Answers
Answer:
[tex]{ \tt{ \tan {}^{4} \theta + { \sec }^{2} \theta }} \\ { \tt{ = ({ \tan }^{2} \theta ){}^{2} + { \sec }^{2} \theta }} \\ = { \tt{ {-(1 - { \sec }^{2} \theta) }^{2} + { \sec }^{2} \theta }} \\ { \tt{ = -(1 - 2 { \sec }^{2} \theta + { \sec }^{4} \theta) + { \sec}^{2} \theta}} \\ { \tt{ = -(1 - { \sec }^{2} \theta) + { \sec }^{4} \theta}} \\ { \tt{ = -{ \tan}^{2} \theta + { \sec }^{4} \theta }} \\ = { \tt{ { \sec}^{4} \theta - { \tan }^{2} \theta}} \\ { \bf{hence \: proved}}[/tex]
Related Questions
Pleaseeee helppppppp
Answers
Answer:
d = 8t
Step-by-step explanation:
Please helppppp!!!!!!!!
Answers
Answer:
128 cm^2
Step-by-step explanation:
The area of a trapezoid is given by
A = 1/2 (b1+b2) h
where b1 and b2 are the lengths of the bases and h is the height
A =1/2( 10+22) * 8
A = 1/2 (32)8
= 128
Answer:
A=128 cm²
Step-by-step explanation:
Hi there!
We are given a trapezoid and we want to find the area of it
The area of a trapezoid is given as [tex]\frac{a+b}{2}h[/tex], where a and b are the bases and h is the height
The bases are the parallel sides
They are the sides marked as 10 cm and 22 cm in this case
The height is the distance between the bases
In this case, it is the side marked as 8 cm
We know everything needed for the area, let's just label everything to avoid any confusion
a=10
b=22
h=8
Now substitute into the formula
A=[tex]\frac{a+b}{2}h[/tex]
A=[tex]\frac{10+22}{2}*8[/tex]
add the numbers on the numerator together
A=[tex]\frac{32}{2}*8[/tex]
Divide 32 by 2
A=16*8
multiply
A=128 cm²
Hope this helps!
Which of the following is equivalent to (x+5)(2x^2 +8)?
A. (x+5)(2x^2)• (X+5)(8)
B. (x+5)(2x^2)+(x+5)(8)
C. (x+5)(2x)+(x+5)(8)
D. (x+5)(2x)• (x+5)(8)
Answers
Answer:
(x+5)(2x^2 +8)
Multiply (x+5) in both sides
(x+5)(2x^2) × (x+5)(8)
Answer is a
Mr. Sun borrowed $15,600 for 54 months at simple interest to pay for a new swimming pool. If Mr. Sun paid the bank a total of $21,567.00, what was the simple interest rate of the loan?
Answers
Given:
Mr. Sun borrowed $15,600 for 54 months at simple interest.
Mr. Sun paid the bank a total of $21,567.00.
To find:
The rate of simple interest.
Solution:
We know that,
12 months = 1 year
1 month = [tex]\dfrac{1}{12}[/tex] year
54 months = [tex]\dfrac{54}{12}[/tex] year
54 months = 4.5 years
Simple interest is:
[tex]S.I.=Amount-Principal[/tex]
[tex]S.I.=21567-15600[/tex]
[tex]S.I.=5967[/tex]
Formula for simple interest is:
[tex]S.I.=\dfrac{P\times r\times t}{100}[/tex]
Where, P is principal, r is the rate of interest in percent and t is the number of years.
Putting [tex]S.I=5967,P=15600,t=4.5[/tex], we get
[tex]5967=\dfrac{15600\times r\times 4.5}{100}[/tex]
[tex]596700=70200r[/tex]
[tex]\dfrac{596700}{70200}=r[/tex]
[tex]8.5=r[/tex]
Therefore, the rate of simple interest is 8.5%.
look at photo! please help needed! 1.
Answers
Answer:
5/12
Step-by-step explanation:
it says in the question that 1/4 +1/3 is used so in order to make it simple we have to find the common denominator that is 12. so converting 1/4 is 3/12 and 1/3 is 4/12.so u add the numerator and u get 7 over 12 .so now the whole container of peanuts is 12/12 but 7/12 is used so 12-7= 5. so ur ans is 5/12
Can some one help me solve these 3 questions?
Answers
8. Is the 1st picture
9.is the second picture
plzzz helpppp dont ignoreeee
Answers
Answer:
X= 40
Step-by-step explanation:
2(110 + 4x) = 220 + 8x = 540
8X = 320
X= 40
x = 17.5
Step-by-step explanation:
Since there’s a dashed line between the shape, the new total = 180* (degrees)
110* + 3x + x = 180*
Subtract 110 from 180
3x + x = 70
x = 17.5
Questlon 4 of 10
What is the midpoint of the segment shown below?
AE
101
O A. (10.)
(5.4)
O B. (5,1)
10
(5,-3)
O C. (5,-)
O D. (10,1)
SUBMIT
Answers
Answer:
c
Step-by-step explanation:
To find the midpoint the formulas
x=x1+x2/2 and y=y1+y2/2 are used
in this case x1 is 5,x2 is 5,y1 is 4 and y2 is -3
therefore
x=5+5/2.
=10/2
=5
y=4+(-3)/2
=1/2
The midpoint of a line segment divides the line into equal segments
The midpoint of the line segment is (5,1/2)
The endpoints of the line is given as:
(5,4) and (5,-3)
The midpoint of the line is calculated as:
(x,y) = 0.5(x1 + x2, y1 + y2)
So, we have:
(x,y) = 0.5(5 + 5, 4 - 3)
Evaluate the sum and difference
(x,y) = 0.5(10, 1)
Evaluate the product
(x,y) = (5, 1/2)
Hence, the midpoint of the line segment is (5,1/2)
Read more about midpoints at:
https://brainly.com/question/16828532
Harry reads that a particular element has an atom with a mass of 0.000000000012 grams. What is the weight of the atom expressed in scientific notation?
A.
1.2 × 10-9 grams
B.
1.2 × 10-11 grams
C.
1.2 × 1011 grams
D.
1.2 × 1012 grams
Answers
Answer:
Since this number is small we know that the exponent will be negative.
In scientific notation the decimal must be between the first two NON zero numbers. So move the decimal and count how many positions it was moved.
1.2 x 10 ^-11
Step-by-step explanation:
3х + 5
Invers of function f
Answers
Answer:
x-2/3 is the answer.......
Please mark me as Brainliest
Emily is entering a bicycle race for charity. Her mother pledges $0.30 for every 0.5 mile she
bikes. If Emily bikes 10 miles, how much will her mother donate?
Her mother will donate $
Answers
Answer:
The mother will donate $5
Another way to solve this is divide 10 by 0.5. This gives us 20, and if we multiply 20 by 0.30 we get $6.
Solve for the missing angle. Round to the nearest degree.
Answers
Step-by-step explanation:
here's the answer to your question
Ahmed is making 8 kites. He uses 5 yards of ribbon for each kite. If he adds 3 more identical kites which he has already made before, how many kites will Ahmed have in toTal
Answers
he would have 11 kites in total, hope this helps!
What are the fractions simplest form
Answers
Answer:
the first one 2/-1, hope it helps...
Can someone help me figure this out?
Answers
Answer:
See picture below.
Step-by-step explanation:
I had to write a new option for one of the lines.
How many real solutions exist for this system of equations?
y=x^2+4
y= 4x
ОА. .
zero
OB.
one
Ос.
two
OD
infinite
Reset
Next
Answers
Answer:
One
Step-by-step explanation:
Set each equations equal to each other
[tex] {x}^{2} + 4 = 4x[/tex]
[tex] {x}^{2} - 4x + 4[/tex]
Find the discrimant.
[tex]{ - 4 {}^{2} - 4(1)(4) } = 0[/tex]
This means there is one real solution. Since the discramnt equal 0.
find the LCM and hcf of 72 and 162 , leaving the LCM in prime factors
Answers
=========================================================
Explanation:
Find the prime factorization of 72 and 162
72 = 8*9 = 2^3*3^2162 = 2*81 = 2*9^2 = 2*(3^2)^2 = 2*3^4Here's a simplified version of each
72 = 2^3*3^2162 = 2*3^4We have these unique primes: 2, 3
Circle the terms that have the largest exponents for each of those unique primes. So you'll circle 2^3 and 3^4. Those items circled will multiply together to get the LCM.
This means 2^3*3^4 is the LCM (lowest common multiple).
2^3*3^4 turns into 648, but your teacher wants you to keep the LCM in prime factor form.
------------------------------
Now onto the HCF (highest common factor; aka GCF).
Looking at
72 = 2^3*3^2162 = 2*3^4We again see '2's and '3's as the unique primes. Both have at 1 copy of '2' between them. They also both have 3^2 between them. It might help to think of 3^4 as 3^2*3^2.
Those common factors you circled are then multiplied.
Overall, the HCF is 2*3^2 = 2*9 = 18
-----------------------------
Side note: The HCF is useful to help reduce fractions, while the LCM is useful to help find the LCD (lowest common denominator) when adding or subtracting fractions of different denominators. There are other applications of each of these.
Answer:
LCM= 648
HCF= 18
Step-by-step explanation:
what is the significant figures for 0.045325
Answers
Answer:
There are 5 significant digits in 0.045325 and they are 4, 5, 3, 2, and 5.
Step-by-step explanation:
Significant digits rules:
All non-zero numbers count as significant digitsLeading zeroes (zeroes in front of any non-zero numbers) are never significant digitsZeroes in-between non-zero numbers count as a significant digitsTrailing zeroes (zeroes after all non-zero numbers) count only if there is a decimalIn 0.045325, the two zeroes are leading zeroes and therefore do not count. The rest of the digits, (4, 5, 3, 2, and 5) are all non-zero and therefore count. Thus, there are 5 significant digits in 0.045325.
2z^8- 32z^8
Help plz
Answers
Answer:
-30z^8
Step-by-step explanation:
[tex]2 {z}^{8} - 32 {z }^{8} \\ = - 30 {z}^{8} [/tex]
Answer:
-30z^8
Step-by-step explanation:
2z^8- 32z^8
-30z^8
Write the equation of the line that passes through the points (8, –1) and (2, –5) in standard form, given that the point-slope form is y + 1 = (x – 8).
Answers
Answer:
A linear equation in the standard form is written as:
y = a*x +b
where a is the slope and b is the y-intercept.
If we know that the line passes through the points (a, b) and (c, d), then the slope can be written as:
a = (d - b)/(c - a)
So we know that our line passes through the points (8, -1) and (2, -5)
then the slope will be:
a = (-5 - (-1) )/(2 - 8) = (-4/-6) = 2/3
Then our line is something like:
y = (2/3)*x + b
to find the value of b, we can use the fact that we know that our line passes through the point (2, -5)
this means that when x = 2, we must have y = -5
replacing these values in the equation we get:
-5 = (2/3)*2 + b
-5 = 4/3 + b
-5 - 4/3 = b
-15/3 - 4/3 = b
-19/3 = b
then the equation is:
y = (2/3)*x - 19/3
(in the question you wrote the point-slope form, but you can see that it does not work for the second point, so there may be a mistake there, as the slope is missing)
The actual equation in the point-slope form is:
y + 1 = (2/3)*(x - 8)
Answer:
The answer is 2x + -3y = 19
Step-by-step explanation:
I Got It Right Instruction on edge
What does x stand for in the equation 1+x=2
Answers
x = 1
Step-by-step explanation:
1 + x = 2
x = 1
Ross walked 3 m east and 6 m north. How far is he from the starting point
Answers
Answer:
3 sqrt(5) meters
Step-by-step explanation:
This is a right triangle so we can use the Pythagorean theorem.
a^2 +b^2 = c^2 where a and b are the legs and c is the hypotenuse
3^2+6^2 = c^2
9+36 = c^2
45 = c^2
Taking the square root
sqrt(45) = sqrt(c^2)
sqrt(9*5) = c
sqrt(9) sqrt(5) =c
3sqrt(5) = c
[tex]\boxed{\large{\bold{\blue{ANSWER~:) }}}}[/tex]
Given:-Ross walked 3 m east and 6 m north. Find:-How far is she from the starting point?solution:-Ross walked 3 m east and 6 m north.
so her path is a right angle triangle path.
we know that,
in a right angle triangle, According to the Pythagorean theorom,
[tex]\boxed{\sf{l^2+b^2=h^2 }}[/tex]
where
l= legs b=baseh=hypotenuse According to the question, [tex]\sf{3^2+6^2=f^2 }[/tex] [tex]\sf{9+36=f^2 }[/tex] [tex]\sf{ f^2=45 }[/tex] [tex]\sf{f=\sqrt{45} }[/tex] [tex]\sf{f=3\sqrt{5} }[/tex] Therefore:-he is [tex]\sf{3\sqrt{5} }[/tex] far from the starting point
3 of 9
Express the ratio below in its simplest form.
2:4:2
Answers
Answer:
1 : 2 : 1
Step-by-step explanation:
2:4:2
Divide each term by 2
2/2:4/2:2/2
1 : 2 : 1
Please help I need this
Answers
Answer:
from side a _2,4.5
from side b _-4
5,-2.
hope this will be helpful for you.
Is (5, 0) a solution to the equation y = x + 5?
Guys I need help
Answers
Answer:
no
Step-by-step explanation:
substitute the x- coordinate 5 into the equation and if the result is equal to the y- coordinate 0 then it is a solution
y = 5 + 5 = 10 ≠ 0
Then (5, 0 ) is not a solution to the equation
Mike, a Salvation Army bell ringer, has 20% as many quarters as nickels in his cup. If Mike has $6.00 in quarters and nickels, how many nickels does he have?
Answers
5.8 Nickels
Step-by-step explanation:
Let x rep no of Nickels in Mike's cup
Then x - 0.2 = Number of quarters in Mike's cup
0.2x = Amount of money that mike has from the nickels
1 ( x - 0.2) = Amount of money that Mike has from the quarter
Then,
0.2x + 1 (x - 0.2) = 6
Expand the bracket
0.2x + x - 0.2x = 6
x = 6
Recall
x - 0.2 = 0
6 - 0.2 = 5.8
Therefore, Mike has 5.8 nickels for the quarter
Find the decay factor from the model y =4520(0.6)square 6
Answers
Answer:
Step-by-step explanation:
Instructions: Find the measure of the indicated angle to the nearest
degree.
26
?
32
? =
Answers
Answer:
36
Step-by-step explanation:
Since this is a right triangle we can use trig functions
cos theta = adj side / hyp
cos ? = 26/32
Taking the inverse cos of each side
cos^-1(cos ?) = cos^-1( 26/32)
? = 35.65908
To the nearest degree
? = 36
SECTION B
A matatu and Nissan left town A for town B 240km away at 8.00 a.m travelling at 90km/hr
and 120km/hr respectively. After 20 minutes the Nissan had a puncture which took 30
minutes to mend.
(5mks
a) How far from town A did the Nissan catch up with the matatu?
Answers
9514 1404 393
Answer:
180 km
Step-by-step explanation:
The Nissan had traveled (120 km/h)(1/3 h) = 40 km when it had the puncture. It started from that location when the puncture was repaired at t = (1/3+1/2) = 5/6, where t is in hours. Then the two vehicles met (again) when ...
Matatu distance = Nissan distance
90t = 40+120(t -5/6)
0 = 40 +30t -100 . . . . . . subtract 90t, eliminate parentheses
60 = 30t . . . . . . . . . . . add 60
2 = t . . . . . . . . . . . . . 2 hours after leaving, the cars meet again
That distance from town A is ...
y = 90t = 90(2) = 180 . . . . km
What number cube has faces numbered 1 to 6.
Answers
Answer:
I don`t see the attachment
Step-by-step explanation:
