How many values of x will satisfy the equation |x-1| = | x+3|

The Linear inequality that is graphed with y > –x – 2 to create the given solution set is; y < x + 1

From the attached graph of inequalities, we see that one of the lines has its' y - intercept as -2 with a slope of -1. Thus, the equation in slope intercept form is; y = -x - 2.

The shaded region will have the inequality; y > -x - 2.

The other line has its' y - intercept as 1 and a slope of 1.

Thus, the equation of line is; y = x + 1.

The shaded part is above the line and as such the inequality region is represented by the inequality y < x + 1.

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Answer:

D

Step-by-step explanation:

Answer:

7.25

Step-by-step explanation:

Simplify

36x = 261

Divide both sides by 36

x = 261/36

Simplify

x = 7.25

Hope this helps!

Answer:

7.25 or 7[tex]\frac{1\\}{4}[/tex]

Step-by-step explanation:

261 ÷ 6 ÷ 6 = 7.25

Inequalities help us to compare two unequal expressions. The value of x must be less than -19/13.

Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed. It is mostly denoted by the symbol <, >, ≤, and ≥.

The given inequalities can be simplified as,

1.)

−9x+2>18

−9x>18-2

−9x>16

x < -16/9

Thus, the value of x must be less than -16/9.

2.)

13x+15≤−4

13x ≤ -19

x ≤ -19/13

Thus, the value of x must be less than -19/13.

For the given condition −9x+2>18 OR 13x+15≤−4, the value of x must follow any one of the inequality. Hence, the value of x must be less than -19/13.

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Answer:

No, it will not pass specifications.

Step-by-step explanation:

It says that the max slope of the wheelchair ramp should be 1/12.

To calculate slope, you do rise over run or y values over x values. In this case, the rise over run is 5/50. 5/50 simplifies to 1/10.

1/10 > 1/12, meaning that it is more than the maximum slope.

There are two(2) possible solutions for the given parameters of a triangle. Using the law of cosines, the parameters of the triangle are calculated.

The law of cosines is used to relate the angles and side lengths of a triangle.

They are given as follows:

a² = b² + c² -2bc cos(A)

b² = a² + c² - 2ac cos(B)

c² = a² + b² - 2ab cos(C)

The given triangle has B = 37°, a = 32 and b = 27

So, using the law b² = a² + c² - 2ac cos(B)

On substituting,

27² = 32² + c² - 2(32)c cos(37°)

⇒ c² - 50.56 c + 1024 = 729

⇒ c² - 50.56 c + 295 = 0

Since the obtained equation is quadratic, it has 2 solutions.

Using quadratic formula the solutions are calculated.

c = [50.56 ± [tex]\sqrt{50.56^2-4(1)(295)}[/tex]]/2(1)

On simplifying,

c = 43.8 and c = 6.7

Therefore, there are 2 possible solutions for the given triangle.

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The solution to the given inequality will be x ≤ -2 and x > -5

Inequality are expressions not separated by an equal sign

Given the expression below

2≤-4-3x<11

Split

2≤-4-3x and -4-3x<11

Solve both inequalities

-4-3x≥2

-3x ≥ 6

x ≤ -2

Similarly

-4-3x<11

-3x < 15

x > -5

The solution to the given inequality will be x ≤ -2 and x > -5

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There are

[tex]\dbinom{2n}2 = \dfrac{(2n)!}{2! (2n-2)!}[/tex]

ways of pairing up any 2 members from the pool of [tex]2n[/tex] contestants. Note that

[tex](2n)! = 1\times2\times3\times4\times\cdots\times(2n-2)\times(2n-1)\times(2n) = (2n-2)! \times(2n-1) \times(2n)[/tex]

so that

[tex]\dbinom{2n}2 = \dfrac{(2n)\times(2n-1)\times(2n-2)!}{2! (2n-2)!} = \boxed{n(2n-1)}[/tex]

The number of different ways in which first-round matches can be conducted is n (2n - 1).

We have,

Number of contestant = 2n

Number of contestants in each match = 2

Now,

The number of different ways in which first-round matches can be conducted.

A combination formula is used.

= [tex]^{2n}C_2[/tex]

= 2n! / 2! (2n - 2)!

= 2n (2n - 1)(2n - 2)! / [2 x (2n - 2)!]

= 2n (2n - 1) / 2

= n (2n - 1)

Thus,

The number of different ways in which first-round matches can be conducted is n (2n - 1).

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The subtraction property of inequality can be used to proof that x = 7 from  x + 8 = 15

An equation is an expression that shows the relationship between two or more variables and numbers.

Given that x + 8 = 15

Hence:

x + 8 - 8 = 15 - 8 (subtraction property of inequality)

x = 7

The subtraction property of inequality can be used to proof that x = 7 from  x + 8 = 15

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The vertex form of the Quadratic equation is y =  [tex](x-3)^{2}[/tex] +5. The vertex is (3, 5), which is a maximum point.

A quadratic equation is an algebraic equation with the power of its variable 2.

it can be written in standard form which is called vertex form or in the general form.

Analysis:

y = [tex]x^{2}[/tex] -6x +14

y = [tex]x^{2}[/tex] -6x +9 +5

Simplifying this perfect square expression y = [tex]x^{2}[/tex] -6x +9

y  = [tex]x^{2}[/tex] -3x -3x +9

y = x(x-3) -3(x-3) + 5

y = (x-3)(x-3) +5

y = [tex](x-3)^{2}[/tex] + 5

In conclusion, the Vertex form of the equation is y = [tex](x-3)^{2}[/tex] + 5

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The value of the variable x equation 0.2x+0.2+0.5x=-0.3x+1.2 is x=1.

Given a linear equation 0.2x+0.2+0.5x=-0.3x+1.2

Equation is a combination between two or more variables which is usually expressed in equal to form. Equation of two variable looks like ax +by=c. It is solved to find the quantity of x.

Given equation is as under:

0.2x+0.2+0.5x=-0.3x+1.2

It is a linear equation and will have only 1 solution. Linear equation is a equation which is having a straight line graph.

Adding the coefficients of variable

0.7x+0.2=-0.3x+1.2

Take -0.3 to other side

0.7x+0.3x=1.2-0.2

Adding the coefficients of variables

x=1

Hence the value of x in the equation 0.2x+0.2+0.5x=-0.3x+1.2 is x=1.

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The dependent variable in the given research description is sleep quality.

Given variables :1) participants, 2) sleep quality, 3) organic cotton shirts and organic linen shirts, 4) different clothing materials.

We have to identify the dependent variable among all the variables.

Dependent variable is a variable whose quantity depends on other variables.

Independent variable is a variable whose value does not depend on other variables.

In the given research there are four variables:

1) participants,

2) sleep quality,

3) organic cotton shirts and organic linen shirts,

4) different clothing materials.

Among all these sleep quality is a dependent variable because it depends on the quality of clothes whether they or organic shirts or organic linen shirts.

It may be possible that some people get quality sleep in organic cotton shirts and some may get in organic linen shirts.

Hence the dependent variable is sleep quality.

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Answer:

Step-by-step explanation:

The equation represents the intersections. The correct option is A:

If we have two functions:

y = f(x) and y = g(x), the equation:

f(x) = g(x) gives the value of x such that the two functions have the same output. So, that equation gives the intersection points between the two graphs.

By looking at the graph, we can see that we have two intersections, one at:

(2, 0) and other at (0, 4).

This means that:

So the correct option is the first one.

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The recursive formula of the arithmetic sequence 13, 6, -1, -8,... is a(n) = 20 - 7n.

It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.

We have an arithmetic sequence:

13, 6, -1, -8,...

The first term:

a = 13

The common difference:

d = 6 - 13 = -7

The recursive formula of the arithmetic sequence:

a(n) = a + (n - 1)d

a(n) = 13 + (n - 1)(-7)

a(n) = 20 - 7n

Thus, the recursive formula of the arithmetic sequence 13, 6, -1, -8,... is a(n) = 20 - 7n.

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The statement which best describes the similarity of the two triangles is; Choice D; There is not enough information to determine whether the triangles are similar.

The two triangles given in the task content are expected to be assessed to determine if they are similar.

From the concept of congruence in triangles, two triangles are congruent only if all 3 angle measures in one are similar to that in the other, or if the ratio of all corresponding pairs of sides are equal.

Hence, since neither of the conditions is satisfied by the information given, it follows that Choice D is correct.

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A quadratic equation in the form of ax²+bx+c. The zeroes of the polynomial are -2.4 and -7.5.

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 Root of the quadratic equation are given as,

[tex]x = \dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

The zeroes of the polynomial are:

f(x)=x² + 9.9x + 18

0 = x² + 9.9x + 18

[tex]x= \dfrac{-9.9\pm \sqrt{(9.9)^2-4(1)(18)}}{2(1)}\\\\[/tex]

x = -2.4, -7.5

Hence, the zeroes of the polynomial are -2.4 and -7.5.

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When drawing the stretch-out arc for the pattern of a cone fitting, the radius should be equal to the true length of the side.

The 3 tactics typically used in developing patterns are parallel-line, radial-line, and triangular improvement.

To make such objects, a drafter has to first draw them as a pattern or pattern improvement. A pattern improvement additionally known as a stretch out or simply an improvement is a format of an object made on a single flat aircraft.

In radial traces, we develop styles for shapes that have a taper, all element lines (bends) should radiate returned to a not unusual factor, a radius point. We want matters for this procedure to paintings: A radius factor is in the center (right cone). A radius point is inside an inexpensive distance.

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Using it's concept, the mean amount of precipitation (in inches) on March 9 for the areas listed the table was of:

C. 1.56.

The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations.

The observations given in the problem are:

0.45, 0.63, 1.34, 3.53, 2.57, 0.84.

Hence the mean is:

M = (0.45 + 0.63 + 1.34 + 3.53 + 2.57 + 0.84)/6 = 1.56.

Which means that option C is correct.

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Answer: B

Step-by-step explanation:

Answer:

Option C

Step-by-step explanation:

We can see that these two triangles are similar triangles. And based on the sides we also know triangle ZXY and triangle FDE have a ratio of 3:2. We can find side x by the equation:

3:2=9:x

3x=18

x=6 or option C

Answer:

C.6

Step-by-step explanation:

12x=8

x=8/12=2/3

2/3*9=18/3=6

The graph that represents the exponential function [tex]y = 8\left(\frac{1}{3}\right)^x[/tex] is given at the end of the answer.

An exponential function is modeled by:

[tex]y = ab^x[/tex]

In which:

In this problem, the function is:

[tex]y = 8\left(\frac{1}{3}\right)^x[/tex]

It has an initial value of 8 and rate of change of 1/3, as shown in the graph given at the end of the answer.

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Answer:

y-intercept = -3

another point on the line = (6,-1)

Step-by-step explanation:

1. Underline important parts of the question (slope of 1/3, point (3, -2))

2. mark the point that is given (3, -2)

3. slope form is rise over run which basically means that the number one is how much the line rises, and the number three is how much the line goes to the right (since the slope is positive then it runs to the right, if it was negative it would go to the left.) Basically 1/3 = rise over run

4. put your pencil on the point (3, -2) and go up one point and over three points. continue doing so from each new point (two or three points is good enough)

5. take a ruler and draw a line that connects all three and keep it going until it crosses the y- axis (which is the vertical line)

6. the point that crosses through the y -axis is the y-intercept.

7. now you can go and look at your points that you have made and choose one of them to answer the question with

(I hope this cleared it up a bit I'm not very good at explaining things this is the best I can do)

Step-by-step explanation:

the y intercept is found by equating X to 0

hence, y = 3

answer is: (0,3)

Answer:

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

Add 2 to both sides of equation:

Then follow the steps:

Take square root of both sides to get:

We are taking the positive value as we are told x > 0, hence the answer is 7.

[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]

[tex] \qquad❖ \: \sf \: {x}^{2} + \cfrac{1}{ {x}^{2} } = 47[/tex]

[tex] \qquad❖ \: \sf \: {x}^{2} + \cfrac{1}{ {x}^{2} } + 2 - 2 = 47[/tex]

( adding and subtracting 2, doesn't change the value )

[tex] \qquad❖ \: \sf \: {x}^{2} + \cfrac{1}{ {x}^{2} } + 2 = 47 + 2[/tex]

[tex] \qquad❖ \: \sf \: {x}^{2} + \cfrac{1}{ {x}^{2} } + \bigg(2 \sdot x \sdot \cfrac{1}{x} \bigg) = 49[/tex]

( x cancel out, so no change in value )

[tex] \qquad❖ \: \sf \: \bigg(x + \cfrac{1}{x} \bigg) {}^{2} = 49[/tex]

( use identity a² + 2ab + b² = (a + b)² )

[tex] \qquad❖ \: \sf \: \bigg(x + \cfrac{1}{x} \bigg) {}^{} = \sqrt{49} [/tex]

[tex] \qquad❖ \: \sf \: x + \cfrac{1}{x} {}^{} = \pm7[/tex]

since we have to take positive value, i.e greater than 0

[tex] \qquad❖ \: \sf \: x + \cfrac{1}{x} {}^{} = 7[/tex]

[tex] \qquad \large \sf {Conclusion} : [/tex]

Therefore, the required value is 7

Step-by-step explanation:

simple answer mate..

under root 2 is right because angle are same.. option d

Answer:

√2

Step-by-step explanation:

Angle ( θ ) = 45

Hypotenuse side = 2

Opposite side = x

Formula : -

sin θ = Opposite side / Hypotenuse side

Note :

The value of sin 45 = 1/√2

sin 45 = x/2

1/√2 = x/2

Cross multiply,

x*√2 = 2*1

x√2 = 2

2 can be simplified as √2 * √2

x√2 = √2*√2

Divide √2 on both sides,

x = √2

Answer:

17.25

Step-by-step explanation:

The point estimation based on the given interval limits is 0.706.

The use of sample data to compute a single value that will serve as a "best guess" or "best estimate" of an unknown population characteristic is referred to as point estimation.

The point estimation based on the given interval limits is,

Point Estimate = (0.688+0.724)/2 = 0.706

Hence, The point estimation based on the given interval limits is 0.706.

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The measure of angle x that is formed around a point is: 145°.

The measure of the angle around a point equals 360 degrees.

The the angles formed by the fork in the road equals 360 degrees.

Therefore, we would have the following equation:

x + 165 + 50 = 360

x + 215 = 360

Subtract both sides by 215

x = 360 - 215

x = 145°

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If triangle RST and RZX are similar then the perimeter of triangle RZX is 150 units.

Given triangle RZX and RST are similar and RZ=28, RY=40,ZY=16 and SW=24.

In the similar triangles the ratio of sides are in proportion to the sides of other triangle.

The ratio of ZY to SW is 16:24 meaning it is 2:3. So all the sides of RST are 1.5 times as long as RZX.

RZ=28 so RS=28*1.5=42

RX=40 so RT=40*1.5=60

ZX=ZY+XY and since they are the of the same length , ZX=32 (ZY given)

Then ST=48

Perimeter of a triangle is the sum of sides of the triangle.

Perimeter of RST=RS+ST+RT

=42+60+48

=150

Hence the perimeter of triangle RST is 150 units.

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Question is incorrect as it should be as under:

Given the following information, calculate the perimeter of triangle RST. Assume triangle RZX is similar to RST. RZ=28, RY=40, ZY=16 and SW=24.

Figure should also be given.