Distributive Property
Factoring
FOIL (First Outside Inside Last)Functions
Function NotationApplicationStep 1: DefineLet's organize what is given to us in the problem.
We are given a function f, defined as f(x) = x² + 3x - 10.
We are asked to find the values of b and c in f(x - 2) = x² + bx + c.
Step 2: SolveIn order to solve the question, we first must find the full function of f(x - 2):
[tex]\displaystyle\begin{aligned}f(x - 2) & = (x - 2)^2 + 3(x - 2) - 10 \\& = \underbrace{x^2 - 4x + 4}_{\text{FOIL}} + \underbrace{3x - 6}_{\text{Distribute}} - 10 \\& = \boxed{ x^2 - x - 12 } \\\end{aligned}[/tex]
∴ [tex]\displaystyle \boxed{ f(x - 2) = x^2 - x - 12 }[/tex]
Now, we can correlate our variables to the f(x - 2) function by comparing them side-by-side:
[tex]\displaystyle\begin{aligned}f(x - 2) & = x^2 - x - 12 \\& = x^2 + bx + c \\& \Rightarrow \boxed{ b = -1 ,\ c = -12 }\end{aligned}[/tex]
∴ we have found the values of b and c.
Answer∴ the value of b is equal to -1 and the value of c is equal to -12.
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___
Topic: Algebra I
Unit: Factoring
What literary devices are used in The Importance of Being Earnest?
Oscar Wilde mocks upper-class Victorian society in "The Importance of Being Earnest" by using the literary devices of irony and hyperbole to a humorous effect.
What is The Importance of Being Earnest?
Oscar Wilde wrote a play titled The Importance of Being Earnest, A Trivial Comedy for Serious People.
It is a farcical farce that was first presented on February 14, 1895, at the St James's Theatre in London.
The characters maintain false personae to avoid onerous social duties.
The play's main themes, which are based on late Victorian London social customs, are the triviality with which it treats institutions as important as marriage and the satire that results.
In "The Importance of Being Earnest," Oscar Wilde employs the literary devices of irony and hyperbole to hilarious effect as he criticizes upper-class Victorian society.
Therefore, Oscar Wilde mocks upper-class Victorian society in "The Importance of Being Earnest" by using the literary devices of irony and hyperbole to humorous effect.
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What is the slope and y-intercept of this linear equation y 3x 5?
The slope of the line is 3 and the y-intercept is -5.
The slope of a line is the coefficient of the x term (in this case, 3). To calculate the y-intercept, we can plug in x = 0 and solve for y. Doing this, we get y = 0 + 3(0) + 5 = -5. Therefore, the slope is 3 and the y-intercept is -5.
The slope of a linear equation is found by looking at the coefficient of the x term. In this case, the coefficient of the x term is 3, so the slope of the line is 3. To find the y-intercept, we can plug in x = 0 into the equation and solve for y. Doing this, we get y = 0 + 3(0) + 5 = -5, so the y-intercept is -5. Therefore, the slope of the line is 3 and the y-intercept is -5. This equation is therefore a linear equation with a slope of 3 and a y-intercept of -5.
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What is 21/4 X 1/3 can u help me please
Answer:
1 3/4
Step-by-step explanation:
1 3/4
Answer:
7/4
Step-by-step explanation:
Multiplying fraction is so easy just multiply the nominators with each other. Then the denominators.
21 *1 =21 and 4 *3=12
21/12 =7/4 just simplify
A student solved a quadratic using the Quadratic Formula and got:
X=4+-(square root)-14/3
Shown in picture
How many solutions did they get?
Answer:
2 solutions
Step-by-step explanation:
the plus or minus sign makes there be 2 solutions
[tex] \frac{4 + i \sqrt{14} }{3} [/tex]
and
[tex] \frac{4 - i \sqrt{14} }{3} [/tex]
A chef that manages two restaurants buys seven bags of rice and six bags of flour.
Restaurant A receives four bags of rice and two bags of flour for a total cost of
$78. Restaurant B receives three bags of rice and four bags of flour for a total
cost of $71.50. What is the cost of each bag of rice and each bag of flour?
Answer:
- A bag of rice is $16.9
- A bag of flour is $5.20
Step-by-step explanation:
Let R and F stand for the price of a bag of Rice and Flour, respectively.
We can use the information provided to set an equation that will predict the total cost for that restaurant, given the quantities of rice and flour received (Restaurants A and B)
A) 4R + 2F = 78 [4 bags of rice and 2 bags of flour, when multiplied by the prices per bag, R and F, will result in a total cost of $78.
B) 3R + 4F = 71.5 [Now it is 3 bags of rice and 4 of flour, for a total cost of $71.50
We have 2 equations and 2 unknowns. We can use substitution to find the answers. Take one of the equations and reorganize it to isolate one of the variables (R or F). We'll take the equation for A and isolate F
---
A) 4R + 2F = 78
2F = 78-4R [subtract 4R from both sides]
F = 39-2R [divide both sides by 2]
We've isolated F, and we can use this definition of F in the second equation:
===
B) 3R + 4F = 71.5
3R + 4(39 - 2R) = 71.5 [Use the definition of F derived above. In this manner, we have legally eliminated one of the two variables. (Sneaky, effective, and fun)]
3R + 156 - 8R = 71.5 [Multiply, combine like terms, and simplify]
-5R = -84.5 [Isolate R]
R = $16.9 A bag of rice costs $16.9
Now use the price of rice (R=$16.9) in one of the equations. Since the rearranged equation we used above is already conveniently written for F, we'll use it:
F = 39 - 2R
F = 39 - 2(16.9)
F = 39 - 33.8
F = $5.20 A bag of flour costs $5.20
===
CHECK:
Do these two prices satisfy both equations we first formulated?
Restaurant A: 4R + 2F = 78?
4(16.9) + 2(5.20) = 78 YES
Restaurant B: 3R + 4F = 71.5?
3(16.9) + 4(5.20) = 71.5 YES
These are the correct answers.
25
1 point
(3x + 32)
(5x - 8)
Select the correct equation to solve for x,
3x + 32 + 5x - 8 = 180
3x + 32 = 5x - 8
3x + 32 + 5x - 8 = 90
The value of x is 20
Now, According to the question:
The given equation is:
3x + 32 = 5x - 8
To solve the equation for finding the value of x .
32 + 3x = -8 + 5x
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-5x' to each side of the equation.
32 + 3x -5x = -8 + 5x -5x
Combine like terms:
3x -5x = -2x
32 -2x = -8 + 5x -5x
Combine like terms: 5x -5x = 0
32 -2x = -8 + 0
32 -2x = -8
Add '-32' to each side of the equation.
32 -32 -2x = -8 -32
Combine like terms: 32 -32 = 0
0 -2x = -8 -32
-2x = -8 -32
Combine like terms: -8 -32 = -40
-2x = -40
Divide each side by '-2'.
x = 20
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Why do we use 1st and 3rd quadrant?
The usage of first and third quadrant is explained below.
The term quadrant in math is known as a region defined by the two axes (x-axis and y-axis) of the coordinate system.
Here we need to list down the usage of first and third quadrant is as follows:
As we all know that the Third Angle Projection schema imagines the object in the third quadrant.
And in one can place an object on the bottom of the horizontal plane and behind the vertical planes.
Where as the first angle projection is utilized mostly in the United States and it places the object between the observer and the object.
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Find the measure of the missing angles.
Answer:
Hello!
y = 90
x = 51
Hope that helps!
5. What is the mean weekly salary at each company?
6. Four of the 5 employees at Company B each received a raise of $30. After the raises, how much greater is the mean salaries for company B than Company A? Explain how to slove the problem.
Answer: picture shown is not available
Step-by-step explanation:
A ship travels 50 km on a bearing of 27°, and then travels on a bearing of 117° for 140 km. Find the distance traveled from the starting point to the ending point
The distance traveled from the starting point to the ending point is 30.35 km.
What is a bearing?
A bearing tracks the rotation of an angle around the north line in a clockwise fashion. The line connecting the compass's centre to a location and measuring its bearing in degrees as it moves clockwise from north is known as the bearing.
The ship travels 50 km on a bearing of 27°, and then travels on a bearing of 117° for 140 km.
The x-coordinate of the final point is -
50 cos (27°) + 140 cos (117°) = -19
The y-coordinate of the final point is -
50 sin (27°) + 140 sin (117°) = 23.67
The distance from (0,0) to the final point is as follows -
d = √(-19)^2+(23.6)^2)
= √(921.27)
= 30.35 km
Therefore, the distance traveled is 30.35 km.
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A car travels 196 miles in 3.5 hours. A. 224 miles in 4 hours B. 356 miles in 6 hours C. 504 miles in 9 hours D. 392 miles in 7 hours
Answer:
A and D
Step-by-step explanation:
distance = rate x time
196 = 3.5r
r = 196/3.5
r = 56 mph
A) 56 x 4 = 224 Yes
B) 56 x 6 = 336 No
C) 56 x 9 = 494 No
D) 56 x 7 = 392 Yes
A researcher wants to set up a hypothesis test to determine if there is a difference in the mean exam scores of students who are visual learners, versus auditory learners, versus kinesthetic learners. What would be the correct setup for the null and alternative hypotheses for this test
On solving the provided question we can say that here in null hypothesis a negative relationship; as anxiety rises less items are remembered
What is null hypothesis?A null hypothesis is a kind of statistical hypothesis that asserts that a specific set of observations has no statistical significance. Using sample data, hypotheses are tested to determine their viability. Sometimes known as "zero" and symbolized by H0. Researchers start off with the presumption that there is a link between the variables. In contrast, the null hypothesis claims that there is no such association. Although the null hypothesis may not appear noteworthy, it is a crucial component of research.
here,
in null hypothesis a negative relationship; as anxiety rises less items are remembered
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Why infinity is open interval?
The number line is drawn to find the open end point interval is infinity.
Number Line of an Open endpoint to the endpoint of number line =?
Selection of Open endpoint to the endpoint of the number line is fit for the following intervals as such determined below :
basically the intervals are mentioned as follow
( ), [ ], ( ], [ )
An open interval is mentioned (a, b), is an interval that does not contain its endpoints. When an interval involves infinity or negative infinity, hence the following rules for whether it is an open or closed interval. (a, and
(-a , a) are open intervals.
For instance [a,∞) doesn't contain all of its endpoints as mentioned . It's a real number where The interval has only one endpoint - a, so it contains all of its endpoints (however it only has one).
Secondly, the definition forgot to add that (−∞,∞) is also open
Take numbers as follows:
Final Answer as followed in intervals
(-2, 2)
[-2, 2]
(-∞, 2]
[2, ∞)
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(5 points) 2. The coordinates of the vertices of ARST are R(1, 6), S(5, 3), and T(3,-2). Triangle R'S'T' is the image of ARST after a reflection in x = -1. Graph and state the coordinates of the vertices of AR'S'T'.
The coordinates of the reflected points are R' (1, -6), S' (5, -3), T' (3, 2) and the graph is attached.
What is reflection of graph?Reflections of graphs involve reflecting a graph over a specific line.Reflecting functions are functions whose graphs are reflections of each otherGiven are the coordinates of the vertices of ΔRST are R(1, 6), S(5, 3), and T(3,-2).
The rule for a reflection over the x -axis is (x, y) →(x, −y). Now we can write the coordinates of the reflection as -
R' (1, -6)
S' (5, -3)
T' (3, 2)
The graph is attached.
Therefore, the coordinates of the reflected points are R' (1, -6), S' (5, -3), T' (3, 2) and the graph is attached.
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Which of these is true?
a) Some ordered pairs of real numbers are not points in the Cartesian coordinate system.
b)Only integer ordered pairs are allowed in the coordinate system.
c)There is no point in the coordinate system with the ordered pair (T, Tt)
d)all of the above are false
9514 1404 393
Answer:
d) all of the above are false
Step-by-step explanation:
Every ordered pair of real numbers is a point in the Cartesian coordinate system.
The various statement saying otherwise are all false.
Hilda filled her aquarium with
water. On Monday, she put 8 cups
into the aquarium. On Tuesday she
put 2 pints. On Wednesday, she put
quarts. How many cups of water dic
she put into her aquarium in all?
The domain and scope of the identity function are the same. Equation for the identity function is f(x) = x, or y = x.
What is function?An statement, rule, or law in mathematics that specifies the connection between an independent variable and a dependent variable (the dependent variable. A relationship between a group of inputs and one output each is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. Y=X2 is an illustration of this. You only receive one output for y if you enter anything for x. The fact that x is the input value leads us to argue that y is a function of x.
identity function are the same.
Equation for the identity function is
f(x) = x, or y = x.
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9. Samuel is comparing the average EPA ratings on 4 types of vehicles. He wants to drive a pickup truck, but he can see from the table below that he would use less gasoline if he drove a compact car. If Samuel
drives an average of 13,000 miles per year, how many more gallons of gas would he need to buy for a pickup truck compared to a compact car?
4-door Sedan
Compact Car
Pickup Truck
Small SUV
EPA rating: 26 mpg (combined city and EPA rating: 32 mpg (combined city EPA rating: 20 mpg (combined city and EPA rating: 22 mpg (combined city and
highway)
and highway)
highway)
highway)
O221.25 gallons
243.75 gallons
250.25 gallons
O261.75 gallons
Answer:
If Samuel drives a compact car, he would need to buy 243.75 gallons of gas per year. If he drives a pickup truck, he would need to buy 250.25 gallons of gas per year. So he would need to buy 6.5 more gallons of gas per year if he drives a pickup truck compared to a compact car.
Step-by-step explanation:
GIVING BRAINLIEST! HELP
Answer:
Its first option. bcz its doubled... right..
If you could buy 500 individual nerd candies for $5 or 186 g of individual nerd candies for $5, which would be the better deal
The better deal would be 500 individual nerds candy for $5.
One of the four basic mathematical operations, along with addition, subtraction, and multiplication, is division. The equal partition of bigger groupings into smaller parts is referred to as division.
The order of work assigned to and completed by the team of employees in order to optimize efficiency is known as the division of labor.
The splitting down of a job into multiple separate parts that make up the total is referred to as the division of labor. 500 individual nerds candy for $5 is preferable since you will have more candy and it will last longer.
Thus, The better deal would be 500 individual nerds' candy for $5 since you will have more candy and it will last longer.
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25 points and brainiest badge
No Links
Select the correct answer.
What is the value of x in the figure?
A. 70°
B. 80°
C. 120°
D. 150°
Answer:
70
Step by step explanation
Answer:
150°
Step-by-step explanation:
The 70° angle is on a straight line so to find the next angel for the triangle
180-70=110
Angles in a triangle adds up to 180
so
110+40=150
180-150=30
Therefore the angle near x in the triangle is 30
To find x
180-30=150°
LORD SOMEONE please help me!! ASAP I will give brainiest! Fr
the public school enrollment of a city is 13,500. Enrollment is declining at a rate of 4.5% per year. predict the enrollment in 5 years.
Answer:
16537.5
Step-by-step explanation:
4.5% of 13500 = 607.5
607.5 x 5 = 3037.5
3037.5 + 13500 = 16537.5
฿₤₦
Find volume of cylinder
I really need an answer for this FAST so if anybody can answer id really appreciate it :)
The volume of the cylinder on the image is:
v = 36,424 in³
So the correct option is the second one.
What is the volume of the cylinder?We know that for a cylinder of diameter D and height H, the volume is given by the formula:
V = pi*(D/2)²*H
Where pi = 3.14
Here we know that:
D = 40 inches.
H = 29 inches.
Replacing that in the formula for the volume we will get:
V = 3.14*(40 in/2)²*29 in = 36,424 in³
So the correct option is the second one.
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select all of the partial products of 5 x 1,234
[] 20
[] 150
[] 1,000
[] 10,000
3. ) Mary is the director of the Washington Performing Arts Center. Her employer offers a pension. Mary’s employer uses a formula to calculate the pension. Marina is planning on retiring at the end of this year after 30 years of employment. A retiring employee receives 1. 6% of his or her average salary for the last 5 years of employment multiplied by the number of years worked. Mary would receive this amount each year until her death. Her salaries for the last 5 years are $80,900; $90,200; $95,000; $99,000; and $104,000. Calculate Marina’s pension
Marina's pension amount is calculated by multiplying 1.6% of her average salary for the last 5 years by the number of years she has worked, which is 30.
1.6% x $80,900 = $1,282.40
1.6% x $90,200 = $1,444.32
1.6% x $95,000 = $1,520.00
1.6% x $99,000 = $1,584.00
1.6% x $104,000 = $1,664.00
Total = $7,604.72
Pension amount = $7,604.72 x 30 years
= $228,141.60
Marina's pension amount is determined using a formula set by her employer, the Washington Performing Arts Center. This formula takes into account her average salary for the last five years, which is $469,100, and multiplies it by 1.6%, then by the number of years she has worked for the Center, which is 30. This results in a pension amount of $228,141.60. This amount will be paid each year until her death. This pension amount is calculated based on the salaries she has earned over the past five years, which include $80,900; $90,200; $95,000; $99,000; and $104,000.
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2/3 of the students in a class passed their math test. If 16 of students passed the test, how many students are in the class
Answer:
24 students are in the class
Step-by-step explanation:
Let x represent the total number of students in the class. We have the equation:
(2/3)x = 16
x = 24 students
So, there are 24 students in the class.
Answer:
24 students
Step-by-step explanation:
16/2=8
8*3=24
Hello! could use some help. (answer all questions in one answer comment)
1. Draw 16 stairs. put them equally into 2 sets. how many stairs are in each set?
2. Abel Drew some Triangles, His drawing had 21 vertices. How many triangles did he draw? write a division equation to answer the question.
3. Equation: 30 ÷ 6 = 5. Write a related multiplication sentence.
4. Terrance tackled a total of 42 football players in the last 6 games. he tackled the same amount of players each game. how many players did Terrance tackle each game?
Answer:
1. 8
2. 21÷3=7
3. 5x6=30
4. 7
The following graph shows the cost of renting a car based on the miles driven including fees. The solid line represents Enterprise and the dotted line represents Dollar Rental Car Agency.
A) What is the initial fee for renting a car from Dollar Rental Car Agency?
B) What does the point of intersection represent?
c) If you were planning on driving 100 miles, which company would you choose? Why?
Company ________________
Explanation ________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________
Answer:
A) $40
B) The number of miles at which the cost will be the same for both companies
C) Enterprise. If you drive 100 miles it costs $35 with Enterprise and $45 with Dollar Rental Car Agency
I NEED HELP PLS PSSSSSSSSSSSSSSS
Answer:
240
Step-by-step explanation:
The total overall profit of all the weekdays is 1200. The question asks for the average. 1200 divided by 5 is 240. the average is 240 dollars per weekday
Answer:
278
Step-by-step explanation:
average = sum/count
count = 7 (7 days)
monday = 150
tuesday = 250
wednesday = 200
thursday = 250
friday = 350
saturday = 450
sunday = 300
sum = 150 + 250 + 200 + 250 + 350 + 450 + 300 = 1950
mean = 1950/7 = 278.571428571 ≈ 278
Jaidyn’s family drinks a total of 10 gallons of milk every 5 weeks . How many gallons of milk does the family drink per week? How many weeks does it take the family to consume one gallon of milk?
Answer:
2 gallons of milk per week
0.35 weeks(3.5 days) to consume 1 gallon
Step-by-step explanation:
Jaidyn's family drinks 10 gallons of milk every 5 weeks, which is a ratio of
10:5
To find how many gallons of milk they drink per week, you'd have to divide 10/5
10 ÷ 5 = 2
Considering that 1 week is 7 days, it would take them 0.35 weeks to consume 1 gallon of milk, which is the same as 3 and a half days.
which point on the graph would best represent unemployment (underutilizing labor)?
Answer:
i think the right one is H