State whether the following is a solution of x ≥ -4.1? Write only YES or NO.
1. -5
2. -4.1
3. 8
4. 0​

There are a couple ways to go about this.

By definition of inverse function, if [tex]j^{-1}[/tex] exists, then

[tex]j\left(j^{-1}(x)\right) = x[/tex]

All this means is that if you provide some input [tex]x[/tex], plug it into [tex]j^{-1}(x)[/tex], then plug that into [tex]j(x)[/tex], you end up recovering the original input [tex]x[/tex] that you started with.

We can also do this in the opposite direction, so

[tex]j^{-1}(j(x)) = x[/tex]

So now if [tex]j(x)[/tex] is invertible, then

[tex]j(x) = -\dfrac23 x - 9 \implies j\left(j^{-1}(x)\right) = -\dfrac23 j^{-1}(x) - 9 = x[/tex]

Solve for [tex]j^{-1}[/tex].

[tex]-\dfrac23 j^{-1}(x) - 9 = x[/tex]

[tex]\dfrac23 j^{-1}(x) = -x - 9[/tex]

[tex]j^{-1}(x) = -\dfrac32 (x+9)[/tex]

[tex]\boxed{j^{-1}(x) = -\dfrac32 x - \dfrac{27}2}[/tex]

Another way to do it is by algebraically substituting [tex]x[/tex] within the definition of [tex]j(x)[/tex]

Starting with the given definition

[tex]j(x) = -\dfrac23 x - 9[/tex]

we replace [tex]x[/tex] with some new expression in a new variable [tex]y[/tex] that makes the right side reduce to just [tex]y[/tex]. To demonstrate, if we multiply [tex]-\frac23 x[/tex] by [tex]-\frac32[/tex], we end up with a coefficient of 1. So let [tex]x=-\frac32 y[/tex]. Then

[tex]j\left(-\dfrac32 y\right) = -\dfrac23 \left(-\dfrac32 y\right) - 9 = y - 9[/tex]

As you can see, this doesn't completely reduce to [tex]y[/tex], so we're not done. To adjust for this, we just add 9 to [tex]y[/tex], so our ultimate substitution is [tex]x=-\frac32(y+9)[/tex]. Then

[tex]j\left(-\dfrac32 (y+9)\right) = -\dfrac23 \left(-\dfrac32 (y+9)\right) - 9 = (y+9) - 9 = y[/tex]

Now applying [tex]j^{-1}[/tex] to both sides,

[tex]j^{-1}\left(j\left(-\dfrac32 (y+9)\right)\right) = j^{-1}(y)[/tex]

[tex]\implies \boxed{j^{-1}(y) = -\dfrac32 y - \dfrac{27}2}[/tex]

(we can freely swap out [tex]y[/tex] for [tex]x[/tex] at this point)

Yet another way, since the function here is quite simple, we can just think about the action of [tex]j[/tex] on a given number [tex]x[/tex] - multiply it by -2/3, and subtract 9.

[tex]x \mapsto -\dfrac23 x \mapsto -\dfrac23x - 9 = j(x)[/tex]

The inverse operation undoes this, so given some number [tex]j(x)[/tex], we recover [tex]x[/tex] by adding the additive inverse of -9, or 9, then multiplying the whole result by the multiplicative inverse of -2/3, or -3/2.

[tex]j(x) \mapsto j(x) + 9 \mapsto -\dfrac32(j(x) + 9) \mapsto -\dfrac32 j(x) - \dfrac{27}2 = x[/tex]

You seem to be using some version of this method. You made the mistake of thinking the "multiply by -3/2" step applies only to [tex]j(x)[/tex], and not [tex]j(x) + 9[/tex].

Answer:

The first choice

Step-by-step explanation:

Since we're looking at 5 × 9, we'd need to group them into 5 groups of 9, or 9 groups of 5. In this case, the first choice is the correct answer.

Mark the other guy with brainliest

The domain and range of the given function are: domain: {-7,-3,-2,2,4,6} range: {-3,0,1,2,3,6}. (Option A).

Now,

In the given function {(-3,4),(0,6),(2,-2),(1,-3),(6,-7),(3,2)},

Thus, According to the definition of domain and range,

Hence, Option A is correct, i.e., the domain and range of the given function are: domain: {-7,-3,-2,2,4,6} range: {-3,0,1,2,3,6}.

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Answer:

Assume one diagonal of 2x and other of x inches. and sides of length =L inches.

Area of rhombus = 2*2x*x/2=2x^2 = 81 x=9/sqrt.2 and 2x=9*sqrt 2.

Diagonals are x=6.365 inch 2x=12.73 inch check area =12.73*6.365= 81.026 sq.inch.

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

If you multiply both together once that will be the lowest it gets

Answer: 6

Step-by-step explanation: compare the multiplication tables ig

The remainder when 17^(77) is divided by 35 is 12

The number being divided = 17^(77)

The number by which 17^(77) is divided = 35

Using a graphing calculator as follows, we have;

[tex] \frac{17^{77}}{35} = V+ \frac{12}{35} [/tex]

Where V is a very large number quotient

From the above fraction, we have;

Expressing the above result using long division gives;

__V___ (Quotient)

35 (17⁷⁷)

____

12 (Remainder)

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Answer:

5s + 3.50d < 40

Step-by-step explanation:

if you were to total up the costs of a snack and drink together you'll end up with $8.50

-multiply $8.50 until you reach $40 mark

i.e 8.50×2(means 2 of each item) = $17

8.50×3 = $25.5

8.50×4 = $34

8.50×5= $42.5

-if you look at it, the calculation for 5, the pricing is now over the budget therefore the answer is then 5s + 3.50d < 40 because she can only spend up to $34 at most

The gravitational potential energy is 2940 Joules

The formula for gravitational potential energy is expressed as;

Gravitational Potential energy = m g h

Where;

Substitute the values into the formula;

⇒ 20 × 9. 8 × 15

Multiply through

⇒ 2940 Joules

Thus, the gravitational potential energy is 2940 Joules

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When working on homework, Jen spends 5 minutes reading for every 10 minutes spent on writing, Andy spends 2 minutes reading for every 5 minutes of writing, and Noor spends 10 minutes reading for every 15 minutes of writing .

Many teachers and parents believe that homework helps students build study skills and review concepts learned in class. Others see homework as disruptive and unnecessary, leading to burnout and turning kids off to school. Decades of research show that the issue is more nuanced and complex than most people think: Homework is beneficial, but only to a degree. Students in high school gain the most, while younger kids benefit much less.

The National PTA and the National Education Association support the “10-minute homework guideline”—a nightly 10 minutes of homework per grade level.                                           https://brainly.com/question/28529831                 #SPJ9

Answer:

e, so she mixes in 1 cup of white paint. The color is still too dark, so Hana keeps mixing in 1 cup of white paint at a time. After adding 4 cups, she decides the color is too light.

A. Explain in words how much paint Hana should have added initially to get the shade she wants.

Enter your answer.

B. Mod

Step-by-step explanation:

The Simplification of the expression 6(3x-17) + 2x -18 = 9(4x+7) -9 + 17 and value for the unknown x, is approximately 11.94

6(3x-17) + 2x -18 = 9(4x+7) -9 + 17

18x - 102 + 2x - 18 = 36x + 63 - 9 + 17

18x + 2x - 36x = 63 - 9 + 17 + 102 + 18

- 16x = 191

x = 191 / - 16

x = 11.9375

Approximately,

x = 11.94

Therefore, the Simplification of the expression 6(3x-17) + 2x -18 = 9(4x+7) -9 + 17 and value for the unknown x, is approximately 11.94

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Answer:

147 cents

Step-by-step explanation:

If 24 inches of wire cost 72 cents then each inch cost 3 cents. 49*3=147

Answer:

= 69k - 18

Step-by-step explanation:

9(7k-2) + 6k

= (9*7k + 9*-2) + 6k

= (63k - 18) + 6k

= 63k + 6k - 18

= 69k - 18

The approximation of the trigonometry ratio cot(5) is 11.43

The trigonometry ratio expression is given as

cot(5)

In trigonometry ratio, we have the following equation

cot(x) = 1/tan(x)

This means that x = 5

Substitute 15 for x in the equation cot(x) = 1/tan(x)

So, we have

cot(5) = 1/tan(5)

Using a calculator, we have:

cot(5) = 1/0.0875

Evaluate the quotient

So, we have

cot(5) = 11.4286

Approximate the above result

So, we have

cot(5) = 11.43

Hence, the approximation of the trigonometry ratio cot(5) is 11.43

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Answer:

I think you're looking for 74,099

If Gabriel continues the pattern of running that he has done on the past four weeks, the miles he will run on the 7th week is 2 miles.

Gabriel's pattern of running is such that he increases the number of miles by 0.25 miles every week.

This is why he ran 0.5 miles, and then 0.75 miles and then 1 mile.

If he keeps going like this, one the 7th week, he will run:

5th week = 1.5 miles

6th week = 1.75 miles

7th week = 2 miles

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Answer:

Step-by-step explanatio

from up to down

12

30

10

Answer:

Yes

Step-by-step explanation:

The value of |-10| is,

→ |-10| = 10

The value of |6| is,

→ |6| = 6

Now the greater value is,

→ 10 > 6

→ |-10| > |6|

Yeah, |-10| greater than |6|.

Answer:

No, it's not

Step-by-step explanation:

Hope it helps you

PLS RATE AS BRAINLIEST ANSWER

The difference between a tax rebate and a discount is For a rebate the tax, the tax is calculated on the full price, and the customer receives the rebate later. For a discount, the tax is calculated on the reduced price after the discount is applied.

A tax rebate is also known as a tax refund and the purpose of it is to pay back a tax payer when they paid more taxes than they were meant to pay. It is therefore calculated on the full amount of tax.

This is different from a tax discount which works by using the discount to reduce the amount of tax owed and then you can pay off the discounted amount as tax.

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Answer:

Equation is 0.5 gal × (0.1) + x gal × (0.35) = (0.5 + x) × (0.15)

0.125 gallons of the 35% acid solution Eli should add.

Step-by-step explanation:

Given: Eli wants to combine 0.5 gallon of a 10% acid solution with some 35% acid solution to make a 15% acid solution.

To find: Equation can you use to determine how many gallons of the 35% acid solution Eli should add?

Solution:

Let x be the gallons of the 35% acid solution.

According to question,

For 0.5 gallon of a 10% acid solution = 0.5×0.1

For x gallon of a 35% acid solution = x×0.35

For (0.5+x) gallon of a 15% acid solution = 0.5 + x × 0.15

The equation form is

0.5 gal × (0.1) + x gal × (0.35) = (0.5+x) × (0.15)

Solving the above equation,

0.05 + 0.35x = 0.075 + 0.15x

0.2x = 0.025

x = 0.025/0.2

x= 0.125

Therefore, 0.125 gallons of the 35% acid solution Eli should add.

Therefore, 0.125 gallons of the 35% acid solution Eli should add.The equation is 0.5 gal × (0.1) + x gal × (0.35) = (0.5 + x) × (0.15)

Answer:

I think it's will be C

Step-by-step explanation:

C I psomes

Answer: C 130%

Step-by-step explanation:

Answer:

In 1864, Sherman succeeded Grant as the Union commander in the Western Theater. He led the capture of the strategic city of Atlanta, a military success that contributed to the re-election of President Abraham Lincoln.

Step-by-step explanation:

The value   [tex]\displaystyle \sum^{2007}_{n = 2} F(n)[/tex] is 2016532.

The collection of positive and negative integers is known as an integer. Integers, like whole numbers, do not include the fractional portion. Integers can therefore be defined as numbers that can be positive, negative, or zero but not as fractions. On integers, we can carry out all arithmetic operations, including addition, subtraction, multiplication, and division. Integer examples include 1, 2, 5, 8, -9, -12, etc. "Z" stands for an integer. The Latin term "Integer," which implies entire or intact, is where the word "integer" first appeared. Zero, positive numbers, and negative numbers make up the particular set of numbers known as integers.

Integer examples include: -1, -12, 6, and 15.

Zero is not an integer that can be positive or negative. There is no (+ or -) sign on zero, making it a neutral number.

F(2) = 3

We learn that for the majority of the graphs by examining different graphs.

F(n) = n+1

3+4+5+5+7+8+9+9+··········+2008

= (1+2+3+4+5+·····+2008)-3-501

= [tex]\frac{(2008) \times( 2009)}{2} -504[/tex]

= 2016532

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The answer is " 7 to the power 3rd ".

We translate the algebraic expression 7³ into a verbal expression. The given expression has a base number of 7 raised to the power of 3 . This means is that 7 is multiplied by itself 3 times. So we should write " 7 to the power 3rd "

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From the given polygons, the pairs of polygons that are congruent are D. pairs 1 and 3.

When two or more polygons are said to be congruent, it means that they have the same shape and that the lengths of their sides are the same.

The orientation of the shape is irrelevant if the above requirements are met.

The pair of polygons in Pair 1 are congruent because they have the same shape and are the same length. The same is true of the polygons in pair 3.

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A declaration of a hits variable that can store how many times a baseball player has hit the ball during a game of baseball int hits;

A programme declares a variable whenever it states that it requires one. Place declaration statements for our brief programmes in-between the main method's two curly braces. The variable's name and data type are provided in the declaration. It could also provide a specific value that has to be entered into the variable.

When a variable is given a value for the first time, it is said to be initialized. The symbol = stands in for the assignment operator. Instead of writing int I and then 9, you can establish a variable for addition and then give it a value in the same line by writing int I = 9.

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Answer:

Brainliest pls

Step-by-step explanation:

a^32