The function f is given below. Find f-¹(z) and evaluate f-¹(-6).

Based on the Alternate Interior Angles Theorem, the degree measure of angle 3 is equal to 153.

Parallel lines can be defined as two (2) lines that are always the same (equal) distance apart and never meet.

The Alternate Interior Angles Theorem states that when two (2) parallel lines are cut through by a transversal, the alternate interior angles that are formed are congruent.

Since line a and m are parallel lines, angle 4 and 6 are alternate interior angles. Therefore, by applying the supplementary angle theorem, the measure of angle 6 is given by:

Q + R = 180°

153° + m<6 = 180°

Angle 6 = 180° - 153°

Angle 6 ≡ Angle 4 = 17°

Now, we can determine the degree measure of angle 3 by applying the supplementary angle theorem:

Q + R = 180°

17° + m<3 = 180°

Angle 3 = 180° - 17°

Angle 3 = 153°

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Answer:

discounting

Step-by-step explanation:

the answer is discounting

The equation of a horizontal line containing the point is y = -8

The point is given as (4,-8)

Rewrite as

(x, y) = (4,-8)

The line is a horizontal line

So, we remove the x value

This gives

y = -8

Hence, the equation of a horizontal line containing the point is y = -8

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Answer:

193,153.72460551

Step-by-step explanation:

Multiply 4 times pi or 3.14 if you are rounding. Then multiply that number by 4.6

Lastly once you done all of put it to the po wer of 3

If we want to have solutions for the linear equation, the value of A must be 4,

Let's define A as the number that should be in the box, now we can write the linear equation in the image as:

A*(5x + 6) = 20x + 24

We want to find the value of A, if we divide both sides by 5x + 6 we will get:

A = (20x + 24)/(5x + 6)

The numerator can be rewritten as:

20x + 24 = 4*(5x + 6), replacing that we will get:

A = 4*(5x + 6)/(5x + 6) = 4

Then we conclude that, if we want to have solutions for the linear equation, the value of A must be 4.

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The angles ∠ABD and ∠CBD are equal to 144° and 50° respectively.

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Answer:

f(g(x)) = 9x² - 6x + 1

Step-by-step explanation:

We are told that:

• [tex]f(x) = x^2[/tex]

• [tex]g(x) = 3x -1[/tex].

In order to find [tex]f(g(x))[/tex], we have to replace [tex]x[/tex] in the definition of [tex]f(x)[/tex] with the definition of [tex]g(x)[/tex]. In other words, [tex]3x -1[/tex] has to be the input for [tex]f(x)[/tex]:

[tex]f(g(x))[/tex] = [tex]f(3x -1)[/tex]

          ⇒ [tex](3x - 1)^2[/tex]

          ⇒ [tex]9x^2 - 6x + 1[/tex]

Therefore, f(g(x)) = 9x² - 6x + 1.

the answer is 2, 590,000

Question:

Round 2,586,991 to the nearest ten thousand

Answer:

2,590,000

Step-by-step explanation:

If you did the 86991 just think of it as 1-10 what is that whole number closer to it would be 90000 if you rounded it to 80000 that would be incorrect because it is not closer to 8 than 9.

I hope it helps you!

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Answer:

im pretty sure its  -20

Step-by-step explanation:

Joseph could use C), D), and E) to make kebabs without any leftovers:

C) 30 pieces of meat and 40 pieces of vegetables

D) 45 pieces of meat and 60 pieces of vegetables

E) 72 pieces of meat and 96 pieces of vegetables

How were the answers determined? To solve for the answer, here are some pointers:

Consider the given which states that each kebab has 3 pieces of meat and 4 pieces of vegetables, and Joseph wanted to make kebabs without any leftovers - meaning, there should be no extra piece of meat or no extra piece of vegetable.

In choosing which is the answer, make sure that the number of pieces of meat must be divisible by 3 (pieces of meat), and the number of pieces of vegetables must be divisible by 4 (pieces of vegetables). This was also based on the given.

Moreover, the quotient for meat and the quotient for vegetables must be equal to each other so that there will be no leftovers.

Therefore, the answers are C), D), and E) because these three answers satisfy the conditions above.

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The approximate location of the dolphin is 155 feet as it moves at the rate of 6.2 feet per second.

Rate in defined as the speed or the distance travelled by the dolphin in unit time.

Given the rate of the dolphin is  feet per second .

Time taken by the dolphin is 25 seconds.

∴ distance travelled is given by rate × time

Hence distance travelled is 6.2 × 25 = 155 feet

Therefore the approximate location is given by 155 feet from the starting point.

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If Amanda distributed 62 pieces of gum among her friends by giving 2 to each friend and she has remaining 8 then we can say that she have 27 friends.

Given that Amanda won 62 pieces of gum and division has been done in such a way that 2 pieces to each friend are given and only 8 has remaining.

We are required to find the number of friends that Amanda have.

If 8 pieces of gums are left then the number of pieces distributed will be 62-8=54 pieces of gums.

Since 2 pieces are given to 1 friend so the number of friends will be=54/2=27 friends.

Hence if Amanda distributed 62 pieces of gum among her friends by giving 2 to each friend and she has remaining 8 then we can say that she have 27 friends.

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Answer:

  3 to 4

Step-by-step explanation:

Perhaps you want to reduce the ratio (5/12) to (5/9).

You have the ratio of two fractions with the same numerator. The ratio of the fractions will be the inverse of the ratio of their inverses:

  (5/12) : (5/9) = (9/5) : (12/5) . . . . . . invert fractions and swap sides

 = 9 : 12 = 3 : 4 . . . . . . . . . . . . . multiply by 5 and divide by 3

The ratio (5/12) to (5/9) is 3 to 4.

The value which is greater than -2.5 as requested in the task content is; -2.25.

It follows from the task content that the value which is greater than -2.5 is to be determined.

On this note, since greater numbers appear to the right on the number line, one can be sure that the number which is greater than -2.5 among the answer choices is; -2.25 as it appears to the right of -2.5.

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Answer: 62, 63, 64, 65

Step-by-step explanation:

254/4=63.5

so, you know that

[tex]63.5+63.5+63.5+63.5=254[/tex]

[tex]62+63+64+65=254[/tex]

You can kind of tell by looking at the 63.5, because integer is a whole number so the two whole number above and below 63.5 would average out to 63.5

Hope this helps!

Step-by-step explanation:

Solving steps

ZX-13 k

Move the constant to the right

zX = 13+k

Divide both sides

Solution

x=13+k/z , z≠0

Answer:

Step-by-step explanation:

Solve the equation for x .

zx-13=k

zx−k−13=0

(z)⋅x+(−k−13)=0

x=−(−k−13)/z

x=(k+13)/z

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

check

z(k+13)/z-13=k

(k+13)−13−{k}=0

k−{k}=0

0=0

the answer is good

Answer: The first one. 2.289<2.297

Step-by-step explanation:

The final simplified expression representing the total miles driven in three days is 4x-90.

Let the miles drove on the day 1 be x

A/Q

On day 2 , we drove 10 more than twice the miles driven on day 1 =2x+10

On day 3 we drove 100 miles less than day 1 = x-100

Simplified expression representing the total miles driven in 3 days

day 1 = x miles

day 2 = (2x+10)miles

day 3 = x-100

total = x+2x+10+x-100

= 4x-90

Some "solving" difficulties are related to "simplification" challenges. Some equations, like some expressions, contain parentheticals and even nested grouping symbols. The technique of simplifying is the same whether we're working with expressions (and therefore only simplifying) or equations (and so including solving).

To simplify an expression, write an equivalent expression with no related terms. This implies we'll rephrase the expression with as few terms as feasible.

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*The values in the question and the image are different. It is solved below according to the image*

The correct answer is 812 and 2/5 feet.

Convert the mixed fraction into improper fraction.

Distance between the bottom of canyon and sea level = 59 and 9/ 10 feet= 599/10 feet

Distance between the bird's nest and sea level = 752 and 1/2 feet = (752×2 + 1) feet =1505/2 feet

So, the difference between elevation between the bottom of the canyon and the bird's nest = 599/10 + 1505/2 feet

= 59.9 + 752.5 feet = 812.4 feet

= 812 and 4/10 feet

= 812 and 2/5 feet

Hence, the difference between elevation between the bottom of the canyon and the bird's nest is 812 and 2/5 feet .

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In linear equation, $1.56 is the price of a pair of sport socks.

What in mathematics is a linear equation?

To find how much it costs for one pair of socks, divide the cost with how many pairs there are.  

12.55/8 = 1.56875

Since we are determining the cost of each pair of socks, it's only justifiable if we round it to the nearest hundredths.

Therefore, a pair of socks cost around $1.56 excluding taxes.  

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Answer:

5

Step-by-step explanation:

The points are (4, -3) and (7, -7).

[tex] d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} [/tex]

[tex] d = \sqrt{(7 - 4)^2 + (-7 - (-3))^2} [/tex]

[tex] d = \sqrt{3^2 + (-4)^2} [/tex]

[tex] d = \sqrt{9 + 16} [/tex]

[tex] d = \sqrt{25} [/tex]

[tex] d = 5 [/tex]

Answer: 5

The money in Frances' account is - $ 120 after the 3 checks and the penalty.

We are given that:

Frances has no money in her account.

Current balance of her account = $ 0

Now she wrote 3 checks of $ 35 each.

Amount written = 3 × $ 35 = $ 105

Now, the balance in her account will be = $ 0 - $ 105 = - $ 105

Also, the bank has imposed a penalty of $ 15 as she has overdrawn her account.

So, the balance now will become:

Balance = - $ 105 - $ 15 = - $ 120

Therefore, the money in Frances' account is - $ 120 after the 3 checks and the penalty.

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The equation of the line that is parallel to y = 4x ₊ 3 and passes through the point (2,6) is  y = 4x ₋ 2.

The slope of the preceding equation is 4 because it is in slope intercept form. The slope of an equation is always equal for parallel lines, hence the slope of the equation we are requested to create is also 4.  We are given that this line passes through (2,6).

In the absence of intersection, two lines are said to be parallel. Each line has the same slope. In the event where m₁=m₂, f(x)=m₁x+b₁ and g(x)=m₂x+b₂ are. parallel

In order to write in y = mx +b form, we need to solve for b (the y-intercept).  

Given, x=2, y=6, and m = 4.

6 = (4) (2) ₊ b

simplify

6 = 8 ₊ b

solve for b.

b = 6 ₋ 8

b = ₋2

So the equation of the parallel line is   y = 4x ₋ 2

Hence we get the equation of the line that is parallel to y = 4x ₊ 3 and passes through the point (2,6) is y = 4x ₋ 2

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Answer:

[tex]=-\frac{37}{24}[/tex]

Step-by-step explanation:

[tex]-\frac{2}{3}+\left(-\frac{7}{8}\right)[/tex]
[tex]=-\frac{2}{3}-\frac{7}{8}[/tex] <- Apply the rule a + (-b) = a - b
[tex]=-\frac{16}{24}-\frac{21}{24}[/tex] <- The LCM of 3 and 8 is 24.
[tex]=\frac{-16-21}{24}[/tex] <- Apply the fraction rule [tex]\frac{a}{c}-\frac{b}{c}=\frac{a-b}{c}[/tex]
[tex]=\frac{-37}{24}[/tex] <- Subtract
[tex]=-\frac{37}{24}[/tex] <- Apply the fraction rule [tex]\frac{-a}{b}=-\frac{a}{b}[/tex]
_____________________________________________________
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Answer:

-1.542

Step-by-step explanation:

(-2/3) + (-7/8)=-37/24=-1 13/24= -1.542

Answer:

(1,-4) (2,0) (3,-11)

Step-by-step explanation:

if you graph these you will see its the same images just turned up i would also know because im from k12 but anyways yea same image just turned counterclockwise ,next time search up "graph 90 counterclockwise" and itll show you step by step not of this exact problem but a similar type, it helps alot

Leah should multiply x with [tex]\frac{12}{5}[/tex].

If we are to divide x by  [tex]\frac{5}{12}[/tex], we need to write it like this,

[tex]\frac{x}{\frac{5}{12} }[/tex]

⇒ x ÷ [tex]\frac{5}{12}[/tex]

⇒ x × [tex]\frac{12}{5}[/tex]

Thus, x should be multiplied  [tex]\frac{12}{5}[/tex] to get the answer.

Answer)  [tex]\frac{12}{5}[/tex]

          In fractional division, we need to find the reciprocal of the divisor fraction and then multiply it with the dividend to find the solution.

         In the given question, the divisor is ' [tex]\frac{5}{12}[/tex].' Thus, it should be reciprocated to find the fraction '   [tex]\frac{12}{5}[/tex].' This should be then multiplied by the variable x to find the answer to the fractional division.

        Fractional multiplication also needs to carry out the arithmetic functions of multiplication and division to find out the answer.

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The complete question is given below:

Leah wants to divide x by [tex]\frac{5}{12}[/tex]. What number should she multiply by x to find the answer??​