Answer:
[tex]x^3-5x^2+4x-20=(x-5)(x+2\mathbf{i})(x-2\mathbf{i})[/tex]
Step-by-step explanation:
Factorization of polynomials
Factor:
[tex]f(x)=x^3-5x^2+4x-20[/tex]
There are several techniques to factor polynomials. We'll use algebraic manipulation and common factor:
Separate in groups:
[tex](x^3-5x^2)+(4x-20)[/tex]
Factor out 4 from 4x-20:
[tex]=(x^3-5x^2)+4(x-5)[/tex]
Factor out [tex]x^2[/tex] from [tex]x^3-5x^2[/tex]
[tex]=x^2(x-5)+4(x-5)[/tex]
Factor out x-5:
[tex]=(x-5)(x^2+4)[/tex]
The roots of
[tex]x^2+4=0[/tex]
Are two complex numbers:
[tex]x=2\mathbf{i}, x=-2\mathbf{i}[/tex]
The complete factorization is:
[tex]\boxed{x^3-5x^2+4x-20=(x-5)(x+2\mathbf{i})(x-2\mathbf{i})}[/tex]
Write the slope-intercept form of the equation of the line.
-4 - y = -2x
A) y = 4x + 2
C) y = 2x - 4
B) y = -4x + 2
D) y = -2x + 2
Answer:
c
Step-by-step explanation:
-4 -y = -2x
+4 +4
-y = -2x + 4
multiple everything by -1 to get y by itself
y = 2x - 4
A toy has various shaped objects that a child can push through matching holes. The area of the square hole is square centimeters. The volume of a cube-shaped block is cubic centimeters. a. Which edge length can be found? Explain. b. Will the block fit in the square hole? Explain.
Answer:
a. We can find edge length of the cube-shaped bock. b. No, it will not
Step-by-step explanation:
Here is the complete question
A toy has various shaped objects that a child can push through matching holes. The area of the square hole is 18 square centimeters. The volume of a cube-shaped block is 729 cubic centimeters. a. Which edge length can be found? Explain. b. Will the block fit in the square hole? Explain.
Solution
a.
Since the volume of the cube 729 cm³ is a perfect cube of 9 cm and the area of the square hole which is 18 cm² is not a perfect square, the edge length of the cube-shaped block is easily found.
b. Since the edge length of the block is 9 cm, the area of one of its faces is (9 cm)² = 81 cm² which is greater than the area of the square hole which is 18 cm². Since their dimensions are not the same, the cube-shaped block will not fit into the square hole.
9 2/3 - 6 1/3
Pls help ask questions if needed
Answer:
3 1/3
Step-by-step explanation:
Answer:
Exact form: 10/3
Decimal form: 3.3
Mixed-number form: 3 1/3
Step-by-step explanation:
hope this helps :)
Solve for x 6x-18-3x<27-2x
Answer:
x=9
Step-by-step explanation: here^
which is more , 1 gallon or 7 pints ,
a. 1 gallon
b. 7 pints
c. nethier ; they are equal
Answer:A
Step-by-step explanation: 1 Gallon is equal to 8 pints.
Answer:
A
Step-by-step explanation:
pint=1/8 of a gallon
therfor 7 pints = 7/8
7/8<1gal
Bridget went fishing with her dad. Bridget Bridget caught the first fish of the day, another was 2 more than 3 times the weight of the first fish, the next was 1/2 the weight of the first fish, and the last was 3/5 the weight of the first fish.
Bridget's dad caught four fish. the first fish he caught weighed 2 more than 3 times a weight of the first fish caught that day. one fish weighed 4/5 in the weight of the first fish caught that day, one weighed 4 more than 2 times the weight of the first fish caught that day, and the last one weighed 1/2 the weight of the first caught that day.
if all the fish Bridget caught have the same total weight as the fish her dad caught, then the first fish Bridget caught weighed ____ ounces in the first fish her dad caught weighed ____ ounces.
Answer:
Bridget's first fish =f = 5 ounces
Bridget's dad first fish weighs 17 ounces
Step-by-step explanation:
Solution:
Bridget's fishes:
f ounces
2f ounces
3f+2 ounces
1/2f ounces
3/5f ounces
Total= f +2f + (3f+2) + 1/2f +3/5f
=3f + 3f + 2 + 5f+6f/10
=6f + 2 + 11f/10
=60f+11f/10 +2
=71/10f +2
Bridget's dad fishes
3f+2
4/5f
2f+4
1/2f
Total =(3f+2) + (2f+4) + 4/5f +1/2f
=3f+2+2f+4 + 8f+5f/10
=5f + 6 + 13/10f
= 50f+13f/10 + 6
=63/10f +6
Equate the total weight
71/10f +2=63/10f +6
Collect like terms
71/10f - 63/10f =6-2
71f-63f/10 = 4
8f/10=4
Cross product
8f=40
Divide both sides by 8
f=5
Bridget's first fish =f = 5 ounces
Bridget's dad first fish = 3f +2
=3(5)+2
=15+2
=17 ounces
Bridget's dad first fish weighs 17 ounces
the relationship among integers, natural numbers, rational numbers, and whole numbers?
Answer:
Rational numbers include all integers and fractions. All negative integers and whole numbers make up the set of integers. Whole numbers comprise of all natural numbers and zero.
Which of the following does not have only one solution.
a. x+3 = 7
b. 7x = 4x + 2
c. (x+3)(x - 2) = 0
d. -3= 2x – 5
Answer:
A. x+3=7[tex]a. \: x + 3 = 7 \\ or \: x = 7 - 3 \\ or \: x = 4[/tex]
Thank you ☺️☺️How does the graph of y = ax2 + c compare to the graph of y
ax2
Answer:
[tex]y = a {x}^{2} + c \\ y = a {x}^{2} \\ \\ y = a {x}^{2} + c \: \: \: is \: translated \: along \: the \: y \: axis\: for \: c[/tex]
Waterco is filling barrels with waste water at the rate of 8 quarts per hour. The recycling facility picks up 150 barrels on each trip, and each barrel holds 15 quarts of wastewater. How many days are between each pick up? Show your work to receive full credit. Round answer to the tenths place 
Answer:
11.7 days
Step-by-step explanation:
Given that:
Filling rate = 8 quarts per hour
150 barrels picked up per trip
One barrel = 15 quarts of waste water
Barrel picked up per trip = 150 barrels
Number of quarts per barrel = 15 quarts
Total quantity of waste water = (150 * 15) = 2250 quarts
Filling rate = 8 quarts per hour
Time taken = quantity / rate
Time taken in days = 2250 quarts /(8*24) = 11.72
11.7 days
Question 4(Multiple Choice Worth 3 points)
(03.01)
Which of the sums below can be expressed as 8(2 + 7)?
O2 +56
O 10 + 15
O 16 + 7
O 16 + 56
Answer:
16+56
Step-by-step explanation:
8(2 + 7)
=8*2+8*7
16+56
I need help I got 10 minutes to turn in my homework
Answer: ( 3 + 6*6 )
Step-by-step explanation
6² = 6*6
Answer:
[tex]3^26^2[/tex]
Step-by-step explanation:
One property of exponent says that you can distribute the exponent to the factors. Therefore, the answer would be 3^2*6^2.
What is the term used to describe the portion of the fraction occupied by the
1 in the fraction below?
1/2
O A. Divisor
B. Factor
O C. Dominator
O D. Denominator
E. Numerator
SUBMIT
PREVIOUS
carlos read 40 pages of a book in 50 minutes. how many pages should he be able to read in 80 minutes
Answer:
70
Step-by-step explanation
!!TIMED!!PLEASE HELP
Answer:
y=3x+1
Step-by-step explanation:
Since the number is going up by three but I could be wrong
Help me pleaaaaaaassssssssseeeeeeee
Answer:
+29
Step-by-step explanation:
(-)(-)=+
x+12= -5 helpppp meeeee
Answer:
The answer is -17.
Step-by-step explanation:
Well since the answer turns out to be a negative, one of the numbers has to be negative.(not all cases but for this one, yes)You have to add 12+5 and you get 17. This has to be a negative because the answer is a negative.
Can someone help me please
Answer:
the answer is 2 hope this help
Step-by-step explanation:
A rectangular garden is fenced on all sides with 234 feet of fencing. The garden is 5 feet longer than it is wide. Find the length and width of the garden.
Answer:
The width in only one side is 56ft and in both it is 112ft. The length in only one side is 61ft and in both sides it is 122ft.
Step-by-step explanation:
Andrea receives a $40 gift card to use at a town pool. It costs her $8 per visit to swim. A
function relating the value of the gift card, v, to the number of visits, n, is v(n) = 40 - 8n.
a. Identify a reasonable domain of the function. Explain why you chose that
domain. (What are reasonable times to visit the pool?)
b. Given that domain, what is the range of the function?
Answer:
The value of the gift card = v = $40
The visit to the skate cost = $8
The number of visits = n
∴ n = the value of the gift card over the cost of one visit to the skate
∴ n = v/8 = 40/8 = 5
Step-by-step explanation:
The general function for relating the value of the gift card, v, in terms if the number of visits, n. ⇒⇒⇒ v = 8n
Solve 3(y-2)=6(y-1)-3y
Answer:
All real numbers are solutions.
Step-by-step explanation:
1. First you want to distribute what is inside the parenthesis. You would want to do 3 × y + 3 × -2 = 6 × y + 6 × -1 -3y.
2. Now that the equation has been distributed, you want to simplify it. 3 × y is equal to 3y, and 3 × -2 is equal to -6. So, 3y + -6 = 6 × y + 6 × -1 -3y.
3. Now you want to simplify the right side of the equation. So, 6 times y is equal to 6y, and 6 × -1 is equal to -6. Now the new equation is 3y + -6 =6y + -6-3y.
4. Also in an equation, if there is a + and - sign together like this +-, it would equal to -. So, 3y + -6 = 6y + -6-3y, is equal to 3y - 6 = 6y -6-3y.
5. Now you want to combine like terms on the right side of the equation. 3y - 6 = 3y -6 because 6y-3y is equal to 3y.
6. Now the rest of the equation has to be combined using like terms. Start by moving the -3y fromthe right side of the equation to the 3y on the left side of the equation. -3y plus 3y is equal to zero so it cancels out. The 3y on the left side plus another 3y is equal to 6y.
7. Now the equation is 6y - 6 = 6y - 6
8. You can add 6 to the -6 on both sides of the equation which would cancel out on both sides leaving you with an equation of 6y = 6y.
9. Divide both sides by 6 to get y = y.
10. This equation means that all real numbers are solutions to this equation. In other words, no matter what real number you use in this equation, it would come out to be true. For example, if y = 3, 3 = 3, so the equation is true.
Find the measure of the following angles. Justify your answers.
Answer:
yes
Step-by-step explanation:
gay by gay
which of the following number is negative chose all that apply
Answer: B,C,D,E
Step-by-step explanation:
B. A - 2 would be lower than one because 2 is bigger than A.
C. Negative B is a negative, obviously.
D. B has to be at least negative 2, and A is only about 1.5, so added together, these numbers will be negative.
E. Same thing as last time pretty much.
A community center charges x dollars for a summer activity if individuals are signed up before the day of the activity. Individuals who sign up the day of the activity are charged a fee of x +0.20x dollars. Which expression also represents the fee for signing up the day of the activity, and what does it mean about the fee?
Answer: 1.2 individual signing up the day of the activitiy get charged 20% more
Step-by-step explanation:
We have a community center that charges x dollars for a summer activity if individuals are signed up before the day of the activity but if individuals who sign up on the day of the activity are charged a fee of x + 0.20x dollars.
We have to determine which expression represents the fee for signing up the day of the activity and investigate what does it mean about the fee.
What do you understand by the Equation Modelling of the process?Equation modelling of a process is a way to formulate the given process mathematically. Generally, it is used in such problems where something is produced on giving some input.
According to question, we have the following equation describing the charging rates -
f(x) = x + 0.2x = x + [tex]\frac{1}{5}x[/tex]
In this the expression, the part [tex]\frac{1}{5}x[/tex] represents the fee for signing up on the day of the activity.
It also indicates that if you you are late for sign up and you are signing on the day of the activity then you will have to pay an extra fine of [tex]\frac{1}{5}[/tex] times of the fees if you signed up before the day.
To solve more questions on Equation modelling, visit the link below -
https://brainly.com/question/11329601
#SPJ6
Solve this system of equations
9-36=13
Sa+60=41
2a4b-c-5
Answer:
-27=13
a=19/a
a=2b−c/2−5/2
Step-by-step explanation:
You read 9.75 pages in your science book and 24.5 pages of a play for English class
It takes you 1.2 minutes to read each page of science and 0.8 of a minute to read each page of the play. How much time do you spend reading?
Answer: 1. You have to multiply 9.75x1.2= 11.7
2.You have to multiply 24.5x0.8= 20.4
3. Add the to products 11.7+20.4= 32.1
4. Answer is- 31.3 minutes
Step-by-step explanation: Hopefully this helped a lot ;D
the square root of 39 is between which 2 integers
9514 1404 393
Answer:
6 and 7
Step-by-step explanation:
6² = 36
(√39)² = 39
7² = 49
The square root of 39 is between 6 and 7.
A triangle has sides with lengths of 42 millimeters, 43 millimeters, and 58 millimeters. Is it a
right triangle?
Answer:
No
Step-by-step explanation:
42 x 42 = 1764
43 x 43 = 1849
1764 + 1849 = 3613
and the sqaure roof of 3613 is 60.11
60.11 does not equal 58
so no it is not a right triangle
yoooo can someone help meeee thanks In advance
Answer:
The slope of F = 5.
Not 100% sure.
Find f(-5) if f(x) = |x + 1|.
A)6
B)5
C)4
