(tan²(θ) cos²(θ) - 1) / (1 + cos(2θ))
Recall that
tan(θ) = sin(θ) / cos(θ)
so cos²(θ) cancels with the cos²(θ) in the tan²(θ) term:
(sin²(θ) - 1) / (1 + cos(2θ))
Recall the double angle identity for cosine,
cos(2θ) = 2 cos²(θ) - 1
so the 1 in the denominator also vanishes:
(sin²(θ) - 1) / (2 cos²(θ))
Recall the Pythagorean identity,
cos²(θ) + sin²(θ) = 1
which means
sin²(θ) - 1 = -cos²(θ):
-cos²(θ) / (2 cos²(θ))
Cancel the cos²(θ) terms to end up with
(tan²(θ) cos²(θ) - 1) / (1 + cos(2θ)) = -1/2
which of the following scenarios could be modeled by the expression 3/2 divided by 1/4
Answer:
I believe C.
Explanation:
I am pretty sure it's C but I don't really see it too well so I can't read the top two the best.
The measures of the angles of a quadrilateral are 3:8:7:2 find the measure of each angle
Answer:
Angle 1= 54°
Angle 2= 144°
Angle 3 = 126°
Angle 4 = 36°
Step-by-step explanation:
We are given measures of the angles of a quadrilateral are 3:8:7:2
Let the common ratio = x
The angles will be:
Angle 1= 3x,
Angle 2= 8x,
Angle 3 =7x
Angle 4 =2x
We know that sum of all angles of quadrilateral = 360°
We can write as: [tex]3x+8x+7x+2x=360[/tex]
Solving to find x,
[tex]3x+8x+7x+2x=360\\20x=360\\x=\frac{360}{20}\\x=18[/tex]
We get value of x = 18
Now, finding angles:
Angle 1= 3x = 3(18) = 54°
Angle 2= 8x = 8(18) = 144°
Angle 3 =7x = 7(18) = 126°
Angle 4 =2x = 2(18) = 36°
12x + 16 = 100
100
(Equation)
Solve it and show your work!
15
Simon & Iris earned money
by selling candy. They
earned $12 by recycling.
They split the total and
each got $100. How much
did they earn selling
candy?
Speaker notes
Answer:
1. x = 7
Step-by-step explanation:
12x + 16 = 100
12x = 84
x = 7
Answer:
1. x = 7
2. Simon and Iris earned $212 selling candy.
Step-by-step explanation:
1. 12(7) + 16 = 100
84 + 16 = 100
100 = 100
Therefore, x = 7.
2. If they split the price by 2, then we need to multiply $100 by 2.
100 x 2 = $200
$200 + $12 = $212
Therefore, Simon and Iris earned $212 selling candy.
please. i’m begging you
Write an inequality with the same meaning as the following
16 > x
Answer:
16>x/2
Step-by-step explanation:
Need this ASAP please help
Answer:
Step-by-step explanation:
b
Answer:
Option b) 3x - 22 = 38 should be the correct answer.
Step-by-step explanation:
If we solve the equation, we get:
x = 20
So each bag had 20 apples. In total, 3 bags held 60 apples. If he gives away 22 apples to his friends, he has 38 remaining and this satisfies the discription given in the question.
Therefore, option B) 3x -22 = 38 should be your answer.
I need help will give brainliest if right
Answer:
X =7
Step-by-step explanation:
find x;
45 IS base,
so 45 power X = 45^7
45^x = 45^7
45 will cancel out remaining x=7
therefore x= 7
The health center of a small, private university requires students to have appointments for visits. Each appointment takes an average of minutes with a standard deviation of minutes. The health center makes appointments each day and is scheduled to be open for hours. What is the probability that the total time spent for students who have appointments for tomorrow will exceed hours? (Hint: hours minutes.) Carry your intermediate computations to at least four decimal places. Report your result to at least three decimal places.
Some data in the question are missing. The complete question is :
The health center of a small, private university requires students to have appointments for visits. Each appointment takes an average of 5.6 minutes with a standard deviation of 3.5 minutes. The health center makes 100 appointments each day and is scheduled to be open for 10 hours. What is the probability that the total time spent for 100 students who have appointments for tomorrow will exceed 10 hours? (Hint: 10 hours=600 minutes.) Carry your intermediate computations to at least four decimal places. Report your result to at least three decimal places.
Solution :
Let the time spent by [tex]$i^{th} $[/tex] students for the appointment be = [tex]$X_i$[/tex]
∴ E([tex]$X_i$[/tex]) = 5.6
V([tex]$X_i$[/tex]) = [tex]$3.5^2$[/tex]
n = 100
The required probability
[tex]$P\left( \sum_{i=1} ^{100} X_i \leq 600 \right)$[/tex]
Now, [tex]$E\left( \sum_{i=1} ^{100} X_i \right) = 100 \times E (X_i) $[/tex]
= 100 x 5.6
= 560
[tex]$V\left( \sum_{i=1} ^{100} X_i \right) = (100)^2 \times (3.5)^2 $[/tex]
Standard deviation = 3.5 x 100
= 35
[tex]$P\left( \sum_{i=1} ^{100} X_i \leq 600 \right)$[/tex]
[tex]$\Rightarrow P\left( \frac{\sum_{i=1}^{100} X_i -560} {35} \leq \frac{600-560}{35}\right)$[/tex]
[tex]$= \phi (1.14286)$[/tex]
= 0.8735
= 0.874 (round to 3 decimal places)
PLEASE OPEN THE PHOTO AND ANSWER ILL GUVE BRAINLIEST (SORRY FOR SPELLINGing)
Answer:
Honestly im confused by this but i think its the second one
Step-by-step explanation:
Line g is dilated by a scale factor of 3 from the origin to create line g'. Where are points E' and F' located after dilation, and how are lines g and g' related? coordinate plane with point E at negative 4 comma 0 and point F at 0 comma 2, line g intersects points E and F The locations of E' and F' are E' (−4, 0) and F' (0, 2), and lines g and g' are the same line. The locations of E' and F' are E' (−2, 0) and F' (0, 1), and lines g and g' intersect at point F. The locations of E' and F' are E' (−1, 0) and F' (0, 0), and lines g and g' are not related. The locations of E' and F' are E' (−12, 0) and F' (0, 6), and lines g and g' are parallel.
Dilation involves changing the size of a shape.
The true statement is that the locations of E' and F' are E' (−12, 0) and F' (0, 6), and lines g and g' are parallel.
The given parameters are:
[tex]k =3[/tex] --- the scale factor
[tex]E = (-4,0)[/tex]
[tex]F =(0,2)[/tex]
Multiply the coordinates of point E and F by the scale factor (k), to determine the new coordinates of E and F.
[tex]E' = E \times k[/tex]
[tex]E' = (-4,0) \times 3[/tex]
[tex]E' = (-12,0)[/tex]
[tex]F' = F \times k[/tex]
[tex]F' = (0,2) \times 3[/tex]
[tex]F' = (0,6)[/tex]
Given that line g is represented by points E and F; line g' would be represented by points E' and F'
So, both lines would be parallel.
Hence, the true option is (d)
Read more about dilation at:
https://brainly.com/question/3457976
Answer:
The locations of E' and F' are E' (−12, 0) and F' (0, 6), and lines g and g' are parallel.
Step-by-step explanation:
Name a point on this line.
y + 2 = 3(x – 4)
Question 3 options:
(4,-2)
(-2,4)
(2,-4)
(-4,2)
Mai earns $7 per hour mowing her neighbor’s lawns. She also earned $14 for hauling away bags of recyclables for some neighbors. Priya babysits her neighbor’s children. She earns $8.40 per hour. Priya and Mai have agreed to go to the movies the weekend after they have earned the same amount of money for the same number of hours. How many hours do they have to work before they can go to the movies? How much will they have earned.
Answer:
5 hours for priya 4 of yard mowing and 1 bag moving and they will both earn 42 dollars
Step-by-step explanation:
Plz help me with this?!?! I will mark you brainliest!!!
Answer: 36
Step-by-step explanation:
Find all solutions to the equation $x^2 - 8x = -16$.
Answer:
x = 4
Step-by-step explanation:
x^2 - 8x = -16
Add 16 to both sides.
x^2 8x + 16 = 0
This may be the square of a binomial.
x^2 is the square of x
16 is the square of 4 and -4.
Let's check the middle term:
2ab = 2(x)(-4) = -8x
Yes, it is the square of a binomial.
x^2 - 8x + 16 = 0
(x - 4)^2 = 0
x - 4 = 0 or x - 4 = 0
x = 4 or x = 4
Answer: x = 4
A recipe for chocolate chip cookies with toffee bits and walnuts serves 8 people and needs 3 cups of flour. If Zachary wants to make the recipe for 14 people, how many cups of flour should he use?
I will mark you as the brainliest IF answered correctly.
Answer:
Im pretty sure it's 5.25 cups of flour
Step-by-step explanation:
so we know that it takes 3 cups for 8 people and we don't know the amount for 14 people so write it as a fraction and cross multipy
For the equation
8/3=14/x
The cross product is
8*x=3*14
Solving for x
x=3×14/8
and reducing
x=5.25
There are 120 students and 23 teachers going on a class trip. The buses used for the class trip hold at most 45 passengers. How many buses will be needed?
Answer: 4 busses if each bus only hold 45 passengers at most.
Step-by-step explanation:
120 students
23 teachers=143 people
143 divided by 3 busses is only 47 so 3
busses wouldn’t be enough
How many laps would be 50 miles on a 1 1/2 mile track?
Answer:
34 laps
Step-by-step explanation:
the specific answer is 33.3 but u have to round the whole number
Determine whether the lines are parallel, perpendicular, or neither. Justify your answer. y = 2x - 8
Y = 1/2x + 6
⚠️if you answer correctly I will give you brainliest
Answer:
perpendicular
Step-by-step explanation:
it is perpendicular because you flipped and negative the slope. if it was parallel the slope would be the same with no negative
Using the graph, determine the coordinates of the x-intercepts of the parabola.
Y
Answer: -2 and 4
Step-by-step: You see the horizontal line? now look at the the numbers -2 and 4 on that line. Notice how the line passes through them? those are your x-intercepts.
The required coordinates of the x-intercepts of the parabola are (0, -2) and (0, 4).
What is x-Intercept?The x-intercept is defined as an intercept that is located at the x-axis of the plane, which is the location or coordinates from where the line crosses.
We have to determine the coordinates of x-intercepts and y-intercepts that would function in the given graph.
The parabola of the graph is given in the question
A horizontal axis, or x-axis, and a vertical axis, or y-axis, are present in a 2-dimensional coordinate graph. Intercepts are the points (0, -2) and (0, 4) here lines representing a range of values intersect these axes.
Therefore, the required coordinates of the x-intercepts of the parabola are (0, -2) and (0, 4).
Learn more about the x-intercept here:
https://brainly.com/question/14180189
#SPJ2
3(x − 5) is equivalent to 3x − 15. False True
Answer:
True
Step-by-step explanation:
You would distribute the 3 across to each term( being x and -5) by multiplying 3 by x and 3 by -5 which would get you 3x-15
Answer:
true
Step-by-step explanation:
Examine the worked problem and solve the equation.
Four-thirds (x) minus one-third = 9. Four-thirds (x) minus one-third + one-third = 9 + one-third. Four-thirds (x) = StartFraction 28 over 3 EndFraction
The solution is x =
.
Answer:
The answer is 7
Step-by-step explanation:
I don't know how to explain it really but just divide 4/3 by 28/3 and you should get the answer of x
Answer:
7
Step-by-step explanation:
I GIVE BRAINLILSET
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Answer:
(C) $1.5
Step-by-step explanation:
Profit Percent * Cost Price = Profit
20% * $1.25 =
20/100 = .2 * $1.25 =
$.25
Selling Price = Profit + Cost Price
$.25 + $1.25 = $1.5
Refer to the graph to estimate x when f(x)= 7/2
Answer:
x = 4
Step-by-step explanation:
We are asked to find the value of x when [tex] \frac{7}{2} [/tex].
Note that [tex] f(x) [/tex] is also y.
What this means is, what is the value of x when y = 7/2 = 3.5.
On the graph given, trace where y = 3.5. check the x-value that corresponds with it on the point on the line.
Thus, at y = 3.5, x = 4.
Therefore,
x = 4, when [tex] \frac{7}{2} [/tex].
I GIVE BRAINLILSTE
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Answer:
A
Step-by-step explanation:
He increased by 10% because of 80% to 90% is 10%
So, the Answer is A
Answer:
12.5%
Step-by-step explanation:
The question is asking for the percent increase of 80%. So how much of 80% was the new percentage (90%) increased by.
First, find the difference 90-80=10
Then find the percent of 80 that the difference is.
10/80=0.125
0.125 in a percent form is 12.5%
So, there was a 12.5% increase.
Which function is graphed?
Answer:
Option A
Step-by-step explanation:
The given piecewise function shows that there is a jump discontinuity at x=1 in the first part of the piecewise function. Hence, this means that for the first part of the piecewise function, x=1 isn't included, but in the second part of the piecewise function, it is.
We can therefore eliminate C and D.
Looking at the first part of the piecewise function, we can see as x grows smaller, y grows larger. Therefore, A is the more preferred answer because the domain x<1 is valid.
Help plsssssssssss number 3
Answer:
a
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
Think of a car. when you are going 15 miles an hour that means that every hour, you are crossing 15 miles. In this situation the dolphin is going 25 km for every hour. one hour would be 25, two hours would be 50 and so on.
What is the radius of a hemisphere with a volume of 6466 to the nearest tenth of a meter?
Answer:
14.6m
Step-by-step explanation:
volume of a hemisphere = (2/3)πr3
Therefore r = Cube root of ( Volume * 3/2 * 1/ pi)
r = cube root ( 6466 * 3/2 * 1/ π)
r = 14.56
in the nearest tenth of a meter = 14.6 m
Need help will mark Brainliest no explanation needed
The variables y and x have a proportional relationship, and y = 7 when x = 2 What is the value of x when y = 212 Enter your answer in the box x = 1
Answer:
proportional relational ship
y= kx
7 = k2
solve for k
7/2 =k
y = 7/2 x
if y = 21
21 =7/2 x
solve for x
multiply by 2/7 on each side
21* 2/7 = 2/7*7/2 x
6 =x
Alberto received an inheritance of $10,000 that he decided to put into a savings account and collect the interest. He has a choice of investing in one of two plans. The Gold savings account will allow him to invest his inheritance at 3% simple interest for 4 years. The Student savings account will allow him to invest his inheritance at 2.75% simple interest for 4 years. As part of a limited time promotion, the bank will give Alberto $1000 to be added to his principal if he opens a Student savings account. which plan will earn Alberto the most money after 4 years.
Answer:
tthw student saavings account
Step-by-step explanation: