===========================================================
Explanation:
We'll use the remainder theorem.
This theorem says that if you divide p(x) over (x-k), then the remainder is p(k).
We have p(x) = x^3 + 3x^2 - 16x - 48 and the denominator is one of the four choices A through D.
Let's go through each of them until we find the answer.
-----------------
For choice A, we have x+2 which is the same as x-(-2). It matches with x-k to show that k = -2.
Plug k = -2 into p(x) to get
p(x) = x^3 + 3x^2 - 16x - 48
p(-2) = (-2)^3 + 3(-2)^2 - 16(-2) - 48
p(-2) = -12
The remainder is -12, which is not 0 like we're after. We can cross A off the list.
-----------------
We'll follow the same ideas for choices B through D
For choice B, we plug in k = 4 because x-4 matches with x-k to show that k = 4.
p(x) = x^3 + 3x^2 - 16x - 48
p(4) = (4)^3 + 3(4)^2 - 16(4) - 48
p(4) = 0
We end up with a remainder of 0, so we can stop here. Dividing (x^3+3x^2-16x-48) all over (x-4) leads to some quotient and a remainder of 0.
Put another way: (x-4) is a factor of x^3+3x^2-16x-48
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Side notes:
x^3+3x^2-16x-48 factors to (x-4)(x+4)(x+3)If you try out choice C, the remainder is -42The remainder for choice D is -240 (you'll use k = -8).What do you think the answer is
Norman purchases five pounds of apples for $10. What is the price per pound?
Answer:
2 dollars per pound
Step-by-step explanation:
10/5=2
Answer:
2 Dollars per pound
Step-by-step explanation:
you can divide $10 by how many bags of apples you bought to get 2 dollars per pound
18 m 13m 13 m find the surface area
Answer:
3510 m² I guess..........
Find the value of x. 2x - 5 > 7 *
Answer:
[tex]x>6[/tex]
Step-by-step explanation:
Answer:
x > 6
Step-by-step explanation:
Find the volume of the cylinder.
Round to the nearest tenth.
r = 5 cm
5 cm
V = [?] cm3
Enter the number that goes in the green box.
Enter
Answer:
392.7
Step-by-step explanation:
The volume of the cylinder of radius 5 cm and a height of 5 cm will be equal to 392.7 cubics cm
What is the volume of a cylinder?The volume of the cylinder is the product of the height, pie, and square of the radius.
The volume of the cylinder = [tex]\pi r^{2} h[/tex]
It is given that the radius of the cylinder is 5 cm and the height of the cylinder is 5 cm also.
So, The volume of the cylinder = [tex]\pi r^{2} h[/tex]
= 3.14 x 5^2 x 5
= 3.14 x 125
= 392.7 cubics cm
Thus, The volume of the cylinder of radius 5 cm and a height of 5 cm will be equal to 392.7 cubics cm.
Learn more about volume;
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plzzzzzzzz help for a brainly
Answer:
246
Step-by-step explanation:
PLEASE HELP MATH QUESTION 99 POINTS ASAP
Function A and Function B are linear functions. Compare the two functions and choose all that are correct.
Answer:
2 .The slope of Function A is less than the slope of Function B
A graph of Function A shows it has a y-intercept of 4, the same as that of Function B. (Statements 3 and 4 are not correct.)
The slope of Function A is 2, which is less than the slope of 3 that Function B has. (Statement 2 is correct; statement 1 is not.)
_____
More detailed working
The slope of Function A can be figured easily between the points with x-values that differ by 1:
m = (y3 -y2)/(x3 -x2) = (24-22)/(10-9) = 2/1 = 2 . . . . . Fun A has slope of 2.
The slope of Function B is the coefficient of x in the equation: 3.
__
The y-intercept of Function A can be found starting with point-slope form:
y -22 = 2(x -9)
y = 2x -18 +22
y = 2x +4 . . . . . . . slope-intercept form
The intercept of +4 is the same as that of Function B.
Step-by-step explanation:
mrk me brainliest plz
Answer:
2 .The slope of Function A is less than the slope of Function B
A graph of Function A shows it has a y-intercept of 4, the same as that of Function B. (Statements 3 and 4 are not correct.)
The slope of Function A is 2, which is less than the slope of 3 that Function B has. (Statement 2 is correct; statement 1 is not.)
_____
More detailed working
The slope of Function A can be figured easily between the points with x-values that differ by 1:
m = (y3 -y2)/(x3 -x2) = (24-22)/(10-9) = 2/1 = 2 . . . . . Fun A has slope of 2.
The slope of Function B is the coefficient of x in the equation: 3.
__
The y-intercept of Function A can be found starting with point-slope form:
y -22 = 2(x -9)
y = 2x -18 +22
y = 2x +4 . . . . . . . slope-intercept form
The intercept of +4 is the same as that of Function B.
Step-by-step explanation:
MARK ME BRAINLEIST PLZ PLZ PLZ
a loaf of bread has 12 slice. micky ate 1/4 of the loaf. write the fraction of the loaf micky ate in twelfths
Answer:
3/12
Step-by-step explanation:
1/4*3/3=3/12
b) The university gym opens at 9 am on Saturday mornings. One Saturday morning at 8:55 am there are 15 students outside the gym waiting for it to open. Should you use the same approach from part (a) to calculate the expected number of smokers among these 15 students
Answer:
The complete question is:
At a university, 13% of students smoke.
a) Calculate the expected number of smokers in a random sample of 100 students from this university:
b) The university gym opens at 9 am on Saturday mornings. One Saturday morning at 8:55 am there are 27 students outside the gym waiting for it to open. Should you use the same approach from part (a) to calculate the expected number of smokers among these 27 students?
Part a is easy, because is a random sample, we can expect that just 13% of these 100 students to be smokers, and 13% of 100 is 13, so we can expect 13 of those 100 students to be smokers.
b) This time we do not have a random sample, our sample is a sample of 15 students who go to the gym in the early morning, so our sample is biased. (And we do not know if this bias is related to smoking or not, and how that relationship is), so we can't use the same approach that we used in the previous part.
PLEASE HELP MATH QUESTION 99 POINTS HELP ASAP PLEASE
LOOK AT LINKED IMAGE FOR QUESTION.
Answer:
Graph A. not a function
Graph B. is a function
Mapping A. is a function
Mapping B. not a function
Table A. not a function
Table B. is a function
Answer:
a graph. not a function
b graph.function
a table. not a function
b table. function
maaping a. function
mapping b. not a function
Step-by-step explanatio n:
mark me brainelst plz
Carmen drives her car 4,629 miles Uma drives her car more miles than Carmen how many miles could on my drive her car
Answer:
4,962
Step-by-step explanation:
This figure consists of a rectangle and semicircle.
What is the perimeter of this figure?
Use 3.14 for pi.
60.84 m
72.84 m
79.68 m
98.52 m
Answer:
hope it helps!
Step-by-step explanation:
Perimeter includes three sides of rectangle:
15m + 12m + 15m
Plus half of circle with diameter 12m
Circumference = diameter * PI
Circumference = 37.68m.
1/2 circumference = 18.84m
Total perimeter is 15m+12m+15m+18.84m
60.84m
Answer:
The answer is 60.84.
Step-by-step explanation:
Can someone please help me on this table?
Answer:
1-16*20*20
2-16*21*21
3-16*22*22
4-16*23*23
Find the value of x | Please!
Answer:
x=20
Step-by-step explanation:
its a straight line.
straight line=180 degrees
60+40=180
80/4=20
20=x
Answer:
20
Step-by-step explanation:
The whole angle is 180 if we add 60 and 40 = 100
then 180 - 100 = 80
then 80 divide by 4 = 20.
PLEASE HELP I DON'T KNOW
Answer:
radius
Step-by-step explanation:
Answer:
It is the radius
Step-by-step explanation:
Let g be the function given by g(x) = 3 − x x + 5 .
Find and simplify g(2) − 1 g(−3)
.A) − 1 21
.B) − 2 21.
C)− 4 21
.D)− 8 21
Answer:C) -4/21
Step-by-step explanation:
Which of the following situations does NOT represent a linear function?
A. Jasmine's mother gives her an allowance of $20 each week.
B. Over the past few months, Cesar's cell phone bill has doubled from the previous month.
Blair is going to earn $7.00 per hour working at a concession stand at a football gamo.
D. The Landscaping company charges the Anderson's $15 for the first hour and $10 for each additional hour to mow the lawn.
C
Answer:
B. Over the past few months, Cesar's cell phone bill has doubled from the previous month.
Step-by-step explanation:
pls I need the answer and explanasion
Answer:
=no of children who like oatmeal/toatal population*100%
=15/50*100%
=(1500/50)%
=30%
Step-by-step explanation:
Sequences:
Determine the first five terms of the following sequences:
A. [tex]a_{n} = \frac{2n+3}{4}[/tex]
B. [tex]a_{n} = \frac{n-3}{n-2}[/tex]
Answer:
A.
aₙ = (2n + 3)/4The first 5 terms:
a₁ = (2*1 + 3) / 4 = 5/4a₂ = (2*2 + 3) / 4 = 7/4a₃ = (2*3 + 3)/ 4 = 9/4a₄ = (2*4 + 3) / 4 = 11/4a₅ = (2*5 + 3) / 4 = 13/4B.
aₙ = (n - 3)/(n - 2)The first 5 terms:
a₁ = (1 - 3) / (1 - 2) = 2a₂ = (2 - 3) / (2 - 2) = undefineda₃ = (3 - 3)/ (3 - 2) = 0a₄ = (4 - 3) / (4 - 2) = 1 / 2a₅ = (5 - 3) / (5 - 2) = 2 / 3From the top of an 95 meter cliff, Tim spots a hiker down below at an angle
of depression of 22 degrees. To the closest meter, how far is the hiker from
the base of the cliff?
Step-by-step explanation:
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After a hailstorm, a large car dealership wants to determine the proportion of cars that have damage. The service
department randomly selects 50 cars on the dealership lot, examines them, and finds that 11 cars have damage.
They want to construct a 99% confidence interval for the true proportion of cars with damage from the storm. Are
the conditions for inference met?
O Yes, the conditions for inference are met.
O No, the 10% condition is not met.
No, the randomness condition is not met.
No, the Large Counts Condition is not met.
Answer:
A, yes the conditions for inference are met
Step-by-step explanation:
I got the question right so it's right
an area of a hexagon of 15 feets sides
Answer:
225
Step-by-step explanation:
Plz help me well mark brainliest if correct..????
Answer:
B.option is the correct answer right no
Answer:
300 miles
Step-by-step explanation:
I couldn't see the top bit by friday because it was outside of the photo, but if my estimations are correct, it should reasonably be 300 miles
Given a feedlot of about 2500 cows, if an individual cow produces about 40 liters of manure per day, how many kiloliters of manure would be produced in one month?
9514 1404 393
Answer:
3000 kL
Step-by-step explanation:
(2500 cows)(40 L/day/cow)(30 day/mo)(1 kL/(1000 L)) = 2.5×40×30 kL/mo
= 3000 kL/mo
About 3000 kL of manure would be produced in one month.
___
That's about 3 cubic meters.
Find the volume of the cylinder.
Either enter an exact answer in terms of \piπpi or use 3.143.143, point, 14 for \piπpi.
Answer: 471
Step-by-step explanation:
3.14 X 5(2) X 6
3.14 X 25 X 6
471 units (3)
Answer:
401.92
Step-by-step explanation:
khan
PQRS is translated 3 units down. What are the coordinates of R' , the image point of R' after the translation
A.(1,0)
B.(1,3)
C.(4,0)
D.(4,-3)
Answer:
I think its D but I might be wrong
Step-by-step explanation:
Round you answer to the nearest cent
Answer:
$2.00
Step-by-step explanation:
For cost $4.23 cost of 1 pound apple = $1.9
For cost $5.9 cost of 1 pound apple = $1.7
For cost $7.61 cost of 1 pound apple = $1.7
For the given mixed fraction,
[tex]2\frac{1}{2}[/tex] pound
The simple faction of it = 5/2 pound
Now dividing 5 by 2 to get decimal form,
Therefore,
5/2 pound = 2.25 pound
2.25 pound apple cost = $4.23
Hence 1 pound cost = 4.23/2.25
= $1.9
For the given mixed fraction,
[tex]3\frac{1}{2}[/tex]
The simple faction of it = 7/2
Now dividing 5 by 2 to get decimal form,
Therefore,
7/2 = 3.5
Since, cost of 3.5 pound apple = $5.9
Therefore,
1 pound apple = 5.9/3.5
= $1.7
For the given mixed fraction,
[tex]4\frac{1}{2}[/tex]
The simple faction of it = 9/2
Now dividing 5 by 2 to get decimal form,
Therefore,
9/2 = 4.5
Since, cost of 4.5 pound apple = $7.61
Therefore,
1 pound apple = 7.61/4.5
= $1.7
Learn more about the fraction visit:
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Write the coordinates of the vertices after a translation 9 units left and 5 units down.
10
Express the null hypothesis and the alternative hypothesis in symbolic form. Use the correct symbol ( μ, rho, σ) for the indicated parameter. A psychologist claims that more than 5.8 percent of the population suffers from professional problems due to extreme shyness. Use p, the true percentage of the population that suffers from extreme shyness.
a) H0 : p = 5.8%
H1 : p < 5.8%
b) H0 : p = 5.8%
H1 : p ≥ 5.8%
c) H0 : p = 5.8%
H1 : p > 5.8%
d) H0 : p = 5.8%
H1 : p ≤ 5.8%
Answer:
c) H0 : p = 5.8%
H1 : p > 5.8%
Step-by-step explanation:
At the null hypothesis, we test that the percentage is equal to a certain value. At the alternate hypothesis, we have a test about this percentage, if it is more, less, or different from the tested value.
A psychologist claims that more than 5.8 percent of the population suffers from professional problems due to extreme shyness
At the null hypothesis, we test if the percentage is 5.8%
[tex]H_0: p = 5.8\%[/tex]
At the alternate hypothesis, we test if this percentage is more than 5.8%. So
[tex]H_a: p > 5.8\%[/tex]
This means that the correct answer is given by option c.
Answer:
c) H0 : p = 5.8%
H1 : p > 5.8%
Step-by-step explanation:
Hope this helps
find the volume of the cone. Round you’re answer to the nearest truth if necessary. Use 3.14
Answer:
1,961.6
Step-by-step explanation: