Answer:
[tex]x=\frac{1}{2}\left(\tan^{-1}{4}+\pi k\right)[/tex], where k is any integer
Step-by-step explanation:
Let's start by getting all the trig functions on one side and all the constants on the other. We can do this by dividing both sides by [tex]\cos{2x}[/tex]:
[tex]\dfrac{\sin{2x}}{\cos{2x}}=4[/tex]
This ratio looks familiar! It just so happens that the tangent function is defined as the ratio of sine to cosine. In our case:
[tex]\dfrac{\sin{2x}}{\cos{2x}}=\tan{2x}[/tex]
Substituting this back into our equation, we have [tex]\tan{2x}=4[/tex]. We can unwrap the 2x by applying the inverse tangent function to both sides, giving us [tex]2x=\tan^{-1}{4[/tex]. Note, this specific solution only accounts for values of 2x between 0 and 2π radians. To make it general, we can add the term πk to the end of the right side, where k is any integer. We use π as a coefficient because the tangent function has a period of π radians, and it repeats its values every period.
Finally, we divide both sides of the equation by 2 to isolate x, giving us
[tex]2x=\tan^{-1}{4}+\pi k\\x=\frac{1}{2}\left(\tan^{-1}{4}+\pi k\right)[/tex]
(x - 2)^2/36-(y+1)^2/64=1The vertices for the hyperbola are (2,5) and (2,-7) true or false
Answer: False
Step-by-step explanation:
I checked with a graphing app huhu... sorry TT
The vertices are (8, -1) , (-4, -1).
pls help me my homework
Answer:
[tex]1.\; \boxed{\sf x=12^o}[/tex]
[tex]\sf 2.\;\boxed{\sf \angle 2=60^o}[/tex]
Step-by-step explanation:
1)
Since ∠1 and ∠ (7x-20) are corresponding angle.
So, ∠1 =∠ (7x-20)
and, ∠1 and ∠(5x+16) are vertically opposite angles.
- - - - -
S0...
[tex]\sf 4x+16=7x-20[/tex]
Subtract 16 from both sides.
[tex]\sf 4x=7x-36[/tex]
Subtract 7x from both sides.
[tex]\sf 4x-7x=7x-36-7x[/tex]
[tex]\sf -3x=-36[/tex]
Divide both sides by -3.
[tex]\sf \cfrac{-3x}{-3}=\cfrac{-36}{-3}[/tex]
[tex]\boxed{\sf x=12^o}[/tex]
- - - - - - - - - - -
2)
∠1 and ∠2 are corresponding angles.
S0,
[tex]\sf \angle 1=\angle 2=\boxed{\sf 60^o}[/tex]
- - - - - - - - - - - - - - - - - -
Additional info:-
Any pair of angles on the same side of one of two lines cut by a transversal and on the same side of the transversal are called corresponding angles.
Vertical angles are angles opposite each other where two lines cross.
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Answer:
x = 12
Step-by-step explanation:
The angles are equal as they are alternate exterior angles.
Solving :
⇒ 4x + 16 = 7x - 20
⇒ 7x - 4x = 16 + 20
⇒ 3x = 36
⇒ x = 12
.
A baseball coach draws names to decide who will be the first player at bat There are 5 girls and 10 boys on the team Describe and explain the probability of each outcome
a. The first batter is a girl
b. The first batter is a boy
Using the probability concept, it is found that:
a) P(girl) = 1/3, which means that 1/3 = 33% of the time, the first batter will be a girl.
b) P(boy) = 2/3, which means that 2/3 = 67% of the time, the first batter will be a boy.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
In this problem, in a total of 15 people, 5 are girls and 10 are boys, hence:
P(girl) = 5/15 = 1/3.P(boy) = 10/15 = 2/3.More can be learned about probabilities at https://brainly.com/question/14398287
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I just need the length of the unknown side and why it makes sense
Answer:
Step-by-step explanation:
According to Pythagorean theorem, the square value of hypotenuse (the side length that sees angle measure 90) is equal to sum of square value of two legs:
let x represent the missing length
x^2 + 3^2 = 7^2
x^2 + 9 = 49 subtract 9 from both sides
x^2 = 40 find the root for both sides
x = [tex]\sqrt{40}[/tex] or 6.3 inches approximately
A recipe calls for 1 ¼ cups of sugar and 1 ¾ cups of flour to make one batch of cookies. How much sugar and flour would it take to make 3 batches of cookies?
Answer:
It will take 3 3/4 cups of sugar and 5 1/4 cups of flour.
Step-by-step explanation:
Multiply 1 1/4 and 1 3/4 by three, because 3 batches of cookies are being made.
1 1/4x3= 3 3/4 cups of sugar
1 3/4x3= 5 1/4 cups of flour
determine if the shape is a polyhedron using eulers formula
Answer:
Yes
Step-by-step explanation:
Euler's Formula for Polyhedrons :
Faces + Vertices = Edges + 2
Given :
Vertices = 12Edges = 18Faces = 8Verifying using Euler's Formula :
F + V = E + 2(8) + (12) = (18) + 220 = 20It is a polyhedronThe given shape is a polyhedron using the Euler's formula.
What is Polyhedron?Polyhedron is defined as the three dimensional shape which consists of flat shapes which are polygons.
Cubes, pyramids are all polyhedrons.
Euler's formula for polyhedron states that,
V - E + F = 2
where V, E and F are the number of vertices, number of edges and the number of faces respectively.
For the given polyhedron,
Number of vertices, V = 6 + 6 = 12
Number of edges, E = 6 + 6 + 6 = 18
Number of faces, F = 1 + 6 + 1 = 8
So, V - E + F = 12 - 18 + 8 = -6 + 8 = 2
Hence the given shape is a polyhedron.
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Keyshawn buys 100 baseball cards to start a collection. He purchases 25 more baseball cards
each week. Which equation could be used to represent the number of baseball cards (b) in
Keyshawn's collection after w weeks?
A. w = 25b + 100
B. w = 100b+25
C. b = 25w + 100
D. b = 100w + 25
Answer:
C. b = 25w + 100
Step-by-step explanation:
Keyshawn starts off with 100 baseball cards. Each week he buys 25 more baseball cards. Given this we want to find an equation that would represent the number of baseball cards (represented by "b") he would have after a number of weeks (represented by "w")
We know that keyshawn buys 25 baseball cards weekly so the number of baseball cards purchased after w weeks can be represented by 25w.
We also know that he started of with 100 baseball cards so the total amount of baseball cards keyshawn has (b) can be represented by the expression b = 25w + 100
If you divide a number by 8, the answer is
20. What is the number?
Answer:
160
Step-by-step explanation:
160 divided 8 =20
Answer:
The answer is 160
Step-by-step explanation:
Let the unknown number be x.
x/8=20
x and 8 are linked by a division so if 8 crossed the equality sign it becomes multiplication. So we'll have
x=20*8
x=160
Therefore x is equal to 160.
LET'S CHECK IF IT'S CORRECT
160/8=20
A can has a height of 11cm and a volume of 486cm^3 . Find the radius of each can . Correct to two decimal places
If the height is 11 cm and the volume is486 cubic cm. Then the radius of the can will be 3.75 cm.
What is a cylinder?A cylinder is a closed solid that has two parallel circular bases connected by a curved surface.
A can has a height of 11 cm and a volume of 486 cubic cm.
Then the radius of the can will be
We know that the volume is given as
Volume = πr²h
486 = π r² x 11
r² = 14.06
r = 3.75 cm
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LAST CHANCE FOR TONS OF POINTS!!!!!!! AND BRAINLIEST!!!
A boat can travel 28 miles up a river in the same amount of time it takes to travel 36 miles down the same river. If the current is traveling at 2 miles per hour, what is the speed of the boat in still water?
Answer:
6
Step-by-step explanation:
A grocery store recently sold 48 cans of soup, 12 of which were minestrone soup. Based on experimental probability, how many of the next 24 cans sold should you expect to be minestrone soup?
Answer:
75% because the ratio is 1:4 so the probability of the next being minestrone is high.
Answer:
6
Step-by-step explanation:
misleading graph. help me how to make brand A popular than brand B
Answer:
use a scale that starts at 0
Step-by-step explanation:
The graph is misleading because the vertical scale does not start at zero.
__
To better represent the brand relationship, the vertical axis should start at zero. The amounts differ by less than 1/2%, so the bars on that scale would appear to have virtually identical heights.
A right circular cone has a base radius of 4 and a height of 6. A right circular cylinder also has a base radius of 4 and a height of 6. Let A be the lateral surface area of the cone, and let B be the lateral surface area of the cylinder. Find A/B.
Answer:
A/B = 0.6Step-by-step explanation:
Given dimensions of
Right circular cone: r = 4 and h = 6Right circular cylinder: r = 4 and h = 6Find the lateral surface area of both figures
The cone[tex]A= \pi r\sqrt{h^2+r^2}=3.14*4\sqrt{6^2+4^2}= 90.57[/tex]The cylinder[tex]B=2\pi rh=2*3.14*4*6 = 150.72[/tex]Find the ratio A/B
A/B = 90.57/150.72 = 0.6 (rounded0x2 + 3x + 1 = 5. know the answer but need to understand how?
Answer:
[tex]x=-4,\: x=1[/tex]
Step-by-step explanation:
[tex]x^2+3x+1=5\\\\x^2+3x-4=0\\\\(x+4)(x-1)=0\\\\x=-4,\: x=1[/tex]
Make sure you use the Zero Product Property to solve for each factor when the equation is set equal to 0 and can be factored.
Can you solve all please
Answer:
A) 3
B) 3
C) 3
D) 3
I think those are the first four
Step-by-step explanation:
An online store typically ships packages at a rate of 15 orders every 5 hours. At this rate, how many hours will it take to ship 156 orders?
Answer:
52 hours
Step-by-step explanation:
figure it out genius
An online store ships 15 orders every 5 hours. It will take approximately 52 hours to ship 156 orders at this rate.
Use the concept of ratio defined as:
A ratio indicates how many times one number contains another number. The ratio of two numbers is written as x : y, which is equivalent to x/y.
Where x and y are individual amounts of two quantities.
And, the Total quantity is given after combining as x + y.
Given that,
Online store ships packages at a rate of 15 orders every 5 hours.
We need to determine how many hours it will take to ship 156 orders.
The rate can be expressed as 15 orders per 5 hours or 15/5.
To figure this out,
Set up a proportion.
If the online store ships 15 orders every 5 hours,
Then the rate is 15 orders per 5 hours, or 15/5.
Now, let's set up the proportion:
15/5 = 156/x
To solve for x, cross multiply:
15x = 5(156)
Now, divide both sides of the equation by 15 to isolate x:
x =780/15
Calculating that out, x is equal to 52.
Hence, it will take approximately 52 hours to ship 156 orders at the given rate.
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How many more pairs of parallel sides does a regular octogon have then a regular hexagon
Answer:
1 more.
Step-by-step explanation:
A regular octagon has 4 pairs.
A regular hexagon has 3 pairs.
Hope this helped. :)
Mrs. Smith gave two classes the same quiz. She randomly selected 5 students from each class to compare the classes. The scores of the five students are shown below.
Class A: 80, 82, 74, 92, 94
Class B: 82, 80, 88, 86, 82
What are the mean and range for each class?
Using the information found in Part A, which class could Mrs. Smith report had the more consistent performance on the unit test? Explain what this means in terms of the situation.
Answer:
class B because every scores range is withing 6 or less
Answer:
See below ~
Step-by-step explanation:
Class A :
Mean = 80 + 82 + 74 + 92 + 94 / 5Mean = 422/5Mean = 84.4Range = Highest score - Lowest scoreRange = 94 - 74Range = 20
Class B :
Mean = 82 + 80 + 88 + 86 + 82 / 5Mean = 418/2Mean = 83.6Range = Highest - LowestRange = 88 - 80Range = 8
Class B had the more consistent performance because the range of scores is significantly less. This means that the students in Class B were more prepared than Class A for a quiz.
A motorboat travels 82 miles in 2 hours going upstream. It travels 106 miles going downstream in the same amount of time. What is the rate of the boat in still water and what is the rate of the current
let's recall d = rt, or namely distance = rate * time.
b = speed of the boat in still water
c = speed of the current
when going Upstream, the boat is not really going "b" fast, is really going slower, is going "b - c", because the current is subtracting speed from it, likewise, when going Downstream the boat is not going "b" fast, is really going faster, is going "b + c", because the current is adding its speed to it.
[tex]\begin{array}{lcccl} &\stackrel{miles}{distance}&\stackrel{mph}{rate}&\stackrel{hours}{time}\\ \cline{2-4}&\\ Upstream&82&b-c&2\\ Downstream&106&b+c&2 \end{array}\hspace{5em} \begin{cases} 82=(b-c)2\\\\ 106=(b+c)2 \end{cases} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{\textit{using the 1st equation}}{82=(b-c)2}\implies \cfrac{82}{2}=b-c\implies 41=b-c\implies \boxed{41+c=b} \\\\\\ \stackrel{\textit{substituting on the 2nd equation}}{106[~(41+c)+c~]2}\implies \cfrac{106}{2}=41+2c\implies 53=41+2c \\\\\\ 12=2c\implies \cfrac{12}{2}=c\implies \blacksquare~~ 6=c ~~\blacksquare~\hfill \blacksquare~~ \stackrel{41~~ + ~~6}{47=b} ~~\blacksquare[/tex]
A 10% increase in cigarette prices has been found to result in a _____ decrease of smokers. a. 2% b. 4% c. 10% d. 20% please select the best answer from the choices provided. a b c d
A 10% increase in cigarette prices has been found to result in a 4% decrease of smokers.
What is the effect of price increase in the demand for cigarettes?An increase in cigarette price will result in a decrease in the demand for cigarettes.
Since more money needs to be spent to but the same product, less consumers can be able to afford it.
Therefore, a 10% increase in cigarette prices has been found to result in a 4% decrease of smokers.
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How many 1-centimeter sugar cubes would be needed to form this rectangular prism?
Answer:
your question is not complete
A car traveled 200 miles on 8 1/2 gallons of gas. How much gas will it take to drive 1 mile?
Answer:
23 1/2 gallons of gas to travel one mile
Step-by-step explanation:
Given the car can travel 200 miles on 8 1/2 gallons of gas, we divide 200 by 8 1/2.
8 1/2 = 8.50 = 8.5
200/8.5 = 23.5 = 23.52 = 23 1/2
Answer:
17/400 gallons or 0.0425 gallons
Step-by-step explanation:
Take the ratio of the scale and the actual values :
200 miles : 8 1/2 gallons = 1 mile : x gallons200/(8.5) = 1/x400/17 = 1/xx = 17/400 gallons or 0.0425 gallonsfind the missing angles
Answer:
the missing angles are 47,° 77,° 56°
Step-by-step explanation:
(133)+(x+13)= 180° (angles on a straight line)
133+x+13= 180°
146+x= 180°
X= 180-146
X= 34°
FOR ANGLE A
2X+9= 2(34)+9= 68+9= 77°
FOR ANGLE C
X+13= 34+13= 47°
FOR ANGLE B
47+77+Y= 180 (SUM OF ANGLES IN A TRIANGLE)
124+Y= 180
Y= 180-124= 56°
Y= 56°
the missing angles are 47,° 77,° 56°
Write 8.6 x 10^-9 in Standard Form
Please help :)
Answer:
8.6 × 10-9
Step-by-step explanation:
How many yards is 6 inches
Answer: 6 inches equals 0.16666667 yards, or about 0.2 yards.
Step-by-step explanation: 1 yard equals 36 inches. By that reasoning, we can divide 6 by 36, since we are trying to find out how many yards are in 6 inches.
6/36 = 0.16666667
The answer is 0.16666667 yards, or about 0.2 yards.
simplify
[tex]\sqrt{29-12\sqrt{5} }[/tex]
Answer:
[tex] \sqrt{29-12\sqrt{5} }[/tex]
[tex]\sqrt{9 - 12 \sqrt{5} + 4 \times 5}[/tex]
[tex]\sqrt{ {3}^{2} - 12 \sqrt{5} + {(2 \sqrt{5}) }^{2} }[/tex]
[tex]\sqrt{{(3 - 2 \sqrt{5} )}^{2}}[/tex]
[tex]{(3 - 2 \sqrt{5} )}[/tex]
I just need the equation. please help me find it
Answer:
y=5x
Step-by-step explanation:
As you can see for the numbers of minutes on the graph, it goes 2,4,6 and on. If you look at the miles you can see the numbers that connect with the numbers of minutes. You can see a pattern. If you multiple 2 x 5 you get 10, if you multiply 4 x 5 you get 20, and etc etc.
Hope this helps <3
Answer:
y = 5x
Step-by-step explanation:
Here :
y = distance covered (in miles)x = time taken (in minutes)The standard form of an equation :
y = mx + cm = rate of change = slopec = y-intercept (which is 0 in this graph)Finding m
Change in rise / Change in run10 - 0 / 2 - 010/2m = 5Equation of the line
y = 5xHelp me please help me
Answer:
g= 8/21
Step-by-step explanation:
[tex]g=\frac{5}{7} -\frac{1}{3} \\g=\frac{15}{21} -\frac{7}{21} \\g=\frac{8}{21}[/tex]
Eight crore thirty four lakh twenty two thousand fifty seven
can anyone solve this step by step
[tex] - 6 \sqrt{243m {}^{4} } n {}^{5} p {}^{2} [/tex]
Answer:
[tex]-54m^{2} n^{2} p \sqrt{3n}[/tex]
Step-by-step explanation:
solved it using a software. check attachment for all the steps