if theta is an angle in standard position and it’s terminal side passes through the point (-3,2) find the exact value of cos theta in simplest radical form. NO TROLLS ANSWER FULLY WITH DETAIL AND EXPLANATION!!!!

The statement that is equivalent to |6x-3|=3 is: 6x-3=3 or 6x-3=-3

For the equation to be true, two scenarios need to be considered:

When the expression 6x-3 is positive and equals 3:

6x-3 = 3

When the expression 6x-3 is negative and equals -3:

6x-3 = -3

By solving these two equations, we can find the equivalent statement:

Solving 6x-3 = 3:

Adding 3 to both sides gives us:

6x = 6

Dividing both sides by 6:

x = 1

Solving 6x-3 = -3:

Adding 3 to both sides gives us:

6x = 0

Dividing both sides by 6:

x = 0

Therefore, the equivalent statement to |6x-3|=3 is:

6x-3=3 or 6x-3=-3, which can be further simplified to:

6x-3=3 or 6x-3=-3

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The length of the arc are

Arc MN =  72 degrees

Arc NQR = 180 degrees

Arc NQ = 108 degrees

Arc MRP =  193 degrees

Arc QR = 72 degrees

Arc QMR = 288 degrees

Arc PQ = 13 degrees

Arc PRN = 265 degrees

Arc MQN = 288 degrees

The relationship between central angle and intercepted arc is that they are equal. This is used in solving the length of arcs

hence we have that

angle ROQ = angle NOM =  72 degrees (vertical angles)

Arc MN = angle NOM =  72 degrees

Arc NQR = 180 degrees (semicircle)

Arc NQ

angle POQ = 180 - 72 - 95

angle POQ = 13

Arc NQ = 95 + 13 = 108 degrees

Arc MRP = 180 + 13 = 193 degrees

Arc QR = 72 degrees

Arc QMR = 360 - 72 = 288 degrees

Arc PQ = 13 degrees

Arc PRN = 360 - 95 = 265 degrees

Arc MQN = 360 - 72 = 288 degrees

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Answer:

1.5

Step-by-step explanation:

Answer:

B. 6

Step-by-step explanation:

Sub in 2 for x:

4² - (2+8)

4² - (10)

16-10

6

Answer:

A. \( 4\sqrt{6} \)

Step-by-step explanation:

Applying the leg rule which is:

\( \frac{Hypotenuse}{leg} = \frac{leg}{part} \)

Hypotenuse = 4 + 8 = 12

Leg = x

Part = 8

Plug in the values

\( \frac{12}{x} = \frac{x}{8} \)

Cross multiply

\( x*x = 8*12 \)

\( x^2 = 96 \)

\( \sqrt{x^2} = \sqrt{96} \)

\( x = \sqrt{16 * 6} \)

\( x = 4\sqrt{6} \)

Step-by-step explanation:

2 Triangles are congrant So AB = DE

so,5 X +2 = 8X _10

3x = 12

X=4 ⇒....1

FE = BC

so,3y -7 = 8

3 y = 15

y= 5 ⇒ . ... 2

Answer:

9 7/8

Step-by-step explanation:

1. 4 3/8 can be converted into the improper fraction 35/8, and 5 1/2 can be converted into 11/2.

2. Now that we have 35/8 + 11/2, we have to find a common denominator. Since 2 goes into 8 four times, we can turn 11/2 into 44/8 by multiplying the numerator and denominator (the top and the bottom numbers) by 4.

3. Now we have 35/8 + 44/8. At this point, the all we have to do is add the numerators (the top numbers). 35+44=79, so our answer is 79/8, which we can simplify to 9 7/8.

Answer:

42.5

Step-by-step explanation:

(180-95)÷2=42.5

Answer: The is down there

Step-by-step explanation: Glad to help but hope it helps you.

The method that will not give the correct number of inches is that the total length of the plant in a week is 19/4 inches.

Length of the small plant = 2 1/2 = 5/2 inches

Rate of growth = 3/4 inches

Increase in length in 3 weeks will be:

= 3 × 3/4 = 4

Total length = 5/2 + 9/4

= 19/4 inches.

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Answer: 180 gallons needed

Step-by-step explanation:

Zykeith,

Assume x gallons of 50% antifreeze is needed

Final mixture is x + 60 gallons

Amount of antifreeze in mixture is 0.4*(x+60)

Amount of antifreeze added is .5x + .1*60 = .5x + 6

so .5x + 6 = .4(x + 60)

.5x -.4x = 24 -6

.1x = 18

x = 180

Let x be the number of gallons of the 50% antifreeze solution needed. We know that the resulting mixture will be 70 + x gallons. To get a 40% antifreeze mixture, we can set up the following equation:

\({\implies 0.5x + 0.1(70) = 0.4(70 + x)}\)

Simplifying the equation:

\(\qquad\implies 0.5x + 7 = 28 + 0.4x\)

\(\qquad\quad\implies 0.1x = 21\)

\(\qquad\qquad\implies \bold{x = 210}\)

\(\therefore\) We need 210 gallons of the 50% antifreeze solution to mix with 70 gallons of 10% antifreeze to get a mixture that is 40% antifreeze.

\(\blue{\overline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}}\)

Without explicitly solving for x, we can conclude that the solution to the equation 2^x - 2 = 8^4 is x = 12.

To solve the equation 2^x - 2 = 8^4 without explicitly solving for x, we can simplify the equation using exponent rules and observe the relationship between the numbers.

First, let's simplify the equation:

2^x - 2 = 8^4

We know that 8 can be expressed as 2^3, so we can rewrite the equation as:

2^x - 2 = (2^3)^4

Applying the exponent rule (a^m)^n = a^(mn), we can simplify further:

2^x - 2 = 2^(34)

Simplifying the right side of the equation:

2^x - 2 = 2^12

Now, we can observe that both sides of the equation have the same base, which is 2. In order for the equation to hold true, the exponents must be equal:

x = 12

Therefore, we may deduce that the answer to the equation 2x - 2 = 84 is x = 12 without having to explicitly solve for x.

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Answer:

57 thousands

5.7 ten thousands

fifty seven thousand

The equivalent expression of 28p⁹q⁻⁵/12p⁻⁶q⁷ is 7p¹⁵/3q¹².

Expression

In math, an expression is combination of numbers, symbols, coefficients, fraction, indeterminants, etc. and it is mostly not found in equal to form.

Given,

Here we have the expression 28p⁹q⁻⁵/12p⁻⁶q⁷.

Now, we have to find the equivalent expression for this one.

Here the given expression is written as,

=> 28p⁹q⁻⁵/12p⁻⁶q⁷  

Now, We have collected variable having positive power in numerator and  negative power in denominator, then we get,

=> 28p⁹p⁶/12q⁵q⁷

Here we have to add the powers of p and q because base are same and they are in multiplication.

Then we get the value as,

=> 28p¹⁵/12q¹²

When simplify this one then we get,

=> 7p¹⁵/3q¹²

I HAVE ANSWERED THE QUESTION IN GENERAL AS GIVEN QUESTION IS INCOMPLETE.

Complete question:

Find the equivalent expression for the equation 28p⁹q⁻⁵/12p⁻⁶q⁷.

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Answer:

8,13,21

Step-by-step explanation:

Basically,add the previous number to next number

Answer:8,13,21

Step-by-step explanation:

The python function is, [1, 4, 9, 16, 25] [1, 4].

What is square of a number?

It is easy to determine a number's square. To determine the given number's square, we must multiply it by itself. A number raised to the power of 2 is always used to represent the square term.

For instance, the square of 6 is equal to 6 times 6, or 6 x 6 = 6^2 = 36.

A "Square Number" is the product of multiplying an integer or number (not a fraction) by itself.

For instance, 3 x 3 = 3^2, or 3 multiplied by 3 equals 3 squared. In essence, a square number is the result of multiplying an integer or number by itself exponentially.

Hence, the python function is, [1, 4, 9, 16, 25] [1, 4].

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80km / 48 min = 1 2/3 km per minute.

1 2/3 km per minute x 60 minutes(1 hour) = 100 km per hour

the correct option is C.

"Her calculations are wrong because there should only be 0.5 inches of paper left over."

We know that the dimensions of the paper are 8.5 inches by 11 inches.

Now, she wants to cut it into 2 inch by 11 inch strips.

Now, notice that if you have 4 of these strips, the width will be:

W = 4*2in = 8in

If we subtract this to the original width, we get:

8.5in - 8in = 0.5in

So what she should got is 0.5 instead of 3, then we conclude that the correct option is C.

"Her calculations are wrong because there should only be 0.5 inches of paper left over."

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Answer:

11y is the exact value.

Step-by-step explanation:

Answer: The length of the prism is 8 yards

Step-by-step explanation:

First, take the volume of the prism, divide it by the width (2 1/2). Once you get that divide that answer by height (5 3/4) getting you the length of the prism (8 yards)

Answer:

25

Step-by-step explanation:

Since both angles are complementary, then Angle 1 + Angle 2 = 90°

Using algebra,

let Angle 2 be X and Angle 1 be (2X + 21°)

Now we have an equation of,

( 2X + 21 ) + X = 90°

step 1 : open up the brackets first.

step 2 : bring 21° to the other side (rmb to flip the sign)

step 3 : bring the 3 over n it becomes " ÷3 "

( 2X + 21° ) + X = 90°

2X + 21° + X = 90°

3X = 90° - 21°

X = ( 90° - 21° ) ÷ 3

= 23°

Sub X=23° into Angle 1 ( 2X + 21° ),

2(23°) + 21° = 67°

Therefore,

Angle 1 = 67°

i hope my solution helps :))

The correct answer is 180 oranges

Explanation:

In mathematics, a ratio expresses two or more numbers that are related. In the case fo the ration 9: 40 this expresses 9 oranges are used to serve fruit salad for 40 people. Now, if you need to determine what is the number of oranges not for 40 people but for 800 people you can use cross multiplication. This process is explained below:

\(\frac{9}{40} = \frac{x}{800}\)   - 1. Multiply  9 x 800 and 40 x x (cross multiplication)

\(7200 = 40x\) - 2. Solve the equation by diving 7200 into 40

\(\frac{7200}{40} = x\)

\(x = 180\) - 3. 180 represents the number of oranges to serve 800 people, which   can be expressed as 180: 800

Answer:

24

Step-by-step explanation:

Answer:

$6.76

Step-by-step explanation:

A.  The payback period is 7.2 years. The net present value of the proposed investment is 3720.55.

B. No, the project does not meet the company's cash payback criteria.

C.  Yes, the project does meet the net present value criteria for acceptance.

A. The truck costs $55,440 and generates annual cost savings of $7,700. So the payback period is the cost of the truck divided the expected amount the truck will generate.

                $55,440 / $7,700 = 7.2 years

To solve for the net present value, we say

Net Present Value = ∑ [(Cash inflow in period t) / (1 + \(r^{t}\)] - Initial Investment.

NPV = (($7,700 / (1 + 0.08)¹) = 7 129.63

+ ($7,700 / (1 + 0.08)²) = 6601.51

+ .($7,700 / (1 + 0.08)³ = 6112.51

+ ($7,700 / (1 + 0.08)⁴) = 5659.73

+ ($7,700 / (1 + 0.08)⁵) = 5240.49

+ ($7,700 / (1 + 0.08)⁶) = 4 852.31

+ ($7,700 / (1 + 0.08)⁷) = 4492.88

+($7,700 / (1 + 0.08)⁸)  = 4160.07

+ ($27,600 / (1 + 0.08)⁸)) = 14911.42

- $55,440

We add all these values together and subtract by  $55,440

7 129.63 + 6601.51 + 6112.51 + 5659.73 + 5240.49 +4 852.31 + 4492.88 + 4160.07 + 14911.42 - $55,440

59160.55 - 55,440

NPV = 3720.55

B. The cash payback period of the project is 7.2 years. The company's cash payback criteria state that a project should not be accepted unless it has a payback period that is less than 50% of the asset's estimated useful life, which would be 4 years which is 50% of 8 years. Since 7.2 years is greater than 4 years, the project does not meet the company's cash payback criteria.

C. The positive NPV of $3,720.55 shows that embarking on the prooject will be valuable to the company. This means the project meets the NPV criteria for acceptance.

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The y-intercept of the line of fit is approximately 43.94 fluid ounces.

What is Probability ?

Probability can be defined as ratio of number of favourable outcomes and total number of outcomes.

The answer is 35. If the theoretical probability of drawing two yellow socks is one fifth, then the experimental probability of drawing two yellow socks in one trial with replacement is also one fifth. Therefore, out of 175 trials, the number of times he will select two yellow socks can be predicted by multiplying the number of trials by the experimental probability: 175 * (1/5) = 35.

No, because for each input there is not exactly one output. The relation is not a function because for the input x = -5, there are two possible outputs: y = 1 and y = -1. Therefore, the relation violates the vertical line test, which requires that every vertical line intersects the graph at most once for the relation to be a function.

The y-intercept of the line of fit is approximately 43.94 fluid ounces. To find the y-intercept, we can look at the point where the line of fit intersects the y-axis (i.e., when x = 0). From the equation of the line of fit, we can see that the y-coordinate when x = 0 is approximately 43.94, which represents the initial amount of diet soda in the machine before it starts to be purchased.

Therefore,  The y-intercept of the line of fit is approximately 43.94 fluid ounces.

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