a) Simplify the expression and explain each step. (2 points)

4(3x + 2) – 2


b)  Factor the expression completely.  (1 point)


20b – 16

b. The slope is  - 400. This means that the helicopter descends 400 ft each minute. The slope is 400. This means that the helicopter ascends 400 ft each minute.

We know lines have various types of equations, the general type is

Ax + By + c = 0, and equation of a line in slope-intercept form is y = mx + b.

Where slope = m and b = y-intercept.

the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.

This situation is mathematically represented as a line and slope.

Points  (0, 10,000) and (15, 4000).

We know slope(m) = (y₂ - y₁)/(x₂ - x₁).

Slope(m) = (4000 - 10000)/(15 - 0).

Slope(m) = - 6000/15.

Slope(m) = - 400.

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Answer:

the answer is C

Step-by-step explanation:

Part 1 (or a if you prefer):

f(x) = 5^x

f(x) = 5^0 = 0

f(x) = 5^1 = 5

Use this formula to solve: f(b) - f(a)/b - a

5 - 0 / 1 - 0 = 5/1 = 5

--

f(x) = 5^2 = 25

f(x) = 5^3 = 125

125 - 25 / 3 - 2 = 100/1 = 100

Average rate of change: 

Section A: 5

Section B: 100

Part 2 (or b if you prefer): 

Section B is 20 times greater then A

This is because Section B is increasing in the equation. Thus, Section B is of greater value than Section A.

Hope this assists you and future students.

To determine the number of general admission tickets sold, two equations were formed using the total number of attendees and total sales. By applying the elimination method to solve the system of equations, it was found that 148 general admission tickets were sold.

To solve this problem, we can set up two equations based on the number of people and the total sales. Let x represent the number of student tickets sold at $3.00 each, and let y represent the number of general admission tickets sold at $7.50 each. We are given that a total of 210 people attended, so:

1) x + y = 210

We are also given that the total sales were $1296, so:

2) 3x + 7.5y = 1296

We can solve this system of equations using the substitution or elimination method. For this example, I will use the elimination method. To eliminate one variable, we can multiply the first equation by 3, which gives us:

3x + 3y = 630

Now, by subtracting this new equation from the second equation, we eliminate x:

7.5y - 3y = 1296 - 630

4.5y = 666

Dividing both sides by 4.5, we find that:

y = 148

So, 148 general admission tickets were sold on the opening night of the school musical.

2x-20 = x+8

x-20 =8

x = 28

28+8 =36

 angle B = 36 degrees

answer is b

line AB the one marked c cm is:

8.2 * sin(49)=

6.1889

round answer to 6.2 cm

By setting up a system of equations and solving for the number of bicycles (B) and tricycles (T) based on the total seats and wheels, we can determine there are 27 bicycles and 5 tricycles.

To determine the number of bicycles and tricycles in the bicycle store given that there are 32 seats and 69 wheels, we can set up a system of equations. Let's let B represent the number of bicycles and T represent the number of tricycles. Since bicycles have 2 wheels and tricycles have 3 wheels, we can express the total number of wheels as:

2B + 3T = 69

Each bicycle and tricycle has one seat, so we can also express the total number of seats as:

B + T = 32

To solve this system, we can multiply the second equation by 2 and subtract it from the first equation to eliminate B:

(2B + 3T) - (2(B + T)) = 69 - 64

2B + 3T - 2B - 2T = 69 - 64

T = 5

Now we substitute T into the second equation:

B + 5 = 32

B = 32 - 5

B = 27

So, there are 27 bicycles and 5 tricycles in the bicycle store.

Answer:  [tex]4.33\text{ cars per month.}[/tex]

Step-by-step explanation:

Given : Ervin sells vintage cars. Every three months, he manages to sell 13 cars.

[tex]m=\dfrac{\text{change in y}}{\text{change in x}}[/tex]

If time in months is along the x-axis and the number of cars sold is along the y-axis

Change in months : 3

Change number of cars : 13

The slope of the line that represents this relationship will be :-

[tex]m=\dfrac{\text{Change in cars}}{\text{Change in months}}\\\\=\dfrac{13}{3}=4.33333\approx4.33\text{ cars per month.}[/tex]

Hence, the slope of the line = [tex]4.33\text{ cars per month.}[/tex]

Answer:

View the picture for your answer!

have a nice day :))

Answer:

A - 6$

You pay six dollars up front, on day zero.

To write 180% as a fraction or mixed number in simplest form, convert the percent to a fraction with a denominator of 100 and simplify the fraction. The simplified fraction is 9/5 or the mixed number is 1 and 4/5.

To convert a percent to a fraction or mixed number in simplest form, we need to write the percent as a fraction with a denominator of 100 and then simplify it. In this case, 180% can be written as 180/100. To simplify, we divide both the numerator and denominator by their greatest common divisor, which is 20. So, the simplified fraction is 9/5. This fraction can also be expressed as a mixed number by dividing the numerator by the denominator. Since 9 is greater than 5, the mixed number is 1 and 4/5.

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An absolute value inequality is solved by re-writing it as compound inequality. For example.

|x+1| < 5

Since the value inside the absolute value brackets: (x+1) can be positive or negative, it is re-written as a compound inequality as the example below.

x+1 < 5

x+1 > - 5

solve for the range of values x can be

-6 < x < 4

Solving absolute value inequalities yields compound inequalities. Absolute value cases create intervals, linking the processes in algebraic solutions.

Solving absolute value inequalities and compound inequalities are related concepts in algebra, both involving multiple solutions and a range of possible values. Absolute value inequalities often result in compound inequalities due to the nature of the absolute value function.

When solving an absolute value inequality, such as [tex]\(|x - a| < b\), where \(a\)[/tex]and[tex]\(b\)[/tex] are constants, it generally leads to two separate cases: [tex]\(x - a < b\)[/tex] and [tex]\(x - a > -b\).[/tex] These cases represent the intervals where the expression inside the absolute value is less than [tex]\(b\)[/tex] and greater than its negative counterpart.

This process connects with solving compound inequalities, which involve combining two or more inequalities using logical connectors like "and" or "or." The solutions to the individual inequalities are then used to determine the overall solution to the compound inequality.

For instance, in the absolute value inequality[tex]\(|x - a| < b\)[/tex], the resulting compound inequality might be [tex]\(a - b < x < a + b\)[/tex]. This demonstrates that the solutions lie within the interval \((a - b, a + b)\), illustrating the linkage between solving absolute value inequalities and dealing with compound inequalities. Both concepts require careful consideration of multiple scenarios and the integration of solutions to find the overall solution set.

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