Part of the value of sin(u) is cut off; I suspect it should be either sin(u) = -5/13 or sin(u) = -12/13, since (5, 12, 13) is a Pythagorean triple. I'll assume -5/13.
Expand the tan expression using the angle sum identities for sin and cos :
tan(u + v) = sin(u + v) / cos(u + v)
tan(u + v) = [sin(u) cos(v) + cos(u) sin(v)] / [cos(u) cos(v) - sin(u) sin(v)]
Since both u and v are in Quadrant III, we know that each of sin(u), cos(u), sin(v), and cos(v) are negative.
Recall that for all x,
cos²(x) + sin²(x) = 1
and it follows that
cos(u) = - √(1 - sin²(u)) = -12/13
sin(v) = - √(1 - cos²(v)) = -3/5
Then putting everything together, we have
tan(u + v)
= [(-5/13) • (-4/5) + (-12/13) • (-3/5)] / [(-12/13) • (-4/5) - (-5/13) • (-3/5)]
= 56/33
(or, if sin(u) = -12/13, then tan(u + v) = -63/16)
Eric and Erica have $5.40 between the two of them. If you double the amount of money Eric has and halve the amount Erica has, then they would have the same amount of money. How much money does Eric have?
Answer:
$1.08
Step-by-step explanation:
Use a system of equations. Let x represent eric's money and y represent erica's money.
x+y=5.40
2x=1/2y
Let's solve for y in the second equation and substitute it into the first.
Double both sides.
4x=y
Substitute
x+4x=5.40
5x=5.40
Divide by 5
x=$1.08
So eric has $1.08
What is 2 x 10/8 in simplest form 4 grade
The fraction is 5/2
The decimal is 2.5
Length (in) of shoe box
Landon and Colin bought 1/3 pound of strawberries. They are sharing the strawberries equally.
each person will receive ?
pound of strawberries.
Answer:
1/6
Step-by-step explanation:
1/3 divided by 2
In quadrilateral ABCD, angle A is 80 degrees, angle B is 90 degrees, and angle D is 100 degrees. What is the measure of angle C?
Answer:
The answer is 105 degrees
Step-by-step explanation:
PLEASE ANSWER AS SOON AS POSSIBLE WILL GIVE BRAINLESS TO THE FIRST CORRECT PERSON!!!
Find the values of x and y. Write your answers in the simplest form.
Answer:
Around x = 3 y = 6
Step-by-step explanation:
I'm not sure if you need to round to the nearest whole or hundreth or tenth
Which equation can be used to determine the distance between the origin and (-2, -4)?
what is the percent increase from 18 to 26
The set of second coordinates in a relation is called
What is second set of coordinate called?
The range of the relation is the set of all possible second coordinates.
Answer:
The set of first coordinates of all the ordered pairs in a relation is called the domain of that relation. Similarly the set of the second coordinates(also called as images) of all the ordered pairs in a relation is called the range of that relation.
Step-by-step explanation:
hope:)
Which statement is true for debit cards
Answer: There are no answer choices but an example of a true statement would be that spending on a debit card will NOT count towards your credit score.
Step-by-step explanation:
14 of 15
14.A bag contains 120 marbles. Some are red and the rest are black. There are 19 red marbles for every black marble. How many red marbles are in the bag? Explain your reasoning.
A pair of shoes was originally priced at 100. The store owner gives a discount discount, and the shoes are now priced at 60
Answer:
i think there was a discount of 40
Step-by-step explanation:
Answer:
The answer is: 40% Off Discount
Step-by-step explanation:
$100 - $60 = 40%
URGENT HELP 20 points
Answer:
5 3/12 cm^2
Step-by-step explanation:
I just put it in the calculator.
can someone help me pleace for 10 points
Answer:6
Step-by-step explanation:
Look at the number 16 on the y side and then go to the dot that is on the 16 line then go all the way down and look at the number of people.
What is 3^8*3^3/3^2 simplified?
Answer:
6561*27/9
Step-by-step explanation:
3^8=6561
6561*27=177,147
177,147/9=19,683
What is the equation in slope-intercept form of the line that passes through the points (-20, 5) and (-10, 6)
Answer:
[tex]y=\frac{1}{10}x + 7[/tex]
Step-by-step explanation:
Hi there!
We are given the points (-20, 5) and (-10, 6)
We want to write the equation of the line in slope-intercept form
Slope-intercept form can be written as y=mx+b, where m is the slope, and b is the y intercept
First, let's find the slope of the line
The formula for the slope (m) calculated from 2 points is [tex]\frac{y_2-y_1}{x_2-x_1}[/tex], where [tex](x_1, y_1)[/tex]and [tex](x_2, y_2)[/tex] are points
We have everything we need to find the slope, but let's label the values of the points to avoid confusion and mistakes
[tex]x_1=-20\\y_1=5\\x_2=-10\\y_2=6[/tex]
Substitute these values into the formula to find the slope
m=[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
m=[tex]\frac{6-5}{-10--20}[/tex]
Simplify
m=[tex]\frac{1}{-10+20}[/tex]
m=[tex]\frac{1}{10}[/tex]
The slope (m) of the line is 1/10
We can substitute this value into the formula y=mx+b
y = [tex]\frac{1}{10}x[/tex] + b
Now we need to solve for b
As the equation passes through the points (-20, 5) and (-10, 6), we can use either point to solve for b.
Taking (-20, 5) for instance:
Substitute -20 as x and 5 as y:
5=[tex]\frac{1}{10}(-20)[/tex] + b
Multiply
5=-2+b
Add 2 to both sides
7=b
Substitute 7 as b.
y=[tex]\frac{1}{10}x + 7[/tex]
Hope this helps!
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Giving Brainliest to who can solve!
Answer:
NF = 16
Step-by-step explanation:
Since N is the incenter of ΔABC then ND = NE = NF
ND = NE ⇔ 6x - 2 = 3x + 7 ⇔ 6x - 3x = 7 + 2 ⇔ 3x = 9 ⇔ x = 3
Now , we calculate ND:
ND = 6(3) - 2 = 18 - 2 = 16
and because NF = ND then NF is also equal to 16
help pls
10 points
Brainleist
thanks
Answer: x=12
Step-by-step explanation:
The two angles provided are on a straight line
A straight line is 180 degrees, so we can add the two angles to make 180 and solve for x
[tex]10x-20+6x+8=180[/tex]
Simplify
[tex]10x-20+6x+8=180\\10x+6x-20+8=180\\16x-12=180[/tex]
Add 12 on both sides
[tex]16x-12=180\\16x-12+12=180+12\\16x=192[/tex]
Divide both sides by 16 to isolate x
[tex]16x=192\\\frac{16x}{16} =\frac{192}{16} \\x=12[/tex]
Please help........ i need help
Answer:
x = 30
Step-by-step explanation:
x/2 = 12 + 3
x = 2(12+3)
x = 30
Graph the solution to the following system of inequalities. y > -2x+7, y ≤ 3x-8
The solution to the system of inequalities y > -2x+7, y ≤ 3x-8 is the set of points ( (x,y) pairs ) in the intersection of the regions these inequalities are true for, as shown in the graph by the intersection of the blue and red colors.
What are system of inequalities?When mathematical expressions are compared, with non-strict equality, then such mathematical statements are called mathematical inequalties.
A collection of inequalities for which we consider common solution for all inequalities is called a system of inequalities.
How to draw regions covered by inequalities?Suppose there is inequality given as: y ≥ f(x)
The region it covers is the region of value pairs (x,y) for which this inequality holds true.
We've to draw the region covered by it.
For a function y = f(x), there is y > f(x) on one side of the graph of the function y = f(x) in XY plane, and on other side there is y < f(x).
We just need to figure out this fact at 1 point on either side of the graph of the function y = f(x) , and then the area where y > f(x) is true, along with the curve of the function y = f(x) is included in the region covered by inequality y ≥ f(x)
For this case, the inequalities given are:
y > -2x+7, y ≤ 3x-8
Their solution is the points lying in the intersection of the regions these inequalities are true for, as shown in the graph by the intersection of the blue and red colors.
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What is the amplitude of the function? Identify the amplitude of a periodic function from its graph. 4 3 2 1
The amplitude of a periodic graph of a function is 2 because the amplitude of the function is half of the difference between the maximum and minimum values of a function.
What is a function?It is defined as a special type of relationship and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have a graph of a function(refer to attached picture)
We know the amplitude of the function is given by:
[tex]\rm Amplitude \ of \ f \ = \frac{1}{2} |max \ f -min \ f|[/tex]
As we can see in the graph the maximum value is 0 and
the minimum value of a function is -4, thus the amplitude
[tex]\rm Amplitude \ of \ f \ = \frac{1}{2} |0 -(-4)|[/tex]
The amplitude of f = 2
Thus, the amplitude of a periodic graph of a function is 2 because the amplitude of the function is half of the difference between the maximum and minimum values of a function.
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Reread the problem described in Question 10.5 on page 191.What form should H0 and H1 take if the investigator is concerned only about salary discrimination against female members? If this hypothesis test supports the conclusion of salary discrimination against female members, a costly class-action suit will be initiated against American colleges and universities. Under these circumstances, do you recommend using the .05 or the .01 level of significance? Why?
The form that the null and alternative hypothesis should take if the investigator is concerned only about salary discrimination include U = $82000 and U < $82000.
How to explain the hypothesis?The alternative hypothesis is the claim of the test. Here, the investigator wants to test whether the average salary of females is less than $82500.
Assuming the hypothesis test supports the conclusion of salary discrimination against female members, the 0.01 level of significance will be recommended.
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Solve the equation please I need help
Answer:
refrence attached
Step-by-step explanation:
hope it helps you<3Lin's puppy is gaining weight at a rate of 0.125 pound per day. Describe the weight gain in days per pound. The weight gain would be days per pound
Answer:
8 days per 1 pound
Step-by-step explanation:
Using the calculator enter 1 divided by .125
Thats all :)
Dempsey Railroad Co. is about to issue $400,000 of 10-year bonds paying an 11% interest rate, with interest payable annually. The discount rate for such securities is 10%. Click here to view the factor table. (For calculation purposes, use 5 decimal places as displayed in the factor table provided.) How much can Dempsey expect to receive for the sale of these bonds? (Round answer to 0 decimal places, e.g. 2,525.) Dempsey can expect to receive
The amount Dempsey can expect to receive from the sale of the bonds is $424,578.27.
What is the amount Dempsey can expect to receive from the sale of the bonds ?The amount that would be recieved from the sale of the bond is the present value of the bond. Present value is the sum of discounted cash flows.
Present value can be determined using a financial calcualtor:
Cash flow each year from year 1 to 10 = 0.11 x 400,000 = 44000Cash flow in year 10 = $400,0000 I = 10%PV = $424,578.27
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Given: mMEJ=30°,
mMFJ= 50°
Find: mKL, mMJ
Applying the angles of intersecting secants theorem, the measures of the arcs are:
m(KL) = 20°; m(MJ) = 80°.
What is the Angles Intersecting Secants Theorem?When two secants intersect and form an angle outside the circle, the measure of the angle formed is half the positive difference of the measures of the intercepted arcs.
Given the following:
m∠MEJ = 30°m∠MFJ = 50°m∠MEJ = 1/2(MJ - KL)
30 = 1/2(MJ - KL)
60 = MJ - KL
KL = MJ - 60
m∠MFJ = 1/2(MJ + KL)
50 = 1/2(MJ + MJ - 60)
100 = 2MJ - 60
2MJ = 100 + 60
2MJ = 160
MJ = 160/2
MJ = 80°
KL = MJ - 60 = 80 - 60
KL = 20°
Thus, applying the angles of intersecting secants theorem, the measures of the arcs are:
m(KL) = 20°; m(MJ) = 80°.
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A university class has 22 students: 3 are nursing majors, 9 are psychology majors, and 10 are business majors. (Each student has only one of these majors.) The professor is planning to select two of the students for a demonstration. The first student will be selected at random, and then the second student will be selected at random from the remaining students. What is the probability that the first student selected is a nursing major and the second student is a business major?
Answer:
27/462
OR
.058
Step-by-step explanation:
the probability that the first student, selected at random, is a nursing student is 3/22.
the probability that the second student, selected at random from the remaining students, is an accounting major is 9/21.
the probability the first student chosen is a nursing student and the second student chosen is an accounting major is therefore 3/22 * 9/21 = 27/462.
CAN SOMEBODY HELP ME PLEASE IM STUCK
Answer:
Step-by-step explanation:
To find the vertex from the given table look when the values of x or y start to switch the pattern. For example look at y value they get lower and lower 15,8,3,0,-1 then they get greater and greater 0, 3,8,15,24,...
So the he vertex is at (-2, -1) because here is where the pattern changed.
Y-intercept of the parabola is where the parabola intersects the y-axis so the x must be 0 there. Look in the table where is x=0 and see is at y=3.
Y-intercept point is at (0, 3)
X-intercept of the parabola is where the parabola intersects the x-axis so the y must be 0 there. Look in the table where is y = 0 and see is at x= -1 and also at x= -3.
X-intercept points are at (-1, 0) and (-3, 0)
Equation of the parabola in factored form is in general
y= (x- x intercept1)(x- x intercept 2), and for our problem is:
y = (x +1)(x +3)
The equation for the axis of symmetry is x = -2 because we have a vertical parabola (since x is squared in the equation) and the vertex is as we said previously at (-2, -1).
Identify the coefficient of 5r2
coefficient of 5r² is 5
hope it helps...!!!
Find the secant of ZI.
H
80
89
39
Answer:
See below
Step-by-step explanation:
[tex] \sec \: I = \frac{HI}{IJ} \\ \\ \implies \: \sec \: I = \boxed{\frac{89}{39} }[/tex]