The remainder theorem says that a polynomial f(x) has a remainder of f(c) upon getting divided by x - c. So if
f(x) = x⁴ + p x³ + q x² + r x + 6
is divisible by x - 1, x - 2, and x - 3, then we have
f (1) = 7 + p + q + r = 0
f (2) = 22 + 8p + 4q + 2r = 0
f (3) = 87 + 27p + 9q + 3r = 0
Solve the system for p, q, r. You can eliminate r by substituting the first equation into the other two:
p + q + r = -7
8p + 4q + 2r = -22 → 6p + 2q - 14 = -22 → 3p + q = -4
27p + 9q + 3r = -87 → 24p + 6q - 21 = -87 → 4p + q = -11
Eliminate q by adding (-1) times the first equation to the second one, then solve for p :
- (3p + q) + (4p + q) = - (-4) + (-11)
-3p - q + 4p + q = 4 - 11
p = -7
Solve for q :
3p + q = -4 → 3 (-7) + q = -4 → q = 17
Solve for r :
p + q + r = -7 → -7 + 17 + r = -7 → r = -17
Si sen A = 7/25 donde "A" pertenece al segundo cuadrante y el cos B = -4/5 donde "B" pertenece al segundo cuadrante Calcular cosec(A).cos(B).tan(A).cot(B)
Which describes the correct way to convert minutes to hours?
Divide the number of minutes by 24.
Multiply the number of minutes by 24.
Divide the number of minutes by 60.
Multiply the number of minutes by 60.
Answer:
Divide the number of minutes by 60.
Step-by-step explanation:
What is the slope of the line?
Answer:
-1
Step-by-step explanation:
Remember, slope is rise/run
Start from a point on the line and count up and over until you reach another point on the line.
For example, start from (0,-2), count up and left until you get to (-2,0). This gets you 2/2, which reduces to 1.
Since the line represents a negative slope, the slope is -1.
Find the inverse of Y=2x-6
Answer:
Step-by-step explanation:
f^-1(x)=x/2+3
hey guys please answer if you know
Answer:
19
Step-by-step explanation:
note that
(a + b)² = a² + b² + 2ab , that is
a² + b² + 2ab = (a + b)² ← subtract 2ab from both sides
a² + b² = (a + b)² - 2ab
= 5² - 2(3)
= 25 - 6
= 19
Answer:
19
Step-by-step explanation:
since value of both a+b and a*b are given
formula for a^2 + b^2 is (a+b)^2-2*a*b
Substituting those value,
a^2+b^2=5^2-2*3
i.e. 25-6
=19
Pls pick one option to help me out
option is c=2/3
2/3+ 1/7 = 17/21
Which figure has line symmetry?
O A.
F
O B.
H
O C.
J
O D.
L
O E.
R
Answer:
??????
Step-by-step explanation:
Answer:
???
Step-by-step explanation:
Collect like terms
2y - y
Answer:
The answer is y
Step-by-step explanation:
2y−y
=2y−1y
=2y+−1y
=y+y+−y
=y
Solve this equation.
Y/4-4=5 y=
Answer:
16/19
Step-by-step explanation:
The scale of a map is 1 clear : 13 km. Find the actual distance corresponding to the map distance. The distance on the map is 4.5 cm The actual distance is ___ km
Answer: The actual distance is 58.5 km.
Step-by-step explanation:
Given: Scale of map = 1 cm : 13 km
The distance on the map is 4.5 cm.
To find : The actual distance corresponding to the map distance.
The actual distance corresponding to the map distance =
( distance on the map) x ([tex]\dfrac{13}{1}[/tex])
[tex]=4.5\times13\\\\=58.5\ km[/tex]
Therefore , the actual distance is 58.5 km.
if you eat 4 medium strawberries you get 48% of your daily recommended amount of vitamin c what fraction of your daily amount of vitamin c do you still need
multiplicaiton problem where both factors are fractions and the product is less than the factors ANSWER NOW PLEASE
Answer:
There is no question attached.
Step-by-step explanation:
Answer:
1/5 * 1/2 = 1/10
Step-by-step explanation:
Choose any two factor fractions less than 1. The result (product) will be necessarily smaller than each of the factors. Above answer is an example
1/5 * 1/2 = 1/10, where it is clear that
1/10 < 1/5 and
1/10 < 1/2
Gianna has 20 cookies in a bag. 20% of the cookies are vanilla. How many cookies are vanilla?
Answer:
4 cookies are vanilla
Step-by-step explanation:
because 20% is technically 1/5th of 100% we need to divide 20 by 5
20/5 = 4
Round 9 1/3 to the nearest whole number
Answer:
Nearest Whole Number: 9
Step-by-step explanation:
Answer:
im guessing it would just be 9
Step-by-step explanation:
because its 1 out of three so that leaves two so its closest to 9
somebody help.. im so lost!!
Hi I need to figure if this is a function?
Answer:
no it is not a function
Step-by-step explanation:
function- for every input there is only one output
(1,7),(2,13),(3,13) it has two 13 so it is not a function
Algebra - Two Questions
1. A system of linear equations is shown below as well as the first steps that Raffi is using to solve this system of linear equations by substitution. Choose the statement that best describes how Raffi is progressing toward a solution.
7x+y=4
3x−2y=3
Solution: Solve the first equation to obtain y=−7x+4. Substitute this into the second equation to get 3x−2⋅−7x+4=3.
2. Solve the following system by the substitution method.
2x−y=−4
−5x+3y=14
Answer:
The answer is below
Step-by-step explanation:
1) Below are the linear equations.
7x+y=4 (1)
3x−2y=3 (2)
The above linear equations are a system of equations. The substitution method is a technique for solving systems of linear equations.
Given that:
7x + y = 4
y = 4 - 7x
substitute y = 4 - 7x in equation 2, hence:
3x - 2(4 - 7x) = 3
3x - 8 + 14x = 3
17x = 3 + 8
17x = 11
x = 11/17
Put x = 11/17 in y = 4 - 7x
y = 4 - 7(11/17)
y = -9/17
2) 2x−y=−4 (1)
−5x+3y=14 (2)
From equation 1:
2x−y=−4
y = 2x + 4
Put y = 2x + 4 in equation 2:
-5x + 3(2x + 4) = 14
-5x + 6x + 12 = 14
x + 12 = 14
x = 2
Put x = 2 in y = 2x + 4:
y = 2(2) + 4
y = 8
Answer:
1. Raffi forgot to place the substituted expression in parentheses.
2. (2, 8)
Step-by-step explanation:
If you are taking the Solving Systems With Substitution Quick Check from Connexus here are all of the answers:
1. Solve one linear function in terms of one of its variables.
2. Substitute 3y from the second equation for x in the first equation.
3. Raffi forgot to place the substituted expression in parentheses.
4. Yes, because substituting the given ordered pair yields two true expressions.
5. (2, 8)
What is absolute value?
The distance a number is from O on a number
line.
The Additive Inverse Property
The opposite of a number
Answer:
the distance a number did from 0 onna number line
Solve this system of linear equations. Separate
the x- and y-values with a comma.
16x = 84 - 2y
14x = 72 - 2y
Answer:
6x = 84 - 2y
14x = 72 - 2y
Step-by-step explanation:
Which is equal to 7√3 ?
7^3
21
(13)^7
7 1/3
Step-by-step explanation:
D is the correct answer of this question ....
which expression can be used to determine the slope of the line that passes through the points (-7,3) and (1, -9)?
1. 1-(-7)/-9-3
2. 1+(-7)/-9+3
3. -9-3/1-(-7)
4. -9+3/1+(-7)
Answer:
-9-3/1--7
Step-by-step explanation:
gradient (m) =-9-3/1--7
m =-12/8
150% of 150 is what number? (15 points I think?)
225 percent
Step-by-step explanation:
150 is the whole and 150 divided by 150 is 1.
1 whole is 100 percent
Answer:
225 will be correct
Step-by-step explanation:
Mrs. Williams combined 3 ½ cups of peat moss, 5 ¼ cups of compost , and 6 ¾ cups of fertilizer to make plant food for her roses. She evenly distributed the plant food among 4 rose bushes. How many cups of plant food were used for each rose bush?
Answer:
3 7/8 cups plants food
Step-by-step explanation:
peat moss = 3 ½ cups
compost = 5 ¼ cups
fertilizer = 6 ¾ cups
Total mixture = peat moss + compost + fertilizer
= 3 ½ cups + 5 ¼ cups + 6 ¾ cups
= 7/2 + 21/4 + 27/4
= 14+21+27/4
= 62/4
Total mixture = 62/4 cups
She evenly distributed the plant food among 4 rose bushes
Each rose bush uses = Total mixture / number of rose bushes
= 62/4 ÷ 4
= 62/4 × 1/4
= 62/16
= 3 14/16
= 3 7/8 cups plants food
Each rose bush uses = 3 7/8 cups of plants food
A new health drink has 150% of the recommended daily allowance (RDA) for a certain vitamin. The RDA for this vitamin is 50 mg. How many milligrams of the vitamin are in the drink? There are nothing mg of the vitamin in the drink.
Answer:
the number of milligrams of the vitamin in the drink is 75 mg
Step-by-step explanation:
The computation of the number of milligrams of the vitamin in the drink is as follows:
= RDA of the vitamin × given percentage ÷ percentage
= 50 mg × 150 ÷ 100
= 75 mg
hence, the number of milligrams of the vitamin in the drink is 75 mg
We simply applied the above formula so that the correct value could come
And, the same is to be considered
Best answer gets brainliest hurry ASAP
Answer:
its b
Step-by-step explanation:
mark as brainliest plz im right
Answer:
b
Step-by-step explanation:
the ratio answer is b.
If it takes 9 3/4 yards of material to make curtains for 3 windows, how much material is needed?
Answer:
3.25 yards of materials will be needed for 1 window
Answer:
3 1/4 (Verified) ✅Step-by-step explanation:
This is a rate problem, so we will write rate as a proportion and write the desired rate with x for the unknown value we need to find.
9.75/3 = x/1
Cross-mulitply
3x = 9.75
Divide by 3
x = 3.25 or 3 1/4
Another great thing with proportions is that we can check them to ensure we got the correct answer. All we do is substitute our determined value in for x
9.75/3 = 3.25/1
9.75 = 9.75 ✅
The answer of x = 3 1/4 is correct.
Find me the point please
Answer:
(-2,-3)
Step-by-step explanation:
What is the percent Of decrease from 50 to 21
Please anwser accurate and I give brailiest
Answer:
29%
Step-by-step explanation:
To find the decrease from 50 to 21 you would subtract 50 - 21. You get 29. This is the same as 29/100. 29/100 is also 0.29 or 29%.
Hope it helps! (I'm so sorry if it's incorrect).
Answer:
57.9% please give me brainliest i used a percentage calculator :)))
Step-by-step explanation:
i. After how many weeks will Jennifer and William have the same amount of money in their bank accounts?
ii. How much will be in their accounts?
Answer:
5 weeks$100Step-by-step explanation:
Part iJennifer's account:
f(x) = 10x + 50William's account can be expressed as:
g(x) = 14x + 30Because the rate of change is 14 and y-intercept is 30
They will be same after x years, f(x) = g(x)
10x + 50 = 14x + 3014x - 10x = 50 - 304x = 20x = 5The accounts will be same after 5 weeks
Part iiThe amount in the accounts after 5 weeks:
f(5) = g(5) = 10*5 + 50 = $100Answer:
5 weeks
Step-by-step explanation:
Find the equation of willam's account:
1. find rate x1-x2
44-30 plug in
14 =rate 30=y-intercept starting valuse is always intercept
44+14=58 check
f(x)= 10x+50
f(x)= 14x+30 solve
10x+50=14x+30 set values together
20=4x subtract 10x and 30 from both sides
x=5
If anyone knows the answer please help!