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1. The equation f = v + at represents the final velocity of an object, f, with an initial velocity, v, and an acceleration rate, a, over time, t.

Which is an equivalent equation solved for t?

t = t equals StartFraction f minus v Over a EndFraction z.
t = t equals StartFraction f minus a Over v EndFraction z.
t = a(f – v)
t = v(f – a)

2. Solve for a.

7a - 2b = 5a + b

a = 2b
a = 3b
a = a equals StartFraction 3 Over 2 EndFraction b.b
a = a equals StartFraction 2 Over 3 EndFraction b.b

3. Solve the equation for a.

K = 4a + 9ab

a = K(4 + 9b)
a = 4(K + 9b)
a = a equals StartFraction 4 plus 9 b Over K EndFraction equals h.
a = a equals StartFraction K Over 4 plus 9 b EndFraction equals h.

4. The circumference of a circle can be found using the formula C = 2r.

Which is an equivalent equation solved for r?

r = C
r = C(2)
r = r equals StartFraction C Over 2 pi EndFraction.
r = r equals StartFraction 2 pi Over C EndFraction.

5. The formula for the lateral area of a right cone is LA = rs, where r is the radius of the base and s is the slant height of the cone.

Which are equivalent equations? Select two correct answers.

s = s equals StartFraction L A Over pi r EndFraction.
s = s equals StartFraction pi r Over L A EndFraction.
s = LAr
r = r equals StartFraction L A Over pi s EndFraction.
r = LAs

6. Marta is solving the equation S = 2πrh + 2πr2 for h. Which should be the result?

StartFraction S Over 2 pi r EndFraction equals h. – r = h
StartFraction S minus r Over 2 pi r EndFraction equals h. = h
S – S minus StartFraction r Over 2 pi EndFraction equals h. = h
S – S minus StartFraction 2 pi Over r EndFraction equals h. = h

7. In physics class, Carrie learns that a force, F, is equal to the mass of an object, m, times its acceleration, a. She writes the equation F=ma.

Using this formula, what is the acceleration of an object with F=7.92 newtons and m=3.6 kilograms? Express your answer to the nearest tenth.

Note: The unit for Force (the Newton) is measured in kgxm/5^2

0.5 m/5^2
1.8 m/5^2
2.2 m/5^2
4.9 m/5^2

8. The equation d = d equals StartFraction m Over V EndFraction. can be used to calculate the density, d, of an object with mass, m, and volume, V. Which is an equivalent equation solved for V?

dm = V
StartFraction d Over m EndFraction equals V. = V
StartFraction m Over d EndFraction equals V. = V
m – d = V

9. The slope-intercept form of a linear equation is y = mx + b, where x and y are coordinates of an ordered pair, m is the slope of the line, and b is where the line crosses the y-axis.

Which is an equivalent equation solved for the slope, m?

m = yx + b
m = m equals StartFraction y minus b Over x EndFraction.
m = m equals StartFraction y Over x EndFraction minus b. – b
m = y – m equals y minus StartFraction b Over x EndFraction.

10. Solve for w.

5w + 9z = 2z + 3w

w = w equals negative StartFraction 7 Over 2 EndFraction z.z
w = w equals negative StartFraction 2 Over 7 EndFraction z.z
w = –2z
w = –7z

3 answers

Here are the answers to your questions:

  1. Equivalent equation solved for t: \[ t = \frac{f - v}{a} \]

  2. Solve for a: To solve \( 7a - 2b = 5a + b \): \[ 7a - 5a = b + 2b \implies 2a = 3b \implies a = \frac{3}{2}b \] Answer: \( a = \frac{3}{2}b \)

  3. Solve for a in the equation \( K = 4a + 9ab \): Factor out \( a \): \[ K = a(4 + 9b) \implies a = \frac{K}{4 + 9b} \] Answer: \( a = \frac{K}{4 + 9b} \)

  4. Equivalent equation solved for r: The circumference formula is \( C = 2\pi r \). Solved for r: \[ r = \frac{C}{2\pi} \] Answer: \( r = \frac{C}{2\pi} \)

  5. Equivalent equations (select two): The lateral area of a cone is given by \( LA = rs \).

    • \( s = \frac{LA}{r} \) rearranged gives us \( s \) in terms of \( LA \) and \( r \).
    • \( r = \frac{LA}{s} \) rearranged gives us \( r \) in terms of \( LA \) and \( s \).
    • Therefore, the equivalent equations are:
      • \( s = \frac{LA}{r} \)
      • \( r = \frac{LA}{s} \)

  6. Result for h: Solve \( S = 2\pi rh + 2\pi r^2 \) for h: Rearranging gives: \[ S - 2\pi r^2 = 2\pi rh \implies h = \frac{S - 2\pi r^2}{2\pi r} \] But none of the answers match this directly; however, it is similar to: \[ \frac{S}{2\pi r} = h + r \] So, we could choose the equation pointing out that: \[ \frac{S}{2\pi r} - r = h \] None are explicitly correct however, there is no direct match available.

  7. Acceleration (F=ma): Using \( F = ma \): \[ a = \frac{F}{m} = \frac{7.92 \text{ N}}{3.6 \text{ kg}} \approx 2.2 , \text{m/s}^2 \] Answer: \( 2.2 , \text{m/s}^2 \)

  8. Equivalent equation solved for V: The density equation is \( d = \frac{m}{V} \): \[ V = \frac{m}{d} \] Answer: \( \frac{m}{d} = V \)

  9. Equivalent equation solved for slope m: From \( y = mx + b \), isolate \( m \): \[ m = \frac{y - b}{x} \] Answer: \( m = \frac{y - b}{x} \)

  10. Solve for w: To solve \( 5w + 9z = 2z + 3w \): \[ 5w - 3w = 2z - 9z \implies 2w = -7z \implies w = -\frac{7}{2}z \] Answer: \( w = -\frac{7}{2}z \)

Let me know if you have any further questions!

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