Given:
The polynomial [tex]x^3-1[/tex] is divided by (x+2).
To find:
The remainder.
Solution:
Remainder theorem: If a polynomial p(x) is divided by (x-c), then the remainder is p(c).
Consider the polynomial:
[tex]p(x)=x^3-1[/tex]
It is divided by (x+2). So, by the remainder theorem the remainder is p(-2).
Substituting x=-2 in the above polynomial, we get
[tex]p(-2)=(-2)^3-1[/tex]
[tex]p(-2)=-8-1[/tex]
[tex]p(-2)=-9[/tex]
Therefore, the remainder is -9.
The remainder when x³ - 1 is divided by (x + 2) is -9
Polynomial is an expression consisting of only the operations of addition, subtraction, multiplication of variables.
The remainder theorem states that when a polynomial f(x), is divided by a linear polynomial x - a, the remainder of that division will be equivalent to f(a).
Given the polynomial f(x) = x³ - 1.
The linear equation is x + 2, hence; x = -2
f(-2) = (-2)³ - 1 = -8 - 1 = -9
The remainder when x³ - 1 is divided by (x + 2) is -9
Find out more at: https://brainly.com/question/13416073
The value of the 9 in 901,532 is how many times the value of the 9 in 157,900?
im pretty sure the 9 is 1000 times the value
A group of scientists have been sent on an expedition to test the soil in the Allegheny Mountains. They need to collect samples from nine sites. The route for the expedition is shown in the image. The group starts at P and works its way around to Q, R, S, T, U, V, W, and X, in that order, before returning to P. What is the length of the route?
A.
50 units
B.
52 units
C.
55 units
D.
58 units
E.
60 units
Answer:
52
Step-by-step explanation:
The solution is, Distance between E and F = 8 units
What is distance?The distance between two points is the length of the line joining the two points.
Formula: distance= √(x_2-x_1)²+(y_2-y_1)²
here, we have,
Given:
Coordinate of E = (3,5)
Coordinate of F = (3,-3)
Find:
Distance between E and F
Computation:
Distance = √(x₁-x₂)² + (y₁-y₂)²
Distance between E and F = √(3-3)² + (5+3)²
Distance between E and F = √(8)²
Distance between E and F = 8 units
To learn more on Distance click:
brainly.com/question/15172156
#SPJ3
Complete question:
During an expedition, archeologists find four objects at the positions labeled E, F, G, and H in the image. How far are the artifacts E and F from each other? A. 5 units B. 8 units C. 10 units D. 12 units
helppp pleasee :))!!
Answer:
13 km
I hope it's helps you
Answer:
13, You have to divide the Diameter by 2. 26 ÷ 2 =13
help me pls quick fill it out
Answer
Step-by-step explanation:
The half-life of radioactive iodine used in medical studies is 8 hours. A doctor wants to know when the amount of radioactive iodine in a patient's body is 20% of the original amount. When will this occur?
Answer:
xgu5 yup is hug is is unfocused
Mr Yates has an $80 budget to purchase 72 pair of sunglasses if there is a 6% sales tax rate How much under budget will Mr. Yates be 
Answer:plz answer quick
Step-by-step explanation:
find ( f•f)(0)
f(x)=x^2-1
A. 1
B. 0
C. -8
D. -1
Answer:
D
Step-by-step explanation:
NO LINKS OR FILES PLEASE!!! -_-
POINTS!!!
Does anyone do FLVS or the program BUZZ?
(I'M IN 8TH GRADE) If so, can you please help me with 06.02 Factory Workers (History) I really need help :(
Answer:
........................The number of children per household in the US is strongly skewed to the right with a mean of 3.1 children per household and a standard deviation of 1.2 children per household. A person studying demographics selects an SRS of size n = 40 from the population of all households in the US and calculates the sample mean number of children per household. What is the standard deviation of the sampling distribution of the sample mean?
Round to 2 decimal places.
Answer:0.19
Thats what i got on edge 2020
Translate this sentence into an equation
The product of donnie’s savings and 3 is 48
Use d to represent Donnie’s savings.
A:90 clockwise
B:90 counterclockwise
C:180
D:270 clockwise
E:270 counterclowise
Answer:
A. 90 clockwise
Step-by-step explanation:
I think...
help me pleaseeeeeeeee
10. A map uses the scale of ã of an inch to represent 3
miles. If the actual distance between two cities is
25 miles, then what is the length on the map?
Find the solutions to x2 = 24.
O A. x = +216
O B. x = 16.6
O C. x= 46
O D. x = +62
Answer:
x =±2 sqrt(6)
Step-by-step explanation:
x^2 = 24
Take the square root of each side
sqrt(x^2) = sqrt(24)
x = ±sqrt(4*6)
x =±sqrt(4) sqrt(6)
x =±2 sqrt(6)
Twice a number x exceed 5 at least by 4. find the possible value of x.
Answer:
5?
Step-by-step explanation:
2x › 5 (buy at least 4)
so you can just start plugging numbers in.
I used 5, 5 times 2 is 10 which is 5 more that 5, which does met the quota.
Answer:
[tex]x \ge 4.5[/tex]
Step-by-step explanation:
The number 2x is larger than 5, so 2x - 5 is the difference between 2x and 5. This difference is at least (greater than or equal to) 4.
[tex]2x-5 \ge 4\\\\2x \ge 9\\\\x \ge 4.5[/tex]
in the given pair of linear equations 3x+ay=50 and 9x-21y=15 find thevalue of a for them to be a parallel
Answer:
[tex]3x + ay = 50\\ay = 50-3x\\ay = -3x + 50\\y =\frac{-3x}{a} + \frac{50}{a} \\\\slope = \frac{-3}{a} \\\\9x -21y = 15\\-21y = 15 -9x\\21y = 9x - 15\\\\y=\frac{9x}{21} - \frac{15}{21} \\\\Slope = \frac{9}{21} \\\\Since \ equations \ are \ parallel \ = m_{1} m_{2} = 1\\\\\frac{-3}{a} \cdot\frac{9}{21} = 1 \\\\\frac{-27}{21a} = 1\\\\\\\frac{-9}{7} = a[/tex]
Please I need help I need it done by today
The top suface of a desk is composed of 2 rectangles and a triangle. some side lengths of the top surface of the desk are shown
Answer:
Full question?
If I am not mistaken, I have seen this question on brainly before.
With two rectangles connecting two sides of a triangle with lengths 1.5ft and 2.5ft.
This would make area of the surface of the top desk 8.625ft².
is x^2+2bx-v^2 a perfect square trinomial?
Answer:
no x² + 5x + c is a perfect square
Step-by-step explanation:
A hot air balloon went from an elevation of 5,038 feet to an elevation of 3,403 feet in 30 minutes. What was its rate of descent? The rate of the descent was ( ) feet per minute.
Answer:
Step-by-step explanation:
In this case, we have a descent of 2,125 feet (initial height of 5,439 - ending height of 3,314). Since it took 34 minutes for the balloon to descend this distance, we divide the descent by the time (2,125/34). This gives us a rate of 62.5 feet per minute.
That means that the balloon traveled downward 62.5 feet every minute.
Please help please
One cube has edges n meters long. Another has edges 3n meters long. What is the ratio of the volume of the first cube to the volume of the second cube
Answer:
1:3
Step-by-step explanation:
The second cube is 3x bigger than the first cube, and since all sides of a cube are the same the ratio for the length of the edges will directly transfer over to the ratio of their volumes.
C. 1 : 27
As an example, let's say that n is equal to 1. The volume of the first cube is n*n*n, since n stands for the measurement of each edge. n*n*n=1*1*1=1 cubic meter. Now, onto the second cube. The volume of the second cube is 3n*3n*3n, since 3n stands for the measurement of each edge. 3n*3n*3n=3*3*3 ( since 3n=3*1=3 ) which is equal to 27. The ratio of the volume of the first cube to the volume of the second cube is represented by n : 3n. Substituting the n on both sides for the n in our example, we get a final result and ratio of 1 : 27.
I need this answered
In a pacemaker factory, all pacemakers must go through a rigorous quality assurance check before being shipped. The table shows the results
of the quality assurance checks. Find the probability that a non-defective pacemaker "fails." Round your answer to the nearest tenth of a percent. NEED ASAP
Answer:
16.1%
Step-by-step explanation:
Answer:
15.0
Step-by-step explanation:
To be considered 18-karat (18K) gold, a piece of jewelry must be made of 75% pure gold. The higher the karats, the more valuable a piece of jewelry. A jewelry designer is purchasing a large quantity of 18K gold from a new supplier. To see if the new supplier is being dishonest about the karat rating in the shipment, the designer melts a random sample of the gold and conducts a hypothesis test with H0: The proportion of metal that is gold is 75%, and Ha: The proportion of metal that is gold is less than 75%. What is a Type I error and its consequence in this context
Answer:
The gold shipment truly is made of 75% gold, but the designer concludes that it is made of less than 75% gold. The designer will reject the shipment of gold and miss out on an honest business relationship with the supplier.
Step-by-step explanation:
Type I error is defined as the rejection of the true null hypothesis. It is also called as the 'false positive' conclusion or 'false positive' findings. The value of alpha or the significance level determines the probability of making the error type I.
In the context, it is given that for a gold piece to be of 18 karat , the piece of jewelry must be made of 75% of pure gold.
The null hypothesis is, H0: The proportion of metal that is gold is 75%
The alternative hypothesis is Ha: The proportion of metal that is gold is less than 75%.
Thus the type I error is when the gold shipment is made of 75% gold but the jewelry designer rejects the shipment thinking that the shipment is made of less than 75% gold.
Thus it shows the error of type I rejecting the null hypothesis.
A soup can has a radius of 4 cm and a height
of 11 cm. There are 24 cans in one case. How
many litres of soup are in one case?
Answer:
13.3L
Step-by-step explanation:
A linear sequence starts
11
20
29
38
Work out an expression for the nth term of the sequence.
The nth term is n+9
Answer:
9n + 2.
Step-by-step explanation:
This is arithmetic with common difference d = 9.
nth term = a1 + d(n - 1) (a1 = 11) 11 + 9n - 9
= 11 + 9(n - 1)
= 9n + 2.
HELPP plzzzz ——————and thanks no filessssss
What is the discriminant for the following quadratic?
x^2 - 2x - 4
Answer:
20
Step-by-step explanation:
The discriminant of a quadratic is the expression inside the radical of the quadratic formula.
b^2-4(ac)
Substitute in the values of a , b , and c .
(-2)^2-4(1*-4)
Elevate the result to find the discriminant.
4+16
=20
Do the points of the following quadrilateral create a square? A(3,4) B(-3,4)
C(-3,-2) D(3,-2)
1) Yes
2) No
Answer:
Yes
Step-by-step explanation:
You can refer to the photo that I attached.
Find the volume of the cylinder. Round your answer to the nearest hundredth of a cubic meter. The radius is 3m and the height is 6m. What is the volume?
Answer:
169.56
Step-by-step explanation:
169.56
If the radius is 3 m and the height is 6 m. Then the volume of the cylinder will be 196.56 cubic meters.
What is the volume of a right circular cylinder?Suppose that the radius of the considered right circular cylinder is 'r' units.
And let its height be 'h' units.
Then, its volume is given as:
V = πr² h
Right circular cylinder is the cylinder in which the line joining the center of the top circle of the cylinder to the center of the base circle of the cylinder is perpendicular to the surface of its base, and to the top.
The radius is 3 m and the height is 6 m.
Then the volume of the cylinder will be
Volume = 3.14 x 3² x 6
Volume = 3.14 x 9 x 6
Volume = 169.56 m³
Learn more about the volume of the cylinder here:
https://brainly.com/question/12763699
#SPJ2