of time she studied on Monday. According to the information given, on Tuesday she spent an extra 15 minutes studying, which means she studied for C + 15 minutes. The total time she studied was 120 minutes. So, we can write the equation as C + (C + 15) = 120.
Now, we can solve this equation to find the values of C and C + 15. Combining like terms, we get 2C + 15 = 120. Subtracting 15 from both sides, we get 2C = 105. Divide both sides by 2, and we get C = 52.5.
Therefore, she studied for 52.5 minutes on Monday and 52.5 + 15 = 67.5 minutes on Tuesday.
Final answer:
Cuharra studied for 52.5 minutes on Monday and 67.5 minutes on Tuesday to make a total of 120 minutes of study time over the two days.
Explanation:
The question involves solving for the number of minutes cuharra studied on Monday and Tuesday. Since the total study time for both days is 120 minutes and she studied 15 minutes extra on Tuesday, we can set up two variables to represent the study times on each day. Let x be the number of minutes studied on Monday, then x + 15 will be the number of minutes studied on Tuesday.
To solve for x, we set up the equation x + (x + 15) = 120. Simplifying, we get 2x + 15 = 120. Subtracting 15 from both sides gives us 2x = 105. Dividing both sides by 2, we find that x = 52.5. Therefore, cuharra studied for 52.5 minutes on Monday and 52.5 + 15 = 67.5 minutes on Tuesday.
The local park has 4 bike racks. Each bike rack can hold 15 bikes. There are 16Bikes in the bike rack’s. What expression shows the total number of empty spaces in the bike racks
"The correct expression to show the total number of empty spaces in the bike racks is [tex]\( 4 \times 15 - 16 \).[/tex]
To arrive at this expression, we start by calculating the total capacity of all the bike racks combined. Since there are 4 bike racks and each can hold 15 bikes, the total capacity is [tex]\( 4 \times 15 \).[/tex] This gives us the maximum number of bikes that can be parked in all the racks.
Next, we subtract the number of bikes that are currently parked in the racks from the total capacity. There are 16 bikes parked. Therefore, the expression to find the number of empty spaces is:
[tex]\[ \text{Total capacity} - \text{Number of bikes parked} \][/tex]
Substituting the given numbers into the expression, we get:
[tex]\[ 4 \times 15 - 16 \][/tex]
This expression represents the total number of empty spaces in the bike racks. When evaluated, it will give us the number of spaces available for additional bikes to be parked."
HELP ME PLEASE
Olga deposited $1500 in a savings account that pays 7.5% interest compounded quarterly. What is the balance in her account at the beginning of the third quarter?
A. $1,590
B. $1,560
C. $1,585.97
D. $1,591.81
ok let me make one thing clear: i have put up questions like this before but i am NOT TRYING TO JUST GET ANSWERS. I legit want to learn this. It is just hard for me i guess.. so sorry if this answer seems simple to you but its not to me so if you could please explain your answer CLEARLY, in particular with "compound quarterly." please explain so i can use the principles later on. Thank you!
Write the following linear equation in standard for: 2y = -8x - 18 ??
A.y = -4x - 9
B.8x + 2y = -18
C.2y + 18 = -8x
D.18 + 8x = -2y
\sqrt{6} + 3 \sqrt{6}
To convert 3.4 hours into seconds which two ratios could you multiply by
find gh if g(5,-1) and h(1,-3). write your answer in simplest radical form.
Please Help! Will give BRAINLIEST! I don't know how to do this.
Determine the x- and y-intercepts of the graph of y=−1/3x+3 .
Then plot the intercepts to graph the equation.
Answer:
you would graph (0,3) and (9,0)
Step-by-step explanation:
Consider the provided equation.
The x intercepts are the points where y value is zero. Similarly the y intercepts are the points where x values is zero.
In order to find the x intercept substitute y = 0 in the provided equation.
0=-1/3x + 3
-3=-1/3(x)
-9=-x
9=x
Thus, the x intercept is (9,0)
In order to find the y intercept substitute x = 0 in the provided equation.
y=-1/3(0) + 3
y=3
Thus, the y intercept is (0,3)
Now use the x and y intercepts to draw the graph of the equation.
The required graph is shown in figure 1.
Therefore, the x- and y- intercepts is (9,0) and (0,3)
Find h(-1), h(0), and h(4) for the given function h(x)=-2x^2-4
A music competition on television had five elimination rounds. After each elimination, only half of the contestants were sent to the next round. The table below shows the number of contestants in each round of the competition:
x
1
2
3
4
5
f(x)
64
32
16
8
4
Compute the average rate of change of f(x) from x = 3 to x = 5 and describe what it represents
A. −6 contestants per round, and it represents the number of contestants who will reach the final round
B. −28 contestants per round, and it represents the number of contestants who will reach the final round
C. −6 contestants per round, and it represents the average rate at which the number of contestants decreased from the third round to the fifth round
D. −28 contestants per round, and it represents the average rate at which the number of contestants decreased from the third round to the fifth round
Answer:
The correct option is C.
Step-by-step explanation:
The given table represent the number of contestants in each round of the competition.
The average rate of change of f(x) from x = 3 to x = 5.
[tex]m=\frac{f(x_2)-f(x_1)}{x_2-x_1}[/tex]
[tex]m=\frac{f(5)-f(3)}{5-3}[/tex]
[tex]m=\frac{4-16}{2}[/tex]
[tex]m=\frac{-12}{2}[/tex]
[tex]m=-6[/tex]
The average rate of change of f(x) from x = 3 to x = 5 is -6, it represents the average rate at which the number of contestants decreased from the third round to the fifth round.
Therefore option C is correct.
What is the smallest integer that is the sum of three different primes, each of which is greater than 10?
How many ways are there to distribute six different toys to three different children such that each child gets at least one toy?
A swimming pool can be filled by either or both of two pipes of different diameters. it takes the smaller pipe twice the time that the larger pipe takes to fill the pool. if water flows through both pipes it take 213 hours to fill the pool. how long will it take the larger pipe to fill the pool? [hint: let x be the amount of the pool filled by the small pipe in one hour]
Step-by-step explanation:
Let r₁ be the rate of filling of small pipe, r₂ be the rate of filling of large pipe and V be the volume of swimming pool.
[tex]\texttt{Rate of small pipe},r_1=\frac{V}{t_1}\\\\\texttt{Rate of large pipe},r_2=\frac{V}{t_2}=\frac{V}{0.5t_1}=2r_1[/tex]
If both pipes are combined it takes 213 hours, that is
[tex]t=\frac{V}{r_1+r_2}\\\\213=\frac{V}{r_1+2r_1}\\\\V=639r_1[/tex]
Now we need to find how much time it takes to fill the pool by large pipe,
That is
[tex]t_2=\frac{V}{r_2}=\frac{639r_1}{2r_1}=319.5hours[/tex]
By large pipe only it will take 319.5 hours to fill the pool.
how do you do number 10?
Calculate population variance from population standard deviation
If u lies on the same line as r and n, what terms describe the relationship the three points must have? (select all that apply.) noncollinear between the points collinear coplanar
Answer:
Collinear, coplanar, and between the points
Step-by-step explanation:
Collinear means that the points are in the same line.
Coplanar means that the points are in the same plane.
Between the points is used when three points are in the same line an you want tro express that one of them is between the others.
So those three relationships can apply for the three points.
noncollinear not apply because it means that the points don't lie in a line.