p(x) = 2x³ + 3x² + ax + b when divided by x - 2 and x + 2 leaves the remainders 2 , - 2.
Find:Value of a and b
Solution:✯ g(x) = x - 2
⟹ 0 = x - 2 [ g(x) = 0 ]
⟹ x = 2
★ p(2) = 2(2)³ + 3(2)² + a(2) + b
⟹ - 2 = 2 * 8 + 3 * 4 + 2a + b
⟹ - 2 - 16 - 12 - 2a = b
⟹ - 30 - 2a = b -- equation (1)
Similarly,
✯ g(x) = x + 2
⟹ 0 = x + 2
⟹ x = - 2
★ p( - 2) = 2( - 2)³ + 3( - 2)² + a ( - 2) + b
Substitute the value of b from equation (1).
⟹ 2 = 2 * ( - 8) + 3 * 4 - 2a - 30 - 2a
⟹ 2a + 2a = - 16 + 12 - 2 - 30
⟹ 4a = - 24
⟹ a = - 24/4
⟹ a = - 6
Substitute the value of a in equation (1).
⟹ - 30 - 2( - 6) = b
⟹ - 30 + 12 = b
⟹ - 18 = b
Therefore,
a = - 6
b = - 18.
I hope it will help you.
Regards.
R(3, 8) is dilated by a factor of 5, centered at (2, 10). Write the coordinates of R’.
Answer:
The coordinates of R' are [tex]R'(x,y) = (8,-2)[/tex].
Step-by-step explanation:
According to Linear Algebra, dilation consist in expanding a given vector with respect to one of its endpoints by a scalar. That is:
[tex]R'(x, y) = C(x,y) + k\cdot [R(x,y)-C(x,y)][/tex] (Eq. 1)
Where:
[tex]R(x, y)[/tex] - Original location with respect to origin, dimensionless.
[tex]C(x,y)[/tex] - Point of reference with respect to origin, dimensionless.
[tex]k[/tex] - Dilation factor, dimensionless.
[tex]R'(x, y)[/tex] - Dilated point with respect to origin, dimensionless.
If we know that [tex]R(x,y) = (3,8)[/tex], [tex]C(x,y) = (2,10)[/tex] and [tex]k = 5[/tex], then the dilated point is:
[tex]R'(x,y) = (3,8) +5\cdot [(3,8)-(2,10)][/tex]
[tex]R'(x,y) = (3,8)+5\cdot (1,-2)[/tex]
[tex]R'(x,y) = (8,-2)[/tex]
The coordinates of R' are [tex]R'(x,y) = (8,-2)[/tex].
Is the relation a function? {(-7, 14), (9, -7), (14, 7), (7, 14)}
Yes, because they all can be graphed and if you use the line hack it works.
Plzz helppp plzzzzzzzzzzz asap
2. Not only is the mean of pairs of clothes purchased is 10, but the population standard deviation is 4.5. When the researcher from problem number 1 calculates a standard deviation for the distribution of sample means for her 2,950, 000 samples, is the standard deviation of sample means likely to be less than, greater than, or equal to 4.5? Explain
Answer:
Less than 4.5
Step-by-step explanation:
Given that :
Mean = 10
Population standard deviation (σ) = 4.5
Sample size (n) = 2950000
The standard deviation of sample means becomes smaller or lesser as the sample size increases according to the central limit theorem. This is because the standard deviation of sample means is obtained by dividing the population standard deviation by the square root of the sample size. Thus is called the standard error.
The standard deviation of sample means is called the standard error ; and is obtained by:
Standard Error = σ/√n
Standard Error = 4.5 / √2950000
Standard Error = 4.5 / 1717.5564
= 0.0026200
A pair of basketball shoes normal shoes is 120 jordan bought it at a discount of 10% he had to pay 8% tax on the discounted price. If jordan put 15% of the cost including tax as a down payment how much money did he have to pay for the down payment
9514 1404 393
Answer:
17.50 down
Step-by-step explanation:
After the discount, the price is 100% -10% = 90% of the original.
After the tax, the amount owed is 100% +8% = 108% of the discounted price.
The amount Jordan put down is 15% of the amount after tax, so is ...
120(0.90)(1.08)(0.15) ≈ 17.50 . . . down payment
Answer:
$17.50
Step-by-step explanation:
A cave explorer travels 12.9 m eastward, 3.4 m northward, and finally 3.4 m
southward. In which direction did the explorer end up traveling?
Answer:
12.26 m, north-west
Step-by-step explanation:From the figure the displacement can be calculated by the Pythagorean law. In this the triangle ABC is the right angle triangle with hypotenous h, base 12 m, and height 2.5 m. Therefore the net displacement is 12.26 m and the displacement we know it is vector quantity and it is the shortest distance between the two points. Therefore the displacement is from point B to A. Then the net displacement is the direction in the north-west direction with a magnitude of 12.26 m.
.$10,000 at 4.2% for 5 years
Answer:
2100
Step-by-step explanation:
Round the money below to the nearest dollar.
$ 5.9091
$ 229.74289
Answer:
1. $6
2.$230
Step-by-step explanation:
Base it of the tenths place. If it is more than five you round up
Answer:
$6 and $230
Step-by-step explanation:
The 95% confidence interval for a certain proportion p is from 0.23 to 0.63. We conducted a hypothesis test for p. The null hypothesis is H0:p=a . The alternative hypothesis is Ha:p≠a. What is the mean for the all possible values of a which would not be rejected as plausible values of the population proportion at a 5% significance level? The mean for the all possible values of a which would not be rejected as plausible values of the population proportion at a 5% significance level is .
Answer:
The answer is "0.43"
Step-by-step explanation:
Population proportion normal distribution is suggested as following:
Confidence Interval = [tex]P \pm Z \times \sqrt{\frac{P \times (1 -p)}{n} }[/tex]
Confidence Interval = [tex]P \pm E[/tex]
Bottom bound [tex]= P-E = 0.23[/tex]
Lower bound [tex]= P + E = 0.63[/tex]
Through connecting additional formulas, we're getting,
[tex]\to 2P = 0.23+0.63\\\\\to 2P = 0.86\\\\\to P= \frac{0.86}{2}\\\\[/tex]
[tex]= 0.43[/tex]
The average with all attribute outcomes a whereby the demographic proportion at 5 % isn't dismissed as plausible values is 0.43.
What’s the perimeter and area?
Answer:
Perimeter= 34a
Area= 42a
Step-by-step explanation:
Perimeter: 3a + 3a + 3a+ 3a +3a + 5a +5a + 9a = 34a
Area: (3a x 9a) + (3a x 5a) = 42a
Help plz plz plz help with math
What is the product of –3 and 5?
(A) -15
(B) -8
(C) 8
(D) 15
Find the distance between the two points in simplest radical form.
(6, 7) and (8,2)
Answer:
+sqrt(29)
Step-by-step explanation:
Note that the change in x (horizontal leg) is 8 - 6, or 2, and that the change in y (vertical leg) is |2 - 7|, or 5. According to the Pythagorean Theorem, the length of the hypotenuse of the right triangle created here is:
distance = +sqrt(2^2 + 5^2), or +sqrt(29)
2x+y=7
solve the literal equation for y
anserw is
3.5
you multiply 2 times 3.5 and get 7
Suppose you choose a number on a piece of paper at random from a bag. The numbers include this set: {7, 9, 10, 11, 12, 13, 14, 15}. There is only one paper for each number, so there are no repeats of the same number. What is the probability that you choose a number less than 10?
Answer:
1/4Step-by-step explanation:
Given the random set of numbers chosen from the bag as {7, 9, 10, 11, 12, 13, 14, 15}
Total outcome = 8 numbers
The numbers that are less than 10 will be the expected outcome, the sets are {7,9}
Expected outcome = 2 elements
Probability = Expected outcome/Total outcome
Pr(that you choose a number less than 10) = 2/8
Pr(that you choose a number less than 10) = 1/4
which expression is four more than s
s×4, 4>s, so, s+4
Answer:
the following user name or not sure about it is the
Answer:
s+4
Step-by-step explanation:
"more than" means to add.
s x 4 would be "four times"
4 > s would be "four is greater than"
Choose the equivalent number.
4,000 + 800 + 20+3=
Answer:
4823 is the answer you're welcome
The recipe for cookies calls for 2 cups of butter to make 48 cookies how much butter will you need to make 72 cookies
Answer: 3 cups of butter
Step-by-step explanation: 2 cups of butter for 48 cookies means 1 cup of butter for 24 cookies. 72 divided by 24=3 That means you need 3 cups of butter for 72 cookies
32. Use < >, or = to compare 0.36 and 0.4.
Answer:
0.36<0.4
Step-by-step explanation:
Answer:
0.36<0.4
Step-by-step explanation:
the area the arrow swallows is the bigger number so
fore example
0.4 is greater then 0.36 so it would be 0.36<0.4 because the area of the arrow eats or swallows the bigger number
James, Priya, and Siobhan work in a grocery store. James makes $9.00 per hour. Priya makes 20% more
than James, and Siobhan makes 5% less than Priya. How much does Siobhan make per hour?
Answer:
Step-by-step explanation:
Don't be too quick to answer 15% of some number. It may be right, but it is likely not.
James makes 9.00 dollars an hour
Priya makes 20% more than James. Stop. Figure that out.
9.00 * 1 + 25/100 * 9 = 9.00 + 2.25 = 11.25
Now, you can figure out 5% less.
Siobhan = 11,25 - 5/100 * 11.25
Siobhan = 11.25 - 0.05 * 11.25
Siobhan = 11.25 - 0.5625
Siobhan = 10.6875 = 10.69
There is no other way that I know of to go directly to Siobhan's wage other than doing it the long way -- at least for the level of math you are taking.
9 * (1.2 - 0.05) might work.
9 * (1.15)
= 10.35 which is close, but not correct.
Moral: do the math. Don't accept a guess as an answer.
which expression simplifies to 3x+5
Answer:
A
Step-by-step explanation:
Becky babysits her younger siblings for $5.00 for the first hour and $3.00 for each
remaining hour. She never babysits them for more than 4 hours. Becky wrote the
following equation to calculate the amount of money, y, she will receive after babysittin
for h hours.
y = 5 + 3(1 - 1)
Which is a reasonable range for the given situation?
A. 1
B. 5
C. 3
D. 3
Answer:
b
Step-by-step explanation:
Answer:
B. 5
Step-by-step explanation:
If you are looking at this equation, you have to follow order of operations. First, you start with the parentheses. 1-1=0. Next you multiply 3(0) to get 0. 5 + 0= 5.
what are the 2 clsest integers to 300
Answer:
299 and 301
Step-by-step explanation:
An integer is colloquially defined as a number that can be written without a fractional component.
Therefore the two closest integers to 300 are 299 and 301.
What is the employee's gross pay?
a $818.05
b. $830.42
C. $840.59
d $852.96
Answer:
It is D
Step-by-step explanation:
Just took the test and got a 100 2021
Answer:
What is the employee's gross pay?
a. }} $818.05
b. }} $830.42
c. }} $840.59
d. }} $852.96 <<<<<<<CORRECT
Step-by-step explanation:
Edge 2021
Your family is driving to the mountains for the weekend You travel 200 kilometers in the first two hours during the next hour you stop for lunch and only travel 25 kilometers. What is your average speed. Can you please use (D=st)
Answer: (D= 87.5 kilometers per hour)
Step-by-step explanation: First, divide 200 by 2, which equals to 100. Next, divide 25 by 2, which is 12.5. Lastly, subtract 100 minus 12.5, which equals 87.5. You should end up with a result of (D= 87.5 kilometers per hour).
Pls help with this it’s math
Answer:
The slope is undefined.
Step-by-step explanation:
A vertical line has undefined, or infinite, slope. If you attempt to find the slope using rise over run or any other slope formula, you will get a 0 in the denominator. Since division by 0 is undefined, the slope of the line is undefined.
Help me guys PLZZ
i'll mark brainllest
Describe two real-life applications of irrational numbers.
Answer:
Calculus and other mathematical domains that use these irrational numbers are used a lot in real life. Irrational Numbers are used indirectly.
Step-by-step explanation:
Graph the equation y=x^2-8x+7y=x on the accompanying set of axes. You must plot 5 points including the roots and the vertex.
what points do i need to plot on the graph from this equation please hurry brainlest for whoever can help and 20 points
Answer: If you're plotting 1 equation (y=x^2-8x):
(-4,16) Vertex
(0,0) root
(8,0) root
If plotting both (y=x^2-8x) & (7y=x):
(-4,16) Vertex
(0,0) root
(8,0) root
(7,1) point on line
(-7, -1) point on line
Step-by-step explanation:
The vertex of the parabolic equation y = x² - 8x + 7 will be at (4, -9).
Now, Let the point (h, k) be the vertex of the parabola and a be the leading coefficient.
Then the equation of the parabola will be given as,
y = a(x - h)² + k
The equation is given below.
y = x² - 8x + 7
Convert the equation into a vertex form. Then we have
y = x² - 8x + 7
y = x² - 8x + 16 - 16 + 7
y = (x - 4)² - 9
Hence, The vertex of the parabolic equation y = x² - 8x + 7 will be at
(4, -9).
So, The graph is given below.
More about the equation of the parabola link is given below.
brainly.com/question/20333425
#SPJ2
Which of the following fractions is not equivalent to 2? 3/6 10/5 2/1 1 4/4
Answer:
3/6 is the correct answer
dose anybody know the answer?
Answer:
they want a fomula that is in respect to 'b" sooo..
Step-by-step explanation:
just do the algebra.... like so..
a/b=c
move 'b" across = sign by multiplying by 1/b like soo.
(1/b)*(a/b)= (1/b)*c
a=c/b
then move the 'c' to the other side of the = sign by multiplying by 1/c
(1/c)*a = (1/c)*(c/b)
a/c = b
makes sense , also.. as a way to speed that up.. just remember you can just swap the 'b' and 'c' in that first equation
b = a/c