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QUESTION 1: True or false:

Do vertical angles prove parallel lines?

QUESTION 2:

Solve for x in the diagram below. PIC ATTACHED

[tex]g( \: f(x) \: ) = x[/tex]

And

[tex]f( \: g(x) \: ) = x[/tex]_________________________________

So :

[tex]g(x) = {f}^{ - 1}(x) [/tex]

And

[tex]f(x) = {g}^{ - 1}(x) [/tex]

_________________________________

So to find g(x) , we must find the inverse of f(x) .

Let's do it .....

[tex]f(x) = 8 {x}^{3} + 1 [/tex]

[tex]y = 8 {x}^{3} + 1 [/tex]

Subtract the sides of the equation minus 1

[tex]y - 1 = 8 {x}^{3} [/tex]

Divided the sides of the equation by 8

[tex] \frac{y - 1}{8} = {x}^{3} \\ [/tex]

From the sides of the equation, we take the radical with interval 3

[tex] \sqrt[3]{ \frac{y - 1}{8} } = x \\ [/tex]

[tex] \sqrt[3]{ \frac{1}{8}(y - 1) } = x \\ [/tex]

[tex] \frac{1}{2} \sqrt[3]{y - 1} = x \\ [/tex]

[tex] \frac{ \sqrt[3]{y - 1} }{2} = x \\ [/tex]

So ;

[tex] {f}^{ - 1}(x) = \frac{ \sqrt[3]{x - 1} }{2} \\ [/tex]

Now we find g(x) which is :

[tex]g(x) = \frac{ \sqrt[3]{x - 1} }{2} \\ [/tex]

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And we're done.

Thanks for watching buddy good luck.

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If f(g(x)) = x and g(f(x)) = x , than  [tex]\rm g(x) = \sqrt[3]{\dfrac{x-1}{8}}[/tex] and this can be calculated by finding the inverse of the given function f(x).

Given :

Given that f(g(x)) = x it means that:

[tex]\rm g(x) = f^{-1}(x)[/tex]

It is also given that g(f(x)) = x that means:

[tex]\rm f(x) = g^{-1}(x)[/tex]

Now, the inverse of f(x) is given by the following calculation:

[tex]\rm f(x) = 8x^3+1[/tex]

Now, replace f(x) with y in the above equation.

[tex]y = 8x^3+1[/tex]

Now, replace y with x and x with y and evaluate 'y'.

[tex]x = 8y^3 +1[/tex]

[tex]\sqrt[3]{\dfrac{x-1}{8}}=y[/tex]

Now, replace y with [tex]\rm f^{-1}(x)[/tex] in the above equation.

[tex]\rm f^{-1}(x) = \sqrt[3]{\dfrac{x-1}{8}}[/tex]

[tex]\rm f^{-1}(x) = \sqrt[3]{\dfrac{x-1}{8}} = g(x)[/tex]

For more information, refer to the link given below:

https://brainly.com/question/13715269

Answer:

40 percent

Step-by-step explanation:

60 plus 60 is 120 and take 20 from 60 and get 40 so 40 times 3 equals 123 so 40 percent

Answer:

No, the opposite would be negative 6/4

Step-by-step explanation:

3/2 is just a simplified version of 6/4

Answer:

x = -6

Step-by-step explanation:

-5x = 30

Divide each side by -5

-5x/-5 = 30/-5

x = -6

Answer:

well you can add another -1, or another 2

Step-by-step explanation:

because more than 1 x is banned

Answer:

27

Step-by-step explanation:

substitute the given value of x: 2(4) + 3 + (4)^2

simplify: 8 + 3 + 16

add: 8 + 3 + 16 = 27

Answer:

<

Step-by-step explanation:

If you add negitives you get a negitive and a plus a positive you get positive positives are bigger than negitives  

Answer:

x = - 2, - 3

Step-by-step explanation:

Given

- 3x + 4 ≥ 9 ( subtract 4 from both sides )

- 3x ≥ 5  

Divide both sides by - 3, reversing the symbol as a result of dividing by a negative quantity.

x ≤ - [tex]\frac{5}{3}[/tex]

The only values of x that satisfy the inequality in the interval { - 3, 3 } are

x = - 2, x = - 3

Answer:

y = 3/4x + 1/2

Step-by-step explanation:

We can use the formula [ y2-y1/x2-x1 ] to solve for the slope.

-4-5/-6-6

-9/-12

9/12

3/4

Find the y-intercept.

y = 3/4x + b

5 = 3/4(6) + b

5 = 4.5 + b

0.5 = b

y = 3/4x + 1/2

Best of Luck!

First of all, Let's find the slope because we need it on the formula for finding the y-intercept.

From the points given in the question,

Plugging in the above formula,

➝ m = -4 - 5 / -6 - 6

➝ m = -9 / -12

➝ m = 3/4

Now finding the y-intercept[tex]:[/tex]

➝ y = mx + b

And if we put in the values from our first point (6, 5) we get

➝ 5 = 3/4 (6) + b

➝ 5 = 9/2 + b

➝ b = 5 - 9/2

➝ b = 1/2

Required equation of the line:

➝ y = 3/4x + 1/2

Carry On Learning !

Answer:

ok

ok

Step-by-step explanation:

ok

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ok

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ok

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ko

k

k

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Answer:

B she left out a zero between the 2 and the 5

Answer:

b) She left a zero in between two and five.

The number given is 12050000, the underlined number is the number she missed while converting it into Scientific notation.

If my answer helped, kindly mark me as the brainliest!!

Thank You!!

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Explanation:

In any quadrilateral, the four angles always add to 360

P+Q+R+S = 360

x+5x+x+5x = 360

12x = 360

x = 360/12

x = 30

This means

P = R = x = 30

Q = S = 5x = 5*30 = 150

So, P+Q+R+S = 30+150+30+150 = 360 which helps confirm the answer.

Answer:

x = 30

Step-by-step explanation:

the sum of all angles is 360

the picture shows that the sum equals 12x

12x=360

x= 360/12

x = 30

Answer:

Use the formula for calculating compound interest PN=P0(1+rk)Nk where P0 is the unknown, PN=10,000, N=10, k=1, and r=0.015. Substitute the values into the formula and simplify.

10000=P(1+0.0151)1⋅10

10000=P(1.015)10

10000=P(1.16054...)

8616.67=P

Therefore, rounded to the nearest dollar, the initial investment needs to be $8617 to have $10,000 in 10 years.

Step-by-step explanation:

Answer:

x > -1

Step-by-step explanation:

Isolate the variable, x. Treat the > sign like an equal sign, what you do to one side, you do to the other.

Subtract 5 from both sides:

x + 5 (-5) > 4 (-5)

x > 4 - 5

x > -1

x > -1 is your answer.

~

Answer:

x > -1

Step-by-step explanation:

Step 1: Write inequality

x + 5 > 4

Step 2: Solve for x

Here we see that any value x that is greater than -1 will work.

Answer:

0.345 thats the answer

Answer:

B. 3.45

I hope it helps you

Answer:

m∠6 = 148°

Step-by-step explanation:

From the figure attached,

AB and CD are two parallel line and another transverse line is intersecting these line at two distinct points.

Since, m∠1 = 32°,

∠1 and ∠4 are supplementary angles [Linear pair of angles]

m∠1 + m∠4 = 180°

32° + m∠4 = 180°

m∠4 = 180° - 32°

m∠4 = 148°

Since, ∠4 ≅ ∠6 [Alternate interior angles]

m∠4 = m∠6 = 148°

Therefore, m∠6 = 148°

Answer:

Step-by-step explanation:

see attached

The answer is:

A

60 degrees

Answer:

Perpendicular lines have opposite reciprocal slopes, so the slope of the line is -.5

Now, y=.5x+b, so you plug in the point -2,6.

6=.5(-2)+b

6=-1+b, so b=7.

The equation is y= .5x+7

Answer:

1. x=2

2. x= -4

3. x= -7

4. x = -4

Step-by-step explanation:

hope this helps :)

Answer:

the first one is x=2 the second one is x=-4 the third one is x= -7the fourth one is x=4

Step-by-step explanation:

Answer:

60

Step-by-step explanation:

Answer:

-6 ... even though it is not one of the options would be the correct answer.

Step-by-step explanation:

In order to solve this problem we can take it one step at a time. Sal started Friday morning with 6ft of sausage

6ft

He used 3ft for dinner on Friday night which means he subtracted 3ft.

6ft - 3ft = 3ft

He made another 6ft Saturday morning which means he added to his existing sausage link.

3ft + 6ft = 9ft

Finally, he used 9ft for dinner Saturday Night which means he subtracted 9ft.

9ft - 9ft = 0ft

Therefore, the net change would be -6 since Sal started with 6ft and ended with 0ft during this time.

yw good luck

i did the three questions then i put some math notes in the bottom right corner

Answer:

the mean is 37.5

Step-by-step explanation:

you get this by adding all the values and then dividing by how many values there are.

The mean of the given values will be equal to 37.5.

The numbers given are 10, 20, 35, 35, 35, 40, 45, 45, 50 and 60

We have to find out the mean of the given numbers.

What is mean ?

The mean is equal to the sum of given numbers divided by the total number of numbers.

As per the question ,

Numbers given are ; 10, 20, 35, 35, 35, 40, 45, 45, 50 and 60

The sum of all above numbers is ;

= 10 + 20 + 35 + 35 + 35 + 40 + 45 + 45 + 50 + 60

= 375

and

Total number of numbers = 10

So , the mean will be ;

Mean = sum of all numbers / total number of numbers

⇒ Mean = [tex]\frac{375}{10}[/tex]

⇒ Mean = 37.5

Thus , the mean of the given values will be equal to 37.5.

To learn more about mean of values click here ;

https://brainly.com/question/256619

#SPJ2

Answer:

A = 54 units ^2

Step-by-step explanation:

The area of a triangle is

A = 1/2 bh where b is the base and h is the height

A = 1/2 ( 18) * ( 6)

A = 54 units ^2

Answer:

54 units²

Step-by-step explanation:

Hello! :)

I don't know which equation your teacher wants you to use for the Area of a Triangle, but this is how I do it:

A= ½(b*h)

A= ½(18*6)

A= ½ (108)

A= 54

--------------------

If you prefer an explanation in word form, here you go:

The area of a triangle is Area= one-half, multiplied by its base and height.

A= ½(b*h)

So in this question, the base(b)= 18 and the height(h)= 6.

A= ½(18*6)

Then, you just solve the math problem (shown up above)!

Good luck with your homework, and I don't need a brainliest I just wanted to help! :)

Answer:

Equation: [tex]x=9[/tex]

Step-by-step explanation:

First graph the points on the coordinate plane, then find the x and y intersections and the slope. Since the slope is 0, and the x intersection is 9, you get [tex]x=9[/tex].

Let's see what to do buddy...

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If 99 & 100 are in Degree

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STEP (1)

The angles 99 and 100 are in the second quarter of the trigonometric circle.

The cosine is negative in the second quarter.

To make things easier, we can use angle conversion.

Look :

[tex]we \: know \: that \: 100 = 90 + 10[/tex]

[tex]also \: we \: know \: 99 = 90 + 9[/tex]

So :

[tex] \cos(100) = \cos(90 + 10) = \cos( \frac{\pi}{2} + 10 ) \\ [/tex]

[tex] \cos(99) = \cos(90 + 9) = \cos( \frac{\pi}{2} + 9 ) \\ [/tex]

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STEP (2)

Well now we have to do the arc deletion.

To remove the arc, we remove π/2 from the arc.

Remember that every time we remove π/2 from the arc, the trigonometric ratio changes.

That is, if it is a sine, it becomes a cosine, and if it is a cosine, it becomes a sine.

Or if it is a tangent, it becomes a cotangent, and if it is a cotangent, it becomes a tangent.

[tex]in \: second \: quarter \: cosine \: is \: negative \\ \\ \cos( \frac{\pi}{2} + 10 ) = - \sin(10) = - 0.173 [/tex]

[tex] \cos( \frac{\pi}{2} + 9 ) = - \sin(9) = - 0.156 \\ [/tex]

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STEP (3)

[tex] \cos(100) - \cos(99) = \\ - \sin(10) - ( - \sin(9) \: ) = \\ - 0.173 - ( - 0.156) = \\ - 0.173 + 0.156 = - 0.017 [/tex]

And we're done here.

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If 99 & 100 are in Radian

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STEP (1)

First we need to know how many degrees 1 radian is.

The following equation is used to convert degrees to radians or radians to degrees.

[tex] \frac{degree}{180} = \frac{radian}{\pi} \\ [/tex]

So we have :

[tex] \frac{d}{180} = \frac{1}{\pi} \\ [/tex]

Multiply the sides of the equation by 180 :

[tex]d = \frac{180}{\pi} = \frac{180}{3.14} = 57.32 \\ [/tex]

So 1 radian is approximately equal to 57 degrees.

And we have :

[tex]100 \: rad \: = 100 \times 57 = 5700 \: deg \\ \\ 99 \: rad \: = 99 \times 57 = 5601 \: deg[/tex]

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STEP (2)

Let's move on to deletion.

Look : 5700° = 15 × 360° + 300°

and : 5601° = 15 × 360° + 201°

We know π rad = 3.14 × 57 = 180° deg

So 2π rad = 2 × 180 = 360 ° deg

Then :5700 = 15 × 2 π + 300° = 30 π + 300°

and :5601 = 15 × 2 π + 201° = 30 π + 201°

Remember that deleting 2π is unconditional.

[tex] \cos(30\pi + 300) = \cos(300) = \cos(360 - 60) = \cos(2\pi - 60) = \cos( - 60) = \\ cosine \: eat \: negative \\ \cos( - 60) = \cos(60) = \frac{1}{2} [/tex]

[tex] \cos(30\pi + 201) = \cos(201) = \\ \cos(180 + 21) = \cos(\pi + 21) = \\ - \cos(21) = - 0.933 [/tex]

[tex] \frac{1}{2} - ( - 0.933) = 0.500 + 0.933 = 1.433[/tex]

And we're done.

Thanks for watching buddy good luck.

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