Two parallel lines are cut by a transversal. Suppose <1 and <2 are alternate interior angles and that m<1=4(x+2) and m<2=2x+24. What is the m<2?

The functions whose graphs consist only of lines are-

A function is a relationship between a set of inputs (referred to as the domain) and a set of permissible outputs (referred to as the codomain), in which each input is connected to exactly one output. A function on one variable is frequently denoted by f.

Linear functions: A straight line just on coordinate plane is represented by a linear function. For instance, y = 3x - 2 symbolizes a straight line on the a coordinate plane and thus a linear function.

Constant functions: A constant function is employed to portray a quantity that remains constant over time and is considered the simplest type of real-valued function.

Linear absolute value functions: The Absolute Value Function is a two-linear function piecewise defined function.

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Consider the formula,

The expression is given as,

Solve the expression as,

Thus, the given expression is evaluated as,

The measure of the angles 2 and 3 are 70°

What is an angle?

An angle is a figure in Euclidean geometry created by two rays, called the sides of the angle, that share a common termination, called the vertex of the angle. Angles created by two rays are located in the plane containing the rays. Angles also were generated when plane cross. These are known as dihedral angles. An angle defined by two intersecting curves is the angle of the rays lying tangent to the respective curves at their point of junction. Angle can also refer to the measurement of an angle or of a rotation. In the case of a geometric angle, the arc is defined by the sides and is centered at the vertex.

Given, angle 1 = 40°

and, angle 2 = angle 3 = x

In a triangle, sum of angles = 180°

or, m∠1 + m∠2 + m∠3 = 180°

or, 2x = 180-40

or, 2x = 140

or, x = 140/2 = 70°

Hence, the measure of the angles 2 and 3 are 70°

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We need to find the function in slope-intercept form. We thus need the y-intercept and slope. We know there are 38000 gallons in the pool already, so the y-intercept is 38000. The pool drains 12 per minute, so the slope is -12.

y = mx + b
y = -12x + 38000

To find the time it takes to drain the pool, we need to find x where y = 0, so we set the equation to 0 and solve for x.

0 = -12x + 38000
-38000 = -12x
-38000/-12 = -12x/-12
3167 = x

Now, to fill it back up, the y-intercept is 0. We know the slope is 16, so the equation is:

y = 16x

Finally, we need to find 16x = 38000. This is simple enough.

y = 16x
38000 = 16x
38000/16 = 16x/16
2375 = x

The union of set A = {1, 5, 8, 12, 17} and B = {5, 17} is

AUB= {1, 5, 8, 12, 17}

This is further explained below.

Generally, The set that contains all of the elements that are part of both sets A and B, or all of the elements that are part of both sets combined, is referred to as the union of the two sets A and B. The symbol is used to represent the union of all the elements in the set.

In conclusion, The union of these sets sees the value of both sets represented

A = {1, 5, 8, 12, 17} and B = {5, 17}

AUB= {1, 5, 8, 12, 17}

Option A

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Answer:

Step-by-step explanation:

just like when you have 5+(17-8) you don't have to do all the work you can just do this 17-8 is 9 and that is  when you add 5+9 is 14

Answer:

Step-by-step explanation:

The wood is (8/9) foot long. If cut into 4 pieces, each piece would be (8/9)/4 foot long.

(8/9)/4

((8/9)(1/4)= 8/36 or 2/9 foot long for each piece.

If he sells all 4 pieces for a total of $10, he will charge $10/4) = $2.50 each.

The value of 'x' is highlighted in the box

The journal entry will be prepared thus:

Date General Journal Debit Credit

2-Aug

Cash $540

Unearned Service Revenue  $378

Sales Revenue  $162

2-Aug

Cost of goods sold $105

Inventory  $105

3-Aug

Accounts receivable $550

Sales revenue  $550

3-Aug

Cost of goods sold $450

Inventory  $450

6-Aug

Sales return (550/5) $110

Accounts receivable  $110

6-Aug

Inventory $90

Cost of goods sold (450/5)  $90

10-Aug

Unearned service revenue $126

Service Revenue  $126

(378/3 = 126 each)  

20-Aug

Cash $350

Sales revenue  $350

20-Aug

Cost of goods sold $121

Inventory  $121

22-Aug

Cash $440

Accounts receivable $440

A journal entry is the act of recording any transaction, whether one that is economic or not.

An accounting diary that displays the debit and credit balances of a corporation lists transactions. Multiple recordings, each of which is either a debit or a credit, may be included in the journal entry.

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Aug.2 Sold a bundle of spa services with a merchandise basket. When sold separately, the spa service part of the bundle sells for $420 and the merchandise basket normally sells for $180. Together, the bundle was sold to Val Amy for cash at a selling price of $540 (total). Val booked a spa treatment for August 10, and she took the basket of goods with her. The goods had cost NGS $105.

Aug.3 Sold 5 identical items of merchandise to Cosmetics R Us on account at a selling price of $550 (total); terms n/30. The goods cost NGS $450.

Aug.6 Cosmetics R Us returned one of the five items purchased on August 3. The item could still be sold by NGS in the future and credit was given to the customer.

Aug.10 Val Amy used one of the three spa treatments she had purchased as part of the bundle sold to her on August 2.

Aug.20 Sold two at-home spa kits to Meghan Witzel for $350 cash. The goods cost NGS $121.

Aug.22 Cosmetics R Us paid its remaining account balance in full.

Prepare all journal entries

The equation of the circle in standard form is (x + 5)² + (y)² = 9/4.

The general representation of the equation is:

(x-h)² + (y-k)²= r²

Where (h,k) is the coordinates of the center of the circle and r is the radius.  And x and y are the corresponding x and y values of the point the circle passes through

Since we have the coordinate of the center as (-5,0)  and the circle passes through (-5, 3/2). Therefore:

h = -5, k = 0, x = -5 and y = 3/2

Let's put these values in the formula.

(x-h)² + (y-k)²= r²

(-5 - (-5) )² + (3/2 - 0)² =  r²  

(-5 + 5)² + (3/2)²= r²

(0)² + (3/2)²= r²

(3/2)² = r²

r = 3/2

Putting radius, r = 3/2,   h = -5 and k = 0 back into the formula wiil give:

(x + 5)² + (y - 0)²= (3/2)²

(x + 5)² + (y)² = 9/4

Therefore,the standard form of the equation of the circle is (x + 5)² + (y)² = 9/4.

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The equation which show the cost of windows:-

C = $75.75 * W

where W = no of windows

What is equation ?

A mathematical equation can be defined in a variety of ways.

The definition of an equation in algebra is a mathematical statement that proves two mathematical expressions are equal.

Consider the equation 3x + 5 = 14, where 3x + 5 and 14 are two expressions that are separated by the symbol "equal."

Mathematical variables are used in even the most fundamental and straightforward algebraic equations.

$227.25 ÷ 3 =  $75.75

The equation which show the cost of windows:-

C = $75.75 * W

where W = no of windows

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Answer:

–87.75

Step-by-step explanation:

Write the equation:

200 ÷ 5 • 32 + 12 – 101 = ?

PEMDAS

200 ÷ (5 • 32) + 12 – 101 = ?

(200 ÷ 160) + 12 – 101 = ?

(1.25 + 12) – 101 = ?

(13.25 – 101) = ?

–87.75 = ?

–87.75

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When analyzing research data, if the difference between group a and group b did not happen by chance and the data showed a real difference, the results are called statistically significant.

Statistically significant results occur in a research data when the difference between two groups is not likely to occur on its own, without the benefit of the independent variable. Statistically significant findings suggest that the researchers' outcomes are unlikely to be a result of chance, and that there is a relationship between the variables under investigation in the larger population. In such cases, the research usually rejects the null hypothesis and accept the alternative hypothesis.

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When we want to find the slope of a line, we divide its increase on the [tex]y[/tex]-axis by its increase on the [tex]x[/tex]-axis. In other words, we look at its [tex]tan(a)[/tex]. As you can see in the photo, I chose two points that exactly intersect the axes and connected them in a right triangle. I then divided the increase in the [tex]y[/tex]-axis ([tex]3[/tex]) by the increase in the [tex]x[/tex]-axis ([tex]4[/tex]). Since the line slopes to the right, its sign will be positive. Also, this line intersects the [tex]y[/tex]-axis [tex](x=0)[/tex] at [tex]1[/tex].

The probability that the nurse will find the two patients is P =  0.49.

We know that the probability that the nurse finds the client on a particular day is 0.7

So, each time that the nurse goes that a home, that probability is the same and is independent of what happened before.

So if the nurse goes to two houses, the probability that she will find the client on the first home is 0.7

And the probability that she will find the client on the second home is 0.7

Then the joint probability (the product of the two individual ones) is:

P = 0.7*0.7 = 0.49

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1080 inches²  are the dimensions of the box with maximum volume .

What is rectangle?

rectangular box length = 24 inches

                       width = 45 inches

maximum volume = 24 * 45

                              = 1080 inches²

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Hope this will be helpful.

The 96th term of the arithmetic sequence (1, -12, -25,.......) is 1234.

We are provided with the arithmetic sequence mentioned below;

1, -12, -25,...........

We know that, the rule to calculate the nth term in an arithmetic sequence is

[tex]a_{n}[/tex] = [tex]a_{1}[/tex] + ( n - 1 ) d                             equation 1

Here, d is the difference between two consecutive terms in the arithmetic sequence , [tex]a_{1}[/tex] is the first term, n is the number of terms and [tex]a_{n}[/tex] is the nth term.

We have,

n = 96

[tex]a_{1}[/tex] = 1

d = -12 -1 = -13

Now, substitute these values in equation 1 i.e, formula of arithmetic sequence and on substituting we will get

[tex]a_{96}[/tex] = 1 + ( 96 - 1 ) ( -13 )

[tex]a_{96}[/tex] = 1 - (95) (13)

[tex]a_{96}[/tex] = 1 - 1235

[tex]a_{96}[/tex] = 1234

So, we can conclude that the 96th term of the arithmetic sequence  is 1234.

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0.578 can be expressed as a percent if we can multiply the decimal by 100%

Step 1: Multiply 0.578 by 100

To multiply by 100, we simply have to shift the decimal point by the number of zeros (twice)

0.578 x 100 = 57.8%

Answer = 57.8%

Answer:

y = 2x+4

Step-by-step explanation:

2x - y = -4

We add y on both sides:

2x - y + y = -4 + y

so 2x = -4 + y

We now add 4 on both sides:

2x + 4 = -4 + 4 + y,

so 2x+4 = y,

so y = 2x+4

So intercept for y = 2x+4

Probability that x greater than or equal to 5 is 0.6 i.e., Probability that x ≥ 5 = 0.6

The probability distribution for a random variable x is given in the table.

x                |  -10       -5       0       5      10    15     20

probability | 0.20   0.15   0.05   0.1  0.25  0.1   0.15

If a random variable x has values x₁, x₂, .. ,xₙ with their corresponding probabilities given for each of them P(xₐ), then probability that x ≥ xₐ, for some a = 1, 2, .. , n is,

        P(x ≥ xₐ) = P(xₐ) + P(xₐ₊₁) +...+P(xₙ).

Here we need to find the probability that the random variable x is greater than equal to 5. So we need to add up the probabilities corresponding to the random variables x  ≥ 5.

So here, probability that x ≥ 5 is

P(x ≥ 5) = P(5) +P(10) + P(15) + P(20)

            = 0.1 + 0.25 + 0.1 + 0.15

            = 0.6

Hence Probability that x ≥ 5 is 0.6.

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Answer:

r=1

Step-by-step explanation:

1=2r-1

Add 1 on both sides

2=2r

Divide 2 on both sides

r=1

Answer: 72

Step-by-step explanation:

The average is 90.

To calculate the average, you add the grades and divide by the total amount of them. The number of grades is 5. We need to know what value of x satisfies the following equation:

[tex]90 = \frac{96+90+87+95+x}{5}[/tex]

To solve the equation, we first multiply each side by 5, netting:

450 = 96 + 90 + 87 + 95 + x.

Then we subtract each grade from each side.

450 - 378 = 378 - 378 + x

72 = x

Answer:

x = 45, y = 85

Step-by-step explanation:

In this figure we can see a Z-angle, which tells us that x = 45

In a triangle, the sum of the angles is 180 degrees,

so the unknown angle in the triangle is 180 - 45 - 85 = 50

For a straight line, the total angle is 180 degrees,

, so y + x + unknown angle of triangle = 180

since x = 45, and unknown angle of triangle = 50,

y = 180 - 45 - 50 = 85

This can also be seen when you realise that the two parallel lines give an F-angle, which tells us that Y = 85

Answer:

tan θ = 4.5

Step-by-step explanation:

tan = opposite/adjacent

The opposite of θ is 45 cm long

The adjacent of θ is 10 cm long

tan θ = 45 / 10 = 4.5

The solution is: the value of tan is : tan θ = 4.5.

Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles

here, we have,

The six trigonometric functions are sin , cos , tan , cosec , sec and cot

Let the angle be θ , such that

sin θ = opposite / hypotenuse

cos θ = adjacent / hypotenuse

tan θ = opposite / adjacent

Here, we have,

we know,

tan = opposite/adjacent

from the given diagram, we get,

given that,

The opposite of θ is 45 cm long

The adjacent of θ is 10 cm long

so, we get,

tan θ = 45 / 10

        = 4.5

Hence, The solution is: the value of tan is : tan θ = 4.5.

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The hypotenuse of the given right angle triangle is: 50 cm

What is hypotenuse?

In mathematics, the hypotenuse is the longest side of a right angle triangle. It is defined as the standard formula, which states that the square of the hypotenuse is equal to the square of their adjacent sides.

According to the question, to calculate the hypotenuse with the given parameters. First name all the three vertices.

AB = 30 cm; BC = 40 cm; AC = ?

Using standard hypotenuse formula, which states:

AB² + BC² = AC²

⇒ 30² + 40² = AC²

⇒ AC² = 900 + 1600 = 2500

⇒ AC = 50 cm

Hence, the hypotenuse of the given right angle triangle is: 50 cm

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[tex]6(y) + 6( -5 ) = 18 - 2y \\ 6y - 30 = 18 - 2y \\ 6y + 2y = 18 + 30 \\ 8y = 48 \\ \frac{8y}{8} = \frac{48}{8} \\ y = 6[/tex]

ATTACHED IS THE SOLUTION

The domain of the function would be a positive integer.

So option 1) positive integer is correct.

Domain of a function is the set of values accepted by the function.

So in this question the value is always a integer.

Consider the function y = f(x), which has the independent variable x and the dependent variable y. A value for x is said to be in the domain of a function if it successfully allows the production of a single value y using another value for x.

And the model is made to determine the amount of money spend to complete the project.

We can't define money in negative term.

So it must be a positive integer.

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Answer:

81, 100, 25, 4

Step-by-step explanation:

The square root of each of these numbers is whole

Answer:

these are the perfect squares

Step-by-step explanation:

(b-2)x = 8

In the given equation, b is a constant. If the equation

has no solution, what is the value of b ?

Step 1

identify

b is a constant, so (b-2) is a constant too.

If the equation has no solution, it is, there is not a value of x to satisfy (b-2)x=8

Step 2

solve for x

This value becomes indeterminate when the denominator takes the value of zero,it is

so , the value of b=2 makes the equation has no solution.

Answer

A) 2