|2x -8| < 2

a. 3 b. -5 c. x>5 or x<3
d. x>-3 or x<-5

Answers

Answer 1

Answer:

[tex]3 < x < 5[/tex]

Step-by-step explanation:

Given inequality:

[tex]|2x - 8| < 2[/tex]

[tex]\textsf{Apply absolute rule}: \quad \textsf{If }|u| < a\:\textsf{ when } \: a > 0,\: \textsf{then }-a < u < a[/tex]

[tex]\implies u=2x-8\: \textsf{ and }\:a=2[/tex]

[tex]\implies -2 < 2x-8 < 2[/tex]

Therefore:

[tex]\implies -2 < 2x-8[/tex]

[tex]\implies 6 < 2x[/tex]

[tex]\implies 3 < x[/tex]

And:

[tex]\implies 2x-8 < 2[/tex]

[tex]\implies 2x < 10[/tex]

[tex]\implies x < 5[/tex]

Merge the overlapping intervals:  [tex]3 < x < 5[/tex]

Proof

Graph:  [tex]y=|2x-8|[/tex]

Add a line at  [tex]y=2[/tex]

The interval that satisfies  [tex]|2x - 8| < 2[/tex]  is the area under the points of intersection (shaded area on the attached graph).

The values of x when [tex]y=|2x-8|[/tex] is less than 2 is more than x = 3 and less than x = 5.

|2x -8| &lt; 2a. 3b. -5c. X&gt;5 Or X&lt;3d. X&gt;-3 Or X&lt;-5
Answer 2
|2x-8|<2

So

Case-1

2x-8<22x<2+82x<10x<5

Case-2

2x-8>-22x>6x>3

So solution is

3<x<5

Related Questions

Find the volume of the rectangular prism in cubic feet. 3.4 ft 0.8ft 0.6ft "these are not the answers these are the ft of the prism

Answers

Answer:

A

Step-by-step explanation:

becaauss im smart and trust me im smart

What expression lets us conclude that the parts of congruent triangles are congruent to each other?

Corresponding Parts of Congruent Triangles are Congruent
Congruent Triangles have Congruent Parts
Opposite parts of Congruent Triangles are Similar

Answers

The expression that allows us conclude parts of congruent triangles are congruent to each other is corresponding parts of Congruent Triangles are congruent

What are congruent triangles?

A triangle is a three-sided polygon with three edges and three vertices. the sum of angles in a triangle is 180 degrees. Two triangles are congruent when they have exactly the same three sides and exactly the same three angles.

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Donations to an annual fundraiser are 15% greater this year than last year. Last year, donations were 10% greater than the year before. The amount raised this year is $10,120. How much was raised two years ago?

Answers

Answer:

8000.

Step-by-step explanation:

um I said so you don't need no step by step.

I need help to find this number in scientific notation form pls.

Answers

Answer:

the answer is (   -0 ) ok?

Step-by-step explanation:

also my name ifs kris ik you from somewhere

i am very embarrest to say this but u are very pretty

are u single? im sorry if its freakish

are u mexican? of Philippians? im from la pearla tapatia mx hbu?

A number cube is rolled 14 times and the results are recorded in the table.

what, in simplest form, is the experimental probability that the number 4?

Answers

Answer:

2.3333 ≈ 2

Step-by-step explanation:

The first step is the 1/6 because you are only counting the value 4 not the other ones like 1,2,3,5,6. So then that is 0.1666666. Then you multiply it by 14 which is rounded to 2. I can tell you are a 6th grader.

DISCLAIMER: THIS ANSWER MAY BE FALSE BECAUSE THERE IS NO PICTURE ATTACHED TO THIS POST. THUS, NEXT TIME YOU SHOULD UPLOAD A PICTURE. THIS IS ONLY A GUESS NOT A REAL ANSWER.

The graph below shows the function f(x)=
x-3
+3
-2x-3•

Answers

The true statement about the graph is that there is a hole at x = 3 and an asymptote at x = -1.

How to explain the  graph?

The expression in the denominator is x^2-2x-3

x² - 2x-3 ≠0

-3 = +1 -4

(x²-2x+1)-4 ≠0

(x²-2x+1)=(x-1)²

(x-1)² - (2)² ≠0

∴a²-b² =(a-b)(a+b)

(x-1-2)(x-1+2) ≠0

(x-3)(x+1) ≠0

x≠3 for all x≠ -1

There is a hole at x=3 and an asymptote at x= -1, so Option B is wrong

Asymptote:

x-3/x^2-2x-3

We know that denominator is equal to (x-3)(x+1)

x-3/(x-3)(x+1)

x-3 will be cancelled out by x-3

1/x+1

We have asymptote at x=-1 and hole at x=3, therefore the correct option is A.

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what is the area of this rectangle

Answers

Answer:

6 cm^2

Step-by-step explanation:

Area of Rectangle is L*W

L=3 and W=2

3*2=6

Please help!

The price of products may increase due to inflation and decrease due to depreciation. Derek is studying the change in the price of two products, A and B, over time.

The price f(x), in dollars, of product A after x years is represented by the function below:

f(x) = 72(1.25)x

Part A: Is the price of product A increasing or decreasing and by what percentage per year? Justify your answer. (5 points)

Part B: The table below shows the price f(t), in dollars, of product B after t years:

t (number of years)
1 2 3 4
f(t) (price in dollars)
65 84.5 109.85 142.81

Which product recorded a greater percentage change in price over the previous year? Justify your answer. (5 points)

Answers

Answer:

A)25% B)Product B

Step-by-step explanation:

A) To find whether product A price is increasing or decreasing, we will find the difference in price between year 0 and 1 year after.

When x = 0,

f(0)  [tex]72(1.25)^{0}\\= 72*1\\= 72[/tex]

when x = 1,

f(1) = [tex]72(1.25)^{1}\\= 72*1.25\\= 90[/tex]

From here we can already see the price is increasing.

% increase = (Difference in price / Original Price) * 100

= [tex]\frac{90-72}{72} *100\\=\frac{18}{72} *100\\=0.25*100\\=25percent[/tex]

Therefore the price is increasing by 25% per year.

B) Same concept as Part A, we will find the price difference between year 1 and 2.

% increase = (Difference in price / Original Price) * 100

[tex]\frac{84.5-65}{65} * 100\\= \frac{19.5}{65} * 100\\= 0.3*100\\= 30 percent[/tex]

Therefore we can see here Product B has a higher increase than Product A.

Step-by-step explanation:

A

f(x) = 72 × 1.25 × x

so, the price is $90 after 1 year (72×1.25×1).

$180 after 2 years (72×1.25×2)

$270 after 3 years (72×1.25×3)

and so on.

or did you mean

f(x) = 72 × (1.25)^x

so, still, the price is $90 after 1 year (72×1.25^1).

$112.50 after 2 years (72×1.25^2).

$140.625 = $140.63 after 3 years (72×1.25^3)

that makes more sense. I will continue with that assumption.

so, the price is increasing, as every factor of the multiplication is positive and larger than 1. therefore, it only goes up.

and due to the formula, the price of every year is the price of the previous year multiplied by 1.25.

a multiplication by 1.25 is an increase of 25% (compared to a constant multiplication by 1).

so, the price increases every year by 25%.

B

year 1

price $65

year 2

price $84.50 difference $19.50

100% = 65

1% = 65/100 = 0.65

19.5/0.65 = 30% difference

year 3

price $109.85 difference $25.35

100% = 84.5

1% = 84.5/100 = 0.845

25.35/0.845 = 30% difference

year 4

price $142.81 difference $32.96

100% = 109.85

1% = 109.85/100 = 1.0985

32.96/1.0985 = 30% difference

so, product B has the greater percentage increase in the price (30% vs. 25%).

100 POINTS PLEAS please help
(-2u3 + 5u - 1) + (7u3 - 2u2 + 9)

A) 5 u3 - 2 u2 + 5 u + 8
B) -5 u3 - 2 u2 + 5 u + 10
C)5 u3 + 3 u + 8

Answers

Answer:

[tex]\textsf{A)} \quad 5u^3-2u^2+5u+8[/tex]

Step-by-step explanation:

Given expression:

[tex](-2u^3+5u-1)+(7u^3-2u^2+9)[/tex]

Remove parentheses:

[tex]\implies -2u^3+5u-1+7u^3-2u^2+9[/tex]

Collect like terms:

[tex]\implies -2u^3+7u^3-2u^2+5u-1+9[/tex]

Combine like terms:

[tex]\implies 5u^3-2u^2+5u+8[/tex]

(-2u³+5u-1)+(7u³-2u²+9)-2u³+5u-1+7u³-2u²+95u³-2u²+5u-1+95u³-2u²+5u+8

Option A

100 POINTS!!! REPOST!!! NEED HELP!!! NO SPAMMING!!!

(Refer to the attached image)​

Answers

Answer:  133 cm

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

Explanation:

I'm going to relabel the figure as triangle ABC.

As the instructions mention, we'll use the law of cosines to find the missing side.

side a = 147side b = 166angle C = 50 degrees

Use these facts to find side c

c^2 = a^2 + b^2 - 2*a*b*cos(C)

c^2 = 147^2 + 166^2 - 2*147*166*cos(50)

c^2 = 17794.393497

c = sqrt(17794.393497)

c = 133.395628

c = 133

Use the vectors to determine two dot products: u•v and u•w
u=9i-6j
v=-3i-2j
w=19i+15j

Answers

A

Take the product of corresponding components, then take the total:

u • v = (9i - 6j) • (-3i - 2j) = 9 (-3) + (-6) (-2) = -15

u • w = (9i - 6j) • (19i + 15j) = 9 × 19 + (-6) 15 = 81

Alternatively, use the definition and algebraic properties of the dot product.

• For any vector x,

x • x = ||x||²

where ||x|| is the magnitude of x.

• i • i = j • j = k • k = 1

• i • j = j • k = k • i = 0

• For any scalar c and any two vectors x and y,

cx • y = x • cy = c (x • y)

• For any vectors x, y, and z,

(x + y) • z = z • (x + y) = x • z + y • z

Then the products you want are

u • v = (9i - 6j) • (-3i - 2j)

… = -27 (i • i) + 18 (j • i) - 18 (i • j) + 12 (j • j)

… = -27 + 12 = -15

u • w = (9i - 6j) • (19i + 15j)

… = 171 (i • i) - 114 (j • i) + 135 (i • j) - 90 (j • j)

… = 171 - 90 = 81

This net folds into the cube shown beside it. On the cube, which letter will be on the side opposite D?

B

A

E

C

Answers

The letter that will be on the side opposite D is letter B

How to determine the letter?

The attached image represents the missing piece in the question

The opposite sides of a cube always have a face in between them, when represented as a net.

From the attached image, the adjacent sides are:

A B C D

F C E

The opposite sides as represented above are;

A and C

B and D

F and E

Hence, the letter that will be on the side opposite D is letter B

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Regina’s work to find the surface area of a square pyramid from its net is shown below.


A square pyramid. The square base has side lengths of 9.4 inches. The triangular sides have a height of 11.9 inches.

Surface area of the pyramid = 4 (one-half (9.4) (12.8)) + 9.4 squared = 329 square inches


What error did Regina make?

She should have used One-half (9.4) (11.9) to represent the area of a single triangle.

She should have multiplied all the terms inside the parentheses by 4 when she simplified.

She should have used One-half (4.7) (12.8) to represent the area of a single triangle.

She should have used a different collection of shapes as the net of the pyramid.

Answers

She put 12.8 in place of 11.9 in the formula of the triangle. Then the correct option is A.

What is Geometry?

It deals with the size of geometry, region, and density of the different forms both 2D and 3D.

Regina’s work to find the surface area of a square pyramid from its net is shown below.

A square pyramid. The square base has side lengths of 9.4 inches. The triangular sides have a height of 11.9 inches.

Surface area of the pyramid = 4 [one-half (9.4) (12.8)] + 9.4² = 329 square inches

Then the error done by Regina will be

She should have used One-half (9.4) (11.9) to represent the area of a single triangle.

Then the correct option is A.

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Answer:

A

Step-by-step explanation:

does someone mind helping me with this question? Thank you!

Answers

Answer:

70

Step-by-step explanation:

ok so we just plug 4 for x in the expression:

5 (2*4 + 6 )

5 ( 8 + 6 )

5*14 = 70

Have a good day! :)

(-2,4) on cordinate plane

Answers

The coordinate -2, 4 implies -2 is the value on the x or horizontal axis and 4 is the value on the y or vertical axis.

What is a coordinate plane?

This a plane used for graphs or points that is based on a vertical axis (y) and a horizontal axis (x).

How does -2,4 look on a coordinate plate?

The first number, -2 indicates the value in x or the horizontal axis, while the second number 4 indicates the position on y or the vertical axis. You can see this in the imaged attached (red dot).

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The coordinate -2, 4 implies -2 is the value on the x or horizontal axis and 4 is the value on the y or vertical axis.

What is a coordinate plane?

This a plane used for graphs or points that is based on a vertical axis (y) and a horizontal axis (x).

How does -2,4 look on a coordinate plate?

The first number, -2 indicates the value in x or the horizontal axis, while the second number 4 indicates the position on y or the vertical axis. You can see this in the imaged attached (red dot).

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2. Mr. Walters starts preparing breakfast at
6:45 AM. He finishes at 7:50 AM. How long
does it take for him to prepare breakfast?

Answers

Answer: 55 minutes

Explanation:

Round 6:45 to 6:50.
From 6:50 it takes 1 hour/60 minutes to become 7:50.
Then subtract the 5 minutes we added when we rounded up to 6:50.
60-5=55 minutes
65 minutes

Between 6:45 and 7:00, there are 15 minutes.

Between 7:00 and 7:50, there are 50 minutes.

15 minutes + 50 minutes = 65 minutes or an hour and 5 minutes

which of the following is the equation of a line in sloep intercept form for a line with slope = 1/3 and y intercept at 0,-4

Answers

Answer:

Step-by-step explanation:

y + 4 = 1/3(x - 0)

y + 4 = 1/3x - 0

y = 1/3x - 4

What is the area of the following circle

Answers

Answer:

Area = 153.86

Step-by-step explanation:

Formula: A = [tex]\pi r^{2}[/tex]

diameter (d) = 14

radius = d / 2

radius is 14 / 2 = 7

A = [tex]\pi (7)^{2}\\\pi 49\\49\pi \\49(3.14) = 153.86[/tex]

As one of the grade 9 top performing students competing for the “Boy Scout of the Year” award, you are assigned by your scoutmaster to design a camping site for the coming Boy Scout in-door camping. You have to maximize the area at which the 20 scouts can assemble their own tents. The tents should be equally spaced and must be situated at the same distance of 20 m from the tent of the scout master, which is located at the center of the scouts. The angle at which the tents are positioned from the scoutmaster should be approximately the same. Would you know how far apart the tents of the scouts are from each other?

Answers

Answer:

Yes you would know

Step-by-step explanation:

We can view these tents as sides on a shape that is 30 sided, with lines connecting each tents together.

After this we calculate the interior angle of each side, and use our given 20m to calculate it.

explanation/proof why the lines are parallel and insights​

Answers

Answer:

The lines are parallel is the will never touch.

Step-by-step explanation:

temp change -4.2 and 9.1

Answers

Subtraction is a mathematical operation that reflects the removal of things from a collection. The temperature change from -4.2 to 9.1 is 13.3.

What is subtraction?

Subtraction is a mathematical operation that reflects the removal of things from a collection. The negative symbol represents subtraction.

The temperature change from -4.2 to 9.1 is,

ΔT = 9.1 - (-4.2) = 9.1 + 4.2 = 13.3

Hence, the temperature change from -4.2 to 9.1 is 13.3.

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Julia surveyed twenty households on her street to determine the average number of children living in each household. the tables below represent the collected data and a randomly selected sample from the population. compare the mean of the population with the mean of the sample. population data 0 3 3 1 3 2 2 2 5 4 3 3 3 0 1 2 0 2 3 3 sample data 5 3 0 2 4 what is the difference between the mean of the sample and the mean of the population? 0.55 1.25 2.25 2.80

Answers

The difference between the mean of the sample and the mean of the population is A. 0.55

Calculations and Parameters:

Given the population data is:

0 3 3 1 3 2 2 2 5 4 3 3 3 0 1 2 0 2 3 3

The sample data is:

5 3 0 2 4

The mean of the population data is:
45/20= 2.25

The mean of the sample data is:

14/5= 2.8

Therefore, the difference between the mean of the sample and the population is:

2.8-2.25= 0.55

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Please help me figure this out

Answers

Step-by-step explanation:

standard form is given by Ax × By = C

hence the answer would be

5x + 8y = 24

comment if you still have any doubts :)

Answer:

5x + 8y = 24

Step-by-step explanation:

Given :

[tex]y=-\frac{5x}{8} +3[/tex]

……………………

[tex]y=-\frac{5x}{8} +3[/tex]

[tex]\Longleftrightarrow 8\times y=8\times (-\frac{5x}{8} +3)[/tex]

[tex]\Longleftrightarrow 8y=-5x+24[/tex]

[tex]\Longleftrightarrow 5x+8y=24[/tex]

For some △MNP: P = 38°, N = 90°, and m = 12 cm. Solve the triangle. Hint: Sketch the
triangle and label all unknown parameters.

Answers

Angle M = 52°, n = 15.2cm, p = 9.4cm

What is a triangle?

A triangle is a plane shape with three sides and three angles.

To define the triangle completely we have to know the measure of the three angles and three sides.

Analysis:

The triangle is a right-angled triangle

we need to find the remaining angle  M and two sides n and p

M + N + P = 180

M + 90 + 38 = 180

M = 180 - 128 = 52°

sin 52 = m/n

m = n sin 52

n = m/sin 52 where m = 12cm

n = 12/0.788 = 15.2cm

sin 38 = p/n

p = n sin 38

p = 15.2 x 0.615 = 9.4cm

In conclusion, solving the triangle means finding M, n and p which are 52°, 15.2cm and 9.4cm respectively.

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Please help me!
Explain how to use the graphs of systems of equations to state when the system has one solution, no solution, or infinite solutions. Be specific.

Answers

Explanation:

The solution set for a system of equation is the set of points where the graphs of the equations intersect.

__

general case

A system will have one solution if there is a single point of intersection of the graphs of the equations.

A system will have no solutions if the graphs have no points of intersection.

A system will have an infinite number of solutions if the graphs intersect at an infinite number of points.

_____

linear equations

When the equations are linear equations, their graphs are straight lines. If the lines have different slopes, they must intersect at exactly one point: there will be one solution.

If the lines have the same slope, there are two possibilities:

the lines are parallel -- no solutionsthe lines are coincident -- infinite solutions

The attached graph illustrates these cases.

the red and blue lines are the graphs of a system of equations with one solution. Those lines have different slopesthe blue and green lines are the graphs of a system of equations with no solution. Those lines are parallel.The red and (dotted) purple lines are the graphs of a system of equations with infinite solutions. Those lines are coincident.

Write a nuclear formula for 37^Ca

Answers

Answer:

37

20

C

a

37

19

K

+

0

+

1

e

This equation shows us the parent atom, which is calcium-37. The mass number is written above the atomic number for the atom. The arrow indicates the decay process with the products to the right of the arrow. The products are an atom of potassium-37 and a positron, which is similar to an electron but it carries a charge of +1 instead of a charge of -1. We can see that the transition of a proton to a neutron in positron decay decreases the atomic number of the atom from 20 to 19, but the mass number of 37 remains the same.

Step-by-step explanation:

Answer:

37

20

C

a

37

19

K

+

0

+

1

e

Step-by-step explanation:

Jamal has run 7 miles from point a to point b of a race. the entire race from point a to point c is 26 miles. how many
more miles will he run to complete the race?

Answers

The number of more miles he needs to run to complete the race is 19 miles.

How to find distance in miles?

He has run 7 miles from point a to point b of a race.

The entire race from point a to point c is 26 miles.

Therefore, the number of more miles he needs to run to complete the race is as follows:

let

x = the more miles he needs to run

Hence,

x = 26 - 7

x = 19 miles

Therefore, he needs to run 19 more miles to complete the race.

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Find the x-intercept and y-intercept of each linear function

Answers

1) x-int=2
y-int=-2
2)x-int=2
y-int=4

triangle png Find the value of x

Answers

Answer:

x+3x+2x=180(sum of triangle)

6x=180

x=180/6

x=30

again

3x=3×30=90

2x=2×30=60

Find the volume of the rectangular prism using the formula v = bh.

the area of the base, b, equals
___ cm2.
the volume of the prism is
___cm3.

Answers

Answer:

v=bh cm3 cm2 is not answer is 903cm2 23

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