a teacher salary went from 48000 to 51360 what is the rate of increase

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y = 88° (opposite are equal)

z = 180° - 128° = 52° (straight angle = 180°)

x = 180° - 140° = 40° (straight angle = 180°)

Answer:

x=40°

y=88°

z=52°

Step-by-step explanation:

Solution Given:

x+140°=180°

Since the sum of the angle of a linear pair or straight line is 180°.

solving for x.

x=180°-140°

x=40°

\(\hrulefill\)

y°=88°

Since the vertically opposite angle is equal.

therefore, y=88°

\(\hrulefill\)

z+128°=180°

Since the sum of the angle of a linear pair or straight line is 180°.

solving for z.

z=180°-128°

z=52°

People at the concession stand as input Cost of their order's output.

(1) The relation in question is a function.

(II) This function is not constant. (Each category of concession has a different order cost.)

Not a 1-1 function (iii). (Several persons arrived seeking the same sort of concession. So they all pay the same price for their order.)

A function describes the relationship between patrons' inputs at the concession stand and the cost of their order as an output. A function is a relationship between a set of possible inputs and outputs, where each input is associated to exactly one output.

The quantity of patrons at the concession stand serves as the input in this scenario, while the cost of their order serves as the output.

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Answer:

right π/2

Step-by-step explanation:

The function f(x) = 2sin(x - π/2) is a sine function with a period of 2π, an amplitude of 2, and a phase shift of π/2. The phase shift of π/2 causes the graph of the function to be shifted π/2 units to the right. .

Therefore, the correct answer is right π/2

The composite function f·g(x) is 4x⁴+24x³.

The given functions are f(x)=x²+6x and g(x)=4x².

We need to find f·g(x).

We know that, f·g(x)=f(x)×g(x)

Here, f·g(x)=(x²+6x)×4x²

= x²×4x²+6x×4x²

= 4x⁴+24x³

Therefore, the composite function f·g(x) is 4x⁴+24x³.

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Answer:

Use the given functions to set up and simplify 3.2 % . 5 = 0 = 3.2 % = 0.032 40 mo = 0.032

Step-by-step explanation:

Answer: 1.5/2 and backwards-1.5/-2

Step-by-step explanation: rise over run

Answer:

24.5

Step-by-step explanation:

Answer:

14 weeks

Step-by-step explanation:

Simply divide 200 by 15, then round up because the answer should be a full week:

200 / 15 = 13.3333 ≈ 14 weeks

For an equation, let x be weeks passed and y be money left. Since the money is spent at a constant rate, the equation will have a constant slope, and the y intercept is 200, since at no money spent, Micah has $200:

y = -15x + 200

For a ratio table, it might look something like this:

weeks  :  money

0       :      $200

1        :      $185

2       :      $160

3       :      $145

Answer:

v= -15x + 200 x 213.33 weeks 6= 15x + 200 the answer is 13

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Step-by-step explanation:

3x + 2y = 9

- (3x + y = 6)

=> y = 3.

Therefore 3x + (3) = 6, 3x = 3, x = 1.

The solutions are x = 1 and y = 3.

Answer:

2401

Step-by-step explanation:

2x³+4x²+1                                      x = 10

2(10)³ + 4(10)² + 1

2(1000) + 4(100) + 1

2000 + 400 + 1

2401

Answer:

The slope of the tangent line to the curve at the given point is -11/7.

Step-by-step explanation:

Differentiation is an algebraic process that finds the gradient (slope) of a curve.  At a point, the gradient of a curve is the same as the gradient of the tangent line to the curve at that point.

Given function:

\(4x^2+5xy+y^4=370\)

To differentiate an equation that contains a mixture of x and y terms, use implicit differentiation.

Begin by placing d/dx in front of each term of the equation:

\(\dfrac{\text{d}}{\text{d}x}4x^2+\dfrac{\text{d}}{\text{d}x}5xy+\dfrac{\text{d}}{\text{d}x}y^4=\dfrac{\text{d}}{\text{d}x}370\)

Differentiate the terms in x only (and constant terms):

\(\implies 8x+\dfrac{\text{d}}{\text{d}x}5xy+\dfrac{\text{d}}{\text{d}x}y^4=0\)

Use the chain rule to differentiate terms in y only. In practice, this means differentiate with respect to y, and place dy/dx at the end:

\(\implies 8x+\dfrac{\text{d}}{\text{d}x}5xy+4y^3\dfrac{\text{d}y}{\text{d}x}=0\)

Use the product rule to differentiate terms in both x and y.

\(\boxed{\dfrac{\text{d}}{\text{d}x}u(x)v(y)=u(x)\dfrac{\text{d}}{\text{d}x}v(y)+v(y)\dfrac{\text{d}}{\text{d}x}u(x)}\)

\(\implies 8x+\left(5x\dfrac{\text{d}}{\text{d}x}y+y\dfrac{\text{d}}{\text{d}x}5x\right)+4y^3\dfrac{\text{d}y}{\text{d}x}=0\)

\(\implies 8x+5x\dfrac{\text{d}y}{\text{d}x}+5y+4y^3\dfrac{\text{d}y}{\text{d}x}=0\)

Rearrange the resulting equation in x, y and dy/dx to make dy/dx the subject:

\(\implies 5x\dfrac{\text{d}y}{\text{d}x}+4y^3\dfrac{\text{d}y}{\text{d}x}=-8x-5y\)

\(\implies \dfrac{\text{d}y}{\text{d}x}(5x+4y^3)=-8x-5y\)

\(\implies \dfrac{\text{d}y}{\text{d}x}=\dfrac{-8x-5y}{5x+4y^3}\)

To find the slope of the tangent line at the point (-9, -1), substitute x = -9 and y = -1 into the differentiated equation:

\(\implies \dfrac{\text{d}y}{\text{d}x}=\dfrac{-8(-9)-5(-1)}{5(-9)+4(-1)^3}\)

\(\implies \dfrac{\text{d}y}{\text{d}x}=\dfrac{72+5}{-45-4}\)

\(\implies \dfrac{\text{d}y}{\text{d}x}=-\dfrac{77}{49}\)

\(\implies \dfrac{\text{d}y}{\text{d}x}=-\dfrac{11}{7}\)

Therefore, slope of the tangent line to the curve at the given point is -11/7.

Answer: a) 2401  b) 840 c)343  d)343  e) 686

Step-by-step explanation:

a) Total are 7 letters

There are 4 possible places in 4-letter word for each of 7 letter.

So total amount of the words is

7*7*7*7= 2401

b) No letter can be repeated mens that in 1st place can stay any of 7 letters,

in 2-nd place- any of 6 letters

in 3-rd place- any of 5 letters

in 4-th place any of 4 letters

Total amount of words is

7*6*5*4=840

c)  It is not written if the letters can be repeated. Assume that they can.

1st place occupied by letter A. So at 2-nd, 3-rd and 4th places can stay any of 7 letters

Total amount of words is

1*7*7*7=343

d) Similar case like c). At 1-st ,2-nd, 3-rd can stay any of 7 letters, and at 4th place the letter C (1 letter). Total amount of words is

7*7*7*1=343

e) There are 2 vowels A and E.  

So at 1st place can stay any of 7 letters, at 2-nd place -any of 2 letters, at 3-rd place- any of 7 letters and at 4th place any of 7 letters. Total amount of words is

7*2*7*7=686

The total number of 4-letter words possible is 2401

The total number of 4-letter words possible with no letter repeated is 840

The total number of 4-letter words possible with the first letter being A is  343

The total number of 4-letter words possible with the letter C at the end is 294.

The total number of 4-letter words possible with the second letter being a vowel is 1029.

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.com

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

(a) No condition is imposed:

There are 7 choices for the first letter, 7 choices for the second letter, 7 choices for the third letter, and 7 choices for the fourth letter.

The total number of 4-letter words possible.

7 × 7 × 7 × 7 = 2401

(b) No letter can be repeated in a word:

For the first letter, there are 7 choices.
For the second letter, there are only 6 choices left (since we cannot repeat the first letter). Similarly, for the third letter, there are only 5 choices left, and for the fourth letter, there are only 4 choices left.

The total number of 4-letter words possible with no letter repeated.

7 × 6 × 5 × 4 = 840

(c) Each word must begin with the letter A:

For the first letter, there is only 1 choice (the letter A). For the second letter, there are 7 choices (since any letter can be used).

For the third letter, there are 7 choices, and for the fourth letter, there are 7 choices.

The total number of 4-letter words is possible with the first letter being A.

1 × 7 × 7 × 7 = 343

(d) The letter C must be at the end:

For the fourth letter, there is only 1 choice (the letter C).

For the first letter, there are 7 choices (since any letter can be used).

For the second letter, there are 7 choices, and for the third letter, there are 6 choices (since the letter C cannot be used).

The total number of 4-letter words possible with the letter C at the end.

7 × 7 × 6 × 1 = 294

(e) The second letter must be a vowel:

For the first letter, there are 7 choices (since any letter can be used). For the second letter, there are 3 choices (the vowels A, E, and I).

For the third letter, there are 7 choices, and for the fourth letter, there are 7 choices.

The total number of 4-letter words possible with the second letter being a vowel.

7 × 3 × 7 × 7 = 1029

Thus,

The total number of 4-letter words possible is 2401

The total number of 4-letter words possible with no letter repeated is 840

The total number of 4-letter words possible with the first letter being A is  343

The total number of 4-letter words possible with the letter C at the end is 294.

The total number of 4-letter words possible with the second letter being a vowel is 1029.

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Answer: the distance is 8

Step-by-step explanation:

Answer:

The distance between numbers is given by the absolute difference between them:

|(-2)-(6)|= 8. Hence, the distance between -2 and 6 on the number line is 8.

Answer: 5850 milliliters

Step-by-step explanation:

First, you have to do 0.65L x 9 days = 5.85L

And then you have to convert it to milliliters so:

5.85L= 5850 milliliters

The missing step of the solution is : Simplify by combining like terms: Option A

You should understand that these are the terms that contain the same variable which has the same power.

The  given question,

In step 2, the left side of the equation is  3/2 - 2x

We get 3/2  by adding 1/2 and 1 on the left side of the equation  1/2-2x+1=-13/2

As  1/2 and 1 are constants and all constant terms are like terms.

The second step would be simplify by combining like terms.

Therefore, the missing step of the solution is : Simplify by combining like terms.

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Answer:

64

Step-by-step explanation:

split it in half den it is two rectangles and they are both 32 so 32 * 2 is 64

Answer:

2x^3-5x^2-28x+15 -------------------------expanded

2x^3-5x^2-28x+15--------------------simplified

Step-by-step explanation:

\left(2x-1\right)\left(x+3\right)\left(x-5\right)

=2x^2x+2x^2\left(-5\right)+5xx+5x\left(-5\right)-3x-3\left(-5\right)

simplyfied

\left(2x^2+5x-3\right)\left(x-5\right)

=2x^2x+2x^2\left(-5\right)+5xx+5x\left(-5\right)-3x-3\left(-5\right)

=2x^3-5x^2-28x+15

Using the concept of word problems and quadratic equation it will take 1 year until the sum of square of their ages be 45.

Word problems are mathematical problems that are delivered in ordinary words, instead of mathematical symbols.

Part of the problem with dealing with word problems that they first need to be translated into mathematical equations, and then the equations need to be solved.In this problem;

let x represent the number of years from now when the sum of square of their respective age will be

45.(x + 2)² + (x + 5)² = 45

Expanding the brackets;

x² + 4x + 4 + x² + 10x + 25 = 45

2x² + 14x + 29 = 45

2x² + 14x + 29 - 45 = 0

2x² + 14x - 16 = 0

Solving the quadratic equation for x;

x = 1, x = -8

Taking the positive value, the value of x is 1

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Answer:

D) Multiply

Explanation:

The word "of" usually means you multiply.

Answer:

57% = 0.57 in decimal form.

Step-by-step explanation:

57% = 0.57 in decimal form. Percent means 'per 100'. So, 57% means 57 per 100 or simply 57/100. If you divide 57 by 100, you'll get 0.57 (a decimal number).

The extremas of the function f(x) = x³ - 7x² + 10x are given as follows:

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Answer:

  x = 3

Step-by-step explanation:

Maybe you want the value of x such that ...

  4(6^x) = 864

Dividing by 4 gives ...

  6^x = 216

You may know that 216 = 6^3. Using that, we can equate exponents:

  6^x = 6^3

  x = 3

Alternatively, we can use logarithms to find x. Taking logs gives ...

  x·log(6) = log(216)

  x = log(216)/log(6) = 3

Answer:

AB/2 = 6 and 12 = AB

Step-by-step explanation:

Answer: (6,11π/6).

Step-by-step explanation:We need to find the radius r and the angle θ. Remember that r2=x2+y2, so

because of the signs of x and y, our angle is in quadrant IV. Therefore, we find that θ=11π/6.

So the final answer is (6,11π6).

Answer:

.764

Step-by-step explanation:

do it on a calculator (TI84)

Answer:

45.6°

Step-by-step explanation:

take the inverse cosine of 7/10: \(cos^{-1}(\frac{7}{10})\)

plug it into a graphing calc and you get ≈ 45.573°, they want 1 decimal place so it would be ≈ 45.6°

The volume of the figure with two rectangular prisms would be 1, 728 ft ³

.

To find the volume of the figure with the two rectangular prisms, you can find the volume of the individual rectangular prisms and then add them up.

Volume of rectangular prism 1:

= Length x Width x Height

= 19 x 12 x 6

= 1, 368 ft ³

Volume of rectangle prism 2:

= Length x Width x Height

= 10 x 12 x 3

= 360 ft ³

The volume of the entire figure is then :

= 1, 368 + 360

= 1, 728 ft ³

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The number 2/5 is both a ratio and a fraction.

The number 2/5 is both a ratio and a fraction. Fractions are meant to signify the numerator and denominator in an expression. in the above expression, we have the denominator as 5 and the numerator as 2.

The expression is also a ratio because it indicates the quantitative relationship between the figures.

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