Write the equation of the absolute value function with the following transformations:

Translate left 12 units, stretch by a factor of 4, and reflect over the x-axis.

The year in which the total personal income will reach 22 trillion dollars is 2033 years.

The year in which the total personal income will reach 22 trillion dollars is calculated by applying a method known as extrapolation for the data in the table.

At year 1996, total personal income = 8429.2

At year 2001, total personal income = 10,239.5

At year ?, total personal income = 22,000

(? - 2001) / (2001 - 1996) = (22,000 - 10,239.5) / (10,239.5 - 8429.2)

(? - 2001 ) / 5 = 6.496

? - 2001 = 5 x 6.496

? - 2001 = 32.48

? = 2001 + 32.48

? = 2033.48

? ≈ 2033 years

Thus, the year in which the total personal income will reach 22 trillion dollars is 2033 years.

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Answer:

The answer is 6!!

Step-by-step explanation: Factors of 18: 1, 2, 3, 6, 9, 18

Factors of 66: 1, 2, 3, 6, 11, 22, 33, 66

After listing all of the factors, simply find the number that is shown in both of their factors but find the greatest number.

For example 3 is a factor that is the same but isn't the highest factor that is shown in both, it is 6! Hope this helps and Happy Halloween!!! :D

Answer:

a=5

Step-by-step explanation:

1. Multiply 4 and 6a by 4.

You'll get 24a + 16.

2. Subtract 16 from 136.

You'll get 120.

3. Divide 120 by 24 to get a by itself.

[tex]\frac{120}{24}[/tex]=a

a=5

Answer:

assuming that n is the "

1. 31

2. 49

Answer:

5

8

6

7

4

Step-by-step explanation:

Divde the top number by bottom number (i.e. 60/12=5)

Answer:

im going to do this top to bottom

Step-by-step explanation:

5

8

6

7

4

Answer:

B. (0.88,0.65)

Step-by-step explanation:

The exact point is (0.882, 0.647)

and just round it out

Answer:

x =Y

Step-by-step explanation:

[tex]Y= 5x-4x[/tex]

Simplify

[tex]Y = x[/tex]

The literal equation for x is x=y.

The given equation is y=5x-4x.

We need to solve the literal equation for x.

Equations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign. It shows the relationship of equality between the expression written on the left side with the expression written on the right side. In every equation in math, we have, L.H.S = R.H.S (left hand side = right hand side). Equations can be solved to find the value of an unknown variable representing an unknown quantity.

Now, y=5x-4x

⇒y=x

Therefore,  the literal equation for x is x=y.

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Answer:

B

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Answer:

yeah your right it equals 45

Step-by-step explanation:

((-3+2)/2),((-5+5)/2)

(-0.5),(0)

Answer:

(-0.5,0)

Step-by-step explanation:

Mid point is the point at the middle of the line, therefore takings the average Y value and the average X value, will obtain the middle point.

Y point: (-3+2)/2 = -0.5

X point: (-5+5)/2 = 0.0

Midpoint: (-0.5,0)

Answer:

3rd value, 4th value, 1st value and then the 2nd value

Two angles are complementary when their sum is equal to 90°.

So, ( 2x + 39 ) + ( 7x - 21 ) = 90°

9x + 18° = 90°

x = 8°

Putting value of x in the angles given :

( 2x + 39 )° = 2(8°) + 39° = 55°.

( 7x - 21 )° = 7(8°) - 21° = 35°.

Therefore, the angles are 55° and 35°.

Hence, this is the required solution.

Answer: Samuel no necesita comprar mas cajas.

Step-by-step explanation:

Cada mosaico es un cuadrado de 20cm por lado.

Entonces el área de cada mosaico es:

A = 20cm*20cm = 400cm^2.

En una caja hay 14 mosaicos, entonces cada caja puede cubrir:

14*400cm^2 = 5,600cm^2.

Ahora, el problema dice que la pared mide 3cm por 2 cm.

En ese caso, con un solo mosaico cubrirías la pared, entonces supongo que esta mal escrito.

Las dimensiones de la pared serian 3 metros por 2 metros.

1 m = 100cm

Entonces la pared es 300cm por 200cm.

El área total de la pared seria:

300cm*200cm = 60,000cm^2.

Ahora, cada caja de mosaicos cubre 5,600 cm^2.

Entonces el numero de cajas necesarias para cubrir toda la pared es:

(60,000cm^2)/(5,600cm^2) = 10.7

Entonces se necesitan 10.7 cajas para cubrir esa pared, y Samuel tiene 11, entonces el no necesita comprar mas cajas.

Samuel necesita 150 mosaicos, y en sus cajas tiene 154, por lo que no necesita comprar más cajas.

Dado que Samuel tiene 11 cajas con mosaicos cuadrados de 20 cm por lado, y quiere cubrir una pared que mide 3 metros de largo y 2 metros de alto, si en caja hay 14 mosaicos, para determinar si será necesario que compre mas cajas se debe realizar el siguiente cálculo:

Por ende, se necesitan 150 mosaicos para cubrir toda la pared.

A su vez, en total Samuel tiene 154 mosaicos.

Por lo tanto, Samuel no necesita comprar más cajas.

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Answer:

She gets an increase of $750 each year so in the tenth year she would make $34,850

Step-by-step explanation:

Answer: B

Step-by-step explanation: $34,850

Answer:

Probability at least one car will get punctured: 0.39347

Step-by-step explanation:

B(10,000 , 0.00005)

P(X ≥ 1) = 1 - P(X = 0)

            = 1 - (1 - 0.00005)^10,000

            = 1 - (0.99995)^10,000

            = 1 - 0.60652...

            = 0.39347 (probability that at least one car will get punctured)

As you can tell P(X ≥ 1) as we have to solve for the probability that at least one car will get punctured. That is of course 1 - [ P(X = 0) ].

How do we know to use a binomial distribution here? Based on these three reasons:

Answer:

1-b 2-c 3-a 4-d 5-d 6-a

Step-by-step explanation:

Answer:

-6 is going to the left while positive 2 is going the opposite way

Answer:

[tex]\boxed{\pink{\sf The \ inverse\ of \ the \ function \ is \ f^{-1}(x)= \dfrac{2}{x}-\dfrac{1}{2} }}[/tex]

Step-by-step explanation:

A function is given to us and we need to find its inverse . So the given function is ,

[tex]\implies f(x) = \dfrac{4}{2x+1} [/tex]

1) So ,let us take f(x) = y . Equation becomes ,

[tex]\implies y = \dfrac{4}{2x+1} [/tex]

2) Firstly replace x with y and y with x. We get ,

[tex]\implies x = \dfrac{4}{2y+1} [/tex]

3) Now , solve for y.

[tex]\implies x = \dfrac{4}{2y+1} \\\\\implies x(2y + 1) = 4 \\\\\implies 2y+1 =\dfrac{4}{x}\\\\\implies 2y = \dfrac{4}{x}-1 \\\\\implies 2y = \dfrac{4-x}{x} \\\\\implies y = \dfrac{4-x}{2x} [/tex]

4) Now replace y with [tex]f^{-1}(x) [/tex]

[tex]\implies f^{-1}(x) = \dfrac{4-x}{2x} \\\\\ \implies f^{-1}(x)= \dfrac{4}{2x} - \dfrac{x}{2x} \\\\\underline{\boxed{\orange{\tt \implies f^{-1}(x) = \dfrac{2}{x}-\dfrac{1}{2} }}}[/tex]

Answer:

10 1/9

Step-by-step explanation:

To make it easier to answer, make both of them into an improper fraction

4 1/5 = 21/3

1 4/9 = 13/9

Now we can multiply them easier

21/3 x 13/9 = 273/27

27 goes into 273 10 times and the left over is 3 so the mixed fraction would be

10 3/27, to simplify

10 1/9

Answer: 56

Step-by-step explanation:

Answer:

100

Step-by-step explanation:

Answer:

A) Each of the smaller donations is $20.

B) The larger donation is greater than the smaller donations by $15.

Step-by-step explanation:

4+4+7 is equal to 15, and divide 75 by 15 to get $5 per part. Multiply 4 by 5 to get $20 for a smaller donation, and 7 by 5 to get $35 for the larger donation. Hope this helped :)

Answer:

Smaller donations each cost $20

The bigger donation is $15 more than the smaller ones.

Step-by-step explanation:

Let 4x be defined as the amount of the smaller donation, and let 7x be defined as the larger amount of the donation. We can then set up an equation:

4x+4x+7x = 75

15x = 75

x = 5

We can now plugin 5 for x to solve for the smaller donation and the larger donation:

Smaller donation = 4*5 = 20

Bigger donation = 7*5 = 35

Now, to find how much greater the bigger donation is, we just subtract 35 from 20, which is 15.

I hope this helped.

Answer:

Step-by-step explanation:

The meaning of the solution x < - 10 or x ≥ 25 is the solution is in the interval (- ∞,- 10) ∪ [25, ∞).

An interval is a collection of real numbers that lie between two given values known as the interval's endpoints.

We are aware that two sets' components were combined to create the set. The set of elements in A, B, or both is the result of adding sets A and B together. It's indicated by '∪'.

For x < - 10 , the solution is in the interval (- ∞,- 10).

For x ≥ 25, the solution is in the interval [25, ∞).

For x < - 10 or x ≥ 25, we can say that the solution is in the interval

(- ∞,- 10) ∪ [25, ∞).

Therefore the meaning of the solution x < - 10 or x ≥ 25 is the solution is in the interval (- ∞,- 10) ∪ [25, ∞).

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Answer:

yes they are equivalent

Step-by-step explanation:

25/45÷5/5=5/9

and 5/9×5/5=25/45

hope this answer helps u...

Answer:

Yes.

Step-by-step explanation:

5/9 is equivalent to 25/45. We can find this out by multiplying both the numerator and the denominator by 5 as 9 x 5 = 45.

So the result is; 5/9 = (5 x 5)/ 9 x 5 = 25/ 45