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4 years ago

Let f(x) = 5x + 12. Find f−1(x).

1 answer:

7 0

Replace,

x = y

Or

x = f(x)

then us stay:

x = 5y + 12

Isolate 5y

5y = x - 12

Dividing both the sides by 5

y = x/5 - 12/5

Then, replace y = f^-(x)

f^-(x) = x/5 - 12/5

Hope this helps

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4. Find the lateral area and surface area of the given prism.

scoundrel [369]

Answer:

Step-by-step explanation:

$\bold{Q4}\\\text{We have}\\\text{two right triangles with legs a = 4m and b = 7m}\\\text{three rectangles}\ 7m\ \times 38m,\ 8.06m\ \times\ 38m\ \text{and}\ 4m\ \times\ 38m\\\\\text{The formula of an area of a right triangle:}\\\\A=\dfrac{ab}{2}\\\\\text{substitute:}\\\\A_1=\dfrac{(4)(7)}{2}=\dfrac{28}{2}=14\ m^2\\\\\text{The formula of an area of a rectangle}\ l\ \times w:\\\\A=lw\\\\\text{substitute:}\\\\A_2=(7)(38)=266\ m^2\\A_3=(8.06)(38)=306.28\ m^2\\A_4=(4)(38)=152\ m^2\\\\\text{The Surface Area:}$

$S.A.=2A_1+A_2+A_3+A_4\\\\S.A.=2(14)+266+306.28+152=752.28\ m^2$

$\bold{Q11}\\(look\ at\ the\ picture)\\\\\text{The formula of a volume of a pyramid:}\\\\V=\dfrac{1}{3}BH\\\\B-\text{area of a base}\\H-\text{height}\\\\\text{In the base we have the square. The formula of an area of a square with side a:}\\\\A=a^2\\\\\text{We have}\ a=12ft.\ \text{Substitute:}\\\\B=12^2=144\ ft^2\\\\\text{For}\ H\ \text{we need use the Pythagorean theorem:}\\\\H^2+6^2=10^2\\\\H^2+36=100\qquad\text{subtract 36 from both sides}\\\\H^2=64\to H=\sqrt{64}\\\\H=8\ m$

$\text{Substitute:}\\\\V=\dfrac{1}{3}(144)(8)=(48)(8)=384\ ft^3$

5 0

3 years ago

a door with width 4.20 m has an arc as shown in diagram .Find: a) radius of the arc B) length of the arc to the nearest cm

EastWind [94]

Answer:

Ok, we know that the width of the door is 4.20m.

Then, if the arc is at the top of the door, we will have that the diameter of that "half circle" will be equal to the width of the door.

Then the diameter of the arc is 4.20m

And the radius is defined as half of the diameter, so we have:

radius = 4.20m/2 = 2.10m

And we can write this in cm (because the probelm ask for it)

1m = 100cm

then 2.10m = 2.1*100cm = 210cm

Now, we know that the perimeter of a circle is:

P = 2*pi*r

where pi = 3.14

Then the perimeter (or arc) of half a circle will be half of that:

Arc = (2*pi*r)/2 = pi*r

and r = 210cm, pi = 3.14

Arc = 3.14*210cm = 659.4cm

4 0

4 years ago

a store owner has 7.11 lbs. of candy. if she puts the candy into 9 jars , how much candy will each jar contain?

larisa [96]

7.11 / 9 = 0.79

This is assuming that they equally split the candy among the jars.

The answer is 0.79 lbs of candy per jar.

Hope this helps! :)

3 0

3 years ago

NEED HELP ASAP, WILL MARK BRAINLIEST!!!

EastWind [94]

Answer:

7. -

a. 3.5 or 7/2 hours

b. 24.5

c. After 7 hours (and at the beginning when t=0)

8. -

a. 4 seconds

b. 1 second

c. 54 meters

Step-by-step explanation:

7. M(t)=-2t^2+14t

M’(t)=-4t+14

-4t+14=0

4t=14

2t=7

t=7/2

b) M(7/2)=24.5

M(t)=0

-2t^2+14t=0

t^2-7t=0

t(t-7)=0

t=0, 7

h(t)=0

-6t^2+12t+48=0

t^2-2t-8=0

(t-4)(t+2)=0

t=-2, 4

t=4

h(t)=-6t^2+12t+48

h’(t)=-12t+12

h’(t)=0

-12t+12=0

12t=12

t=1

c) h(1)=54

I hope this helps; please vote brainliest!

3 0

3 years ago

Solve the system PLEASE HELP ME

Colt1911 [192]

I cant see anything. It is too blurry.

5 0

3 years ago