3
2.
4
5
1
5
The Substitution Property of Equality states that if m_2+ m_3-m25 and m_2 - 25, then
-m25
m_2+ m23
25+ m23
25+ m22
25

Answer:

x^2-10

Step-by-step explanation:

the area of whole square is x^2, not shaded area is 5*2=10, so shaded area equals to x^2-10

Answer:

1)  The functions are not inverses.

\(\textsf{2)} \quad g^{-1}(n)=&\dfrac{3}{8}n-\dfrac{7}{8}\)

\(\textsf{3)} \quad g^{-1}(x)&=\sqrt[3]{\dfrac{1}{2}-\dfrac{1}{2}x}\)

Step-by-step explanation:

The inverse composition rule states that if two functions are inverses of each other, then their compositions result in the identity function.

Given functions:

\(g(x) = 4 + \dfrac{7}{2}x \qquad \qquad f(x) = 5 - \dfrac{4}{5}x\)

Find g(f(x)) and f(g(x)):

\(\begin{aligned} g(f(x))&=4+\dfrac{7}{2}f(x)\\\\&=4+\dfrac{7}{2}\left(5 - \dfrac{4}{5}x\right)\\\\&=4+\dfrac{35}{2}-\dfrac{14}{5}x\\\\&=\dfrac{43}{2}-\dfrac{14}{5}x\\\\\end{aligned}\)                 \(\begin{aligned} f(g(x))&=5 - \dfrac{4}{5}g(x)\\\\&=5 - \dfrac{4}{5}\left(4 + \dfrac{7}{2}x \right)\\\\&=5-\dfrac{16}{5}-\dfrac{14}{5}x\\\\&=\dfrac{9}{5}-\dfrac{14}{5}x\end{aligned}\)

As g(f(x)) or f(g(x)) is not equal to x, then f and g cannot be inverses.

\(\hrulefill\)

To find the inverse of a function, swap the dependent and independent variables, and solve for the new dependent variable.

Calculate the inverse of g(n):

\(\begin{aligned}y &= \dfrac{8}{3}n + \dfrac{7}{3}\\\\n &= \dfrac{8}{3}y + \dfrac{7}{3}\\\\3n &= 8y + 7\\\\3n-7 &= 8y\\\\y&=\dfrac{3}{8}n-\dfrac{7}{8}\\\\g^{-1}(n)&=\dfrac{3}{8}n-\dfrac{7}{8}\end{aligned}\)

Calculate the inverse of g(x):

\(\begin{aligned}y &= 1-2x^3\\\\x &= 1-2y^3\\\\x -1&=-2y^3\\\\2y^3&=1-x\\\\y^3&=\dfrac{1}{2}-\dfrac{1}{2}x\\\\y&=\sqrt[3]{\dfrac{1}{2}-\dfrac{1}{2}x}\\\\g^{-1}(x)&=\sqrt[3]{\dfrac{1}{2}-\dfrac{1}{2}x}\\\\\end{aligned}\)

Answer:

1.

If the composition of two functions is the identity function, then the two functions are inverses. In other words, if f(g(x)) = x and g(f(x)) = x, then f and g are inverses.

For\(\bold{g(x) = 4 + \frac{7}{2}x\: and \:f(x) = 5 -\frac{4}{5}x}\), we have:

\(f(g(x)) = 5 - \frac{4}{5}(4 + \frac{7}{2}x)\\ =5 - \frac{4}{5}(\frac{8+7x}{2})\\=5 - \frac{2}{5}(8+7x)\\=\frac{25-16-14x}{5}\\=\frac{9-14x}{5}\)

\(g(f(x)) = 4 + (\frac{7}{5})(5 - \frac{4}{5}x) \\=4 + (\frac{7}{5})(\frac{25-4x}{5})\\=4+ \frac{175-28x}{25}\\=\frac{100+175-28x}{25}\\=\frac{175-28x}{25}\)

As you can see, f(g(x)) does not equal x, and g(f(x)) does not equal x. Therefore, g(x) and f(x) are not inverses.

Sure, here are the inverses of the functions you provided:

2. g(n) = (8/3)n + 7/3

we can swap the roles of x and y and solve for y to find the inverse of g(n). In other words, we can write the equation as y = (8/3)n + 7/3 and solve for n.

y = (8/3)n + 7/3

n =3/8*( y-7/3)

Therefore, the inverse of g(n) is:

\(g^{-1}(n) = \frac{3}{8}(n - \frac{7}{3})=\frac{3}{8}*\frac{3n-7}{3}=\boxed{\frac{3n-7}{8}}\)

3. g(x) = 1 - 2x^3

We can use the method of substitution to find the inverse of g(x). We can substitute y for g(x) and solve for x.

\(y = 1 - 2x^3\\2x^3 = 1 - y\\x = \sqrt[3]{\frac{1 - y}{2}}\)

Therefore, the inverse of g(x) is:

\(g^{-1}(x) =\boxed{ \sqrt[3]{\frac{1 - x}{2}}}\)

Answer:

The value for 6 is ones that's the answer

Answer:

14) 0.01 or 1/100

15) 0.06

16) 3.02

17) >

18)0.6

19) 100

20) 0.35

Answer:

its -1.5

I got u trust me

aaaaaaaaa

Answer:

224

Step-by-step explanation:

360.-136.

Answer: 14π

Step-by-step explanation: The formula for circumference is 2 * pi * the radius. However, we are looking for the terms of pi, so we will multiply 2 times pi to get 2 pi. then we get 2 pi x 7 which gives us 14pi, the answer.

Answer:

weetablx is heavier

Step-by-step explanation:

lets simplify

wheat wheat - 0.35 kg

weetablx - 9/25

simplify into decimals

wheat wheat- 0.35 kg

weetablx- 0.36 kg

brainliest appreciated!

Answer:

19.5

Step-by-step explanation:

39 x 0.50 = 19.5

Answer:

The equation is 5x+25=40

The answer is x=3

Step-by-step explanation:

The equation is 5x+25=40

Subtract 25 on both sides:

5x=15

Divide 5 on both sides:

x=3

Hope this helps!

Answer:

Step-by-step explanation:

5 ) c

6) c

7) b

8) a

Answer:

It will take 9 years

Step-by-step explanation:

use formula A=P(1+ r/n)^nt

37,500= 25,475(1+.046/1)^1*x

37,500/25,475=1.046^x

1.47203= 1.046^x

try out different numbers for x and use whole number since it asks for the nearest year

1.046^8 = 1.43302 and 1.046^9 = 1.4989

so we know its inbetween

8 and 9 to figure out one is the closest whole number try raising it to the power of 8.5 and if it passes 1.47203 then its 9, if it doesnt then its 8

1.046^8.5 = 1.46561

1.46561< 1.47203

since 1.046561 is lower than 1.47203 its safe to assume that the year is between 8.5-8.99 thus we can round up to 9

Answer:

Step-by-step explanation:

Answer:13

Step-by-step explanation:

Answer: n = 15

Step-by-step explanation: 2x15 = 30

Answer:

15

Step-by-step explanation:

15 times 2 is 30. Therefore, 15 can be the correct answer!

Please mark me brainliest if I helped you! Thank you so much!

:)

Answer:

What are the answer choices?

y values: 3,4,5,6

x values: 5,10,15,20

Step-by-step explanation:

I used a graphing calculator but y is increasing by one and x increases by 5 each time

Answer:

See below.

Step-by-step explanation:

A's number is x. B's number is y.

x = 5y - 10

First row: What is x when y= 3?

                             x = 5y - 10 = 5*3 - 10 = 15 - 10 = 5; x = 5

Second row: What is x when y = 4?

                             x = 5y - 10 = 5*4 - 10 = 20 - 10 = 10; x = 10

Third row:      What is y when x = 15?

                             x = 5y - 10

  Add 10 both sides     x + 10 = 5y - 10 +10

                                      x + 10 = 5y

But we're told x = 15, so   15 + 10 = 5y

                                             25 = 5y

Divide both sides by 5         25/5 = 5y/5

                                                  5 = y                      y = 5

Fourth row: What is x when y = 6?

                                        x = 5y - 10 = 5*6 - 10 = 30 - 10 = 20; x = 20

Answer:

The y value of a point where a vertical line intersects a graph represents an output for that input x value. If we can draw any vertical line that intersects a graph more than once, then the graph does not define a function because that x value has more than one output.

Answer: lowestmutliple=1320   highestfactor=11

Step-by-step explanation:

I did some work and calculated this and that's what I got. I hope it's right and I hope it helps! ^w^

E(Y|X) is the conditional expectation of Y given X. We can use the law of iterated expectations to show that E(u) = 0.

This law states that E(E(X|Y)) = E(X). Therefore, E(u) = E(Y - E(Y|X)) = E(Y) - E(E(Y|X)) = E(Y) - E(Y) = 0.

b. We can use the law of iterated expectations again to show that E(uX) = 0. This law states that E(E(XY|Z)) = E(X)E(Y|Z). Therefore, E(uX) = E(YX - E(YX|X)) = E(YX) - E(E(YX|X)) = E(YX) - E(Y)E(X) = 0.

c. Let Ỹ = g(x) denote a different prediction of Y using X and let v = Y - Ỹ denote its error. We can use the equation h(X) = g(x) - E(Y|X), so that v = [Y - E(Y|X)] - h(X). Using this equation, we can derive E(v2) = E[(Y - E(Y|X))2] - 2E[(Y - E(Y|X))h(X)] + E[h(X)2]. Since E(Y - E(Y|X)) = 0, this reduces to E(v2) = E[h(X)2] < E[(Y - Ỹ)2], which shows that E[(Y - Ỹ)?] > E[(Y - Ỹ)2].

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Answer:

#28: 13

#29: 22

Step-by-step explanation:

The first question

f(5) =3(5) -2

f(5) = 15 -2

f(5) = 13

Second question

P(2,9) = 2(2) + 2(9)

P(2,9) = 4 + 18

P(2,9) = 22

Sarah spends reading 30 min + \(0.05 min^{2}\).

An expression or mathematical expression is a finite collection of symbols that is well-formed according to context-dependent norms. To assist identify the sequence of operations and other features of logical syntax, mathematical symbols can denote numbers (constants), variables, operations, functions, brackets, punctuation, and grouping.

However, in modern mathematics, and particularly in computer algebra, formulae are considered expressions that may be evaluated as true or false based on the values assigned to the variables in the expressions.

The problem is in a mathematical expression.

30 min+3s min did Sarah spend reading

Convert s to min

.30min+3s min× 1min/60s

Cancel the common units and simplify.

Cross-cancel units.

30 min + \(0.05 min^{2}\)

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Answer:

18 jars can be filled completely.

Step-by-step explanation:

7L=7000ml

1 jar contain 375 ml

375ml can be filled in 1 jar

375ml=1 jar

1 ml = 1/375 jar

7000 ml = 7000× 1/375 jar

7000ml= 18.67 jar

hence 18 jars can be filled completely.

The total number of jars that can be filled with sauce is A = 18 jars

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

Saj has made 7 litres of curry sauce = 7000 mL

And , each jar can be completely filled with 375 millilitres of cury sauce

So , the number of jars A = 7000 / 375

On simplifying the equation , we get

A = 18.67 jars

Hence , the number of jars is A = 18 jars

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Answer:

= 12 miles per hour

Step-by-step explanation:

This is a fraction equal to

30 miles ÷ 2.5 hours

We want a unit rate where

1 is in the denominator,

so we divide top and bottom by 2.5

30 miles ÷ 2.5

2.5 hours ÷ 2.5

=  

12 miles

1 hour

=  

12 miles

hour

= 12 miles per hour

Answer:

p=10

Step-by-step explanation:

-7+p=3

+7-7+p=3+7

p=10

Answer:

Hello! The answer to this question is 10.

Step-by-step explanation:

You have to get p by itself so we will add 7 to both sides:

-7 + p = 3

+7        +7

-------------

p = 10

When doing so, we get p = 10.

You can check your work:

-7 + 10 ⇒ 10 - 7 = 3

Therefore, p = 10 is the correct answer.

Answer:

0.21875

Step-by-step explanation:

7/8 divided by 4 = 0.21875lb

Answer:

B, all the numbers make the inequality true:).

Step-by-step explanation:

Answer:

5 bracelets per hour

Step-by-step explanation:

60 minutes in hours /12 minutes per bracelet = 5 bracelets per hour

Answer: 5

Step-by-step explanation:

to find the unit rate, you want to divide 60 by the unit rate we currently have, 12 minutes per braclet.

60/12=5.

This equation shows that Sarah can make 5 beaded braclets every hour. 5 is your unit rate.

Answer:

5 hours= $37.50

$60= 8 hours

Step-by-step explanation:

if you make 7.50 and hour your equation would be 7.50x you plug how many hours into x and that's how you get the money tou earned.

Answer:

5 is 37.5 and the time for 60 is 8

Step-by-step explanation:

5 hours times 7.5 dollars per hour is 37.5$. 60 dollars divided by 7.5 dollars per hour is 8 hours

Answer:

2.01) Multiply x by 3 and add 1 (x*3+1)

2.02) Add 7 to x (x+7)

Step-by-step explanation:

2.01:

2*3+1=7

4*3+1=13

6*3+1=19

8*3+1=25

2.02:

-2+7=5

0+7=7

2+7=9

Answer:

y=9/4x-15/4

Step-by-step explanation:

9x-4y=15

4y=9x-15

y=9/4x-15/4