Part A: Given the function g(x) = |x + 3|, describe the graph of the function, including the vertex, domain, and range.
explanation is ideal but not essential :)

2. >>>>>>>b {18x,-x,21x} is an example of like terms because they both hold the same variables.

4.>>>>>>

[tex] = - 7(2x - 3) \\ = - 7(2x) - 7( - 3) \\ = - 14x + 21[/tex]

ATTACHED IS THE SOLUTION

SOLUTION

From the what is given

We have the graph as shown below

We are told that the MAX is

Substituting these required points into the equation, our maximum becomes

We can see that the maximum is 25 at for units of 5, that is x = 5

But we are told in (B) that

Hence the surplus unit is

Hence the answer is 2

800 miles is going to be the distance that separates the two aircraft. The distance between the two airplanes will be 1,300 kilometers at the very least.

It is important to keep in mind that the two aircraft's combined speed will be equal to the sum of their separate speeds when calculating their overall speed. In addition, the pilots of the two aircraft have one hour to find each other.

According to the information that was provided, the distance that separates the aircraft after they have flown for forty-five minutes is two hundred miles. As a result, the following will constitute the remaining distance:

= 1 hour - 45 minutes = 15 minutes.

When this occurs, the distance between the planes will be as follows:

= 200/15 × 60

= 200 × 4

= 800 miles

As a result, there will be a gap of 1300 kilometers between the two aircraft.

Check out this related link on distance:

https://brainly.com/question/15172156

#SPJ1

The missing proof in the given congruence of triangle is;

∠FAB = ∠FBA.

For the given question;

The given data in the triangle FAB is;

In the step two,

FA = FB (Property of isosceles triangle)

Then, step 4 will be ∠FAB = ∠FBA.

Thus, the missing proof will be ∠FAB = ∠FBA.

To know more about the isosceles triangle, here

https://brainly.com/question/28226565

#SPJ13

The rational equation is equivalent to the polynomial 27 · x² - 36 · x + 12.

In this case we find a rational equation whose numerator and denominator are polynomials, which must be simplified by using algebra properties. The complete procedure is now shown:

(9 · x - 6)² / (2 · x⁴ + 4 - 2 · x⁴ - 1)                  Given

(81 · x² - 108 · x + 36) / (3)                             Perfect square binomial / Associative, commutative and modulative properties / Existence of additive inverse /Definition of subtraction

27 · x² - 36 · x + 12                                        Addition and subtraction of fractions with same denominator / Associative and commutative properties / Definition of division

The rational equation is equivalent to the polynomial 27 · x² - 36 · x + 12.

To learn more on rational equations: https://brainly.com/question/19245813

#SPJ1

We have

tennis racket price $54

Firs we need to obtain the 30 %

54*.30=16.2

then in order to know the sale price we need to substract the 30% of the original price

54-16.2=37.8

the sale price is $37.8

The required equation is m/w = 900/18

What is meant by an equation?

An equation is a formula in mathematics that expresses the equality of two expressions by linking them with the equals sign. The word equation and its cognates in various languages may have somewhat different definitions; for example, in French, an équation is defined as including one or more variables, but in English, an equation is any well-formed formula consisting of two expressions linked by an equals sign. Differential equations are equations in which one or more functions and their derivatives are involved. They are solved by locating a function expression that does not use derivatives. Differential equations are used to represent processes with variable rates of change in fields such as physics, chemistry, biology, and economics.

The required equation is m/w = 900/18

To know more about an equation, click on then link

https://brainly.com/question/27893282

#SPJ9

Answer: x=-3(-y+3)

Step-by-step explanation:

Answer:

1. 15 pieces of candy

2. 48 cows

3. 81 ham subs

4. 24 boys

Step-by-step explanation:

Assuming you just want answers, but lmk

Answer:

A' = (6, 3)

B' = (1, 1)

C' = (8, 7)

Step-by-step explanation:

Vertices of triangle ABC:

Given mapping rule:

(x, y) → (x + 4, y + 6)

This notation tells you that the x-coordinate is translated 4 units to the right, and the y-coordinate is translated 6 units up.

Substitute the coordinates of each point into the mapping rule to find the vertices of triangle A'B'C':

⇒ A' = (2 + 4, -3 + 6) = (6, 3)

⇒ B' = (-3 + 4, -5 + 6) = (1, 1)

⇒ C' = (4 + 4, 1 + 6) = (8, 7)

The number of times for which the train must be used so that the monthly cost without the pass is same as with the pass is; 6.25 times.

It follows from the task content that the regular train ticket costs, 3.00.

Therefore, the cost for travelling x times with the month is; 3x.

On this note, for the total monthly cost without the pass to be same as that with the pass; the equation which must hold is;

3x = 18.75

x = 18.75/3

x = 6.25 times.

Therefore, after taking the train 6.25 times, the cost without the pass is same as that with the pass.

Read more on word problems;

https://brainly.com/question/21405634

#SPJ1

1. There will be $102, 826 in the account in 25 years.

2. The total amount of money you will put into the account is $60, 000

3. The total interest that you would have earned is $42,826.

For us to calculate the future value of the account in 25 years, we shoud use the formula; FV = P x (((1 + r)^nt - 1) / r)

When we insert the values, it will be

FV = 200 x (((1 + 0.04/12)^(12 x 25) - 1) / (0.04/12))

= 102, 825. 9. If we round this up, we should get

$102, 826

For us to calculate the total amount of money you put into the account, we should us the formula;

Total Deposits = Monthly Deposit x Number of Months

If we insert the values it wil be

200 x (25 x 12)

60,000

Lasty, if we are to find the total interest earned:

Total Interest = Future Value - Total Deposits

$102, 826 - 60,000

=  $42,826

Find more exercises on calculating total interest;

https://brainly.com/question/31608291

#SPJ1

The point B has a coordinates of (-3, 7) after the dilation

From the question, the coordinates of the point B are given as

B = (1, 7)

The scale factor of dilation is given as

k = 3

The center of dilation is given as

Center = (3, 7)

The rule of the dilation is calculated using

B' = (k(x - a) + a, k(y - b) + b)

Where

(a, b) = (3, 7)

k = 3

(x, y) = (1, 7)

So, we have

B' = (3 * (1 - 3) + 3, 3 * (7 - 7) + 7)

Evaluate

B' = (-3, 7)

Hence, the coordinates of the point B is (-3, 7)

Read more about dilation at

https://brainly.com/question/3457976

#SPJ1

The value of the unknown angle in the triangle is as follows;

The exterior angle theorem states that the measure of an exterior angle of a triangle is greater than either of the measures of the remote interior angles.

In other words,  an exterior angle of a triangle is equal to the sum of the two opposite interior angles.

The external angle is ∠JRS.

Therefore, m∠S can be found as follows:

∠JRS = m∠S + m∠T

Hence,

m∠S  = 3x + 4

m∠T = 8x + 4

∠JRS = 140°

Hence,

140 = 3x + 4 + 8x + 4

140 = 3x + 8x + 4 + 4

140 = 11x + 8

140 - 8 = 11x

132 = 11x

x = 132 / 11

x = 12

Therefore,

m∠S  = 3(12) + 4 = 40 degrees.

learn more on angle and triangle here:https://brainly.com/question/25950519

#SPJ1

Answer:equal

Step-by-step explanation: no number but equal as it is tossed 4 times

Answer:

16

Step-by-step explanation:

The number of possible outcomes at each coin toss = 2.

The total number of possible outcomes after 4 times = 2⁴ = 16.

Answer: 2/3

Jenna had 3 boxes of cocoa and gave away 2, for each friend the fraction is 1/3 therefore 1/3 +1/3 =2/3.... the final fraction is 2/3.

Answer: 2/3

Step-by-step explanation:

total, Jenna had 3/3, then she gave 1/3 to two of her friends. Which makes the total boxes 2/3 of what she gave away with a remaining of 1/3. (1 box of the three boxes)

Answer:

x=62

Step-by-step explanation:

X=62 because all angles of a triangle should add up to 180 degrees no matter what. All you have to do is subtract the already known angles in the triangles from 180 to receive your x value. 180-65-53=x 180-65-53=62.

-Hope this helps

The amount Ali will pay is  £25.80

Define Multiples

A number that can be divided by another number without a remainder.

Multiples of 8 and 12

8 : 8 , 16, 24, 32, 40, 48, 56, 64, 72

12 : 12, 24, 36, 48, 60, 72

common element is 72

72 cakes cost for 12 cakes in each box = 72/12

                                                                 = 6 packs

cost of 6 packs = 6 * £2.50 = £15

72 sausage rolls for 8 sausage in each box = 72 / 8

                                                                       = 9 packs

cost of 9 packs = 9 * £1.20 = £10.80

Total cost will be = £15 +  £10.80 =  £25.80

Hence, the amount Ali will pay is  £25.80

To read more about multiples

https://brainly.com/question/26856218

#SPJ9

The variables we need to use in the question are defined. We will call the price of a knife as [tex]k[/tex] and the price of a spoon as [tex]s[/tex].

The total price of [tex]12[/tex] spoons and [tex]16[/tex] knives is then given. Let's write knives instead of [tex]4[/tex] spoons.

===================================================

Explanation:

k = cost of one knife

s = cost of one spoon

costs are in pounds

12s = cost of 12 spoons

16k = cost of 16 knives

12s+16k = 105.64 pounds is the total cost

We can replace k with 4s because of the phrasing "a knife is 4 times the cost of a spoon". Whatever s might be, quadruple it and it leads us to the value of k.

So,

12s+16k = 105.64

12s+16(4s) = 105.64

12s+64s = 105.64

76s = 105.64

s = 105.64/76

s = 1.39 pounds is the cost of one spoon

k = 4s = 4*1.39 = 5.56 pounds is the cost of one knife

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

Check:

1 spoon = 1.39 pounds

12 spoons = 12*1.39 = 16.68 pounds

1 knife = 5.56 pounds

16 knives = 16*5.56 = 88.96 pounds

12 spoons + 16 knives = 16.68+88.96 =  105.64 pounds total

This fully verifies the answer.

In this case, the alternate interior angles are for example angles 6 and 3 because they are on the inner side of each of the lines (m and l) but on opposite sides of the transversal (t).

m∠6 = m∠3

or

m∠4 = m∠5

The equation of a parabola with a focus at (-2,-3) and a directrix at y = -5  is y =  1/7(x + 2)^2 - 8/7 vertex is (2, -8/7)

What is Parabola?

A parabola is the location of a moving point whose distance from a given focus point and directrix line, respectively, is always constant.

let's keep it simple: (x, y). Focus is on (7,5)

When the separation from focus is

[tex]\sqrt{(x - (-2)^{2}) + (y - (-3)^{2} ) }[/tex] . Its distance from directrix y = -5 i.e.

y + 5 = |y + 5|^2

Hence, equation of parabola:

(x - (-2))^2 + (y - (-3))^2 = |y + 5|^2

or, (x + 2)^2 + (y + 3)^2 = |y + 5|^2

x^2 + 4x + 4 + y^2 + 3y + 9 = y^2 + 10y + 25

or, x^2 + 4x + 13 + y^2 + 3y = y^2 + 10y + 25

x^2 + 4x - 12 = 7y

y = (x^2 + 4x - 12)/7

y = 1/7(x^2 + 4x +4 - 4) - 12/7

y = 1/7(x + 2)^2 - 12-4/7

y =  1/7(x + 2)^2 - 8/7

Hence, parabola's equation is y =  1/7(x + 2)^2 - 8/7 vertex is (2, -8/7)

To learn more about Parabola click on the link

https://brainly.com/question/4061870

#SPJ13

The base of the garden is 14.4 feet.

The height of the garden is 6 feet.

Given,

Corey is designing a rectangular garden;

The diagonal of the garden = 15.6 feet

Ratio  between garden's base and height = 12:5

We have to find the length of base and height of the garden.

Here,

Diagonal of a rectangle, d = [tex]\sqrt{base^{2}+ height^{2} }[/tex]

Base = 12x

Height = 5x

Then,

Diagonal, 15.6 = [tex]\sqrt{(12x)^{2} + (5x)^{2} }[/tex]

15.6 = [tex]\sqrt{144x^{2} +25x^{2} }[/tex]

15.6 = √169x²

15.6 = 13 √x²

15.6 = 13x

x = 15.6/13

x = 1.2

Then,

Base of the garden = 12 x 1.2 = 14.4 feet

Height of the garden = 5 x 1.2 = 6 feet

Learn more about diagonal of a rectangle here;

https://brainly.com/question/22530917

#SPJ1

Answer:

Step-by-step explanation:

The approximate net pay of Juanita is $500. Therefore, option B is the correct answer.

Given that, Juanita has a part-time job that pays $12/hour and works about 50 hours every month.

Net pay means take-home pay or the amount employees earn after all payroll deductions are subtracted from their gross pay.

Now, total money earned in a month

= 12 × 50 = 600

Now

6.2% of 600 = $37.2

= 600 - 37.2 = $562.8

1.45% of 562.8 = $8.1606

= 562.8 - 8.1606 = $554.6394

10% of 554.6394 = $55.46394

= 554.6394 - 55.46394 = $499.17546

Total deductions = $499.17546

So, net pay = grass pay - deductions

= 600 - 105.9

= $499.17546

The approximate net pay of Juanita is $500. Therefore, option B is the correct answer.

To learn more about the net pay visit:

https://brainly.com/question/14690804.

#SPJ2

Total time = 2 hours

Time playing video games = 50 minutes

We have to write an equation:

Total time (2hours) multiplied by the percentage in decimal form (x) must be equal to 50 minutes

Time must be in the same unit ( minutes)

since 60 minutes =1 hour

2 hours = 2 (60) =120 minutes

Back with the equation:

120 x = 50

Solving for x

x = 50/120

x = 0.42

In percentage form:

0.42 x 100 = 42%

Answer: 1

Step-by-step explanation: Rise over run, Rise/run. The rise is how much the line goes up or down vertically. The run is how far the line goes until it intersects through a square. The slope is 1 because if you look at the line specifically at the first dot, you just have to go down one and right one as it intersects the square to find the slope.

In the first graph, we have that the whole figure is 1

it is divided in 4 parts:

Then, we want to divide 1 into 4 parts. That is

Then, we have that:

It is the same for the second figure:

Each 1/4 corresponds to each part. Then if we add them:

Given

Answer

Which is triangle 2