Mathematics College

Solve both equations the lines are absolute value and please include detailed steps for each
I’ll report you if you don’t put a legit answer.

Answers

Answer 1

Answer:

see below

Step-by-step explanation:

|x+8| ≤ 4

Separate into two equations one positive and one negative , remembering to flip the inequality for the negative

x+8 ≤ 4 x+8 ≥ -4

Subtract 8 from each side

x+8 -8 ≤ 4-8 and x+8-8 ≥ -4-8

x ≤-4 and x ≥ -12

Writing as one function

-12 ≤x ≤-4

|x-8|+5 ≥ 11

Subtract 5 from each side

|x-8|+5-5 ≥ 11-5

|x-8| ≥ 6

Separate into two equations one positive and one negative , remembering to flip the inequality for the negative

x-8 ≥ 6 or x-8 ≤ -6

Add 8 to each side

x-8+8 ≥ 6+8 or x-8+8 ≤ -6+8

x ≥ 14 or x ≤ -2

Answer 2

Answers and Step-by-step explanations:

9. | x + 8 | ≤ 4

Remember that absolute value just denotes the distance between the argument within the absolute value signs and 0 on a number line. That means that if the item within the absolute value is negative, the absolute value of it will be the positive value because distance is always positive.

That means we have 2 cases here: x + 8 > 0 (positive) or x + 8 < 0 (negative).

Case 1: x + 8 > 0

x + 8 ≤ 4

x ≤ -4

Case 2: x + 8 < 0

-(x + 8) ≤ 4

-x - 8 ≤ 4

-x ≤ 12

x ≥ -12

Combining these two inequalities, we get:

-12 ≤ x ≤ -4

10. | x - 8 | + 5 ≥ 11

Let's isolate the absolute value expression by subtracting 5 from both sides: | x - 8 | ≥ 6

We again have two cases: x - 8 > 0 and x - 8 < 0.

Case 1: x - 8 > 0

x - 8 ≥ 6

x ≥ 14

Case 2: x - 8 < 0

-(x - 8) ≥ 6

-x + 8 ≥ 6

-x ≥ -2

x ≤ 2

Combining these two inequalities, we get:

x ≤ 2 and x ≥ 14

Related Questions

4¹²=4ᵃ‐3, what is the value of a?

Answers

Answer:

a = 15

Step-by-step explanation:

Perhaps your question is:

[tex] 4^{12}= 4^{a-3}[/tex]

If it is so then let us solve:

[tex] 4^{12}= 4^{a-3}[/tex]

Since, bases are equal hence exponents will also be equal. Therefore,

12 = a - 3

12 + 3 = a

a = 15

Find the mode of the data. please Helppppp!!!

Answers

Answer:

pizza

Step-by-step explanation:

Mode is the one that appears most often

Pizza appears 4 times

Cheeseburger, spaghetti appears only 3 times

apples, hot dogs 2 times

Answer: the mode is pizza

Step-by-step explanation:

Pizza: 4

Spaghetti: 3

Cheeseburger: 3

Apples: 2

Hotdog: 2

Pizza is the most so, it is the mode.

For each right triangle fine the length of the side that is not given. Round your answer to the nearest tenth.(one Decimal place)

Answers

Answer:

√157

Step-by-step explanation:

Use Pythagorean theorm.

[tex]11^2 + 6^2 = ?^2[/tex]

121 + 36 = ?^2

157 = ?^2

√157 = ?

Can't simplify.

Answer:

12.5 m

Step-by-step explanation:

You are given the lengths of the legs of a right triangle.

We can use the Pythagorean theorem to find the length of the hypotenuse.

a^2 + b^2 = c^2

(6 m)^2 + (11 m)^2 = c^2

36 m^2 + 121 m^2 = c^2

c^2 = 157 m^2

c = sqrt(157 m^2)

c = sqrt(157) m

Answer: 12.5 m

John wants to evaluate the expression (5 + 3)^2.
As a first step, he writes 5^2+ 3^2. Will he get the correct value for the
expression? If not, what should he do to evaluate the expression?
Please help write the correct answer.

Answers

Answer:

5+3 x 2=64

Step-by-step explanation:

(5+3) x 2 5^2+3^2=34 not 64

8 x 2 = 64

Answer:

Step-by-step explanation:

Hope this helped

Consider the polynomial function p(x) = 4x^8- 6x^7+ 3x^3- 10.
What is the end behavior of the graph of p?

Answers

Answer:

As x gets smaller, pointing to negative infinity, the value of p increases, pointing to positive infinity.

As x increases, pointing to positive infinity, the value of p increases, pointing to positive infinity.

Step-by-step explanation:

To find the end behaviour of a function f(x), we calculate these following limits:

[tex]\lim_{x \to +\infty} f(x)[/tex]

And

[tex]\lim_{x \to -\infty} f(x)[/tex]

At negative infinity:

[tex]\lim_{x \to -\infty} (4x^{8} - 6x^{7} + 3x^{3} - 10)[/tex]

When the variable points to infinity, we only consider the term with the highest exponent. So

[tex]\lim_{x \to -\infty} (4x^{8} - 6x^{7} + 3x^{3} - 10) = \lim_{x \to -\infty} 4x^{8} = 4*(-\infty)^{8} = \infty[/tex]

Plus infinity, because the exponent is even.

So as x gets smaller, pointing to negative infinity, the value of p increases, pointing to positive infinity.

At positive infinity:

[tex]\lim_{x \to \infty} (4x^{8} - 6x^{7} + 3x^{3} - 10) = \lim_{x \to \infty} 4x^{8} = 4*(\infty)^{8} = \infty[/tex]

As x increases, pointing to positive infinity, the value of p increases, pointing to positive infinity.

Answer:

A - As x -> infinity, p(x) -> infinity, and as x -> -infinity, p(x) -> infinity.

Step-by-step explanation:

Given the system y= 2x + 2 and y= 2*, which statement below is true?
There are no solutions
The system has exactly one solution.
(3, 8) is a solution of the system.
(8,3) is a solution of the system.

Answers

Answer:

(3, 8) is a solution of the system

Step-by-step explanation:

We assume your second equation is intended to be ...

y = 2^x

This system of equations can be solved graphically or by trial and error. There are no algebraic methods for solving it.

A graph shows that (3, 8) is one of the two solutions.

Discuss a recent bill presented in the House. List the Title and the Representative that introduced (signed) the bill.

Answers

Answer:

This is what I found on the internet

Step-by-step explanation:

2019 LEGISLATIVE RECORD OF THE HOUSE OF REPRESENTATIVES TO DATE

11/27/19

The House has passed MORE THAN 275 BIPARTISAN BILLS this Congress that are stuck in the Senate, where Mitch McConnell refuses to bring them for a vote.

This includes bipartisan legislation to:

Give American workers a long overdue raise by raising the minimum wage and making sure women are paid fairly for their work.

Protect the retirement of Americans who worked hard all their lives.

Enact gun safety background checks.

Cut taxes for Gold Star families.

Protect consumers from being ripped off by fine print contracts.

Protect people with pre-existing conditions, reverse health care sabotage & lower drug costs.

Support veterans.

BY THE NUMBERS

The House has passed nearly 400 bills this Congress. More than 300 bills, or 80% of the bills the House has passed, are stuck in the Senate, where McConnell refuses to bring them for a vote. Most ofthe bills that are stalled in the Senate,more than 275, are bipartisan.

Examples of Bipartisan Bills McConnell is Refusing to Act on Include:

H.R.5, Equality Act

H.R.6, The American Dream and Promise Act

H.R.7, Paycheck Fairness Act

H.R.8, Bipartisan Background Checks Act

H.R.9, Climate Action Now Act

H.R.987, Protecting People With Pre-Existing Conditions/Lowering Drug Costs

H.R.582, Raise The Wage Act

H.R.397, Rehabilitation For Multiemployer Pensions Act (The Butch Lewis Act)

H.R.1585, Violence Against Women Reauthorization Act

H.R.1644, Save The Internet Act

H.R 2722, Securing America’s Federal Elections (SAFE) Act

H.R.2513, The Corporate Transparency Act

H.R.1112, Enhanced Background Checks

H.R.1994, Secure Act/Gold Star Family Tax Relief Act

H.R.205, 1146, 1941 – Banning Offshore Drilling on Atlantic, Pacific, Eastern Gulf & ANWR Coasts

H.R.1423, Forced Arbitration Injustice Repeal (FAIR) Act

More than 30 bills to support veterans

Other Examples of Bills McConnell is Refusing to Act on that Democrats Support:

H.R.1, For The People Act

H.R.4617, Stopping Harmful Interference in Elections for a Lasting Democracy (SHIELD) Act

H.R.1500, Consumers First Act

What is the area of ABCDE?____sq cm
got very confused on this part

Answers

Answer:

A= 30 sq. cm

Step-by-step explanation:

We want to find the area of both triangles seprately than add them together. For the area of a traingle, we use the equation 1/2 base times height. For triangle ABE we do this:

[tex]A = \frac{1}{2} (12)(4)[/tex]

[tex]A = (6) (4)[/tex]

[tex]A = 24[/tex]

For triangle BDC, we do this:

[tex]A = \frac{1}{2} (6) (2)[/tex]

[tex]A = (3) (2)[/tex]

[tex]A=6[/tex]

Now we have to add both areas ot get A=30 sq cm

Factor this expression completely
100x + 1000
A)
100(x + 10)
B)
100(x + 100)
C)
10(10x + 100)
D)
1000(10x + 1)

Answers

Answer:

Answer is A

Step-by-step explanation:

100× x is 100x

100 × 10 is 1000

Answer:

A is the answer

Step-by-step explanation:

PLZZZ give me brainliest

Which equation is the inverse of (x-4)2- ß-by-122
O y=6x2-3x+42
6x-
34
O y=4+ /6x-
34
O y=-4+ /6x-
0 -(x-4)2 -> --6y+12

Answers

Answer:

see below

Step-by-step explanation:

Interchange x and y, then solve for y.

[tex](x-4)^2-\dfrac{2}{3}=6y-12\qquad\text{given}\\\\(y-4)^2=6x-\dfrac{36-2}{3}\qquad\text{swap x,y; add 2/3}\\\\y-4=\pm\sqrt{6x-\dfrac{34}{3}}\\\\\boxed{y=4\pm\sqrt{6x-\dfrac{34}{3}}}[/tex]

Which inequality is equivalent to y-8 less than or equal to -2

Answers

I think the answer is a slope -5/66

The Acme Class Ring Company designs and sells two types of rings: the VIP and the SST. They can produce up to 24 rings each day using up to 60 total man-hours of labor. It takes 3 man-hours to make one VIP ring, versus 2 man-hours to make one SST ring. How many of each type of ring should be made daily to maximize the company's profit, if the profit on a VIP ring is $40 and on an SST ring is $35?

Answers

Answer:

The combination that gives the most profit is 12 VIP rings and 12 SST rings (900 $/day).

Step-by-step explanation:

This is a linear programming problem.

The objective function is profit R, which has to be maximized.

[tex]R=40V+35S[/tex]

being V: number of VIP rings produced, and S: number of SST rings produced.

The restrictions are

- Amount of rings (less or equal than 24 a day):

[tex]V+S\leq24[/tex]

- Amount of man-hours (up to 60 man-hours per day):

[tex]3V+2S\leq60[/tex]

- The number of rings of each type is a positive integer:

[tex]V, \;S\geq 0[/tex]

This restrictions can be graphed and then limit the feasible region. The graph is attached.

We get 3 points, in which 2 of the restrictions are saturated. In one of these three points lies the combination of V and S that maximizes profit.

The points and the values for the profit function in that point are:

Point 1: V=0 and S=24.

[tex]R=40V+35S=40\cdot 0+35\cdot 24=0+840\\\\R=840[/tex]

Point 2: V=12 and S=12

[tex]R=40V+35S=40\cdot 12+35\cdot 12=480+420\\\\R=900[/tex]

Point 3: V=20 and S=0

[tex]R=40V+35S=40\cdot 20+35\cdot 0=800+0\\\\R=800[/tex]

The combination that gives the most profit is 12 VIP rings and 12 SST rings (900 $/day).

b) Would you consider it unusual to find a college student who never wears a seat belt when riding in a car driven by someone else? A. Yes, because 0.01less than<P(never)less than<0.10. B. Yes, because P(never)less than<0.05. C. No, because there were 139139 people in the survey who said they never wear their seat belt. D. No, because the probability of an unusual event is 0.

Answers

Answer:

Step-by-step explanation:

Hello!

Full text

In a national survey college students were asked, "How often do you wear a seat belt when riding in a car driven by someone else?" The response frequencies appear in the table to the right. (a) Construct a probability model for seat-belt use by a passenger. (b) Would you consider it unusual to find a college student who never wears a seat belt when riding in a car driven by someone else?

Response , Frequency

Never 102

Rarely 319

Sometimes 524

Most of the time 1067

Always 2727

n= 102+319+524+1067+2727= 4739

(a) Complete the table below.

Response

Probability To calculate the probability for each response you have to divide the frequency of each category by the total of people surveyed:

Never P(N)= 102/4739= 0.0215