According to Remainder Theorem for the polynomials, for every polynomial P(x) there exist such polynomials G(x) and R(x), that [tex] P(x)=(x\pm a)G(x)+R(x) [/tex].
When the polynomial in P(x) is divided by (x + a), then there exist such polynomials G(x) and R(x), that P(x)=(x+a)G(x)+R(x). Note that for x=-a:
Answer:
false
Step-by-step explanation:
What is the next number in the sequence?
1,4,13,40,121,...
6 2/3 greater than 6 12/15
My rectangular cabbage patch has a total area of 110 sq. ft. Find its perimeter in terms of the width x ...?
How do I compete the two-way table for #4
Johann maintains a$75,000 insurance policy on his boat. He pays $50 per month in premium and his deductible is $2,500 if he is involved in a accident and make a claim of 15,000 on the policy, how much will his insurance company pay ?
A. $2,500
B.$12,500
C.$15,000
D.$17,500
Answer:
B) 12,500
Step-by-step explanation:
Just took the quiz :)
18 + x > 40
a. x > 58
b. x > 22
c. x > -58
d. x > -22
Ariane gets paid $0.50 for the first 100 craft kits that she assembles. She earns $0.75 for each kit over 100. This week she assembled 135 kits. How much did she earn?
A. $67.50
B. $72.50
C. $76.25
D. $101.25
Final answer:
Ariane earned $50 for the first 100 kits at $0.50 per kit, and for the additional 35 kits at $0.75 per kit, she earned $26.25. Adding these amounts, her total earnings are $76.25.
Explanation:
To calculate Ariane's earnings for assembling 135 craft kits, we need to consider two different pay rates: one rate for the first 100 kits and a higher rate for each kit above 100.
For the first 100 kits, she earns $0.50 per kit, which is 100 kits × $0.50/kit = $50. For the remaining 35 kits (135 total - 100), she earns a higher rate of $0.75 per kit, which is 35 kits × $0.75/kit = $26.25.
Now, we add both amounts to find the total earnings:
$50 (first 100 kits) + $26.25 (kits over 100) = $76.25 total earnings
Thus, Ariane earned $76.25 for assembling 135 craft kits this week.
For which values of x and y is line p parallel to line q?
X=5,y=3
x=1, y=5
x=3, y=5
x=3, y=6
Step 1
Find the value of x
we know that
If lines p and q are parallel
then
[tex](45x-5)+(16x+2)=180\°[/tex] ------> by consecutive interior angles
Solve for x
[tex](45x-5)+(16x+2)=180\° \\61x=180+3 \\x=3\°[/tex]
Step 2
Find the value of y
we know that
If lines p and q are parallel
then
[tex](26y)=(45x-5)[/tex] ------> by corresponding angles
substitute the value of x and solve for y
[tex](26y)=(45*3-5)[/tex]
[tex](26y)=130[/tex]
[tex]y=5\°[/tex]
therefore
the answer is the option
[tex]x=3\°[/tex] , [tex]y=5\°[/tex]
A package of baseball cards includes 5 cards how many baseball cards are in 6 packages
Convert 2/5 to a percent
2/5 to a percent would be 40%.
The work is attached in the image provided.
Does a translation produce congruent figures?
What is 4 and 1/2 as a percent??
Loren puts £600 in a bank account.
The account pays 3% compound interest each year after ONE year she withdraws £200.
How much will she have in the account after 2 years?
To solve the problem we will first calculate the remaining balance in Loren's Account after a year.
The balance in Loren's account after two years is £430.54.
Given to us
Loren puts £600 in a bank account,the account pays 3% compound interest each year,after ONE year Loren withdraws £200Principal Amount that Loren put in her account, P = £600Rate of interest that bank pays, r = 3% = 0.03Balance of Loren after one yearUsing the compound interest formula,
Balance of Loren after one year = [tex]P(1+r)^t[/tex]
Substituting values,
[tex]=600(1+0.03)^1\\= 600(1.03)\\= 618[/tex]
Remaining Balance of Loren after one yearNow, as Loren takes £200 out of the account, the remaining balance would be,
= Balance of Loren after one year - £200
= £618 - £200
= £418
Balance in Loren's account after two yearsIn the second year, the balance will be paid on the remaining balance, therefore, applying the formula of compound interest,
P = £418
r = 0.03
t = 1
[tex]=P(1+r)^t\\=418(1+0.03)^1\\=418(1.03)\\= 430.54[/tex]
Hence, the balance in Loren's account after two years is £430.54.
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Line AB contains points A (8, −4) and B (1, −5). The slope of line AB is....
Answer:
[tex] The\ slope\ of\ the\ line\ AB\ is \frac{1}{7} .[/tex]
Step-by-step explanation:
Formula for slope
[tex]m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}[/tex]
As the Line AB contains points A (8, −4) and B (1, −5).
Put points value in the above
[tex]m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}[/tex]
[tex]m = \frac{- 5- (-4)}{1 - 8}[/tex]
[tex]m = \frac{- 5 + 4}{1 - 8}[/tex]
[tex]m = \frac{- 1}{-7}[/tex]
[tex]m = \frac{1}{7}[/tex]
[tex]Therefore\ the\ slope\ of\ the\ line\ AB\ is \frac{1}{7} .[/tex]
What is the LCM of 24a^3 b and 36ab^2?
12ab
24a 3b^2
36ab
72a 3b^2
Answer:
12ab
Step-by-step explanation:
i got a 100%
Two accounts earn simple interest. The balance y (in dollars) of Account A after x years can be modeled by y=10x 500. Account B starts with $400 and earns 5% simple annual interest.
Question I need help with: Which account has a greater principal, and how much greater is the principal? Which account has a greater annual interest rate, and how much greater is the annual interest weight?
After k payments, the amount A still owed is
A = P(1+[i/q])k - Mq([1+(i/q)]k-1)/i, = (P-Mq/i)(1+[i/q])k + Mq/i. The amount of the fixed payment is determined byM = Pi/[q(1-[1+(i/q)]-nq)]. The amount of principal that can be paid off in n years isP = M(1-[1+(i/q)]-nq)q/i. The number of years needed to pay off the loan isn = -log(1-[Pi/(Mq)])/(q log[1+(i/q)]). The total amount paid by the borrower is Mnq, and the total amount of interest paid isI = Mnq - P.Let f(x) = -4x + 7 and g(x) = 2x - 6. Find (f.g)(1)
Answer:
The answer would be 23
Step-by-step explanation:
I think this is a composite function, so it would be
f(g(1))
you must first replace all the "x" in f(x) with g(x)
f(g(x) = -4(g(x))+7
f(g(x)) = -4(2x-6)+7
f(g(x)) = -8x+24+7
f(g(x)) = -8x+31
If x=1
f(g(1)) = -8*1+31
f(g(1)) = -8+31
f(g(1)) = 23
In the diagram below, what is the relationship between the number of parallelograms and the perimeter of the figure they form?
The relationship is as you join more parallelograms together, the base length increases, and thus, the perimeter of the figure formed by these parallelograms also increases.
What happens to the parallogram ?The perimeter of each individual parallelogram can be calculated using the formula for the perimeter of a parallelogram:
P = 2(base + side)
P = 2(5 + 4) = 2(9)
= 18 units
The second parallelogram has a base of 10 units and a side length of 4 units. The perimeter of the second parallelogram is:
P = 2(10 + 4) = 2(14)
= 28 units
The perimeter of the third parallelogram is:
= P = 2(15 + 4) = 2(19)
= 38 units
The relationship is such that the perimeter is directly proportional to the number of parallelograms joined together, with each additional parallelogram adding 10 units to the base length and subsequently increasing the perimeter by 20 units.
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A sector of a circle is shown. Find its area, rounded to the nearest tenth.
a)9.8 cm^2
b)10.5 cm^2
c)11.2 cm^2
d)12.3 cm^2 ...?
The area of the sector of the circle whose radius is 4.2 cm while the angle made at the center is 68° is 10.5 cm².
What is a circle?A circle can be defined as a shape that consists of all points in a plane that are at equal distance from a given point, therefore, the center.
As it is given that the length of the radius of the circle is 4.2 cm, while the angle made by the sector at the center of the circle is 68°. Therefore, the area of the sector of the circle can be written as,
[tex]\text{Area of the sector of the circle} = \pi r^2\times \dfrac{\theta}{360^o}[/tex]
Substituting the value, we will get,
[tex]\text{Area of the sector of the circle} = \pi \times(4.2^2)\times \dfrac{68^o}{360^o}[/tex]
[tex]= 10.472 \approx 10.5\rm\ cm^2[/tex]
Hence, the area of the sector of the circle whose radius is 4.2 cm while the angle made at the center is 68° is 10.5 cm².
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Multistep sandy charges each family that she babysits a flat fee of $10 for the night and an extra $5 per child.kimmi charges $25 per night no matter how many children a family has write a equation that compare the two girls also is the fees are the same how many children a family have to have in order to be the same
Roland Corporation buys stoves from a wholesaler. The list price of a stove is $900, with a trade discount of 30 percent. The net price is: ...?
100% - 30% = 70%
P = 0.7*900
which equals $630
Answer:
The net price of the stove is $630.
Step-by-step explanation:
The list price of a stove = $900
Trade discount on the price = 30%
The net price = 900 - (30% of 900)
= 900 - ([tex]\frac{30}{100}[/tex] × 900)
= 900 - (0.30 × 900)
= 900 - 270
= $630
The net price of the stove is $630.
0x6+12 divided by 3-1 answer
A father is 1 year older than 3 times the age of his son. The son is 20 years old.
Let F = the age of the father.
Which formula would calculate the father's age?
1. F=3(20-1)
2. F + 1 = 3(20)
3. F - 1 = 3(20)
Factor: 4x^2-12x+9=0
Rearrange the formula C = 2πr for r.
Answer:
[tex]\frac{C}{2\pi }=r[/tex]
Step-by-step explanation:
[tex]C=2\pi r[/tex]
WE need to solve for 'r'. Our aim is to get 'r' alone
2πr mean 2 times pi times r
To remove 2π we do opposite operation
Opposite operation of multiplication is division.
To remove 2π , divide both sides by 2π
[tex]\frac{C}{2\pi }=\frac{2\pi r}{2\pi}[/tex]
Now simplify it
[tex]\frac{C}{2\pi }=r[/tex]
Which of the following could be an example of a function with a range (-∞,a] and a domain [b, ∞) where a < 0 and b < 0?
A. ƒ(x)= √(x-a)+b
B. ƒ(x)=3√(x-b)+a
C. ƒ(x)=-3√(x+a)-b
D. ƒ(x)=-√(x+b)-a ...?
The correct answer is D. ƒ(x)=-√(x+b)-a. This function satisfies the range and domain conditions stated in the question.
Explanation:The correct answer is D. ƒ(x)=-√(x+b)-a.
A function with a range of (-∞, a] means that the output values of the function are less than or equal to a. In option D, the function is defined as ƒ(x)=-√(x+b)-a, where a < 0 and b < 0. When we substitute negative values for x in this function, the output values will be less than or equal to a, satisfying the range condition. Similarly, when x tends to positive infinity, b becomes negligible, and the function approaches -∞. This satisfies the domain condition [b, ∞).
Therefore, option D is a possible example of a function with the given range and domain conditions.
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rachel bought 1 3/5 pounds of peaches for $.60 and 3 1/2 pounds of apples for $1.75. which fruit costs more per pound ? explain how you know
the volume of a rectangular prism is 72 cubic centimeters the prism is 2 centimeters wide and 4 centimeters high what is the length of the prism
Frank had $25 in his checking account he withdrew $15 cash and $9 to pay his bill what is the expression
A family of four goes to a salon for haircuts the cost of each haircut is $13 use distributive property to find the product 4*13 for the total cost