Solve and graph. |2x(x-1)+12|<=18

Mathematics College

Solve and graph. |2x(x-1)+12|<=18

Answers

Answer 1

The solution of the inequality is -1 ≤ x ≤ 3.

To solve the inequality |2x(x-1)+12| ≤ 18, we can break it down into two separate inequalities:

2x(x-1) + 12 ≤ 18

-(2x(x-1) + 12) ≤ 18

Solving the first inequality:

2x(x-1) + 12 ≤ 18

2x² - 2x + 12 ≤ 18

2x² - 2x - 6 ≤ 0

Solving the second inequality:

-(2x(x-1) + 12) ≤ 18

-2x(x-1) - 12 ≤ 18

-2x² + 2x - 12 ≤ 18

2x² - 2x + 30 ≤ 0

Now, let's solve each inequality separately.

For the first inequality, 2x² - 2x - 6 ≤ 0:

We can factor this quadratic equation:

(2x + 2)(x - 3) ≤ 0

To determine the sign of the inequality, we need to consider the intervals where the expression is positive or negative. We set each factor equal to zero to find the critical values:

2x + 2 = 0 => x = -1

x - 3 = 0 => x = 3

Plotting these critical values on a number line and testing intervals, we find that the solution is -1 ≤ x ≤ 3.

For the second inequality, 2x² - 2x + 30 ≤ 0:

This quadratic equation does not have real solutions, so there are no solutions to this inequality.

Combining the solutions from both inequalities, we have -1 ≤ x ≤ 3.

To graph the solution, we plot the interval -1 ≤ x ≤ 3 on the number line. The shaded region on the number line represents the solution set.

To learn more about inequality;

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Related Questions

Which three side lengths best describe the triangle in the diagram

Answers

I think the answer is 6cm, 8cm, 10cm

Answer:

its 6 cm, 8cm, and 10 cm

Step-by-step explanation:

i just took the quiz

Translate the following phrases into mathematical statements.
r ) is less than or equal to ten.

s )is more than negative one

t ) isn't the same as negative
five.

x ) is at most negative three.

y )is never one.

Answers

Answer:

[tex]r \le 10[/tex]

[tex]s > -1[/tex]

[tex]t \ne 5[/tex]

[tex]x \le -3[/tex]

[tex]y \ne 1[/tex]

Step-by-step explanation:

Required

Translate to mathematical statements

a) r is less than or equal to ten.

less than or equal means [tex]\le[/tex]

So, the expression is:

[tex]r \le 10[/tex]

b) s is more than negative one

More than means >

So, the expression is:

[tex]s > -1[/tex]

c) t isn't the same as negative five.

isn't the same means not equal to ([tex]\neq[/tex])

So, the expression is:

[tex]t \ne 5[/tex]

d) x is at most negative three.

At most means [tex]\le[/tex]

So, the expression is:

[tex]x \le -3[/tex]

e) y is never one.

is never means not equal to ([tex]\neq[/tex])

So, the expression is:

[tex]y \ne 1[/tex]

¿Cómo se dice 2021 en números romanos?

Answers

La respuesta es MMXXl

Answer:

MMXXI Hope this helps :)

Step-by-step explanation:

what is 445 + (67 x 958) x (3n - 31) x 67

Answers

Step-by-step explanation:

−

please solve the question below

Answers

Answer:

x = 5.61

Step-by-step explanation:

Applying the knowledge of similarity between two figures, thus:

Height of flag : height of Tommy = shadow length of flag : shadow o

Length of Tommy

30:5.5 = (25 + x) : x

30/5.5 = (25 + x)/x

30×x = 5.5(25 + x)

30x = 137.5 + 5.5x

30x - 5.5x = 137.5

24.5x = 137.5

x = 137.5/24.5

x = 5.61 (nearest hundredth)

Compare the fractions using >,<, or = 3/15 and 1/3

Answers

Answer:

3/15 < 1/3

Step-by-step explanation:

We have two fractions, 3/15 and 1/3. The question is asking us to compare them using the less than sign <, greater than sign >, or equal sign =.

To solve this question, what we must do is try to get both fractions the same denominators, which will be done through multiplying 3 by a certain number to get to 15, then doing the same for the numerator.

So what multiplied by 3 gets us 15?

Multiply both the numerator and denominator by 5.

[tex]\frac{1*5}{3*5}[/tex]

[tex]\frac{5}{15}[/tex]

Now that they both have the same denominator, we can compare and see which is bigger.

5/15 (1/3) and 3/15.

By this we can see that 3/15 is less than 5/15.

Therefore 3/15 < 1/3

HELP EMERGANCY FAST ANSWERS TIME LIMIT
Assume Sheila's nominal salary increases from $42,000 in 2003 to $69,000 in 2004.
If the Deflator increased from 106 in 2003 to 109 in 2004 and the CPI increased
from 184 in 2003 to 190 in 2004, what was Sheila's percentage increase in real
income?
6

Answers

Answer:

Step-by-step explanation:

1 - (69,000 / 42,000) = .64285 * 100% = 64.3%

Which choice is equivalent to the product below? Square root of 8 Times Square root 5?

Answers

Answer:

Step-by-step explanation:

Can y’all help pls ;)

Answers

Answer:

A. 5x+6

Step-by-step explanation:

-[tex]\frac{1}{3}[/tex](9x-18)+8x

-3x+6+8x (multiply across the -1/3)

5x+6 (combine 8x and -3x)

which is the graph of y - 3 = -2/3 (x+6)? PLEASE ANSWER QUICK IM TAKING A TIMED TEST

Answers

Answer:

the first graph

Step-by-step explanation:

the one with (0,-1) (-3,1) (3,-3)

WILL MARK BRAINLIEST
What is the volume of the shape in the image?

Answers

Answer:

18inches I HOPE IM RIGHTTT

Answer:

350

Step-by-step explanation:

you do length•width•height. so

10•7=70 and 70•5=350

cuales son los divisores de 12

Answers

Answer:

1, 2, 3, 4, 6, 12

Step-by-step explanation:

Answer:

1,2,3,4,5,6,12 esos son

Sara had fourteen peaches and forty pears left at her roadside fruit
stand. She went to the orchard and picked more peaches to stock up the
stand. There are now eighty-one peaches at the stand, how many did
she pick ?

Answers

Answer:

Step-by-step explanation:

she picked 67 because if you take how many she had at the end and subtract it from the starting number it gives you 67

In triangle ABC, one angle measures 68°, another measures 19°, what is the measure of the third angle? *

Answers

Answer:

93°

Step-by-step explanation:

In triangle ABC

one angle = 68°

Another angle = 19°

Let the third angle be X Then

x + 68° + 19° = 180° { being sum of angles of triangle }

x = 180° - 87°

x = 93°

The measure of the third Angle is 93°

Hope it will help :)

how do you write this number 0.1709 in words?

Answers

Answer:

0.1709 in words-

Point one seven zero nine

1
Add or subtract and simplify. *

(3d + 5) + (40 – 1)

Answers

3d +4

How to:
Combine like terms

The senior class is making T-shirts as a fundraiser. The material needed to make each T-shirt costs $3.75. The students sell each shirt for $10.To increase sales, the students spend $350 on advertising. How many t-shirts must the students sell to breakeven?

Answers

Answer:

the number of t-shirts sold to breakeven is 56 t-shirts

Step-by-step explanation:

The computation of the number of t-shirts sold to breakeven is shown below:

= Fixed cost ÷ (Selling price - cost price)

= $350 ÷ ($10 - $3.75)

= $350 ÷ 6.25

= 56 t-shirts

Hence, the number of t-shirts sold to breakeven is 56 t-shirts

what is the area of a figure what is the area of a figure with a 16 inch base a 10 inch base and a height of 8 in on the left and 6in on the right

Answers

So I’m thinking of this as two triangles. So I would do 16x8/2 which equals 64 and 10x6/2 which equals 30. So my guess is that the area is 94in^2. Hope this helps you out!

Solve these with work shown please.

Answers

Step-by-step explanation:

substitute the value in the value of x and u will get the result.

Hope this helps have a nice day

which phrases represent the expression k/2 - 5

Answers

Answer:

K over two minus five

Step-by-step explanation:

I think?

Pls help I’m failing math

Answers

`Answer:

a)x=-9

b)x=71

c) x=3

d)x=9

Step-by-step explanation:

thats what i got unless im really stoopid

Which professionals most directly use geometry In their work?
O A. accountants
© B. astronomers
O C. judges
© D.
pharmacists
O E. politicians

Answers

Answer:

Step-by-step explanation:

submit your answers in simplest radical form.

help :(

Answers

Answer:

x = 6√2, y = 6

Step-by-step explanation:

This is an isosceles triangle as one angle measures 45° and the other is a right angle, so it measures 90°.

Therefore, you know that y will equal 6.

You have to multiply a by √2 to find x.

6 x √2 = 6√2

Hope this helps!

Answer:

x = 6[tex]\sqrt{2}[/tex]

y = 6

Step-by-step explanation:

in a 45-45-90 triangle the two legs are equal, so XY = YZ

also, the leg to hypotenuse ratio is 1 : [tex]\sqrt{2}[/tex]

so x = 6 · [tex]\sqrt{2}[/tex]

Graph x+y=3 , ILL MARK BRAINLIST

Answers

The answer is d when you graph

Answer:

Are you sure?

None

Step-by-step explanation:

A. x= -3 , y= 3

x + y =

-3 + 3 = 0

B. x= -3 , y= -3

x + y =

-3 + -3 = -6

C. x= 3 , y= 3

x + y =

3 + 3 =6

D. x= 3 , y= -3

x + y =

3 + -3 = 0

what does b = help plzz

Answers

Answer:

128

Step-by-step explanation:

Answer:128

Step-by-step explanation:

It is 128 because the WHOLE angle is 180 degrees and if 52 degrees are covered the other remaining is b so 180 degrees-52 degrees is 128 degrees

Matthew has a loyalty card good for a discount at local hardware store. The item he wants to buy is priced at $13 before discount and tax. After the discount and before tax a price is $12.48. Find the percent discount.

Answers

Answer:

Step-by-step explanation:

Your answer

Old price = 13$

New price = 12.48$

DISCOUNT price = 0.52$

Discount rate = 0.52/13 * 100= 4%

Mark it as Brainlist answer. Follow me.

The length of each side of an equilateral triangle is increased by 6 inches, so the perimeter is now 60 inches. What was the original length of each side of the equilateral triangle?

Answers

Answer:

14 inches

Step-by-step explanation:

Using this information, we can form an equation.

Since there are 3 sides in a triangle, and each side increased by 6, that means that the perimeter increased by 18 inches. Down below, I did 3x because there are 3 sides in a triangle.

(This is the equation you'd want to do to get the answer)

3x + 3 * 6 = 60

Simplify:

3x + 18 = 60

Same to both sides

3x = 42

Isolate x:

x = 14

Let me know if you have any questions

I need help!!!!! Solve for n 6n=72

Answers

Answer:

6n=72

n=72/6

n=12

.....................

Answer:

n = 12

Step-by-step explanation:

n = 72÷ 6

n = 12

thats the answer

841 rounded to the nearest 10th

Answers

841 rounded to the nearest 10th is 840...hope this helps u :)

The answer is 840.

I hope am right

75+11(1777-S)=16,671

Answers

Answer:

s = 268.27

Step-by-step explanation:

simplify: 75+19547-11s=16671

simplify more: 19622-11s=16671

subtract 19622 on both sides: -11s=-2951

divide both sides by -11: s=268.27

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