An employee earned $21,871 this year. This was a raise of 4% over last year. What was his salary last year? Round to the nearest dollar, if necessary.
O A. $21,784
O B. $21,030
OC. $21,867
OD. $20,996
O E. None of these

Answer: 4.8

Step-by-step explanation:

The two integers are equal to 1 and 7 respectively.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Let x represent the smaller number. Then the given relationships say ...

1/x + 2/(x+6) = 9/7

Multiplying by 7x(x+6), we have ...

7(x+6) +14x = 9x(x+6)

9x² +54x = 21x +42 . . . . .eliminate parentheses, swap sides

9x² +33x = 42 . . . . . . . . ...subtract 21x

3x² +11 -14 = 0 . . . . . . . . . .subtract 42 and divide by 3

(3x +14)(x -1) = 0 . . . . . . . . factor

Values of x that make this true are x = 1 and x = -14/3. Then for the positive integer x=1, the other integer is x+6=7.

Therefore, the two integers are equal to 1 and 7 respectively.

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Answer:

The answer is b..

Step-by-step explanation:

hope its helpful

According to the information, we can infer that the area of this polygon is 34 units².

To find the area of the figure we must graph it and divide it into different segments. Then we find the area of all the segments and add them to get the total area.

Rectangle 1

6 * 3 = 18

Rectangle 2

2*4=8

Triangle 1

2 * 4 / 2 = 4

Triangle 2

2 * 4 / 2 = 4

Total Area

18 + 8 + 4 + 4 = 34

Based on the above, we can infer that the total area of the polygon is 34 ² units.

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Answer:

m∠1 = 97

m∠2 = 83

m∠3 = 97

m∠4 = 83

Answer:

m∠1 = 97°

m∠2 = 83°

m∠3 = 97°

m∠4 = 83°

Step-by-step explanation:

180 - 97 = 83°

180 - 83 = 97°

The probability of the four events are: Event 1: 1/84Event 2: 3/14Event 3: 15/28 Event 4: 5/21

The total number of drinks = 9The number of sweet teas = 3The number of unsweetened teas = 6If you select 3 drinks at random, the following events can take place:

Event 1: All three drinks are sweet teas. The probability of event 1 = (Number of ways in which all three drinks can be sweet teas) / (Number of ways to select 3 drinks)The number of ways in which all three drinks can be sweet teas = 3C3 = 1 (because all three sweet teas are already fixed)The number of ways to select 3 drinks = 9C3 = (9 × 8 × 7)/(3 × 2 × 1) = 84Therefore, the probability of event 1 = 1/84 = 1/84

Event 2: Exactly two drinks are sweet teas. The probability of event 2 = (Number of ways in which two drinks are sweet teas and one is an unsweetened tea) / (Number of ways to select 3 drinks)The number of ways in which two drinks are sweet teas and one is an unsweetened tea = (3C2 × 6C1) = 18 (because you can choose 2 sweet teas from 3 and 1 unsweetened tea from 6)The number of ways to select 3 drinks = 9C3 = (9 × 8 × 7)/(3 × 2 × 1) = 84Therefore, the probability of event 2 = 18/84 = 3/14

Event 3: Exactly one drink is a sweet tea. The probability of event 3 = (Number of ways in which one drink is a sweet tea and the other two are unsweetened teas) / (Number of ways to select 3 drinks)The number of ways in which one drink is a sweet tea and the other two are unsweetened teas = (3C1 × 6C2) = 45 (because you can choose 1 sweet tea from 3 and 2 unsweetened teas from 6)The number of ways to select 3 drinks = 9C3 = (9 × 8 × 7)/(3 × 2 × 1) = 84Therefore, the probability of event 3 = 45/84 = 15/28

Event 4: All three drinks are unsweetened teas. The probability of event 4 = (Number of ways in which all three drinks can be unsweetened teas) / (Number of ways to select 3 drinks)The number of ways in which all three drinks can be unsweetened teas = 6C3 = 20 (because you can choose 3 unsweetened teas from 6)The number of ways to select 3 drinks = 9C3 = (9 × 8 × 7)/(3 × 2 × 1) = 84 Therefore, the probability of event 4 = 20/84 = 5/21

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Answer: Ans is 990. First such a number is 5×0 +2=2, then 5×1 +2=7, like that in all 20 numbers are there from 2 to 97 in A.P.with common difference of 5.

Step-by-step explanation:

Answer:

2 gallons

Step-by-step explanation:

(1.5 gallons)/(3/4 Room) = 2 gallons/Room

Answer:

\(1. \;\;y = \dfrac{1}{3}x - 1\\\\2.\;\;y = -\dfrac{2}{5}x\\\\3.\;\;y = x + 8\)

Step-by-step explanation:

The slope intercept form equation is y = mx + b

where m = slope and b = y-intercept

So for each case, substitute for slope(m) and y-intercept(b)

Answer:

1.  y = 1/3x + (-1)

2. y = -2/5x

3. y = 1x + 8 = 1x + 8 or  y = x + 8

Step-by-step explanation:

1. First of all, we need to know the slope-intercept form. The formula is y = mx + b. M represent the slope and b represents the y-intercept. So the question asked for the slope-intercept form for the slope that is 1/3 and the interception of -1. So we need figure out how to write it. It asked for -1/3 and -1 and we use the formal y = mx + b and it'll help us on figuring out how to write it. So far we have y = 1/3x + b, b is the intercept. The intercept would be -1. So the way we'd right it out is y = 1/3x + (-1). But first you have to multiply the + with -1. When we would multiply the signs you do it like this: (+) (+) = + and (-) multiplied by (-) is +. As well as (-) multiplied by (+) is -.

So for 1 the slope would be 1/3 and the (0, -1) . But we have to write it in the given form: y = mx + b ... m = slope, b = y intercept. So the way we'd right it is y = mx + b and m = slope, b = y intercept. Therefore the answer for this one is y = 1/3x - 1.

2. First we should know that we have the slope of -2/5 and the y-intercept is 0. The right form for this is y = -2/5x +. So for this one we got y = -2/5x because we said that the first one is 1/3 and -1. As well as the second is -2/5 and 0. The third is 1 and 8 as we wrote it earlier. So that's how we got our answer y = -2/5x for this question. Therefore our answer to this question is y = -2/5x.

3. For this one we first know slope = 1 and intercept =8. This equation is easier than both number 1 and 2 all we need to do is just put every given number in the right place. So we'll need to write the y as it is then add the = sign. Then write the slope which is given above. Then we have to write the x. We'll need to add the + sign and write the intercept given above next to it. After doing these steps you we'd have the answer because this is the general formula. So we would write 1 instead of m and the intercept is 8 so you need to write it instead of b. Therefore our answer would be y = 1x + 8 = 1x + 8 or another way we could write it is  y = x + 8 either way would be correct.

I hope this helps, have a blessed day! :)

The polygon has 21 sides whose interior angle are in Arithmetic Progression (A.P.)

The interior angles of a polygon are in an arithmetic progression (A.P) if the difference between any two consecutive angles is constant. To find the number of sides in a polygon given its smallest angle and the common difference of its interior angles, we can use the formula:

n = (180° - smallest angle) / common difference + 1, where n is the number of sides in the polygon.

In this case, the smallest angle is 100° and the common difference is 4°, so the number of sides can be calculated as follows:

n = (180° - 100°) / 4° + 1 = (80°) / 4° + 1 = 20 + 1 = 21.

Therefore, the polygon has 21 sides. It is important to note that a polygon with 21 sides is called an icosikaihenagon, which is a highly unusual and exotic shape, as most polygons have a smaller number of sides.

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Answer:

\(\textsf{23.} \quad c)\;\;y=-2x+7\)

\(\textsf{24.} \quad 12\)

\(\textsf{25.} \quad -2.33\:\:\sf (2\:d.p.)\)

Step-by-step explanation:

Given equation:

\(y=\dfrac{1}{2}x-1\)

If two lines are perpendicular to each other, the slopes are negative reciprocals.  

Therefore, the slope of a line perpendicular to the given equation is -2.

Substitute the found slope and the given point (3, 1) into the point-slope formula to find the equation of the line:

\(\implies y-y_1=m(x-x_1)\)

\(\implies y-1=-2(x-3)\)

\(\implies y-1=-2x+6\)

\(\implies y=-2x+7\)

Define the variables:

Given information:

Create two equations with the given information:

\(\begin{cases}x+y=15\\20x+50y=390\end{cases}\)

Solve the first equation for y:

\(\implies y=15-x\)

Substitute the found expression for y into the second equation and solve for x:

\(\implies 20x+50(15-x)=390\)

\(\implies 20x+750-50x=390\)

\(\implies -30x+750=390\)

\(\implies -30x=-360\)

\(\implies x=12\)

Therefore, Kerry received 12 twenty-dollar bills.

Given expression:

\(\dfrac{6^2-4^2}{-10+\sqrt{2}}\)

Following the order of operations (PEMDAS), simplify the numerator:

\(\implies \dfrac{36-16}{-10+\sqrt{2}}\)

\(\implies \dfrac{20}{-10+\sqrt{2}}\)

Calculate the square root:

\(\implies \dfrac{20}{-10+1.414213...}\)

Simplify the denominator:

\(\implies \dfrac{20}{-8.5857864...}\)

Divide the numerator by the denominator:

\(\implies -2.3294313...\)

Therefore:

\(\implies \dfrac{6^2-4^2}{-10+\sqrt{2}}=-2.33\:\: \sf (2\:d.p.)\)

Answer:

2 is 67

3 is 45

4 is 71

6 is x(all angles)

7 is 28

8 is 33

Answer:

Buffalo

Thats the answer because temp is decreasing back so 10 is higher plus lower than all

Answer:

£153

Step-by-step explanation:

If Saji bought a normal ticket for all 19 games, they would have to make 19 payments of £28. So, 28*19 would let us know that he would spend £532 in total. Then it's simply 532-379 to find the answer.

Answer:

Step-by-step explanation:

Answer:

which grade do you want to get helped by ?

Answer:

5/4

Simplified: 1 1/4

Step-by-step explanation:

Have a good day!

Answer:

5/4 ——> 1 1/4 simplified

Step-by-step explanation:

3/4 + 1/2

To add fractions, you need a common denominator so multiply 2 1/2 by 2 to have both fractions  denominator 4.

3/4 + 2/4 and now simply add 3 and 2 and keep the same denominator. Which gives you 5/4 but since it’s importer fraction, you need to simplify it and turn it into mixed fraction which is 1 1/4.

It looks like the integral might be

\(\displaystyle \int (9 - x^2)^{3/2} \, dx\)

or perhaps

\(\displaystyle \int \frac1{(9 - x^2)^{3/2}} \, dx\)

Take note of the fact that both integrands are defined only over the interval -3 < x < 3.

For either integral, we substitute x = 3 sin(θ) and dx = 3 cos(θ) dθ.

Note that we want this substitution to be reversible, so we must restrict -π/2 ≤ θ ≤ π/2, an interval over which sine has an inverse. Then θ = arcsin(x/3).

The first case then reduces to

\(\displaystyle \int (9 - (3\sin(\theta))^2)^{3/2} (3 \cos(\theta) \, d\theta) = 3 \times 9^{3/2} \int (1 - \sin^2(\theta))^{3/2} \cos(\theta) \, d\theta \\\\ = 81 \int (\cos^2(\theta))^{3/2} \cos(\theta) \, d\theta \\\\ = 81 \int |\cos^3(\theta)| \cos(\theta) \, d\theta\)

By definition of absolute value,

\(\displaystyle 81 \int |\cos^3(\theta)| \cos(\theta) \, d\theta = \begin{cases}\displaystyle 81 \int \cos^4(\theta) \, d\theta & \text{if }\cos(\theta) \ge 0 \\ \displaystyle -81 \int \cos^4(\theta) \, d\theta & \text{if }\cos(\theta) < 0\end{cases}\)

and these cases correspond to 0 ≤ θ < π/2 and π/2 < θ ≤ π, respectively. But we are assuming -π/2 ≤ θ ≤ π/2, so the negative case doesn't matter to us.

You can compute the remaining antiderivative by exploiting the half-angle identity for cosine,

\(\cos^2(\theta) = \dfrac{1 + \cos(2\theta)}2\)

Then

\(\cos^4(\theta) = \left(\cos^2(\theta)\right)^2 = \dfrac{1 + 2\cos(2\theta) + \cos^2(2\theta)}4 = \dfrac{3 + 4\cos(2\theta) + \cos(4\theta)}8\)

and so

\(\displaystyle \int \cos^4(\theta) \, d\theta = \dfrac{12\theta + 8\sin(2\theta) + \sin(4\theta)}{32} + C\)

We can simplify this using the double angle identity for (co)sine,

sin(2θ) = 2 sin(θ) cos(θ)

cos(2θ) = 1 - 2 sin²(θ)

as well as the relations,

sin(arcsin(x/3)) = x/3

cos(arcsin(x/3)) = √(9 - x²)/3

which gives us

\(\displaystyle \int \cos^4(\theta) \, d\theta = \dfrac{12\theta + 16 \sin(\theta) \cos(\theta) + 4 \sin(\theta) \cos(\theta) (1 - 2\sin^2(\theta))}{32} + C\)

Putting this in terms of x, we get

\(\displaystyle \int (9 - x^2)^{3/2} \, dx \\ = 81 \times \dfrac{12\arcsin\left(\frac x3\right) + 16 \times \frac x3 \times \frac{\sqrt{9-x^2}}3 + 4\times\frac x3\times\frac{\sqrt{9-x^2}}3 \left(1 - 2\left(\frac x3\right)^2\right)}{32} + C\)

\(\displaystyle \int (9 - x^2)^{3/2} \, dx = 81 \times \dfrac{12\arcsin\left(\frac x3\right) + \frac{16x\sqrt{9-x^2}}9 + \frac{4x(9-2x^2)\sqrt{9-x^2}}{81}}{32} + C\)

\(\boxed{\displaystyle \int (9 - x^2)^{3/2} \, dx = \dfrac{12\arcsin\left(\frac x3\right) + (180x-8x^3)\sqrt{9-x^2}}{32} + C}\)

If you were asking about the other integral, the first few steps are similar and you end up with the far more trivial integral and antiderivative

\(\displaystyle \frac19 \int \frac{d\theta}{\cos^2(\theta)} = \frac19 \int \sec^2(\theta) \, d\theta = \frac19 \tan(\theta) + C\)

Putting it back in terms of x, we get

\(\displaystyle \int \frac1{(9 - x^2)^{3/2}} \, dx = \frac19 \tan\left(\arcsin\left(\frac x3\right)\right) + C\)

Recall that tan(θ) = sin(θ)/cos(θ), so

\(\displaystyle \int \frac1{(9 - x^2)^{3/2}} \, dx = \frac19 \times \frac{\frac x3}{\frac{\sqrt{9-x^2}}3} + C\)

\(\boxed{\displaystyle \int \frac1{(9 - x^2)^{3/2}} \, dx = \frac{x}{9\sqrt{9-x^2}} + C}\)

Carol should decide on the average of the two anticipated numbers. She must thus decide to select  \(\frac{13}{24}\).

Probability is an area of mathematics that examines the possibility that a particular event will occur. In most cases, the probability values for the specified experiment are specified between a range of numbers. The values fall in the range of 0 and 1. A negative number cannot be the probability value. Experimental probability, also known as Empirical probability, is based on actual experiments and adequate recordings of the happening of events. For Alice's number, the anticipated value is \(\frac{1}{2}\) and the expected value of Bob's number is \(0.5*[\frac{1}{2} +\frac{2}{3} ]\). Carol should pick the middle between these two projected figures to increase her chances of winning. She must thus choose \(0.5*[\frac{1}{2} + \frac{7}{12} ]\) = \(\frac{13}{24}\). Alternatively, once we recognize that the answer lies in the interval \((\frac{1}{2},\frac{7}{12} )\), it is straight forward that she has chosen the right number.  

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Answer:

Step-by-step explanation:

the answer is 2250 percent is = 22.5

Answer:

18% discount

Step-by-step explanation:

Percent discount is found by the following formula:

\(\frac{original-discount}{original}\)

In this scenario, the original is 12500 and the discount, or special is 10250.

We can plug this into the formula to get

\(\frac{12500-10250}{12500}\)

We can simplify the numerator by subtracting, and we get that answer as 2250.

We get the remainder of the answer as 2250 divided by 12500. We divide that, and get the answer as 0.18, which can be rewritten as 18%.

Answer:

x = -1

Step-by-step explanation:

Step 1: Write equation

-4(-5x + 2) - 3x - 5 = -30

Step 2: Solve for x

Distribute -4: 20x - 8 - 3x - 5 = -30

Combine like terms: 17x - 13 = -30

Add 13 on both sides: 17x = -17

Divide both sides by 17: x = -1

Answer:

x = -1

Step-by-step explanation:

invere operation

−4(−5x+2)−3x−5= -30

20x - 8 -3x - 5 = -30

17x -13 = -30

17x = -17

x = -1

Answer:

This isnt even a question, wheres the rest of it?

Answer:

The angles combined together are 200, so you will have to subtract the difference of 200 and 180 from the combined angles. The angle of line JKL is 160 degrees.

Step-by-step explanation:

Please mark as brainliest!

Answer:

The measure of angle JKL is 97 degrees.

Step-by-step explanation:

Triangles A and triangle E is the right angle triangle, and triangles B, C, and D are not right-angle triangles.

It is defined as a triangle in which one angle is 90 degrees and the other two angles are acute angles. In a right-angled triangle, the name of the sides are hypotenuse, perpendicular, and base.

We know the Pythagoras theorem:

\(\rm Hypotenuse^2= perpendicular^2+base^2\)

Applying in Pythagoras theorem in the triangle A:

\((\sqrt{5})^2= (\sqrt{3})^2 +(\sqrt{2} )^2\)

5 = 5

Triangle A is the right-angle triangle.

For triangle B:

(√5)² = (√4)²+ (√3)²

5 ≠ 7

Triangle B is not the right-angle triangle

Similarly for triangle C:

16 + 25 ≠ 36

Not a right-angle triangle

For  triangle D:

25 + 25 ≠ 49

Not a right angle triangle

For triangle E:

100 = 36 + 64

It is a right-angle triangle.

Thus, triangles A and triangle E is the right angle triangle, and triangles B, C, and D are not right-angle triangles.

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Answer:

Aircraft A: 403 seats

Aircraft B: 298 seats

Step-by-step explanation:

Let's x represent the seats in Aircraft B

We have the equations:

Aircraft A: (x + 105)

Aircraft B: x

We Know

Their total number of seats is 701; find the number of seats for each aircraft.

We Take

x + (x + 105) = 701

2x + 105 = 701

2x = 596

x = 298 seats

So, there are 298 seats in Aircraft B

Aircraft A has how many seats?

We Take

701 - 298 = 403 seats

So, there are 403 seats in Aircraft A

Final Answers:

Aircraft A: 403 seats

Aircraft B: 298 seats

Answer:

Scott

Step-by-step explanation:

you got it right, -20 absolute value is 20

1) Examining that right triangle, and deriving from the similarity ratios, we can write down the following formulas:

Note that in this equation, we are not taking into consideration the negative 10 as a possible result since dimensions can only be written as positive numbers.

2) Now, with the length of the height (n) we can find the length of that hypotenuse m using this formula:

And that is the answer.