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Papessa [141]
3 years ago
8

It's due in 20 minutes!!

Mathematics
2 answers:
slega [8]3 years ago
7 0

Answer:

A. 18 sit-ups in one minute

B. 30 doors per hour

D. 18 words per minute

F. $30 per night

C. 3.5 miles per hour

E. $10.50 per pair of pants

Step-by-step explanation:

A. 36/2 = 18

B. 15 * 2 = 30

D. 72/4 = 18

F. 150/5 = 30

C. 10.5/3 = 3.5

E. 31.50/3 = 10.50

JulijaS [17]3 years ago
5 0

Just divide

Step-by-step explanation:

31.50÷3= 10.50

36÷2= 18

150÷5= 30

10.5÷3= 3.5

72÷4=18

B 3.5

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Find the inverse when f(x)=3x^2-3x-2
Vikentia [17]

Answer:

The inverse of f(x) is f^{-1}(x) =  ± \sqrt{\frac{x+\frac{11}{4}}{3}} + \frac{1}{2}

Step-by-step explanation:

To find the inverse of the quadratic function f(x) = ax² + bx + c, you should put it in the vertex form f(x) = a(x - h)² + k, where

  • h = \frac{-b}{2a}
  • k is the vlue f at x = h

∵ f(x) = 3x² - 3x - 2

→ Compare it with the 1st form above to find a and b

∴ a = 3 and b = -3

→ Use the rule of h to find it

∵ h = \frac{-(-3)}{2(3)} = \frac{3}{6} = \frac{1}{2}

∴ h =  \frac{1}{2}

→ Substitute x by the value of h in f to find k

∵ k = 3( \frac{1}{2})² - 3( \frac{1}{2}) - 2

∴ k = -\frac{11}{4}

→ Substitute the values of a, h, and k in the vertex form above

∵ f(x) = 3(x -  \frac{1}{2})² + -\frac{11}{4}

∴ f(x) = 3(x -  \frac{1}{2})² - \frac{11}{4}

Now let us find the inverse of f(x)

∵ f(x) = y

∴ y = 3(x -  \frac{1}{2})² - \frac{11}{4}

→ Switch x and y

∵ x = 3(y -  \frac{1}{2})² - \frac{11}{4}

→ Add \frac{11}{4} to both sides

∴ x + \frac{11}{4} = 3(y - \frac{1}{2})²

→ Divide both sides by 3

∵ \frac{x+\frac{11}{4}}{3} = (y - \frac{1}{2})²

→ Take √ for both sides

∴ ± \sqrt{\frac{x+\frac{11}{4}}{3}} = y - \frac{1}{2}

→ Add  \frac{1}{2} to both sides

∴ ± \sqrt{\frac{x+\frac{11}{4}}{3}} + \frac{1}{2} = y

→ Replace y by f^{-1}(x)

∴ f^{-1}(x) =  ± \sqrt{\frac{x+\frac{11}{4}}{3}} + \frac{1}{2}

∴ The inverse of f(x) is f^{-1}(x) =  ± \sqrt{\frac{x+\frac{11}{4}}{3}} + \frac{1}{2}

       

4 0
3 years ago
All diagonals from a single vertex of a hexagon are drawn. Four triangles will result. True or False.
alexdok [17]

Answer:

Step-by-step explanation:

true

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3 years ago
Determine the general solution of:<br><br> sin 3x - sin x = cos2x
SpyIntel [72]
Sin³ x-sin x=cos ² x

we know that:
sin²x + cos²x=1  ⇒cos²x=1-sin²x
Therefore:

sin³x-sin x=1-sin²x
sin³x+sin²x-sin x-1=0

sin³x=z

z³+z²-z-1=0

we divide by Ruffini method:
              1     1     -1     -1
        1           1      2      1                z=1
-------------------------------------
              1     2      1      0
       -1         -1      -1                       z=-1
--------------------------------------
              1     1       0                       z=-1

Therefore; the solutions are z=-1 and z=1

The solutions are:
if z=-1, then
sin x=-1   ⇒x= arcsin -1=π+2kπ    (180º+360ºK)   K∈Z


if z=1, then
sin x=1   ⇒ x=arcsin 1=π/2 + 2kπ   (90º+360ºK)   k∈Z

π/2 + 2kπ    U   π+2Kπ=π/2+kπ     k∈Z    ≈(90º+180ºK)

Answer: π/2 + Kπ    or     90º+180ºK          K∈Z
Z=...-3,-2,-1,0,1,2,3,4....
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schepotkina [342]
-3x-3 = 4x-3

-3 = 7x-3

0 = 7x

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4 years ago
Sarah was cutting fabric for a quilt. She cut a strip of fabric that was 19 1/8 inches long into 5 equal pieces. When she was fi
goldenfox [79]
We need a least common denominator
19 1/8 and 2 1/4 (also = to 2 2/8)
19 1/8-2 2/8= 16 7/8
16 7/8 divided by 5
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3 0
4 years ago
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