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Using the substitution method and showing all of your steps. Solve the following System of Equations. Make sure to write your answer as an order pair.



`2x+y=20`

`6x-5y=12`​

Answer:

First, let's define the transformations in a general way.

Vertical translation:

A vertical translation of N units is defined as:

g(x) = f(x) + N

if N is positive, the translation is up

if N is negative, the translation is down.

Horizontal translation:

A horizontal translation of N units can be written as:

g(x) = f(x - N)

if N is positive, the translation is to the right

if N is negative, the translation is to the left.

Reflected vertically (or a reflection over the x-axis)

This type of reflection changes the sign of the y component.

We can write those as:

g(x) = -f(x)

Then:

We start with the function:

f(x) = 2^x

First we reflect it vertically.

g(x) = -2^x

now we do a vertical translation of 5 units up, then:

g(x) = -2^x + 5

Now we do a translation of 3 units to the left, then we get:

g(x) = - 2^(x + 3) + 5

Then we already did the first step.

Now we want to find the domain for this function, the domain will be the set of the possible values of x that we can input in the function g(x).

Notice that in this function the denominator is never zero, so there are no values of x that generate problems here, so the domain will be the set of all real numbers, that can be written as:

(-∞, ∞)

3) Now we want to find the range, this is the set of the possible values of g(x).

The Largest value of g(x) will be when the exponential part tends to zero, this is for really small values of x, such that when x goes to minus infinity, -2^(x + 3) goes to zero.

Then:

g(-∞) ≈ 5

The maximum of the range is 5.

And we do not have a minimum, because as x increases the function will decrease infinitely.

Then the range will be:

(-∞, 5)

(A graph of the function can be seen below)

Answer:

x<=12

Step-by-step explanation:

3x+(-4)<=2x+8

3x-4<=2x+8

3x-2x-4<=8

x-4<=8

x<=8+4

x<=12

Answer:

12 ≤ x

Step-by-step explanation:

3x-4 ≥ 2x+8

3x-3x-4 ≥ 2x-3x+8

-4-8 ≥ -1x+8-8

-12 ≥ -1x

You divide -1 on both sides and get...

12 ≤ x

Because you have to switch the sign around. I hope this helps!!

Answer:

y=-5x-8

Step-by-step explanation:

Answer:

...

Step-by-step explanation:

Answer:

17m

Step-by-step explanation:

a^2+b^2=c^2

there's a character limit so hiii

Answer:

It would be C

Step-by-step explanation:

Use a calculator, or go in Accounting.

Hope this helps :)

Answer:

B. Baseball cap

Step-by-step explanation:

Given that:

Total money available with Annabeth = $29.00

Amount at which T-shirt was bought = $15.32

Things that Annabeth wants to buy:

Soccer ball for the price of $12.87 or

Baseball cap for the price of $8.39 or

Set of shin guards for the price of $14.98 or

Water bottle for the price of $5.93

The equation that can be used to find the cost of most expensive item with the remaining amount of money:

$15.32 + [tex]c[/tex] = $29.00

[tex]\Rightarrow c = 29 - 15.32\\\Rightarrow c= \$13.68[/tex]

Cost of items that can be bought in the decreasing order is:

Cost of pair of shin guards ( $14.98 ) > Cost of soccer ball ( $12.87 ) > Cost of baseball cap ($8.39) > Cost of water bottle ( $5.93 )

The most expensive item that can be bought is the Soccer ball at $12.87.

Answer is:

B. Soccer ball

Cost of shin guards is more than the amount of money remaining.

Answer:

The answer is the first one

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

6.5

Cause when u reciproce it this iswhat u get

Step-by-step explanation:

13/10÷2/10

13/10×10/2

1.3×5

=6.5

Answer: See explanation

Step-by-step explanation:

From the question, we are informed that a coach has 17 pompoms to give to her cheerleading team and that each cheerleader needs 2 pompoms to compete.

The greatest number of cheerleaders that can compete will be calculated as:

= 17 / 2

= 8 1/2

Therefore, the greatest number of cheerleader is 8.

There be 1 pompom remaining.

Answer:

the answer is D.

Step-by-step explanation:

math and my 6th grade year

Answer:

exact form:  -5/4

Decimal Form: -1.25

Answer:

-5/4

Step-by-step explanation:

so, in order to divide fractions you can switch the numerator and denominator of the second fraction, then multiply.

5/6 divided by -2/3

5/6 multiplied by -3/2

then multiply

5 times -3 is -15

6 times 2 is 12

-15/12

simplify

-5/4

Answer:

5b - 3

Step-by-step explanation:

5b-3 is the algebraic expression for "3 less than the product of 5 and b"

Expression is a combination of variables, numbers and Operators.

The given sentence is

"3 less than the product of 5 and b"

Let us write the sentence in algebraic form.

We know that product of 5 and b means multiplication of 5 and b that means five times of b.

3 less than means subtracting 3 from another number.

So 3 less than the product of 5 and b is 5b-3.

Hence 5b-3 is the algebraic expression for "3 less than the product of 5 and b"

To learn more on Expressions click:

https://brainly.com/question/14083225

#SPJ2

Answer:

D. twenty-eight and nine tenths

Answer:

12

Step-by-step explanation:

Area = length * width

length = area ÷ width

Answer: a. 5x + 8

b. 3

c. It means that Leila picked a number higher that isn’t between 1 and 10 so Julius wouldn’t be able to guess the number

Answer:

CD = -2x

Step-by-step explanation:

Negative reciprocal

Answer: $70.49

Step-by-step explanation:

Cost of gasoline = $2.75 per gallon

Cost of diesel fuel = $3.02 per gallon.

Since Gabriel needs to purchase 15.2 gallons of gasoline for his truck, the amount spent on gasoline will be:

= 15.2 × $2.75

= $41.80

Since he needs to spend 9.5 gallons of diesel fuel for his tractor, the amount spent on diesel fuel will be:

= 9.5 × $3.02

= $28.69

Total cost spent will be:

= $41.80 + $28.69

= $70.49

Step-by-step explanation:

Kinetic Energy (K. E) = 25 J

Mass ( m) = 2 kg

Velocity or speed (v) = ?

We have the formula that

[tex]ke \: = \frac{1}{2} m {v}^{2} \\ or \: 25 = \frac{1}{2} \times 2 \times {v}^{2} \\ or \: 25 = {v}^{2} \\ or \: {5}^{2} = {v}^{2} \\ therefore \: v \: = 5 \: m |s[/tex]

it's speed is 5 m/s .

Hope it helps. :)

The speed of the body is 5 m/s

Applying the formular of kinetic energy

Kinetic energy: This can be defined as the energy posses by a moving body or that depends on the speed of a body.

The formular for kinetic energy is

E = mv²/2.................... Equation 1

Where E = Kinetic energy of the body, m = mass of the body, v = veocity/ speed of the body.

make v the subject of equation 1 above

v = [tex]\sqrt{2E/m}[/tex]................ Equation 2

From the question,

Given: E = 25 J, m = 2 kg

Substitute these values into equation 2

v = [tex]\sqrt{2*25/2}[/tex]

v = [tex]\sqrt{50/2}[/tex]

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

v = 5 m/s.

Thus, the speed of the body is 5 m/s

Learn more about Kinetic energy here: https://brainly.com/question/20658056

Answer:

4(7a+6)

Step-by-step explanation:

Factor 28a+24

28a+24

=4(7a+6)

the answer:

= 3457.24

Answer:2/3

Step-by-step explanation:

Steps in pic below

Answer:

Rory rode 1.55 miles each day

Step-by-step explanation:

7.75 divided by 5

Answer:

y = 4

Step-by-step explanation:

21 = 3(y + 3), Distribute

21 = 3y + 9, Subtract 9 on both sides

12 = 3y, Divide 3 on both sides

4 = y

Plus or Minus.

For example.

5 ± 2 = 5 + 2 or 5-2

Therefore the answer is 7 or 3.

Answer:

It means that the number can be positive or negative.

Step-by-step explanation:

I hope this helps!!!

Answer:

I will explain each step

3(x-y) / 2 =9

so first you have to make the equation equal to 0 so you can find the intercepts

3(x-y) /2  -9 =0

now simplify

3x-3y/2 -9 =0

2(3x-3y/2 -9)=0(2)

3x-3y-18

we will factor

3(x-y-6)

3=0

(x-y-6)=0

make the x=0 to find y and vise versa

(-y-6)=0

-y=6

y=6/-1 or -6

(x-6)=0

x=6/1 or 6

2/3x +4(y-2)=0

it is already equal to 0 to we simplify and factor

3(2/3x = 4(y-2)= 0(3)

2x+ 4y -8

2(x+y-4)

2=0

as we did in the last problem make x=0 then do the same to y

(y-4)=0

y=4

(x-4)=0

x=4

Step-by-step explanation:

Answer:

A = 60 degrees

C = 8 m

Step-by-step explanation:

Whenever we are faced with a geometry problem, and we have a right-angled triangle within the problem, we are to remember Pythagoras' Law first, and the fact that a right-angled triangle always has an angle that measures 90 degrees.

We will also need to know that the sum of the angles in a triangle is 180 degrees.

Therefore, angle A will be = 180 - (90 +30) = 60 degrees

From Pythagoras' Law, we can see that [tex]c= tan 30 \times 8\sqrt{3} =8[/tex]

therefore, line c = 8m