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 percentage of the class voted for Maria?
combine like terms:
Like terms for the given data are: 17x² and 3x²; -3xy and -2xy. Combining the like terms we get: 20x² and -5xy
What is like terms?In algebra, the term "equal terms" refers to words with the same variable to the same power.
Similar variables and powers are called similar words in algebra. Matching coefficients is not required. When two or more words do not share the same variable or power, they are called inequal terms. The order of both variables is irrelevant unless there is a power. All of these have the same terminology.
17x² and 3x²
-3xy and -2xy
Combine the same terms obtained.
17x² + 3x² = 20x²
-3xy + (-2xy)
= -3xy -2xy
= -5xy
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Suppose you know the answer to 4/5*(20*1 7/8). Explain how the Commutative and Associative Properties of Multiplication can make the computation easier. Then find the answer
You can rearrange terms in an expression using the commutative and associative qualities to arrange compatible numbers next to one another and in groups.
What distinguishes an associative property from a commutative property?According to the associative property, numbers can be added to or multiplied while still maintaining the same result. According to the commutative property, even if the numbers are added or multiplied, the solution will remain the same.
Explain:
[tex]\frac{4}{5}[/tex] ×(20×17/8)
20×17/8
340÷8
[tex]\frac{4}{5}[/tex]×[tex]\frac{340}{8}[/tex]
= [tex]\frac{64}{2}[/tex]
= 32
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Solve the following system of equations graphically on the set of axes below.
y = x + 8
y = -1/2x+5
Plot two lines by clicking the graph. Click a line to delete it.
By graphing both equations on the same axis and findin where do they intercept, we willsee that the solution is (-2, 6).
How to solve the system of equations?Here we have the following system of equations:
y = x + 8
y = -(1/2)x+5
And we want to solve it graphically.
To solve it in that way, we just need to graph both equations on the same coordinate axis and find the ponit where the graphs intercept, that point will be the solution for the system.
The graph of the system of equations can be seen in the image below:
There, we can see that the lines intercept at the point (-2, 6), so that is the solution of our system.
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Is Infinity a interval?
To represent "infinity" or the notion that an interval lacks an ending, we use the symbol.
Is infinity an open interval?The endpoints of infinity and negative infinity can be seen in two different ways. One the one hand, we can never get to infinity because it is a concept and not a real quantity.
In this sense, the interval is said to be open because it excludes the endpoints infinity and negative infinity. The infinity symbol is placed on the right side since there is no higher endpoint (all values must be larger than or equal to -3). An interval is closed if its boxed end is on -3. Because there is no endpoint on that side, infinity always has a curved end.
To represent "infinity" or the notion that an interval lacks an ending, we use the symbol. The symbol shouldn't be used with a square bracket because it's not a number. Visit this tutorial on set-builder and interval notation for a more thorough discussion of set notation and interval notation.
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What are 4 ways to solve a problem?
The 4 ways to solve a problem are understanding the problem, devising a plan, carrying out the plan, look back.
A problem is any type of disruption from normality that is impeding progress. A problem can be time-consuming and requires too much energy to solve it.
Polya created his famous four-step process for problem-solving, which is used all over to aid people in problem-solving:
Step 1. Understand the problem.
x = a number
Step 2. Devise a plan (translate).
Twice the difference between a number and 1 is equal to 4 more than that number
Step 3. Carry out the plan (solve).
2(x - 1) = (x + 4)
2x - 2 = x + 4
2x - 2 - x = x + 4 - x
x - 2 + 2 = 4 + 2
x = 6
Step 4. Look back (check and interpret).
If we take twice the difference of 6 and 1, that is the same as 4 more than 6. Thus the final answer is 6.
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3. Birr 6,500 was divided equally among a certain number of persons. Had there been 15 more persons, each would have got Birr 30 less. Find the original number of persons.
If the population grows by 15 people. The original number of people was 50, hence the new share of each person was Rs. (which is refused).
What is meant by Mathematical equation?The definition of an equation in algebra is a mathematical statement that proves two mathematical expressions are equal. Consider the equation 3x + 5 = 14, where 3x + 5 and 14 are two expressions that are separated by the symbol "equal."
Let no. of persons = x
Each person get
= 6500/x
If there 15 persons were added more
= 6500/(x + 15)
(6500/x) - 6500/(x + 15) = 30
[tex]\Rightarrow 6500\left[\frac{(\mathrm{x}+15)-(\mathrm{x})}{\mathrm{x}(\mathrm{x}+15)}\right]=30[/tex]
[tex]\Rightarrow 6500\left[\frac{x+15-x}{x^2+15 x}\right]=30[/tex]
[tex]& \Rightarrow 1625\left[\frac{15}{x^2+15 x}\right]=3 \\[/tex]
Then,
[tex]& \Rightarrow \frac{24375}{x^2+15 x}=3 \\[/tex]
Simplifying the above equation,
[tex]& \Rightarrow 3 x^2+45 x=24375 \\[/tex]
[tex]& \Rightarrow 3 x^2+45 x-24375=0 \\[/tex]
[tex]& \Rightarrow x^2+15 n-3250=0 \\[/tex]
[tex]& \Rightarrow x^2+(65 n-50 n)-3250=0 \\[/tex]
Then we get,
[tex]& \Rightarrow x^2+65 n-50 n-3250=0 \\[/tex]
[tex]& \Rightarrow x+65)-50(x+65)=0[/tex]
[tex]\Rightarrow(\mathrm{x}-50)(\mathrm{x}+64)=0[/tex]
x = 50, x = -65
Since the number of people cannot be zero,
the number of people is 50.
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What is a 9 sided shape called?
A 9-sided shape is called a nonagon.
Therefore the answer is nonagon.
A nonagon is a polygon with nine sides and nine angles. A nonagon can be regular or irregular, depending on the lengths of its sides and angles. A regular nonagon has equal sides and angles, while an irregular nonagon has sides and angles of different lengths.
Nonagons are two-dimensional shapes, and they can be described by their number of sides, angles, and vertices. They are considered a type of polygon, which is a closed geometric figure that is made up of straight lines. In addition to nonagons, there are other types of polygons such as triangles, quadrilaterals, pentagons, hexagons, heptagons, and so on.
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knowing the difference between an experimental group and a control group is most relevant to understanding the nature of: group of answer choices random sampling. replication. hindsight bias. independent variables.
The experimental group is given the experimental treatment, and the comparison group is statistically significant.
Which three attitudes are the basis of the scientific viewpoint?Curiosity, scepticism, and humility are described by historians of science as the three attitudes that form the bedrock of the scientific viewpoint. Larger, more representative sample sizes aid in the production of accurate and valid data.When random sampling is used, every member of the population has an equal chance of being chosen, resulting in the collection of a representative sample. The odds of generalising the study's findings to the population increase with the use of a random sample. The study's margin of error is reduced with higher study sample sizes.) Researcher control over the possibility of reporting false-negative or false-positive findings is made possible by larger sample sizes. Results will be more precisely predicted with a larger sample size.To learn more about random sampling refer to :
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write days in May to days in a year as a ratio.
Answer:
Step-by-step explanation:
Days in may = 31
Days in a year = 365
therefore, expected ratio = 31/365
One bottle holds 67.34 onces and another bottle holds 48.5 onces combined how much do they hold?
After combine they hold 115.84 ounces.
What is Addition?A process of combining or adding two or more numbers is called addition.
We have to given that;
One bottle holds 67.34 ounces and another bottle holds 48.5 ounces.
So, After combine, we get;
Both bottle hold = 67.34 ounces + 48.5 ounces
= 115.84 ounces
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The coordinates of 3 of the vertices of a parallelogram are (-3, 4), (-2, 1), and (2, 6). What is the equation for the
line containing the side opposite the side containing the first two vertices? (Remember, opposite sides of a
parallelogram are parallel.)
The equation for the side of the line that contains the first two vertices' opposite side is 3x+y=12
Given that,
Three of a parallelogram's vertices have the coordinates (-3, 4), (-2, 1), and (2, 6).
We have to find what is the equation for the side of the line that contains the first two vertices' opposite side.
We know that,
The equation of the line is
y=mx+b
Here, we find m and d
Take the points (-3,4) (-2,1)
m = y₂-y₁ / x₂-x₁
m = 1 - 4 / -2-(-3)
m = -3 / 1
m = -3
Now take point (2,6)
6 = -3(2) + b
6 = -6 + b
6 + 6 = b
12 = b
We get m =-3 and b=12
The equation will be y=-3x+12
3x+y=12
Therefore, the equation for the side of the line that contains the first two vertices' opposite side is 3x+y=12
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Rent-A-Car charges $50 to rent a car plus $0.25 per mile. Save-To-Rent charges $25 to rent a car plus $0.41 per
After how many miles will the cost be the same to rent a car?
miles
After 156.25 miles will the cost be the same to rent a car. This can be solved by the concept of cross-multiplication.
What is cross-multiplication?Fractions are multiplied by multiplying the numerator of the first fraction by the denominator of the second fraction, and the numerator of the second fraction by the denominator of the first fraction.
In order to get the second fraction's numerator, multiply the first fraction's denominator by it. Cross multiply is another name for the butterfly technique of multiplication. The cross-multiply technique is used to find one or more variables in a fraction.
Let, assume miles be m.
and, Let the total cost be x.
According to the question,
0.25m + 50 = x ........(i)
0.41m + 25 = x ........ (ii)
By solving equation (ii) by (i) we get -
0.16 m - 25 = 0
or, 0.16m = 25
or, m = 25 /0.16
or, m = 156.25
Thus, number of miles = 156.25 miles.
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There are 14 teams in a basketball league.
Each team plays every other team twice
during the season.
a) Suppose that you want to determine
how many games, in total, are played.
Suggest a simpler problem that you
could solve first.
b) How many games, in total, are played
during the season?
Please I need deep explaining.
Therefore , the solution of the given problem of combination comes out to be there were 182 games played in all.
Definition of combinationCombinations are operations in mathematics that count the number of possible combinations that can be created from a set of items, where the selection's direction is immaterial. You are free to select any arrangement of the parts. Permutations and combinations can be mixed up.
Here,
There still are 14 teams in all, but each team plays the other twice.
Every team plays almost every team twice, hence the total amount of games played is simply the permutations of 2 out of 14, which is determined by:
₁₄P₂
=14!/((14-2)!)
= (14×13×12!)/ 12!
= 14×13
=182
Consequently, there were 182 games played in all.
Therefore , the solution of the given problem of combination comes out to be there were 182 games played in all.
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The graph below models the value of a $20,000 car fyears after it was purchased.
20000
18000
16000
14000
12000-
10000
8000
6000
4000
2000-
Dollars
Value of Car
52:25
2 4 6 8 10 12 14 16 18 t
Years
Which statement best describes why the value of the car is a function of the number of years since it was purchased?
A. Each car value y, is associated with exactly one time, t.
B. Each time, t, is associated with exactly one car value, y.
C.The rate at which car decreases in value is not constant.
Your answer should be B. Each time, t, is associated with precisely one car value, y.
Solve the following equation by first writing the equation in the form a x squared = c: 3 a squared minus 21 = 27 a. a = 4 b. a = plus-or-minus 4 c. a = plus-or-minus 16 d. a = 16 Please select the best answer from the choices provided A B C D
The best answer from the choices provided is a = plus-or-minus 16 . Option C
What is a quadratic equation?A quadratic equation can be defined as an equation that can be rearranged in a standard form
Such that;
x represents an unknown value or variableThe variables, a, b, and c represent known numbersThe variable, a ≠ 0These quadratic equation are also described as polynomial equation having its highest degree as 2.
From the information given, we have that;
3a² - 21 = 27
collect like terms
3a² = 27 + 21
Add the values
3a² = 48
Divide both sides by 3
a² = 48/3
a² = 16
Hence, the value is a² = 16
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At Florida A&M University, the ratio of students from Florida to students not from Florida is about `3\ :\ 1`.
How many of its `12000` students are from Florida?
Based on the information given, the number of students from Florida will be; 9000 students.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.
We are given that At Florida A&M University, the ratio of students from Florida to students not from Florida is about 3 : 1
The Total number of students = 12000
Fraction from Florida = 3/4
Fraction of students not from Florida = 1/4
Therefore, the students from Florida will be:
= 3/4 × 12000
= 9000
Hence, the number of students from Florida is 9000.
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At a fancy dinner party, the number of courses that will be served determines how many forks will be set out by the hostess.
c = the number of courses served during dinner
f = the number of forks set out by the hostess
Which of the variables is independent and which is dependent?
Answer:
c is the independent variable and f is the dependent variable
Step-by-step explanation:
Select the correct answer. how many particles are in one mole?
a. 6.022 × 1023
b. 2.066 × 1023
c. 6.023 × 1022
d. 3.026 × 1022
6.022× [tex]10^2^3.[/tex]particles are in one mole.
The correct option is 6.022× [tex]10^2^3.[/tex]
Now, According to the question:
Avogadro's number
Avogadro's number, number of units in one mole of any substance (defined as its molecular weight in grams), equal to 6.02214076 × [tex]10^2^3.[/tex] The units may be electrons, atoms, ions, or molecules, depending on the nature of the substance and the character of the reaction.
Now, According to Avogadro's law, one mole of any substance contains a fixed number of particles i.e.,6.022× [tex]10^2^3.[/tex]particles (atoms, molecules or ions) which is also known by the name Avogadro's number.
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Gaya buys 2 oranges and 1 cauliflower she pays £2.00
Esteben buys 4 oranges and 1 cauliflower he pays £2.90
Work out the price of one orange
Answer:
Step-by-step explanation:6
PLEASE SOMEONE HELPPPPP
Simplify (36)18
O a
Ob
Oc
Od
33
312
324
3108
Answer:
d. 3^108
Step-by-step explanation:
Just multiply 6 and 18.
Donna reads 56 chapters of a book in 7 hours. What is her rate in chapters per hour?
Answer:
To find what her rate for how many chapters she reads per hour, you want to find out what times 7 gives you 56, or you can simply divide:
56/7 = 8
Donna reads 8 pages per hour.
Step-by-step explanation:
Hope it helps! =D
Consider the expression.
2x (x + 3y) +5 (2x - 2)
How many terms does the expression have when simplified completely?
When given expression 2x (x + 3y) +5 (2x - 2) simplified completely then it would have 4 terms.
Consider given expression.
2x (x + 3y) +5 (2x - 2)
We simplify above expression.
2x (x + 3y) +5 (2x - 2)
= [(2x × x) + (2x × 3y)] + [(5 × 2x) - (5 × 2)] ......(distributive property)
= [2x² + (2 × 3)xy] + [(5×2)x - 10] ............(commutative property)
= (2x² + 6xy) + (10x - 10)
= 2x² + 6xy + 10x - 10
= 2x² + 10x + 6xy - 10 ...........(by commutative property of addition)
when given expression simplified completely then it would be,
2x (x + 3y) +5 (2x - 2) = 2x² + 10x + 6xy - 10
The number of terms in an expression 2x² + 10x + 6xy - 10 are 4
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5 parents and 3 children cost £ 13.20
2 parents and 1 child cost £ 5.10
Find the cost of 1 child
Find the cost of 1 parent
Answer:
The cost of 1 child is £ 3.40 and the cost of 1 parent is £ 4.10. To determine this, we can use the following equation:
Cost of 1 child = (13.20 - 5.10) / (5 parents + 3 children)
Cost of 1 parent = (13.20 - 5.10) / (2 parents + 1 child)
Hope this helps!
Step-by-step explanation:
HELP PLEASE 10 POINTS!
pls explain
a. 160 is what percentage of 40?
b. 40 is 160% of what number?
c. What number is 40% of 160?
Answer:
a) 400% b) 1/4 c) 64
Step-by-step explanation:
Answer:
a. 400%
b. 25
c. 64
Step-by-step explanation:
a. 160 ÷ 40/100
160 × 100 / 40
4 × 100 = 400%
b. 40 ÷ 160%
40 ÷ 160/100
40 × 100/160 = 25
c. 40% × 160
40/100 × 160
4 × 16 = 64
The daily recommended allowance of vitamin c for a sixth grader is 45 mg. 1 orange has about 75% of the recommended daily allowence of vitimin c. How many milligrams are in 1 orange?
Proportionately, the quantity of milligrams of vitamin c in 1 orange is 33.75 mg.
What is proportion?Proportion refers to the part of a whole contained in another value.
Proportion is a ratio representation, which is fractional in value.'
We depict proportions using decimals, fractions, or percentages.
The daily recommended allowance of vitamin c for a sixth grader = 45 mg
The content of 1 orange to the daily recommended allowance = 75%
75% of 45 mg = 33.75 mg.
Thus, 1 orange will proportionately contain 33.75 mg, which is 75% of 45 mg.
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What is the simplified form of this expression?
(-3x2 + 2x − 4) + (4x2 + 5x + 9)
7x2 + 7x + 5
x2 + 7x + 5
x2 + 7x + 13
x2 + 11x + 1
Answer:
x² + 7x + 5
Step-by-step explanation:
(- 3x² + 2x - 4) + (4x² + 5x + 9)
since both parenthesis are being multiplies by 1 , remove parenthesis
= - 3x² + 2x - 4 + 4x² + 5x + 9 ← collect like terms
= (- 3x² + 4x²) + (2x + 5x) + (- 4 + 9)
= x² + 7x + 5
Use a calculator to find cos 149° rounded to the nearest hundredth. Identify the angle of depression
The value of cos 149 degree as calculated from the calculator is found out to be -0.857167301.
Which on round off is , -0.85.
The formula to calculate the angle of depression is , θ = tan-1 (Opposite Side/Adjacent Side) .
Therefore, the AOD for cos149 degree is found out to be as ,
α = arctan(vertical distance / horizontal distance)
α = arctan(10 / 11.998)
α = arctan(0.83347224537423)
α = 0.69482025147278 ° ≈ 0.69 °
The angle of depression is defined as the point of meeting of a horizontal line with the line between the item and the observer's eye. This angle is determined by two factors , which are their height and distance. If the item is below the observer's level, the angle produced between the horizontal line and the observer's line of sight is known as the angle of depression.
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A line that includes the points (k,
–
4) and (5,
–
2) has a slope of
–
1. What is the value of k?
The required value of k is 7 for a line that includes the points (k,–4) and (5,–2).
What is the slope of the line?The slope of a line is defined as the gradient of the line. It is denoted by m
Slope m = (y₂ - y₁)/(x₂ -x₁ )
As per the question, the slope of the line is -1, and the given points are (k, -4) and (5, -2).
So we can substitute these values into the formula:
-1 = (-2 - (-4)) / (5 - k)
-1 = 2 / (5 - k)
-1 × (5 - k) = 2
-5 + k = 2
k = 2 + 5
k = 7
Therefore, the value of k is 7.
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In a middle-school mentoring program, a number of the sixth graders are paired with a ninth-grade student as a buddy. No ninth grader is assigned more than one sixth-grade buddy. If 13 of all the ninth graders are paired with 25 of all the sixth graders, what fraction of the total number of sixth and ninth graders have a buddy
Answer:
13/25
I hope this is the correct answer.