Answer the questions below.

1. Angle j and k

j || k is a result of the Converse of Corresponding Angles Postulate.

2. The alternating inner angles of the lines j and k are angles 2 and 5. If angle 2 = angle 5, then

Alternate Interior Angles in Reverse According to the theorem, j || k.

Alternate interior angles are conversed by J and K.

How do parallel angles work?

3. Similarly Angle 3 equals Angle 10.

Angle 3 and Angle 10 are the exterior angles of the lines l and m, respectively. Angle 3 equals angle 10 according to the Converse of Alternate Exterior Angles Theorem, therefore l || m.

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Given:

Number of friends = 5

Total amount they earn = $33.75

Let's find how much each friend earn.

To find the amount each friend earn, take the formula below:

Substitute values into the equation above and evaluate:

Therefore, each friend earns $6.75

ANSWER:

$6.75

Answer: $6.75

Step-by-step explanation: Divided 33.75 by 5 which is equal to $6.75

Answer:

Explanation:

Given the improper fractions:

In order to arrange the fractions, first, find the lowest common multiple of the denominators.

• LCM of 7, 6, 14, and 21 = 42

Next, rewrite each fraction as an equivalent fraction using the LCM as the new denominator.

Since all the denominators are the same, order the numerators from the greatest to the least:

Thus, the fractions ordered from greatest to least is:

EPS for recession is $3.7975, EPS for normal is $4.8686, EPS for expansion is $5.5015, and Percentage change in EPS for expansion is 13% and for recession is -22%, EPS under each of the three scenarios after recapitalization is 4360 and percentage change in EPS after the recapitalization is -31.17% and 18.42% for recession and expansion respectively.

A-1) Calculation of EPS under each scenario:

EBIT for expansion condition,

= EBIT × 113%

= $53,000 × 113%

= $59,890

EBIT for recession conditions,

= EBIT × 78%

= $53,000 × 78%

= $41,340

Tax = EBT × 21%

Net income = EBT - Taxes

EPS = Net income ÷ No. of shares

EPS for recession = $3.7975

EPS for normal = $4.8686

EPS for expansion = $5.5015

A-2) Calculation of Percentage change in EPS,

For Expansion = (Expansion EPS - Normal EPS) ÷ Normal EPS

= (5.05 - 4.86) ÷ 4.86

= 13%

For Recession = (Recession EPS - Recession EPS) ÷ Recession EPS

= (4.86 - 3.79) ÷ 4.86

= -22%

B-1) Calculation of EPS under each of the three scenarios after recapitalization,

Market to Book ratio (l) = Market value ÷ Book value

l = $395,600 ÷ Book Value

Book Value = $395,600

Stock Price = Book Value ÷ No. of outstanding shares

= $395600 ÷ 8,600

= 46

No. of shares repurchased = Debt ÷ Stock Price

= $195,000 ÷ 46

= 4240

No. of shares after repurchasing = No. of outstanding shares - No. of shares repurchased

= 8,600 - 4240

= 4360

B-2) Calculating percentage change in EPS after recapitalization,

For Recession = (Recession EPS - Recession EPS) ÷ Recession EPS

= (4.66 - 6.77) ÷ 6.77

= -31.17%

For Expansion = (Expansion EPS - Normal EPS) ÷ Normal EPS

= (8.02 - 6.77) ÷ 6.77

= 18.42%

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The equation of a straight line is y = mx + b where m is the slope and b is the y-intercept then the two points exist (0, -2) and (6, 0).

A straight line's general equation is y = mx + c, where m denotes the gradient and y = c denotes the point at which the line crosses the y-axis. On the y-axis, this value c is referred to as the intercept. Y = mx + c represents the equation of a straight line with gradient m and intercept c on the y-axis.

The equation of a straight line is:

y = mx + b where m is the slope and b is the y-intercept.

Therefore, the equation for this line is:

y = (1/3)x - 2

To graph it we can identify two points on the line and connect them.

If x = 0, then y = -2 this is the y-intercept given in the problem.

If x = 6, then y = 0 this is the x-intercept

Therefore, the two points exist (0, -2) and (6, 0).

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Answer:

1-4<58

Step-by-step explanation:

poor Greg is broke and yea

The surface area of a rectangular prism can be represented below

Therefore,

Explanation:

Mr. Coffey bought a house for $195,000 with a 20% down payment.

A 20% down payment, would be 0.20, so $195,000 times 0.20 equals $39,000. Then $195,000 - $39,000 = $156,000.

He bought the bouse for $156,000.

5.25% is 0.525, because you move the decimals back. Understanding the total cost of the house is $156,000 now, we can do $156,000 times 5.25% (0.0525) which equals $8,190.

He would pay $8,190 every 30 years. (if this was the interest rate.)

Assuming if the cost was 20% down payment with the 5.25% interest rate then it would have been: $39,000 times 5.25% = 2047.5.

He would pay $2,047.50 every 30 years. (if this was the interest rate.)

There was no context between the interest rate, so let's assume the obvious which is $2,047.50 every 30 years.

Answer:

h < 11

Step-by-step explanation:

Thats what i get when i work it out lol

We are given the information that the equation of the line is of the form:

y = a x + b

where a is a negative number and b is a positive number.

And we are asked to select among a number of options that represent the situation.

SInce b is a positive number (being "b" what is understood as the y-intercept) the line DOESN'T pass through the origing of coordinates. So the first option is discarded.

SInce "a"is a negative number (this is the so called "slope' of the line) the line must be slanted, and dropping from left to right Therefore option b is also discarded because that represents a line going up from left to right.

Option c is also discarded, because a is a negative number (not a zero) and lines parallel to the x axis have slope zero.

The last option is the correct one, since the intercept oo the y-axis is at a positive value for y, the line must be going down due to the negative slope, and therefore going across the II, I and IV quadrant as shown below: (give me a few minutes to draw a line with this characteristics)

Then, please mark the last option (d) as the correct answer.

From the information given, the area of the kitchen is 54 square feet and it is 9 times as many square feet as does Tina's pantry. This means that the area of Tina's pantry is

54/9 = 6 square feet

If the pantry is 2 feet wide, we would determine its length by applying the formula for determining the area of a rectangle which is expressed as length * width

Therefore,

2 * length = 6

length = 6/2 = 3 feet

Length of the pantry is 3 feet

Given: 8abcd

The number of degrees is the sum of the exponent of each variable in the monomial

The answer is 4

Answer:

How many hours during the week do you eat in the cafeteria?

Step-by-step explanation:

since susan wants to find out how much time they are spending, the appropriate question would be the one asking about how many hours (time) they spend in the cafeteria

The standard form of the quadratic equation is given as follows:

y = x² - 2x - 15.

A quadratic equation is modeled according to the following rule:

y = ax² + bx + c.

From the given table, when x = -3, y = 0, hence the first equation is given by:

(-3)²a + (-3)b + c = 0

9a - 3b + c = 0.

When x = -1, y = -12, hence the second equation is given by:

-12 = a(-1)² + b(-1) + c

a - b + c = -12.

When x = 1, y = -16, hence the third equation is given by:

-16 = a(1)² + b(1) + c

a + b + c = -16.

Then the system of equations to find the coefficients is given as follows:

Using a calculator, the solution to the system is:

a = 1, b = -2, c = -15.

Hence the equation is given by:

y = x² - 2x - 15.

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We have a parallelogram and we have to find the length of side RQ.

Opposite sides of a parallelogram besides being parallel, they also have the same length.

Then, we can write:

We can use that to find the value of x as:

Knowing x = 4, we can find RQ as:

Answer: QR = 15

Answer: 45/10

Explanation:

We want to add

11/5 + 23/10

The first step is to find the lowest common multiple, LCM of the denominators. The LCM of 5 and 10 is 10. We would divide the LCM by each denominator and multiply each numerator by the results. The common denominator of the final fraction would be the LCM. We have

For the first fraction,

10/5 = 2

2 x 11 = 22

For the second fraction,

10/10 = 1

1 x 23 = 23

Thus, the final fraction would be

(22 + 23)/10

= 45/10

The equation of the line k parallel to line j and passes through (-4, 4) is

y = - 9 / 7 x - 8 / 7

Equation of a line can be represented as follows:

y = mx + b

where

Therefore, the line k is parallel to the line j, y =  - 9 / 7 x + 10 / 7  and passes through (-4, 4),

Parallel lines have the same slope.

Hence, let's find the y-intercept of the equation k using (-4, 4)

4 = - 9 / 7 (-4) + b

4 - 36 / 7 = b

b = - 8 / 7

Therefore,

the equation is y = - 9 / 7 x - 8 / 7

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The Dosage in milligrams per​ min, mg/min : 0.01mg / min

The Dosage in milligrams per​ hour, mg/hr : 0.6mg/hr

The dosage available in milliliters per hour, ml/hr: 6ml/hr

What is Dosage ?

A dosage is a predetermined amount of a drug, food, or pathogen that is administered as a single unit. The dose increases with the amount administered. In medicine, doses are most frequently calculated for substances.

Given,

Dose(mcg) = 10mcg/min

Dose available = 50mg

Volume of dose available = 500ml

a) The dosage in milligram per minute will be:

                                    = 10mcg / 1000mcg

                                    = 0.01mg / min

b) The dosage in milligrams per​ hour, mg/hr :

                                    = 10mcg x 60min / 1000mcg

                                    = 0.6mg/hr

c) By dosage formula we can write:

                                    = OxV / A

Where,

O = Dose ordered

V = Volume of dose available

A = Dose available

So that we know,

Dose ordered (mg) = 0.6 mg

Volume of dose available (mL) = 500 mL

Dose available (mg) = 50 mg

                                                  = 0.6 x 500 / 50

                                                  = 6ml/hr

Hence,

The Dosage in milligrams per​ min, mg/min : 0.01mg / min

The dosage in milligrams per​ hour, mg/hr : 0.6mg/hr

The dosage available in milliliters per hour, ml/hr: 6ml/hr

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Answer: Mr. Bond is gonna be mad at youuuuuuuuuuu.

Step-by-step explanation: But I think Batman is like 40 and robin's like 18. I had problems with this too and I can't rlly give u proof rn. Good luck with the unit testtt.

Answer:

C.

Step-by-step explanation:

The relationship is proportion if y/x is constant.

So it is C because 12/4 = 15/5 = 18/6 = 3.

you can do this I know you can !!!!!

Given the equation

-x = 2 -3x + 6

To solve this:

Step 1: collect like terms

-x + 3x = 2 + 6

2x = 8

Step 2: Divide both sides by 2

The value of x = 4

The given sequence is

To find the explicit formula, first, we have to find the difference by subtracting two consecutive terms.

As you can observe, the difference is 4.

From the sequence, we observe that the first term is -7.

The formula for arithmetic sequences is

Now, let's replace the values we've got.

Then, we simplify.

Its better to buy second set of candy. That is, candy which is $7.14 for 7 bars.

Given,

The cost for first candy = $4.12 for 4 bars.

The cost for second candy = $7.14 for 7 bars.

We have to determine which candy is better to buy.

For that we have to find the cost of one candy.

That is,

The cost for one candy in first candy set = 4.12/4 = 1.03

The cost for one candy in second candy set = 7.14/7 = 1.02

Here,

1.02 is less than 1.03.

That is, second set of candy has lesser cost than first set.

So, its better to buy second set of candy. That is, candy which is $7.14 for 7 bars.

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Answer:

Slope is 2/3

Step-by-step explanation:

Answer:

x=55

Step-by-step explanation:

2x+6+x+9=180

3x=165

x=55

:]

Answer: x=55

Step-by-step explanation:

Since the lines are parallel, the two angles on the line are supplementary angles.

It means they would add to 180.

1) Set up the equation

(2x+6)+(x+9)=180

2) Combine like terms

3x+15 = 180

3) Move the 15 to the other side to leave x

3x = 180 - 15

3x = 165

4) Set x by itself

x = 165/3

x=55

Answer:

Explanation:

Given the polynomial:

To divide the polynomial by the linear function x-2 using synthetic division, first, set the linear function equal to 0 and solve for x:

The result is written outside the line as shown below:

Next, write the coefficients of the polynomial inside as shown above:

Applying the exterior angle theorem, the measure of angle LJK is: 28°.

Where an external angle is formed by an extended side of a triangle, its measure is equal to the two remote angles of the triangle, according to the exterior angle theorem.

Given the following:

Angles LJK and JKL are remote angles of the triangle which are opposite the exterior angle KLM.

Therefore:

m∠LJK + m∠JKL = m∠KLM

Substitute

2x + 12 + 3x + 7 = 7x + 3

Combine like terms and find the value of x:

5x + 19 = 7x + 3

5x - 7x = -19 + 3

-2x = -16

-2x/-2 = -16/-2

x = 8

Find

m∠LJK = 2x + 12

Plug in the value of x:

m∠LJK = 2(8) + 12

m∠LJK = 28°

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To find the volume of a similar ballon with radius 10.4 cm, we will simply take the proportion

Let v be the volume of the similar ballon;

Cross -multiply

Divide both-side by 2.6