Convert the following rectangular equation to polar form.Assume a>0 3x^2+3y^2-4x+2y=0

The value of the trigonometric function is;  sin(A) =√51/10.

Trigonometric identities are the functions that include trigonometric functions such as sine, cosine, tangents, secant, and, cot.

We have been given that  angle A lies in Quadrant IV and cos(A)= 7/10 then;

cos(A)= 7/10

Hence, base = 7

hypotenuse = 10

Therefore, perpendicular

h² = b² + p²

10² = 7² + p²

100 = 49 + p²

p = √51

Then  sin(A = perpedicular/ hypotenuse

sin(A) = √51/10

Hence, the value of the trigonometric function is;  sin(A) =√51/10.

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         A vertex is a point on a polygon where two rays or line segments meet, the sides, or the edges of the object come together. Vertex is the plural form of vertices.

Response: C

        A node of a graph, or one of the points on which the graph is defined and which may be connected by graph edges, is referred to as a "vertex" in computing.

For instance, a rectangle's four sides result in its four vertices.

   Response:  C . The coordinates are obtained by first subtracting 1 from 4 to obtain 3 and then adding 3 to -2 to obtain 1. (3, 1)

       The vertex is the collective endpoint. Vertex, on the other hand, refers to the common terminal point where two rays converge to make an angle. In a similar manner, we must understand an angle's arm. The term "arm of an angle" refers to the two rays that unite to make an angle.

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Percent is given by the expression:

So, he is paying 74% more using the quarterly rate

solution

For this case we have the following equation:

Then we can add 5 in both sides and we got:

Then we can multiply both sides by 4/3 and we got:

And the final solution for this case is x= 12

Answer:

24.0 cm

Explanation:

To find the value of a, we will use the Law of sines, so

So, replacing A = 150°, B = 12°, and b = 10 cm, we get:

Now, we need to solve for a. First, cross multiply

Then, divide by sin12

Therefore, a = 24.0 cm

Problem N 2

we have

12x-14=8x+16

solve for x

subtract 8x both sides

12x-14-8x=8x+16-8x

4x-14=16

Adds 14 both sides

4x-14+14=16+14

4x=30

divide by 4 both sides

x=30/4

x=7.5

Problem N 4

we have

12x-14=6x+16

solve for x

subtract 6x both sides

12x-14-6x=6x+16-6x

6x-14=16

adds 14 both sides

6x=16+14

6x=30

divide by 6 both sides

x=30/6

x=5

1 sample t-test

Calculating t test statistic

Plugging in the values, we have:

t test statistic = 2.9207

degrees of freedom = n - 1 = 50 - 1 = 49

Using a calculator, we can calculate the p-value.

Since p value is less than significance level (p value < alpha), then we will reject H_0 and take the alternate hypothesis.

Thus the test suggests that the new batteries do last more than 45 hours.

E)

We could've done Type I error here.

Type I error or α: Reject the null when it’s true.

Answer:

After tax interest expenses = Interest expenses x (100 - Tax Rate) 

= 70000 x (100 - 30)% 

= 70000 x 70% 

= $49,000.00

Step-by-step explanation:

Answer:

1 comic book costs $4.5

Explanation:

Given that 8 comic books cost $36

To know how much 1 comic book costs, let x be the cost of 1 comic book, then, we have:

8 comic books = $36

1 comic book = x

Then we have the equation

8x = 36

where we can solve for x

Divide both sides by 8

8x/8 = 36/8

x = 4.5

Therefore, 1 comic book costs $4.5

Replacing with the values we already know, we have:

PV = 10,000

i = 5% or 0.05 but it is compounded monthly, then it is 0.05/12

n = 18 years or 216 months

10,000 = FV * 0.4073

FV = 10,000/0.4073

FV = $ 24,551.93

It is very close to option D, where the term "about" is included.

ANSWER

EXPLANATION

The roots are the x values where the equation intercepts the x-axis.

Given:

-2x ≥ 6

Solve for x

Divide both sides by -2

-2x/-2 ≤ 6/-2

x ≤ -3

Graph:

Interval notation (-∞, -3 ]

Answer:

y intercept= (0,-3)

slope= 2/1 or simplified 2

Step-by-step explanation:

f(7) gives 5 1/2.

the position is the 7th term

Explanation:

f(1)= 8 1/2

f(n)= f(n-1) - 1/2

we are looking for the function that gives 5 1/2

We have been given f(1), this means n = 1

f(1) = f(1-1) - 1/2

8 1/2 = f(0) - 1/2

f(0) = 8 1/2 + 1/2

f(0) = 8 + 1 = 9

when n = 2

f(2) = f(2-1) - 1/2

f(2) = f(1) - 1/2

f(2) = 8 1/2 - 1/2

f(2) = 8

when n = 3

f(3) = f(3-1) - 1/2

f(3) = f(2) - 1/2

f(3) = 8 - 1/2

f(3) = 7 1/2

when x = 4

f(4) = f(4-1) - 1/2

f(4) = f(3) - 1/2

f(4) = 7 1/2 - 1/2

f(4) = 7

when n = 5

f(5) = f(5-1) - 1/2

f(5) = f(4) - 1/2

f(5) = 7 - 1/2

f(5) = 6 1/2

f(6) = f(6-1) - 1/2

f(6) = f(5) - 1/2

f(6) = 6 1/2 - 1/2 = 6

when n = 7

f(7) = f(7-1) - 1/2

f(7) = f(6) - 1/2

f(7) = 6 -1/2 = 5 1/2

f(7) gives 5 1/2.

Hence, the position is the 7th term

Given the sum of the functions expressed as:

Collecting the like terms:

Group the terms based on their degrees

Simplify the result to determine the final answer:

Hence the required sum of the functions is x^2 - 3x + 7

Notice that the number of students that got a grade below 80 is:

and the total number of students is:

Therefore, we have to determine what percentage 7 represents from 20. To determine the percentage that x represents from y, we can use the following expression:

Finally, we get that 7 represents the

of 20.

Answer:

Using the area of the rectangle we know that 80½ tiles will be needed to cover the wall.

So, tiles needed to cover the wall:

Calculate the area of a tile as follows:

Now, calculate the area of the wall as follows:

Then, tiles needed to cover the wall:

Which means: 80½

Therefore, using the area of the rectangle we know that 80½ tiles will be needed to cover the wall.

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The solution of the linear system of three simultaneous equations is presented as follows; x = 2, y = 1 and z = 4

Simultaneous system of equations consists of a finite set of equations for which a solution to the equation system is required.

The linear system of three equations can be presented as follows;

13•x - 17•y + 16•z = 73...(1)

-11•x + 15•y + 17•z = 61...(2)

46•x + 10•y - 30•z = -18...(3)

The above system of equations can be solved using common multiples of the coefficients as follows;

Multiply equation (2) by 2 and equation (3) by 3 to get;

2 × (-11•x + 15•y + 17•z) = 2 × 61 = 122

3 × (46•x + 10•y - 30•z) = 3 × (-18) = -54

Subtracting equation (4) from equation (5) gives;

138•x + 30•y - 90•z - (-22•x + 30•y + 34•z) = -54 - 122 = -176

138•x - (-22•x) + 30•y - 30•y - 90•z - 34•z = -176

160•x - 124•z = -176

40•x - 31•z = 44

[tex] \displaystyle {z = \frac{(44 + 40\cdot x)}{31}}[/tex]

Plugging in the value of z in equation (1) and (2) gives;

1043•x - 527•y + 704 = 73 × 31 = 2236...(6)

Which gives;

[tex] \displaystyle {y = \frac{(1043\cdot x - 1559)}{527}}[/tex]

339•x + 465•y + 748 = 61 × 31 = 1891...(7)

Which gives; [tex] \displaystyle {y = \frac{(381 - 113\cdot x )}{155}}[/tex] which gives;

[tex] \displaystyle { \frac{(1043\cdot x - 1559)}{527}= \frac{(381 - 113\cdot x )}{155}}[/tex]

Therefore; 221216•x - 442432 = 0

x = 442432 ÷ 221216 = 2

x = 2

y = (1043×2 - 1559)÷527 = 1

y = 1

z = (44 + 40×2) ÷ 31 = 4

z = 4

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First let's find the amount Sonia puts in her account each week.

To do so, let's find the amount increased between weeks 5 and 10:

The account increased $25 in 5 weeks, so for each week, we have:

So Sonia puts $5 in her account each week. Now, we need to find the initial value in the account. If after 5 weeks the account has $45, we can subtract $45 by 5 times the amount per week:

So the initial amount is $20.

Now that we have the initial amount and the amount she puts per week, we have the following equation for the amount of money y after x weeks:

So the correct option is the third one.

0.0404

Repeating decimal (periodic)

1) Let's proceed with the long division of 4 by 99:

1.1) Since 4 is way smaller than 99 let's add one zero to the dividend and another for the quotient followed by a dot.

But 40 is still lesser than 99, so let's add another zero after the dot to make it 400. Now we can divide 400 by 99

1.2) Again to proceed with that division we'll need to write a zero at that 4 and another one in the quotient.

As and we can see already this a repeating decimal or periodic. This division will yield 0.0404040404.....

2) Hence, the answer is 0.0404

Answer: 35.8

Step-by-step explanation: 40x?=1432

40x35.8=1432

The Hooke's law is given by:

F = k*x

Where:

F = force

k = constant factor

x = distance

If F = 20 and x = 20

20 = k*20

Solving for k:

20/20 = k

k = 1

So: how far will a 29 pound mass stretch the spring?

29 = 1* x

Solving for x:

29/1 = x

x = 29 in

Answer

Check Explanation

Explanation

The laws of logarithms will come in handy in helping to obtain the points for the log from its inverse.

Before we commence, the two laws of logarithms that we will be using is that

log₄ 4ᶜ = c (log₄ 4)

And

log₄ 4 = 1

So, no matter the value of inverse given, a simple mathematical evaluation will give the log points.

when x = 1

f(x) = log₄ x

f(1) = log₄ 1 = log₄ 4⁰ = 0 log₄ 4 = 0 × 1 = 0

when x = 4

f(x) = log₄ x

f(4) = log₄ 4 = log₄ 4¹ = 1 (log₄ 4) = 1 × 1 = 1

when x = 16

f(x) = log₄ x

f(16) = log₄ 16 = log₄ 4² = 2 (log₄ 4) = 2 × 1 = 2

when x = 64

f(x) = log₄ x

f(64) = log₄ 64 = log₄ 4³ = 3 (log₄ 4) = 3 × 1 = 3

Hope this Helps!!!

Given,

Multiplying equation (ii) by 2 as it make the coefficent of x in both equation equal.

Substracting equation (i) from equation (iii) then we get,

The value of y is -2.

Substituting the value of y in equation (i) then,

Hence, the solution of the linear pair (x, y) is (3, -2).

The function being one-to-one implies that every value of x, has one one vaue of y, and every value of y, has one value of x.

The inverse uses the output(y value) as an input(x value) and spits it out to get the original x value inputted into f.

Using the given point ( 2, -5 ), it implies of f(2) = -5. Since the function is one-to-one, this implies that:

Hence, the correct option is option B

The first complement of the binary addition is 00011111.

The binary addition operation works similarly to the base 10 decimal system, except that it is a base 2 system. The binary system consists of only two digits, 1 and 0.

Given that, the addition of the given number

  00011101 + 11111101

In the binary addition,

0+1 = 1

1+0 = 1

1+1 = 0

00011101 + 11111101 = 11100000

Then inverse code means first complement of the answer.

In the first complement, 0 is the inverse of 1 and 1 is inverse of 0.

11100000 = 00011111

Hence, The first complement of the binary addition is 00011111.

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EXPLANATION

we are asked to use the long division method to solve the division

We will have

Given:

The trinomial equation is given as,

The objective is to choose the correct value for which the factors are to be obtained for factorization.

Explanation:

From the step 1, to perform the factorization the values of a and c has to be multiplied.

Then in step 2, the factors need to be calculated for the product of a and c.

Product of a and c :

The product of a and c will be,

Thus, factors are to be listed for the number 21.

Hence, option (1) is the correct answer.