One factor of the function f(x) = x3 − 6x2 + 11x − 6 is (x − 3). Describe how to find the x-intercepts and the y-intercept of the graph of f(x) without using technology. Show your work and include all intercepts in your answer
One factor of the function f(x) = x3 − 6x2 + 11x − 6 is (x − 3). the x-intercepts and the y-intercept of the graph of f(x) are
x = 2, x = 3, and x = 4.(0, -6), (2, 0), (3, 0), and (4, 0). RespectivelyWhat are the x-intercepts?Generally, To find the x-intercepts, we set y equal to 0 and solve for x. In this case, the equation we need to solve is:
f(x) = x^3 - 6x^2 + 11x - 6 = 0
To solve this equation, we can use the fact that (x - 3) is a factor of the function. This means that we can write the function as:
f(x) = (x - 3)(x^2 - 3x + 2)
If (x - 3) is a factor, then x - 3 must equal 0. This gives us one x-intercept at x = 3.
To find the other x-intercepts, we can set the quadratic factor (x^2 - 3x + 2) equal to 0 and solve for x. This gives us the following equation:
x^2 - 3x + 2 = 0
We can use the quadratic formula to solve this equation:
x = (3 +/- √(9 - 8)) / 2 = (3 +/- √(1)) / 2 = (3 +/- 1) / 2
This gives us two more x-intercepts at x = 2 and x = 4.
So the x-intercepts of the graph of f(x) are x = 2, x = 3, and x = 4.
To find the y-intercept, we set x equal to 0 and solve for y. In this case, the equation we need to solve is:
f(0) = 0^3 - 6(0)^2 + 11(0) - 6 = -6
This gives us a y-intercept at (0, -6).
So the y-intercept of the graph of f(x) is (0, -6).
All of the intercepts of the graph of f(x) are, therefore (0, -6), (2, 0), (3, 0), and (4, 0).
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American children watch an average of 25 hours of television per week with a standard deviation of 8 hours. A random sample of 40 children is selected. What is the probability the mean number of hours of television they watch per week is less than 22? Question 15 options: 1) 0.3520 2) 0.0089 3) 0.9911 4) 0.6480
If American children watch an average of 25 hours of television per week with a standard deviation of 8 hours. the probability the mean number of hours of television they watch per week is less than 22 is: 2) 0.0089.
How to find the probability?First step is to find the standard deviation
σ = 8/√40
σ = 1.2649
Using this formula to find the Z-score
Z = x - μ/σ
Z =22-25/1.2649
Z = -3//1.2649
Z = -2.37
Hence,
P-value=P(Z < -2.37)
P-value =0.0089
Therefore the correct option is 2.
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You need a $12,000 loan to buy a good used car. Your bank offers a 3-year loan with an APR of 5% and a 5-year loan with an APR of 8%. Find the monthly payment and total interest paid for each loan option. Which would you choose? What is the better deal?
In case of APR 5% total payment made is $12,947.42 and in case of APR 8% total payment made is $14,598.94. Therefore the better deal to choose to pay the less payment is 1st case.
Define APR.APR is the annual interest produced by a sum that is paid to investors or charged to borrowers is referred to as the annual percentage rate (APR). This does not account for compounding and includes any fees or additional expenditures related to the transaction. Consumers can evaluate lenders, credit cards, or investment goods using the APR as a benchmark figure.
Initial payment is $12,000 with 5% APR and 3 year loan
Monthly payment = P[ i(1+i)ⁿ] / [(1+i)ⁿ-1]
= 12,000[0.05(1+0.05)³]/[1+0.05)³-1]
=$359.65
Over 36 payments total payment is $12,947.42
And in case of 8% APR with a 5 year loan
Monthly payment = 12,000[0.08(1+0/08)⁵] / [(1+0.08)⁵-1]
=$243.31
Over 60 payments total payment is $14,598.94
So, the best deal is 5% APR with a 3 year loan.
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What is the solution and how do I solve?
20 + 4x+2 = 6x+8 --- By exterior angle
4x+22=6x+8
4x-6x=8-22
-2x=-14
x=7
Hope it helps
Nine less than two times a number is five more than this number.
The statement as an expression is 2x - 9 = 5 + x
How to determine the statement as an expression?From the question, we have the following statement that can be used in our computation:
Nine less than two times a number is five more than this number.
Express the numbers properly
So, we have the following representation
9 less than 2 times a number is 5 more than this number.
Introduce the equality symbols
So, we have the following representation
9 less than 2 times a number = 5 greater than this number.
Next, we apply the mathematical operators
So, we have the following representation
2 times a number - 9 = 5 + number.
Express the number as x
So, we have
2x - 9 = 5 + x
Hence, the expression is 2x - 9 = 5 + x
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Can someone evaluate these for me
1×(– 6 × –18 –8) ÷4
4– – 20+ – 5 ×( –11 – –18)
13– – 10 × 16 ÷ (14 + –16)
1– – 9 × 12 ×(–19 +20)
The answer of the given expression using BODMAD rule is 25.
What is BODMAS rule?
The BODMAS rule states that the brackets must be solved first, then powers or roots (i.e., of), Division, Multiplication, Addition, and finally Subtraction. Only when the BODMAS rule or the PEDMAS rule is used to solve an expression is the solution deemed to be correct.
(a) 1 x (-6 x -18 - 8) ÷ 4
By using first to simplify the bracket.
1 x ((-6 x -18) - 8) ÷ 4
1 x (108 - 8) ÷ 4
(1 x 100) ÷ 4
100 ÷ 4
25
Hence, the answer of the given expression using BODMAD rule is 25.
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358.584 divided by 8.92 using mental math and the division algorithm
Answer:
Below
Step-by-step explanation:
358.584 is about 360 8.92 is about 9
360 / 9 = 40 approx by' doing it in your head '
ACTUAL answer = 358.584/8.92 = 40.2 Pretty darn close !
A tortoise and a hare are competing in a 2000-meter race. The arrogant hare decides to let the tortoise have a 820-meter head start. When the start gun is fired the hare begins running at a constant speed of 7.5 meters per second and the tortoise begins crawling at a constant speed of 4.5 meters per second.
a. Write an expression in terms of t that represents the hare's distance from the starting line (in meters)
b. Write an expression in terms of t that represents the tortoise's distance from the starting line (in meters).
c. Write an expression in terms of t that represents the number of meters the tortoise is ahead of the hare.
a. The hare's distance from the starting line is represented by the expression 7.5t.
b. The tortoise's distance from the starting line is represented by the expression 4.5t+820.
c. The number of meters the tortoise is ahead of the hare is represented by the expression 4.5t+820-7.5t.
In the race, the hare is running at a constant speed of 7.5 meters per second, so their distance from the starting line is equal to their speed multiplied by the time it takes them to run that distance. This is represented by the expression 7.5t, where t is the time in seconds it takes the hare to run.
Similarly, the tortoise is crawling at a constant speed of 4.5 meters per second, so their distance from the starting line is equal to their speed multiplied by the time it takes them to crawl that distance, plus the 820-meter head start they were given. This is represented by the expression 4.5t+820, where t is the time in seconds it takes the tortoise to crawl.
To find the number of meters the tortoise is ahead of the hare, we subtract the hare's distance from the starting line from the tortoise's distance from the starting line, which gives us the expression 4.5t+820-7.5t.
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r²-6 r+9 can be factorized to give an expression of the form (r+a)²,
where a is an integer.
Work out the value of a.
The value of a in the expression is -3
How to determine the value of a?From the question, we have the following parameters that can be used in our computation:
r²-6 r+9 can be factorized to give an expression of the form (r+a)²
This means that
r² - 6r + 9 = (r+a)²
Factorize the expression r² - 6r + 9
So, we have
(r - 3)² = (r + a)²
By comparison, we have
a = -3
Hence, the solution of a is -3
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Solve for m in the equation below. It may be helpful to convert the equation into exponential form. Write answer as an integer or reduced fraction. -2. log,(m) - 24 = - 20 m = > Next Question Find the largest value of 2 that satisfies: log, () – log (2 + 1) = 9 =
The largest possible value of 2 that satisfies the equation is approximately 1.1.
What is Exponential Form Equation?
Since y=bx, y = b x is a one-to-one inverse of the exponential function, x=by x = b y, it too is a function. We simply swap x and y and solve for y to discover the inverse function, as is the case with all inverse functions.
To solve for m in the equation -2 * log(m) - 24 = -20, we can start by converting the equation into exponential form. To do this, we can raise both sides of the equation to the power of e:
[tex]e^(-2 * log(m) - 24) = e^(-20)[/tex]
Then we can simplify:
[tex]m^(-2) = e^(-20)[/tex]
Then we can solve for m:
[tex]m = sqrt[e^20]\\\\= sqrt[20*e^9]\\\\= sqrt[20] * sqrt[e^9]\\\\= 2 * 3^(1/2)= 2 * 1.732\\\\= 3.464[/tex]
So m is approximately equal to 3.464
To find the largest value of 2 that satisfies the equation [tex]log(2^2) - log(2 + 1) = 9[/tex], we can start by expanding the left-hand side of the equation:
[tex]log(2^2) - log(2 + 1) \\\\=log(2^2 / (2 + 1))\\\\ = log(4/3) = 9[/tex]
Then we can rewrite the equation as:
log(4/3) = 9
Then we can solve for 2:
[tex]2 = (4/3)^(1/9)\\\\= (4^(1/9)) / 3^(1/9)\\\\= 1.5874010519681994 / 1.4422495703074083\\\\= 1.1[/tex]
So, The largest possible value of 2 that satisfies the equation is approximately 1.1.
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work out the area of a rectangle with base, b = 9.6mm and hight, h = 2mm
Answer: 19.2mm^2
Step-by-step explanation: the area of a rectangle is simply base x height
so do 9.6 x 2 to get 19.2mm^2
-15x + 20y = 15
0=18x + 24y - 18
Answer:
Step-by-step explanation:
given:
-15x + 20y =15
0 = 18x + 24y -18
let's get the 2nd equation into a form like the top equation
-18x -24y = -18
multipy thur by -1
18x +24y = 18
we'll need to use substitution for this problem. elimination has a zero issue.
18x = -24y +18
x = -[tex]\frac{4}{3}[/tex] y + 1
now plug this into the 1st equation
-15( -[tex]\frac{4}{3}[/tex] y + 1 ) + 20 y = 15
20y -15 +20y = 15
40y = 30
y = 3/4
now that we've found y, plug that into our x = -[tex]\frac{4}{3}[/tex] y + 1 , to find x
x = -1 +1
x = 0
The maximum weight, w, that an elevator can hold is 2200 pounds. Which inequality represents the situation?
Answer: w ≤ 2200 would represent the situation
Algebraically prove that x^3 + 9 / x^3+8 = 1 + 1/x^3 +8 , where x ≠ -2
Can someone help me with this question????
Answer:
[tex]P = \boxed{\sf 4000}[/tex]
[tex]r=\boxed{\sf 0.03}[/tex]
[tex]n=\boxed{\sf 4}[/tex]
[tex]t=\boxed{\sf 5}[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{8.5 cm}\underline{Compound Interest Formula}\\\\$ A=P\left(1+\frac{r}{n}\right)^{nt}$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $n =$ number of times interest is applied per year \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}[/tex]
If you invest $4,000 then the principal amount is $4,000. As P represents the principal amount:
[tex]\implies P = \boxed{\sf 4000}[/tex]
The interest is 3%. 3% = 3/100 = 0.03. Therefore:
[tex]\implies r=\boxed{\sf 0.03}[/tex]
"n" represents the number of times interest is applied per year.
Therefore, if the interest is applied quarterly then:
[tex]\implies n=\boxed{\sf 4}[/tex]
"t" represents the time in years. Therefore, if you plan to leave the money in the account for 5 years then:
[tex]\implies t=\boxed{\sf 5}[/tex]
-----------------------------------------------------------------------------------------
To calculate the amount in the account after 5 years, substitute the values into the formula and solve for A:
[tex]\implies A=4000\left(1+\dfrac{0.03}{4}\right)^{4 \times 5}[/tex]
[tex]\implies A=4000\left(1+0.0075\right)^{20}[/tex]
[tex]\implies A=4000\left(1.0075\right)^{20}[/tex]
[tex]\implies A=4000(1.16118414...)[/tex]
[tex]\implies A=\$4644.74[/tex]
Eileen is making lemonade with water and lemon concentrate. What percent of each mixture is
lemon concentrate?
a. The ratio of water to lemon concentrate is 3 to 1.
b. Eileen mixes 4 parts water for each part of lemon concentrate.
c. 4 out of every 5 cups of the mixture is water.
a) The percentage of lemon is 25%
b) The percentage of lemon is 20%
c) The percentage of lemon is 20%
What is a percentage?The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
Example:
50% = 50/100 = 1/2
25% = 25/100 = 1/4
20% = 20/100 = 1/5
10% = 10/100 = 1/10
We have,
a)
Water : Lemon = 3 : 1
Percent of lemon concentrate:
= 1/4 x 100
= 25%
b)
1 part of lemon = 4 part of water
Percent of lemon.
= 1/5 x 100
= 20%
c)
Cups of lemon = 1
Cups of water = 4
Percent of lemon.
= 1/5 x 100
= 20%
Thus,
The percent of each answer is given above.
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Yes, by ASA and AAS
yes SAS
Yes by HL
yes by SSS
the two triangles are not congruent
Answer:
yes, by ASA
Step-by-step explanation:
sum of interior angles of a triangle = 180°
180 - (45+63) = 180 - 108 = 72°
the two triangles have two congruent angles and the side between them.
They are congruent for (ASA) angle side angle
I NEED HELP ASAPPPPPP
Answer:
2.5
Step-by-step explanation:
m is the gradient
to find this we do the change in y/change in x
using the first 2 values we have been given:
change in y= 15-10
change in x= 4-2
5/2= 2.5
the gradient in 2.5
Which of the following is a true statement? A. All real numbers are rational numbers. B. All whole numbers are natural numbers. C. All integers are whole numbers. D. All natural numbers are integers.
Answer: It is D
Step-by-step explanation:
a small bookshelf is 8/12 yard long. How many books can fit on the shelf if the width of each book is 1/24 yard? Explain
Answer:
16 books
Step-by-step explanation:
8/12 is equivalent to 16/24. If each book is 1/24 width, 16/1 = 16
PLEASE HELP IM TIMED I WILL GIVE BRAINLIST!!!!!!!!
The distance between the line segments PQ, RS and TV are √53 respectively
Distance Between Two PointsThe distance between any two points is the length of the line segment joining the points. There is only one line passing through two points. So, the distance between two points can be calculated by finding the length of this line segment connecting the two points.
The formula is given as;
d = √(x₂ - x₁)² + (y₂ - y₁)²
In the first line segment;
P = (0,4), Q = (7, 2)
d = √((7-0)² + (2 - 4)²)
d = √53
b)
R = (-7, 6), S = (-5, -1)
d = √((-1 - 6)² + (-5 --7)²)
d = √53
c)
T = (0, -8), V = (2, -1)
d = √((-1 --8)² + (2 - 0)²)
d = √53
The distance between the lines are all √53 units
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A cake recipe asks for 1/4 cup of oil for each cake. How many cakes can be made from a bottle of oil that has 4 cups in it?
Answer: 16
Step-by-step explanation:
there are 4 1/4 in 1 cup. so it'll be 4 cakes for each cup of oil you have. multiply the number of cakes that can be made per cup (4) by the number of cups you have (4)
(4) x (4) = 16
Work out the surface area of this solid
prism.
10cm
8cm
27cm
6cm
17cm
30cm
The diagram is not drawn to scale.
Answer:
2064 cm²
Step-by-step explanation:
You want the surface area of a prism that is 30 cm between bases that are trapezoids with parallel sides 27 cm and 6 cm that are 8 cm apart, and slant sides that are 10 cm and 17 cm.
Base areaThe area of each trapezoidal base is ...
A = 1/2(b1 +b2)h
There are two identical bases, so their total area is ...
2A = (b1 +b2)h = (27 cm +6 cm)(8 cm) = 264 cm²
Lateral area
The lateral area of the prism is the area of the four rectangular faces. Each is 30 cm wide, and their total length is the perimeter of the base;
P = 27 cm +10 cm +6 cm +17 cm = 60 cm
lateral area = Ph = (60 cm)(30 cm) = 1800 cm²
Total surface area
The total surface area of the prism is the sum of the base area and the lateral area:
total area = base area + lateral area
total area = 264 cm² +1800 cm² = 2064 cm²
The surface area of the solid prism is 2064 cm².
I need help with my math homework
Answer: Work shown below. Have a nice day! :)
1/4+1/6 in fractions
Please help me I’m giving you 25 pints things
What are the solutions to this system? Select all that apply. Y+2x^2 =14
y= 3x^2-6
The solution to the system of equation y + 2x² = 14 , y = 3x² - 6 is as follows:
x = 2y = 6How to solve system of equation?System of equation can be solved using different method such as elimination method, substitution method and graphical method.
Let's solve the system of equation by substitution method.
Therefore,
y + 2x² = 14
y = 3x² - 6
Therefore, using substitution method,
3x² - 6 + 2x² = 14
5x² - 6 = 14
5x² = 14 + 6
5x² = 20
x² = 20 / 5
x² = 4
x = √4
x = 2
Therefore, let's find the value of y using y = 3x² - 6.
y = 3x² - 6
y = 3(2)² - 6
y = 12 - 6
y = 6
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A student receives a subsidized student loan for $10,000 with a 10-year repayment term and interest compounded monthly. Six months after she graduates from college, she will have to begin making payments. Find her monthly payment and total interest paid if the interest rate is 5.5%.
If the interest rate is 5%, the monthly payment and total interest would be $2.439.
Define interest.Interest is the sum of money that must be repaid on a loan or received in exchange for a loan. Principal refers to the borrowed or lent funds. The Amount is the total of the principal plus interest. The term "rate of interest" refers to the rate at which interest is applied to the principal.
Given,
A student receives a subsidized student loan for $10,000 with a 10-year repayment term and interest compounded monthly. Six months after she graduates from college, she will have to begin making payments.
A $10,000 subsidized student loan
Ten-year term of repayment
5.5% interest rate
First, we must determine the loan's future value (FV) over the next six months using the formula below:
FV in 6 months
= Loan Amount× (1 + Interest Rate)⁶ ($10,000×(1 + 0.055) ×6
= $2.7680.
Second, the formula for determining future value is used to determine the monthly payment:
M = FV in 6 months / (((((r)n) - 1) / r).......... (1)
When you enter all the pertinent values into equation (1), you get:
M = $2.7680 / ((((1 + 0.00466666666666667)^144) – 1) / 0.00466666666666667)
M = $2.439
Therefore, if the interest rate is 5.5%, the total amount paid in interest plus monthly payments would be $2.439.
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Can someone do these 4 questions For 40 points
The gradient of the blue line as shown in the graph is 0.25
What is gradient?The gradient of any line or curve tells us the rate of change of one variable with respect to another.
To calculate the gradient of the blue line, we use the formula below.
Formula:
S = Δy/Δx = (y₂-y₁)/(x₂-x₁)................. Equation 1Where:
S = Gradient of the blue lineΔy = Change in y-axisΔx = Change in x-axisFrom the graph,
Given:
x₁ = 0y₁ = 1x₂ = 8y₂ = 3Substitute these values into equation 1
S = (3-1)/(8-0)S = 2/8S = 1/4S = 0.25Hence, the gradient of the blue line is 0.25.
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The graph of linear function k passes through the points (-7, 0) and (1, 8).
Domain
2
Range
Slope
Y-intercept
X-intercept
The linear function is y = x + 7 and it has it domain and range at (-∞, ∞) respectively while it x and y - intercepts are (-7, 0) and (0, 7) respectively.
Linear FunctionA linear function has one independent variable and one dependent variable. The independent variable is x and the dependent variable is y.
The linear function always model the form of y = mx + c
m = slopec = y-interceptTaking the points, we can find the slope of the line
m = y₂ - y₁ / x₂ - x₁
m = 8 - 0 / 1 - (-7)
m = 8 / 8
m = 1
The slope of the line is 1
Using the slope to find the y - intercept;
y = mx + c
8 = 1(1) + c
8 = 1 + c
c = 8 - 1
c = 7
The linear function is y = x + 7
The range of this function is (-∞, ∞) and the domain of the function is
(-∞, ∞).
The x and y -intercept of the function are
x - intercept = (-7, 0)
y - intercept = (0, 7)
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Dajon already knows that he will have $500,000 when he retires. If he sets up a payout annuity for 15 years
in an account paying 2.05% interest, how much could the annuity provide each week? Round your answer to
the nearest dollar.
The annuity provide each week is $547.59 (approx.)
Define Annuity
A fixed sum of money paid to someone each year, typically for the rest of their life.
Given,
Dajon already knows that he will have $500,000 when he retires.
P = $500,000
Next, he sets up a payout annuity for 15 years in an account paying 2.05% interest.
r = 2.05 % or 0.0205
t = 15 years
Since, annuity provide each week then
n = 52 weeks (in a year)
The Annuity formula is,
P = d [ ( 1 + r/n)^nt - 1 ] / (r/n)
where, d = regular deposit
Now, plug in the values and find the value of d
P = d [ ( 1 + 0.0205/52)^52*15 - 1 ] / (0.0205/52)
Calculate the value it gives,
P = $547.5936993 or 547.59
Hence, the annuity provide each week is $547.59 (approx.)
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