Find the value of x in each case. Show your work with proper statements and notation. P belongs to line MQ

Answer:

An equilateral triangle with a length of 2

Step-by-step explanation:

A 2-by-2 square implies that the square has a length and width of 2. Since equilateral triangles have the same length for all sides, it tells you that if one side is a certain length, all the other sides must have the same length. The largest length we can fit into this square would be 2 because any larger, the sides of the triangles would not fit into the square. Under the assumption that the length needs to be a whole number, the answer would be 2.

The solution of x in the given expression [tex]\mathbf{\sqrt{(3x-8)}+1 = \sqrt{(x+5)}}[/tex] is 4. However, if it is [tex]\mathbf{\sqrt{(3x-8)+1} = \sqrt{(x+5)}}[/tex], it is 6.

The solution to the given algebra expression involving surds can be seen in the steps below.

Given that:

[tex]\mathbf{\sqrt{(3x-8)}+1 = \sqrt{(x+5)}}[/tex]

Remove the square roots, we have:

12x - 32 = 4x² - 48x + 144

Solving the quadratic equation at the RHS and equating it to LHS, we have:

x = 11, x = 4

Verifying the solutions by replacing the value of x with the given equation:

Therefore, we can conclude that the value of x = 4

NOTE:

Given that:

[tex]\mathbf{\sqrt{(3x-8+1)} = \sqrt{(x+5)}}[/tex]

Square both sides

3x - 7 = x +5

Solve for x

3x - x = 5 + 7

2x = 12

x = 6

Learn more about solving to algebraic expressions here:

https://brainly.com/question/4344214

#SPJ1

The expected value of the outcome of the bid is $0.18

So let's start by counting how many bids are placed up to a total of 160.

100*160 = 16000.

What will be your arbitrary bid? As each bid has an equal chance of success, the average of all bids is used. (One cent plus 160 dollars) / 2 = 80 dollars (rounded)

Your odds of winning are 1/16000 (1 bid out of 16000).

If you win, your profit is 1920 ($2000 minus $80.00).

1920/16000 is $0.12

Your cost to enter the auction is $1, and your average winning offer is $0.12.

The result is $0.18 (0.12-1=-0.88).

Thus the expected value of the outcome of the bid is $0.18

Learn more about expected value here :

https://brainly.com/question/23509883

#SPJ1

Considering the given equations for revenue and cost, the company will break-even when 356 widgets are sold.

The break-even point is the value of x for which:

R(x) = C(x).

In this problem, the functions are:

Hence:

R(x) = C(x)

16x = 12x + 1424

4x = 1424

x = 1424/4

x = 356

The company will break-even when 356 widgets are sold.

More can be learned about the break-even point of a company at https://brainly.com/question/9212451

#SPJ1

Using the z-distribution, the p-value would be given as follows:

b) 0.0086.

At the null hypothesis we test if the means are equal, hence:

[tex]H_0: \mu_D - \mu_C = 0[/tex]

At the alternative hypothesis, it is tested if they are different, hence:

[tex]H_1: \mu_D - \mu_C \neq 0[/tex]

For each sample, they are given as follows:

Hence, for the distribution of differences, they are given by:

The test statistic is given by:

[tex]z = \frac{\overline{x} - \mu}{s}[/tex]

In which [tex]\mu = 0[/tex] is the value tested at the null hypothesis.

Hence:

[tex]z = \frac{\overline{x} - \mu}{s}[/tex]

[tex]z = \frac{-2 - 0}{0.76}[/tex]

z = -2.63.

Using a z-distribution calculator, for a two-tailed test, with z = -2.63, the p-value is of 0.0086.

Hence option B is correct.

More can be learned about the z-distribution at brainly.com/question/13873630

#SPJ1

Answer: the speed of the stream is 9mph

The logarithmic function expresses the output variable, y, as a function of the logarithm of the input variable, x, as a function of a base b. The true statements are therefore;

The given logarithmic equation is presented as follows;

[tex]y = log_{b}(x) [/tex]

Therefore, we have;

[tex]x = {b}^{y} [/tex]

Where b = 1, we have that x will always be 1, therefore;

[tex]b = \sqrt[y]{x} [/tex]

Therefore;

Which gives;

The statements that are true is therefore;

Learn more about logarithms and logarithmic functions here:

https://brainly.com/question/13473114

#SPJ1

Answer:

The solution for the above fraction is

[tex] \frac{146}{167} [/tex]

Step-by-step explanation:

Greetings!

look at the attachment above for the explanation.

The two statements that are true for g(x ) are:

g(x) = [tex]4^{x}[/tex] - 1

g(x) is translated both vertically and horizontally.

A function is a relation showing the relationship between two or more variables.

A function produces a unique output when a unique input is given to it. The input is called the domain and the output is called the Range.

Analysis:

If we use the values of x as 0,1,2,3

for x = 0

g(0) = [tex]4^{0}[/tex] -1  = 1 -1 = 0

for x = 1

g(1) = [tex]4^{1}[/tex] -1  = 4 - 1 = 3

for x = 2

g(2) = [tex]4^{2}[/tex] - 1 = 16 - 1 = 15

for x = 3

g(3) = [tex]4^{3}[/tex] - 1 = 64 - 1 = 63

Therefore g(x) = [tex]4^{x}[/tex] - 1

Also since the values of g(x) changes along the y - axis and x-axis also changes, therefore, g(x) is translated along both axes.

Learn more about functions: brainly.com/question/25638609

#SPJ1

The two sets of parametric equations for the rectangular equation are;

It follows from the task content that the parametric equations can be determined as follows;

By substituting the x= t+6 into the rectangular equation; we have;

y = (t+6-6)²-7(t+6)

y = t²-7t-42.

By substituting the x= 7t into the rectangular equation; we have;

y = (7t-6)² -7(7t)

y = 49t² - 84t +36 - 49t

y = 49t² - 133t +36.

Read more on parametric equations from rectangular equations;

https://brainly.com/question/23312942

#SPJ1

The cubic function can be graphed using the function behavior and the points.

x   0    1     2        3      4

y   0  −4   −12   −18  −16

Put  x = 0.

Replace the variable x with 0 in the expression.

[tex]f(0)=(0)^3-5(0)^2[/tex]

Raising 0 to any positive power yields 0.

f(0) = 0 − 5⋅0

f(0) = 0

y = 0

Put x = 1.

Replace the variable x with 1 in the expression.

[tex]f(1)=(1)^3-5(1)^2[/tex]

f(1) = 1− 5⋅1

f(1) = −4

y = −4

Put x = 2.

Replace the variable x with 2 in the expression.

[tex]f(2)=(2)^3-5(2)^2[/tex]

[tex]f(2)=8-5(2)^2[/tex]

f(2) = 8 − 5⋅4

f(2) = −12

y = −12

Put x = 3.

Replace the variable x with 3 in the expression.

[tex]f(3)=(3)^3-5(3)^2[/tex]

f(3) = 27 − 45

f(3) = −18

y = −18

Put x = 4.

Replace the variable x with 4 in the expression.

[tex]f(4)=(4)^3-5(4)^2[/tex]

[tex]f(4)=64-5(4)^2[/tex]

f(4) = 64 − 5 ⋅16

f(4) = 64 − 80

f(4) = −16

y = −16

The cubic function can be graphed using the function behavior and the points.

x   0    1     2        3      4

y   0  −4   −12   −18  −16

To learn more about functions refer to:

https://brainly.com/question/19809998

#SPJ9

When x = -2, we use the second part of the function, so g(-2)=0.

Similarly, g(4) = -4.

Answer:

Did you know that the first person convicted of speeding was going eight mph.

Step-by-step explanation:

Answer:

y = - 2x - 4

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 2, 0) and (x₂, y₂ ) = (0, - 4) ← 2 points on the line

m = [tex]\frac{-4-0}{0-(-2)}[/tex] = [tex]\frac{-4}{0+2}[/tex] = [tex]\frac{-4}{2}[/tex] = - 2

the line crosses the y- axis at (0, - 4 ) ⇒ c = - 4

y = - 2x - 4 ← equation of line

Work Shown:

m^2+9m=0

m(m+9)=0

m = 0 or m+9 = 0

m = 0 or m = -9

For more information, check out the topics about factoring and the zero product property.

Answer:

45 meters

Step-by-step explanation:

[tex]Area=\frac{1}{2}bh\\ A=\frac{1}{2}(6)(15)\\ A=3(15)\\A=45[/tex]

⊱________________________________________________________⊰

Answer:

A=45 m²

Step-by-step explanation:

The formula for the area of a triangle is, [tex]\bigstar\underline{\boxed{\sf{A=\frac{bh}{2}}}}[/tex].

where :

[tex]\triangleright\sf{A=Area,b=base,h=height}\triangleleft[/tex]

Substitute the values,

[tex]\large\begin{gathered}\sf{A=\frac{6*15}{2} \\ \sf{A=\frac{90}{2}\\\bigstar\underline{\boxed{\sf{A=45 \ m^2}}}} \end{gathered}[/tex]

Done !! Hope this made sense to you :)

[tex]\small\boldsymbol{Calligraphy}[/tex]

⊱______________________________________________________⊰

By definition of vectors exist as quantities that contain magnitude (positive or negative) and direction.

A) The unit vector in the direction of [tex]$F = i + \frac{3j}{2} +2k.[/tex]

B) The distance between [tex]F_{1}[/tex] and [tex]F_{2}[/tex] exists 2.

C) i.) Required vector = −4j − 5k

ii.) Required vector = 5i − 6j − 8k

To estimate the unit vector in the direction of V = 2i+3j+4k

|V| [tex]$= \sqrt{2^2+3^2+4^2}[/tex]

[tex]$= \sqrt{29}[/tex]

A) Unit vector

[tex]$F= \frac{V}{ |V|}[/tex]

[tex]$F= \frac{2i+3j +4k}{2}[/tex]

[tex]$F = \frac{2i}{2} + \frac{3j}{2} +\frac{4k}{2}[/tex]

[tex]$F= i + \frac{3j}{2} +2k.[/tex]

Therefore, unit vector in the direction of [tex]$F = i + \frac{3j}{2} +2k.[/tex]

B) To estimate the distance between [tex]F_{1}[/tex] = 3i+2j+ 5k and [tex]F_{2}[/tex] = 3i +4j +5k

[tex]$d = \sqrt{(3-3)^{2}+(4-2)^{2}+(5-5)^{2}}[/tex]

= 2

Therefore, the distance between [tex]F_{1}[/tex] and [tex]F_{2}[/tex] exists 2.

C) i.) P, (3,2,2), P₂(3,-2,-3)

Required vector =|[tex]P_{1}[/tex]P₂|=(3−3)i + ((−2)-2)j ​+ ((-3)-2)k

= −4j − 5k

ii.) P₂ (2,-3,-6), [tex]P_{3}[/tex] (-3,3,2) ​

Required vector =|P₂[tex]P_{3}[/tex]|=(-3-2)i + (3-(-3))j ​+ (2-(-6))k

= 5i − 6j − 8k

To learn more about vectors refer to:

https://brainly.com/question/2166498

#SPJ9

The equation of the polynomial function from the given table is; Option B: h(x) = x³ - 7x + 6

From the given table, we see that the x-intercepts are;

(-3, 0), (1, 0) and (2, 0)

Now, we are told the the x-intercepts have a multiplicity of one which means they occur as roots only once. Thus, we can say that the roots in factor form are;

(x + 3), (x - 1), (x - 2)

Then, the polynomial will be;

h(x) = (x + 3) * (x - 1) * (x - 2)

h(x) = (x + 3)(x² - 3x + 2)

h(x) = x³ + 3x² - 3x² - 9x + 2x + 6

h(x) = x³ - 7x + 6

Thus, the equation of the polynomial function from the given table is; Option B: h(x) = x³ - 7x + 6

Read more about Equation of Polynomial at; https://brainly.com/question/24348936

#SPJ1

The terms that completes the sentence are zeros; vertical. Option A

The functions of a sign chart include;

From the mentioned functions, we can se that the terms that completes the sentence are zeros and vertical asymptotes.

Thus, the terms that completes the sentence are zeros; vertical. Option A

Learn more about asymptotes here:

https://brainly.com/question/4138300

#SPJ1

The two-column proof that proves that ∠O ≅ ∠R using the SSS and CPCTC theorems is shown in the image attached below.

The side-side-side congruence theorem (SSS) states that when three sides of a triangle are congruent to the corresponding three sides of another triangle, then both triangles are considered congruent to each other.

The CPCTC theorem states that when two triangles are proven to be congruent by any triangle congruent theorem, then all the corresponding parts of the congruent triangle are congruent. This implies that the corresponding sides and angles of both triangle are equal or congruent.

We are asked to prove that ∠O ≅ ∠R.

With the given image, we would draw segment UP. Thus, based on the reflexive property, UP ≅ UP (one pair of congruent sides).

We are given two pairs of corresponding sides already, which are: UO ≅ UR and PO ≅ PR.

This means that triangles OUP and RUP have three pairs of corresponding congruent sides. Therefore, ΔOUP ≅ ΔRUP.

Applying the CPCTC theorem, ∠O ≅ ∠R.

The two-column proof is attached in the image below.

Learn more about the Side-side-side Congruence Theorem (SSS) on:

https://brainly.com/question/4280133

#SPJ1

Answer:

y= 4x -4

Step-by-step explanation:

Slope-intercept form is given by y= mx +c, where m is the slope and c is the y-intercept.

Given that the slope is 4, m= 4.

Substitute the value of the slope into the equation:

y= 4x +c

The value of c can be found by substituting any point in which the line passes through into the equation above.

When x= 4, y= 12,

12= 4(4) +c

12= 16 +c

Subtract 16 from both sides:

c= 12 -16

c= -4

Thus, the equation of the line is y= 4x -4.

Additional:

For more questions on slope-intercept form, do check out the following!

Answer:

0

Step-by-step explanation:

8z +12 = 12

8z = 0

z =0

Answer:

The answer is 0

Step-by-step explanation:

4(2z+3)=12?=

We use the distributive property to distribute the 4 into the 2.

8z=3=12?=

8 + 3 is 12 so the z has no part to play in this.

z=0

You could also have divided from both sides of the equation, but doing it this way is easier for me.

Answer: B is dependent and M is independent

Step-by-step explanation:

This is because the question says that they are raising money to buy books. In order to buy the books, they must raise money. So they raise money than buy the books which makes buying the books dependent on how much they raise.

Using the normal distribution, it is found that the cut-off time which 75.8% of the college students exceed when trying to find a parking spot in the library parking lot is of 3.7 minutes.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation are given as follows:

[tex]\mu = 4.5, \sigma = 1[/tex]

The cut-off time is the 100 - 75.8 = 24.2th percentile, which is X when Z = -0.7, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]-0.7 = \frac{X - 4.5}{1}[/tex]

X - 4.5 = -0.7

X = 3.7.

More can be learned about the normal distribution at https://brainly.com/question/4079902

#SPJ1

Answer:

6 x 2 x 2 x 1

Step-by-step explanation:

6 x 2 = 12

12 x 2 = 24

24 x 1 = 24

The function y = -16x² + 48x + 64 is a non linear function with a parabolic shape graph.

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

A non linear function is a function whose graph is not linear or can be represented by a straight line.

The function y = -16x² + 48x + 64 is a non linear function with a parabolic shape graph.

Find out more on equation at: https://brainly.com/question/2972832

#SPJ1

Given the diameter of the circular garden, the area of the garden is 28.36 yd².

The area of a circle is expressed as; A = πr²

Given that;

A = πr²

A = 3.14 × (3yd)²

A = 3.14 × 9yd²

A = 28.36 yd²

Given the diameter of the circular garden, the area of the garden is 28.36 yd².

Learn more about circles here: brainly.com/question/11952845

#SPJ1

The probability that a person chosen at random have run a red light in the past year is 0.45.

Given that 150 people have responded yes and 185 have responded no in a group of people when they asked whether they have run a red light.

Probability lies between 0 and 1. The value of probability can be find by :

Probability= Number items/total items.

Number of people who said that they have run red light=150

Number of people who said that they have not run red light=185

Total people=150+185

=335 people

Probability that a person chosen at random have run red light in the past year=

=Number of people who said that they have run red lights / total people

=150/335

=0.447

After rounding off it will be 0.45.

Hence the probability that a person chosen at random have run a red light in the past year is 0.45.

Learn more about probability at https://brainly.com/question/24756209

#SPJ1

Answer:

C) 100

Step-by-step explanation:

250+600-350-400

850-350-400

500-400=100