Answer:
The equivalent function of [tex]sin\left(180^{\circ }+x\right)[/tex] will be: [tex]-\sin \left(x\right)[/tex]
i.e.
[tex]\sin \left(180^{\circ \:}+x\right)=-\sin \left(x\right)[/tex]
Step-by-step explanation:
Considering the function
[tex]sin\left(180^{\circ }+x\right)[/tex]
Solving
[tex]sin\left(180^{\circ }+x\right)[/tex]
Using the angle sum identity:
[tex]\sin \left(s+t\right)=\sin \left(s\right)\cos \left(t\right)+\cos \left(s\right)\sin \left(t\right)[/tex]
[tex]=\sin \left(180^{\circ \:}\right)\cos \left(x\right)+\cos \left(180^{\circ \:}\right)\sin \left(x\right)[/tex]
as
[tex]\cos \left(180^{\circ \:}\right)=\left(-1\right)[/tex]
[tex]\sin \left(180^{\circ \:}\right)=0[/tex]
so
[tex]=0\cdot \:\cos \:\left(x\right)+\left(-1\right)\cdot \:\sin \:\left(x\right)[/tex]
[tex]=0\cdot \cos \left(x\right)-1\cdot \sin \left(x\right)[/tex]
[tex]=0-1\cdot \sin \left(x\right)[/tex]
[tex]=0-\sin \left(x\right)[/tex]
[tex]=-\sin \left(x\right)[/tex]
So, the equivalent function of [tex]sin\left(180^{\circ }+x\right)[/tex] will be: [tex]-\sin \left(x\right)[/tex]
Therefore:
[tex]\sin \left(180^{\circ \:}+x\right)=-\sin \left(x\right)[/tex]
If it exists, solve for the inverse function of each of the following:
1. f(x) = 25x - 18
6. gala? +84 - 7
7. 10) = (b + 6) (6-2)
3. A(7)=-=-
4. f(x)=x
9. h(c) = V2c +2
+30
10. f(x) =
5. f(a) = a +8
ox-1
2. 9(x) = -1
2x+17
8. () - 2*
Answer:
The solution is too long. So, I included them in the explanation
Step-by-step explanation:
This question has missing details. However, I've corrected each question before solving them
Required: Determine the inverse
1:
[tex]f(x) = 25x - 18[/tex]
Replace f(x) with y
[tex]y = 25x - 18[/tex]
Swap y & x
[tex]x = 25y - 18[/tex]
[tex]x + 18 = 25y - 18 + 18[/tex]
[tex]x + 18 = 25y[/tex]
Divide through by 25
[tex]\frac{x + 18}{25} = y[/tex]
[tex]y = \frac{x + 18}{25}[/tex]
Replace y with f'(x)
[tex]f'(x) = \frac{x + 18}{25}[/tex]
2. [tex]g(x) = \frac{12x - 1}{7}[/tex]
Replace g(x) with y
[tex]y = \frac{12x - 1}{7}[/tex]
Swap y & x
[tex]x = \frac{12y - 1}{7}[/tex]
[tex]7x = 12y - 1[/tex]
Add 1 to both sides
[tex]7x +1 = 12y - 1 + 1[/tex]
[tex]7x +1 = 12y[/tex]
Make y the subject
[tex]y = \frac{7x + 1}{12}[/tex]
[tex]g'(x) = \frac{7x + 1}{12}[/tex]
3: [tex]h(x) = -\frac{9x}{4} - \frac{1}{3}[/tex]
Replace h(x) with y
[tex]y = -\frac{9x}{4} - \frac{1}{3}[/tex]
Swap y & x
[tex]x = -\frac{9y}{4} - \frac{1}{3}[/tex]
Add [tex]\frac{1}{3}[/tex] to both sides
[tex]x + \frac{1}{3}= -\frac{9y}{4} - \frac{1}{3} + \frac{1}{3}[/tex]
[tex]x + \frac{1}{3}= -\frac{9y}{4}[/tex]
Multiply through by -4
[tex]-4(x + \frac{1}{3})= -4(-\frac{9y}{4})[/tex]
[tex]-4x - \frac{4}{3}= 9y[/tex]
Divide through by 9
[tex](-4x - \frac{4}{3})/9= y[/tex]
[tex]-4x * \frac{1}{9} - \frac{4}{3} * \frac{1}{9} = y[/tex]
[tex]\frac{-4x}{9} - \frac{4}{27}= y[/tex]
[tex]y = \frac{-4x}{9} - \frac{4}{27}[/tex]
[tex]h'(x) = \frac{-4x}{9} - \frac{4}{27}[/tex]
4:
[tex]f(x) = x^9[/tex]
Replace f(x) with y
[tex]y = x^9[/tex]
Swap y with x
[tex]x = y^9[/tex]
Take 9th root
[tex]x^{\frac{1}{9}} = y[/tex]
[tex]y = x^{\frac{1}{9}}[/tex]
Replace y with f'(x)
[tex]f'(x) = x^{\frac{1}{9}}[/tex]
5:
[tex]f(a) = a^3 + 8[/tex]
Replace f(a) with y
[tex]y = a^3 + 8[/tex]
Swap a with y
[tex]a = y^3 + 8[/tex]
Subtract 8
[tex]a - 8 = y^3 + 8 - 8[/tex]
[tex]a - 8 = y^3[/tex]
Take cube root
[tex]\sqrt[3]{a-8} = y[/tex]
[tex]y = \sqrt[3]{a-8}[/tex]
Replace y with f'(a)
[tex]f'(a) = \sqrt[3]{a-8}[/tex]
6:
[tex]g(a) = a^2 + 8a- 7[/tex]
Replace g(a) with y
[tex]y = a^2 + 8a - 7[/tex]
Swap positions of y and a
[tex]a = y^2 + 8y - 7[/tex]
[tex]y^2 + 8y - 7 - a = 0[/tex]
Solve using quadratic formula:
[tex]y = \frac{-b\±\sqrt{b^2 - 4ac}}{2a}[/tex]
[tex]a = 1[/tex] ; [tex]b = 8[/tex]; [tex]c = -7 - a[/tex]
[tex]y = \frac{-b\±\sqrt{b^2 - 4ac}}{2a}[/tex] becomes
[tex]y = \frac{-8 \±\sqrt{8^2 - 4 * 1 * (-7-a)}}{2 * 1}[/tex]
[tex]y = \frac{-8 \±\sqrt{64 + 28 + 4a}}{2 * 1}[/tex]
[tex]y = \frac{-8 \±\sqrt{92 + 4a}}{2 * 1}[/tex]
[tex]y = \frac{-8 \±\sqrt{92 + 4a}}{2 }[/tex]
Factorize
[tex]y = \frac{-8 \±\sqrt{4(23 + a)}}{2 }[/tex]
[tex]y = \frac{-8 \±2\sqrt{(23 + a)}}{2 }[/tex]
[tex]y = -4 \±\sqrt{(23 + a)}[/tex]
[tex]g'(a) = -4 \±\sqrt{(23 + a)}[/tex]
7:
[tex]f(b) = (b + 6)(b - 2)[/tex]
Replace f(b) with y
[tex]y = (b + 6)(b - 2)[/tex]
Swap y and b
[tex]b = (y + 6)(y - 2)[/tex]
Open Brackets
[tex]b = y^2 + 6y - 2y - 12[/tex]
[tex]b = y^2 + 4y - 12[/tex]
[tex]y^2 + 4y - 12 - b = 0[/tex]
Solve using quadratic formula:
[tex]y = \frac{-b\±\sqrt{b^2 - 4ac}}{2a}[/tex]
[tex]a = 1[/tex] ; [tex]b = 4[/tex]; [tex]c = -12 - b[/tex]
[tex]y = \frac{-b\±\sqrt{b^2 - 4ac}}{2a}[/tex] becomes
[tex]y = \frac{-4\±\sqrt{4^2 - 4 * 1 * (-12-b)}}{2*1}[/tex]
[tex]y = \frac{-4\±\sqrt{4^2 - 4 *(-12-b)}}{2}[/tex]
Factorize:
[tex]y = \frac{-4\±\sqrt{4(4 - (-12-b))}}{2}[/tex]
[tex]y = \frac{-4\±2\sqrt{(4 - (-12-b))}}{2}[/tex]
[tex]y = \frac{-4\±2\sqrt{(4 +12+b)}}{2}[/tex]
[tex]y = \frac{-4\±2\sqrt{16+b}}{2}[/tex]
[tex]y = -2\±\sqrt{16+b}[/tex]
Replace y with f'(b)
[tex]f'(b) = -2\±\sqrt{16+b}[/tex]
8:
[tex]h(x) = \frac{2x+17}{3x+1}[/tex]
Replace h(x) with y
[tex]y = \frac{2x+17}{3x+1}[/tex]
Swap x and y
[tex]x = \frac{2y+17}{3y+1}[/tex]
Cross Multiply
[tex](3y + 1)x = 2y + 17[/tex]
[tex]3yx + x = 2y + 17[/tex]
Subtract x from both sides:
[tex]3yx + x -x= 2y + 17-x[/tex]
[tex]3yx = 2y + 17-x[/tex]
Subtract 2y from both sides
[tex]3yx-2y =17-x[/tex]
Factorize:
[tex]y(3x-2) =17-x[/tex]
Make y the subject
[tex]y = \frac{17 - x}{3x - 2}[/tex]
Replace y with h'(x)
[tex]h'(x) = \frac{17 - x}{3x - 2}[/tex]
9:
[tex]h(c) = \sqrt{2c + 2}[/tex]
Replace h(c) with y
[tex]y = \sqrt{2c + 2}[/tex]
Swap positions of y and c
[tex]c = \sqrt{2y + 2}[/tex]
Square both sides
[tex]c^2 = 2y + 2[/tex]
Subtract 2 from both sides
[tex]c^2 - 2= 2y[/tex]
Make y the subject
[tex]y = \frac{c^2 - 2}{2}[/tex]
[tex]h'(c) = \frac{c^2 - 2}{2}[/tex]
10:
[tex]f(x) = \frac{x + 10}{9x - 1}[/tex]
Replace f(x) with y
[tex]y = \frac{x + 10}{9x - 1}[/tex]
Swap positions of x and y
[tex]x = \frac{y + 10}{9y - 1}[/tex]
Cross Multiply
[tex]x(9y - 1) = y + 10[/tex]
[tex]9xy - x = y + 10[/tex]
Subtract y from both sides
[tex]9xy - y - x = y - y+ 10[/tex]
[tex]9xy - y - x = 10[/tex]
Add x to both sides
[tex]9xy - y - x + x= 10 + x[/tex]
[tex]9xy - y = 10 + x[/tex]
Factorize
[tex]y(9x - 1) = 10 + x[/tex]
Make y the subject
[tex]y = \frac{10 + x}{9x - 1}[/tex]
Replace y with f'(x)
[tex]f'(x) = \frac{10 + x}{9x -1}[/tex]
what is 4.25% as a decimal
Answer:
0.0425
Step-by-step explanation:
Answer:
0.0425
Step-by-step explanation:
hope this helped ^^
Molly and Cody are selling pies for a school fundraiser. Customers can buy apple pies and
pumpkin pies. Molly sold 1 apple pie and 13 pumpkin pies for a total of $160. Cody sold 14
apple pies and 7 pumpkin pies for a total of $140. What is the cost each of one apple pie and one
pumpkin pie?
Answer:
12 dollars and 6
Step-by-step explanation:
12 divided by 160 = 12
Sove the equation for all real solutions
-d^2-12d+4=-6d^2
Answer:
d=25 or d=2
Step-by-step explanation:
hope that helps!
Answer:
d=2/5 or d=2
Step-by-step explanation:
Step 1: Subtract -6d^2 from both sides.
−d2−12d+4−−6d2=−6d2−−6d2
5d2−12d+4=0
Step 2: Factor left side of equation.
(5d−2)(d−2)=0
Step 3: Set factors equal to 0.
5d−2=0 or d−2=0
d= 2/5 or d=2
Find the slope given the two points:
(3, 70) , (15, 90)
Answer:
x= 5/3
Step-by-step explanation:
I need help with this
Answer:
A, B, and C
Step-by-step explanation:
We can substitute each number into each equation
2 < -1 + 5 true
2 > 1 true
1 > 0 true
A is correct
4 < -1 + 5 true
4 > 1 true
1 > 0 true
B is correct
3 < -0 + 5 true
3 > 0 true
0 > 0 true
C is correct
5 < -2 + 5 false
D is incorrect
What are the zeros of this function
1. At the beginning of the year, Maria had $100 in her savings account. She plans to spend $10 a
month on a music app. By the end of January, she will have $90, 580 by the end of February,
$70 by the end of March, and so on. Write an equation that describes the amount in her savings
at any given month. Be sure to describe what your variables represent.
I will mark brainly if anyone can answer this
-2-4(6p-5)
-5(v-6)+10v
and 25 pts
Answer:
Ich weiß nicht =13
die Antwort -2 -4 (6p-5)
Step-by-step explanation:
PLEASE HELP ME WITH MY MATHE HOMEWORK!
Answer:
59/6
Step-by-step explanation:
9x6=54
54+5= 59
put the denominator of the fraction to the denominator to the new fraction. I hope this helps.
Which is greatest: 75%, 4/5, or 0.75?
Answer:
4/5
Step-by-step explanation:
75% = 75/100 = 0.75 = 3/4
4/5 = 80/100 = 80% = 0.80
75 = 75% = 3/4 = 75/100
75%
80% - this is the biggest
75%
HOPE THIS HELPS
PLZZ MARK BRAINLIEST
Answer: 4/5
Step-by-step explanation:
75% = 75/100 same as 0.75
4/5 = 0.80
0.75 already in decimal
Therefore 0.80 is the greatest
The product of 5 and a number x is 1/4 What is the value of x?
x=19/4
x=1/20
x =5/4
x =4 3/4
Answer:
x=19/4
Step-by-step explanation:
The product of 5 and a number x is 1/4
Which of the following graphs represents the equation above?
y=1/2x-2
Answer:
There’s no graphs
Step-by-step explanation:
Answer:
Step-by-step explanation:
Find the missing terms in each geometric sequence.
1. 3, 12, 48 __, __
2. __, __, 32, 64, 128, ...
3. 120, 60, 30, __, __
4. 5, __, 20, 40, __, __
5. __, 4, 12, 36, __, __
the first blank is 25 the second blank is 10 what is the slope
Answer:
5/2
Step-by-step explanation:
25 and 10 so 25/10 or 5/2 or 2 1/2
Jermaine buys T-shirts for $6 each and marks up the price by 45%.
How much does Jermaine charge for each T-shirt (with the mark-up)?
Answer:
8.7
Step-by-step explanation:
6*1.45=8.7
Find the slope of the line without graphing using the 2 points below.
(-3 , 4) & (13 , 8)
m = _______
Answer:
Step-by-step explanation:
1. use the slope formula --> (y2-y1)/(x2-x1)
2. (8 - 4)/(13 -(-3))
3. 4/16
4. m = 1/4
SOMEONE ANWSER QUIKLY PLEASE !!!!!
The second of two numbers is one more than twice the first. The sum of the numbers is
40. What are the numbers?
Answer:
13 + 1/3 and 26+2/3
Step-by-step explanation:
so one is twices a large as the first. so 40/3 = 13 + 1/3 so thats one of your awnsers the larger one is 2 times larger so13 +1/3 * 2 is 26+2/3 hope this helps! :D
Answer:
First Number is 13
Second Number is 27
Step-by-step explanation:
let x = first number
let 2x + 1 = second number
x + (2x + 1) = 40
3x + 1 = 40
- 1 -1
3x = 39
/3 /3
x = 13
13 x 2 = 26 + 1 = 27
12 IF APOR is similar to AXYZ, which of the following statements must be true?
Answer:
F
Step-by-step explanation:
There's no Q in APOR or AXYZ
1. Dilate A using P as the center of dilation and a scale factor of 3. Label the new point
A'.
2. Dilate Busing Pas the center of dilation and a scale factor of 2. Label the new point B'
Answer:
Step-by-step explanation:
Rule for the dilation of a point by a scale factor 'k',
(x, y) → (kx, ky)
If we impose this rule in this problem,
k = [tex]\frac{\text{Distance of A' from P}}{\text{Distance of A from P}}[/tex]
1). If k = 3
Therefore, Distance of A' from P = 3(Distance of A from P)
And point A' will be on the third circle.
2). If k = 2
Distance of B' from P = 2(Distance of B from P)
Since, B is on circle 2, B' will be on circle 4.
Now we can plot these points A' and B' on the graph.
After the dilation point A becomes A' and it is at a distance of 3 units from point P and after the dilation point B becomes B' and it is at a distance of 2 units from point P.
1)
Given :
Dilate A using P as the center of dilation and a scale factor of 3.
Let the coordinates of point A be (x,y) then after dilation point A becomes A'(3x , 3y). So, the distance of the point A' from the point P is 3 units
2)
Given :
Dilate Busing P as the center of dilation and a scale factor of 2.
Let the coordinates of point B be (x',y') then after dilation point B becomes B'(2x' , 2y'). So, the distance of the point B' from the point P is 2 units
For more information, refer to the link given below:
https://brainly.com/question/2856466
What is the rectangular form of r=8sin(0)
Step-by-step explanation:
the regular form of r=8
If you earn $134 in 8 hours, how much do you earn per hour?
Answer:$16.75
Step-by-step explanation:
Please Help
Please let me know how to do it, I don't only want the answer. Thank you!
(4y+3)-(y-2)
(There is no equal sign in the math problem)
please help i’ll give brainliest
Answer:
87.5
Step-by-step explanation:
2 inches is 70 miles. .5 inches is 17.5 and add them together and you get 87.5.
Please mark brainliest.
Answer: D. 87.5 miles
Step-by-step explanation:
They have given us a scale that 1 inch = 35 miles.
Since the distance is 2.5 inches, we have to multiply 2.5 inches by 35 miles.
1 in. = 35 miles
2.5 in = x
2.5 times 35 = 87.5 miles
hope this helps!
what is 9 time 64 what does it equal to
Answer:
It's 576 if you mean 64 times 9!
Step-by-step explanation:
z = 24a - 2b
solve for a
Answer:
a= (Z + 2b)/24
Step-by-step explanation:
given:
Z = 24a - 2b
to solve for a, we will try to move "a" to one side of the equation and all other terms to the other side:
Z = 24a - 2b (add 2b to both sides)
Z + 2b = 24a -2b +2b
Z + 2b = 24a (switch sides)
24a = Z + 2b (divide both sides by 24)
a/24 = (Z + 2b)/24
a= (Z + 2b)/24
I WILL GIVE THE BRAINLIEST
Jack works after school. each day he earns a set amount, plus an hourly wage. the following table represents a linear function f jack can use to determine to his pay.
hours: 1, 2, 3 | Pay: 18, 28, 38
SLOPE is 10.
Using the slope, find the y-intercept and write the function.
Answer:
The y intercept is (0, 8). The equation of the function is f(x) = 10x + 8
Step-by-step explanation:
Given that after 1 hour of work, Jack will make 18 dollars and the slope is 10, subtract 10 dollars from 18 dollars to find his set amount, or y-intercept.
18 - 10 = 8 dollars.
Now that we have the m and b values, we can create our equation.
The equation in standard form is f(x) = mx +b, where m = the slope and b = the y-intercept. Plug our values in and the equation will be f(x) = 10x + 8. You can test if this is correct by plugging in x values from the table and seeing if your calculated value correctly corresponds to the given y value in the table.
the time, t, in seconds, is required for an object accelerating at a constant rate of a meters/second to travel a distance of d meters is given this equation
Answer:
C. [tex] d = \frac{at^2}{2} [/tex]
Step-by-step explanation:
Given:
[tex] t = \sqrt{\frac{2d}{a}} [/tex]
Required:
Make d the subject of the formula.
SOLUTION:
[tex] t = \sqrt{\frac{2d}{a}} [/tex]
Square both sides
[tex] t^2 = (\sqrt{\frac{2d}{a}})^2 [/tex]
[tex] t^2 = \frac{2d}{a} [/tex]
Multiply both sides by a
[tex] a*t^2 = \frac{2d}{a}*a [/tex]
[tex] at^2 = 2d [/tex]
Divide both sides by 2
[tex] \frac{at^2}{2} = \frac{2d}{2} [/tex]
[tex] \frac{at^2}{2} = d [/tex]
[tex] d = \frac{at^2}{2} [/tex]
32a + 28 = 0
(Factor completely.)
Answer: 0.875
Step-by-step explanation:
Which property should be used next in this solution process?
3x + 2 + 3 = 7(x - 1) – 4
3x + 5 = 7(x - 1) – 4
A. Commutative Property of Addition
B. Identity Property of Multiplication
C. Associative Property of Multiplication
D.
Distributive Property
Answer:
niwebfasfbjsdfb
Step-by-step explanation:
jsdfhsdbfjhadsjbdsfhb