Mathematics High School

Solve the inequality for x and identify the graph of its solution.
|x+ 2|>2

Answers

Answer 1

Answer:

A. x < -4 or x > 0

Step-by-step explanation:

[tex]|x+2| > 2\iff x+2 > 2\ \vee\ x+2 < -2[/tex]

subtract 2 from both sides

[tex]x > 0\ \vee\ x < -4[/tex]

Related Questions

rne subtracted 6x3 2x
find the difference.
from -3.x3 +
4x - 7. Use the drop-down menus
to identify the steps Lorne used
(-3x' + 5x7,+ 4x - 7) + (-6x3 + 2x -3)
(-3x°) + 5x2 + 4x + (-7) + (-6x3) + 2x + (-3)
[(-3x*) + (-6x°)] + [4x + 2x] + [(-7) + (-3)] + [5x2)
-9x° + 6x + (-10) + 5x2
-9x' + 5x2 + 6x - 10

Answers

F(x) = 3-2x/x that is the answer

Estimate the roots of f(x)

Answers

Answer:

Step-by-step explanation:

Which of the following is the graph of the piecewise function h of x is defined as negative x squared plus 2 for x is less than or equal to negative 2, or one half times x for negative 2 is less than x is less than 2, or x squared minus 2 for x greater than or equal to 2.?

Answers

The attached graph represents the piecewise function h(x)

Complete question

Which of the following is the graph of the piecewise function

[tex]h(x) = \left[\begin{array}{cc}-x^2 + 2 &x \le -2\\ \frac 12x&-2 < x < 2\\x^2 - 2&x \ge 2\end{array}\right[/tex]

How to determine the graph of the function?

The function is given as:

[tex]h(x) = \left[\begin{array}{cc}-x^2 + 2 &x \le -2\\ \frac 12x&-2 < x < 2\\x^2 - 2&x \ge 2\end{array}\right[/tex]

The above means that the piecewise function has 3 domains

2 of which are quadratic functionsThe last one is a linear function

Next, we plot the graph using a graphing tool

See attachment for the graph of the piecewise function h(x)

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If a is a negative number, then a
always, always
and b is a negative number, then product ab is ?

Answers

Answer:

if a and b are both negative numbers, the product is a positive number

Memories this in your life ,

odd x odd= even

It’s also the same as saying ,

Negative x Negative = positive

Use the drawing tool(s) to form the correct answer on the provided number line.
Consider the given functions.
Function 1
f(x) = -5x + 11 + 10
Function 2
g(x)
-2
Represent the interval where both functions are decreasing on the number line provided.
30
20
10-
-10-
-20-
-30-
2
6
x

Answers

This means that the function is dropping throughout this range[tex](-1,\infty).[/tex]Using the point where the intervals with decreasing functions overlap, the number line will represent

[tex](-1,\infty)\cap (-2,2) ---- > (-1,2)[/tex]

What is the function's decreasing in the interval?

Generally, the equation for the function is mathematically given as

f(x) = -5x + 11 + 10

Therefore

When x >= -1, the function decreases because f(x) = -5(x+1)+10.

This means that the function is dropping throughout this range[tex](-1,\infty).[/tex]

A look at the graph reveals a decreasing trend in the function over the timeframe (-2,2).

In conclusion, The number line will represent

Using the point where the intervals with decreasing functions overlap

[tex](-1,\infty)\cap (-2,2) ---- > (-1,2)[/tex]

Answers

The statement "when 6 + 4i is multiplied by 3, the result is 18 + 12i. Graphically, this shows that the product is a scalar of the complex number." is correct.

What is a complex number?

It is defined as the number which can be written as x+iy where x is the real number or real part of the complex number and y is the imaginary part of the complex number and i is the iota which is nothing but a square root of -1.

We have a complex number:

= 6 + 4i

Multiplied by 3:

= 18 + 12i

If we plot on the coordinate plane there will be no rotation the scalar has changed by multiplying with a real number.

Thus, the statement "when 6 + 4i is multiplied by 3, the result is 18 + 12i. Graphically, this shows that the product is a scalar of the complex number." is correct.

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In triangle nql, point s is the centroid, ns = (x 10) feet, and sr = (x 3) feet. triangle n q l has centroid s. lines are drawn from each point to the midpoint of the opposite side to form line segments n r, q m, and l p. the length of line segment n s is x 10 and the length of line segment s r is x 3. what is rs? 4 feet 7 feet 10 feet 14 feet

Answers

The complete question is

"In triangle NQL, point S is the centroid, NS = (x + 10) feet, and SR = (x + 3) feet. Triangle N Q L has centroid S. Lines are drawn from each point to the midpoint of the opposite side to form line segments N R, Q M, and L P. The length of line segment N S is x + 10 and the length of line segment S R is x + 3.

What is RS?

4 feet, 7 feet, 10 feet, 14 feet"

Answer:

The Length of RS would be 7 ft. so the correct option is B.

What is a line segment?

A line segment is a straight line with finite length, and thus, have to endpoints(points on either ends).

Given:

NS = (x + 10) ft

SR = (x + 3) ft

Based on the centroid theorem, the centroid, S will divide the median, line segment NR, into NS and SR,

NS : SR = 2 : 1.

Therefore:

NS = 2(SR)

x + 10 = 2(x + 3)

Solve for x

x + 10 = 2x + 6

x - 2x = -10 + 6

-x = -4

x = 4

SR = (x + 3) ft (SR is same as RS)

substitute the value of x

SR = (4 + 3) ft

SR = RS = 7 ft

Hence, The Length of RS would be 7 ft. so the correct option is B.

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Answer: B, 7 feet

Step-by-step explanation:

49. Luke is putting a floor mat on his bathroom floor. The mat is
4 feet wide and 5 feet long. The floor is square with sides that
are 12 feet. The center of the mat is 73 feet from the wall.
X
733 ft
- Floor mat
bes stser pelazar to vilidad
Determine the distance from the edge of the mat, x, to the
opposite wall.

Answers

Answer:

Step-by-step explanation

(area of mat subtracted from area of room)-center of mat to wall

hii can someone help me find the area of this square

Answers

Answer:6.76 cm2

Step-by-step explanation:

You have multiply 2.6 by 2.6 and then you have to square the cm so it will be 6.76 cm2

Answer: A. 6.76 [tex]cm^2[/tex]

Step-by-step explanation:

Area is just length times width.

The length is 2.6 cm and the width is 2.6 cm, so just multiply the two.

2.6 x 2.6 = 6.76 [tex]cm^2[/tex]

Make sure you don't forget the squared in questions that ask for area.

8.6 + 5.6x - 1.5 = 40.7

Answers

Answer:

[tex]x=6[/tex]

Step-by-step explanation:

[tex]8.6 + 5.6x - 1.5 = 40.7\\5.6x = 33.6\\x=6[/tex]

Answer:

x = 6

Step-by-step explanation:

solve for x

8.6 + 5.6x - 1.5 = 40.7

5.6x = 40.7 - 8.6 + 1.5

5.6x = 33.6

x = 33.6 : 5.6

x = 6

-----------------------------

check

8.6 + 5.6 * 6 - 1.5 = 40.7

40.7 = 40.7

the answer is good

Using two six-sided number cubes, each labeled with the numbers 1 through 6, event A is defined by rolling a sum greater than 8Which of the following shows the sample space of event A?

Answers

Answer:{(3, 6), (4, 5), (4, 6), (5, 4), (5, 5), (5, 6), (6, 3), (6, 4), (6, 5), (6, 6)}

Step-by-step explanation:

Event A is defined by rolling a sum greater than 8 will be {(3, 6), (4, 5), (4, 6), (5, 4), (5, 5), (5, 6), (6, 3), (6, 4), (6, 5), (6, 6)}.

What is a random sample?

Random sampling is the method of selecting the subset from the set to make a statical inference.

Utilizing two six-sided number solid shapes, each named with the numbers 1 through 6.

The number of the total events will be given as,

Total events = 6²

Total events = 6 x 6

Total events = 36

The total sample is given below.

(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6)

(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6)

(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6)

(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6)

(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6)

(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)

Event A is defined by rolling a sum greater than 8 will be {(3, 6), (4, 5), (4, 6), (5, 4), (5, 5), (5, 6), (6, 3), (6, 4), (6, 5), (6, 6)}.

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If point C is between points A and B, then ___ + CB = AB.
A. BC
B. CA
C. ABC
D. AB

Answers

Answer:

[tex]\fbox {B. CA}[/tex]

Step-by-step explanation:

Picture the line segment :

⇒ A ---------------- C ------------------ B

Then :

⇒ CA + CB = AB

A hiker in Africa discovers a skull that contains 72% of its original amount of C- 14. A hiker in Africa discovers a skull that contains 72 % of its original amount of C 14 .

Answers

If the 72% of its original amount of C-14. Then the number of years will be 3285.

The complete question is attached below.

What is an exponent?

Let b is the base and x is the power of the exponent function and a is the leading coefficient. The exponent is given as

y = a(b)ˣ

A hiker in Africa discovers a skull that contains 72% of its original amount of C- 14.

Then the function is given below.

[tex]\rm N= N_0 \ e^{-kt}[/tex]

Where, N₀ is the initial amount of C - 14, t is the number of the years, k is constant that is 0.0001, and N be the amount of the C - 14 at t years.

[tex]\rm N= N_0 \ e^{-0.0001 \times t}[/tex]

We have N = 0.72N₀, the time will be

[tex]\rm 0.72N_0 = N_0 \ e^{-0.0001 \times t}\\\\\rm 0.72 \ \ \ \ = \ e^{-0.0001 \times t}[/tex]

Take log on both side, then we have

ln 0.72 = -0.001 × t × ln e

-0.33 = -0.001 × t

t = 3285 years

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I’m not sure how to do this if someone could help it would be much appreciated

Answers

Answer:

(b) y = 18/x; y = 9/4

Step-by-step explanation:

Different kinds of variation are generally described by the equation ...

y = k·( ) . . . . . . . where k is the constant of proportionality

kinds of variation

What goes in parentheses depends on the kind of variation. Here is a partial list of kinds that may be seen in algebra problems.

direct: xinverse: 1/xas the square: x²as the square root: √xas the inverse of the square: 1/x²jointly as: xz

The value of k can be found by solving the variation equation with given values of the variables.

inverse variation

The variables x and y are said to vary inversely, so the appropriate equation is ...

y = k(1/x) = k/x

Using the given values, we can find k:

9 = k/2

9·2 = k = 18

So, the equation is ...

y = k/18

for x=8

Using the above equation, the value of y for x=8 is ...

y = 18/8 = 9/4

Note: you can also get there by realizing that x=8 is 4 times x=2, so the new value of y will be the old value of y multiplied by the inverse of this factor. 1/4 times the old value of y: (1/4)9 = 9/4.

Two numbers are in the ratio of 2 to 3. Their sum is 30. What are the numbers? 3. Two numbers are in the ratio of 2 to 3. Their sum is 30. What are the numbers ?

Answers

Answer:

12 and 18

Step-by-step explanation:

Lets say the two numbers are A and B, with A the smaller.

We are told that A/B = 2/3 [in the ratio of 2 to 3]

We also find that A + B = 30 [Their sum is 30]

Rearrange the first equation to isolate A:

A/B = 2/3

A = 2B/3 [multiply both sides by B]

Now use this value of A in the second equation:

A + B = 30

2B/3 + B = 30

(2/3)B + (3/3)B = 30

(5/3)B = 30

B = (30)(3/5)

B = 6*3

B = 18

Since A + B = 30:

A + B = 30

A + 18 = 30

A = 12

A is 12 and B is 18

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

Check:

Does A/B = 2/3??

(12/18) = (6/9)

(6/9) = (2/3) YES

Does A + B = 30 ???

12 + 18 = 30 YES

find the volume of the composite figure

Answers

Volume is a three-dimensional scalar quantity. The volume of the composite figure is 14 ft³.

What is volume?

A volume is a scalar number that expresses the amount of three-dimensional space enclosed by a closed surface.

The volume of the composite figure is,

Volume = (1/3 ×1.5 × 2 × 2) + (2 × 1.5 × 4)

= 2 ft³ + 12 ft³

= 14 ft³

Hence, the volume of the composite figure is 14 ft³.

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Lines l1 and l2 are parallel and l3 is a transversal.

Which statement is true?

A
m∠2+m∠4=180°

B
m∠2+m∠3=180°

C
m∠1=m∠4

D
m∠1=90°

Answers

Answer:

C. m∠1 = m∠4

Step-by-step explanation:

A. m∠2 + m∠4 = 180°

∠2 and ∠4 are vertically opp. angles which means m∠2 = m∠4.

Hence, it's a false statement.

B. m∠2 + m∠3 = 180°

∠2 and ∠3 are corresponding angles which means m∠2 = m∠3.

It's a false statement.

C. m∠1 = m∠4

∠1 and ∠4 are another pair of corresponding angles which clearly states that m∠1 = m∠4.

Therefore, it's a true statement.

D. m∠1 = 90°

As clearly visible in the diagram;

It's a false statement.

Gracie earns 17.25/h for a 37.5h week, plus extra for overtime. During store inventory she worked 48.5h. Her gross earnings were $1,471.88. What is Gracie’s overtime rate of pay? show work please

Answers

Gracie’s overtime rate of pay would be $635.06.

What is the unitary method?

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

Gracie earns 17.25/h for a 37.5h week, plus extra for overtime.

For one hour she earns $17.25

For 37.5h she earns = 37.5h x 17.25

= $646.87

The total money she earns = $646.87 + overtime pay

During store inventory, she worked 48.5h. Her gross earnings were $1,471.88.

= 48.5h x 17.25

= $836.625

So, $836.625 + overtime pay = $1,471.88

overtime pay = $1,471.88 - $836.625 = $635.06

Hence, Gracie’s overtime rate of pay would be $635.06.

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Solve

A.
A bag has 18 marbles of three different colours.
There are twice as many red marbles as blue
ones.
There are two fewer green marbles than blue ones.
Form an equation to model this situation, and solve
to determine the number of each color marble in
the bag.

B.
The perimeter of a large triangle is 237 cm.
The lengths of the three sides are consecutive
integers, Form an equation to model this situation,
and solve to find the lengths of the three sides.

Answers

Answer:

5 blue marbles

10 Red marbles

3 Green marbles

Step-by-step explanation:

5 times 2 = 10

then 5-2 =3

Add 5+10+3

=18 Marbles in total

does this table represent a function? why or why not x:2,2,3,4,5 y:1,4,4,2,5

Answers

Answer:

No, the table does not represent a function.

Step-by-step explanation:

By definition, a function will not have 2 or more results for the same input.

The table shows two values of y for the same x: (2,1) and (2,4). The same input, 2, results in two different values, 1 and 4.

See attached image.

Please Help!! [ tough geometry question :( ]

Answers

Answer: [tex]133^{\circ}[/tex]

Step-by-step explanation:

Opposite angles of a cyclic quadrilateral are supplementary, so:

[tex]4x+5+x+15=180\\\\5x+20=180\\\\5x=160\\\\x=32[/tex]

This means that [tex]m\angle A=4(32)+5=\boxed{133^{\circ}}[/tex]

Answer: 133

explanation: stole it ngl

A ball is thrown from an initial height of 2 feet with an initial upward velocity of 31 ft/s. The ball's height h (in feet) after t seconds is given by the following.

Answers

A quadratic equation is in the form of ax²+bx+c. The time at which the height of the ball is 16 feets is 0.717 seconds and 1.221 seconds.

What is a quadratic equation?

A quadratic equation is an equation whose leading coefficient is of second degree also the equation has only one unknown while it has 3 unknown numbers. It is written in the form of ax²+bx+c.

The complete question is:

A ball is thrown from an initial height of 2 feet with an initial upward velocity of 31 ft/s. The ball's height h (in feet) after 7 seconds is given by the following, h=2+31t-16t². Find all values of t for which the ball's height is 16 feet. Round your answer(s) to the nearest hundredth.

The time at which the height of the ball is 16 feet can be found by,

h = 2 + 31t - 16t²

16 = 2 + 31t - 16t²

16 - 2 - 31t + 16t² = 0

16t² - 31t + 14 = 0

[tex]t = \dfrac{-(-31)\pm \sqrt{(-31)^2-4(16)(14)}}{2(16)}\\\\[/tex]

t = 0.717 , 1.221

Hence, the time at which the height of the ball is 16 feets is 0.717 seconds and 1.221 seconds.

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Which equation represents a side that is perpendicular to side d? O y = 2x+5 Oy=-2x+5 NG 0 Y=2x-5/2 OY--12-12 = Which equation represents a side that is perpendicular to side d ? O y = 2x + 5 Oy = -2x + 5 NG 0 Y = 2x - 5 / 2 OY -- 12-12 =

Answers

The equation represents a side that is perpendicular to side d is y = -2x+5. Option B is correct.

What is the slope?

A numerical assessment of a line's angle relative to the ground is known as the slope.

The inclination of any line, ray, or line segment is the fraction of the perpendicular to the horizontal distance between any two positions on it.

The given linear equation in the problem is;

y = 2x+5

Compare the equation with the standard equation;

[tex]\rm y = mx+ c[/tex]

where,

m is the slope and c is the intercept. After comparing, we will get; Hence, the slope and y-intercept will be;

m = 2

The product of the slope of the two-line perpendicular to each will be -1.

m₁×m₂ = -1

The equation represents a side that is perpendicular to side d is;

y = -2x+c.

m₁=2

m₂=-2

m₁×m₂ = -1

The equation represents a side that is perpendicular to side d is y = -2x+5.

Hence, option B is correct.

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A rectangular swimming pool measures 40 meters in length and 30 meters in width. in the scale drawing of the pool, 1 centimeter represents 2 meters

Answers

The area of the swimming pool on the scale drawing will be 300 sq. centimeters.

What is the scale ratio?

A model's scale ratio is the proportionate ratio of a linear dimension of the model to the equivalent characteristic of the original.

For the given scale drawing 1 centimeter represents 2 meters, therefore, the length of 40 meters in one scale drawing will be equal to,

40 meters = 40/2 centimeters = 20 centimeters

The width of 30 meters one scale drawing will be equal to,

30 meters = 30/2 centimeters = 15 centimeters

Now, the area of the swimming pool on the scale drawing will be,

Area= 20 centimeters × 15 centimeters = 300 sq. centimeters

Hence, the area of the swimming pool on the scale drawing will be 300 sq. centimeters.

The complete question is:

A rectangular swimming pool measures 40 meters in length and 30 meters in width. in the scale drawing of the pool, 1 centimeter represents 2 meters. then what is the area of the swimming pool on the scale drawing?

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Brainliest!
Which system is represented in the graph?
y>x²-2x-3
y > x + 3
Oy y Oy2x²-2x-3
y ≤ x + 3
Oy>x²-2x-3
y

Answers

Answer:

y ≥ x² -2x -3y ≤ x +3

Step-by-step explanation:

When matching graph to inequality, the first things to look for are the nature of the boundary line (solid or dashed), and the direction of shading relative to the boundary line (above or below, left or right).

Boundary line

The boundary line of the solution set of an inequality will be solid if the line is included in the solution. That is, the inequality will include the "or equal to" case. The corresponding inequality symbols are ≤ or ≥.

The boundary line of the solution set will be dashed if the line is not included in the solution. The corresponding inequality symbols are < or >.

Shading

The shading will be above the boundary line if the solution set includes larger y-values than those on the boundary. This will be the case when the inequality is of the form y > ( ) or y ≥ ( ).

For inequalities of the form y < ( ) or y ≤ ( ), the shading will be below the boundary line.

Similarly, the shading for an inequality of the form x > ( ) will be right of the boundary line, where x-values are greater. For inequalities of the form x < ( ), the shading will be to the left of the boundary line.

Application

In the given graph, both boundary lines are solid, so both inequalities will include the "or equal to" case. This eliminates choices A, B, D.

The shading is above the quadratic boundary line, and below the linear boundary line, so the inequalities can be expected to be of the forms ...

y ≥ x² +...y ≤ x +...

These forms match choice C:

y ≥ x² -2x -3y ≤ x +3

The coordinates of triangle LMN are shown. L(-1,4) M(-1, -3) V N (4, -1) What is the length of LM? Enter the answer in the box. unit(s) The coordinates of triangle LMN are shown . L ( -1,4 ) M ( -1 , -3 ) V N ( 4 , -1 ) What is the length of LM ? Enter the answer in the box . unit ( s )

Answers

Answer:

Explanation:

Use the distance formula to find the answer

Answer:

7 units

Step-by-step explanation:

since the x- coordinates of L and M are equal , both - 1 then the length of LM is the absolute value of the difference of the y- coordinates.

LM = | 4 - (- 3) | = | 4 + 3 | = | 7 | = 7

LM = | - 3 - 4 | = | - 7 | = 7

13 t-shirts cost total of $156. What is the unit cost per t-shirt?

Answers

Step-by-step explanation:

please mark me as brainlest

If f(x)=x^2 then evaluate (2+3i)

Answers

Answer:

-5 + 12 i

Step-by-step explanation:

(2 + 3i)^2 = 4 + 6i + 6i + 9i^2

= 4 + 12 i + 9(-1)

= - 5 + 12 i

What should be done to both sides to solve the equation?

Solve x-2=10

Answers

Answer:

add 2 to each side of the equation

Step-by-step explanation:

x-2=10

To solve for x, we need to add 2 to each side of the equation

x-2+2 = 10+2

x = 12

Bonnie and Connie ran a total of 135 miles last week. Bonnie runs at a constant speed of 7 miles per hour, and Connie runs at a constant speed of 5 miles per hour. If Bonnie and Connie ran for a total of 24 hours last week, how many minutes did Bonnie run

Answers

Answer: 450 Minutes

Step-by step explanation:

135-x)/5 = hours connie runs

x/7 = hours Bonnie runs

(135-x)/5 + x/7 = 24

135-x + 5x/7 = 120

945-7x+5x = 840

-2x = -105

x = 52.5 miles = distance of Bonnie

52.5 miles / 7 m/hr = 7.5 hours = 450 minutes

Other Questions

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Solve the inequality for x and identify the graph of its solution. |x+ 2|>2

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Solve the inequality for x and identify the graph of its solution.
|x+ 2|>2