Answers
Answer:
We will use a Pythagorean identity and alegbra to prove this.
sin^2 + cos^2 = 1, dividing by cos^2 gives
tan^2 + 1 = sec^2.
Now, breaking down the fraction into parts and simplifying gives:
(1-sin^4)/cos^4 = 1/cos^4 - sin^4/cos^4 = sec^4 - tan^4
Now use difference of squares factoring from alegbra.
= (sec^2 + tan^2)*(sec^2 - tan^2)
By rewriting our Pythagorean identity to
sec^2 - tan^2 = 1 and tan^2 = sec^2 - 1,
we can finish the problem.
= (sec^2 + tan^2) * 1 = sec^2 + tan^2
= sec^2 + (sec^2 - 1) = 2*sec^2 - 1.
Related Questions
Tp 3 Work Backwards
1. Bowser, Abby, and Chuckles are 3 dogs with a
combined age of 44. Bowser is 6 years older than
Abby. Abby is 2 years younger than Chuckles, c.
Which expression could be used to find the age of
Chuckles?
Answers
Answer:
Your equation option is possibly in here somewhere.
Step-by-step explanation:
A = C - 2
B = A + 6 → A = B - 6
C - 2 = A = B - 6 → B = C + 4
44 = C + B + A
44 = C + (C + 4) + (C - 2)
44 = 3C + 2
42 = 3C
C = 7
Heeeeelllllllppppppp
Answers
1.
[tex]y=\frac{5}{3} x-2[/tex]
2.
[tex]y=-2x+2[/tex]
3.
[tex]y=x+5[/tex]
4.
[tex]y=\frac{1}{4}x[/tex]
Can somebody answer this?
Answers
True
One from of the linear function is Y = mx + b where b is the y intercept.
The y intercept is where x is 0 so it would be at (0,6)
Find the cardinal number of the set:
C={1/x x is an integer that's greater than or equal to 4 and less than or equal to 9}.
Answers
Answer: 6
Step-by-step explanation:
Ok lemme actually format this set
[tex]$C = \left\{\frac 1x : x \in \mathbb{Z}\ \text{and}\ 4 \leq x \leq 9\right\}$[/tex]
Well the only integers from 4 to 9 are 4, 5, 6, 7, 8, 9. So this set is just
[tex]$C = \left\{\frac 14, \frac 15, \frac 16, \frac 17, \frac 18, \frac 19\right\}$[/tex]
which has cardinality [tex]\boxed{6}[/tex] .
A student's cost for last semester at her community college was 2800. She spent 448 of that on books. what percent of semester's college costs was sp books?
Answers
16%
Step-by-step explanation:
Percent can by calculated by part divided by whole multiplied by one hundred so (448/2800)*100=16
what is the measure of x?
Answers
Answer:
Hello!
After reviewing the problem you have provided I have come up with the correct solution:
x= 9
Step-by-step explanation:
To come up with this solution you have to first realize that the smaller triangle is a proportionally scaled down version of the entire larger triangle! (I will show what I mean in a linked picture)
So after we have realized that the smaller triangle is a scaled down version of the larger one, we can then create a formula or ratio to calculate the value of the missing side of the larger triangle (being x+6=??).
To create the formula/ratio I divided 10inches by 4inches. Thus the larger triangle is 2.5 times larger than the smaller one.
I then use this ratio to figure out the missing length of the larger triangle by doing:
6inches x 2.5 = 15inches.
I then inputed the 15inches into the formula of the missing side:
x+6=15
Subtracted 6 from both sides to simplify, and came up with the solution!
x=9
Let me know if this helps!
please help with this
Answers
Answer:
2,4,6,
6,12,18
10,20,30
Write the equation of the line in Point-Slope Form given the information below.
Slope=7
Point=(1,4)
Answers
Answer:
Step-by-step explanation:
y - 4 = 7(x - 1)
y - 4 = 7x - 7
y = 7x - 3
i need help on this math problem
Answers
Answer:
Natalie pays $9 every week.
d = 9w + 72
Step-by-step explanation:
hi if you know 8th grd math pls help
Answers
Answer:
all correct except A.
Step-by-step explanation:
pls mark me brainly if u can
John drives from home to his
parents house and then to a
cafe. His parents house is 13
miles south of his home and
the cafe is 6 miles east of his
parents house. What is the
distance, in miles, between his
home and the cafe SHOW YOUR WORK
Answers
Answer:
13=6 and no
Step-by-step explanation:
Answer:
The distance is 19 miles
Step-by-step explanation:
I know that because you have to add how many he drove to his parents and the amount of miles driven to the cafe and then it will give the total amount driven.
Assume that a set of test scores is normally distributed with a mean of 80 and a standard deviation of 10.
Use the 68-95-99.7 rule to find the following quantities.
a. The percentage of scores less than 80 is _%.
Answers
Answer:
I don't know
Step-by-step explanation:
you have to estimate
Answers
802x94
=75388
Answer:
75,388
Step-by-step explanation:
Long Multiplication form
[tex]\mathrm{Mutliply\:the\:bold\:numbers}[/tex]
[tex]\frac{\begin{matrix}\space\space&8&0&\textbf{2}\\ \times \:&\space\space&9&\textbf{4}\end{matrix}}{\begin{matrix}\space\space&\space\space&\space\space&8\end{matrix}}[/tex]
[tex]\frac{\begin{matrix}\space\space&8&\textbf{0}&2\\ \times \:&\space\space&9&\textbf{4}\end{matrix}}{\begin{matrix}\space\space&\space\space&0&8\end{matrix}}[/tex]
[tex]\mathrm{Multiply}\\\\8\cdot \:4=32[/tex]
[tex]\mathrm{Carry\:}3\mathrm{\:to\:the\:column\:on\:the\:left\:and\:write\:}2\mathrm{\:in\:the\:result\:line}[/tex]
[tex]\frac{\begin{matrix}\space\space&3&\space\space&\space\space&\space\space\\ \space\space&\space\space&\textbf{8}&0&2\\ \times \:&\space\space&\space\space&9&\textbf{4}\end{matrix}}{\begin{matrix}\space\space&\space\space&2&0&8\end{matrix}}[/tex]
[tex]\mathrm{Add\:the\:carried\:digit,\:}3\mathrm{,\:to\:the\:result}[/tex]
[tex]\frac{\begin{matrix}\space\space&3&\space\space&\space\space&\space\space\\ \space\space&\space\space&8&0&2\\ \times \:&\space\space&\space\space&9&4\end{matrix}}{\begin{matrix}\space\space&3&2&0&8\end{matrix}}[/tex]
[tex]\mathrm{Multiply\:the\:top\:number\:by\:the\:bolded\:digit\:of\:the\:bottom\:number}[/tex]
[tex]\frac{\begin{matrix}\space\space&\space\space&\textbf{8}&\textbf{0}&\textbf{2}\\ \space\space&\times \:&\space\space&\textbf{9}&4\end{matrix}}{\begin{matrix}\space\space&3&2&0&8\end{matrix}}[/tex]
[tex]\mathrm{Mutliply\:the\:bold\:numbers}:\quad \:2\cdot \:9=18[/tex]
[tex]\mathrm{Carry\:}1\mathrm{\:to\:the\:column\:on\:the\:left\:and\:write\:}8\mathrm{\:in\:the\:result\:line}[/tex]
[tex]\frac{\begin{matrix}\space\space&\space\space&\space\space&1&\space\space\\ \space\space&\space\space&8&0&\textbf{2}\\ \space\space&\times \:&\space\space&\textbf{9}&4\end{matrix}}{\begin{matrix}\space\space&3&2&0&8\\ \space\space&\space\space&\space\space&8&\space\space\end{matrix}}[/tex]
[tex]\mathrm{Add\:the\:carried\:number\:to\:the\:multiplication}:\quad \:1+0\cdot \:9=1[/tex]
[tex]\frac{\begin{matrix}\space\space&\space\space&\space\space&\textbf{1}&\space\space\\ \space\space&\space\space&8&\textbf{0}&2\\ \space\space&\times \:&\space\space&\textbf{9}&4\end{matrix}}{\begin{matrix}\space\space&3&2&0&8\\ \space\space&\space\space&1&8&\space\space\end{matrix}}[/tex]
[tex]\mathrm{Mutliply\:the\:bold\:numbers}:\quad \:8\cdot \:9=72[/tex]
[tex]\mathrm{Carry\:}7\mathrm{\:to\:the\:column\:on\:the\:left\:and\:write\:}2\mathrm{\:in\:the\:result\:line}[/tex]
[tex]\frac{\begin{matrix}\space\space&7&\space\space&1&\space\space\\ \space\space&\space\space&\textbf{8}&0&2\\ \times \:&\space\space&\space\space&\textbf{9}&4\end{matrix}}{\begin{matrix}\space\space&3&2&0&8\\ \space\space&2&1&8&\space\space\end{matrix}}[/tex]
[tex]\mathrm{Add\:the\:carried\:digit,\:}7\mathrm{,\:to\:the\:result}[/tex]
[tex]\frac{\begin{matrix}\space\space&7&\space\space&1&\space\space\\ \space\space&\space\space&8&0&2\\ \times \:&\space\space&\space\space&9&4\end{matrix}}{\begin{matrix}\space\space&3&2&0&8\\ 7&2&1&8&\space\space\end{matrix}}[/tex]
[tex]\mathrm{Add\:the\:rows\:to\:get\:the\:answer.\:\:\:Fill\:in\:trailing\:zeros\:\:(not\:required)}[/tex]
[tex]\frac{\begin{matrix}\space\space&\space\space&8&0&2\\ \space\space&\times \:&\space\space&9&4\end{matrix}}{\begin{matrix}0&3&2&0&8\\ 7&2&1&8&0\end{matrix}}[/tex] [tex]=75,388[/tex]
See Image for the addition:
find the sum of all the odd numbers between 51 and 99 inclusive
Answers
Answer:
1875
Step-by-step explanation:
9) You want to buy a backpack which costs $34.82. Now it is on sale of 30% off. What is the
discount amount? What is the final cost with the discount?
Answers
Answer:
10.446
Step-by-step explanation:
John has $50 he spent 1/5 of it on a book and 1/10 on a flashlight how much money did he have left
Answers
please help struggling a lot!
Answers
Answer:
- 162, 486, - 1458
Step-by-step explanation:
To find the next term in a geometric sequence , multiply the previous term by the common ratio r
r = [tex]\frac{T_{2} }{T_{1} }[/tex] = [tex]\frac{-18}{6}[/tex] = - 3 , then
T₄ = T₃ × - 3 = 54 × - 3 = - 162
T₅ = T₄ × - 3 = 486
T₆ = T₅ × - 3 = - 1458
hey yall it's holiday season and I want to wish you all a good Christmas and Thanksgiving anyways what is your favorite nintendo game?
Answers
Answer:
Merry xmas bro
Step-by-step explanation:
fav nintendo game is the first mario
A rectangular garden is 20ft longer than it is wide. It’s area is 6300ft^2. What are its dimensions
Answers
Answer:
Length = 90 feet
Width = 70 feet
Step-by-step explanation:
The area of a rectangle is found by finding the product of the length. Therefore, the following formula equation can be made:
[tex]A=lw[/tex]
The problem tells us that the area of the garden is 6,300 square feet and that the length is 20 feet longer than the width. Therefore, our equation can be rewritten as such:
[tex]6300=(w+20)(w)~or~6300=w(w+20)[/tex]
Now that there are no longer two different variables, we can solve for w.
[tex]6300=w(w+20)\\\\6300=w^2+20w\\\\0=w^2+20w-6300[/tex]
We are left with a trinomial so we'll use the quadratic formula to further solve for w.
[tex]w=\frac{-20\pm\sqrt{20^2-4(1)(-6300)} }{2(1)}\\\\w=\frac{-20\pm\sqrt{400+25200} }{2}\\\\w=\frac{-20\pm\sqrt{25600} }{2}\\\\w=\frac{-20\pm160}{2}\\\\\\w=70\\or\\w=-90[/tex]
Since distance cannot be negative, w = -90 cannot be a solution for this problem. Therefore, the width of the rectangular garden is 70 feet.
Now that the width has been found, we know the length is 20 feet longer than it. Therefore, the length is 90 feet.
Which expression is equivalent to the given expression?
5x – 2
A2 – 5x
B 2x – 2 + 3x
C 3 – 5 + 2x
D 5x — 2х
Answers
Answer:
I DON'T KNOW WHERE YOu belong because im in philippines
Solve for r.
4r–3r=20
r=
Answers
Answer:
20
Step-by-step explanation:
4r - 3r = 20
r = 20
There you go.
Answer:
r = 20
Step-by-step explanation:
Let's solve your equation step-by-step.
4r − 3r = 20
Step 1: Simplify both sides of the equation.
4r − 3r =20
4r + −3r =20
(4r + −3r) =20 (Combine Like Terms)
r = 20
Hope this helps
they are sixty four thousand people at a football game 80% of the people were supporting the home team how many people were supporting the home team
Answers
Answer:
51200
Step-by-step explanation:
64000×80%=51200
[tex]\huge\mathfrak{question}[/tex]
they are sixty four thousand people at a football game 80% of the people were supporting the home team how many people were supporting the home team
[tex] \huge \mathfrak step \: by \: step[/tex]
First we will look for how much 80% of 64,000 is.
Lets put our equation
[tex]64000 \times 80 \div 100[/tex]
solve it and we get
[tex]{{\boxed{{51200}}}}}[/tex]
as our answer
Suppose that we compute a 90% confidence interval for an unknown population mean . Which of the following is a correct interpretation?
90% of all possible
Answers
Are the following two lines parallel, perpendicular, neither, or the same line?
3x+4y = 2
4x+3y = 2
what are they?
Answers
Answer:
Neither.
Step-by-step explanation:
Manipulate the formulas into slope-intercept form which is [tex]y=mx+b[/tex].
In order for them to be parallel, m needs to be the same. Perpendicular, m for one needs to be the negative reciprocal of the other [tex]m=-\frac{1}{m}[/tex].
Let's see what we get.
(1)
[tex]3x+4y=2\\4y=-3x+2\\y=-\frac{3}{4}x+1/2[/tex]
(2)
[tex]4x+3y=2\\3y=-4x+2\\y=-\frac{4}{3}x+2/3[/tex]
They are reciprocals, but they are both negative. So, they are not the same line, perpendicular, nor parallel.
Also, you can graph these equations on desmos and see easily that they have none of these relationships.
use a calculator to find the square for 7.6
Answers
Answer:
Using a calcuator, [tex]7.6^{2} =57.76[/tex]
Answer:
Hey mate....
Step-by-step explanation:
This is ur answer....
Shows me 57.76 well....Hope it helps!
Brainliest pls!
Follow me! ♧
I just need the properties in order help plz
Answers
[tex] \: \: \: \: [/tex]
[tex]6x - 30 - 3x = - 12[/tex]
move the variable to the left hand side and change its sign, move the constant to the right hand side and change its sign[tex]6x - 30 = - 12[/tex]
collect like terms and calculate the sum[tex] 3x = - 18[/tex]
divide both sides of the equation by 3[tex]x = 3[/tex]
hope it helps[tex] \: \: \: \: \: [/tex]
[tex]\sf \longmapsto6(x−5)=3x−12[/tex]
Simplify both sides[tex]\sf \longmapsto(6)(x)+(6)(−5)=3x+−12[/tex]
[tex]\sf \longmapsto6x+−30=3x+−12[/tex]
[tex]\sf \longmapsto \: 6x - 30 = 3x - 12[/tex]
Subtract 3x from both sides[tex]\sf \longmapsto \: 6x−30−3x=3x−12−3x[/tex]
[tex]\sf \longmapsto3x−30=−12[/tex]
Add 30 to both sides[tex]\sf \longmapsto3x−30+30=−12+30[/tex]
[tex]\sf \longmapsto3x=18[/tex]
Divide both sides by 3[tex]\sf \longmapsto \: \dfrac{3x}{3} = \dfrac{18}{3} [/tex]
[tex]\sf \longmapsto \: x = 6[/tex]
[tex] \boxed{\sf \: x = 6 }[/tex]
If Esteban continues at the same rate, how many miles will he have traveled in 6 hours?
A. 36
B. 300
C. 360
D. 420
Answers
Answer360
Step-by-step explanation:
Jackie works as a server at a local restaurant. She makes $8 per hour. She worked 34 hours last week. She made $250 in tips. What was her gross pay?
Answers
272 plus. 250 = 522
Each square below represents one whole …. What percent is represented by the shaded area?
Answers
we see that one half of the square is shaded. therefore that’s 1/2. and to cover to a percentage, we multiply the fraction by 100%!
therefore: 1/2 x 100%= 50%
hope this helped❤️
Answer:
50%
Step-by-step explanation:
The diagonal line divides the square in half
I hope this help you
paki sagot po kailangan na kasi..
thank you in advance ☺
Answers
1. 5
2.2
3.2,5
4.2,5
5.2
HOPE IT HELPS:)
PLS FOLLOW:)
#BRAINLIEST:)