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DanielleElmas [232]
2 years ago
15

F (x) = 3x +2 fine the inverse of the function

Mathematics
1 answer:
Hitman42 [59]2 years ago
7 0
.................F^-1 (x) =x/3-2/3 .................
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At what value of x do the graphs of the equation below intersect ?<br> 2x-y=6<br> 5x+10y=-10
Y_Kistochka [10]

Answer:

x = 2

Step-by-step explanation:

Solve the two equations simultaneously....whereby you substitute y = 2x - 6 from the above equation into the second equation...

where...; 5x + 10(2x - 6) = -10

5x + 20x - 60 = -10...then move the variables with x to one side...

5x + 20x = -10 + 60

25x = 50

;Therefore...the value of x at intersection point = 2

5 0
3 years ago
A corporate team-building event costs $8 for every attendee. How many attendees can there be, at most, if the budget for the cor
egoroff_w [7]

The answer 850709 is

6

because

if there is $48 to spend on the event and it costs $8 for each attendee, divide 48 by 8 to get 6.

7 0
3 years ago
Read 2 more answers
Any help would be appreciated ❤ ❤ Thank you
Paladinen [302]
The solid shape is a cone and a half sphere. So the equation would be (cone volume) + (1/2 sphere volume):
cone =  \frac{1}{3} \pi {r}^{2} h \\ sphere =  \frac{4}{3} \pi {r}^{3}  \\ object = ( \frac{1}{3} \pi  {r}^{2} h) +  \frac{1}{2} ( \frac{4}{3} \pi  {r}^{3} )
If the volume of the cone is 270pi and the height of the cone is 10, then:
270\pi =  \frac{1}{3} \pi {r}^{2} (10) \\ 27 =  \frac{1}{3}  {r}^{2}  \\ 80 =  {r}^{2}  \\ r = 9
The radius of the object is 9 cm. Therefore, we can plug into the formula for the total volume:
object = 270\pi +  \frac{1}{2} ( \frac{4}{3} \pi {(9)}^{3} ) \\  = 270\pi +  \frac{2}{3} (729\pi) \\  = 270\pi \: + 243\pi \\  = 513\pi
The total volume is 513 pi cm^3
7 0
3 years ago
Show that the plane and line with the given equations intersect, and then find the acute angle of intersection between them. (Gi
Reptile [31]

Answer:

  angle of intersection: 5.2°

Step-by-step explanation:

The direction vector normal to the plane is ...

  n = (1, 1, 3)

The direction vector of the line is ...

  m = (1, -3, 1)

Then the angle θ between them can be found from the dot product:

  n•m = |n|·|m|·cos(θ)

  (1·1 +1(-3) +3·1) = 1 -3 +3 = 1 = √(1²+1²+3²)·√(1²+(-3)²+1²)·cos(θ)

  1 = 11·cos(θ)

  θ = arccos(1/11) ≈ 84.8°

This is the angle between the line and the normal to the plane, so the angle between the line and the plane will be the complement of this. Since this angle is not 90°, <em>the line and plane must intersect</em>.

  acute angle = 90° -84.8° = 5.2°

_____

The attached graph shows the line and plane meet at a shallow angle, consistent with the above answer.

8 0
3 years ago
The perimeter of a rectangular garden is 37.5 feet (ft). The width is x and the length is 15 ft. What is the width, in feet, of
nikitadnepr [17]

Answer:

the width is 22.5 ft

Step-by-step explanation:

8 0
3 years ago
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