[tex]\tt (1 - sin ^2x)\times(1+tan^2x) = 1[/tex]
L.H.S
[tex]\tt cos^2x \times sec^2x[/tex]
[tex]\tt cos^2x \times \frac{1}{cos^2x}[/tex]
[tex]\tt \cancel{ cos^2x} \times\cancel{ \frac{1}{cos^2x}}[/tex]
[tex]\tt 1[/tex]
R.H.S
Hence proved
Step-by-step explanation:
[tex]{ \tt{ \blue{(1 - { \sin}^{2}x )(1 + { \tan }^{2}x) = 1 }}}[/tex]
• Remember → 1 + tan²x = sec²x
[tex] = { \tt{ \blue{(1 - { \sin }^{2}x)( { \sec}^{2}x) }}}[/tex]
• But sec²x → 1/cos²x
[tex] = { \tt{ \blue{(1 - { \sin}^{2} x)( \frac{1}{ \cos {}^{2} x} )}} }\\ \\ = { \blue {\tt{ \frac{1 - { \sin }^{2}x }{ { \cos }^{2}x } }}}[/tex]
• Remember from the first identity of trignometry;
[ cos²x + sin²x = 1 ].
• Therefore: [ cos²x = 1 - sin²x ]
[tex] = { \blue{\rm{ \frac{1 - { \sin}^{2}x }{1 - { \sin }^{2}x } }}} \\ \\ { \rm{ \blue{= 1 \: }}}[/tex]
Hence proved.
Find the missing side of triangle
Final Answer:
x = 20
Step-by-step explanation:
we'll be using the pythagorean theorem method, in this triangle the missing letter is a.
formula: [tex]a=\sqrt{c^2-b^2}[/tex]
a = x
b = 21
c = 29
a = [tex]\sqrt{29^2-21^2}[/tex]
a = [tex]\sqrt{841-441}[/tex] (note: 29² = 29 × 29 = 841 and 21² = 21 × 21 = 441)
a = [tex]\sqrt{400}[/tex]
a = 20
x = 20
10 • 4/10y = -28 • 10
Answer:
y=-70
Step-by-step explanation:
10.4/10y=-28.10
4y=-280
y=-70
Is the following number rational or irrational?
-117
Choose 1 answer:
Rational
Irrational
Answer:
-117 is irrational number
Answer:
Irrational
Step-by-step explanation:
Irrational number can't be written as a faction, -11pie can't be written as a fraction. Therefore it is a irrational number.
Which of the following is the domain of the function based on the input-output table below?
Answer:
C
Step-by-step explanation:
The domain is the left side of the table
What is the sum of the polynomials?
(7x3 – 4x2) + (2x3 – 4x2)
9x3 – 8x2
5x3
5x3 – 8x2
9x3
Answer:
9x3 - 8x2
Step-by-step explanation:
7x3+2x3 = 9x3
-4x2+(-4x2) = -8x2
Answer:
D
Step-by-step explanation:
what is the side length of the square in cm
Answer:
8.4 cm^2
Step-by-step explanation:
The area of the rectangle is
A = lw
A = 3x *5x = 15x^2
126 = 15x^2
126/ 15 =15x^2/15
42/5 = x^2
We want to find the area of the square
A = l*w
A = x*x
A = x^2 = 42/5 = 8.4 cm^2
In triangle ABC, AC=13, BC=84, and AB=85. Find the measure of angle C
Answer:
90°
Step-by-step explanation:
Angle C = arccos((84²+13²-85²)/(2×84×13))
= arccos(0/2184)
= arccos(0)
= 90°
Answered by GAUTHMATH
this graph represents the function f(x)=4sin(x) which statement is true about this function
Answer:
A
Step-by-step explanation:
The function is increasing in the interval in A because as the x-values increase so do the y-values on the graph, which can be shown by the graph sloping upwards at that specific section.
The graph of a function is increasing on the interval (3π/2, 2π) option (A) is correct.
What is trigonometry?Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.
We have given a graph of a trigonometric function,
As we know, the trigonometric function is sinusoidal in nature, and it has a domain of all real numbers and lies between the [a, a]where is the amplitude of the function.
The trigonometric ratio is defined as the ratio of the pair of a right-angled triangle.
From the graph, the function is increasing from 3π/2 to 2π
The graph slopes upward at that particular segment, indicating that the function is increasing in the interval in A as the x-values increase and the y-values on the graph follow suit.
Thus, the graph of a function is increasing on the interval (3π/2, 2π) option (A) is correct.
Learn more about trigonometry here:
brainly.com/question/26719838
#SPJ5
The Cave of Swallows is a natural open-air pit cave in the state of San Luis Potosí, Mexico. The 1220-foot-deep cave was a popular destination for BASE jumpers. The function 1/4sqrt(d) represents the time t (in seconds) that it takes a BASE jumper to fall d feet. How far does a BASE jumper fall in 3 seconds? Pls answer this as quickly as possible. Thanks.
Answer:
The depth to which a BASE jumper jumps in 3 seconds is 144 feet
Step-by-step explanation:
The details of the Cave of Swallows are;
The depth of the cave = 1,220 ft.
The function that represents the duration, t, in seconds it takes to fall d feet is given as follows;
[tex]t = \dfrac{1}{4} \cdot\sqrt{d}[/tex]
The distance a BASE jumper jumps in 3 seconds = Required
By substituting t = 3 in the given function, we get;
[tex]t = 3 = \dfrac{1}{4} \cdot\sqrt{d}[/tex]
Therefore;
4 × 3 = 12 = √d
d = 12² = 144
The distance a BASE jumper jumps in 3 seconds is d = 144 feet.
Need help asap, thanks :)
Answer:
937
425
Step-by-step explanation:
9 is the square of 3
7 is 1 more than 6, the double of 3
4 is the square of 2
5 is 1 more than 4, 2x 2
Is there more?
Answer:
425
Step-by-step explanation:
1st = 2^2
3rd = 2*2 + 1
A square has a perimeter of 80 m. What is the length of each side?
Answer:
20 m
[tex]p = 4a \: thus \: a = p \div 4 = 80 \div 4 = 20 \: m[/tex]
Answer:
20
Step-by-step explanation:
P=4L
80=4L
L=80/4
L=20m
Mike has a total of 1371 coins in his piggy bank if the total value of his coins is $230.25 and make it only has dimes and quarters how many more times than quarters does Mike have
Answer:129
Step-by-step explanation:(621 x 0.25) + (750 x 0.10) = 230.25
750 - 621 = 129 more dimes than quarters
4x^2-12x+9.
4x^2+4x+1.,
1+12x+36^2
Answer:
Step-by-step explanation:
3+3+3+3+3+3+3+333333
Answer:
333354
Step-by-step explanation:
Simplify the expression.
Answer:
333,354
Step-by-step explanation:
First, we add the 3's. And get 21.
333,333 + 21 = 333,354
Given the following coordinates complete the reflection transformation.
Answer:
For a general point (x, y), a reflection across the line x = a transforms the point into:
(a + (a - x), y) = (2a - x, y)
So if we first do a reflection across the line x = 1, the new point will be:
(2*1 - x, y) = (2 - x, y)
And if we now do a reflection across the line x = 3, the new point will be:
(2*3 - (2 - x), y) = (6 - 2 + x, y) = (4 + x, y)
Now that we have the general formula we can solve the question.
For the point (-5, 2)
The generated point after the reflections is:
(4 + (-5), 2) = (-1, 2)
For the point (-1, 5)
The generated point after the reflections is:
(4 + (-1), 5) = (3, 5)
For the point (0, 3)
The generated point after the reflections is:
(4 +0, 3) = (4, 3)
Which statement is true? O A. The number 23 is prime, but 36 is composite. B. The number 33 is prime, but 42 is composite. OC. The number 21 is prime, but 25 is composite. D. The number 27 is prime, but 39 is composite.
Answer: A. The number 23 is prime, but 36 is composite.
=====================================================
Explanation:
Let's go through the possible answer choices
A) This is true because 23 only has the factors 1 and 23. So that's why 23 is prime. We can say 36 is composite since 2 is a factor, ie 36 = 2*18.B) This is false because 33 is not prime. Note how 33 = 3*11, showing that 3 is a factor of 33.C) Similar to B, the statement "21 is prime" is false. Note how 21 = 3*7.D) Like the other false statements, 27 is not prime because 27 = 3*9.23 is indeed prime, and 36 is indeed composite.
33 is composite, and 42 is indeed composite.
21 is composite, and 25 is composite as well
27 is not prime, and 39 is composite.
Primes have only 2 factors: 1 and themselves.
And 33, 21 and 27 definitely have more than 2 factors. Hope this helps!
~Just a joyful teen
[tex]GraceRosalia[/tex]
for f(x)= -4x + 5, find f(x) when x = -2.
Answer:
13
Step-by-step explanation:
f(x)= -4x + 5
Let x = -2
f(-2) = -4(-2) +5
= 8+5
= 13
Step-by-step explanation:
x = - 2
f ( x ) = - 4x + 5
f ( - 2 )
= - 4 ( - 2 ) + 5
= 8 + 5
= 13
dleleleleldldldldlldldldldlddl
find the slope of the tangent line of the curve r = cos (3theta) at theta = pi / 3
The slope of the tangent line to the curve at a point (x, y) is dy/dx. By the chain rule, this is equivalent to
dy/dθ × dθ/dx = (dy/dθ) / (dx/dθ)
where y = r(θ) sin(θ) and x = r(θ) cos(θ). Then
dy/dθ = dr/dθ sin(θ) + r(θ) cos(θ)
dx/dθ = dr/dθ cos(θ) - r(θ) sin(θ)
Given r(θ) = cos(3θ), we have
dr/dθ = -3 sin(3θ)
and so
dy/dx = (-3 sin(3θ) sin(θ) + cos(3θ) cos(θ)) / (-3 sin(3θ) cos(θ) - cos(3θ) sin(θ))
When θ = π/3, we end up with a slope of
dy/dx = (-3 sin(π) sin(π/3) + cos(π) cos(π/3)) / (-3 sin(π) cos(π/3) - cos(π) sin(π/3))
dy/dx = -cos(π/3) / sin(π/3)
dy/dx = -cot(π/3) = -1/√3
Please help me solve this I’m really struggling
Answer:
y =x^2 +8x +15
factories form
y =( x+5 )( x+3 )
x intercept where the graph meet the x axis
y = x^2 +8x +15
let y =0
0 = x^2 +8x +15
0 = ( x + 5) (x+3)
o = x+5 or 0 = x+3
-5 = x or x = - 3
x intercept
(-5;0)
(-3 ;0)
axis of symmetry : where you will cut the graph into two half
x = - b/2a
x = - 8/2(1)
x = - 8/2
x = - 4
Domain
XER
Range
y > -1
Consider the following function.
Place the steps for finding f -1(x) in the correct order.
↓
↓
↓
↓
Answer:
if f(x) = ax + b then f-1(x) = (x - b)/a
Step-by-step explanation:
Now
f(x)=ax + b
then y = ax + b
interchanging x and y , we get
or, x = ay + b
or, x - b = ay
or, (x - b)/a = y
therefore,f-1(x) = (x - b)/a
help me with this math question pls!! Find the value of x
Answer:
x = 3
Step-by-step explanation:
using the mid segment formula since quadrilateral WZYP is similar to that of MZYT, this is expressed as;
29 = 1/2(23 +11x+2)
Cross multiply
2(29) = 23+11x+2
58 = 25 + 11x
11x = 58 - 25
11x = 33
Divide both sides by 11
11x/11 = 33/11
x = 3
Hence the value of x is 3
Please answer this!!!!!!
Answer: 39°
Step-by-step explanation:
Angle of depression must be less than 90° but greater than 0°
8
20
х
18
Solve for x.
O A) 40
B) 38
C) 45
D) 46
Answer:
its A
Step-by-step explanation:
Chase buys a bag of cookies that contains 6 chocolate chip cookies, 6 peanut butter cookies, 6 sugar cookies and 6 oatmeal cookies. What is the probability that Chase randomly selects a peanut butter cookie from the bag, eats it, then randomly selects a chocolate chip cookie
Answer:
0.0652173
Step-by-step explanation:
Given that :
6 chocolate chip cookies
6 peanut butter cookies
6 sugar cookies
6 oatmeal cookies
Total number of cookies purchased = (6+6+6+6) = 24
Probability, P= required outcome /total possible outcomes
This is a selection without replacement probability problem :
P(peanut butter cookies) = 6/24 = 1/4
Then ;
P(chocolate chip cookie) = 6/23
Hence,
P(peanut butter cookies then chocolate chip cookie) = 1/4 * 6/23 = 0.0652173
can she get some help
Answer:
-55
Step-by-step explanation:
the sqeuence seems to be subtracting by 2 everytime.
so it will be -1,-3,-5,-7,-9,-11,-13,-15,-17,-19,-21,-23,-25,-27,-29..
the answer will be 27*-2(-54) -1(because we start at -1 , not 0)
Answer:
Step-by-step explanation:
the formula for an arithmetic sequence that is explicit is
[tex]a_n=a_1+d(n-1)[/tex] where [tex]a_1[/tex] is the first term (so -1), and d is the common difference (-2). n is the number position in the sequence. As soon as we find the formula or model for this sequence we can find any number term we want. Filling in the formula:
[tex]a_n=-1-2(n-1)[/tex] and we'll clean that up just a bit:
[tex]a_n=-1-2n+2[/tex] (I just distributed through the parenthesis) and a bit more to
[tex]a_n=-2n+1[/tex] and if we want the 21st term, fill in a 21 for n:
[tex]a_{21}=-2(21)+1[/tex] and
[tex]a_{21}=-42+1[/tex] so
[tex]a_{21}=-41[/tex]
SOMEONE HELP ME PLEASE
Decide if the following scenario involves a permutation or combination. Then find the number of possibilities.
There are 50 applicants for two Systems Engineer positions at a local company.
Answer:
you did not provide the numbers to answer any question...
but the formula that you want is probably this one
Combination Formula nCr=n!(n−r)!r!
Step-by-step explanation:
Sarah took the advertising department from her company on a round trip to meet with a potential client. Including Sarah, a total of 8 people took the trip. She was able to purchase coach tickets for $300 and first-class tickets for $1060. She used her total budget for airfare for the trip, which was $6960. How many first-class tickets did she buy?
How many coach tickets did she buy?
number of first-class tickets bought nothing number of coach tickets bought nothing
Answer:
She bought 6 first class tickets and 1 coach ticket
Step-by-step explanation:
1060(6)= 6360 and 6960-6360=300 and 300 is the price for a coach ticket.
I need help I don't understand this.
9514 1404 393
Answer:
∠4 = 108°
Step-by-step explanation:
Angles 2 and 4 together form a "linear pair". That is, the sum of them is 180°, a "straight angle." They are supplementary.
∠4 = 180° -∠2 = 180° -72°
∠4 = 108°
Which algebraic expression represents the phrase "six less than a number"?
Answer:
[tex]x-6[/tex]
Step-by-step explanation:
We can let the 'number' in the expression be equal to [tex]x[/tex]. Something 6 less than x would x minus 6, or [tex]x-6[/tex].
Answer:
x-6
Step-by-step explanation:
Let the number be x
Less than means subtract from
x-6
