Mathematics High School

Use the given point on the terminal side of angle 0 to find the value of the trigonometric function indicated.
1)tan0;(10,-18)
2)tan0;(4,3)

Answers

Answer 1
1 is tan 0 = -18/10 = -9/5
2 is tan 0 = 3/4

In general, an angle with a terminal side on the point (x, y) the tan of that line is the fraction y/x

Related Questions

In 2004, the world's largest carousel was located at the House on the Rock, in Spring Green, Wisconsin. Suppose that the center of the carousel is at the origin and that one of the animals on the circumference of the carousel has coordinates (24, 32). If one unit of the coordinate plane equals 1 foot, what is the diameter of the carousel

Answers

1. You have that the Standard form for the equation of a circle when its center is at the origin, is:

 x²+y²=r²

 2. You must calculate the radius. Then:

 r=√(x²+y²)

 x=24
 y=32

 3. When you substitute the values of "x" and "y" into the equation r=√(x²+y²), you obtain:

 r=√(x²+y²)
 r=√(24²+32²)
 r=√(576+1024)
 r=√1600
 r=40 feet

 4. Therefore, the diameter (D) of the circle, is:

 D=2r
 D=2(40 feet)
 D=80 feet

A little help pwease :o ? A group of 45 people attended a ball game. There were twice as many children as adults in the group. Set up a system of equations that represents the numbers of adults and children who attended the game and solve the system to find the number of children who were in the group. O.o

Answers

45= 2(a) + a
45= 2a + a
45= 3a
15= a
30. Since there are twice as many children as adults, let's say the number of adults is x. That means the amount of children is 2x. You know that in total there are 45 people. This means that the number of adults plus the number of children is 45. So we can set up x + 2x = 45. We can solve for x. 3x = 45 so x = 15. Remember, as we stated before, x is the number of adults. 2x is the number of children. Since x = 15, 2x = 30 so there are 30 children in the group.

Write the equation, in slope-intercept form, of the line passing through the origin and the point $(-4,3)$.

Answers

If the equation is passing trough the origin, it will be passing trough the point (0,0). We now for our problem that the equations is also passing trough the point (-4,3). So, our line is passing trough the points (0,0) and (-4,3). To write the equation in slope-intercept form, first, we need to find its slope [tex]m[/tex]. To do that we are going to use the slope formula: [tex]m= \frac{y_{2}-y_{1}}{x_{2}-x_{1}} [/tex].
From our two points we can infer that [tex]x_{1}=0[/tex], [tex]y_{1}=0[/tex], [tex]x_{2}=-4[/tex], [tex]y_{2}=3[/tex]. Lets replace those values in the slope formula:
[tex]m= \frac{y_{2}-y_{1}}{x_{2}-x_{1}} [/tex]
[tex]m= \frac{3-0}{-4-0} [/tex]
[tex]m= \frac{3}{-4} [/tex]
[tex]m=- \frac{3}{4} [/tex]

Now that we have our slope, we can use the slope-intercept formula:
[tex]y-y_{1}=m(x-x_{1})[/tex]
[tex]y-0=- \frac{3}{4} (x-0)[/tex]
[tex]y=- \frac{3}{4} x[/tex]

We can conclude that the equation of the line passing trough the points (0,0) and (-4,3) is [tex]y=- \frac{3}{4} x[/tex].

What is another way to write this number 300+70+5/10+8/100

Answers

Hello!

Your answer is 370 [tex] \frac{29}{50} [/tex]
Another way to write that number would be 370 58/100.
I hope this helped! :-)

If ED = 10 and DB = 3x-8, what is the length of EB

1. 32
2. 22
3. 10
4. 20

Answers

Based on the picture, we know that ED is equal to DB. Therefore:

2 times ED=EB
2(10)=20

EB is 20
Answer:
EB = 20 units

Explanation:
This question can be solved using two methods:
Method #1:
From the image, we can note that D is the midpoint of EB, therefore, ED = DB
This means that:
EB = 2*10 = 20 units

Method #2:
From the image, we know that ED = DB
We are given that ED = 10 units
Therefore:
DB = 3x - 8 = 10
3x = 18
x = 6
DB = 3(6) - 8 = 18 - 8 = 10 units
EB = EB + DB = 10 + 10 = 20 units

Hope this helps :)

Two 6-sided dice are rolled. what is the probability that the sum of the two numbers on the dice will be greater than 9?

Answers

What combination of numbers are needed in order to get a sum of 9?
        It can be:
             •  First die is 6 , second die is 3 
             •  First die is 3 , second die is 6
             •  First die is 4 , second die is 5
             •  First die is 5 , second die is 4

How many possible combinations are made? Yep, 4 possible combinations.

Recall the formula for probability
       [tex]Probability = \frac{Number of desired outcomes}{Number of all possible outcomes} [/tex]

There are 4 desired number of outcomes.
How about the total possible outcomes?
     • How many numbers are possible to appear when the first die is rolled?
        Answer: 6
     • What about the second die?
        Answer: Also 6
     • Therefore, total possible outcomes = 6 * 6 = 36 outcomes

You can now solve for the probability.

      [tex]Probability = \frac{4}{36} = \frac{1}{9} [/tex] or approximately 11.11%

In july in seattle, the grass grows 1/2 inch a day on a sunny day and 1/4 inch a day on a cloudy day. in seattle, in july, 75% of the days are sunny and 25% of the days are cloudy.
a.find the expected value of grass growth for the day
b.find the expected value of grass growth for the month of july ( 31 days ) -- round both to 2 decimal placees

Answers

expected value equals sum of the product of each value and its possibility.
a.
1/2×75％＋1/4×25％=0.4375
the expected value of grass growth for the day is 0.4375
b.
0.4375×31=13.5625
the expected value of grass growth for the month of july is 13.5625

Final answer:

Calculate the expected grass growth in Seattle based on the daily growth rates for sunny and cloudy days, then find the expected growth for the month of July.

Explanation:

a. Expected value of grass growth for the day:

Expected growth = (0.75 x 0.5) + (0.25 x 0.25) = 0.4375 inches

b. Expected value of grass growth for the month of July:

Expected growth for July = 31 days x Expected growth per day = 31 x 0.4375 = 13.56 inches

Which of the following statements is true about the given function?

Answers

I think the answer is c
The quadratic formula is:

x = (-b plus or minus √b² - 4ac)/2a

Therefore, the other answer would be √7 - 5i

identify a counterexample for the following conditional: if you live in Springfield, then you Iive in Illinois.

Answers

You could live in Springfield, MO. Then you would not be living in Illinois.

The area of a rectangular classroom is given by the trinomial 10x^2 + 3x - 4 What are the possible dimensions of the classroom? Use Factoring.

Answers

Answer: The expression factors to (2x - 1)(5x + 4)

In a rectangle the area is L x W. So if we know the area is 10x^2 + 3x - 4, then all we have to do is factor it to find possible values for the L and W.

If you factor the expression by grouping, you will get (2x - 1) and (5x + 4).

Your questions asks for possible dimensions, you could give the two expressions as dimensions.

If you wanted to select a value for x, you could plug it in and get values that could be dimensions.

For example if you let x = 10, you would have a rectangle that has a width of 19 and a length of 54.

Answer:

(5x + 4) and (2x – 1)

Step-by-step explanation:

John bikes for 2 hours at a speed of 15 miles per hour. How many hours will it take Shannon to cover the same distance at a speed of 10 mi/h?

Answers


if john bikes for two hours 15 miles per hour two hours is thirty miles of biking
D=RT
Distance= 30 miles 
Rate= 10 miles per hour 
Time= t 
plug numbers in 
30 = 10t 
divide each side by ten to get t by itself 
t= 3 
time = 3 
3 hours to travel 30 miles biking at 10mph 

Answer:

3 hours to travel 30 miles biking at 10mph

Step-by-step explanation:

hope this helps... :)

Find the measure of each angle please?

Answers

Hi!

The measure of angle x is 60 degrees so the measure of angles 2x is 120 degrees.
Each exterior angle measuring 2x forms a linear pair with an interior angle measuring an unknown measure. Angles in a linear pair are supplementary.
Since both interior angles are supplementary to congruent angles, they are congruent.
Let z be the measure of each upper interior angle.

2x + z = 180

z = 180 - 2x

Each upper interior angle measures 180 - 2x.

The sum of the measures of the interior angles of a triangle is 180.

180 - 2x + 180 - 2x + x = 180

-3x + 360 = 180

-3x = -180

x = 60

One interior angle measures x, so it measures 60 deg.
The other two interior angles measure 180 - 2x = 180 - 2(60) = 180 - 120 = 60

Answer: all interior angle measure 60 deg.
The exterior angles shown measure 120 deg each.



When the town of Bradyville first started its voluntary recycling program, 1500 of the town’s residence participated. The town predicts that the number of people participating in the recycling program will increase by 15% each year.

Which explicit rule can be used to determine the number of people participating in the program in the fifth year?



an=1500(1.15)^n−1

an=1500(0.15)^n

an=1500(1.15)n

an=1500(0.15)^n−1

Answers

Answer: an = 1500(1.15)^n (It looks like you have a typo in the third choice)

This is an example of an exponential equation. 
These types of equations are in the form: y = ab^x

A is the starting amount, b is the rate and x is the number of years.

All you have to do is put the pieces in place. Since it is a 15% increase, we are using 1.15 for the rate. And the starting value (a) is 1500.

Answer:

Here you go. :)

Find the inverse function for the function f(x) = mx + b?

Answers

y = mx + b
The inverse is created by interchanging x and y like this.
x = my + b and solving for y
(x - b) = my Now divide by m
(1/m) * (x - b) = y

The difference of two numbers is 44 1/2 . If the smaller of the two numbers increases 7 times then the difference will be 10 3/14 . Find the numbers.

The numbers are: ___ ,___ or ____,___

Answers

Answer: The smaller number is 9 and 5/42. The larger number is 53 and 13/21.

To find these answer you have to write the following two equations.

x - y = 44 and 1/2
7y - x = 10 and 3/14

Then, you can use the substitution method to solve them. Change the first equation to: x = 44 + y. Substitute that into the second equation and solve for y. Once you have that, plug it back into the first equation and solve for x.

The smaller number is 11 and the larger number is [tex]55 \frac{1}{2}[/tex].

Let's denote the two numbers as x and y, where x is the smaller number. We're given that [tex]y - x = 44 \frac{1}{2}[/tex] and [tex]7x - y = 10 \frac{3}{14}[/tex].

To solve this system of equations, we can use substitution or elimination. Let's use elimination:

1. Multiply the second equation by 2 to clear fractions: [tex]14x - 2y = 20 \frac{6}{14}[/tex].

2. Add the modified second equation to the first equation:

[tex](y - x) + (14x - 2y) = 44 \frac{1}{2} + 20 \frac{6}{14}[/tex]

[tex]13x - y = 64 \frac{11}{14}[/tex]

Now, we have a simpler equation: [tex]13x - y = 64 \frac{11}{14}[/tex].

3. Add this equation to the original second equation to find x:

[tex]7x - y + 13x - y = 10 \frac{3}{14} + 64 \frac{11}{14}[/tex]

[tex]20x - 2y = 75[/tex]

4. Now, we can solve this equation along with the first equation to find x and y.

After solving, we get x = 11 and [tex]y = 55 \frac{1}{2}[/tex].

The smaller number is 11 and the larger number is [tex]55 \frac{1}{2}[/tex].

Thus, the numbers are [tex]{11 \text{ and } 55 \frac{1}{2}}[/tex].

Correct Question:

The difference of two numbers is 44 1/2 . If the smaller of the two numbers increases 7 times then the difference will be 10 3/14 . Find the numbers.

want 100p and brainiest answer first, ((((please))))

what is   2        1
             1__ - 2__ = ?
               3         3

Answers

I believe it’s -2 over 3

HELP PLEASE
Find the value of x, if you know the hypotenuse is 10 and 1 of the sides is 5. X is the other side.

Answers

We can use Pythagorean's Theorem to solve for the unknown side:
[tex]a^2+b^2=c^2[/tex]

Solve for b (c is the hypotenuse and it doesn't matter which side is a or b):
[tex]b = \sqrt{c^2-a^2} = \sqrt{10^2-5^2} = \sqrt{100-25} = \sqrt{75} [/tex]

We can simplify this:
[tex] \sqrt{75} = \sqrt{25*3} = 5 \sqrt{3} [/tex]

So, your answer is, b = [tex]5 \sqrt{3} [/tex]
Hey there! :) 

For questions like these, where you are given the hypotenuse & one side of a triangle, then we can very simply use the Pythagorean Theorem to find x.

Pythagorean Theorem : a² + b² = c²

Where :

a = side length 
b = another side length
c = hypotenuse

Since we are given 10 as the hypotenuse and 5 as a side length, we can very simply plug these into the Pythagorean theorem. 

a² + b² = c²

We'll plug 10 into 'c' and 5 into 'a.'

(5²) + b² = (10²)

Simplify.

25 + b² = 100

Now, subtract 25 from both sides.

b² = 100 - 25

Simplify.

b² = 75

Now, find the square root of b² and 75.

[tex] \sqrt{b^2} = \sqrt{75} [/tex]

Simplify.

[tex]b = 5 \sqrt{3} [/tex]

Therefore, our final side length is : [tex]5 \sqrt{3} [/tex]

~Hope I helped!~

simplify 8v + W + 7 - 8v + 2w

Answers

8v + w + 7 - 8v + 2w
= 3w + 7
The answer is 3w +7.
8v +-8v is just 0. That is why it is not included in the equation.

Solve the inequality
-40 > -10k

Answers

Hi! 

-40>-10k

Divide both sides by -10, and flip the inequality sign since we are dividing by a negative.

4<k

Have a nice day! 

PLEASE HELP ASAP! BRAINLIEST TO BEST/RIGHT ANSWER

Answers

a(n) = -3 * 2^(n-1)

first term, you substitute 1 into n
-3 * 2^(1-1)
-3 * 2^0
-3 * 1= -3

fourth term, you substitute 4 into n
-3 * 2^(4-1)
-3 * 2^3
-3 * 8 = -24

eighth term, you substitute 8 into n
-3 * 2^(8-1)
-3 * 2^7
-3 * 128 = -384


AAAAAAAAAAAAAASSSSSSSSSSAAAAPPPPPPPPP.........

Answers

The y-intercept is the base pay.
Choice A).

jack lease a car for $159\month for 39 months. the amount due when he signed the lease was 2399. how much did jack pay during the first year of the lease.

Answers

The answer is $4,307. If he is paying 159 a month for 39 months, then you take 159 and muliply it by 12 for the year. That gives you 1908. You then add the 2399 that you paid when he signed the lease and it gives you the 4307.

How would you factor

4x^3 + 2x^2 + 2x?

Please explain in steps not just give me the straight answer.

Answers

[tex]\bf 4x^3+2x^2+2x\implies 2x(2x^2+x+1)[/tex]

so in short, the only factoring doable to it, without any complex factors, is that of taking the common factor of 2x.

now, the trinomial of 2x²+x+1, will not give us any "real roots", just complex or "imaginary" ones.

if you have already covered the quadratic formula, you could test with that, or you can also check that trinomial's discriminant, and notice that it will give you a negative value.

[tex]\bf \begin{array}{llcccll} & 2 x^2& +1 x& +1\\ &\uparrow &\uparrow &\uparrow \\ &a&b&c \end{array}\qquad \qquad 1^2-4(2)(1) \\\\\\ discriminant\implies b^2-4ac= \begin{cases} 0&\textit{one solution}\\ positive&\textit{two solutions}\\ negative&\textit{no solution} \end{cases}[/tex]

Answer:

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

Step-by-step explanation:

We have been given an expression and we are asked to find factor out our given expression.

[tex]4x^3+2x^2+2x[/tex]

To factor our given expression we need to factor out the greatest common factor of each term of our given expression.

We can rewrite our given expression as:      

[tex](2\cdot 2\cdot x\cdot x\cdot x)+(2x\cdot x)+2x[/tex]

We can see that the greatest common factor of our given expression is 2x.

Upon factoring out 2x from our given expression we will get,

[tex]2x(2\cdot x\cdot x+x+1)[/tex]

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

Therefore, the factored form of our given expression is [tex]2x(2x^2+x+1)[/tex] .

a(t) = (t - k)(t - 3)(t - 6)(t + 3) is a polynomial function of t, where k is a constant. Given that a(2) = 0, what is the absolute value of the product of the zeros of a?

Answers

If a(2) = 0, then k=2. The product of the zeros is
(2)*(3)*(6)*(-3) = -108

The absolute value of the product of zeros of a(t) is 108.
zeros:
t-k=0, t=k
t-3=0, t=3
t-6=0, t=6
t+3=0, t=-3
abs value of the product= abs value of (t*3*6*-3)=54t

20 POINTS! What is the slope of the line through the points (2, 5) and (6, 13)?

Answers

Slope can be found using the formula [tex] \frac{y2-y1}{x2-x1} [/tex].

[tex] \frac{13-5}{6-2} [/tex]
[tex] \frac{8}{4} [/tex]
Slope = 2

So the slope of the line that passes through that point is 2.

Hope this helps :)
your answer is 2. have a great day

When a number is divided by -3, the result is 12 more than the number what is the number?

Answers

Final answer:

To find the number that, when divided by -3, the result is 12 more than the number, we set up an equation and solve it to get the answer, which is -9.

Explanation:

When a number is divided by -3, and the result is 12 more than the number itself, we can set up the following equation to find the number: number / -3 = number + 12. Following division and multiplication rules for signs, and executing proper algebraic manipulations, we can solve this equation.

First, we multiply both sides by -3 to get rid of the fraction:
-3 * (number / -3) = -3 * (number + 12),
which simplifies to:
number = -3(number) - 36.
Next, we add 3(number) to both sides to get:
4(number) = -36.
Finally, we divide both sides by 4 to isolate the 'number':
number = -36 / 4
number = -9.

Therefore, the number in question is -9.

90% * x = 50 pounds of money

Answers

Divide by 90%.
  x = £55.56

Please help!!! Thank you!!!

Answers

To find the total area of this figure, it would be easiest to find the area of the left part (rectangle) and then find the area of the right part (triangle), and then add the two area values together.

First, we will find the area of the rectangle, using the formula A = lw, where l is the length of the rectangle and w is the width of the rectangle.
The length of the rectangle is 13 cm and the width is 9 cm. If we substitute in these values into our equation, we get:
A = (13cm)(9cm)
A= 117 cm^2

Next, let’s find the area of the triangle, using the formula A=(1/2)bh, where b is the base of the triangle and h is the height.
The base of the triangle is 11 cm and the height of the triangle is 5 cm (found by subtracting 13-8 as seen in the figure). If we substitute in these values and simplify, we get:
A=1/2(11cm)(5cm)
A=1/2(55cm^2)
A=27.5 cm^2.

When we add together the area of the rectangle with the area of the triangle, we will get the total area of the figure.

117 cm^2 + 27.5 cm^2 = 144.5 cm^2
Your answer is 144.5 cm^2 or the first option.

Hope this helps!

If a family has three children draw a tree diagram representing the possible outcomes for the genders of the children and then list the sample space

Answers

Each child has a 50/50 chance of being boy or girl whether the other child was a boy or girl. The possible chances are BBG, BBB, BGG, GGG

Each blade on a windmill is in the shape of a triangle with a base of 7 feet and a height of 4 feet. If there are four blades on the windmill, what is the total area of the blades 1.56 ft2 2.14 ft2 3.28 ft2 or 4.96 ft2 im unsure of this one but im going with 2.,

Answers

The area of a blade with rectangular shape = 1/2 * b * h where b is the base and h, the height. Here b = 7 and height = 4 So the area of the blade = 1/2 * 7 * 4 = 14ft^2 If the are four blades the total area is the summation of individual blade. So area = 14 + 14 + 14 + 14 = 56ft^2. Hence none of the option satisfies the answer.
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