The inequality −6(x − 3) > 42 is given.Part A: Solve the inequality and show every step of your work. (4 points)

Part B: Explain in words how to graph the solution to the inequality on a number line. (4 points)

Part C: Find two values that would make the inequality true. Explain how you know the values are solutions to the inequality. (4 points)

Answers

Answer 1

Answer:

Answer: Sure, I can help you with that!

Part A: To solve the inequality −6(x − 3) > 42, we first need to distribute the -6 to the expression inside the parentheses:

-6(x - 3) > 42 -6x + 18 > 42

Next, we’ll subtract 18 from both sides:

-6x > 24

Finally, we’ll divide both sides by -6. Since we’re dividing by a negative number, we need to flip the inequality sign:

x < -4

Therefore, the solution to the inequality is x < -4.

Part B: To graph the solution to this inequality on a number line, we’ll start by drawing an open circle at -4 (since x is not equal to -4). Then, we’ll draw an arrow pointing to the left of -4 to indicate that all values less than -4 are solutions to the inequality.

Part C: To find two values that would make the inequality true, we can choose any two values less than -4 and substitute them into the original inequality. For example, if we choose x = -5, then:

-6(-5 - 3) > 42 -6(-8) > 42 48 > 42

Since 48 is greater than 42, this confirms that x = -5 is a solution to the inequality. Similarly, if we choose x = -10, then:

-6(-10 - 3) > 42 -6(-13) > 42 78 > 42

Since 78 is also greater than 42, this confirms that x = -10 is also a solution to the inequality.

I hope this helps!

Related Questions

50 kg of grade a coffee beans is mixed with 100 kg of grade b coffee beans. what will be weight in kg of grade b coffee beans in 60 kg of mixture?
Find the sum. Do not round.39.882 + 11.03 =
PLEASE HELP!!! WILL GIVE CROWN!!!
TIMED PLEASE HURRYTwo hundred students were surveyed about their favorite fruit. How many more students preferred apples than cherries? 2 4 35 70
Factor completely and then place the factors in the proper location on the grid.b 2 + 12b + 32

How many solutions does the equation 4n + 6 = 4 + 2 + 4n have?Two
Many
None
One

Answers

Answer:

many solutions

Step-by-step explanation:

4n + 6 = 4 + 2 + 4n

We try to solve for n

we try to get the variable alone

4n + 6 = 4 + 2 + 4n

combine like terms

4n + 6 = 6 + 4n

subtract 4n from both sides

6=6

If we arrive at a true statement like 5=5 then the equation has infinitely many soltions

We arrived at a true statement 6=6 so infinitely many solutions

4n+6=4+2+4n, well first combine like terms, 4n+6=6+4n and those are exactly the same, there's no magical n that can make 4n+6 not equal 4n+6, so many

HELP PLEASE!! Give an example of two irrational numbers whose product is an irrational number. AND Give an example of two irrational numbers whose product is a rational number.

Answers

(pi) x 3pi = 3 pi²

pi x 3/pi = 3

Please answer as soon as possible

Answers

I believe its 84, because basically if you take the 6×6 for the top layer it equals 36 and there's two layers so 36+36= 72, then you add the top half which is 12, which would equal 84.

Use the function f(x)=x 2 −6x+8 to answer the following questions: a. What is the y-intercept? b. What are the x-intercepts? c. What is the vertex? d. What is the axis of symmetry?

Answers

Answer:

see explanation

Step-by-step explanation:

given the function

f(x) = x² - 6x + 8

(a)

to find the y- intercept , let x = 0 in f(x)

f(0) = 0² - 6(0) + 8 = 0 - 0 + 8 = 8 ← y- intercept

(b)

to find the x- intercepts , let f(x) = 0 , that is

x² - 6x + 8 = 0 ← in standard form

(x - 2)(x - 4) = 0 ← in factored form

equate each factor to zero and solve for x

x - 2 = 0 ⇒ x = 2

x - 4 = 0 ⇒ x = 4

the x- intercepts are x = 2 and x = 4 or (0, 2 ), (0, 4 ) in coordinate form

(c)

given a quadratic in standard form

f(x) = ax² + bx + c ( a ≠ 0 )

then the x- coordinate of the vertex is

$x_(vertex)$ = - $(b)/(2a)$

f(x) = x² - 6x + 8 ← is in standard form

with a = 1 and b = - 6 , then

$x_(vertex)$ = - $(-6)/(2)$ = - (- 3) = 3

evaluate f(3) for corresponding y- coordinate

f(3) = 3² - 6(3) + 8 = 9 - 18 + 8 = - 9 + 8 = - 1

vertex = (3, - 1 )

(d)

the axis of symmetry is a vertical line , passing through the vertex with equation

x = c ( c is the value of the x- coordinate of the vertex )

equation of axis of symmetry is then x = 3

If sin x=0.5, what is the value of cos x?

Answers

The period is πNote that the function f(x) can be simplified as 14sin(2x). This is because of the identity sin(2x)=2sinxcosx.

so you answers is π

The function f(x)=600+2x over x yields the average cost in dollars for a company to produce x calendars. Which statement best fits the situation modeled by the function? a) The company spends $600 on a new computer and printer before beginning the project.
b) The company takes 600 photos before selecting which ones to use for its calendars.
c) The company expects to sell 600 calendars each month.
d) The company will sell the calendars for $6.00 each.

Answers

Answer:

The correct option is a.

Step-by-step explanation:

The average cost function is

$f(x)=(600+2x)/(x)$

Where x is the number of calendars produced.

The average cost formula is

$AC=\frac{\text{Total Cost}}{\text{Number of items}}$

Therefore the total cost is defined b the function

$g(x)=600+2x$

Here 600 is the initial cost and the cost each unit is 2.

Initial cost is the fixed cost which occurs at zero level of productivity.

The company spends $600 on a new computer and printer before beginning the project. The option (a) is correct.

The function f(x)=600+2x over x yields the average cost in dollars for a company to produce x calendars. The statement best fits the situation modeled by the function "The company spends $600 on a new computer and printer before beginning the project.". The answer is letter A.

Other Questions

7. Find the value of Z in the following equation: 8Z = 64.

Square root of 9610 by division method

3,9,6,9,27,24,27,81,78,81,243,?find out last figure to complete series

How many positive factors does 2023 have?