3. the volume (v) of a rectangular pyramid can be determined by using the formula ( v = \frac{lwh}{3} ) where ( l ) is the length of the rectangle, ( w ) is the width of the rectangle, and ( h ) is the height of the pyramid. which of the following is the result of solving this equation for ( w )?
a) ( w = 3v - lh ) c) ( w = v + 3 - lh )
b) ( w = \frac{v + 3}{lh} ) d) ( w = \frac{3v}{lh} )

4. counting the number of cricket chirps can provide an estimate of the temperature. the formula below gives the temperature in degrees celsius based on the number of cricket chirps (( n )) in 15 seconds. ( c = \frac{5n + 40}{9} )
this formula can be rearranged to solve for the number of chirps as a function of the temperature in degrees celsius. which formula has been rearranged correctly?
a) ( n = \frac{9}{5}c - 8 ) c) ( n = \frac{9}{5}c - 40 )
b) ( n = \frac{9}{5}(c - 8) ) d) ( n = \frac{9}{5}(c - 40) )

5. the area of a trapezoid can be found using the formula: ( a = \frac{h(b + c)}{2} ). which of the following equations is equivalent to the formula solved for ( b ), one of the bases of the trapezoid.
a) ( b = \frac{2a - h}{c} ) c) ( b = \frac{h(a + c)}{2} )
b) ( b = \frac{2a - c}{h} ) d) ( b = \frac{2a}{h} - c )

6. the formula ( s = (n - 2) cdot 180 ) can be used to find the sum of the interior angles of a polygon with ( n ) sides. which formula can be used to find the number of sides a polygon has?
a) ( n = \frac{s}{180} - 2 ) c) ( n = \frac{s}{180} + 2 )
b) ( n = \frac{s}{360} + 2 ) d) ( n = 180s + 2 )

7. the surface area, ( s ), of a cylinder is calculated using the formula ( s = 2pi rh + 2pi r^2 ). which equation is equivalent to the formula solved for ( h ), the height of the cylinder?
a) ( h = \frac{s - 1}{r} ) c) ( h = \frac{s - 2pi r}{2pi r^2} )
b) ( h = \frac{s}{2pi r} ) d) ( h = \frac{s - 2pi r^2}{2pi r} )

Question

3. the volume (v) of a rectangular pyramid can be determined by using the formula ( v = \frac{lwh}{3} ) where ( l ) is the length of the rectangle, ( w ) is the width of the rectangle, and ( h ) is the height of the pyramid. which of the following is the result of solving this equation for ( w )?
a) ( w = 3v - lh )  c) ( w = v + 3 - lh )
b) ( w = \frac{v + 3}{lh} )  d) ( w = \frac{3v}{lh} )

4. counting the number of cricket chirps can provide an estimate of the temperature. the formula below gives the temperature in degrees celsius based on the number of cricket chirps (( n )) in 15 seconds. ( c = \frac{5n + 40}{9} )
this formula can be rearranged to solve for the number of chirps as a function of the temperature in degrees celsius. which formula has been rearranged correctly?
a) ( n = \frac{9}{5}c - 8 )  c) ( n = \frac{9}{5}c - 40 )
b) ( n = \frac{9}{5}(c - 8) )  d) ( n = \frac{9}{5}(c - 40) )

5. the area of a trapezoid can be found using the formula: ( a = \frac{h(b + c)}{2} ). which of the following equations is equivalent to the formula solved for ( b ), one of the bases of the trapezoid.
a) ( b = \frac{2a - h}{c} )  c) ( b = \frac{h(a + c)}{2} )
b) ( b = \frac{2a - c}{h} )  d) ( b = \frac{2a}{h} - c )

6. the formula ( s = (n - 2) cdot 180 ) can be used to find the sum of the interior angles of a polygon with ( n ) sides. which formula can be used to find the number of sides a polygon has?
a) ( n = \frac{s}{180} - 2 )  c) ( n = \frac{s}{180} + 2 )
b) ( n = \frac{s}{360} + 2 )  d) ( n = 180s + 2 )

7. the surface area, ( s ), of a cylinder is calculated using the formula ( s = 2pi rh + 2pi r^2 ). which equation is equivalent to the formula solved for ( h ), the height of the cylinder?
a) ( h = \frac{s - 1}{r} )  c) ( h = \frac{s - 2pi r}{2pi r^2} )
b) ( h = \frac{s}{2pi r} )  d) ( h = \frac{s - 2pi r^2}{2pi r} )

Accepted Answer

### Question 3
# Explanation:
## Step1: Start with the formula $ V = \frac{lwh}{3} $. Multiply both sides by 3 to eliminate the denominator.
$ 3V = lwh $
## Step2: Divide both sides by $ lh $ to solve for $ w $.
$ w = \frac{3V}{lh} $
# Answer: D) $ w = \frac{3V}{lh} $

### Question 4
# Explanation:
## Step1: Start with the formula $ C = \frac{5n + 40}{9} $. Multiply both sides by 9.
$ 9C = 5n + 40 $
## Step2: Subtract 40 from both sides.
$ 9C - 40 = 5n $
## Step3: Divide both sides by 5.
$ n = \frac{9C - 40}{5} = \frac{9}{5}C - 8 $
# Answer: A) $ n = \frac{9}{5}C - 8 $

### Question 5
# Explanation:
## Step1: Start with the formula $ A = \frac{h(B + C)}{2} $. Multiply both sides by 2.
$ 2A = h(B + C) $
## Step2: Divide both sides by $ h $.
$ \frac{2A}{h} = B + C $
## Step3: Subtract $ C $ from both sides.
$ B = \frac{2A}{h} - C $
# Answer: D) $ B = \frac{2A}{h} - C $

### Question 6
# Explanation:
## Step1: Start with the formula $ s = (n - 2) \cdot 180 $. Divide both sides by 180.
$ \frac{s}{180} = n - 2 $
## Step2: Add 2 to both sides.
$ n = \frac{s}{180} + 2 $
# Answer: C) $ n = \frac{s}{180} + 2 $

### Question 7
# Explanation:
## Step1: Start with the formula $ S = 2\pi rh + 2\pi r^2 $. Subtract $ 2\pi r^2 $ from both sides.
$ S - 2\pi r^2 = 2\pi rh $
## Step2: Divide both sides by $ 2\pi r $.
$ h = \frac{S - 2\pi r^2}{2\pi r} $
# Answer: D) $ h = \frac{S - 2\pi r^2}{2\pi r} $

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Question 3

Step1: Start with the formula \( V = \frac{lwh}{3} \). Multiply both sides by 3 to eliminate the denominator.

Step2: Divide both sides by \( lh \) to solve for \( w \).

Step1: Start with the formula \( C = \frac{5n + 40}{9} \). Multiply both sides by 9.

Step2: Subtract 40 from both sides.

Step3: Divide both sides by 5.

Step1: Start with the formula \( A = \frac{h(B + C)}{2} \). Multiply both sides by 2.

Step2: Divide both sides by \( h \).

Step3: Subtract \( C \) from both sides.

Answer:

Question 4