Answer:
See below for the proof of the identity
Step-by-step explanation:
I read your statement as [tex]\displaystyle \frac{\tan\theta-\cot\theta}{\tan\theta+\cot\theta}+2\cos^2\theta=1[/tex]:
[tex]\displaystyle \frac{\tan\theta-\cot\theta}{\tan\theta+\cot\theta}+2\cos^2\theta\\\\\frac{\frac{\sin\theta}{\cos\theta}-\frac{\cos\theta}{\sin\theta}}{\frac{\sin\theta}{\cos\theta}+\frac{\cos\theta}{\sin\theta}} +2\cos^2\theta\\\\\frac{\frac{\sin^2\theta-\cos^2\theta}{\sin\theta\cos\theta}}{\frac{\sin^2\theta+\cos^2\theta}{\sin\theta\cos\theta}} +2\cos^2\theta\\\\\frac{\frac{\sin^2\theta-\cos^2\theta}{\sin\theta\cos\theta}}{\frac{1}{\sin\theta\cos\theta}} +2\cos^2\theta[/tex]
[tex]\displaystyle \sin^2\theta-\cos^2\theta+2\cos^2\theta\\\\\sin^2\theta+\cos^2\theta\\\\1[/tex]
Thus, the identity is proven.
can anyone help me determine if the figure is a trapezoid and why? anyone who answers will get a thanks and 5 stars of course (and brainly). any help appreciated
Given triangle HJK and triangle RST, what is
tan(R)?
Answer:
B) [tex]\frac{5}{12}[/tex]
Step-by-step explanation:
Tan= Opposite/Adjacent
HJK = RST
Tan H = Tan R
Tan H = 5 (Opposite) / 12 (Adjacent)
So...
Tan R= 5/12
What is 5.2% of 6 x 10^8
Answer:
31200000
Step-by-step explanation:
Jeez who gave you this question?
If you roll two fair six -sided dice, what is the probability that the sum is 5 or lower?
Answer:
The probability that the sum is 5 or lower for each dice when rolled is 25/36, since all numbers equal to or below 5 count. Since there are 5 numbers out 6 possible, 5/6 is the probability fo rolling 5 or lower for one. Multiply 5/6 by itself, since we are rolling twice 5/6 * 5/6 = 25/36 or about a 69.5% chance
Step-by-step explanation:
Answer:
5/18
Step-by-step explanation:
Khan Academy
Us mathematical symbols to write an inequality that compares -2 and -9
Answer:
-2 > -9
or
-9 < -2
Step-by-step explanation:
-2 > -9
Step-by-step explanation:Inequalities represent values by comparing their size to other numbers.
Negative Numbers
While positive 9 might be larger than positive 2, remember that negative numbers work in the opposite way. -9 is more negative than -2, thus it is smaller. Another way to think about it is that -9 is further below 0 than -2.
Inequality Symbols
There are 2 main inequality symbol < (less than) and > (greater than). The symbol opens to the side of the larger number. Because we know that -2 is greater than -9, we can make the inequality -2 > -9.
(05.02) Find the measure of angle x in the figure below:
55
45
80
55
100
To find x, first find y.
In a triangle, all the angles add up to 180. So we can create the equation:
45+55+y=180
100+y=180
y=80
Since x and y are vertical angles, that mean they are equal so that means angle x is also 80.
Need help, don't know this
[tex]\textit{area of a sector of a circle}\\\\ A=\cfrac{\theta r^2}{2} ~~ \begin{cases} r=radius\\ \theta =\stackrel{radians}{angle}\\[-0.5em] \hrulefill\\ r=\stackrel{KL}{2}\\ \theta =\stackrel{\widehat{LM}}{\frac{14\pi }{9}} \end{cases}\implies A=\cfrac{ ~~ \left( \frac{14\pi }{9} \right)(2)^2 ~~ }{2}\implies A=\cfrac{28\pi }{9}[/tex]
Aakesh has two bags of marbles. The first bag contains 6 red marbles, 5 blue
marbles, and 4 green marbles. The second bag contains 3 red marbles, 2 blue
marbles, and 4 green marbles. Aakesh will randomly select one marble from
4
each bag,
What is the probability that Aakesh will select a blue marble from each bag?
O A.
B.
oc
C.
D.
27
Answer:
A
Step-by-step explanation:
Answer:
It is 2/27
Step-by-step explanation:
Took the test.
1) write a system on equations with the solution (2, -3). Work the problem out using the substitution method
The system of the equations that have the solution of (2, -3) are given below.
3x + 2y = 0 and 3y = 2x - 13
What is the linear system?A Linear system is a system in which the degree of the variable in the equation is one. It may contain one, two, or more than two variables.
Write a system of equations with the solution (2, -3).
From a single point, an infinite number of lines pass through this point.
Let one line is passing through the origin. Then the equation of the line will be
[tex]\rm y = \dfrac{-3}{2} (x)\\\\y = -1.5x[/tex]
And the other line is perpendicular to the line which is passing through the origin and a point (2, -3).
[tex]\rm y = \dfrac{2}{3} x + c[/tex]
Then this line also passes through a point (2, -3). Then the value of c will be
[tex]\rm -3 = \dfrac{2}{3} \times 2 + c\\\\c \ \ = -13[/tex]
Then the equation of the line will be
3y = 2x -13
More about the linear system link is given below.
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Anna paid $4 for renting a video game for 4 days
Answer:
$16
Step-by-step explanation:
You would just multuply the amount of time and the amount of money it costs.
Answer:
$1
Step-by-step explanation:
4 divided by 4 is 1 like the other person said. You can give them brainliest.
Hope It Helps
Please help me solve my last math problem on my test I'm a bit stuck and don't know if I'm doing it correctly.
What is the value of x in this triangle?
Enter your answer as a decimal in the box. Round only your final answer to the nearest hundredth.
x = ___°
A right triangle. The perpendicular is labeled as 5. The base is labeled as 20. The alternate base angles are labeled as right angle and x degrees, respectively.
image of triangle in the file below.
Answer:i think you are on the right track
Step-by-step explanation:
I am not very good at this,but i think you have it right so far
Answer:
14.04
Step-by-step explanation:
A plastic container holds 3 red balls, 2 green balls, and 3 yellow balls. What is the probability of choosing a green ball, replacing it, and then choosing a yellow ball?
Answer:
[tex]0.09375[/tex]
Step-by-step explanation:
the total number of balls = 3 + 3 + 2 = 8
Let p be the probability of choosing a green ball, replacing it, and then choosing a yellow ball.
[tex]p=p\left( \text{choosing a green ball} \right) +p\left( \text{choosing a yellow ball} \right)[/tex]
[tex]=\frac{2}{8} \times \frac{3}{8}[/tex]
[tex]=\frac{6}{64}[/tex]
[tex]= 0.09375[/tex]
Simplify (0%)
.
O A. 6
O B.
01
6
O C. 64
O D. 616
Answer:
Simplify (0%)
.
O A. 6
O B.
01
6
O C. 64
O D. 616
Step-by-step explanation:
help me solve for x
Answer:
x=26
Step-by-step explanation:
4x+4+4x-32=180
8x-28=180
8x=180+28
x=26
[tex]cos(21) = \frac{4}{x} [/tex]
Please help! brainliest to first correct answer!
find average of the numbers 8 , 13 , 15.
Answer:
12
Step-by-step explanation:
SUM/COUNT = formula
8+13+15/3
36/3
= 12
Which is the equation of a parabola with a directrix at y=2 and a focus at (5,0)
Check the picture below, so the parabola looks more or less like so.
the vertex is always half-way between the focus point and the directrix, and since the parabola is opening downwards, the "p" distance is negative.
[tex]\textit{vertical parabola vertex form with focus point distance} \\\\ 4p(y- k)=(x- h)^2 \qquad \begin{cases} \stackrel{vertex}{(h,k)}\qquad \stackrel{focus~point}{(h,k+p)}\qquad \stackrel{directrix}{y=k-p}\\\\ p=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix}\\\\ \stackrel{"p"~is~negative}{op ens~\cap}\qquad \stackrel{"p"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\begin{cases} h=5\\ k=1\\ p=-1 \end{cases}\implies 4(-1)(y-1)~~ = ~~(x-5)^2\implies -4(y-1)=(x-5)^2 \\\\\\ y-1=-\cfrac{1}{4}(x-5)^2\implies y=-\cfrac{1}{4}(x-5)^2 + 1[/tex]
Can someone help me please?!!
Reason:
Plug in w = 16 and compute.
D = 4w + 30
D = 4(16) + 30
D = 64 + 30
D = 94
This says at week 16, Jose will have $94 in his piggy bank.
Can someone help me?
for anyone who cant see it:
Find the surface area of the pyramid. The side lengths of the base are equal.
__________
If you cant see the numbers
* Bottom number is 13m and the one with an arrow is 18 m
Again sorry if you cant see it
Answer: 637 m²
Step-by-step explanation:
We need to find the area of four triangles and one square.
The square: 169 m²
A = L²
A = (13 m)²
A = 169 m²
The triangles: 468 m²
-> We have four congruent triangles. I will find the area of two (skipping the "divide by two" part of the formula) and multiply by two to find all four at once.
A = B * H
A = (13 m) * (18 m)
A = 234 m²
-
234 m² * 2 = 468 m²
Total surface area:
169 m² + 468 m² = 637 m²
A parallelogram has an area of 150 square yards and a height of 5 yards.
what is the length of the base of the parallelogram?
enter your answer in the box. a parallelogram has an area of 150 square yards and a height of 5 yards.
what is the length of the base of the parallelogram?
enter your answer in the box.
The length of the base of the parallelogram that has a height of 5 yards and an area of 150 square yards is 30 yards
How to determine the base length?The given parameters are:
Area = 150
Height = 5
The area of a parallelogram is:
Area = Base * Height
So, we have:
Base * 5 = 150
Divide both sides by 5
Base = 30
Hence, the length of the base of the parallelogram is 30 yards
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Which number set correctly represents the range of the given data? {(0, 0), (2, 0), (3, 0), (5, 0)} {0, 2, 3, 5} {0, 2, 3} {0, 2} {0}
{0}
Step-by-step explanation:The range of a function is the set of y-values within a function.
Finding the Range
As stated above, the range is all of the y-values. To find the y-values remember that in a coordinate pair the second point is the y-value. So, look at the second value of each pair. For all 4 points, the y-value is 0. This means that the range is 0.
Range Notation
Now that we know the range, we need to use the correct notation. When writing domain or range, make sure that the values are listed in order from least to greatest. Additionally, even if y-values repeat in the coordinate pairs, only state them once in the range. In this case, there is only 1 unique value, so the range should only have 1 value. Finally, the range is surrounded by braces. Therefore, the range should be written as {0}.
Change the subject of the formula L = v 4kt - p to k.
Answer:
[tex]\boxed{k = \frac{L^2 + p}{4t}}[/tex]
General Formulas and Concepts:
Algebra I
Basic Equality Properties
Multiplication Property of EqualityDivision Property of EqualityAddition Property of EqualitySubtraction Property of EqualityStep-by-step explanation:
Step 1: Define
Identify given.
[tex]\displaystyle L = \sqrt{4kt - p}[/tex]
Step 2: Solve for k
We can use equality properties to help us rewrite the equation to get k as our subject:
Let's first square both sides:
[tex]\displaystyle\begin{aligned}L = \sqrt{4kt - p} & \rightarrow L^2 = \big( \sqrt{4kt - p} \big) ^2 \\& \rightarrow L^2 = 4kt - p \\\end{aligned}[/tex]
Next, add p to both sides:
[tex]\displaystyle\begin{aligned}L = \sqrt{4kt - p} & \rightarrow L^2 = \big( \sqrt{4kt - p} \big) ^2 \\& \rightarrow L^2 = 4kt - p \\& \rightarrow L^2 + p = 4kt \\\end{aligned}[/tex]
Next, divide 4t by both sides:
[tex]\displaystyle\begin{aligned}L = \sqrt{4kt - p} & \rightarrow L^2 = \big( \sqrt{4kt - p} \big) ^2 \\& \rightarrow L^2 = 4kt - p \\& \rightarrow L^2 + p = 4kt \\& \rightarrow \frac{L^2 + p}{4t} = k \\\end{aligned}[/tex]
We can rewrite the new equation by swapping sides to obtain our final expression:
[tex]\displaystyle\begin{aligned}L = \sqrt{4kt - p} & \rightarrow \boxed{k = \frac{L^2 + p}{4t}}\end{aligned}[/tex]
∴ we have changed the subject of the formula.
---
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---
Topic: Algebra I
can someone please help with this q^q
Answer:
[tex]y = -\frac{3}{4} sin(\frac{2}{3}x)[/tex]
Step-by-step explanation:
First determine whether it is a sine function or a cosine function. Since
sin(x) = 0 at x = 0 and we see indeed that the value of the function is 0 at x = 0 it must be a sine function
The general equation of a sine function is [tex]a sinbx[/tex]
where a is the amplitude. The amplitude is one-half the difference between the lowest and highest values in the graph.From the graph we can see that the highest value is 3/4 and lowest is -3/4 so the amplitude = 1/2 (3/4 + 3/4) = 3/4
If the amplitude were positive, the function would be increasing at (0,0) and going up to its amplitude value. However we can see that the function is decreasing at (0,0 ) and goes down to -3/4. Therefore the amplitude a has a negative sign so a = -3/4
To compute b, note that the period of the function ie where it finishes a full cycle is 3π since the function at that x value repeats itself. The relationship between b and the period is 2π/b = 3π in this particular case
This gives b = 2/3
So a = -3/4, b = 2/3 and the equation is [tex]y = -\frac{3}{4} sin(\frac{2}{3}x)[/tex]
the diagram shows a regular dodecagon
work out the size of one interior angle
the diagram shows a regular dodecagon is the size of one interior angle
i need help with this
[tex]\text{Apply Pythagorean theorem,}\\\\~~~~x^2 = 6^2 +8^2\\\\\implies x = \sqrt{6^2 +8^2}\\\\\implies x = \sqrt{36 +64}\\\\\implies x =\sqrt{100}\\\\\implies x = 10~~ \text{units.}[/tex]
Janice has room for 6 books on a shelf.
How many different ways can she arrange the books on the shelf?
Enter your answer in the box.
Answer:
For the book standing on the left you have a choice out of all
6
, for the next one you choose from the
5
left, and so on.
Explanation:
So the total number of arrangements you have:
6
×
5
×
4
×
3
×
2
×
1
=
720
Usually this is written as
6
!
, pronounced "6 factorial"
(factorial meaning the product of all whole numbers from
1
up to and including the one before the
!
)
Step-by-step explanation:
CORRECT ME IF IM WRONG
Olivia saves $15 each week and has $20 in an
account. She is saving for a bicycle that costs $110.
How many weeks will it take for her to have enough
money for the bicycle?
Answer:
5 weeks
needs 75 more $$$
Step-by-step explanation:
Find the GCF of 2y²z and 8yz²
Answer:
GCF(2y²z , 8yz²) = 2yz
Step-by-step explanation:
2y²z = (2yz) × y
8yz² = (2yz) × 4z
then
GCF(2y²z , 8yz²) = 2yz
6x + 5y =20 solve for y step by step
Answer:
Move all terms that don't contain y to the right side and solve.y=4−6x/5
Step-by-step explanation:
How many seconds will it take an echo to reach your ears if you yell toward a mountain
92.0 m away on a day when the air temperature is 0°C?
O 0.556 s
O 1.80 s
0 3.60 s
O 0.277 s
It will take 0.556 seconds for an echo to reach one's ears
Calculating the time to hear an echoFrom the question, we are to determine how long it would take an echo to reach one's ears
From the formula,
[tex]Speed = \frac{2 \times distance \ travelled\ by \ sound}{Time}[/tex]
NOTE: To hear an echo, the sound will travel to and fro, hence, it will cover twice the distance
From the given information,
Distance = 92.0 m
NOTE: Speed of sound in air at 0 °C ≅ 331 m/s
Putting the parameters into the formula, we get
[tex]331 = \frac{2 \times 92.0}{Time}[/tex]
[tex]Time = \frac{2 \times 92.0}{331}[/tex]
Time = 0.556 secs
Hence, it will take 0.556 seconds for an echo to reach one's ears.
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