The side lengths of a 30-60-90 triangle are in the ratio 1: √3:2. What is
cos 60°?

Answer:

142

Step-by-step explanation:

Definition: an = a1 + f × (n-1)

Sequence: 9, 16, 23, 30, 37, 44, 51, 58, 65 ...

Common Difference: +7

The sum of all numbers up through the 20th: 1510

20th value: 142

Hope this helps! :)

Answer:

The first expression, (5^2*x^6*y^(-7))(5*x^0*y^28)

Step-by-step explanation:

Basically, add up the exponents for each unique base. We have two exponents with bases of 5 in this expression, 5^2 and 5 (which is equal to 5^1). Add the exponents together to get 3, so you have 5^3 = 125.

Add up the exponents for bases of x this time. We have x^6 and x^0. 6 + 0 = 6, so we have x^6.

Finally add up the exponents for bases of y. We have y^28 + y^(-7) = 28 + (-7) = 21, so we have y^21.

Answer:

18.85

Step-by-step explanation:

C=2πr

2(pi)3=18.85

Answer:

3x + 6 =27

Step-by-step explanation:

A. The solution is 7! First I Subtracted 6 from both sides of the equation, Then I Divided both sides of the equation by the same term. Then I got "7" from doing the following.

B. The solution is the x in the answer which is the amount of juice he poured.

"Diego has 27 ounces of juice. He pours equal amounts for each of his 3 friends and has 6 ounces left for himself"

Answer:

11

Step-by-step explanation:

6x3

=18

-2

=16

divided by 4

=4

+7

=11

Answer:13.5

Step-by-step explanation:

6x3-2/4+7

First multiply 6 and 3. Then divide 2 and 4.

18-0.5+7

Then subtract 0.5 from 18 and add 7

18-0.5= 16.5

16.5+7= 13.5

Answer:

15

Step-by-step explanation:

Vcone = πr²h/3

125π = πr²(3r/3)

π cancels out, 3 cancels out leaving:

125 = r³

r = ∛125 = 3

h = 3r = 3 x 5 = 15

Answer:

2/35

Step-by-step explanation:

[tex]\frac{9}{35}-\frac{1}{5}=\frac{9}{35}-\frac{7}{35}=\frac{2}{35}[/tex]

(A)  The system of equations is,

6A + 3S = $51          

9A + 6S = $90    

(B) The price of one adult ticket is $4 and the price of one student ticket is $9.

What is system of equations?

A set of one or more equations involving numerous variables is referred to as a system of equations. The variable mappings that satisfy all component equations are the solutions to systems of equations, or the points where the components of these equations intersect.

Given:

Juan's school is selling tickets to the annual talent show.

On the first day of ticket sales the school sold 6 adult tickets and 3 student tickets for a total of $51.

The school took in $90 on the second day by selling 9 adult tickets and 6 student tickets.

Let A be the number of adult tickets sold.

S be the number of students ticket sold.

⇒ 6A + 3S = $51            ..(1)

9A + 6S = $90              ..(2)

Multiply first equation by (2)

12A + 6S = $102            ..(3)

Subtract equation (2) and (3)

   12A + 6S = $102

-   9A + 6S = $90

________________

   3A        = 12

⇒ A = $4

Plug A = 4 in equation (1)

6(4) + 3S = $51

24 + 3S = $51

3S = $51 - $24

3S = $27

S = $9

Hence,

(A)  The system of equations is,

6A + 3S = $51          

9A + 6S = $90    

(B) The price of one adult ticket is $4 and the price of one student ticket is $9.

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The total square footage of the house is 3776 square feet.

What is dimension?

A database of research grants called Dimensions connects funding to publications, clinical trials, and patents as well as other outcomes. Dimensions is a part of the technology firm Digital Science, which has its global headquarters in London, United Kingdom.

Given:

The dimensions of each room are,

Living room = 20 ft x 15 ft

Kitchen = 12 ft x 10 ft

Bedroom 1 = 12 ft x 12 ft

Bedroom 2 = 12 ft x 10 ft

Bathroom = 8ft x 12 ft

So, the total square footage is,

(20 + 12 + 12 + 12 + 8) ft x (15 + 10 + 12 + 10 + 12) ft = 64 ft x 59 ft = 3776 square feet.

Hence, the total square footage of the house is 3776 square feet.

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Answer:

a

Step-by-step explanation: becasue i said so

Answer:

d) B => b. 0

Step-by-step explanation:

Now we have to,

→ find the y-intercept of the line.

Formula we use,

→ y = mx + b

→ b = y-intercept

Then the y-intercept is,

→ y = mx + b

→ y = (-2/3)x + 0

→ [ b = 0 ]

Hence, the y-intercept is 0.

Answer:

the answer is 2

Step-by-step explanation:

Answer:

Step-by-step explanation:

It is 2, because it is the only factor that can go with both of the numbers.

Answer:

write the given equation in a standard form

6x - 2y = 6

-2y = -6x + 6

y = 3x - 3

m = 3

if the lines are perpendicular to each other the product of their gradient is equal to -1

m1 × m2 = -1

3 × m = -1

3m = -1

m = -1/3

y - y1 = m(x - x1 )

y - (-1) = -1/3 ( x - (-3) )

y + 1 = -1/3 (x + 3 )

y + 1 = -1/3x - 1

y = -1/3x - 1 + 1

y = -1/3x

Applying the alternate interior angles theorem, the measure of angle FBC is determined as: 67°.

If two angles are alternate interior angles formed along a transversal on two parallel lines, then their measures are congruent or the same.

Angles on a straight line are angles that lie along a straight line, and the sum of the angles equals 180 degrees.

Given the following:

m∠BFC = 75°

m∠GFC = 38°

∠EFB, ∠BFC,  and ∠GFC are angles on a straight line, therefore:

m∠EFB = 180 - m∠BFC - m∠GFC

Plug in the values

m∠EFB = 180 - 75 - 38

m∠EFB = 67°

Find the measure of angle FBC:

Angles FBC and EFB are alternate interior angles, therefore:

m∠FBC = m∠EFB = 67° [alternate interior angles theorem]

m∠FBC = 67°

In summary, using the alternate interior angles theorem, the measure of angle FBC is determined as: 67°.

The gross pay of worker this week is $432.325

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

Number of money made in one hour = $ 14.35

Number of hours, worked on Monday = 8 hours

Number of hours, worked on Tuesday = 1/2 hours

Number of hours, worked on Wednesday = 8¾ hours

Number of hours, worked on Thursday = 4 hours

Number of hours, worked on Friday = 8¼ hours

Total number of worked = 4 + 8 + 8¼ + 8¾ + 1/2

                                             = 29.5

Total gross pay = 14.35 × 29.5

                         = $432.325

Thus, The answer is $432.325

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The experiment is the development of a new soft drink

From the question, we understand that:

The Fresno Mall plans to survey teenagers about a newly developed soft drink

This implies that the experiment is the survey of teenagers for a new soft drink

Also from the question, we have:

The teens will be asked to compare it with their favourite soft drink

In terms of preference, one outcome could be "Prefer this new drink"

Also from the question, we have:

The teens will be asked to compare it with their favourite soft drink

In terms of preference, one event could be "The event that 5 of 10 teenagers prefer this new drink to their favourite drink"

Using the question as a guide, a survey could be:

In a survey of 500 randomly selected adults, 68% of the respondents think that the government should require parents to have their children vaccinated.

Here, we have:

Probabilities, in this scenario are used to determine the proportions of outcomes, events and it is used to make informed decisions

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The value of the expression 10⁹ by the repeated multiplication will be 1,000,000,000.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

The expression is given below.

⇒ 10⁹

The value of the expression by the repeated multiplication will be given as,

⇒ 10⁹

⇒ 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10

⇒ 1,000,000,000

The value of the expression 10⁹ by the repeated multiplication will be 1,000,000,000.

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Answer:

  9. see below for proof; θ ∈ {45°, 135°, 225°, 315°}

  11. see below for proof; x ∈ {109.47°, 250.53°}

Step-by-step explanation:

You want to prove two trig identities, then use those to solve trig equations.

It is often useful to use the identities ...

(i) Doing that here, we get ...

  [tex]2\tan^2\theta \sin^2 \theta=1\\\\2\dfrac{\sin^2\theta}{\cos^2\theta}\sin^2\theta=1\qquad\text{replace tan}\\\\\dfrac{2\sin^4\theta}{1-\sin^2\theta}=1\qquad\text{replace $\cos^2$}\\\\2\sin^4\theta=1-\sin^2\theta\qquad\text{multiply by $(1-\sin^2\theta)$}\\\\2\sin^4\theta+\sin^2\theta-1=0\qquad\text{put in standard form}[/tex]

(ii) Substituting x=sin²(θ), we have the quadratic ...

  2x² +x -1 = 0

The quadratic formula gives the solutions as ...

  x = (-1 ±√(1 -4(2)(-1)))/(2(2)) = (-1±3)/4 = -1, 1/2

The value of sin(θ) is the square root of these values. √-1 is imaginary, so does not give us any solutions. √(1/2) = (±√2)/2, corresponding to ...

  sin(θ) = (±√2)/2

  θ ∈ {45°, 135°, 225°, 315°}

(i) Substituting as suggested above, we have ...

  [tex]\dfrac{\sin x\tan x}{1-\cos x}=1+\dfrac{1}{\cos x}\\\\\dfrac{\sin^2 x}{\cos x(1-\cos x)}=\qquad\text{substitute for $\tan x$}\\\\\dfrac{1-\cos^2 x}{\cos x(1-\cos x)}=\qquad\text{substitute for $\sin^2 x$}\\\\\dfrac{1+\cos x}{\cos x}=1+\dfrac{1}{\cos x}\qquad\text{cancel the common factor}\\\\1+\dfrac{1}{\cos x}=1+\dfrac{1}{\cos x}\qquad\text{Q.E.D.}[/tex]

(ii) Using this result, the equation can be written ...

  (1 +1/cos(x)) +2 = 0

  1/cos(x) = -3 . . . . . . . . . subtract 3

  x = arccos(-1/3) . . . . . . . solve for x

  x ∈ {109.47°, 250.53°} . . . . approximately

The scientific notation of the decimal number 0.0005682 is 5.682×10⁻⁴

A number system is defined as a system of writing to express numbers.

The given decimal number is 0.0005682.

We need to convert to the scientific notation.

Scientific notation is a way of expressing numbers that are too large or too small to be conveniently written in decimal form.

The decimal number 0.0005682 is too small. So we are converting it to the scientific notation.

If we take the decimal value to the right side of 5.

Then scientific notation of  0.0005682 is 5.682×10⁻⁴.

Hence,  5.682×10⁻⁴ is the scientific notation of the decimal number 0.0005682.

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The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. Graph C represents the equation y = x + 5.

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

Let the equation be y = x + 5

The values of m = 1 and b = 5

The slope of the line exists the value of [tex]$$m_r$[/tex] and the y-intercept exists the value of b.

Slope: 1 and y-intercept: (0, 5)

Any line can be graphed utilizing two points. Select two x values, and plug them into the equation to estimate the corresponding y values.

Create a table of the x and y values.

x           y

0          5

1           6

Graph the line utilizing the slope and the y-intercept, or the points.

Slope: 1

Therefore, the correct answer is option b) Graph C.

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Answer:

y = -8x + 10.

Step-by-step explanation:

The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept. In this case, the slope is -8 and the y-intercept is (0, 10), so the equation is y = -8x + 10.

Jakes shipping box.

Volume of box = W * L * H

Volume of box = 4 * 12 * 8

= 48 * 8

= 384

Volume of havanas shipping box

W = 2

L = 6

H = 4

Volume of box = 2 * 6 * 4

= 48

384 / 48 = 8

Jake's box has 8 times more volume than Havana's box.

Hope this helps :)

If you need any more explanation, feel free to ask.  If this really helps, consider marking brainliest.

- Jeron

Answer:

Nun, ich denke, das ist die Hoffnung, dass dies wirklich hilft und sich daran erinnert, dass nur Jesus rettet

Step-by-step explanation:

Danke!

The graph of the function x = [tex]e^t[/tex], y = [tex]e^{3t} +4[/tex] has been shown

The rectangular equation is [tex]y = x^3+4[/tex]

What is graph of a function?

A function from A to B is a rule that assigns to each element of A a unique element of B. A is called the domain of the function and B is called the codomain of the function.

There are different operations on functions like addition, subtraction, multiplication, division and composition of functions.

Graph of a function f(x) is the collection of all points of the form (x, f(x))

x = [tex]e^t[/tex], y = [tex]e^{3t} +4[/tex]

[tex]x^3 = e^{3t}[/tex]

So the required curve  in rectangular equation is

[tex]y = x^3+4[/tex]

The graph has been given

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The equation of a line is given by y = mx + c

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

Example:

The slope of the line y = 2x + 120.

The slope of a line that passes through (4,440) and (6,560) is 0.676.

We have,

The equation of the line y = mx + c.

The line passes through (4,440) and (6,560).

This means,

We can find the slope using the coordinates (4,440) and (6,560).

Slope = m

m = (4,440) / (6,560)

m = 0.676

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The aggregate volume of the two rectangular prisms is 330 cubic cm.

The base's area multiplied by the height gives the rectangular prism its volume. So the formula for a rectangular prism's volume is as follows. Using cubic units, the volume of a rectangular prism = length × breadth × height

The volume is going to be the addition of two volumes.

We are going to divide the shape into two.

Volume = length × breadth × height

Section A and section B

Volume = length × breadth × height

Volume of section A is = 2 × 10 × 9

Volume of section A = 180 cm³

Volume = length × breadth × height

Volume of section B is = 3 × 5 × 10

Volume of section B = 150cm³

Total volume = volume of section A + volume of section B

Total volume = 180cm³ + 150cm³

Total volume = 330cm³

The complete question is:

The figure below is made of 2 rectangular prisms.

What is the volume of this figure?

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Answer:$24

Step-by-step explanation: if she started with $60 and she bought 4 neckless with the cost of each $9 we get so $9x4 is 36

$60-$36=24

$24

Answer:

length = 8 yds

width = 5.5 yds

Step-by-step explanation:

Area of rectangle = l * w

w = width

length = 2w - 3

Substitute l with 2w - 3:

(2w - 3)*w = 44

2w² - 3w = 44

2w² - 3w - 44 = 0

Solve for w (AC method):

2w² + 8w - 11w - 44 = 0

2w(w + 4) - 11(w + 4) = 0

(2w - 11)(w + 4) = 0

w = 5.5 or w = -4

note: length cannot be negative, so w = 5.5 yds

Substitute w with 5.5 in either equation:

5.5 * l = 44 yds²

l = 44/5.5 = 8 yds

or

l = 2(5.5) - 3

l = 11 - 3 = 8 yds

The length of the other side is  4x⁻².6y⁻².9z .

How to calculate area of rectangle ?

The area of a rectangle is equal to its length times its width. Follow the steps mentioned below to find the area of a rectangle:

Step 1: Note the dimensions of length and breadth from the given data.

Step 2: Find the product of length and breadth values.

Step 3: Give the answer in square units.

Given :

Area = 40x.6y.9z

length of one side = 10 x ³y ³

∵Area of rectangle = length ˣ breadth

∴ 40x.6y.9z  = 10 x ³y ³  × length of other side

length of other side =  [tex]\frac{40x.6y.9z}{10 x^{3} y^{3} } = 4x^{-2} . 6y^{-2} . 9z[/tex]

Hence , the length of the other side is  4x⁻².6y⁻².9z .

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