P is a point on the terminal side of θ in standard position. Find the exact value of the six trigonometric functions for θ.
18. P(-3, 2)
19. P(4, -2)
20. P(0, -6)
21. P(-3, -4)

Answer:

[tex]x=-\frac{39}{2}\\ y=51[/tex]

Step-by-step explanation:

[tex]8x+4y=48\\12x+5y=21[/tex]

Let's solve the first equation for x or y. I'll do it for y.

[tex]8x+4y=48[/tex]

Subtract 8x

[tex]4y=-8x+48[/tex]

Divide by 4.

[tex]y=-\frac{8}{4}x+\frac{48}{4}\\[/tex]

Simplify.

[tex]y=-2x+12[/tex]

Now replace the value of y in the second equation for this.

[tex]12x+5y=21\\12x+5(-2x+12)=21[/tex]

Distribute 5

[tex]12x-10x+60=21[/tex]

Subtract 60

[tex]12x-10x=21-60[/tex]

Combine like terms;

[tex]2x=-39[/tex]

Divide by 2.

[tex]x=-\frac{39}{2}[/tex]

Now replace this in any of the equations to find the value of y.

[tex]8x+4y=48\\8(-\frac{39}{2})+4y=48\\[/tex]

8 and 2 can be simplified.

8/2=4

2/2=1

[tex]4(-39)+4y=48[/tex]

Distribute 4.

[tex]-156+4y=48[/tex]

Add 156

[tex]4y=48+156\\4y=204[/tex]

Divide by 4

[tex]y=\frac{204}{4}[/tex]

[tex]y=51[/tex]

Proof:

[tex]8x+4y=48\\8(-\frac{39}{2} )+4(51)=48\\4(-39)+204=48\\-156+204=48\\48=48[/tex]

Answer:

5/6

Step-by-step explanation:

Answer: 8.54701% difference

Step-by-step explanation: (61-56)/[(61+56)/2] x 100= 8.55%

Answer:

x=-5.5

Step-by-step explanation:

-3(x+4)=(-x-1)

1. Distribute

-3x+(-12)=-x-1

2. Simplify

-3x-12=-x-1

-2x-12=-1

-2x=11

x=-11/2

x=-5.5

Answer:

-11/2 or 5.5

Step-by-step explanation:

Answer:

divide both sides by 2

Step-by-step explanation:

divide both sides by 2 then simplify and get x = 9 over 32

Answer:

Transposing square to rhs,it becomes root

Step-by-step explanation:

[tex]x^{2} =9/16[/tex]

[tex]x=[/tex][tex]\sqrt{9}/\sqrt{16\\[/tex] (transposing square to rhs,it becomes root)

[tex]x= 3/4[/tex]

Hope it helps...Pls mark as Brainliest!!!

Answer:

D; D

Step-by-step explanation:

The common difference of the first sequence is 10, so the coefficient is 10. The first term minus the common difference is -8, so that is the constant

The common difference of the second sequence is 3, so the coefficient is 3. The first term minus the common difference is -9, so that is the constant.

Answer:

Slope = 4, y-intercept = (0,0)

Step-by-step explanation:

This problem is written in slope-intercept form. Meaning it is in the form y=mx+b. "M" is the slope, and "B" is the y-intercept. With that information, we easily see that 4 is the slope of the graph (it will go up 4 points for everyone one point it goes right). It seems that there is no y-intercept though, that is because we are expected to know that y=4x is the same as y=4x+0. Meaning, the problem can also be written this way and the y-intercept must be 0.

Answer:

[tex]763 ft^3[/tex] or 763 cubic feet.

Step-by-step explanation:

The tank is cylindrical and the volume of a cylinder is given as:

[tex]V = \pi r^2h[/tex]

where r = radius and h = height

The radius, r, of the tank is 4.5 ft and the height, h, of the tank is 12 ft.

Therefore, the volume of the cylindrical water tank is:

[tex]V = \pi * 4.5^2 * 12\\V = 763.407 ft^3[/tex]

Approximating to whole number, the volume of the tank is [tex]763 ft^3[/tex] or 763 cubic feet.

Answer:

The answer is 9/4

Step-by-step explanation:

Answer:

475

Step-by-step explanation:

1021-71

950/2

Answer:F

Step-by-step explanation:

Answer:

i honestly think that its A, C, D, F.

Step-by-step explanation:

for the A i think that you need to write down the facts so you dont forget and you remember when someone asks you a question.

For C you should gather your resources so you can do the experiment again if your not satisfied with the first result.

For D you should draw a diagram so you can keep track of your information that you used to get the final solution.

For F, you should always make sure that you didn't mess up and that you can redo it to double check.

Answer:

x < 4

Step-by-step explanation:

12 – 5x > -8

Subtract 12 from each side

12-12 – 5x > -8-12

-5x> -20

Divide each side by -5, remembering to flip the inequality

-5x/-5 < -20/-5

x < 4

Answer:

Step-by-step explanation:

interest = Amount - principal

A = P(1+r)^t

r = 5.5% = 5.5/100 = 0.055

A = 1663(1+ 0.055)^19

A = 1663 (1.055)^19

A = 4,599.270812203411

Let’s say A = 4,599

interest = 4,599-1663 = 2,936

Answer: The value of x is 479

Step-by-step explanation:

x -14 = 465

   +14     +14

x=  479

Answer:

x=479

Step-by-step explanation:

x-14=465 Move constant to the right-hand side and change its sign

x=465+14 add the numbers

x=479

HOPE THIS HELPS :)

The four integers are 7, 7, 8, 10

Four integers are a, b, c, d

Mean = Sum of integers/Total number of integers

         = (a+b+c+d)/4

According to the question,

Mean = 8

i.e. (a+b+c+d)/4 = 8

⇒ a+b+c+d = 32 ......(1)

Median (for even no. of integers) = ([tex]\frac{n}{2}^{th} +(\frac{n}{2}+1)^{th}[/tex] term)/2

                                                       = (2nd+3rd term)/2

                                                       = (b+c)/2

According to the question,

Median = 7.5

i.e. (b+c)/2 = 7.5

⇒ b+c = 15  .....(2)

We know that, most frequent data is the mode.

So, mode = 7 means the number 7 occurs most frequently.

7 is not more than 2 times, because if 7 occurs 3 times, then 2nd & 3rd term will be 7 & median will be (7+7)/2 i.e. 7, so 3rd term must be larger than 7 to adjust the median value, which is 7.5

Then 1st two integers are 7 & 7

i.e. a = b = 7

Now, from (2), b+c = 15  

                    ⇒ 7+c=15

                    ⇒ c =15-7

                    ⇒ c = 8

Now, from (1) we get, a+b+c+d = 32

                                 ⇒ 7+7+8+d = 32

                                 ⇒ 22+d = 32

                                 ⇒ d = 32-22

                                 ⇒ d = 10

So, a = 7, b = 7, c = 8, d = 10

Learn more about mean, median, mode here :

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Answer: 101

Step-by-step explanation:

45 women total

17 women will not watch the game

So 33 people did not want to watch the game and 17 are women

33-17 = 16 men who won’t watch the game

So 40 men who will and 16 men who won’t equals 56 men and 45 women

56+45= 101

Answer:

The pizza parlors cost the same when delivering 4 pizzas.

Step-by-step explanation:

For each store, the total price is

cost of pizzas + cost of delivery

The cost of delivery is just a fixed number for each store, $20 or $12.

The cost of the pizzas is the price of a pizza multiplied by the number of pizzas.

Let x = number of pizzas

The cost of the pizzas is

Jacob's: 10x

Ashley's: 12x

Jacob's total cost (pizzas + delivery):

10x + 20

Ashley's total cost (pizzas + delivery):

12x + 12

We want the total costs to be the same, so we set our two total cost expressions equal and solve for x.

12x + 12 = 10x + 20

Subtract 10 from both sides.

2x + 12 = 20

Subtract 12 from both sides.

2x = 8

Divide both sides by 2.

x = 4

Answer: The pizza parlors cost the same when delivering 4 pizzas.

Answer:

84.1% of all values in a normal distribution have z ≤ 1.00.

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question:

The percent of all values in a normal distribution for which z ≤ 1.00.

This is the pvalue of Z = 1.

Z = 1 has a pvalue of 0.8413.

Converting to percentage, to the nearest tenth.

84.1% of all values in a normal distribution have z ≤ 1.00.

Answer: x = 9, y = 5

Step-by-step explanation:

If all of the sides are equal, it is an equilateral triangle. Equilateral triangles are also equiangular. The angles of a triangle add up to 180 degrees, so each angle must equal 60 degrees.

set the equation equal to 60 to solve for x

7x - 3 = 60

add three to both sides

7x = 63

divide both sides by 7

x = 9

find y by setting the equation equal to 60

11y + 5 = 60

subtract 5 from each side

11y = 55

divide both sides by 11

y = 5

Answer:

7/16 or (if you are looking for a word) likely

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

To find how much you can get for one dollar, you have to divide 9 by 3. If you have to find how many units can you get for one dollar, (you need to divide the larger number by the smaller)

Divide 9 by 3.

9/3=3

So, with $1, you can get 3 chicken wings.

Answer:

P(A) x P(B) = 35 x 13 = 455

P(A∩B) = 18

=> P(A) x P(B) ≠ P(A∩B).

=> A and B are not independent.

=> Option A (No, because 35(13)≠18) is correct.

Hope this helps!

:)

A and B are not independent because 35(13)≠18), the correct option is A

Independent events and probability can be defined as those occurrences that are not dependent on any specific event.

P(A)=35, P(B)=13, and P(A∩B)=18, are A and B independent.

It is to note here that A and B are the odd number outcome and multiples of 3 respectively. So, P (A ∩ B) = 18

P(D│E) = P (D ∩ E)/ P(B)

P(D│E) = 18/13

Here P(D) = P(D│E) = 18/13, which entails that the occurrence of event E will not be affected by the probability of event D’s occurrence.

Taking A and B as independent events, then P(D│E) = P(D).

Here, A and B are not independent because 35(13)≠18), the correct option is A.

Learn more about probability here;

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Answer: [tex]m=\frac{1}{9}[/tex]

Step-by-step explanation:

[tex]\frac{9}{7}m=\frac{1}{7}[/tex]

Multiply by the reciprocal to isolate m.

[tex](\frac{7}{9} )\frac{9}{7}m=\frac{1}{7}(\frac{7}{9} )[/tex]

[tex]m=\frac{1}{9}[/tex]

Answer:

Beth made 60% of her shots.

Step-by-step explanation:

Given:

Total shots take = 10

Total goal = 6

Find:

Best describer this number.

Computation:

Converting goal numbers into percentage:

⇒ Total goal percentage = [Total goal/Total shots take]100

⇒ Total goal percentage = [6/10]100

⇒ Total goal percentage = 60%

Beth made 60% of her shots.

Answer:

6:10 is the ratio

Step-by-step explanation:

as a fraction it would be 6/10

as a decimal it would be 0.60 or 0.6

and she made 60% of her shots

Answer:

x = 2

y = 6 1/3

Step-by-step explanation:

5x - 6y = -32

3x + 6y = 48

-----------------

8x = 16

x = 2

5(2) - 6y = 48

10 - 6y = 48

-6y = 48 - 10

-6y = 38

y = 6 1/3

Answer:

Step-by-step explanation:

−189=4x−3(−4x+15)

−189=16x−45

16x−45=−189

16x−45+45=−189+45

16x=−144

16x /16

= −144 /16

x=−9

Good luck honey !!

Answer:

x=-9

Step-by-step explanation:

-3×-4= 12x -3×15=-45

4x+12x-45=-189

4x+12x=16x

16x-45=-189

16x=-144

x=-9