The polynomial remainder theorem says that a polynomial p(x) leaves a remainder of p(k) when it's divided by x - k.
We're given that dividing p(y) = 2y³ + by² - cy + d leaves the same remainder R after dividing it by y + 1, y - 2, and 2y - 1. So we have
p(-1) = 2(-1)³ + b(-1)² - c(-1) + d = R
==> R = -2 + b + c + d
p(2) = 2(2)³ + b(2)² - c(2) + d = R
==> R = 16 + 4b - 2c + d
p(1/2) = 2(1/2)³ + b(1/2)² - c(1/2) + d = R
==> R = 1/4 + b/4 - c/2 + d
We're also given that y + 2 is a factor, which means dividing p(y) by it leaves no remainder, and so
p(-2) = 2(-2)³ + b(-2)² - c(-2) + d = 0
==> 0 = -16 + 4b + 2c + d
Solve the system of equations in boldface. You can eliminate d from the first 3 to first solve for b and c, then solve for d :
(-2 + b + c + d) - (16 + 4b - 2c + d) = R - R
-18 - 3b + 3c = 0
b - c = -6
(-2 + b + c + d) - (1/4 + b/4 - c/2 + d) = R - R
-9/4 + 3b/4 + 3c/2 = 0
b + 2c = 3
(b - c) - (b + 2c) = -6 - 3
-3c = -9
c = 3
b - 3 = -6
b = -3
-16 + 4(-3) + 2(3) + d = 0
d = 22
The ratio of apples to oranges in a basket of fruit is 2:7. There are 21 oranges in the
basket. How many apples are in the basket?
Answer:
6
Step-by-step explanation:
The given ratio specifies the number of apples to be found in the basket
for a given number of oranges.
Correct response:
The number of apples in the basket are 6 applesMethods of calculationThe given ratio of apples to oranges in the basket of fruits = 2:7
The number of oranges = 21 oranges
Required:
The number of apples in the basket.
Solution:
The given ratio can be expressed as follows;
[tex]\mathbf{\dfrac{Number \ of \ apples}{Number \ of \ oranges}} = \dfrac{2}{7} [/tex]Which gives;
[tex]\dfrac{Number \ of \ apples}{21} = \dfrac{2}{7} [/tex]
7 × (Number of apples) = 2 × 21
[tex]Number \ of \ apples = \dfrac{2 \times 21}{7} = 6[/tex]
The number of apples in the basket = 6 applesLearn more about ratios here:
https://brainly.com/question/2645778
Evaluate the following.
Answer:
5
Step-by-step explanation:
|8| - |14 - 11|
8 - 3
5
Combine like terms.
y+6 - 2 – 4y^3– 5y + 2y^3 – 2y^3
Answer: −4[tex]y[/tex] + 4 − 4[tex]y^{3}[/tex]
Step-by-step explanation:
Hey there! I will give the following steps, if you have any questions feel free to ask me in the comments below.
Step 1: Collect like terms.
([tex]y[/tex] − 5[tex]y[/tex]) + (6 − 2) + (−4[tex]y^{3}[/tex] + 2[tex]y^{3}[/tex] − 2[tex]y^{3}[/tex])
Step 2: Simplify.
−4[tex]y[/tex] + 4 − 4[tex]y^{3}[/tex]
~I hope I helped you! :)~
Brett made a scale drawing of a rectangular room in his house.
The actual length of the room is 12 4/5 ft. The scale used to make the
drawing was 1/4 in. = 1 ft. What is the length, in inches, of the room
on the drawing?
Answer:
Step-by-step explanation:
Length of the room = 12 4/5 ft = 12.8 ft
Scale is 0.25 inches = 1 ft.
This means that every 1ft is shown as 1/4 inch on the map.
To find what 12 4/5ft on the map, you would multiply 12.8 by 0.25.
12.8 x 0.25 = 3.2 inches
help me with ten please
Answer:
H
Step-by-step explanation:
Simplify 5a-(-9)-7a-12
Answer:
-2a = 0 + 3
Step-by-step explanation:
hope this helps.
Plot the line for the equation on the graphy,−5=3/2(x−2)
Answer:
The equation of the line is:
y - 5 = 3/2 (x - 2)
Transforming the line into the slope intercept form:
y = 3x/2 - 3 + 5
y = 3x/2 + 2
The slope is 3/2 and the y-intercept is 2.
Plotting this on the graph can be done using these steps:
Locate the point (0,2) on the graph.
From (0,2), count 3 units up and 2 units to the left and indicate that point.
Finally, connect the two points and extend the line.
Line a passes through points (-2, 1) and (2,9). Write an equation in slope intercept form that is parallel to line a.
Answer:
y=ax+9−2a (i think )
Step-by-step explanation:
A straight line is represented by a linear function
The equation of line a is: [tex]\mathbf{y = 2x +5}[/tex]
The points are given as:
(x1,y1) = (-2,1)
(x2,y2) = (2,9)
Calculate the slope (m)
[tex]\mathbf{m = \frac{y_2 - y_1}{x_2 - x_1}}[/tex]
So, we have:
[tex]\mathbf{m = \frac{9-1}{2--2}}[/tex]
[tex]\mathbf{m = \frac{8}{4}}[/tex]
[tex]\mathbf{m = 2}[/tex]
The equation in slope intercept form is:
[tex]\mathbf{y = m(x - x_1) + y_1}[/tex]
So, we have:
[tex]\mathbf{y = 2(x +2) + 1}[/tex]
[tex]\mathbf{y = 2x +4 + 1}[/tex]
[tex]\mathbf{y = 2x +5}[/tex]
Hence, the equation of line a is: [tex]\mathbf{y = 2x +5}[/tex]
Read more about slope intercept form at:
https://brainly.com/question/11824567
The roots of a quadratic equation are
1/ 3 and -2. Determine the equation
Answer: God
Step-by-step explanation:
The reason it’s god is because god created everything so he know everything. So your answer is god
Joseph is tracking the progress of her plant's growth. Today the plant is 8 cm high. The plant grows 1.5 cm per day
What is the linear model that represents the height of the plant after d days.
Answer:
y = 1.5x(or d) + 8
Step-by-step explanation:
1.5 is the slope and 8 is the y intercept(the constant term)
Dave cleans pools at a constant rate of 2/5 pools per hr what is the ratio of the number of pools he cleans to the number of hours
How many pools can dave clean in 20 hrs
Answer:
For every 1 hour he cleans 2/5 pools, so the ratio of pools to hours is 0.4:1
In 20 hours, Dave can clean 2/5 • 20 = 8 pools.
Three times a number minus 5 plus the same number
Answer:
15
Step-by-step explanation:
How much of the circle is shaded? Write your answer as a fraction in simplest form.
GUYS CAN SOMONE anser 2 QUESTIONS!? WHATS 8.97 IN WORD FORM AND EXPANDED FORM!?
Answer:
eight point nine seven, 8+0.9+0.07
Step-by-step explanation:
Question 1
Select ALL expressions that are equivalent to 4x + 2(2x - 5) - (3 - 5x).
A
82 - 10 - 3 - 52
B
3.2 - 13
С
13 – 13
82 - 10 - 3 + 5%
E
83 - 5 - 3 - 5x
Answer:
B
Step-by-step explanation:
Some transportation experts claim that it is the variability of speeds, rather than the level of speeds, that is a critical factor in determining the likelihood of an accident occurring (Update, Virginia Department of Transportation, Winter 2000). One of the experts claims that driving conditions are dangerous if the variance of speeds exceeds 75 (mph)2. On a heavily traveled highway, a random sample of 55 cars revealed a mean and a variance of speeds of 62.5 mph and 94.7(mph)2, respectively. (You may find it useful to reference the appropriate table: chi-square table or F table)
1. Set up the competing hypothesis to test wxpert,s claim.
2. At the 5% significance level find the critical value and state the decision rule.
3. Can you conclude that driving conditions are dangerous on this highway? explain.
Answer:
Explained below.
Step-by-step explanation:
The claim made by an expert is that driving conditions are dangerous if the variance of speeds exceeds 75 (mph)².
(1)
The hypothesis for both the test can be defined as:
H₀: The variance of speeds does not exceeds 75 (mph)², i.e. σ² ≤ 75.
Hₐ: The variance of speeds exceeds 75 (mph)², i.e. σ² > 75.
(2)
A Chi-square test will be used to perform the test.
The significance level of the test is, α = 0.05.
The degrees of freedom of the test is,
df = n - 1 = 55 - 1 = 54
Compute the critical value as follows:
[tex]\chi^{2}_{\alpha, (n-1)}=\chi^{2}_{0.05, 54}=72.153[/tex]
Decision rule:
If the test statistic value is more than the critical value then the null hypothesis will be rejected and vice-versa.
(3)
Compute the test statistic as follows:
[tex]\chi^{2}=\frac{(n-1)\times s^{2}}{\sigma^{2}}[/tex]
[tex]=\frac{(55-1)\times 94.7}{75}\\\\=68.184[/tex]
The test statistic value is, 68.184.
Decision:
[tex]cal.\chi^{2}=68.184<\chi^{2}_{0.05,54}=72.153[/tex]
The null hypothesis will not be rejected at 5% level of significance.
Conclusion:
The variance of speeds does not exceeds 75 (mph)². Thus, concluding that driving conditions are not dangerous on this highway.
Angle 3 and angle 4 are supplementary angles angle 3 is 88° what is the measure of angle 4?
Answer:
92°
Step-by-step explanation:
Supplimentary angle = 180°
So, 180° - 88° = 92°
I need to write a proportion to the following problem:
3 folders cost $2.91. What written proportion would help determine the cost of 2 folders?
Answer:
The cost of two folder is $ 1.94
Solution:
Given that 3 folders cost $ 2.91
We have to determine the cost of 2 folder
From given,
Cost of 3 folder = $ 2.91
To find the cost of 1 folder, divide 2.91 by 3
Thus cost of 1 folder is $ 0.97
We are asked to find cost of two folders.
Therefore, multiply cost of 1 folder by 2
Thus cost of two folder is $ 1.94
A box of spaghetti at the grocery store is purchased for $1.60 wholesale and is marked up by 60 percent. Then, the store marks down the item by 20 percent. A customer wants to buy three boxes of spaghetti. How much will the customer pay, including paying 8 percent sales tax? Round your answer to the nearest cent.
Look at the table below.
Steps
Moses’s work
Step 1
1 dollar and 60 cents (1.6) = 2 dollars and 56 cents
Step 2
2 dollars and 56 cents (0.80) = 2 dollars and 5 cents
Step 3
2 dollars and 5 cents (3) = 8 dollars and 20 cents
Step 4
8 dollars and 20 cents (1.08) = 8 dollars and 86 cents
In which step did Moses first make a mistake in his work?
Step 1
Step 2
Step 3
Step 4
PLEASE HELP I BEG YOU!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
R1: Given
R2: Subtraction Property of Equality
R3: Distribute Property
R4: Addition Property of Equality
R5: Division Property of Equality
Write a paragraph proof for the following conjecture: m∠1 + m∠2 = m∠4
Prove: m∠3 + m∠1 + m∠2 = 180°
Given: ∠1 + ∠2 = ∠ 4
∠4 + ∠3 must be 180° because they are supplementary
If ∠4 + ∠3 is 180, and ∠1 + ∠2 = ∠4, you can substitute ∠4 in the first equation for ∠1 + ∠2.
Hence, we arrive at the answer ∠1 + ∠2 + ∠3 = 180.
Plz mark brainliest:)
what is 917 divided by 63
Answer:
14.55
Step-by-step explanation:
I think I know the answer but I just want to double check.
Answer:
D
Step-by-step explanation:
I think it's same with what ur thinking
What is the value of the expression below? (9 divided by 3) + 4 (6 minus 7) –7 –1 7 20
PLEASE ANSWER QUiCK I’m on timer
Answer:
The answer is -1.
Step-by-step explanation:
Answer:
-1 is the answer saw it on clculator
Round the numbers to the nearest ten thousands.
62 389-
65 405-
51 330-
343 021-
102 779-
Answer:
60,00070,00050,000340,000100,000
Jane bought 12 identical beanie babies for her sister’s birthday goody bags. Is it possible that without tax her purchase was: $16.20, $18.32, $18.42
Answer:
$18.32
Step-by-step explanation:
First one is not possible. Same for 18.42
pls help thanks alot
Answer:
A, C, D
Step-by-step explanation: the side of the > that has the opening is the side that should have the greater number, so if its like answer A its true
Which correctly describes the points of discontinuity of the function? Select all that apply.
A. There is an infinite discontinuity at x equals negative 2.
B. There is a jump discontinuity at x equals negative 2.
C. There is a removable discontinuity at x equals negative 1.
D. There is an infinite discontinuity at x = 1.
E. There is a jump discontinuity at x = 1
Answer:
A, C, and E
Step-by-step explanation:
6(5−8v)+12=−54 can you help me with this?
Answer:
v=2
Step-by-step explanation:
6(5-8v)+12=-54
6(5-8v)=-66
(6(5-8v))/6=-66/6
5-8v=-11
-8v=-11-5
-8v=-16
Which of the following is a geometric sequence?
A. 3, 6, 9, 15, 24
B. 2, 4, 8, 16, 32
C. 6, 13, 20, 27, 34
D. 2,5,7,12,19
I mark as brainliest
Answer:
.1
Step-by-step explanation:
Answer:
Point Q is represented by the ordered pair (-2,9)