Answers
Answer: see proof below
Step-by-step explanation:
Use the Sum & Difference Identity: tan (A - B) = (tanA - tanB)/(1 + tanA tanB)
Use the Half-Angle Identity: tan (A/2) = (1 - cosA)/(sinA)
Use the Unit Circle to evaluate tan (π/4) = 1
Use Pythagorean Identity: cos²A + sin²A = 1
Proof LHS → RHS
[tex]\text{Given:}\qquad \qquad \qquad\dfrac{2\tan\bigg(\dfrac{\pi}{4}-\dfrac{A}{2}\bigg)}{1+\tan^2\bigg(\dfrac{\pi}{4}-\dfrac{A}{2}\bigg)}[/tex]
[tex]\text{Difference Identity:}\qquad \dfrac{2 \bigg( \frac{\tan\frac{\pi}{4}-\tan\frac{A}{2}}{1+\tan\frac{\pi}{4}\cdot \tan\frac{A}{2}}\bigg)}{1+ \bigg( \frac{\tan\frac{\pi}{4}-\tan\frac{A}{2}}{1+\tan\frac{\pi}{4}\cdot \tan\frac{A}{2}}\bigg)^2}[/tex]
[tex]\text{Substitute:}\qquad \qquad \dfrac{2 \bigg( \frac{1-\tan\frac{A}{2}}{1+\tan\frac{A}{2}}\bigg)}{1+ \bigg( \frac{1-\tan\frac{A}{2}}{1+\tan\frac{A}{2}}\bigg)^2}[/tex]
[tex]\text{Simplify:}\qquad \qquad \qquad \dfrac{1-\tan^2\frac{A}{2}}{1+\tan^2\frac{A}{2}}[/tex]
[tex]\text{Half-Angle Identity:}\qquad \quad \dfrac{1-(\frac{1-\cos A}{\sin A})^2}{1+(\frac{1-\cos A}{\sin A})^2}[/tex]
[tex]\text{Simplify:}\qquad \qquad \dfrac{\sin^2 A-1+2\cos A-\cos^2 A}{\sin^2 A+1-2\cos A+\cos^2 A}[/tex]
[tex]\text{Pythagorean Identity:}\qquad \qquad \dfrac{1-\cos^2 A-1+2\cos A}{2-2\cos A}[/tex]
[tex]\text{Simplify:}\qquad \qquad \qquad \dfrac{2\cos A-2\cos^2 A}{2(1-\cos A)}\\\\.\qquad \qquad \qquad \qquad =\dfrac{2\cos A(1-\cos A)}{2(1-\cos A)}[/tex]
= cos A
LHS = RHS: cos A = cos A [tex]\checkmark[/tex]
Related Questions
If a = B and b = C, which statement must be true?
a
a = C
a + c = 0
-a - C = 0
d a>c
Answers
Answer:
If a = B and b = C, then
a = C
A car rental agency has 18 vehicles available, of which 3 are convertibles. What is the probability that a randomly selected vehicle will be a convertible? Write your answer as a fraction or whole number.
Answers
Answer:
[tex]\frac{1}{6}\\[/tex]
Step-by-step explanation:
To find the probability, divide the number of desired outcomes by the total:
This will be 3/18, since there are 3 convertibles and there are 18 total cars
Simplify 3/18
= [tex]\frac{1}{6}[/tex]
please help on 13 and 14
Answers
Answer:
13) The planes ABF and FHG are perpendicular
14) Segments Ab and CD are parallel.
Step-by-step explanation:
13)
Planes ABF and FHG are perpendicular (they intersect along side EF)
14)
In order to find out about the segments AB and CD, let's use the formula for the slope that joins any two points [tex](x_1,y_1)\,\,\&\,\,(x_2,y_2)[/tex] on the plane:
[tex]slope=\frac{y_2-y_1}{x_2-x_1}[/tex]
Therefore, given:
A = (-3, 2)
B = (1, 4)
C = (-3, -1)
D = (1, 1)
we have for segment AB the following slope:
[tex]slope_{AB}=\frac{4-2}{1+3} =\frac{2}{4} =\frac{1}{2}[/tex]
and for segment CD the following slope:
[tex]slope_{CD}=\frac{1+1}{1+3} =\frac{2}{4} =\frac{1}{2}[/tex]
Since they show the same slope, these two segments are parallel.
Select the correct answer.
Consider the function fx) = 10' and the function g(x), which is shown below. How will the graph of g(x) differ from the graph of
g(t) = f(x – 6) = 10(– 6)
Answer choice options are above.
Answers
Answer:
B The graph of g(x) is the graph of f(x) shifted to the right 6 unit
Relation between the graph of g(x) and f(x) is option (B) The graph of g(x) is the graph of f(x) shifted to right 6 units
What is a Function?Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given,
[tex]f(x) =10^{x}[/tex]
[tex]g(x)=f(x-6)=10^{(x-6)}[/tex]
f(x) shift right 6 units to get f(x-6)
Given that
g(x) = f(x-6)
Therefore graph of g(x) is the graph of f(x) shifted to the right 6 units
Hence, Relation between the graph of g(x) and f(x) is option (B) The graph of g(x) is the graph of f(x) shifted to right 6 units
Learn more about Function here
https://brainly.com/question/12431044
#SPJ2
2. One school has 97 students.
Another school has 72 students.
How many more students does the
larger school have?
Answers
Answer:
25
Step-by-step explanation:
97-72= 25
Hope this helped!
Answer:
25
Step-by-step explanation:
97-72= 25
Which of the following is a proportion? Please help!! D:
Answers
Answer:
the second one
Step-by-step explanation:
Please help find the value of x for this equation
Answers
Answer:
A
Step-by-step explanation:
We would like to find the value of x.
Since the triangle is isosceles, the drawn altitude bisects the base of length 8. This means that the big triangle is split into two congruent triangles with base 4 and height 5.
Notice that by definition, as well, the altitude of 5 is perpendicular to the base of length 8. So, we have two right triangles, each with legs of 4 and 5 and hypotenuse x.
We apply the Pythagorean Theorem, which states that for a right triangle with legs a and b and hypotenuse c:
a² + b² = c²
Here, we have:
4² + 5² = x²
16 + 25 = x²
41 = x²
x = √41
The answer is thus A.
~ an aesthetics lover
Does f(x)=x^2-3x have a 5 in its domain?
Answers
Answer:
yes
Step-by-step explanation:
Every polynomial has "all real numbers" in its domain. 5 is a real number, so is in the domain of f(x).
Find the value of x round to the nearest tenth
Answers
Answer:
x = 80.4
Step-by-step explanation:
Step 1: Realize you have to use tangent to solve
[tex]tan()=\frac{o}{a}[/tex]
Step 2: Use tangent to solve
o = x
a = 300
[tex]tan()=\frac{o}{a} \\tan(15)=\frac{x}{300}\\x = 300tan(15)\\x = 80.4[/tex]
Therefore x is equal to 80.4 rounded to the nearest tenth
Answer:
x = 80.4Step-by-step explanation:
[tex]Opposite = x\\Adjacent = 300\\\alpha =15\\Using \: SOHCAHTOA\\\\Tan \alpha = \frac{Opposite}{Adjacent} \\\\Tan 15 =\frac{x}{300} \\\\2-\sqrt{3} = \frac{x}{300}\\\\ 2-\sqrt{3} \times 300=x\\\\80.384=x\\\\x = 80.4[/tex]
The graph of the function, f(x)=x^2-5x-7 opens __ and has a ____ value.
Answers
Answer:
opens UP and has a minimum value.
Step-by-step explanation:
The given quadratic function opens UP (the branches of the associated parabola open up) because the coefficient that accompanies the leading term (leading coefficient) is positive.
Since the graph is a parabola with arms pointing up, the graph should have a minimum located at the vertex of the parabola.
Given f(x) = 3x - 40. If f(x)= 8, what is the value of x?
A. - 96
B. -16
C. 16
D. -32/3
E. 32/3
Answers
Answer:
C
Step-by-step explanation:
Given
f(x) = 3x - 40 and f(x) = 8 , then equate the right sides, that is
3x - 40 = 8 ( add 40 to both sides )
3x = 48 ( divide both sides by 3 )
x = 16 → C
Can someone help been stuck all day idk wat to do
Answers
#2 is $13.75
And idk how to do percents, I’m literally in high school and forgot how!!
A white tailed deer can sprint at speeds up to 30 miles per hour America bison can run at speeds up to 3,520 feet per minute which animal is faster and by how many miles per hour? There are 5,280 feet in one mile
Answers
In 1 minute, bison runs 3520 feet
In 60 minutes, the bison would run
3520*60 feet
211200 feet per hour.
These are equivalent to;
40 miles per hour since 1 mile is equivalent to 5280 feet.
The bison is faster by 10 miles per hour
Twice the difference between of a number 5 ?
Answers
Answer:
2(x-5)
Step-by-step explanation:
the number will be ''x''
difference between the number (x) and 5 =
x-5
twice the difference is =
2(x-5)
A countrys population in 1991 was 147 million. In 1998 it was 153 million. Estimate the population in 2017 using exponential growth formula. Round your answer to the nearest million. P=Ae to the power kt
Answers
Answer:
171 millionStep-by-step explanation:
Given the exponential growth formula expressed as [tex]P = Ae^{kt}[/tex] where P is the countrys population and t is the time.
Initially in 1991, at t= 0, P = 147 million
[tex]P = Ae^{kt}\\147 = Ae^{k(0)}\\147 = Ae^0\\147 = A(1)\\A = 147[/tex]
If by 1998 it was 153 million, this means that the population is 153 million 7 years later i.e when t = 7, P = 153. On substituting into the formula to get the constant 'k';
[tex]P = Ae^{kt}\\153 = 147e^{k(7)}\\153 = 147e^{7k}\\153/147 = e^{7k}\\e^{7k} = 1.041\\Taking \ ln \ of \ both \ sides\\lne^{7k} = ln 1.041\\7k = 0.04018\\k = 0.04018/7\\k = 0.00574[/tex]
To estimate the population in 2017, to number of years from 1991 to 2017 is 26 years. Hence we are to find the value of P given t = 27, A = 147 and k = 0.00574
[tex]P = Ae^{kt}\\P = 147e^{0.00574*26}\\P = 147e^0.14924\\P = 147*1.16095\\P = 170.659[/tex]
Hence the population in 2017 using exponential growth formula to the nearest million is 171 million.
evaluate plz plz plz help me i am soo confused
Answers
Hey there! I'm happy to help!
QUESTION 100
Here, we are looking for the number of permutations. A permutation is the number of possible arrangements you can make from a given set of things (order matters). If you have 6 kids standing in alphabetical order in line, that is one permutation. If you do reverse alphabetical order, that is a different permutation.
We are asked to find the number of permutations using the given format:
[tex]_{n}P_{r}\\[/tex]
This is simply a representation of what we want to find. The P means we are looking for the number of permutations. The n is the total number of objects in the set (for example, if there were 26 kids we could choose from to make this 6 person line, n would be 26). The r is the number of things chosen from the set (in our line example, the r would be six because we are choosing 6 kids).
The formula for finding the number of permutations is [tex]\frac{n!}{(n-r)!}[/tex]. The ! is factorial, it means you multiply that number by every integer counting backwards towards 1. 6! is 6×5×4×3×2×1. There is an option to do this on your calculator, though.
Let's solve this problem.
[tex]_{5}P_{4}=\frac{5!}{(5-4)!}= \frac{120}{1} =120[/tex]
This means that there are 120 permutations.
QUESTION 101
Now we have a C. This is similar to permutations but with combinations order does not matter. With our line example, having the same six kids in alphabetical order is a different permutation than having it in backwards alphabetical order. With combinations, if you have those specific six kids, it is just one combination; the order does not matter.
The formula for combinations is [tex]\frac {n!}{r!(n-r)!}[/tex]. Let's plug in our numbers and solve for this.
[tex]_{8}C_{2}=\frac{8!}{2!(8-2)!} =\frac{8!}{2!(6!)}=\frac{40320}{1440} =28[/tex]
QUESTION 102
Quick note: 0! is equal to 1. I don't really know why but there's probably proof somewhere.
[tex]_{7}C_{0}=\frac{7!}{0!(7-0)!} =\frac{7!}{7!} =1[/tex]
And I believe you already have Question 103 figured out.
4!=4×3×2×1=24
Have a wonderful day! :D
m-m-1/2=1-m-2/3
Pls help me with this question fast
Answers
Answer:
m=5/6
Step-by-step explanation:
arrange all the "m's" at the left side and the numbers at the right side doing that we get
m-m+m=1-2/3+1/2
m=5/6
Explanation:
M-m+m=6/6-4/6+3/6
M=5/6
I really need help with this question. can someone help me!
Answers
Answer:
144
Step-by-step explanation:
Using the rule of radicals
[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] ⇔ [tex]\sqrt{ab}[/tex]
Given
4[tex]\sqrt{2}[/tex] × 6[tex]\sqrt{18}[/tex]
= 4 × 6 × [tex]\sqrt{2}[/tex] × [tex]\sqrt{18}[/tex]
= 24 × [tex]\sqrt{36}[/tex]
= 24 × 6
= 144
A group of hikers keep track of their elevation as a function, E, to determine the
different elevation levels as they travel along the trail in Possum Kingdom State
Park. E(d) represents the height of elevation in feet where d is the distance the
hiker travels along the trail. What would be the most appropriate domain for the
function?
{-1,-2,0,1,2,3)
O ,-1,0, 1, 2, 3, ...)
{0,1,2,3,4,...}
C-3,0,1,2,3...
)
Answers
Calculate the distance between the two quantities: 4 ft and 12 ftCalculate the distance between the two quantities: 4 ft and 12 ft
Answers
Answer:
8 feet
Step-by-step explanation:
Distance can be explained as the way to measure how far a thing or something is apart from each other numerically, it shows how close or far apart between two point
From the question, we are given two point
Point1= 12 feet
Point 2= 4 feet
Then Distance between the two point= 12feet-4feet
= 8feet
Hence the distance= 8 feet
Which statements are true about the estimation of decimal products? Check all that apply. Estimation gives an approximate answer. Estimation always results in a product greater than the exact answer. Estimation always results in a product less than the exact answer. Estimation can be done by rounding each decimal to the nearest whole number.
Answers
Step-by-step explanation: the answers are a and d
Answer:
a d
Step-by-step explanation:
got it right
The perimeter of a basketball court is 84 meters and the length is 6 meters longer than twice the width. What is the length and width
Answers
Answer:
length: 30 meters
width: 12 meters
Step-by-step explanation:
2(a+b) = 84
a = 2b + 6
a = length
b = width
then:
2((2b+6)+b) = 84
2b + 6 + b = 84/2
3b + 6 = 42
3b = 42 - 6
3b = 36
b = 36/3
b = 12
a = 2b + 6
a = 2*12 + 6
a = 24 + 6
a = 30
Check:
84 = 2(12+30)
84 = 2*42
(8x3-3x2+x)+(2x2-5x+4)
Answers
Answer:
-4x+26
Step-by-step explanation:
Answer:
[tex] \boxed{ \bold{ { \boxed{ \sf{8 {x}^{3} - {x}^{2} - 4x + 4}}}}}[/tex]
Step-by-step explanation:
[tex] \sf{(8 {x}^{3} - 3 {x}^{2} + x) + (2 {x}^{2} - 5x + 4)}[/tex]
When there is a ( + ) in front of an expression in parentheses , no need to change the sign of each term. That means , The expression remains the same. Also , remove the unnecessary parentheses
⇒[tex] \sf{8 {x}^{3} - 3 {x}^{2} + x + 2 {x}^{2} - 5x + 4}[/tex]
Collect like terms
⇒[tex] \sf{8 {x}^{3} - 3 {x}^{2} + 2 {x}^{2} - 5x + x + 4}[/tex]
⇒[tex] \sf{8 {x}^{3} - {x}^{2} - 4x + 4}[/tex]
Hope I helped!
Best regards!!
will give brainliest
Answers
Answer:
B
Step-by-step explanation:
Answer:
6 1/4 cup of soda for one cup of pineapple
Step-by-step explanation:
2/ 5 of pineapple for every 2 1/2 cups of soda
1 cup of pine apple ??
(2 1/2)/(2/5)
5/2 ÷2/5 ( when divide fraction,change ÷ to × and flip the fraction (reciprocal)
5/2×5/2=25/4 or 6 1/4
for the ap 3/2. 1/2. -1/2.-3/2... write the first term a and common difference d
Answers
Answer:
First term is [tex]\frac{3}{2}[/tex].
Common difference: -1
Step-by-step explanation:
Given the sequence:
[tex]\frac{3}{2} , \frac{1}{2} , -\frac{1}{2}, -\frac{3}{2}, ...[/tex]
we notice that one term is generated from the previous one by subtracting from it "1". That means that the common difference for this sequence is "-1", and its first term is [tex]\frac{3}{2}[/tex].
. Find the measure of an angle which is 46° less than its complement
Answers
Answer:
Complementt angle = 44°
Step-by-step explanation:
Given:
One angle = 46°
Find:
Complementt angle
Computation:
In complement angle
∠A + ∠B = 90°
46° + ∠B = 90°
∠B = 90° - 46°
∠B = 44°
Complementt angle = 44°
calculate the perimeter of a triangle whose dimensions are 1m 60cm, 1m 80cm and 2m.
Answers
Answer:
5 m 40 cmStep-by-step explanation:
a = 1 m 60 cm = 1.6 m
b = 1 m 80 cm = 1.8 m
c = 2 m
perimeter = a + b + c = 1.6 + 1.8 + 2 = 5.4 m = 5 m 40 cm
★ AnsWer :
➨ 540 cm
★ Step by step Explaination :
Let triangle be ABC,
1m = 100 cm
[tex]\begin{lgathered}\bullet\:\:\textsf{AB = 1m 60cm = \textbf{160 cm}}\\\bullet\:\:\textsf{BC = 1m 80cm = \textbf{180 cm}}\\\bullet\:\:\textsf{CA = 2m = \textbf{200 cm}}\end{lgathered}[/tex]
[tex]\setlength{\unitlength}{1.5cm}\begin{picture}(6,8)\linethickness{0.5mm}\qbezier(1,.5)(2,1)(4,2)\qbezier(4,2)(2,3)(2,3)\qbezier(2,3)(2,3)(1,0.5)\put(.7, .3){$C$}\put(4.05, 1.9){$B$}\put(1.7, 2.95){$A$}\put(3.2, 2.5){\sf{160 cm}}\put(0.7,1.7){\sf{200 cm}}\put(2.7, 1.05){\sf{180 cm}}\end{picture}[/tex]
[tex]\rule{130}1[/tex]
[tex]\underline{ \large \purple{ \mathscr{\dag\:A \bf{ccording} \: to \: \mathscr {Q} \bf{uestion} ....}}}[/tex]
[tex]\begin{lgathered}\dashrightarrow\tt\:\: Perimeter_{{\tiny\triangle ABC}}=Sum\:of\:all\:sides\\\\\\\dashrightarrow\tt\:\: Perimeter_{{\tiny\triangle ABC}} = AB + BC + CA\\\\\\\dashrightarrow\tt\:\: Perimeter_{{\tiny\triangle ABC}} = 160 + 180 + 200\\\\\\\dashrightarrow\:\:\underline{\boxed{\tt Perimeter_{{\tiny\triangle ABC}} = 540 \:cm}}\end{lgathered}[/tex]
[tex]\therefore\:\underline{\textsf{Perimeter of triangle ABC is \textbf{540 cm}}}.[/tex]
a _____ function is a function that is defined on a sequence of intervals.
Answers
Answer: a piecewise function is a function that is defined on a sequence of intervals.
Step-by-step explanation:
A piecewise function is a function that is "different" at different intervals.
The function may behave linearly between x = 0 and x = 10, and after that point, the function may be constant for a while, then change again.
This type of functions can be written as:
f(x) = g(x) if x1 ≤ x ≤ x2
f(x) = h(x) if x2 ≤ x ≤ x3
f(x) = k(x) if x3 ≤ x ≤ x4
and so on, where g(x), h(x) and k(x) are different functions, and those functions only act on the givenintervals: (x1, x2), (x2, x3) and (x3, x4)
Sue has 18 sweets.
Tony also has 18 sweets.
Sue gives Tony x sweets.
Sue then eats 5 of her sweets.
Tony then eats half of his sweets.
Write expressions for the number of sweets Sue and Tony now have.
Help pleaseeeeee
Answers
Answer:
sue = 18
tony = 18
sue = 18 - x
tony = 18 + x
sue = 18 - x - 5
tony = (18 + x) / 2
sue = 13 - x
tony = (18 + x) / 2
Step-by-step explanation:
You Simplify The Equation by using PEMDAS
P: Parentheses
E: Exponents
M: Multiplication
D: Division
A: Addition
S: Subtraction
(9.5 minus 3 times 1 and one-half) divided by 0.5 0.5 5 10 19.5
Answers
Answer:
Your value expression is 10
Step-by-step explanation:
We know that [tex]1\frac{1}{2}=\frac{3}{2}=1.5[/tex]
The value experssion:
Giving: [tex]\frac{9.5-3(1\frac{1}{2}) }{0.5}[/tex]
Change [tex]1\frac{1}{2}[/tex] into a whole number: [tex]\frac{9.5-3(1.5)}{0.5}[/tex]
Multiply 3 into 1.5: [tex]\frac{9.5-4.5}{0.5}[/tex]
Divide: [tex]\frac{5}{0.5}[/tex]
Your answer equals: 10