Answer:
a= -7
Step-by-step explanation:
I hope this helps! :)
The polynomial x^4+px^3+qx^2+rx+6 is exactly divisible by each of (x-1), (x-2) and (x-3).
Find the values of p, q and r.
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
Alfred and Larissa have $21.00 each to spend at a book fair, where all students receive a 35% discount. They both want to purchase a copy of the same book, which normally sells for $28.50 plus 10% sales tax. To check if he has enough to purchase the book, Alfred takes 35% of $28.50 and subtracts that amount from the normal price. He takes 10% of the discounted selling price and adds it back to find the purchase amount. Larissa takes 65% of the normal purchase price and then computes 110% of the reduced price. Is Alfred correct? Is Larissa correct? Do they have enough money to purchase the book? Explain your answer using complete sentences and show your work.
Answer: See explanation
Step-by-step explanation:
The normal cost of the book plus the sales tax will be:
= $28.50 + ($28.50 × 10%)
= $28.50 + ($28.50 × 0.1)
= $28.50 + $2.85
= $31.35
Since there's a discount of 35%, the amount they'll have to pay will be:
= $31.35 - ($31.35 × 35%)
= $31.35 - ($31.35 × 0.35)
= $31.35 - $10.9725
= $20.3775
They do not have enough money to make the purchase.
Alfred takes 35% of $28.50 and subtracts that amount from the normal price. Alfred's calculation is shown below:
= $28.50 - (35% of $28.50)
= $28.50 - (0.35 × $28.50)
= $28.50 - $9.975
= $18.525
He takes 10% of the discounted selling price and adds it back to find the purchase amount. This will be:
= $18.525 + (10% × $18.525)
= $18.525 + $1.8525
= $20.3775
Alfred is correct
Larissa takes 65% of the normal purchase price and then computes 110% of the reduced price. This will be:
= 65% × $28.50
= 0.65 × $28.50
= $18.525
= 110% × $18.525
= 1.1 × $18.525
= $20.3775
Larisa is also correct
ANSWER PLS!!
What is the answer
Answer:
C is the correct answer.(Plus I remember this question)find the interest earned on 45,000 at 14% for 8 years
Answer:
$128366.39
Step-by-step explanation:
We will use the Simplified Compound Interest Equation:
P = C(1 + r)^t
P = 45000(1+0.14)^8
P = 45000(1.14)^8
P = 128366.389
So about $128366.39
Answer:
simple
Step-by-step explanation:
45000×14×8/100
5040000/100
=50400
SOMEONE HELP PLEASE ASAP
Answer:
The last one: Decreasing then increasing
Step-by-step explanation:
Answer:
d?
Step-by-step explanation:
BRAINIST & 20 POINTS
*random answers will be reported*
Answer:
6-1
Step-by-step explanation:
Using the elimination method and showing all of your steps. Solve the following System of Equations. Make sure to write your answer as an order pair.
`-3x-4y=2`
`3x+3y=-3`
Answer:
ummm......i need more details.
Step-by-step explanation:
Please help
Have a merry Christmas
Answer:
32 :)
Step-by-step explanation:
1.
Which equation is true when m = 12?
Answer:
are there any more details? cant solve anything from what you have provided
Step-by-step explanation:
A share is sold for the market value of ₹1000. Is the face value of share is ₹100 and brokerage is paid at the rate of 0.1%what is the amount received of the Sale?
hope this will help you
Use the graph that shows the solution to f(x) = g(x).
f(x) = -(x + 2)(x - 2)
8(x) = 2x + 21
fx)
What is the solution to f(x) = g(x)?
1
3
Select each correct answer
-2
0
2
3
2
3
-32
Consequently, the graph is correct; and the x values for the solutions are x = -2 and x = 0.
What is the solution to f(x) = g(x)?The solution to f(x) = g(x) is the value(s) of x that satisfy the equation. In other words, it is the value(s) of x that make f(x) equal to g(x).
The only problem here is determining which graph is correct:
f(x) is the same on both graphs;
g(x) = 2 |x + 2| is the absolute value graph of lxl stretched vertically two units to the left;
the "vertex" of lxl is (0, 0);
consequently, the first graph is correct; and the x values for the solutions are x = -2 and x = 0.
To know more about graph, visit:
https://brainly.com/question/11803331
#SPJ1
Joel needs 785 tickets to get the prize he wants at the arcade. He already has 284 tickets and can earn 35 tickets each time he plays an arcade game. How many games will he have to play in order to have enough tickets to win the prize he wants?
He needs to play 23 more times. 785 / 35 = 23
He will have extra points but it will be enough to get the prize.
Which ordered pair is a solution to the equation 8x - 2y = 4?
Question 1 options:
(0, -1)
(1, 3)
(2, 6)
(3, 4)
Answer:
i think 0,1
Step-by-step explanation:
bc iit goes like that lol
Debora plans to sew 3 blankets for each of her nieces.
How many blankets will Debora sew if she has 5 nieces?
Answer:
well for me I think it's
Step-by-step explanation:
15
5×3 each
Answer:
15 blankets
Step-by-step explanation:
Debora plans to sew 3 blankets for each of her nieces. If she has 5 nieces, that means she will sew 3 blankets for each of them.
Number of blankets Debora sews = 3 blankets × 5 nieces
= 15 blankets
Therefore, Debora will sew 15 blankets in total.
I hope this helps!
Length of a rectangle swimming pool is 50 yards and the width of the pool is 60 yards what is the approximate length of the diagonal of pool
Answer:
Approximately 78 yards
Step-by-step explanation:
From the question, I was able to deduce that the swimming pool is a cuboid because the length and width step different in yards. After sketching a cuboid, length= 60 yards, width= 50 yards, then draw a diagonal across the upper rectangle of the cuboid, to get the diagonal, use Pythagoras theorem, Hypotenuse²= opposite²+adjacent²;. x²=60²+50²=3600+2500=6100 ;.
x²=6100 therefore X=√6100 =78.1024 yards, but approximately 78yards, since the question instructed that answer should be approximated.
192/38 with remanders
Answer:
5 Remainder 2
Answer:
The answer is 5 remainder 2
Step-by-step explanation:
Pets R Us claims in their advertisement that they have the best price in town for ChowChow dog food. They sell 20-pound bags for s1695. Stuffapets also claims to have the best price in town for
ChowChow dog food. They are selling 30-pound bags for $24.95. Which store has a valid claim?
Pets R Us: 20-
pound bags for
$16.95
Stuff4Pets: 30-
pound bags for
$24.95
Answer:
stuff4pets has better price by 2 cents
Step-by-step explanation:
unit rate for chowchow is 16.95/20 = $.85 per pound
unit rate for stuff4pets is 24.95/30 = $.83 per pound
Answer:
Stuff4pet has a valid claim
I am very sure
Step-by-step explanation:
Haley is printing admission tickets for the school dance. So far, she has printed 112 tickets. She knows that she needs to print 320 tickets in total. What percent of the tickets does Haley still have to print?
Answer:
Answer:
Haley needs to print 65% of the tickets.
Step-by-step explanation:
Given that:
Tickets printed by Haley = 112
Tickets needed to print = 320
Tickets left to print = 320-112 = 208
Percent of tickets left to print =
Percent of tickets left to print =
Percent of tickets left to print = 0.65*100
Percent of tickets left to print = 65%
Hence,
Haley needs to print 65% of the tickets.
Step-by-step explanation:
Answer:
Step-by-step explanation:
Haley needs to print:
320-112=208 tickets
1% of 320 is equal to 320/100=3.2
208/3.2=65
She needs to print 65% more tickets
Jorge has a Total of 67 coins. All of which are dimes and nickels. The total value of the dimes and nickels i $5.40. Find the number of each type of coin.
Answer:
There are 41 dimes and 26 nickels.
Step-by-step explanation:
From the information given, you know that you have 67 coins which would be:
x+y=67
Also, you now that the value of each coin is:
dimes= $0.10
nickels=$0.05
With this you can say that the number of dimes for its value plus the number of nickels for its value is equal to $5.40:
0.10x+0.05y=5.40
You will have the following equations:
x+y=67 (1)
0.10x+0.05y=5.40 (2), where:
x are the number of dimes
y are the number of nickels
First, you can solve for x in (1):
x=67-y
Then, you can replace (3) in (2):
0.10(67-y)+0.05y=5.40
6.7-0.10y+0.05y=5.40
1.3=0.05y
y=1.3/0.05
y=26
Now, you can replace the value of y in (3) to find x:
x=67-y
x=67-26
x=41
According to this, the answer is that there are 41 dimes and 26 nickels.
Use the Quotient Rule to find the UNSIMPLIFIED version of the derivative. R(w)=3w+w^4/ 2w^2+1.
Pls show work!!!
From your previous questions, you know
(3w + w⁴)' = 3 + 4w³
(2w² + 1)' = 4w
So by the quotient rule,
R'(w) = [ (2w² + 1)•(3w + w⁴)' - (3w + w⁴)•(2w² + 1)' ] / (2w² + 1)²
That is, the quotient rule gives
R'(w) = [ (denominator)•(derivative of numerator) - (numerator)•(derivative of denominator) ] / (denominator)²
I'm not entirely sure what is meant by "unsimplified". Technically, you could stop here. But since you already know the component derivatives, might as well put them to use:
R'(w) = [ (2w² + 1)•(3 + 4w³) - (3w + w⁴)•(4w) ] / (2w² + 1)²
need help please, will give Brainly
Answer:
evaluate C2 + 4a - b
-2 +4(-5)-3
4=-2-5-3
4=4
=4-4
=0
I'll give brainliest to the right answer! I need help ASAP!
Answer:
answer: y= 1^2+ -8 I think I did this right.
Answer:
y=-1/2x-8
Step-by-step explanation:
I NEED HELP PLS!
Part A: Explain why the x-coordinates of the points where the graphs of the equations y = 4x and y = 2x−1 intersect are the solutions of the equation 4x = 2x−1. (4 points)
Part B: Make tables to find the solution to 4x = 2x−1. Take the integer values of x between −4 and 4. (4 points)
Part C: How can you solve the equation 4x = 2x−1 graphically? (2 points)
(10 points)
Answer:
es a través de los ejes x si lo cuenta, puede ver lo que es en su cuadrícula y encontrará la respuesta exacta
Pleaseeee helpppp !!!!!! Will mark Brianliest !!!!!!!!!!!!!!
Answer:
8
Step-by-step explanation:
AC=2DE
48-4x=2(64-7x)=128-14x
14x-4x=128-48
10x=80
x=80/10=8
DE=64-7x=64-7*8=64-56=8
Help me i can’t do this
Answer:
[tex]\huge\boxed{\sf Star = 14}[/tex]
Step-by-step explanation:
Let snowman be x , star be y and shopping bag be z.
So, the given equations are:
1) x + y = 20 (Eq. 1)
2) z = x + x
z = 2x (Eq. 2)
3) z + x = 18 (Eq. 3)
Put Eq. (2) in Eq. (3)
2x + x = 18
3x = 18
Divide both sides by 3
x = 18 / 3
x = snowman = 6
Now, Put x in (Eq. 1)
6 + y = 20
Subtract 6 to both sides
y = 20 - 6
y = 14
So,
Star = 14
[tex]\rule[225]{225}{2}[/tex]
Hope this helped!
~AH1807In a heard of x cattle, the ratio of the number of bulls to cows is 1:6. Find the number of bulls in the herd in terms of x.
Answer:1/6*x
Step-by-step explanation:
Answer:
1/6=x
Step-by-step explanation:
How can we use ratios and proportional relationships to help us in our daily lives?
Answer:
In cooking (recipes).
Step-by-step explanation:
If the serving size for a recipe is not adequate for the number of people you are serving, you will have to convert the amounts(measurements) of the ingredients to suit your needs. You will do this by first creating a ratio defining the relationship between the serving size of the given recipe to the number of people needed to be served. For example, if a recipe serves 4 people, and you need to serve 8, your ratio would simplify to 1/2. This means you must proportionally relate this ratio to the individual amounts of each ingredient.
Use the following information to answer Part A Part B
*2 Systems of Equations
John wants to join a gym so that he can work out during the evenings. There are two gyms in his town that he is considering. Extreme
Fitness charges a $50 Signup fee and then $10 per month. Ultimate Fitness charges a $30 initiation fee and then $15 per month. Extreme
Fitness is closer to John's home and has more equipment than Ultimate Fitness. Find the number of months where the cost of the membership will be the same for both gyms
Answer:
can some one please answer it please
Step-by-step explanation:
Help me with this pls :')
Mary wants to fill in a cylinder vase. At the flower store they told her that the vase should be filled 2/3 for the flowers to last the longest. Her cylinder vase has a radius of 3 in and a height of 8 in. Using the equation below, how much water should Mary pour into the vase?
The volume of a cylinder with height h and radius r is given by the formula:
V = πr²h
Answer:
150.796 in³ of water
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Geometry
Volume of a Cylinder: V = πr²hStep-by-step explanation:
Step 1: Define
Radius r = 3 in
Height h = 8 in
Step 2: Find Volume V
Substitute [VC]: V = π(3 in)²(8 in)Exponents: V = π(9 in²)(8 in)Multiply: V = 72π in³Multiply: V = 226.195 in³Step 3: Find Water
2/3 of vase should be filled with H₂O.
Set up: 2/3(72π in³)Multiply: 48π in³Evaluate: 150.796 in³Answer:
We know the formula for the volume of a cylinder is V=πr^2has given.
That said, we can plug our values in.
V=π3^2(8)
Simplify.
V=π9*8
V=72π
It needs 72π cubic inches of water.
This is also equivalent to around 226.19 cubic inches of water.
Step-by-step explanation:
hope this helps
The table shows the number of wins and losses for four hockey teams.
Which two teams have the same ratio of wins to losses?
(pls help!)
Lightning and Thunder
Wolves and Eagles
Thunder and Wolves
Eagles and Lightning
Answer:
Thunder and Wolves
Step-by-step explanation:
If its right can I get Brainllest? Please