The answer is c.
If you have a root (a), it can also be written as (x-a).
(x+6),(x-1),(x-4)
Multiply all of them together to get the equation
(x+6)(x-1)(x-4)=
(x2-x+6x-6)(x-4)=
(x2+5x-6)(x-4)=
(x3+5x2-6x-4x2-20x+24)=
x3+x2-26x+24
To find a polynomial with given roots −6, 1, and 4, we create factors (x + 6), (x - 1), and (x - 4). Multiplying these factors, we get the polynomial x3 - 5x2 - 21x + 24.
Finding the Polynomial with Given Roots
To find a polynomial with roots of −6, 1, and 4, we need to create factors that each set to zero at these roots. A polynomial is a product of its factors, and a root is a solution to the equation where the polynomial is equal to zero. The factors corresponding to the roots −6, 1, and 4 are (x + 6), (x - 1), and (x - 4) respectively. Multiplying these factors gives us the polynomial:
(x + 6)(x - 1)(x - 4) = x3 - (1 + 4)x2 + (4 - 1 - 24)x + (6 x 1 x 4)
Let's expand and simplify:
x3 - 5x2 - 21x + 24
Therefore, the polynomial with roots of
−6, 1, and 4 is x3 - 5x2 - 21x + 24.
Suppose 18 gallons of water care out of a pipe in 6 minutes. What was the rate in gallons per minute?
A 9cm wife cross section pipe has a height of 13cm . What is the volume of the pipe
To find the volume of a pipe, use the formula V = Ah where A is the cross-sectional area and h is the height of the pipe. Substituting the values given, the volume of the pipe is 826.805 cm³.
The volume of the pipe can be calculated using the formula V = Ah, where A is the cross-sectional area and h is the height of the pipe. In this case, the cross-sectional area can be found using the formula for the area of a circle, A = πr². Given that the pipe has a diameter of 9 cm, the radius (r) is half of the diameter, which is 4.5 cm.
Substitute the values into the formulas to find the volume: A = π(4.5 cm)² = 3.142 x 20.25 cm² = 63.585 cm². Now, calculate the volume using V = 63.585 cm² x 13 cm = 826.805 cm³.
Solve the equation, justify each step with an algebraic property:
-8=-18+2x
Giving 30 points whoeve helpsssss me fasttttt. No wrong answers
a chef used 1/10 of a bag of potatoes to make 1/6 of a gallon of stew. if he wanted to make a full gallon of stew how many bags of potatoes would he need?
After the party, there was 0.5 of the pizza left. Angela ate 0.2 of the leftover pizza.
Angela said that she ate 0.01 of the whole pizza but Cal and Martha disagreed. Cal said it was 0.10 and Martha said it was 0.1
Mark all statements that are true.
True Not True
Angela is correct.
Cal is correct.
Martha is correct.
Nobody has the correct answer.
Multiply 6/5 x 25/24 ??
help word problem gross
The perimeter of this Hexagon is 162 cm. Each longer side measures 1 cm more than twice a shorter side. Find the length of the labled x.
The length of the shorter side [tex]\( x \)[/tex] is 20 cm.
The length of each shorter side labelled [tex]\( x \)[/tex] in the hexagon is 20 cm. Here's the step-wise calculation:
1. Let [tex]\( x \)[/tex] represent the length of the shorter side.
2. The length of each longer side is given as [tex]\( 1 \)[/tex] cm more than twice a shorter side, so it is [tex]\( 2x + 1 \)[/tex] cm.
3. The perimeter of the hexagon is the sum of the lengths of all its sides, which is given as [tex]\( 162 \)[/tex] cm.
4. Since the hexagon has four shorter sides and two longer sides, the perimeter [tex]\( P \)[/tex] can be expressed as:
[tex]\[ P = 4x + 2(2x + 1) \][/tex]
5. Plugging in the given perimeter value and simplifying the equation:
[tex]\[ 162 = 4x + 4x + 2 \][/tex]
[tex]\[ 162 = 8x + 2 \][/tex]
6. Solving for [tex]\( x \)[/tex] gives:
[tex]\[ 160 = 8x \][/tex]
[tex]\[ x = \frac{160}{8} \][/tex]
[tex]\[ x = 20 \][/tex]
Therefore, the length of the shorter side [tex]\( x \)[/tex] is 20 cm.
9 is 63% of what number
Pacey, Alex, and Paul went fishing. They each caught one fish. Alex’s weighed twice as much as Pacey’s fish. Paul’s weighed three times as much as Pacey’s fish. Total the 3 fish weighed 342lbs. How much did each boy’s fish weigh?
pacey = x
alex = 2x
paul = 3x
x + 2x + 3x = 342
6x =342
x = 342 / 6
x = 57
Pacey's fish = 57 pounds
Alex's fish = 57*2 = 114 pounds
Pauls fish = 57*3 = 171 pounds
An airplane flew 2,400 miles in 4 hours if the plane flew the same numbers of miles each hour how many miles did it fly in one hour
PLEASE HELP
x 1 2 3 5 6
y 0 1 2 4 5 Are the paired points in a proportional relationship?
Answer:
Hope this helps. ARE NOT
Step-by-step explanation:
Explain how to subtract 247 from 538
Answer:
After subtracting 247 from 538, we will get 291.
Step-by-step explanation:
We are asked to subtract 247 from 538.
Convert in a subtraction problem:
538
-247
Now, we will subtract each digit in the lower line from upper line as:
538
-247
291
Therefore, the answer to our given problem would be 291.
What is the value of the expression-2.1(4.7+(-7.4)
The table shows five transactions and the resulting account balance in a bank account, except some numbers are missing. Fill the missing numbers
Answer:
transaction 3 (account balance) = 143
transaction 4 (account balance) = -86
transaction 5 (transaction amount) = 86
Step-by-step explanation:
From the table it is seen that after transactions the account balance either increases or decreases.
Transaction 1
transaction amount was 200 while account balance became 200
Transaction 2
the initial startup balance will be = transaction amount + current account balance which is = 147 + 53 = 200 .
Note: the account balance of the previous transaction becomes the initial account balance of the next transaction
Transaction 3
account balance = initial account balance + transaction amount
= 53 + 90 = 143
Transaction 4
account balance = initial account balance + transaction amount
= 143 + ( - 229 ) = - 86
Transaction 5
transaction amount = account balance - initial account balance
= 0 - ( -86 ) = 86
The account balance after transaction 3 is 143
The account balance after transaction 4 is -86
Transaction amount of transaction 5 is 0
What does a debit and credit transaction mean?When money is withdrawn from an account, a debit transaction occurs, it is represented with a negative sign. When money is deposited from an account, a credit transaction occurs, it is represented with a positive sign.
What is the value of the missing numbers?
Account balance after transaction 3 = 53 + 90 = 143Account balance after transaction 4 = 143 - 229 = -86Transaction amount of transaction 5 = -86 + 86 = 0To learn more about addition, please check: https://brainly.com/question/19628082
a concrete stepping-stone measures 20 square inches. What is the area of 30 such stones?
1 stone is 20 square inches
multiply that by 30 for total
20 *30 = 600 square inches total
Please help me my 3rd grade teacher never though got me how to divide
Answer: 6: 300 7: 20 9: 300 10: 800 12: 800 13: 700 15: 700 16: 700
Step-by-step explanation: Step 1: D for Divide. How many times will 5 go into 65?
Step 2: M for Multiply. You multiply your answer from step 1 and your divisor: 1 x 5 = 5.
Step 3: S for Subtract. Next you subtract.
Step 4: B for Bring down.
Step 1: D for Divide.
Step 2: M for Multiply.
Step 3: S for Subtract.
what are the names of four
coplanar points
The slope of the graph of the equation y=2x-2 is 2. What is the y-intercept?
y-intercept =
Answer:
-2
Step-by-step explanation:
-2 is indeed correct, props to my man above me that did all that hard work.
What is 9,000,009 in word form?!?
I need a answer cause this is my homework Which is a true statement 5 x4 + 1 equals 25 or 3 + 7x2 equals 17
5 x 4 +1 = 20+1 = 21 this does not equal 25
3 +7*2 = 3+14 = 17 this is true
so 3+7x2 = 17 is the true statement
To which płace would you round to estimate 6,904-4,111 explain
Solve the equation 3/7k=12/35
Alicia drove at a constant speed and traveled 183 miles in 3 hpues how many miles would Alicia travel in 11 hours at the same speed
Answer:
Alicia will travel 671 miles in 11 hours
Step-by-step explanation:
Alicia traveled 183 miles in 3 hours.
in 1 hour Alicia will travel=[tex]\dfrac{183}{3}[/tex]
=61 miles
Hence, in 11 hours Alicia will travel=61×11 miles
= 671 miles
Hence, Alicia will travel 671 miles in 11 hours
a student answers 90% of the questions on math axam correctly. if he answers 27 questions correctly How many questions are on the exam
The total number of questions in the exam will be 30 questions.
What is the percentage?The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates for one hundred percent. It is symbolized by the character '%'.
The percentage is given as,
Percentage (P) = [Final value - Initial value] / Initial value x 100
A student answers 90% of the questions on the math exam correctly. If he answers 27 questions correctly.
Let the total question in the exam be 'x'. Then the total number of questions in the exam is calculated as,
90% of x = 27
0.90 x = 27
x = 27 / 0.90
x = 30
The total number of questions in the exam will be 30 questions.
More about the percentage link is given below.
https://brainly.com/question/8011401
$SPJ2
Which of the following points lies on the graph of ( x , y ) (x,y) lies on the graph of 8 x + 2 y = 24 ?
Answer:
x=3
y=12
Step-by-step explanation:
x+5*3 divided by 4-2=7
Answer:7 - 2 -. 8. +. 7 21. 1 8. 8 7. C. 4. 56 21. 8 8. ASSET 1. 3 7. 3 ... multiply and solve for x. Divide both sides by 2.5. 23). = = X.
Step-by-step explanation:
sid is $300 in debt. he needs to get the debt down to no more than $100 within the next 8 months. if he pays the same amount each month, what is the minimum he must pay off each month to manage this?
Which expression is equal to 6(-3m)^4