In the accompanying diagram of a unit circle, the ordered pair (x,y) represents the point where the terminal side of 0 intersects the unit circle. If 0=150, what is the value of x.
A.
B.
C.
D.
Answers
Answer:
Below in bold.
Step-by-step explanation:
tan 150 = -tan 30
= -1/√3 = y/x (1)
This is a unit circle so the hypotenuse = 1.
so sin 150 = y/1 = y
y = 1/2
So substituting in equation (1)
1/2 / x = -1/√3
-x = √3/2
x = -√3/2.
The value of x in the unit circle is -√3/2.
Option B is the correct answer.
What is a circle?A circle is a two-dimensional figure with a radius and circumference of 2pir.
The area of a circle is πr².
We have,
Since the angle is 150 degrees, we know that it is in the second quadrant, where the x-coordinate is negative and the y-coordinate is positive.
Since the circle has a radius of 1, the y-coordinate is sin(150) = 1/2.
To find the x-coordinate, we can use the formula x = cos(θ), where θ is the angle in radians.
To convert 150 degrees to radians, we multiply by π/180:
150 degrees x π/180 = 5π/6 radians
So,
x = cos(5π/6) = -√3/2.
Therefore,
The value of x is -√3/2.
Learn more about circle here:
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Related Questions
TEST IV. Suppose mZ1 = 651 = 650 and m29 = 132º. Find the measure of the following:
Answers
Answer:
1.65°
2.115°
3.132°
4.48°
5.67
MARK A BRAINLESS THIS ANSWER
A model robot uses the scale 1 inch : 2 feet. If the model robot was 5 inches tall, the real robot would be __ feet tall
Answers
Answer: 10 feet
The ratios:
1 inch : 2 feet
5 inch : x feet
Finding x:
1 * 5 = 5
2 * 5 = 10
The real robot would be 10 feet tall.
Answer:
10 inches
Step-by-step explanation:
because 1 in= 2 ft
we can multiply 5 by 2 which is 10
your answer is 10 ft tall.
The Yert family hires a landscaping company for 30 weeks. There are two companies to choose from. Green Lawns charges $2 for the first time they service your lawn, and the price will multiply by a factor of 0. 85 every week thereafter. Green Thumbs charges $350 for the first time they service your lawn, and then charges an additional $30 every week thereafter. At 30 weeks, if the Yert family chooses the company that is cheaper, how much money will they save?
Answers
The cost-savings if the Yert Family chooses the cheaper company is: $450.50
How do you determine the cheaper company?First, we determine the cost of the service of each company. Comparing that will give us an idea of the company whose service is cheaper.
Second, we subtract the lower sum from the higher. This gives us the cost savings by the Yert Family.
Step 1
Expressing the payment plan for Green Lawns, we have:
First week= $2
Second week = (2 + (2*0.85) ) = 3.7
Third week= (3.7 + (2*0.85) ) = 5.4
Using the above cumulative method, we arrive at the series of payments due per week
The series of payment are given as follows:
2 + 3.7 + 5.4+7.1+8.8+10.5+12.2+13.9+15.6+17.3+19+20.7+22.4+24.1+25.8+27.5+29.2+30.9+32.6+34.3+36.0+37.7+39.4+41.1+42.8+44.5+46.2+47.9+49.6
= $799.50
Step 2
Expressing the payment plan for Green Thumbs, we have:
350 + (30*30) = $1,250
Step 3
Hence (assuming they go for Green Lawns) the cost savings will be:
$1,250.00 - $799.50 = $450.50
Learn more about Cost-Saving exercises at:
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Find the value of each variable. Write your answer in simplest radical form.
Answers
Answer:
Step-by-step explanation:
Guiding Statement
You must find x before you can find y. If an altitude is dropped from the right angle to the hypotenuse, then the value of the altitude = the two parts of hypotenuse multiplied together = the altitude squared.
Formula
Perhaps, instead of all that language, it is easier just to show you this in terms of what you have been given.
Solution
x^2 = 72 Factor 72 into prime factors.
x^2 = 8 * 9
x^2 = 2 * 2 * 2 * 3 * 3 Take the square root of both sides.
√x^2 = √(2 * 2 * 2 * 3 * 3)
Rule
For every pair of equal prime factors, take 1 factor outside the root sign and throw the other one away.
√x^2 = √(2 * 2 * 2 * 3 * 3)
x = √(2 * 2 * 2 * 3 * 3) Apply the rule
x = 2 * 3 √2
x = 6√2
Now with y
a = 6√2
b = 12
c = y Use the Pythagorean Theorum
c^2 = a^2 + b^2
c^2 = (6√2)^2 + 12^2
c^2 = 36*2 + 144
c^2 = 72 + 144
c^2 = 216
c = 6 √6
answer
x = 6√2
y = 6√6
Question
Find the circumference of the circle. Round your answer to the nearest hundredth.
The circumference is about
inches.
Answers
Answer:
Circumference of a cicle in terms of radius:
Circumference = 2·π·r = 2·3.14·3 = 18.85(*)
In terms of diameter:
Circumference = π·d = 3.14·6 = 18.84(*)
In terms of area:
Circumference C = √4·π·A = √4·π·28.27 =18.85
Step-by-step explanation:
radius= 3in.
to find:the circumference of the circle.
solution:formula C=2πr
=2·π·3
≈18.84956in
nearest hundredth= 18.85in
2 Demi teaches drum classes. The equation B = 50t gives the dollar amount she earns as a function of the time in hours she teaches. Demi also takes spin classes. The graph shows how much she has left on a gift card as a function of the time in hours Demi is in class. Does Demi earn more teaching 1 hour of drum class or spend more taking 1 hour of spin class? Show your work.
Answers
B = -100/5t + 500 or B = -20t + 500.
After 1 hr or t = 1 Demi earns B = 50(1) or $50 teaching
After 1 hr or t = 1 Demi spends B = -20(1)
-$20 on spin class (and her gift card amount would equal $480, although I think the GC amount is irrelevant to the question of earn more or spend more).
If it’s asking just the rate of increase or decrease the slope of 50t is greater than the slope of -20t.
The answer should be Demi earns more teaching drum class regardless of how many hours she puts in.
The answer should be Demi earns more teaching drum class regardless of how many hours she puts in.
What is the Slope intercept form?The equation of a straight line whose slope and y-intercept are given. Suppose a non-vertical line has a gradient or slope of m and y-intercept equal to c. Let (x, y) be any point on the line and a line intersect the y-axis at the point (0, c).
y = mx + c
Using the slope-intercept form (y = mx + b) to find the function of the graph,
B = -100/5t + 500
Or B = -20t + 500.
After 1 hr or t = 1 Demi earns B = 50(1) or $50 teaching
After 1 hr or t = 1 Demi spends B = -20(1)
-$20 on spin class.
If it’s asking just the rate of increase or decrease, the slope of 50t is greater than the slope of -20t.
Thus, The answer should be Demi earns more teaching drum class regardless of how many hours she puts in.
Learn more about slope;
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What is the slope of the line that passes through the points(1,6) and (13,2)?
Answers
Answer:
[tex]\boxed{\sf{-\dfrac{2}{3} }}[/tex]Step-by-step explanation:
Use a slope formula.
Slope formula:
[tex]\Longrightarrow: \sf{\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{RISE}{RUN} }[/tex]
y2=2
y1=6
x2=13
x1=1
Rewrite the problem.
[tex]\sf{\dfrac{2-6}{13-1}=\dfrac{-8}{12}=\dfrac{-8\div4}{12\div4}=\dfrac{-2}{3}=\boxed{\sf{-\dfrac{2}{3}}}[/tex]
Therefore, the slope is -2/3, which is our answer.I hope this helps you! Let me know if my answer is wrong or not.
Find the x - Please help.
Answers
Answer:
x = 7
Step-by-step explanation:
the given angles are vertically opposite and are congruent , then
4x - 5 = x + 16 ( subtract x from both sides )
3x - 5 = 16 ( add 5 to both sides )
3x = 21 ( divide both sides by 3 )
x = 7
find the missing side.
1) 2304
2) 3600
3) 1296
4) 36
Answers
Answer:
heya! ^^
here , we've been given a right angled triangle along with the measure of two of its sides.
and , we've to find the measure of its third side.
so , we'll be using Pythagoras Theorem to find the measure of the third side.
but first , let's take a look at what Pythagoras Theorem is-
Pythagoras theorem states that the square of the hypotenuse of the triangle is equal to the sum of squares of the remaining two sides.
according to the figure ,
side AB = hypotenuse = 60 cm
side AC = perpendicular = 48 cm
side BC = base = a
now by using Pythagoras Theorem ,
[tex]H {}^{2} = P {}^{2} + B {}^{2} \\ \\ (60) {}^{2} = (48) {}^{2} + a {}^{2} \\ \\ 3600 = 2304 + a {}^{2} \\ \\ a {}^{2} = 1296 \\ \\ a = \sqrt{1296} \\ \\ a = 36[/tex]
therefore ,
option ( 4 ) 36 is correct.
hope helpful :D
Answer:
36. (Option 4)[tex] \\ [/tex]
Step-by-step explanation:
Here, A right angled triangle is given with the measure of two sides and we are to find the measure of the third side.
We'll find the measure of third side with the help of the Pythagorean theorem,
[tex] \\ {\longrightarrow \pmb{\sf {\qquad (Base) {}^{2} + (Perpendicular {)}^{2} = (Hypotenuse {)}^{2} }}} \\ \\[/tex]
Here,
The base (BC) is aThe perpendicular (AC) is 48The hypotenuse (AB) is 60.[tex] \\ [/tex]
So, substituting the values in the formula we get :
[tex]\\ {\longrightarrow \pmb{\sf {\qquad (a) {}^{2} + (48 {)}^{2} = ( 60{)}^{2} }}} \\ \\[/tex]
[tex] {\longrightarrow \pmb{\sf {\qquad (a) {}^{2} = ( 60{)}^{2} - (48 {)}^{2}}}} \\ \\[/tex]
[tex] {\longrightarrow \pmb{\sf {\qquad (a) {}^{2} =3600 - 2304}}} \\ \\[/tex]
[tex] {\longrightarrow \pmb{\sf {\qquad (a) {}^{2} =1296}}} \\ \\[/tex]
[tex] {\longrightarrow \pmb{\sf {\qquad a = \sqrt{1296}}}} \\ \\[/tex]
[tex] {\longrightarrow \pmb{\frak {\qquad a = 36 }}} \\ \\[/tex]
Therefore,
The measure of the third side (a) is 36.HELP ASAP!!
I really need to get my grades up and make my family proud because right now thats not going too well>
Answers
10 (as 14-4=10, 24-14=10…)
The explicit formula of this sequence is:
Because Tn=4+(n-1)•10
T1=4+(1-1)•10=4
T2=4+(2-1)•10=14
.
.
.
Therefore T8=4+(8-1)•10=74
So the answer is the second option:)
Choose the correct definition of volume.
the amount of space a 3-dimensional object takes up
distance from one point to another
the amount of space a 2-dimensional object takes up
the distance from the bottom to the top of an object
Answers
Answer:
the amount of space a 3-dimensional object takes up
Step-by-step explanation:
Of the four definition options, the first is the only only that incorporates a three dimension explanation. The others only describe a two dimension object. Units for the first would be unit^3. The other three would only be one-dimensional "units."
He can Have Brainliest Now!
Val is going to plant b vegetable seeds in one garden and 3b + 10 vegetable seeds in another. How
many seeds is Val going to plant?
Val is going to plant seeds.
Answers
Answer:
The question is not showing what we are supposed to find.
b+3b+10
help please thankkkkk youuuuuuuu :))))))))))
Answers
Answer:
426
Step-by-step explanation:
To determine how to round up or down, we look at the place after the one we want to round to. In this case, we look at the tenths place.
If the tenths place is [tex]\geq 5[/tex] then you round up, and if it is [tex]\leq 4[/tex] you round down.
We see that the number is five and we round up to 426
How do you find the surface area of a cube if one side measures 10cm? show your solution.
Answers
Answer:
600 cm squared :)
Step-by-step explanation:
Surface area of cube: 6 x s^2
Now lets solve!!
6 x 10^2
6 x 100
600
Have an amazing day!!
Please rate and mark brainliest!!
Suppose you are interested in studying whether temperature affects spatial reasoning abilities. You decide to test spatial reasoning using completion time scores for the paper-folding test with five people, repeating the test on each person with three different temperatures (40 degrees, 60 degrees, and 80 degrees Fahrenheit).
In this experiment, the null hypothesis is that:
a. There are no differences in the mean completion times among the temperatures compared
b. There are no individual differences in the completion time means
c. The completion time mean for at least one temperature is different from another
The factor of interest is the ____________, and the dependent variable is the ___________
Answers
The null hypothesis in this situation is "There are no differences in the mean completion times among the temperatures compared".
What is a null hypothesis?This is a hypothesis that states the independent variable or factor being studied has not effect on the dependent variable.
This implies the temperature has no effect on the completion times of the paper-folding test.
What is the factor of interest?It is the effect of temperature because this is the factor being manipulated on purpose.
What is the dependent variable?This refers to the factor being studied, in this case, these are the spatial reasoning abilities, which are tested through a specific test.
Learn more about null hypothesis in: https://brainly.com/question/16261813
Students voted to have a guinea pig or a hamster qs a class pet. Of thise students, 18 voted to have a guinea pig. This number represents 72% of the students who voted. What is the toatal number of students who voted
Answers
Answer:
The total number of students that voted is 25.
Step-by-step explanation:
18 students = 72% of the students who voted
Divide the percentage of students by 100.
72% ÷ 100 = 0.72%
Then, divide 18 by 0.72%.
18 ÷ 0.72% = 25
So, the total number of students that voted is 25 students.
Hope this helped !
Find a pair of negative integers with a sum of 5
Answers
A fruit seller sells 41 watermelons on Thursday and 59 watermelons on Friday. The cost
of each watermelon is ₹99. Find the total amount earned by the fruit seller.
Answers
Answer:
₹9900
Explanation:
On thursday sold : 41 watermelonsOn friday sold : 59 watermelonsTotal sold : (41 + 59) = 100 watermelons
Amount earned : 100 * 99 = ₹9900
#Thursday
Melons sold=41Money earned=41(99)
4059$#Friday
Melons sold=59Money earned
59(99)5841Total:-
5841+4059=$9900
At a carnival game, you may win an inflatable crayon, you may win a small stuffed animal, or you may win nothing at all. If the probability of winning nothing is 0.72 and the probability of winning a small stuffed animal is 0.19, what is the probability of winning an inflatable crayon? Express your answer as a decimal.
A:0.91
B:0.28
C:0.09
D:0.81
Answers
Answer:
C:0.09
Step-by-step explanation:
probability of winning nothing = 0.72 = [tex]\frac{72}{100}[/tex]
probability of winning a small stuffed animal = 0.19 = [tex]\frac{19}{100}[/tex]
probability of winning nothing + probability of winning a stuffed animal
= [tex]\frac{72}{100}[/tex] + [tex]\frac{19}{100}[/tex] = [tex]\frac{91}{100}[/tex]
probability of winning an inflatable crayon = 1 - [tex]\frac{91}{100}[/tex]
= [tex]\frac{100}{100}[/tex] - [tex]\frac{91}{100}[/tex]
= [tex]\frac{9}{100}[/tex]
= 0.09
 Find the length of the third side. If necessary, write in simplest radical form.
IMAGE DOWN BELOW!
SOMEONE PLEASE HELP ME!! ILL GIVE YOU BRAINLIST ANSWER
Answers
Answer:
7
Step-by-step explanation:
As it is a RIGHT triangle, the formula is a^2+b^2=c^2.
We are given one leg and the hypotenuse. That means 4^2x2+b^2=81.
To find 4 root 2 square, you square them individually then multiply.
4^2=16 times 2 (root 2 squared is 2).
Simplified, that gives 16x2=32,
81-32=49.
The last leg is seven.
Please find x ft, pleeaase help
Answers
Answer:
x=238 plus 0
Step-by-step explanation:
think
Which is the coldest temperature? Explain how you determined this using the number
Answers
Find the value of m, expressed as a common fraction so that this relation is not a function.
{(-2m+1,-4),(-6m+8,0)}
Answers
Answer:
m = 7/4Step-by-step explanation:
If the two points have same input with different outputs, then this relationship is not a function, according to definition of the function.Make the x-values same and solve for m
- 2m + 1 = - 6m + 86m - 2m = 8 - 14m = 7m = 7/4Let's see
x must be equal on both sides as it's not a function
-2m+1=-6m+84m=8-14m=7m=7/413
3. It's About Time, in Langley, British
Columbia, is Canada's largest custom clock
manufacturer. They have a grandfather
clock that, on the hours, chimes the
number of times that corresponds to the
time of day. For example, at 4:00 p.m., it
chimes 4 times. How many times does the
clock chime in a 24-h period?
9. A training program requires a pilot to fly
Answers
Using an arithmetic sequence, it is found that the clock chimes 132 times in a 24-h period.
What is an arithmetic sequence?In an arithmetic sequence, the difference between consecutive terms is always the same, called common difference d.
The nth term of an arithmetic sequence is given by:
[tex]a_n = a_1 + (n - 1)d[/tex]
In which [tex]a_1[/tex] is the first term.
The sum of the first n terms is given by:
[tex]S_n = \frac{n(a_1 + a_n)}{2}[/tex]
In this problem, as the day is divided in two 12-hours period, the total will be twice the sum of the 12 elements of the following sequence:
{0, 1, 2, 3, ..., 11}
In which [tex]a_1 = 0, a_11 = 11, n = 12[/tex].
Then:
[tex]T = 2\frac{12(0 + 11)}{2} = 12 \times 11 = 132[/tex]
The clock chimes 132 times in a 24-h period.
More can be learned about arithmetic sequences at https://brainly.com/question/6561461
A rectangular piece of metal is 10 inches wide and 14 inches long.
a. What is the perimeter?
b. What is the area?
!need to finish test by 2:20!
Answers
[ rectangle perimeter = (wide +long)x2 ]
Answer: 48 inches
Length= 14inches and breadth= 10inches
1) To Find Perimeter of rectangleWe know, Perimeter of rectangle= 2(Length+Breadth)
[tex]2(14 + 10) \\ = 2 \times 24 \\ = 48 \: \text{inches}[/tex]
2)To Find Area of rectangleWe know, Area of rectangle= Length × Breadth
[tex]14 \times 10 \\ = 140 \: \text{in} ^{2}[/tex]
Hope This Helpsy=-1/4x+3
Convert to standard form
I need help understanding how to do this...
Answers
Answer:
y=y
Step-by-step explanation:
y=y because y has the same value as y
Can y’all help with this? (It’s exponential and decaying factors). Thanks!!
Answers
Answer:
2.37×10^-11 milliliters
Step-by-step explanation:
The exponential model for decay is ...
y = a·b^x
where 'a' is the initial value, 'b' is the decay factor, and x is the number of intervals over which the decay is taking place.
__
Here, you're given an initial value of a=500 mL.
The decay factor is 1 more than the decay rate, so is ...
b = 1 -12% = 0.88
We are asked for the remaining amount after 240 intervals (breaths), so that will be ...
y = 500·0.88^x
y = 500·0.88^240 ≈ 2.37×10^-11 . . . . milliliters
__
Additional comment
That's about 640 million molecules of air--not very much. After 400 breaths, there is about 1 molecule of the original air remaining.
The center of the circle is located at (-4,-3). What is the area? Use 3.14 as an approximation for pi.
Answers
Answer:
78.5 units²
Step-by-step explanation:
First, we need to plot the center point of the circle. (Shown in image). Once we plotted the center point, we need to count how many units is the radius away from the boundary.
Note: I have marked each unit by a "red point". Simply, count the number of "red points" to determine the radius.
⇒ Radius according to graph: 5 unitsWe can substitute the radius in the "area of circle" formula to determine the area. Keep in mind that pie is represented as 3.14.
⇒ Area of circle = πr²⇒ Area of circle = π(5)²Now, let's evaluate the area by simplifying the expression. Keep in mind that pie is represented as 3.14.
⇒ Area of circle = π × (5)²⇒ Area of circle = π × 5 × 5⇒ Area of circle = π × 25⇒ Area of circle ≈ 3.14 × 25 [π = 3.14]⇒ Area of circle ≈ 78.5 units²If f(x) = x3 + 12x2 +41x + 30 and f(-6) = 0, then find all of the zeros of
f(x) algebraically.
Answers
Answer:
-6, -5, -1
Step-by-step explanation:
Based on the question, (x+6) is a factor of f(x).
With this, you can do the long division method of dividing f(x) with (x+6) {Refer to the image}.
You'll get x²+6x+5 as a result.
Factorise it and you'll get
x²+6x+5 = (x+1)(x+5)
Then let (x+1)(x+5) = 0, x = -1, -5
Zero's of f(x) are -6, -5 -1
[tex]\text{Given that,}\\\\f(x) = x^3 +12x^2 +41x +30~~ \text{and} ~~ f(-6)=0\\\\\text{Since f(x)=0 when x = -6,}~ ~x-6 ~\text{is a factor of f(x).}\\\\x^3+12x^2+41x+30 = 0\\\\\implies x^3+6x^2+6x^2+36x+5x+30=0\\\\\implies x^2(x+6) +6x (x+6) +5(x+6)=0\\\\\implies (x+6)(x^2+6x+5)=0\\\\\implies (x+6)(x^2+5x+x+5)=0\\\\\implies (x+6)\textbf{[}x(x+5)+(x+5)\textbf{]}=0\\\\\implies (x+6)(x+1)(x+5)=0\\\\\text{Hence the roots are,}~ x = -6,~ x=-1~ \text{and}~ x = -5[/tex]
Help please + I need explanation
Answers
Answer:
61 degrees
Step-by-step explanation:
The THREE angles in the diagram sum to 180 degrees ( straight line = flat wall)
3x+1 + 58 + 4x-19 = 180
solve for x = 20 then A = 3x+1 = 61 degrees