Find the exact values of the indicated trigonometric functions. Write fractions in lowest terms

Answer:

5.52 billion

Step-by-step explanation:

2% s .02 in decimal    from '87 to '92 is 5 years ( the exponent in the following:

5 (1.02)^5   = 5.52 billion

Answer:

5.52 billion

Step-by-step explanation:

i got this my doing math

a)What is the value of y?   y= 6

b)The value of RS is 57 and ST is 16.

a) How is the value of y calculated?

From the number line,

RS = 9y +3

ST= 2y + 4

RT = 73

Rewriting as equation,

RT = RS + ST

73 = 9y +3 + 2y + 4

73 = 11y  + 7

11 y = 73 - 7

11y = 66

y = 66/11

y = 6

b) What is the value of RS and ST ?

Considering the equation,

RS = 9y + 3

     =9(6) +3

     =54 +3

RS = 57

Considering the equation,

ST = 2y + 4

     =2(6) +4

     = 12 +4

ST = 16

What is an equation?

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All groups of animals could be found in temperate grasslands.

Mammals including wolf, prairie animals, reindeer, mice, coyotes, wolves, and jackrabbits are among the inhabitants of this biome. Starlings, sparrows, owls, raptors, and quails are some of the birds found in this biome. The most common insects are grasshoppers and snakes.

All groups of animals could be found in temperate grasslands.

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A parallelogram is an easy quadrilateral with two pairs of parallel aspects. the other or dealing with facets of a parallelogram are of equal length and the other angles of a parallelogram are of equal measure. Hence, proved  p + q = r.

A parallelogram has four sides overall and two pairs of facets that might be parallel. A square is a parallelogram that has four equal sides. the other facets are parallel and all corners of the rectangular shape the right attitude. A rectangle is a parallelogram that has 4 contrary, parallel, congruent aspects.

proving p + q = r;

q = ∠OCD = ∠BAO   ( alternate angle)

In Δ AOB

∠OAb  + ∠DBA = p + q -------------------(1)

& ∠AOD + ∠BOA = 180° ------------(2)

Also,

∠OAB + ∠OBA + ∠BOA = 180° --------- some of angle in a triangle.

⇒ ( p + q) + (180° - ∠BOA) = 180° --------using 1 & 2

⇒  p + q - r = 0

⇒  p + q = r

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The linear function that gives the remaining distance to Austin for a car that travels from Fort Worth at a rate of 65 miles per hour is:

y = 190 - 65x.

The general format of a linear function is defined as follows:

y = mx + b.

In which:

The parameters in the context of this problem are as follows:

Hence the equation is:

y = 190 - 65x.

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To find the GCF of an expression, find the greatest number that every term can divide by. One way we can do this is by factoring the expression.

[tex]5xy+10xy^2+5x[/tex]

Here, each term has the variable x. Factor this out by dividing each term by x:

[tex]x(5y+10y^2+5)[/tex]

Now, each term has a factor of 5. Divide each term by 5:

[tex]5x(y+2y^2+1)[/tex]

Now, there are no more common factors between each term.

Therefore, the GCF is 5x.

5x

Given:

Required:

To find the volume of the solid by using washer method.

Explanation:

Volume formula of Washer method is,

Therefore,

Final Answer:

Volume is

Check the answers below, please

1) Since we have this linear function:

a) We can proceed to state the Domain, the set of inputs for this function as:

Since this Linear function does not have any restraint or discontinuity.

b) The Range, i.e. the set of outputs for this function will be defined for this function as:

c) The Zero, can be found algebraically by plugging f(x)=0

d) Y-intercept is the point in the y-axis where the line intercepts it. Looking at the rule of the function, we can state the y-intercept as:

e) Slope, the measure of how steep a line of a function is, it's always the coefficient of x, in this case:

f) Type of slope. Since the slope is -1/3 , i.e. lesser than 0, then we can classify it as decreasing

g) Evaluating f(3):

h) The value of x, where f(x)= -4 Similarly to the previous item, we can plug into that f(x)= -4 like this:

i) The graph can be traced having the zero, the y-intercept the type of the slope we can plot this:

ANSWER

(7, 5)

EXPLANATION

We want to find the reflection image of X.

The coordinates of X is (-1, 5).

When reflecting over a vertical axis, the x coordinate changes but the y coordinate does not change.

To reflect a point (x, y) (i.e. to find the new x coordinate) across the line x = a, find the distance between a and x, then add that to a.

That is the new x coordinate.

For the question, a = 3.

Therefore, for X(-1, 5):

Adding that to a, the new coordinates are:

That is the reflection image of X.

Answer:

answer is c-(2,3)

Step-by-step explanation:

......................m

The z-score of a normal distribution is defined by

where

Then, using the formula for the z-score in our problem we have

Then the z score for that punt is 4.3.

The cost of the canvas will be 6x.

What is Equation of line?

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

The equation of line is,

⇒ y - 14 = 6 (x - 2.5)

Now,

The line represents Barry’s profit, y, from selling x painting, after buying some canvas.

Here, The equation of line is,

⇒ y - 14 = 6 (x - 2.5)

Simplify the equation as;

⇒ y - 14 = 6 (x - 2.5)

⇒ y - 14 = 6x - 15

⇒ y = 6x - 15 + 14

⇒ y = 6x - 1

Since, Barry’s profit, y, from selling x painting, after buying some canvas.

Thus, The cost of the canvas 6x.

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The product of -1/a and its reciprocal will be equal to unity or 1.

For any number [a], the reciprocal will be given by [1/a] such that -

a x 1/a = 1

Given is the following expression -

A = -1 / a

From the definition of the reciprocal of a number, the reciprocal of the number -

A = -1 / a

will be

1/A = 1/(-1/a) = -a

Now, the product of the number and its reciprocal will be -

A x 1/A = -1/a x -a = 1

A x 1/A = 1

Therefore, the product of -1/a and its reciprocal will be equal to unity or 1.

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19770609664 is simple power of 52⁶ .

What is exponent and power?

= 52⁶

= 52 × 52 × 52 × 52  × 52 × 52

=  19770609664

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Here, we are comparing Daniels's class periods and pie. They equal each other.

The required ratio is 1:1.

Given,

P-1c

Solution:

P-1c, where c is class periods and p is pies.

P-1c = 0

1p = 1c

Which means,

He bakes 1 pie per class period.

His total number of pies equals his total number of class periods.

The equation can be written in ratios

1p = 1c i.e., they are in 1:1 ratio.

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1. The equation that represents the situation is 500 + 150h = 1700

2. The number of hours used to rent the helicopter is 8 hours.

It should be noted that an equation is used to show the relationship between the variables.

In this case, John rented a helicopter, there was a one-time charge of $500, plus an hourly rate of $150 and his total for the night was $1700.

Let the number of hours be represented as h.

The equation will be 500 + 150 × h = 1700

500 + 150h = 1700

The number of hours used will be:

500 + 150h = 1700

Collect like terms

150h = 1700 - 500

150h = 1200

Divide

h = 1200/150

h = 8

The helicopter was for 8 hours.

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The option that is to equal to the ratio,  4,200 to 5,000, is 0.84

What is ratio?

Ratio mean expressing one variable as a fraction of the other variable, in this case, 4,200 is expressed as a fraction of a bigger number which is 5,000, intuitively, the correct answer in this scenario is 0.84 because when viewed in percentage terms, 4000 is 80%,hence, 4,200 is greater than 4000, it would be more 80% which is 84%, without mincing words, the computation can be done as shown below:

ratio 4,200 to 5,000=4,200/5,000

ratio 4,200 to 5,000=0.84

Invariably, as stated earlier, all the options from a-c are incorrect as they are not even up 0.80, which means 0.84 is the most appropriate

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To solve this problem we can write one equation for each condition so:

the width of a rectangle is 2 its length so:

and one for the perimeter so:

Now we replace the first equation into the second one so:

So the length of the rectangle is 90 ft

[tex]2x^{6}[/tex] is the Simplify of the expression   2x² x x³

[tex]2x^{2} xx^{3} = 2x^{6}[/tex]

what is simplify?

To simplify means to make anything basic or simpler, for example. a: to reduce to the bare minimum. b: to become simpler or broader in scope: It was advised to streamline management processes.

The fundamental guidelines and procedures to simplify any algebraic statement are as follows:

When you describe a complex mathematical idea to a child in words they can easily understand, you are simplifying. When you eliminate many of the tasks that were keeping you occupied and stressed out, you have simplified.

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Here, we are told y stands for the unknown number: Sixteen more than five times a number.​

Converting to an algebraic expression, we have:

16 + 5y

Here, y is the unknown number.

16 + 5y

The equation of the line y=-5/2x-4 is perpendicular to the given equation of the line.

Given that,

The given equation of the line is y=2/5x-1.

We have to find the equation of the line that is perpendicular to the given equation of the line.

We know Equation of the line formula,

y=mx+c

Here,

m denotes the line's slope, and c the y-intercept.

Take the equation of the line y=2/5x-1

m is 2/5

The perpendicular line is m is -5/2

We get the perpendicular line is y=-5/2x-4.

Therefore, The equation of the line y=-5/2x-4 is perpendicular to the given equation of the line.

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Answer:

182

Step-by-step explanation:

728 divided by 4 is 182.

Total gallons of water used in the park after the ride is installed

 = 9.51 * 10^5 GALLONS.

Exponent addition is the process of multiplying a number by its exponents or powers, whether or not the base is the same. Exponents, which show how many times a number can be multiplied by itself, are also known as the power of numbers. As an illustration, 3^2 = 3*3, where 3 is the base and 2 the exponent.

When the base and exponents are the same, exponents can be added. Sometimes the base and exponent will differ, but adding can still be done for certain formulas. Let's examine the procedures for adding exponents.

Step 1: Verify that the expression's terms all have the same base and exponents. 22 + 22, as an illustration. As can be seen, the exponent and base are both 2.

Step 2: Calculate the expression using individual terms if the base and exponent are different. for instance, 53 plus 42. Exponents and bases are different.

Step 3: Add the results together.

water used in the park initially                  = 8.6*10^5 gallons

water used by the additional ride added = 9.1 *10^4 gallons

                                                                    =0.91*10^5 gallons

Total gallons of water used in the park after the new ride is installed

                                                                   = (8.6*10^5 + 0.91*10^5) gallons

                                                                   = (8.6+0.91) *10^5 gallons

                                                                   = 9.51* 10^5 gallons

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Using the augmented matrix, we find that:

The first system has no solutions.

The second system has infinite solutions, given by: (-3t, 0, t).

Augmented Matrix:

An augmented matrix for a system of equations is a matrix of numbers in which each row represents the constants from one equation and each column represents all the coefficients for a single variable.

Given:

The matrix is,

[tex]\begin{bmatrix}1 & 0 & 3&| & 0 \\ 0& 1 & 1 & | & 5 \\0 & 0 & 0 & | & 1\end{bmatrix}[/tex]

Here we need to find the solution of the system.

While we looking at the first system, at the third row of the matrix, the relation is written as,

0t=1

This one is not possible, therefore, there are no solutions for the first system.

Now when we looking at the second system, the third line has the value of,

0t=1

This refers that there are infinite solutions, therefore here t is the free parameter.

From the second line, y = 5.

From the first,

=> x + 3t

=> x = -3t

The solutions are: (-3t, 0, t).

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1. The journal entries recording the transactions for Winkelvoss Inc. are as follows:

Year 1:

July 1: Debit Cash $64,222,669

Debit Bonds Discount $7,677,331

Credit Bonds Payable $71,900,000

Oct. 1: Debit Cash $420,000

Credit Bank Notes Payable $420,000

Dec. 31 Debit Interest Expense $5,250

Credit Installment Note Interest Payable $5,250

Dec. 31 Debit Interest Expense $2,708,433

Credit Cash $2,516,500

Credit Bond Amortization $191,933

Year 2:

June 30 Debit Interest Expense $2,516,500

Credit Cash $2,324,567

Credit Bond Amortization $191,933

Sept. 30 Debit Interest Expense $15,750

Debit Installment Note Interest Payable $5,250

Debit Notes Payable $61,747

Credit Cash $82,747

Dec. 31 Debit Interest Expense $4,478

Credit Installment Note Interest Payable $4,478

Dec. 31 Debit Interest Expense $2,708,433

Credit Cash $2,516,500

Credit Bond Amortization $191,933

Year 3:

June 30 Debit Bonds Payable $64,990,401

Debit Bond Redemption Premium $5,471,599

Credit Cash $70,462,000

Sept. 30 Debit Interest Expense $13,435

Debit Installment Note Interest Payable $4,478

Debit Notes Payable $64,834

Credit Cash $82,747

2. The amounts of the interest expense in Year 1 and Year 2 are as follows:

                                     Year 1             Year 2

Total interest         $2,713,683      $2,72,8661

3. The bond's carrying amount as of December 31, Year 2, is $64,798,468.

Year 1:

July 1: Cash $64,222,669 Bonds Discount $7,677,331 Bonds Payable $71,900,000

Oct. 1: Cash $420,000 Bank Notes Payable $420,000

Dec. 31 Interest Expense $5,250 Installment Note Interest Payable $5,250

Dec. 31 Interest Expense $2,708,433 Cash $2,516,500 Bond Amortization $191,933

Year 2:

June 30 Interest Expense $2,516,500 Cash $2,324,567 Bond Amortization $191,933

Sept. 30 Interest Expense $15,750 Installment Note Interest Payable $5,250 Notes Payable $61,747 Cash $82,747

Dec. 31 Interest Expense $4,478 Installment Note Interest Payable $4,478

Dec. 31 Interest Expense $2,708,433 Cash $2,516,500 Bond Amortization $191,933

Year 3:

June 30: Bonds Payable $64,990,401 Bond Redemption Premium $5,471,599 Cash $70,462,000

Sept. 30 Interest Expense $13,435 Installment Note Interest Payable $4,478 Notes Payable $64,834 Cash $82,747

                                     Year 1             Year 2

Bonds Payable      $2,708,433     $2,708,433

Notes Payable             $5,250            $15,750

Notes Payable                                      $4,478

Total interest         $2,713,683      $2,72,8661

July 1:                              $64,222,669

Dec. 31 Bond Amortization   $191,933

June 30 Bond Amortization $191,933

Dec. 31 Bond Amortization   $191,933

Dec. 31 Year 2 Carrying Amont = $64,798,468

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ANSWER

81.68 ft

EXPLANATION

The circumference of a circle = 2 * pi * r

We can translate the wording part as follows:

1. Multiply the quantity 2 more than a number by 8:

8 * (2 + n)

2. The result is at least: it means that the value is the value in question or values greater than this number, therefore, we have an inequality here ( >=).

3. The result is at least 12 times the number subtracted from 76:

76 - 12n

Therefore, the inequality that represents the description is:

Then, the correct option is C.

Answer:

a = [tex]\frac{m-q}{d}[/tex]

Step-by-step explanation:

q + ad = m ( subtract q from both sides )

ad = m - q ( isolate a by dividing both sides by d )

a = [tex]\frac{m-q}{d}[/tex]

Answer:

a = (m - q)/d

Step-by-step explanation:

Given that,

→ q + ad = m

Now solving for the value of a,

→ q + ad = m

→ ad = m - q

→ a = (m - q)/d

Hence, the value is (m - q)/d.