ANYONE GOOD AT MATH COME ON OVER AND HELP A FELLOW SLOW PERSON PLEASE WILL GIVE 30 POINTS!!!
Answers
The completed table with the values for composite functions in column 3, f(g(x)) and column 4, g(f(x)) included is presented as follows;
[tex]\begin{array}{|c|c|c|c|}f(x) & g(x) & f(g(x)) &g(f(x)) \\&&&\\x^2+1 &-2\cdot x + 5 &4\cdot x^2 -20\cdot x +26 & -2\cdot x^2+3 \\&&&\\2\cdot x^2 - 2\cdot x + 4 & x+3 & 2\cdot x^2 + 10\cdot x + 16& 2\cdot x^2 - 2\cdot x + 7 \\&&&\\ \sqrt{x-4} &2\cdot x^2+ 4 &x\cdot \sqrt{2} & 2\cdot x - 4 \\\end{matrix}[/tex]
f(g(x)) ≠ g(f(x)), because the operations and the order of operations in the functions are different
What are composite functions?Composite functions are functions in which the input or argument are also functions.
The values of the composite functions based on the defined functions are found as follows;
f(x) = x² + 1, g(x) = -2·x + 5
Therefore; f(g(x)) is obtained by plugging in x = g(x) in f(x) as follows;
f(x) = x² + 1
f(g(x)) = (-2·x + 5)² + 1 = -2·x × (-2·x + 5) + 5 × (-2·x + 5) + 1
-2·x × (-2·x + 5) + 5 × (-2·x + 5) + 1 = 4·x² - 10·x - 10·x + 25 + 1
4·x² - 10·x - 10·x + 25 + 1 = 4·x² - 20·x + 26
When f(x) = x² + 1, and g(x) = -2·x + 5, f(g(x)) = 4·x² - 20·x + 26
g(f(x)) = is obtained by plugging in x = f(x) in g(x) as follows;
g(x) = -2·x + 5
f(x) = x² + 1
g(f(x)) = -2 × (x² + 1) + 5 = -2·x² - 2 + 5
g(f(x)) = -2·x² + 3
When f(x) = 2·x² - 2·x + 4, and g(x) = x + 3, we get;
f(g(x)) = 2×(x + 3)² - 2×(x + 3) + 4 = 2×(x² + 6·x + 9) - 2·x - 6 + 4
2×(x² + 6·x + 9) + 2·x + 6 + 4 = 2·x² + 10·x + 16
f(g(x)) = 2·x² + 10·x + 16
When f(x) = 2·x² - 2·x + 4, and g(x) = x + 3, f(g(x)) = 2·x² + 10·x + 16
g(f(x)) = is obtained by plugging in x = f(x) in g(x) as follows;
g(x) = x + 3
f(x) = 2·x² - 2·x + 4
g(f(x)) = 2·x² - 2·x + 4 + 3 = 2·x² - 2·x + 7
g(f(x)) = 2·x² - 2·x + 7
When f(x) = [tex]\sqrt{x - 4}[/tex], and g(x) = 2·x² + 4, we get;
f(g(x)) = [tex]\sqrt{2\cdot x^2 + 4 - 4} = x\cdot \sqrt{2}[/tex]
g(f(x)) = 2 × ([tex]\sqrt{x - 4}[/tex])² + 4 = 2 × (x - 4) + 4 = 2·x - 4
g(f(x)) = 2·x - 4
The values of the composite functions in column 3 and column 4 are included in the table in the first section of the response.
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Related Questions
6. Find the slope of the graphed line (-5,7) (0,4.5)
Answers
Answer:
[tex]\boxed{\boxed{\mathrm{m=-\cfrac{2.5}{5}}}\:or\:\boxed{\mathrm{m=-0.5}}}[/tex]Step-by-step explanation:
[tex]\mathrm{Slope=\cfrac{y_2-y_1}{x_2-x_1}}[/tex]
[tex]\mathrm{\left(x_1,\:y_1\right)=\left(-5,\:7\right)}[/tex]
[tex]\mathrm{\left(x_2,\:y_2\right)=\left(0,\:4.5\right)}[/tex]
[tex]\mathrm{m=\cfrac{4.5-7}{0-\left(-5\right)}}[/tex]
[tex]\mathrm{m=-\cfrac{2.5}{5}}[/tex]
[tex]\mathrm{m=-0.5}[/tex]
-Hope this helps!
What is 1/8 3/6 because im
Helping my son and I don’t know this I wasnet really a math guy
Answers
The value of 1/8 = 0.125 and 3/6 = 0.5.
What is the simplification of the expressions?To simplify an expression, you can use algebraic rules such as combining like terms, using the distributive property, and applying the order of operations (PEMDAS). Additionally, you can use properties of exponents, logarithms, and trigonometric functions to simplify expressions that involve those operations.
For example, you can simplify the expression 2x + 3x by combining the like terms 2x and 3x to get 5x. Another example, you can simplify the expression (3x + 2)(4x - 1) by using the distributive property to get 12x^2 + x - 8.
According to question:-
To simplify 1/8 * 3/6, you can first convert the fractions to have a common denominator. In this case, the least common multiple of 8 and 6 is 24. So you can convert 1/8 to 3/24 and 3/6 to 12/24.
Then, you can multiply the numerators and denominators separately:
(1/8) * (3/6) = (3/24) * (12/24) = 3/24 * 12/24 = 3/24 * 1 = 3/24
So the simplified form of the expression is 3/24.
As a side note, if you want to further simplify, you can divide the numerator and denominator by their greatest common divisor, which is 1 in this case, then you will get 3/24 equals to 1/8.
Hence, the value of 1/8 = 0.125 and 3/6 = 0.5.
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Which equations have the same value of x as Three-fifths (30 x minus 15) = 72? Select three options. 18 x minus 15 = 72 50 x minus 25 = 72 18 x minus 9 = 72 3 (6 x minus 3) = 72 x = 4.5
Answers
Answer:
18x - 9 = 72
3(6x - 3) = 72
x = 4.5
Step-by-step explanation:
Given equation:
[tex]\dfrac{3}{5}\left(30x-15\right)=72[/tex]
Separate the fraction:
[tex]\implies 3 \cdot \dfrac{1}{5}\left(30x-15\right)=72[/tex]
Multiply the terms inside the parentheses by 1/5:
[tex]\implies 3\left(\dfrac{1}{5}\cdot30x-\dfrac{1}{5}\cdot 15\right)=72[/tex]
[tex]\implies 3\left(6x-3\right)=72[/tex]
Expand the brackets:
[tex]\implies 3\cdot6x-3\cdot3=72[/tex]
[tex]\implies 18x-9=72[/tex]
Add 9 to both sides of the equation:
[tex]\implies 18x-9+9=72+9[/tex]
[tex]\implies 18x=81[/tex]
Divide both sides pf the equation by 18:
[tex]\implies \dfrac{18x}{18}=\dfrac{81}{18}[/tex]
[tex]\implies x = 4.5[/tex]
Therefore, the three equations that have the same value as the given equation are:
18x - 9 = 723(6x - 3) = 72x = 4.5Use the distributive property to write an equivalent expression. Then
evaluate the expression.
(10-7)5
Equivalent Expression
=
Answers
Answer:
Equivalent expression:
= 15
Step-by-step explanation:
Distributive proprty:
(10-7)5 = 10*5 + 10*-7
= 50 - 35
= 15
Evaluate:
(10-7)5 = 3*5
= 15
f(x) = x2. What is g(x)?
g(x)
H
-5
y
f(x)
-5-
-
O A. g(x) = 3x²
OB. g(x)=x²
OC. g(x)=
g(x)-(3x)²
(3, 3)
OD. g(x)=x²
5
X
Answers
On solving the provided question we cans ay that the value of the function will be x(x−2)=0 => x=0,2
What is a function?A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.
The given functions are -
f(x)=x^2, g(x)=2^x
Find the value for -
fog(x)= gof(x)....equation 1
f(g(x)={g(x)}^2
First find solution for function f(g(x) -
⇒ f(g(x)={2^x}^2=2^2x
Now find solution for function g(f(x)) -
g(f(x))=2^f(x)
⇒g(f(x))=2^x^2
Now, substitute the values in equation 1 -
gof(x)=fog(x)
2^x^2=2^2x
⇒x^2=2x
x^2−2x=0
Therefore, the solution set is obtained as x=0,2.
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Which of these is the result of form having the illusion of the third dimension?
Answers
Depth is the result of form having the illusion of the third dimension.
Even while the human brain perceives many flat pictures, such as those in movies and photographs, as being two dimensional, nothing actually exists without all three dimensions (2D). This is due to the fact that everything physically existing is made of atoms, which are imperceptible to the human sight yet include all three spatial dimensions. Human eyes have the capacity to perceive "depth" or three dimensions. The three spatial dimensions of the world may be perceived by someone who possesses depth perception. Each human eye's visual brain first interprets the three spatial dimensions as 2D pictures. Contrarily, stereoscopic vision, which is unique to humans, alters the image seen by the two eyes.
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eduardo rivas works in sales for straight commission. his gross pay of $680 last week was based on his sale of $13,600. what rate of commission was eduardo paid?
Answers
Therefore , the solution of the given problem rate of interest comes out to be he get commission of 4.9%.
What exactly is meant by interest?Simple interest is calculated by dividing the principal by the borrowing cost, the remaining time, and other elements. The simple return formula in marketing is principal + interest plus hours. Utilizing this method is the simplest way to calculate interest. As a percentage of the principle sum is the most frequent way to calculate income. For instance, he will only pay his portion of the 100% cost if he borrows $100 from a friend and agrees to pay the loan back with 5% interest.. You have to pay interest on money you borrow, and you have to charge interest on money you lend.
Here,
Given :
Gross pay = $680
Sales = $13,600
To find the what rate of commission he get on sale:
=> 680/13800 * 100
=> 0.049 * 100
=> 4.9%
Thus , he get commission of 4.9%
Therefore , the solution of the given problem of interest comes out to be
he get commission of 4.9%.
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Meg's mom makes homemade salad dressing by mixing oil and vinegar in
measuring cup when the mixture settles, Meg can see how much
used Look at the measuring cup and
mine how much of and vinegar was used to
epare the dressing
600 mL
500 mL
400 mL
300 mL
200 mL
100 mL
Answers
The typical oil to vinegar ratio is three parts oil to one part vinegar/acid, though this ratio might change depending on the vinegar/acid you use.
What is the ratio for oil to vinegar?One part vinegar to three parts oil is the general ratio for vinaigrettes. I learned this general principle from French culinary school, which results in a somewhat acidic dressing that goes well on salads. This implies that if you start with a cup of vinegar, you would need one cup of oil.
The typical oil to vinegar ratio is three parts oil to one part vinegar or acid, however this ratio might change based on the vinegar or acid you choose and your preferences. Less oil is required the less acidic the vinegar or acid.
Salad dressing mixing involves a physical alteration. Shaking the bottle creates a transient emulsion and suspension since the dressing's constituents are layered and immiscible.
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[tex]6+\frac{3}{x+1}[/tex]
Answers
The value of x would be -3/2.
What is the linear equation in one variable?
A linear equation in one variable is an equation in which the highest power of the variable is 1. A linear equation in one variable can be written in the form of y = mx + b, where m is the slope and b is the y-intercept. The graph of a linear equation in one variable is a straight line.
6 + 3/(x + 1) = 0
3/x+1 = -6
3 = -6(x + 1)
3 = -6x - 6
-6x= 9
x = -9/6
x = -3/2
Hence, the value of x would be -3/2.
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Tiana tried to evaluate an expression. Here is her work
Answers
Note that Tiana's work is wrong. Tiana made a mistake going from Step 2 to Step 3. Tiana should have subtracted 2 from 21 before adding. The order of operations says to add and subtract from left to right. The rule in operation here is known as PEMDAS. Note that when corrected and evaluated, the expression results in 27. (Option B)
What is PEMDAS?
The order of operations is a rule that specifies the right sequence of actions to be taken while evaluating a mathematical equation. PEMDAS stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).
Using the order of operations (PEMDAS), the expression 21 - 2 + 60 ÷ 15*2 would be evaluated as follows:
Parentheses - None
Exponents - None
Multiplication and Division (from left to right) - 60 + 15 = 4
Addition and Subtraction (from left to right) - 21 - 2 + 4*2 = 19 + 8 = 27
So the correct result is 27.
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Full Question:
See attached Image.
PLEASEEEEEEE HELPPPPPPPP!!!!!!!!!
Answers
Answer: 2
Step-by-step explanation: The value x in f(x) is a value on the x-axis that we input into the function. F(x) is a value on the y-axis. F(2) means we are inputting the value of 2 on the x-axis and looking for the corresponding point on the y-axis. If we look at the graph at x=2, we can see that the graph is above when y=2. This means that (2,2) is a point that satisfies f(x).
Rewrite the following equation in slope-intercept form.
10x + 11y = 9
Write your answer using integers, proper fractions, and improper fractions in simplest form.
Answers
Answer:
y=(-10x+9)/11
Step-by-step explanation:
10x+11y=9
11y=9-10x
y=(9-10x)/11
y=(-10x+9)/11
A dairy farm ships crates of milk to food stores. There are 48 quarts of milk
for every 3 crates shipped. Plot points on the graph to show how many
quarts of milk there are for shipments of 3, 4, 6, and 9 milk crates. Label each
point with its ordered pair.
WANNOW SNG.2006mol
sway
Ay
sdruouo 30 0/losy Sma
Quarts of Milk
128.
96
64
32
0
0
44
2 4 6 8
Milk Crates
X
Answers
There are 48, 64, 96 and 144 quarts of milk for 3,4,6 and 9 crates shipped.
What is coordinate pair?
Coordinate pair means the two numerical pair bounded by a parenthesis but separated by comma. The first numerical term denotes the X coordinate and the 2nd numerical term indicate Y coordinate. The coordinate pair is used to locate a point on the cartesian plane.
What is the coordinate pair for the given statement?A dairy farm ships crates of milk to food store. There are 48 quarts of milk for every 3 crates shipped.
for every 3 crates shipped there are 48 quarts of milk.
for 4 crates shipped there will be milk quarts = (48 × 4) / 3
= 64 quarts
for 6 crates shipped milk quarts = (6 × 48) / 3 = 96 quarts milk
for 9 crates shipped number of milk quarts = (9×48)/ 3 = 144
if ship crates are denoted by X axis and milk quarts is denoted by Y axis
then the coordinate pairs will be (3, 48), (4, 64), (6, 96) and (9, 144)
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Write the following mixed number as a decimal 9 3/8
Answers
Answer:
9.38
I believe this is the answer
The prices for different types and amounts of building bricks are given. Select the options that have the same cost per brick.
Answers
The bricks having same cost per brick are 1500 bricks for $1,110, 35 bricks for $25.90 and 230 bricks for $170.20. The solution has been obtained using the unitary method.
What is a unitary method?
The value of a single unit is calculated in the unitary approach before the value of the necessary number of units is determined. In order to obtain value of a single unit from a given multiple, the unitary technique is used, to put it simply.
We know that Cost per brick = number of bricks / price of bricks
Therefore, using this, we get
1500/$1110 = $1.35
1300 / $845 = $1.54
230 / $170.20 = $1.35
100 / $75 = $1.33
35 / $25.90 = $1.35
Hence, the bricks having same cost per brick are 1500 bricks for $1,110, 35 bricks for $25.90 and 230 bricks for $170.20.
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Question: The prices for different types and amounts of building bricks are given. Select the options that have the same cost per brick.
1500 bricks for $1,110.00
1300 bricks for $845.00
230 bricks for $170.20
100 bricks for $75.00
35 bricks for $25.90
The assets and liabilities of a local surf shop are listed below.
Building Mortgage $78,280
Other Debt $21,987
Accounts Receivable $15,403
Property Value $130,284
Long Term Investments $106,987
Small Business Loan $28,950
Long Term Liabilities $48,970
Owned Inventory $38,671
Cash $208,634
Savings Account $172,839
Owned Equipment $38,291
The surf shop owner receives notice that the property value has increased by $40,000. What is the net worth of the surf shop?
$532,922
$572,922
$711,109
$731,109
Answers
The net worth of the surf shop would be $572,922.
Option (B) is correct.
What is the net worth?
Net worth is a financial metric that represents the value of an individual or a company, and it is calculated by taking the total assets and subtracting the total liabilities.
To calculate this, you would add up all of the assets (property value, long term investments, cash, savings account, owned inventory, and owned equipment) and subtract all of the liabilities (building mortgage, other debt, small business loan, and long term liabilities).
In this case, the assets total:
$130,284 (property value) + $106,987 (long term investments) + $208,634 (cash) + $172,839 (savings account) + $38,671 (owned inventory) + $38,291 (owned equipment) = $731,109
And the liabilities total:
$78,280 (building mortgage) + $21,987 (other debt) + $28,950 (small business loan) + $48,970 (long term liabilities) = $178,187
So,
$731,109 (assets) - $178,187 (liabilities) = $572,922 (net worth)
hence, The net worth of the surf shop would be $572,922.
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given the angle ABC equals 114. What is the angle BAD
Answers
Answer:
A. 63°
Step-by-step explanation:
You want to know the base angle in the isosceles triangle in the given figure.
Angle sumAngle ABC is the sum of its parts:
∠ABC = ∠ABD +∠DBC
The figure shows ∆DBC is equilateral, so ∠DBC = 60°. This lets us solve for the measure of angle ABD:
114° = ∠ABD +60°
54° = ∠ABD
Base angle∆ABD is isosceles, so the two base angles are congruent. The sum of angles in the triangle is 180°, so we have ...
∠ABD +∠BAD +∠BDA = 180°
54° +2(∠BAD) = 180° . . . . . . . ∠BAD =∠BDA
∠BAD = 90° -27° . . . . . . divide by 2, subtract 27°
∠BAD = 63°
Select the graph that would represent the best presentation of the solution set. \(4x-2 < 10\)
Answers
Answer:
A bar graph with x-axis labeled from 0 to 10, and y-axis labeled from 0 to 4, with 4x-2 marked with a solid line.
Which expression is equal to 2√-28
Answers
Answer:
B) [tex]4i\sqrt{7}[/tex]--------------------------
We know that:
[tex]i = \sqrt{-1}[/tex]Therefore the given expression is simplified as:
[tex]2\sqrt{-28} =2\sqrt{-1*4*7} =2i\sqrt{4} \sqrt{7} =2i*2\sqrt{7} =4i\sqrt{7}[/tex]Answer:
b) 4i√7
Step-by-step explanation:
Given problem,
→ 2√-28
Let's solve the given problem,
→ 2√-28
→ 2√(-1) × √(28)
→ 2i × √(4) × √(7)
→ 2i × 2 × √7
→ 4i√7
Hence, option (b) is correct.
A line passes through the points (0, 5) and (1, 10). What is its equation in slope-intercept form?
Answers
The equation of the line in the slope-intercept form will be y = 5x + 5.
What is the equation of a line passing through two points?Let the equation of the line pass through (x₁, y₁) and (x₂, y₂).
Then the equation of the line is given as,
[tex]\rm (y - y_2) = \left (\dfrac{y_2 - y_1}{x_2 - x_1} \right ) (x - x_2)[/tex]
A line passes through the points (0, 5) and (1, 10). Then the equation of the line is given as,
(y - 5) = [(10 - 5) / (1 - 0)] (x - 0)
y - 5 = 5x
y = 5x + 5
The equation of the line in the slope-intercept form will be y = 5x + 5.
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Karen has 20 one-dollar bills. She wants to give each of her 6 children the same number of bill
give each child How many bills will Karen have remaining?
Answers
Answer:
2
Step-by-step explanation:
because 6 can't Divide 20 so,
18/6
rem:2
now,
Total money-Giving money
20-18
2$
The triangle shown below has an area of 5 units 2 squared.
Find the missing length: x
Answers
The missing length x is equal to the square root of 10 units.
What is triangle?A triangle is a three sided polygon with 3 angles and three sides it is one of the most basic and fundamental safe in geometry and is used in many different areas of methane science triangle are also after use in architecture art in other areas of the design triangle come in many different form such as equatorial isosceles and scalene and can be classified by their angles side or both.
The formula for finding the area of a triangle is A = 1/2(base × height). In this case, the base and height are both x, so A = 1/2(x2). Plugging in the given area of 5, we have 1/2(x2) = 5 and solve for x to get x = √(10). So the missing length x is equal to the square root of 10 units.
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Sophia is going to invest in an account paying an interest rate of 3.4% compounded monthly. How much would Sophia need to invest, to the nearest dollar, for the value of the account to reach $1,450 in 14 years?
Answers
Answer:
To calculate the amount Sophia needs to invest to reach a certain value in a specific time, given an interest rate compounded monthly, we can use the formula:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment
P = the initial principal or investment amount
r = the annual interest rate (expressed as a decimal)
n = the number of times the interest is compounded per year
t = the number of years the investment is held
Since the interest is compounded monthly, we need to divide the annual rate by 12 to find the monthly rate. So:
r/12 = 0.034/12 = 0.002833
Now we can plug in the values into the formula:
A = P(1 + 0.002833)^(12*14)
A = P(1.002833)^(168)
We know that A = $1,450 and we want to find P (the initial principal or investment amount).
So we can rearrange the equation to find P:
P = A/(1.002833)^(168)
Solving for P, we get:
P ≈ $973.99
So Sophia would need to invest around $973.99 to reach $1,450 in 14 years with an annual interest rate of 3.4% compounded monthly.
Step-by-step explanation:
Is 24/36 equal to 4/5?
Answers
what is the half-life of the radionuclide that shows the following decay curve?
Answers
Decay constant: the ratio of the number of radioactive atoms in a population to the rate at which they are vanishing due to radioactive decay. The rate of change is determined by the equation dN/dt = N, where is the decay constant, assuming N is the size of a population of radioactive atoms at a particular time t and dN is the amount by which the population declines in time dt.
When this equation is integrated, N = N0et is obtained, where N0 is the starting population size of radioactive atoms at time t = 0. This demonstrates that the rate of population decay is dependent on the decay constant and is exponential.
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The decay constant: the ratio of the number of radioactive atoms in a population to the rate at which they are vanishing due to radioactive decay.
The rate of change is determined by the equation dN/dt = N,
where is the decay constant, assuming N is the size of a population of radioactive atoms at a particular time t and dN is the amount by which the population declines in time dt.
When this equation is integrated, N = N0et is obtained, where N0 is the starting population size of radioactive atoms at time t = 0. This demonstrates that the rate of population decay is dependent on the decay constant and is exponential.
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Multiply. V6. V22 . v55
Answers
Using exponents law, the required product is [tex]v^{83}[/tex]
What are Exponents?
A number's exponent demonstrates how many times we are multiplying a given number by itself. 3^4, for instance, indicates that we are multiplying 3 by four. 3*3*3*3 is its expanded form. The power of a number is another name for an exponent. A whole number, fraction, negative number, or decimal are all acceptable. Exponent times power is how you raise a number with an exponent to a power.
[tex]v^6 \times v^{22} \times v^{55}[/tex]
Use the exponents law:
[tex]a^m \times a^n = a^{m+n}[/tex]
So, we get [tex]v^{6+22+55} = v^{83}[/tex]
Thus, the required product is [tex]v^{83}[/tex]
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What should I do please help
Answers
3⁵ means, multiply 5 factors of 3.
938.120 in word form
Answers
Answer:
Nine hundred thirty-eight one hundred twenty thousandths.
-Hope this helps!
Four times a number is at least 10
Answers
Answer:
4x>= 10
Step-by-step explanation:
i believe thats the answer
Find all the missing side and angles < p
Answers
The angles are 90 degree and 30 degree and side PQ=6.93 and PN=8 units.
What characteristics does a triangle have?Three sides and three angles make up a triangle. A triangle's total angles are always 180 degrees. A triangle's exterior angles are always a sum of 360 degrees. The total of the parallel interior and exterior angles is additional.
Since, it is a right angle triangle, we can use Pythagoras theorem.
Sum of all angles is 180 degree in a triangle.
hence,
60+x+90=180
x=30 degrees.
cos 60=base/hypotenuse
1/2=4/Hypotenuse
Hypotenuse=2*4=8 units
Hypotenuse=PN=8 units.
now,
sin 60=perpendicular/hypotenuse
[tex]\sqrt{3}/2=PQ/8[/tex]
PQ=6.93 units
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