Answers
Remember the following:
[tex]\begin{gathered} \sin(0)=0 \\ \\ \sin\left(\frac{\pi}{6}\right)=\frac{1}{2} \\ \\ \sin\left(\frac{\pi}{4}\right)=\frac{\sqrt{2}}{2} \\ \\ \sin\left(\frac{\pi}{3}\right)=\frac{\sqrt{3}}{2} \\ \\ \sin\left(\frac{\pi}{2}\right)=1 \end{gathered}[/tex][tex]\begin{gathered} \cos(0)=1 \\ \\ \cos\left(\frac{\pi}{6}\right)=\frac{\sqrt{3}}{2} \\ \\ \cos\left(\frac{\pi}{4}\right)=\frac{\sqrt{2}}{2} \\ \\ \cos\left(\frac{\pi}{3}\right)=\frac{1}{2} \\ \\ \cos\left(\frac{\pi}{2}\right)=0 \end{gathered}[/tex]The terminal point of an angle θ is given by:
[tex](\cos\theta,\sin\theta)[/tex]For θ=π/2, we have:
[tex](\cos\frac{\pi}{2},\sin\frac{\pi}{2})=(0,1)[/tex]Therefore, the answer is: option B) Terminal point: (0,1), sinθ=1.
Related Questions
Solve the equation graphically and check the solution. 2x+5y=0. X+6y=14
Answers
Given:
The system of equations is,
[tex]\begin{gathered} 2x+5y=0 \\ x+6y=14 \end{gathered}[/tex]First, find the points on both lines to draw the graph of the line.
Then find the point of intersection of the line.
[tex]\begin{gathered} 2x+5y=0 \\ x=0\Rightarrow y=0 \\ x=5\Rightarrow y=-2 \\ x=-10\Rightarrow y=4 \end{gathered}[/tex]And,
[tex]\begin{gathered} x+6y=14 \\ x=0\Rightarrow y=\frac{7}{3} \\ x=14\Rightarrow y=0 \\ x=-10\Rightarrow y=4 \end{gathered}[/tex]The graph is,
As the point of intersection is (-10,4).
The solution of the given system of equation is x = -10 and y =4
What is the value of x in the diagram below? Х 15 7 20 O 15 O 24 26 0 28
Answers
Explanation
the Pythagorean theorem states that for all rigth triangles:
[tex]a^2+b^2=c^2[/tex]Step 1
so, we have two rigth triangles:
so,
the variance for the given data 18,20,18,2,7
Answers
Solution
Given 18,20,18,2,7
The variance formula is given as;
[tex]undefined[/tex]Solve for m 18 = -6m
Answers
we have the expression
18 = -6m
solve for m
that means
isolate the variable m
so
Divide both sides by -6
18/-6=-6m/-6
simplify
-3=m
Rewrite
m=-3A train at the local fair is 6 feet long. This is a 1;10 scale of a actual passenger train. You want to draw a mural that includes a 1:30 scale picture of the actual passenger train. Train at the fair scale 1:10 Length ft 6 Real passenger train scale 1:1. Length?? Mural of train Scale 1;30 Length?? Fair Train: Mural of Train =? :1
Answers
Too Fly For You, this is the solution:
• Race route in reality = 3 + 2 + 3 + 2 = 10 kilometers
,• Race route ion poster = 8 inches * 20 = 160 inches
,• 160 inches divided by 12 = 13.33 feet
Rounding to the next tenth of a feet = 13.3
4. Mr. Wisharts rectangular garden has a width of 4 meters and an area of 20 square meters. a. Solve for the length of the garden. 온 Length
Answers
Area of a rectangle: length*width
Replacing with Area = 20 and width = 4:
20 = lenth*4
4 is multiplying on the right, then it will divide on the left
20/4 = length
5 meters = length
The graph shows the cost,c, in dollars of using a food-delivery service for w weeks which equation represents the cost of food-delivery service?
A c=1/60w
B w=60c
C c=60w
D c=60
show ur work plsssssssssssssss
Picture:
Answers
The equation for a straight line can be found if its slope and coordinate of the point it passes through is given. The equation for the given graph is c = 60w. The correct answer is option C.
What is the equation for a straight line?A straight line can be written in the form of equation as, y = mx + c.
Two straight lines intersect each other only at one point.
When two straight lines are parallel to each other the angle between them is zero.
Given that,
The cost of food delivery is taken as c.
The number of weeks is w.
Since the graph given in the problem is a straight line, in order to find its equation its slope has to be found as follows,
From the graph, it is clear that at w = 2, c = 120.
Now, there are two points for the given straight line as (0, 0) and (2, 120).
Thus, the slope is given by (120 - 0) / (2 - 0) = 60
Then the equation for the straight line is,
(c - 0) / (w - 0) = 60
=> c = 60w
Hence, the equation of the given graph is c = 60w.
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What is the scale factor of a pair of figures whose preimage has coordinates(2, 3), (3, 1), and (4,5), and whose image has coordinates (4, 6), (6, 2), and (8, 10)?
Answers
The scale factor is a factor that affects coordinate x and y of all the points in an image, using one of the points of th preimage and the image we can find the realtion between both
[tex](2,3)\rightarrow(4,6)[/tex]if we analyse this the scale factor is 2, since both x and y coordinate are doubling the pre image.
Also if we analyse the other 2 points the same happens.
Answer:
The scale factor is a factor that affects coordinates x and y of all the points in an image; using one of the points of the preimage and the image, we can find the relation between both
If we analyze this, the scale factor is two since both the x and y coordinates are doubling the pre-image.
Also, if we analyze the other 2 points, the same happens.
Step-by-step explanation:
write the equation of the line in point slope form then rewrite the equation intercept form
Answers
We are given the slope m=-1 and the point (0,-2)
The point-slope form of the line is:
y - k = m(x - h)
Substituting:
y - (-2) = -1(x - 0)
Operating:
y +2 = -1(x - 0)
This was the point-slope form of the line
Rewriting in slope-intercept forn:
y +2 = -x
Subtracting 2:
y = -x - 2
That is the slope-intercept form of the line
48% in simple fraction
Answers
To transform a percentage to a simple fraction we divide the number by a 100, then we have:
[tex]\frac{48}{100}=\frac{12}{25}[/tex]Therefore 48% in simple fraction is equal to 12/25
First we start to convert 48% to a fraction.
48% = 48/100
Now we find the (GCF) or the greatest common factor of 48 and 100.
4 is the greatest common factor.
We divide the numbers by the greatest common factor to simplify the fraction to its’ simplest form.
(48/4) / (100/4) = 12/25
Find the missing arc:
Arc BC =
Answers
Let the measure of arc [tex]BC[/tex] be [tex]\alpha[/tex].
[tex]\frac{70+\alpha}{2}=85 \\ \\ 70+\alpha=170 \\ \\ \alpha=\boxed{100^{\circ}}[/tex]
What is the Identity Property of multiplication?Select one:a. The product of 2 and any number is that number. b. The product of 1 and any number is that number.c. The product of 10 and any number is that number.
Answers
The Identity Property of multiplication is a property that states that there exist a number such that when you multiply it to second number, the product is still the second number.
The product of 1 and any number is that number.
6 of the people in Bob's family like dolphins and 6 like polar bears. 3 people like both dolphinsand polar bears. How many people like dolphins but not polar bears?
Answers
ANSWER
3
EXPLANATION
To answer this question we can make a Venn diagram. Each circle will represent the people who like dolphins and the people who like polar bears. We know that 3 people like both, so there are 3 people in the area shared by both circles. If 6 people like dolphins and 6 like polar bears, knowing that already 3 people are in the area shared by both circles, in the individual area of each circle there will be 3 people:
So, we can see that there are 3 people out of the 6 that like dolphins that also like polar bears.
Hence, there are 3 people that like dolphins but not polar bears.
12. A number is decreased by 50%, and the resulting number is then increased by 300%. The original number is what percentage of the final number? F. 20% G. 25% H. 40% J. 50% K. 400% Sprance Ticket Learning Targets Percent Increase Percent Deco 7
Answers
50% means 50/100 = 0.5
300% means 300/100 = 3
Now,
A number, let it be "100" (you can take any number, the answer would be the same).
It is decreased by 50%, so
100 - (0.5)(100) = 50
Then, it is increased by 300%, so
50 + 3(50) = 200
So, we started off with 100 and now we're at 200.
The questions asks ORIGINAL is what percent of FINAL.
So, original was 100 and final is 200, essentially:
100 is what percent of 200??
100/200 = 0.5
In percentage,
0.5 * 100 = 50 %
J is the correct choice.
The Study Hall Tutoring Company charges a fixed fee of $10 for coming to your house, then charges a fixed amount of $40 per hour on top of this. Which of the followinganalytical models illustrates this situation?
Answers
It is given that the company charges a fixed fee of $10 on comiing to home and then the additional charges are $40 per hour.
Let x be the number of hours and y be the total charges
then the linear equation will be:-
y=40x+10
So the correct option is the last one y = 40x+10
Solve y³ = 64.
O A. y = 64
OB. y = 16
OC. y = 4
OD. y = 8
Answers
Answer:y=4
Step-by-step explanation:
Answer: y= 4
Step-by-step explanation:
4 x 4 = 16
16 x 4 = 64
find the sum of the first 46 terms of the following series to the nearest integer 12,15,18
Answers
Here, we want to find the sum of the first 46 terms of the series
Here, what we have is a series with a first term of 12 and a common difference of 15-12=18-15 = 3
Before we proceed to get the sum of the first 46 terms, we can calculate the last term
The last term is given as;
[tex]\begin{gathered} a_n\text{ = a + (n-1)d} \\ \\ a_{46}\text{ = 12 + (46-1)3} \\ \\ a_{46}\text{ = 12 + 45(3)} \\ \\ a_{46}\text{ = 12 + 135 = 147} \end{gathered}[/tex]Now, we can apply the formula to get the sum
The formula is given as;
[tex]\begin{gathered} Sn\text{ = }\frac{n}{2}\text{ (a + l)} \\ \\ S_{46}\text{ = }\frac{46}{2}(12\text{ + 147)} \\ \\ S_{46}\text{ = 23(159)} \\ \\ S_{46}\text{ = 23 }\times\text{ 159 = 3657} \\ \text{Where the last term is given as l above} \end{gathered}[/tex]Help find the unit prices while rounding to the nearest cent.
Answers
It is clear that brand A has the lower unit price hence it is the better buy.
Which is the better buy?We know that the better buy has to do with the commodity that would give us the least unit price for the item. Hence we must have to look at the unit price of each of the items before we decide the better buy. The unit price is the price of only one spoon.
In the first case;
Unit price = $2.17/42 = $0.05
In the second case;
Unit price = $3.97/48
= $0.08
The brand that has a higher unit price here is Brand B.
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Graph the equation Y =7x
Answers
step 1
we have the equation
y=7x
This is the equation of a line that passes through the origin (0,0)
To graph a line we need at least two points
so
assume any value of x and then calculate the value of y
For x=2
y=7(2)=14
the second point is (2,14)
step 2
Graph the line
Plot the points (0,0) and (2,14)
join them to graph the line
using a graphing tool
see the figure below
Solve for tH=1/2gt^2+v0t(note that the 0 is like an exponent but lower than the v)
Answers
Let's solve for t, the following equation:
H = 1/2gt^2 + v0t
Using the quadratic formula, we have:
t = - (v +/- √v² + gh)/g
find the area of a circle if the diameter is 40 meters
Answers
Area of a circle = pie x r x r
where pie = 3.14, r = radius
r = 40m/2 = 20 meters
[tex]\begin{gathered} \text{Area of the circle = 3.14 x 20 x 20} \\ =1256m^2 \end{gathered}[/tex]A farmer gets 24.5 L of milk from each of his cows per day.He milks all five cows and pours the milk equally into 0.5-L bottles. How many 0.5-L bottles can he fill?
Answers
There are 245 bottles to fill the milk.
What is Division method?
Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications.
For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
Given that;
A farmer gets 24.5 L of milk from each of his cows per day.
And, He milks all five cows and pours the milk equally into 0.5-L bottles.
Now,
Since, A farmer gets 24.5 L of milk from each of his cows per day.
And, He milks all five cows.
So, The total amount of milk = 24.5 x 5 L
= 122.5 L
Since, He pours the milk equally into 0.5-L bottles.
So, The number of bottles = 122.5 L ÷ 0.5 L
= 245
Thus, There are 245 bottles to fill the milk.
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Evaluate the expression for r = 4, s = -4, and t = 6. 8+s^2(t +4-4r)
Answers
Given the below expression;
[tex]8+s^2(t+4-4r)[/tex]We're asked to evaluate for r = 4, s = -4 and t = 6, all we need to do is substitute the given values of r, s and t into the expression above;
[tex]\begin{gathered} 8+(-4)^2\lbrack(6)+4-4(4)\rbrack \\ \end{gathered}[/tex]Let's go ahead and clear the brackets and solve;
[tex]\begin{gathered} 8+16(-6) \\ =8-96 \\ =-88 \end{gathered}[/tex]Therefore, our answer is -88.
Frederick needs to borrow $3000 for a down payment on a new car. His uncle decided to loan him the money as a 4.7 % loan. Frederick doesn't want to pay more than $423 in interest. How many years does Frederick have to pay back the loan? years
Answers
Given:
The initial money = $3000
Rate = 4.7% = 0.047
Frederick doesn't want to pay more than $423 in interest.
So, we need to find the number of years
Assume simple interest rate:
[tex]\begin{gathered} I=P\cdot r\cdot t \\ I=423 \\ P=3000 \\ r=0.047 \\ \\ 423=3000\cdot0.047\cdot t \\ 423=141\cdot t \\ \\ t=\frac{423}{141}=3 \end{gathered}[/tex]so, the number of years = 3 years
For the function f(x) = x^2 + 4, identify the values of f(0), f(1/2), and f(-1).
Answers
Explanation:
The function is given below as
[tex]f(x)=x^2+4[/tex]Find
[tex]\begin{gathered} f(0) \\ put\text{ }x=0 \\ f(0)=(0)^2+4 \\ f(0)=4 \end{gathered}[/tex][tex]\begin{gathered} f(\frac{1}{2}) \\ put\text{ }x=\frac{1}{2} \\ f(\frac{1}{2})=(\frac{1}{2})^2+4 \\ f(\frac{1}{2})=\frac{1}{4}+4 \\ f(\frac{1}{2})=\frac{17}{4} \end{gathered}[/tex][tex]\begin{gathered} f(-1) \\ put\text{ }x=-1 \\ f(-1)=(-1)^2+4 \\ f(-1)=1+4 \\ f(-1)=5 \end{gathered}[/tex]Hence,
The final answer is
[tex]4,\frac{17}{4},5[/tex]The FIRST OPTION is the correct answer
State the coordinates of the image of point A(-5,2) after a R270
Answers
The formula for rotation 270° counterclockwise is: A(x,y) ---> A'(y,-x)
If the point is A(-5,2) then the answer would be: A'(2,-(-5)) = A'(2,5) after rotating 270° counterclockwise.
How to solve mixed applications.Last month 1/10 of the tshirts sold were size extra large and 1/8 were extra small. Were more extra large or extra small t shirts sold last month?
Answers
We have the next information:
1/10 of the T-shirts sold were size extra
1/8 were extra small
Now, we need to find which fraction represents a higher number.
Convert to decimal each fraction:
[tex]\frac{1}{10}=0.1[/tex]and
[tex]\frac{1}{8}=0.125[/tex]Hence, 1/8 is greater than 1/10. So, more extra small tshirts were sold.
Given the equation f(t) = -16t^2+24tFind f(1) = ?
Answers
ANSWER
f(1) = 8
EXPLANATION
In this problem, we have to evaluate the function f(t) in t = 1. To do so, substitute t with 1 in the equation, and solve,
[tex]f(1)=-16\cdot1^2+24\cdot1=-16+24=8[/tex]Hence, f(1) = 8.
Select all intervals where h is increasing A:-5
Answers
Given the graph of the function y = h(x) as shown below
From the plot, it's observed that h increases at the interval as shown below
Thus, h is increasing at the intervals
[tex]-2 The correct option is BThe graph shows f(x) (1/2) and it transitions, g(x). Witch discribes the translation of (x) to g (x)
Answers
The translation from f(x) to g(x) is a translation of 4 units up (option A)
Explanation:Given:
Graph of f(x) =(1/2)^x ang g(x)
To find:
the transformation from f(x) to g(x)
To determine this, we will pick points on the x-axis and compare the result on the y axis for both graphs
when x = 0
f(x) = 1
g(x) = 5
The difference in value = 5 - 1 = 4
when x = 5
f(x) = 0
g(x) = 4
The difference in value = 4 - 0 = 4
We see the difference in value for the y is constant. This means to get g(x), we will add 4 units to the y coordinates of f(x)
The translation from f(x) to g(x) is a translation of 4 units up (this is because the value of y is positive and on the graph g(x) moves above f(x) on the vertical)