[tex]\qquad \sf \: \huge \bf༆ Answer ༄[/tex]
Here's the solution ~
[tex]\qquad \sf \dashrightarrow \: f(x) = \tan(x) [/tex]
[tex]\qquad \sf \dashrightarrow \: f(2x) = \tan(2x) [/tex]
[tex]\qquad \sf \dashrightarrow \: f(2x) = \dfrac{2 \tan(x) }{1 - { \tan {}^{2} (x) }^{} } [/tex]
replace tan(x) with f(x) in the given equation ~
[tex]\qquad \sf \dashrightarrow \: f(2x) = \dfrac{2 (f(x) )}{1 - { (f {}^{} (x)) {}^{2} }^{} } [/tex]
The expression that was proved is [tex]tan2x=\frac{2[f(x)]}{1-[f(x)^2]}[/tex]
Double angle of functionGiven the trigonometry identity
f(x) = tanx
f(2x) tan2x
From double angle theorem;
[tex]tan2x=\frac{tanx+tanx}{1-tanx(tanx)} \\tan2x=\frac{2tanx}{1-tan^2x}[/tex]
Since f(x) = tan(x), substitute into the result to have:
[tex]tan2x=\frac{2[f(x)]}{1-[f(x)^2]}[/tex] (Proved)
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How do I do this? Please help!
I already answered this question, if you look back in your questions you should find this answered along with another one. I'll do it again just in case you don't find it.
Answer:
{y,x} = {-4,-2}
Expanation:
Solve by Substitution :
// Solve equation [1] for the variable y
[1] y = 2x
// Plug this in for variable y in equation [2]
[2] -2•(2x) - 8x = 24
[2] - 12x = 24
// Solve equation [2] for the variable x
[2] 12x = - 24
[2] x = - 2
// By now we know this much :
y = 2x
x = -2
// Use the x value to solve for y
y = 2(-2) = -4
Nick was surveying his field and saw some cows and ducks. Nick counted a total of 80 heads and
248 legs. Assuming there are no mutations in the animals, determine exactly how many ducks and cows he saw. Let
X represent the number of ducks and y represent the cows.
Total Equation:
Legs Equation:
How many ducks?
How many cows?
Answers:
Total equation: x+y = 80Legs equation: 2x+4y = 248How many ducks? 36How many cows? 44====================================================
Further explanation:
x = number of ducksy = number of cowsx+y = 80 is the total equation (ie the head count equation) since we assume each animal has 1 head, and there are 80 heads total.
That equation can be solved to y = 80-x after subtracting x from both sides.
The legs equation is 2x+4y = 248 because...
2x = number of legs from all the ducks only4y = number of legs from all the cows only2x+4y = total number of legs from both types of animals combinedWe're told there are 248 legs overall, so that's how we ended up with 2x+4y = 248
------------
Let's plug y = 80-x into the second equation and solve for x.
2x+4y = 248
2x+4( y ) = 248
2x+4( 80-x ) = 248
2x+320-4x = 248
-2x+320 = 248
-2x = 248-320
-2x = -72
x = -72/(-2)
x = 36
There are 36 ducks
Now use this x value to find y
y = 80-x
y = 80-36
y = 44
There are 44 cows.
------------
Check:
36 ducks + 44 cows = 80 animals total
36*2 + 44*4 = 72 + 176 = 248 legs total
The answers are confirmed.
An angle bisector of a triangle divides the opposite side of the triangle into segments2 cm and 5cm long. The second side of the triangle is 7.5 cm long. Find all possible lengths for the third side of the triangle.
Answer:
3 cm or 18.75 cmStep-by-step explanation:
Let the third side is x.
According to Triangle-angle-bisector theorem, we have the possible ratios:
x/7.5 = 2/5or
x / 7.5 = 5/2Solve for x in each case:
1)
x = 7.5*2/5 = 3 cm2)
x = 7.5*5/2 = 18.75 cmim having trouble solving this. y=5(x-3)
Hi there!!
If you need X to be solved then the answer is X=Y over 5+3 and if your looking for the answer for Y then the answer is Y=5x−15
When you are solving for X you will need to use the distributive property so you can multiply 5 by X-3.
Y=5x-15. Once you've done that then you need to swap sides so all of the variables are on the same side as each other (they need to be on the left side) 5x-15=Y.
Then you need to add 15 to both of the sides to make it look like this ->5x=Y+15
When that's done you then need to divide both sides by 5 so it then looks like this when done.
5x over 5= Y+15 over 5
When you divide this by 5, it then undoes the multiplication by 5.
X= Y+15 over 5
Finally, you need to divide Y+15 by 5
X=Y over 5 plus 3
When solving for Y, all you will need to do is use the distributive property to multiply 5 by X-3.
I REALLY HOPE THIS HELPED YOU OUT AND THAT I DIDN'T WASTE YOUR TIME WITH A WRONG ANSWER . BUT IF THIS WAS CORRECT THEN YOU ARE VERY WELCOME
What is the surface area of this triangular prism rounded to the nearest tenth?
The surface area of the triangular prism, rounded to the nearest tenth is: 85.7 cm²
What is the Surface Area of a Triangular Prism?Surface area (SA) = bh + (s1 + s2 + s3)H
Given:
s1 = 6.8 cm
s2 = 5.1 cm
s3 = 8.5 cm
H = 2.5 cm
b = 6.8 cm
h = 5.1 cm
Plug in the values
Surface area of the triangular prism = 6.8 × 5.1 + (6.8 + 5.1 + 8.5)2.5
Surface area of the triangular prism = 85.7 cm²
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The cost of 3 scarves is $80.25. What is the unit price?
Answer:
$26.75 per scarf
Step-by-step explanation:
3 scarves = $80.25 (quite expensive)
1 scarf = $80.25/3
1 scarf = $26.75
Answer:
$8.75 because 26.25 divided by 3 equals 8.75.
Step-by-step explanation:
HELP MY GRADE 9 PLS AND THANK YOU
Answer:
64x²y²
Step-by-step explanation:
Use the great smart calculator
hope it helpz uuuuuuu
The product of 20 any y (Pls i need help in this)
Answer:
Step-by-step explanation:
20y
Meaning 20xy
Y=1
So 20 is 20
Two fair 6 sided number cubes are rolled. What is the probability of rolling a sum of 11?
Question 3 options:
1/6
1/36
1/18
11/36
9. Which set of ratios below is NOT equivalent
to 3:4?
the
bu
A. 6 to 9,
q
12
B.) 9 to 12, 20
15
Answer:
A
Step-by-step explanation: {reduction}
{[tex]\frac{2X3}{3X3}=\frac{2}{3}[/tex]} {[tex]\frac{3X3}{3X4}=\frac{3}{4}[/tex]}
A. 6 to 9 7'5 [tex]\frac{6}{9}=\frac{2}{3} , \frac{9}{12}=\frac{3}{4}[/tex]
{[tex]\frac{3X3}{3X4}=\frac{3}{4}[/tex]}
B. 9 to 12 7'5 [tex]\frac{9}{12}=\frac{3}{4} , \frac{15}{20}=\frac{3X5}{4X5}=\frac{3}{4}[/tex]
C. [tex]\frac{15}{20}=\frac{3}{4} ,[/tex] 24 = 32 = 3 × 8: 4 ×8 = 3 = 4
D. [tex]\frac{30}{40}=\frac{3X10}{4X10}=\frac{3}{4} , 18:24=3X6=4X6=3:4[/tex]
choose A
A random sample of 24 corporate-owned stores finds an average number of customers of 313 with a standard deviation of 34.9. What is the upper bound of a 95% confidence interval for the average number of customers in corporate-owned stores
Answer:
95% is 1700 customers
Step-by-step explanation:
JK i actually dont know but thnks for the points BTW
If f(x)= x^2-25 and g(x)=x-5, what is the domain of (f/g)(x)?
Answer:
B) all real values of x except x=5
Step-by-step explanation:
If [tex]f(x)=x^2-25[/tex] and [tex]g(x)=x-5[/tex], then [tex]\bigr(\frac{f}{g}\bigr)(x)=\frac{f(x)}{g(x)}=\frac{x^2-25}{x-5}=\frac{(x-5)(x+5)}{(x-5)}[/tex].
Given that [tex]x-5[/tex] exists in both the numerator and denominator, this creates a hole on the graph of the function where [tex]x=5[/tex] since [tex]5-5=0[/tex]all real values of x except x=5 is correct.
Review the attached graph for more information
Math asap!! Will give brainliest
Step-by-step explanation:
line QS = RS
line KJ = half of line KC
please can someone explain to me how this is done the answer is 85 but how to figure it out I am giving away 10 points the question is one the image and the answer is 85 but just explain how it is done
Answer:
Step-by-step explanation:
A = [tex]\frac{hb}{2}[/tex]
h = 10 cm , b = 17 cm
A = 10 × 17 ÷ 2 = 85 cm²
please help!! Tysm <33
Answer:
[tex] \frac{p}{3} = 5[/tex]
p = 15
[tex] \frac{15}{3} = 5[/tex]
!!!HURRY PLS!!!
My BraIns nOt wOrkIng-
Answer:
x=5
Step-by-step explanation:
x+3=2x-2
1. take the square root's out
2. subtract -3 from both sides of the equation.
x+3-3=2x-2-3
3. subtract.
x=2x-5
4. subtract 2x from both sides of the equation.
x=-2x=2x-5-2x
5. solve
x=5
The points F(4,
-2), G(9,
-6), H (8, -1), and I (5, 2) form a quadrilateral. Find
the desired slopes and lengths, then fill in the words that BEST identifies the type of
quadrilateral.
(PICTURE BELOW)
slope of GH
and
lenght of FG
Solve the equation below pls show your work no links pls.
[tex](9^{2} )^{-1/3}[/tex]
Given :-
[tex](9^{2} )^{-1/3}[/tex]To Find :-
To solve the expression .Solution :-
Given expression to us is ,
[tex](9^{2} )^{-1/3}[/tex]
We know that ,
[tex] 9 = 3^2[/tex]
So our expression becomes ,
[tex]\{ (3^2)^2\}^{\frac{-1}{3}}[/tex]
And , [tex] (a^m)^n =a^{mn}[/tex] . Using this ,
[tex] (3^4)^{\frac{-1}{3}}[/tex]
Again using the same law ,
[tex] 3^{\frac{-4}{3}}[/tex]
We know that , [tex] a^{-m}=\frac{1}{a^m}[/tex] . Therefore ,
[tex] (3^{-4})^{\frac{1}{3}}[/tex]
[tex]\\\bigg( \dfrac{1}{3^4}\bigg)^{1/3}[/tex]
[tex]\\ \dfrac{1}{\sqrt[3]{3^4}}[/tex]
Simplify ,
[tex] \dfrac{1}{3\sqrt[3]{3}}[/tex]
This is the simplified expression.
I hope this helps.
Which value of x makes the equation 0.1x – 2.5 = 1.0 true?
a. 10
b. 15
c. 20
d. 35
Answer:
d) 35
Step-by-step explanation:
0,1 *35 - 2,5 = 1,0
True
Consider the equation q = 4 +0.8p.
=
What value of p would make the equation to
12?
Answer:
p=10
Step-by-step explanation:
q = 4 +0.8p
Let q = 12
12 = 4 +0.8p
Subtract 4 from each side
12-4 = 4+.8p -4
8 = .8p
Divide each side by .8
8/.8 = .8p/.8
10 =p
I need helppppp plssssssssss
Answer:
(x, y) = (9, 17)
Step-by-step explanation:
Any two pairs of equations can be used to form a system of equations that will give appropriate values of x and y. Let's set the upper and lower left expressions equal to the middle one.
2x +3y -20 = 4x +5y -72 . . . . upper left = middle
52 = 2x +2y . . . . . . . . add 72-2x-3y
x + y = 26 . . . . . . . . . . divide by 2
and ...
5x -2y +38 = 4x +5y -72 . . . . lower left = middle
110 = -x +7y . . . . . . . . . . . . . add 72-5x+2y
Now we have two equations in two unknowns that will give us the common values of x and y. Adding these equations eliminates x and gives the value of y:
(x +y) +(-x +7y) = (26) +(110)
8y = 136 . . . . . . . . simplify
y = 17 . . . . . . . . . divide by 8
x = 26 -y = 26 -17 = 9
The values of x and y that make all of these expressions equal are ...
(x, y) = (9, 17)
The value they are equal to is ...
2x +3y -20 = 2(9) +3(17) -20 = 18 +51 -20 = 49
__
Check
upper right = 9 -4(17) +108 = 9 -68 +108 = 49
lower right = 3(9) -17 +39 = 27 -17 +39 = 49
Choose the correct product of (7x − 6)2. 49x2 84x 36 49x2 − 36 49x2 36 49x2 − 84x 36.
Answer:
the answer for this question is 49x²-84x+36
hope it helps
Answer:49x²-84x+36
Step-by-step explanation:
A small school employs 5 teachers who make between $40,000,and 70,000 per year.
The newest teacher, Valerie, decides to teach part-time which decreases her salary from 40,000 to 20,000 per year. The rest of the salaries stay the same.
How will decreasing Valerie's salary affect the mean and median?
HELP PLEASE
Answer:
Its B
Step-by-step explanation:
No of teachers in the school = 5
Salaries they make =40000 to 70000
When one of the five teachers reduce salary to 20000/- per year, median may or may not shift one number to the left
Mean will definitely decrease by difference/5 = 4000 dollars
Thus mean will defintely change by reduction of 4000 dollars.
Median has a chance to remain the same or may shift left side one item.
WHAT IS THE VOLUME OF THE PRISM????
Answer:
78 3/4
Step-by-step explanation:
Convert all the mixed numbers to fraction : 4 1/2 = 9/2 ; 3 1/2 = 7/2
V = 9/2 x 5 x 7/2 = 315 / 4 = 78 3/4
Hope it helps
what is -5/2dividedby5/7
[tex]\frac{ - 5}{2} \: by \: \frac{5}{7} [/tex]
[tex] - 3.5[/tex]
Answer : [tex] - 3.5[/tex]
the Nth term of a geometric sequence is given by this equation, solve it and show ALL of your steps. 4 through 7
Answer:
I dont know the answers but here is an example( look at screenshots)
Step-by-step explanation:
y=28(0.25)^x WHAT IS THE FREAKING PERCENT? Thank you! <3?
Answer:
75%
Step-by-step explanation:
Amy is trying to determine how many different outfits she can make. She has 4 bottoms 7 tops, 2 belts, and 5 pairs of shoes. Assuming she wears one of each item, how many different outfits can
she make?
Answer:
Amy puede hacer 4 conjuntos.
Step-by-step explanation:
La solución sería
Se sabe que un conjunto de vestir se compone de camisa o blusa, pantalones, zapatos y cinturones, aunque este ultimo es opcional.
Lo que haremos es esto, empezamos a coger una pieza de cada prenda para armar un conjunto.
Primer conjunto:
1 blusa, 1 pantalón, 1 cinturón, y 1 par de zapatos.
Y esto quedaría así: 3 pantalones, 6 blusas, 1 cinturón y 4 pares de zapatos.
Segundo conjunto:
1 blusa, 1 pantalón, 1 cinturón y 1 par de zapatos.
Esto quedaría así: 2 pantalones, 5 blusas, 0 cinturones, 3 pares de zapatos. Sabemos que el cinturón es opcional, así que podemos continuar.
Tercer conjunto:
1 blusa, 1 pantalón y un par de zapatos.
Esto quedaría así: 1 pantalón, 4 blusas, 0 cinturones y 3 pares de zapatos.
Cuarto conjunto:
1 blusa, 1 pantalón y un par de zapatos.
Esto quedaría así: 0 pantalones, 3 blusas, 0 cinturones y 2 pares de zapatos. Como en un conjunto el pantalón es prioridad, al no tener más pantalones los conjuntos quedarían hasta aquí.
¡Recuerda!
No es lo mismo organizar tu ropa en conjuntos, a que hagas variaciones con ella.
what is 4.09 less than 5.6 ??
Answer: -1.51, or it could be 4.09 < 5.6 (Im sorry if I get it wrong I just wanted to help)
Step-by-step explanation:
The value of the subtraction is 1.51.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given numbers are 4.09 and 5.6. The value of 4.09 less than 5.6 will be calculated as:-
Subtraction = 5.6 - 4.09
Subtraction = 1.51
Therefore, the value of the subtraction is 1.51.
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What is the volume of this sphere? Use 3. 14 for pi and round to the nearest hundredth when necessary. 50. 24 m³ 267. 95 m³ 1607. 68 m³ 2143. 57 m³.
Volume of a figure is the measurement of space occupied by the figure. The volume of the specified sphere is given by Option B: 267. 95 m³
What is the volume of sphere?If the given sphere is of radius r units, then its volume is given as:
[tex]V= \dfrac{4}{3} \pi r^3 \: \rm unit^3[/tex]
For the given sphere, its diameter is 8 units, thus, its radius is half of its diameter and thus, of 4 units.
Thus, volume of specified sphere is obtained as:
[tex]V= \dfrac{4}{3} \pi r^3 \: \rm unit^3\\\\V = \dfrac{4}{3} \pi (4)^3 =\dfrac{256}{3} \times 3.14 \approx 267.95 \: m^3[/tex]
Thus,
Volume of a figure is the measurement of space occupied by the figure. The volume of the specified sphere is given by Option B: 267. 95 m³
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