If x + 1 is a factor of p(x) = x³ + k x² + x + 6, then by the remainder theorem, we have
p (-1) = (-1)³ + k (-1)² + (-1) + 6 = 0 → k = -4
So we have
p(x) = x³ - 4x² + x + 6
Dividing p(x) by x + 1 (using whatever method you prefer) gives
p(x) / (x + 1) = x² - 5x + 6
Synthetic division, for instance, might go like this:
-1 | 1 -4 1 6
... | -1 5 -6
----------------------------
... | 1 -5 6 0
Next, we have
x² - 5x + 6 = (x - 3) (x - 2)
so that, in addition to x = -1, the other two zeros of p(x) are x = 3 and x = 2
Hassan's soccer team is trying to raise $688 to travel to a tournament in Florida, so they decided to host a pancake breakfast. Each person must pay $43 for the breakfast. How many people need to attend their breakfast in order to raise $688?
Answer:
5 people
Step-by-step explanation:
True False x-sqrt6 is a factor of x^4-36
-3[7+ 5)
What is the value of
Answer:
-36
Step-by-step explanation:
Step-by-step-explanation
The first thing you would do is multiply both numbers inside the parenthesis by -3.
You would get -21 + (-15) or you could just wrtie -21 - 15, whichever is easier for you.
Then you'd simply add both -21 and -15 together, and you get -36. :D
A race car driver completes 5 laps in 3 minutes and 30 seconds. Then the driver continues driving at this rate. How many laps will the driver complete in 17.5 minutes.
Part A: What is the ratios of laps to minutes? Explain.
Answer:
The driver will complete 12.25 laps.
Step-by-step explanation:
Each lap takes 42 seconds. ( 210÷5=42)
42×17.5=735
735÷60=12.25
Please help :( I need your help. If you help you get points. If you get points your smart. So please help.
Answer:
6.3333
Step-by-step explanation:
Answer:
6.3333
Step-by-step explanation:
Mason gave the waiter a $14.58 tip, which was 15 percent of the dinner bill. What was the amount of the dinner bill before he added the tip? $9.72 $21.87 $97.20 $218.70
Answer:
C. You take the tip amount devided by 15%. Thats 0.15. You the get the answer 97.20
Step-by-step explanation:
Answer:
C/ $97.20
Step-by-step explanation:
i did the quiz
Find the slope and y-intercept from the following graph of a linear equation.
Answer:
A
Step-by-step explanation:
The equation of line is y= -4x -23
What is slope- intercept form?A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively.
The slope of the line is the ratio of the rise to the run, or the rise divided by the run, therefore the change in y coordinate with regard to the change in x coordinate may be expressed as follows. In the coordinate plane, it describes the slope of the line.
Given:
We can take the coordinates from the given graph as (0, 3) and (2, -5)
Now, the slope = (-5 - 3)/ (2 - 0)
slope= -8/ 2
slope= -4
Now, using the point- slope form
(y - [tex]y_1[/tex]) = m(x - [tex]x_1[/tex])
(y- (-3))= -4( x- (-5))
y+3 = -4(x+5)
y+ 3= -4x - 20
y= -4x -23
Hence, the equation of line is y= -4x -23.
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Helpppppp??????? ???????
Answer:
rectangle
Step-by-step explanation:
a kite and a rhombus both have acute angles
Coach Matta ran 3 laps in 180 seconds. Which of the following is an equivalent rate of running?
2 laps in 130 seconds
5 laps in 215 seconds
1 lap in 60 seconds
6 laps in 130 seconds
Answer:
1 lap in 60 seconds
Step-by-step explanation:
This is the answer because:
1) Think of it as ratios or fractions
Ratio: 3:180
2) Next, we have to find something equivalent. Since 3 can only be multiplied by one or itself, we have to dived 3 by 3.
3) 3 divided by 3 is 1
2) 180 divided by 3 is 60
4) This equals to 1:60
Therefore, the answer is 1 lap in 60 seconds
Hope this helps!
There are 2.54 centimeters per inch. If a pencil is 4.5 inches long, what is its length in centimeters?
Please explain
Answer:
11.025
Step-by-step explanation:
you have to add 2.45, 4.5 times. Or you can just multiply 2.45 by 4.5.
Hope this helps you ;}
A poll agency reports that 45% of teenagers aged 12-17 own smartphones. A random sample of 152 teenagers is drawn. Round your answers to four decimal places as needed. Part 1 out of 6 Find the mean The mean il ESSENEN IN
Answer:
Mean = 0.45
Standard deviation = 0.04035
Step-by-step explanation:
This is actually a very simple problem.
The question gives us the report that 45% of the teenagers in the age bracket own smartphones.
P = mean = 45%
Therefore the mean is 0.45.
I will go ahead to help you calculate the standard deviation.
√p(1-p)/n
n = 152
P = 0.45
√0.45(1-0.45)/152
= √0.45(0.55)/152
= √0.2475/152
= √ 0.001628
= 0.04035
who want crown things
Answer:
meeee plzzzzzzz even thow i have no idea whta that ios
Step-by-step explanation:
Laura participated in a gymnastics competition. She got scores of 7.88, 9.42,
7.49 and 8.64. What is her total score?
Danielle needs to pay $50.00 to attend her college's semi-formal. When she works in the dining hall, she makes $20.00 per day plus $6.00 for every additional hour she works. If she wants to earn at least $50.00 by Friday, she thinks that she only needs to work 3 additional hours but her friend Jurrae thinks that she needs to work 5. Explain if you agree with Jurrae and Danielle. Use details to support your answer.
Answer:Her friend is right Danielle needs to work for 5 hours
Step-by-step explanation:
hope this help
help :((
Provide a small explanation if possible!!
Answer:
r = 24
Step-by-step explanation:
Just reverse everything,
3 x 16 = 48,
48 ÷ 2 = 24,
to double-check,
if you plug in 24 for r then you have,
2(24)/3 = 16
48/3 = 16
16 = 16
Write the equation of a line that is parallel to x = -7 and
passes through (-1,8)
Answer:
y=-7x+1
Step-by-step explanation:
Evaluate the function for x = 2,3,4
F(x) =2x-7-3
Answer:
below in bold
Step-by-step explanation:
f(x) = 2x - 7 - 3
~Combine like terms
f(x) = 2x - 10
When x = 2...
f(x) = 2(2) - 10
f(x) = 4 - 10
f(x) = -6
When x = 3...
f(x) = 2(3) - 10
f(x) = 6 - 10
f(x) = -4
When x = 4...
f(x) = 2(4) - 10
f(x) = 8 - 10
f(x) = -2
Best of Luck!
FOR 20 POINTS! GIVE REAL ANSWERS PLEASE. THANKS!
Davon's solution to the equation -2(x - 5) + 3 = -4 is shown below.
-2(x - 5) + 3 = -4
Step 1 -2x - 5 + 3= -4
Step 2 -2x - 2 = -4
Step 3 -2x = -2
Step 4 x = -1
In which step did the first mistake occur?
Step 1
Step 4
Step 2
Step 3
Answer:
8.5
Step-by-step explanation:
-2(x-5)+3=-4
Step 1 distribute
−2+10+3=−4
Step 2 add the numbers
-2x+13=-4
Step 3 subtract 13 from both sides of the equation
−2-13+13=-4-13
Step 4 get ride of the two 13
-2x=-4-13
Step 5 subtract -4 subtract 13
-2x=-17
Step 6 divide -17 by -2
-2x/-17
Step 6 answer
8.5
Which graph represents -5x+4y > -1
Answer:
Were is the graph
Step-by-step explanation:
show me the graph
john sort his 200 buttons into 4 groups.Each group has the same numbers of buttons .He gives the buttons in one group to Markie.Which equation can be used to find n,the number of buttons that john has now.n÷4=200. or 200-50=n or 200÷4=n or n-50=200
Answer:
200-50+n
Step-by-step explanation:
Suppose that a random sample of size 64 is to be selected from a population with mean 40 and standard deviation 5. (a) What is the mean of the xbar sampling distribution
Answer:
Sample mean (xbar) = 40
Step-by-step explanation:
Given that :
Sample size (n) = 64
Population mean (μ) = 40
Standard deviation (σ) = 5
The sample mean is equal to the population mean according to the central limit theorem.
The sample standard deviation = standard error = ;
Standard Error = σ / √n
Standard Error = 5 / √64
Standard Error = 5 / 8
Standard Error = 0.625
Find the value of X, I need help solving this
Answer:
16
Step-by-step explanation:
180-97 =83 5x16=80
=3 soooo yeah
Answer:
97+5x+3=180
5x=180-100
5x=80
x=80/5
x=16
:ans is 16
Which ordered pair is a solution to the system of inequalities?
y > 3x
y <2 +5
The ordered pair which is the solution of the given inequalities is (A) (1,5).
What are inequalities?An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made. A difference between two values indicates whether one is smaller, larger, or simply not equal to the other. If a and b are equal, then an is greater than b.So, to find the correct values we need to use the hit-and-trial method:
Then, taking (1, 5):
y > 3x5 > 3(1)5 > 3 (Satisfied)Similarly,
5 ≤ x + 55 ≤ 1 + 55 ≤ 6 (Satisfied)So, option (A) (1, 5) is correct.
Therefore, the ordered pair which is the solution of the given inequalities is (A) (1, 5).
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A package of 3 pairs of gloves costs $16.17. What is the unit price per pair of gloves. PLS HELP ASAP
THERE ARE 40 PUPILS IN MRS. SANTOS GRADE 5 CLASS.1/4 OF THE CLASS ARE ABSENT,HOW MANY PUPILS ARE PRESENT?
Answer:
30 kids are present
Step-by-step explanation:
Hey there champ! Basically you wanna divide 40 by 4, or the fraction 1/4 to get the number of kids absent which is 10. From here you subtract 10 from your og class size, 40 and get thirty! Have a great day :)
i need help with math please to solve the problem and explain asap thank you so much...
Answer:
99
Step-by-step explanation:
1, 3, 5,... 50th?
arithmetic sequence:
d=3-1=2, a1= 1, n= 50
an= a1 + d (n-1)
an= 1 + 2 (n-1)
a50= 1 + 2 (50-1)
a50= 99
PLEASEE HELPPPP PLEASEE thiss IS FOR MY FRIEND I BEGG YOUUU PLEASEEE
Answer:
Step-by-step explanation:
Why are you asking? Why isn't your friend?
The diagram assumes that the angle on the lower left of the triangle is a right angle. If it is not, then I don't think there is a way that this can be solved.
Tan(A) = opposite / adjacent
opposite = 7
Adjacent = 4
Tan(A) = 7/4 = 1.75
A = inverseTan (1.75)
A = 60.60 degrees
Valerie had $1.87 in her bank at home. She adds $2.67 in change how much does she have now?
Answer: $4.54
1.87+2.67=4.54
I hope this is good enough:
The art teacher has 48 boxes of crayons.
There are 64 crayons in each box. Which
is the best estimate of the number of
crayons the art teacher has?
Answer:
3072 Crayons
Step-by-step explanation:
Crayons = C
48C * 64C = 3072C
3072C = 3072 Crayons
In triangle RST, m∠T is 5° more than m∠R, and m∠S is 10° less than m∠T. What is the measure of each angle?
Answer:
R=60
S=55
T=65
Step-by-step explanation:
[tex]\boldsymbol{m\angle R, m\angle S, m\angle T}[/tex] are equal to [tex]\boldsymbol{60^{\circ},55^{\circ},65^{\circ}}[/tex] respectively.
According to angle sum property of a triangle, sum of all angles of a triangle is equal to [tex]\boldsymbol{180^{\circ}}[/tex]
Let [tex]m\angle R=x[/tex]
As [tex]m\angle T[/tex] is [tex]5^{\circ}[/tex] more than [tex]m\angle R[/tex],
[tex]m\angle T=5^{\circ}+m\angle R[/tex]
[tex]\boldsymbol{m\angle R=m\angle T-5^{\circ}}[/tex]
Also,
[tex]m\angle S[/tex] is [tex]10^{\circ}[/tex] less than [tex]m\angle T[/tex],
[tex]\boldsymbol{m\angle S=m\angle T-10^{\circ}}[/tex]
So,
[tex]\boldsymbol{m\angle R+m\angle S+m\angle T=180^{\circ}}[/tex]
[tex]m\angle T-5^{\circ}+m\angle T-10^{\circ}+m\angle T=180^{\circ}[/tex]
[tex]3m\angle T-5^{\circ}-10^{\circ}=180^{\circ}[/tex]
[tex]m\angle T=\frac{195^{\circ}}{3}[/tex]
[tex]\boldsymbol{=65^{\circ}}[/tex]
[tex]m\angle R=65^{\circ}-5^{\circ}[/tex]
[tex]\boldsymbol{=60^{\circ}}[/tex]
[tex]m\angle S=65^{\circ}-10^{\circ}[/tex]
[tex]\boldsymbol{=55^{\circ}}[/tex]
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