Find A and B if Cos(A - B) = (sqrt(3))/2 ; Sin(A + B) = 1​

Answer:

[tex] (\frac{{m}^{2} }{4} )\pi[/tex]

Step-by-step explanation:

we can find the radius from the diameter by dividing the diameter by 2 (radius is half the diameter)

the formula for the area of a circle is r²π (with r being radius) but since we must use diameter we have to replace r with (m/2)

this gives us our new formula of (m/2)²π, which simplifies to (m²/4)π

that is the answer

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The angle of depression is 35 degree in the right angle triangle if the angle BAC is 55 degree.

Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.

We have shown a right-angle triangle in the picture.

In the right angle triangle, ABC

The angle BAC = 55 degree

Angle BAA' = 90 degree

In the figure, the angle of depression = CAA'

= BAA' - BAC

= 90 - 55

= 35 degree

Thus, the angle of depression is 35 degree in the right angle triangle if the angle BAC is 55 degree.

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There are 11 elements are in (A U B)

The given parameters are:

n(A) = 4

n(B) = 7

The number of elements in (A U B) is calculated using:

n(A U B) = n(A) +n(B) - n(A U B)

Given that the sets have distincts elements, we have:

n(A U B) = 4 + 7 - 0

Evaluate

n(A U B) = 11

Hence, there are 11 elements are in (A U B)

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Answer: There are 11 elements are in (A U B)

Step-by-step explanation:

The question requests proof that WV = VR. See the definition of Mathematical proof and the explanation for the proof below.

Mathematical proof refers to the steps of logical arguments which are given to show that a mathematical statement is true or correct.

Reason: This is given. The image is a parallelogram.

Therefore if  ΔSVR ≅ PVW;

Then WV = VR.

QED.

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Answer:#1 A, #2 B

Step-by-step explanation:

Heres the proof

The inequality which represents this is x ≥ 22 , Option C is the right answer.

When two algebraic expressions are equated using an inequality operator, <, > etc then the expression formed is called Inequality.

IT is given in the question that

There is a number line , with points marked for eighteen, nineteen, twenty, twenty one, twenty two, twenty three.

The twenty two point is marked with an open circle pointing left

The inequality which represents this is

x ≥ 22 , Option C is the right answer.

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Answer: x (x - 1)

Step-by-step explanation:

[tex]2x^{2} - x^{2} -x[/tex]

[tex]x^{2} -x[/tex]

x (x - 1)

Step-by-step explanation:

coordinates of center is 0,0 there are no hints given to find radius

Answer:

all rhombuses are parallelograms, all trapezoids are quadrilaterals 

Step-by-step explanation:

rhombuses have all equal sides, 2 sets of parallel lines and are a diamond shape. a quadrilateral is a shape with 4 sides (quad means 4) therefore, all rhombuses are parallelograms. we know that all trapezoids have 4 sides, so we can conclude that all trapezoids are quadrilaterals i hope this helped because i know that end of year tests are super hard.

Answer:

p=Parentheses

e=Exponents

m=Multiplication

d=Division

a=Addition

s=Subtraction

its an order of solving a equation

The function f(x) = 2|x – 2| + 6 has a vertex at (2, 6) option second is correct.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have a function that has vertex at (2, 6)

The options are:

f(x) = 2|x – 2| – 6

f(x) = 2|x – 2| + 6

f(x) = 2|x + 2| + 6

f(x) = 2|x + 2| – 6

As we know the vertex form of a quadratic function is given by:

f(x) = a(x - h)² + k

Similarly, mod function  can be expressed as:

m(x) = a|x - h| + k

Here (h, k) is the vertex of a function.

In the function:

f(x) = 2|x – 2| + 6

The vertex of the function is (2, 6)

Thus, the function f(x) = 2|x – 2| + 6 has a vertex at (2, 6) option second is correct.

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The interval where |q| will fall will be[ 12√2−7√3,∞ ).

A complex number is an element of a number system that contains the real numbers and a specific element.

In this case, p and q are complex numbers such that |p|=7√3 and |p+q|=12√2. The interval where |q| will fall will be[ 12√2−7√3,∞ ).

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Area of sector

option B

Answer:

b

Step-by-step explanation:

The area of a sector is (the angle) over 360 multiplied by pi (radius) squared

This would be 45/360 pi (4.5) squared, resulting in option b.

Answer:

Step-by-step explanation:

we know that

Solve for x

so

therefore

The number of pounds of apples is 4.5 and the number of pounds of grapes is 2.5

The area of the trapezoid is 284.31 square inches

The area of a trapezoid is:

Area = 0.5 * (Sum of parallel sides) * height

Using the given figure, we have:

Area = 0.5 * (17 + 31.6) * 11.7

Evaluate

Area = 284.31

Hence, the area of the trapezoid is 284.31 square inches

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Answer: 6 children

Step-by-step explanation:

Given:

Children - 24

Groups - 4

Number of children per group - x

Solve:

24 ÷ 4 = x

x = 6

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Answer:

180

Step-by-step explanation:

Find the value of x and the measure of angleMNQ.

3x − 11°62°

The value of x is

90

° and the measure of angleMNQ is

180

°.

Answer:

Hi,

a=b+3

Step-by-step explanation:

[tex]\begin{array}{c||c|c|c|c}&x^3&x^2&x&1\\---&---&---&---&---\\&1&-a&b&c\\x=-1&&-1&a+1&-a-b-1\\---&---&---&---&---\\&1&-a-1&a+b+1&c-a-b-1\\\end{array}[/tex]

[tex]\begin{array}{c||c|c|c|c}&x^3&x^2&x&1\\---&---&---&---&---\\&1&-a&b&c\\x=2&&2&4-2a&2b+8-4a\\---&---&---&---&---\\&1&2-a&b+4-2a&c+2b+8-4a\\\end{array}[/tex]

Thus:

c+2b+8-4a=c-a-b-1

3b-3a=-9

a=b+3

Answer:

C

Step-by-step explanation:

-4x+2<6

-4x<4

x<-1

because the sign doesnt have a line under it, it is an open hole

Answer:

  g(x) = -√(x+6)

Step-by-step explanation:

The inverse of the function y = f(x) can be found by solving for y the relation x = f(y).

__

  x = f(y)

  x = y^2 -6

  x +6 = y^2 . . . . . . add 6

  -√(x +6) = y . . . . . negative square root

The negative root produces y ≤ 0, equivalent to x ≤ 0 for f(x).

The inverse of f is g(x) = -√(x +6).

_____

Additional comment

The graph of a function and its inverse are mirror images of each other across the line y=x. This is shown in the attachment for the f(x) and g(x) in this problem.

Answer:

8.25 feet

Step-by-step explanation:

to find the width, you divide the area by the length

103 1/8 / 12 1/2 = 8.25

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Hope this helps :)

Answer: [tex]109^{\circ}[/tex]

Step-by-step explanation:

The exterior angles of a polygon add to 360 degrees, so the sixth angle measures [tex]360-39-47-42-59-64=\boxed{109^{\circ}}[/tex]

Answer:

The median of the data is 12.

Step-by-step explanation:

The median is really just another word for the average. To find that, you add all of the numbers and divide that sum by the number of numbers there are.

9+15+17+18+6+20+8+5+18+18+10+5+14+12+10+7=192

There are 16 numbers in this data set. So, we will divide the sum by 16.

192÷16=12

I hope this helps!! :)

Answer:

Hi,

Step-by-step explanation:

Using the pythagorean theorem , let's calculate the apothem of a side:

a²=26²-10²=57=24²

Area of a side: 24*10*2/2=240 (ft²)

Lateral area=240*4=960(ft²)

Area of the base: 20²=400 (ft²)

Total area=1360(ft²)

Answer:

Right Triangles

Step-by-step explanation:

Answer:

If you entered the function correctly there is not a range  

Step-by-step explanation:

Answer: {y|-♾<y<0}

Step-by-step explanation: i’m taking this summer school class

Using it's formula, it is found that the value of the monthly payment for the loan to buy the drum set is of $50.32.

It is given by:

[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]

In which:

In this problem, the parameters are given as follows:

P = 1800, r = 0.1525, n = 4 x 12 = 48.

Hence:

r/12 = 0.1525/12 = 0.01270833.

Hence, the monthly payments will be of:

[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]

[tex]A = 1800\frac{0.01270833(1 + 0.01270833)^{48}}{(1 + 0.01270833)^{48} - 1}[/tex]

A = 50.32.

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Differentiating each function, we have for all x, unless otherwise indicated,

[tex]h(x) = 2^x - 1 \implies h'(x) = \ln(2) \, 2^x > 0[/tex]

[tex]g(x) = -4 (2^x) \implies g'(x) = -4 \ln(2) \, 2^x < 0[/tex]

[tex]f(x) = -3x+7 \implies f'(x) = -3 < 0[/tex]

[tex]j(x) = x^2 + 8x + 1 \implies j'(x) = 2x + 8 > 0 \text{ only when } x > -4[/tex]

and only h(x) has a strictly positive derivative. (A)