[tex]~~~~~5\sin 2x +4 =10 \sin^2 x\\\\\implies 5\cdot 2\sin x \cos x+4 =10 \sin^2 x\\\\\implies 10 \sin x \cos x +4 = 10\sin^2 x\\\\\implies 10\tan x + 4\sec^2 x = 10\tan^2 x~~~~~;[\text{Divide both sides by}~ \cos^2 x]\\\\\implies 10\tan^2 x -10 \tan x -4(1+ \tan^2 x)=0\\\\\implies 10\tan^2 x -10 \tan x -4 -4\tan^2 x =0\\\\\implies 6 \tan^2 x -10 \tan x -4 =0\\\\\implies 3 \tan^2 x -5 \tan x -2 =0~~~~~;[\text{Divide both sides by 2}]\\\\\implies 3\tan^2 x - 6\tan x +\tan x -2 =0\\\\[/tex]
[tex]\implies 3 \tan x( \tan x -2) + (\tan x -2) = 0\\\\\implies (\tan x -2) ( 3 \tan x +1) = 0\\\\\implies \tan x = 2 ~~ \text{or}~~ \tan x = - \dfrac 13\\\\\text{Showed.}[/tex]A store charges a restocking fee for any returned item based upon the item price. An item priced at $200 has a fee of $12. An item priced at $150 has a fee of $9.
What percentage of the item is a restocking fee?
Divide the restocking fee by the price of the item:
12/200 = 0.06
9/150 = 0.06
Multiply by 100 to get the percent:
0.06 x 100 = 6%
Answer: 6%
Hoy Many times as great as 10% is 100% answer
Answer: 100% is 10 times as great as 10%
Step-by-step explanation: 10 * 10 = 100 or 100 divided by 10 equals 10. Have a nice day~
Answer:
um.....10
Step-by-step explanation:
100% (1) ÷ 10% (0.10) = 10
[tex]Hope[/tex] [tex]this[/tex] [tex]helps![/tex] [tex]Have[/tex] [tex]a[/tex] [tex]great[/tex] [tex]day![/tex] [tex]:)[/tex]
What is the percent of the silo that is filled with corn at 10 hours. Use the picture bellow to get the answer.
Answer:
90.93%
Step-by-step explanation:
It is clear that the table is a linear function. That is, every hour, the amount of corn increases by the same amount. You can find the slope of the linear function by using the slope formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
In your case, the number comes out to be 825. So the number of corn will be 825*10 = 8250 cu ft.
Now, we know that the volume is area times height. So if the area is pi * r * r, then the volume of the shape is 2888*pi.
Therefore, the answer is 8250/2888*pi or 90.93%.
A group photograph of a family of six (4children and their parents)is to be taken.if the parents must occupy the two middle seats.then the number of different arrangements is
Answer:
Let's find the number of arrangements with mother and father together, say N & then subtract it from total number of arrangements.
Total arrangements = 6! = 720.
Now, as mother & father are together, let's treat mother and father as a single person. Now, there're 5 persons.
Number of arrangements in this way = 5! = 120.
But mother and father can change their places in 2! = 2 ways.
N = 120 × 2 = 240.
Ans. = 720-240 = 480.
Step-by-step explanation:
I need help quick with sampling methods
The local fighter fighters collect toys to distribute a various give-away events they have 4569 toys and will sponsor 129 giveaway events. how many toys can they each give away at each event? how many toys if any, will be left over?
What is the first part of the second step to prove that Sn 1 + 2 + 4 +. + 2n - 1 = 2n - 1? a. Show that Sn is valid for n = k c. Assume that Sn is valid for n = k b. Verify that Sn is valid for n = 1 d. Prove that Sn is valid for n = k + 1
The first part of the second step to prove the sequence is to prove that Sn is valid for n = k + 1, Option D is correct.
What is geometric sequence?Geometric sequence is the sequence in which the next term is obtained by multiplying the previous term with the same number for the whole series.
The sum of geometric sequence is given as,
[tex]s_n=\dfrac{r^n-1}{r-1}[/tex]
Here, a is the first term of the sequence, n is total terms and r is the common ratio.
The given equation which need to be proved is,
[tex]S_n= 1 + 2 + 4 +. ...+ 2n - 1 = 2n - 1[/tex]
This can be proved by induction method. This can be done by induction method with two steps:
Prove n=0, without getting any data of other cases.If the data or problem is given then assume n=k. For the given case is also true for n=k+1. Thus, in second step prove that Sn is vaild for n=k+1.Thus, the first part of the second step to prove the sequence is to prove that Sn is valid for n = k + 1, Option D is correct.
Learn more about the geometric sequence here;
https://brainly.com/question/1509142
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Write an expression that is equivalent to 16 + 56 using the product of the greatest common factor and a sum. ____ • ( 2 + ____ )
Answer:
Factors of 56: 1, 2, 4, 7, 8, 14, 28 and 56
Prime Factorization of 56: 56 = 23 × 7
Step-by-step explanation:
Please help me i don get it please show your work I will give brainyleast
Answer:
81.1 in
Step-by-step explanation:
To find the surface area of a triangular prism:
Find the base area and the remaining 3 rectangles and add them all together.
1.5*2=3 (base of the shape)
2*13=26
1.5*13=19.6
2.5*13=32.5
3+26+19.6+32.5=81.1
A farmer is planting a circular garden with a radius of 32 feet and needs to know the area to determine how many plants to purchase.
What is the area of the garden?
Use 3.14 for π.
Enter your answer, as a decimal, in the box.
Answer:
3215.36 ft^2.
Step-by-step explanation:
Area = 3.14 * r^2
= 3.14 * 32^2
= 3215.36 ft^2.
What is the value of w?
Answer:
x=29.3 degrees
Step-by-step explanation:
Vertical angles are congruent therefore the angle with the dot in it is 60.7 degrees and the combination of the dot and w is 90 degrees. 90-60.7=29.3
What is the axis of symmetry of the following equation?
Find the LCM of the following.
A. 28,42,35
B. 48,72,96
C. 36, 44
28/2= 14 42/2= 21 35/7= 5
14/ 2= 7 21/3= 7
28= 2^2 × 7
42= 2 × 3 × 7
35= 7 × 5
LCM= 420
B. 48,72,9648/2= 24. 72/2= 36. 96/3= 32
24/2= 12. 36/3= 12. 32/2= 16
12/3= 4. 12/3= 4. 16/2= 8
4/2= 2. 4/2= 2. 8/2= 4
4/2= 2
48= 2^4 × 3
72= 2^3 × 3^2
96= 2^5 × 3
LCM= 288
C. 36, 4436/3= 12. 44/2= 22
12/3= 4. 22/2= 11
4/2= 2
36= 3^2 × 2^2
44= 2^2 × 11
LCM= 396
Answer:
The answer is in the attachment
Step-by-step explanation:
!!PLEASE PLEASE PLEASE PLEASE MARK ME THE BRAINLIEST!!
What is the line of the slope shown below
Answer:
3
Step-by-step explanation:
[tex]\frac{-3-6}{2--1}=\frac{-9}{3}=3[/tex]
[tex] - 5 = a - 3[/tex]
I need help with this problem
[tex]~~-5=a-3\\\\\implies a =-5+3\\\\\implies a = -2[/tex]
how would i find the volume ?
Answer:
4900
Step-by-step explanation:
You multiply lengthxwidthxheight, all the given dimensions to get (25x14x14) 4900
What is the probability of choosing a gray button not replacing it and choosing gray again?
answer:
the probability of choosing a gray button is 3/5
after putting it back the probability remains the same, so 3/5 for both answers
Answer:
[tex]\sf \dfrac{3}{10}[/tex] = 0.3 - 30%
Step-by-step explanation:
[tex]\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}[/tex]
Given:
Grey buttons = 3White buttons = 2Total buttons = 5[tex]\sf P(gray) = \dfrac35[/tex]
If the button is not replaced, there are now:
Grey buttons = 3 - 1 = 2White buttons = 2Total buttons = 5 - 1 = 4[tex]\sf P(gray) = \dfrac24=\dfrac12[/tex]
Therefore,
[tex]\sf P(gray)\:AND\:P(gray)= \dfrac35 \times \dfrac12=\dfrac{3}{10}[/tex]
PLEASE FAST!!!! WILL GIVE BRAINLIEST!!!
Answer: 3 2/9
Step-by-step explanation:
It would be the numbers exact form. Not totally sure but it would be my best guess.
Use the segmants tanget to a circle theorem to find perimeter of JLNQ
Answer: 28
Step-by-step explanation:
If the sum of a number and six is doubled, the result is two less than the number. Find the number.
X =
Answer:
-14
Step-by-step explanation:
let the number= X
from the statement,
(X+6)×2 = X - 2
open bracket
2X +12 = X- 2
2X-X = -2-12
X = -14
The triangular base of the given prism has an interior angle with a measure of 80° and an interior angle with a measure of 55°. What is the measure of the unknown angle?
A. 45°
B. 65°
C. 75°
D. 85°
Answer:
A. 45°
Step-by-step explanation:
When we are given two measurements of interior angles we add both of those angles together.
Also know that a triangle equals 180 degrees
So when we write out this expression [tex]80+55+x=180[/tex]
[tex]135+x=180\\-135=-135\\x=45[/tex]
Hope this helps
The regular tax to be paid with any purchase is 8%. How much tax did Anthony pay if he bought school supplies worth ₱5 000?
Answer:
400
Step-by-step explanation:
8% of 5000 is 400. Math:
5000 x 0.08 = 400
Can someone help please. 'Preciate it.
Answer:
c = 9
Step-by-step explanation:
Given equation:
[tex]\sf 6(c-1)=48[/tex]
Divide both sides by 6:
[tex]\implies \sf \dfrac{6(c-1)}{6}=\dfrac{48}{6}[/tex]
[tex]\implies \sf c-1=8[/tex]
Add 1 to both sides:
[tex]\implies \sf c-1+1=8+1[/tex]
[tex]\implies \sf c=9[/tex]
Answer:
9
Step-by-step explanation:
There are now 48 total cookies shared by the 6 plates after he takes 1 cookie (6 cookies)
48+6 is 54/6 is 9
Please help! Will mark brainlyest.
Answer:
8
Step-by-step explanation:
5 - (-3) is like adding 5 + 3 which is 8
Please give me brainlist
Answer:
8
Step-by-step explanation:
To approximate the length of a marsh, a surveyor walks x=420 meters from point A to point B,then turns 75 degrees and walks 220 meters to point C (see figure). Approximate the length AC of the marsh. (Round your answer to one decimal place. )
Applying the law of cosine, b² = a² + c² - 2ac(cos B), the length of AC of the marsh, to one decimal place, is: 522.1 meters
What is the Law of Cosine?The Law of Cosine is given as, b² = a² + c² - 2ac(cos B).
From the diagram given, we have the following:
B = 180 - 75 = 105°b = AC (length of the marsh)a = 220 mc = 420 mPlug in the values into the law of cosine formula:
b² = 220² + 420² - 2(220)(420)(cos 105)
b² = 272,629.8
b = √272,629.8
b = 522.1 meters. (Length of AC of the marsh)
Learn more about the law of cosine on:
https://brainly.com/question/7872492
need help finding x
Answer:
The answer is X equals 12
Step-by-step explanation:
I hope you get it right!
Barnabas Price. Answer question attached. No reasoning required. Brainliest for first to answer correctly. Barnabas Price.
Y = 2.9
Or
X= 2.9, y= - 0.9
Hope this helps!
HELP ME PLEASEEEEE, DUE IN A FEW MINUTES!
Step-by-step explanation: 130
[tex]g(n) = 3n + 1[/tex]
[tex]h(n) = 4n + 3[/tex]
[tex](goh) (n)= g(h(n))[/tex]
[tex] = g(4n + 3) = 3(4n + 3) + 1[/tex]
[tex] = 12n + 9 + 1 = 12n + 10[/tex]
Therfore
[tex](gof)(n) = 12n + 10[/tex]
Now
[tex](gof)(10) = 12(10) + 10 = 120 + 10 = 130[/tex]
[tex](gof)(10) = 130[/tex]
I hope it helped you
Step-by-step explanation:
g(n) × h(n)
=(3n+1)(4n+3)
= 12n² +9n +4n +3
= 12n² +13n + 3
then sub 10 in place of n
12n² +13n + 3
= 12(10)²+13(10)+3
=1200+130+3
=1333
1/4x + 1 + 3/4x - 2/3 - 1/2x =
Answer:
1/2x + 1/3
Step-by-step explanation:
1/2x + 1/3
0.67 divided by 10 help someone
Answer:
0.067
Step-by-step explanation:
We just move 0.67's decimal point to the right by one since we are dividing by 10.
0.67 / 10 = 0.067
Sure hope this helps you :)
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