Write a congruence statement for the triangles. Then identify all pairs of congruent corresponding paris.
∠Q≅ ?
∠R≅ ?
∠P≅ ?
PQ≅ ?
QR≅ ?

Answer:

A. 200 square inches

Step-by-step explanation:

First, use Pythagorean Theorem to find the base of each triangle.

\(a^2+b^2=c^2\\20^2+b^2=(28\frac{1}{4})^2\\400+b^2=798.0625\\b^2=398.0625\\b=\sqrt{398.0625}\\b=19.9515037\)

Finally, use the area of a triangle formula to find the area of each triangle.

\(A=\frac{1}{2}bh\\A=\frac{1}{2}(19.9515037)(20)\\A=199.515037\)

Therefore, the area of each triangle is approximately 200 in².

The area of each triangle in square inches is 200 square inches.

The area of triangle is defined as the region enclosed by its perimeter or the three sides of triangle.

Mathematically,

Area of triangle = 1/2(base*height)

Now given that,

Base of the triangle, B = 20''

Hypotenuse of the triangle, H = 28(1/4)'' = 28.25''

So, Height of the triangle, P = \(\sqrt{H^2 - B^2}\)

or,  Height of the triangle, P = \(\sqrt{28.25^2 - 20^2}\)

or,  Height of the triangle, P = \(\sqrt{398.0625} }\)

or,  Height of the triangle, P = 19.95 inches

Finally, use the area of a triangle formula to find the area of each triangle.

Area of triangle = 1/2*(BasexHeight)

⇒Area of triangle = 1/2*(20x19.95)

⇒Area of triangle = 1/2*399

⇒Area of triangle = 199.5 square inches

or, Area of triangle ≈ 200 square inches.

Hence, The area of each triangle in square inches is 200 square inches.

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Answer:

Step-by-step explanation:

\(2^{1/2} - 2^{-1/3} = 2^{1/2 + 1/3} = 2^{3/6} = 2^{1/2} = \sqrt{2}\)

Answer:

\(\sqrt[6]{2}\)

Step-by-step explanation:

2 ^ 1/2 ÷ 2 ^ 1/3

We know that a^b ÷ a^ c = a^(b-c)

2 ^ (1/2 -1/3)

2^ (3/6 - 2/6)

2 ^ 1/6

\(\sqrt[6]{2}\)

Answer:

2x^7

Step-by-step explanation:

add the exponents because they both are x

2x^4*x^3=2x^7

Given statement solution is :- The present value of R13,000 per year invested for 8 years at 10% compound interest is approximately R69,776.60.

To calculate the present value of an investment with compound interest, we can use the formula for the present value of an annuity:

PV = A *\((1 - (1 + r)^(-n)) / r\)

Where:

PV = Present value

A = Annual payment or cash flow

r = Interest rate per period

n = Number of periods

In this case, the annual payment (A) is R13,000, the interest rate (r) is 10% per year, and the investment is made for 8 years (n).

Using the formula and substituting the given values, we can calculate the present value:

PV = \(13000 * (1 - (1 + 0.10)^(-8)) / 0.10\)

Calculating this expression:

PV = \(13000 * (1 - 1.10^(-8)) / 0.10\)

= 13000 * (1 - 0.46318) / 0.10

= 13000 * 0.53682 / 0.10

= 6977.66 / 0.10

= 69776.6

Therefore, the present value of R13,000 per year invested for 8 years at 10% compound interest is approximately R69,776.60.

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The required length of the base of the triangular pane of glass is 22 inches.

We know that the formula for the area of a triangle is:

Area = 1/2 * base * height

We are given that the height of the triangular pane of glass is 32 inches and the area is 352 square inches. Substituting these values into the formula, we get:

352 = 1/2 * base * 32

Multiplying both sides by 2 and dividing by 32, we get:

base = 22

Therefore, the length of the base of the triangular pane of glass is 22 inches.

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Answer: If you minus it the answer is -0.488692191 rad

I think

Step-by-step explanation:

How do you find the second of an angle?

The whole part of the measure of an angle in decimal degrees is the whole number of degrees. Multiplying the decimal part by 60 gives the number of minutes. If this number of minutes has a decimal part, then multiplying this decimal part by 60 gives the number of seconds.

These are my opinion

Answer:

Part A:

1. Computation of Basic EPS

Basic EPS = (Net Income - Preferred Dividends) / Weighted Average Shares Outstanding²

Net Income = $120,000

Preferred Dividends = 4% x $50,000 = $2,000

Weighted Average Shares Outstanding = 100,000 (assuming no change in common stock during the year)

Basic EPS = ($120,000 - $2,000) / 100,000

Basic EPS = $1.18

2. Individual dilution/anti-dilution with decision making

We need to check if any of the convertible securities or stock options are dilutive or anti-dilutive by comparing their impact on EPS with the basic EPS.

Convertible Preferred: Each preferred share can be converted into 1.9 common shares (1,900 / 1,000). The conversion would increase the common shares outstanding by 1,900 and decrease the preferred dividends by $2,000.

EPS after conversion = ($120,000 - $0) / (100,000 + 1,900)

EPS after conversion = $1.16

Since this is lower than the basic EPS of $1.18, the convertible preferred is dilutive and should be included in the diluted EPS calculation.

Stock Options - A: Each option can be exercised at $12 to buy one common share when the average market price is $11. This means that the options are out of the money and would not be exercised by the holders. Therefore, they have no impact on EPS and are anti-dilutive.

Stock Options - B: Each option can be exercised at $7 to buy one common share when the average market price is $8. This means that the options are in the money and would be exercised by the holders. The exercise would increase the common shares outstanding by 4,000 and generate cash proceeds of $28,000 ($7 x 4,000). The cash proceeds can be used to buy back some common shares at the market price of $8. The number of shares bought back is 3,500 ($28,000 / $8). The net increase in common shares outstanding is 500 (4,000 - 3,500).

EPS after exercise = ($120,000 - $2,000) / (100,000 + 500)

EPS after exercise = $1.17

Since this is lower than the basic EPS of $1.18, the stock options - B are dilutive and should be included in the diluted EPS calculation.

Convertible Bonds: Each bond can be converted into 40 common shares (40,000 / 1,000). The conversion would increase the common shares outstanding by 40,000 and decrease the interest expense by $50,000 ($1,000,000 x 5%). The interest expense is net of tax, so we need to multiply it by (1 - tax rate) to get the after-tax amount. The tax rate is 30%.

EPS after conversion = ($120,000 - $2,000 + $50,000 x (1 - 0.3)) / (100,000 + 40,000)

EPS after conversion = $1.19

Since this is higher than the basic EPS of $1.18, the convertible bonds are anti-dilutive and should be excluded from the diluted EPS calculation.

3. Ranking of potential dilutors

We need to rank the potential dilutors from the most dilutive to the least dilutive based on their impact on EPS.

The most dilutive security is the convertible preferred with an EPS of $1.16.

The second most dilutive security is the stock options - B with an EPS of $1.17.

The least dilutive security is the convertible bonds with an EPS of $1.19.

4. Step-by-step inclusion of individual dilutors to arrive at reportable EPS with decision making.

We need to include the potential dilutors in order of their dilution until we reach a point where the next security would be anti-dilutive.

The first security to include is the convertible preferred.

EPS with convertible preferred = ($120,000 - $0) / (100,000 + 1,900)

EPS with convertible preferred = $1.16

The next security to include is the stock options - B.

EPS with stock options - B = ($120,000 - $0) / (100,000 + 1,900 + 500)

EPS with stock options

Answer:

-52

Step-by-step explanation:

I hope this helps!

Answer:

27.5

Step-by-step explanation:

Please let me know if you want an explanation for why this is the answer (comment on this answer). A lot of people don't actually read the explanations, so I wouldn't want to waste my time. However, if you would like it I would be more than happy to type one out for you. Thanks!

Answer:

y=-5

Step-by-step explanation:

Answer:

680

Step-by-step explanation:

Vito works at a clothing store. He earns a weekly salary of $500 plus 5% commission on sales. His sales last week totaled $3600. What was his total pay (salary and commission) last week?

therefore the answer is $680.

The simplified expression in mathematical form is -45.36.

What is an expression?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

The expression given is -

(-15 + (-1.6 + 9.34) / 6) × (3² - 5.7)

Simplifying the terms inside the parentheses first, we get -

(-15 + 7.74 / 6) × (9 - 5.7)

Next, we simplify 7.74 / 6 by dividing the numerator by the denominator -

(-15 + 1.29) × (9 - 5.7)

We add -15 and 1.29 inside the first set of parentheses -

(-13.71) × (9 - 5.7)

We subtract 5.7 from 9 inside the second set of parentheses -

(-13.71) × 3.3

Multiplying these two terms, we get -

-45.363 ≈ -45.36

Therefore, the value is obtained as -45.36.

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Answer:

\(y=\frac{1}{3}x+7.6666\)

Step-by-step explanation:

First we must convert  \(3x+y=-7\) into slope-intercept form!

To do this we simply just need to subtract -3x from the 3x on the left and move it to the right side. This would result in: \(y = -3x-7\)

Now that we have our slope-intercept form for the equation remember that to find the equation that is perpendicular to the given equation, you need to use the opposite reciprocal of the slope. This would be \(\frac{1}{3}\) as that is the reciprocal and opposite of \(-\frac{3}{1}\)

Now in order to find the "b" variable of the equation that goes through the ordered pair (1, 8) we need to plug it in to the given equation!

That equation would be: \(y=\frac{1}{3}x-7\)

Given that x = 1 and y = 8 we can plug those in like so:

\(8=\frac{1}{3}(1)+b\)

(make sure to set the -7 to b as that's what we're solving for)

1 / 3 is 0.3333 (infinitely repeating)

Next we need to subtract 0.3333 from 8, which would be 7.6666 (infinitely repeating) Remember that the variable needs to be "alone"!

Now we have our "b" for the equation! Hence the equation would be:

\(y=\frac{1}{3}x+7.6666\)

(you can also use \(\frac{23}{3}\) for the b as that is the "exact form" of 1 / 3 but they both work)

Hope this helps! Feel free to ask questions!

The equation of the line in slope-intercept form is y = (3/4)x.

To write the equation of a line in slope-intercept form, we need to use the slope-intercept form equation: y = mx + b,

where m is the slope and b is the y-intercept.

Given that the line passes through the point (-8, 5) and has a slope of 3/4, we can substitute the values into the equation to find the y-intercept (b).

First, let's find the value of b using the point-slope form equation: y - y1 = m(x - x1), where (x1, y1) is a point on the line.

Using (-8, 5) as the point and 3/4 as the slope, we have:

5 - 5 = (3/4)(-8 - x)

0 = (3/4)(-8 - x)

0 = (-3/4)(8 + x)

0 = -6 - (3/4)x

Next, we can solve for x:

(3/4)x = -6

x = -6 \(\times\) (4/3)

x = -8

Now that we have the value of x, we can substitute it back into the equation to find the value of b:

0 = -6 - (3/4)(-8)

0 = -6 + 6

0 = 0

So, the value of b is 0.

Finally, we can write the equation of the line in slope-intercept form:

y = (3/4)x + 0

y = (3/4)x.

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Answer:

D.18

Step-by-step explanation:

6-x=-12

-x=-12-6

-x=-18   divide both sides by -1

x=18

Answer:

9) 15/16

10) 3/10

Step-by-step explanation:

The answers shown are simplified.

I used a calculator to make sure they were right.

Answer:

y = 1.705882353

Step-by-step explanation:Combine like terms: 20 + 9 = 29

29 + -10y + -7y = 0

Combine like terms: -10y + -7y = -17y

29 + -17y = 0

Solving

29 + -17y = 0

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.

Add '-29' to each side of the equation.

29 + -29 + -17y = 0 + -29

Combine like terms: 29 + -29 = 0

0 + -17y = 0 + -29

-17y = 0 + -29

Combine like terms: 0 + -29 = -29

-17y = -29

Divide each side by '-17'.

y = 1.705882353

Simplifying

y = 1.705882353

When applying the some rule, we only combine two equal ratios at once. Consequently, we deal with pairs of sides and angles that have equivalent ratios.

When two ratios are equal, a percentage is formed; alternatively, two equal ratios can be said to produce a proportion. When we understand that two ratios are equal, you can write a proportion. The ratios of these two numbers are equal.

When two variables are correlated in a manner that their ratios are equal, this is known as a proportional relationship. In a proportional connection, one variable is always a constant value multiplied by the other, which is another way to think of them. The "constant of proportionality" is the term used to describe that constant. Two angles are said to be complimentary if their sum is 90 degrees. Alternatively put, two angles are said to be complimentary if they combine to make a right angle.

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Answer:

Buddhism split into three groups based on the places where it spread.

Step-by-step explanation:

Answer:

Buddhism split into three groups based on the places where it spread.

Step-by-step explanation:

Answer:

The correct answer is 5in

Step-by-step explanation:

6+4=10÷2=5in

Answer:

82

41% of 100 = 41

41x2=82

100x2=200

Answer:

82

Step-by-step explanation:

You need to (41/100) * 200 which gives you the answer 82.

Answer:

1/2(6-8), 1/2(-3+7)=-1,2

Answer: C - (-1, 2)

Step-by-step explanation:

The number that represents the position of the fish relative is the opposite number of 14 which is: -14.

An opposite number of a number can be described as the number on the number line that has the same distance from 0, relative to the other number.

This means, if "a" is on a number line, and the distance of "a" from point 0 is x, therefore, the opposite number of "a" would be "-a". This also means that the distance from 0 to "-a" would also be x.

In the scenario given, we can deduce the following:

Distance of the bird above the surface of the water = 14 feet

The distance of the fish below the surface of the water = the opposite number of 14 = -14 feet (see image below).

Therefore, the number that represents the position of the fish relative is the opposite number of 14 which is: -14.

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Answer:

A, C, and D

Explanation:

32 rows

15 seats per 1 row

So,

32 × 15 = k

You can try arranging to get more choices.

32 × 15 = k

32 = k ÷ 15

and

32 × 15 = k

15 × 32 = k

15 = k ÷ 32

Answer:

6, 13 and 14

Step-by-step explanation:

A zero has the same meaning as the vertex.

The point where two lines meet forming an angle or set of angles is referred to as a vertex. This can also be called a point of origin especially when considering the axis of a Cartesian coordinate.

The vertex can be taken as zero since it is referred to as the point of origin. This is different to the axis of symmetry; as the axis of symmetry is one that splits a given plotted points i.e. a graph into two equal parts.

Thus, a zero has the same meaning as the vertex.

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Answer:

box plot titled ACT Score with a minimum of 24, quartile 1 of 27, median of 28, quartile 3 of 30, and maximum of 35

Step-by-step explanation:

The scores of the students represented on the dot plot are:

1 dot => 24

3 dots => 26, 26, 26

3 dots => 27, 27, 27

5 dots => 28, 28, 28, 28, 28

3 dots => 30, 30, 30

3 dots => 32, 32, 32

1 dot => 35

Quickly, we can ascertain 3 values from these data points of which we can use to find out which box plot represents the dot plot data.

The minimum score = 24

The maximum score = 35

The median score is the 10th value, which is the middle value of the data point = 28

Therefore, we can conclude that: "box plot titled ACT Score with a minimum of 24, quartile 1 of 27, median of 28, quartile 3 of 30, and maximum of 35".

Marina could use for the third side of the triangular sandbox the option: C - 7.25 ft.

In mathematic, there is a rule for triangle side lengths. This rule says that the sum of the lengths of any two sides of a triangle is greater than the length of the one side (third side).  Therefore,

                                       \(L_1+L_2 > L_3\, (1)\\ \\ L1+L_3 > L_2\, (2)\\ \\ L_2+L_3 > L_1\, (3)\)

The question gives two sides: 3 ft (L1) and 7.25 ft (L2), applying the equation (1) of rule for triangle side lengths, you have:

                                          \(L_1+L_2 > L_3\\ \\ 3+7.25 > L_3\\ \\ 10.25 > L_3\\ \\ L_3 < 10.25\)

The options for answer are: 4.25ft, 10.25ft,  7.25ft and 3ft. According to triangle inequality \(L_3 < 10.25\), hence, the letter B is not the answer.

After that, you can apply equations (2) or (3) for testing the options. For solution below, it was used the equation (2).

                                 \(L_1+L_3 > L_2\\ \\ 3+4.25 > L_2\\ \\ 7.25 > L_2\\ \\ L_2 < 7.25\)

The second side is exactly equal to 7.25, according to the rule this side should be less than 7.25. Therefore, the option 4.25 ft is not the answer.

                                 \(L_1+L_3 > L_2\\ \\ 3+7.25 > L_2\\ \\ 10.25 > L_2\\ \\ L_2 < 10.25\)

The question informs that the second side is 7.25 ft. Then 7.25 < 10.25, so the option 7.25 ft is the answer.

You can continue to test the last option, but it is not necessary since you have already found the corrected answer.

                                 \(L_1+L_3 > L_2\\ \\ 3+3 > L_2\\ \\ 6 > L_2\\ \\ L_2 < 6\)

The second side is equal to 7.25, hence, the option 3 ft is not the answer.

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