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Which expression represents the phrase, "half the sum of 10 and a number"?

1/2x+10

1/2+10+x

1/2(10)+x

1/2(10+x)

11 answers

The phrase "half the sum of 10 and a number" can be broken down as follows:

  1. "the sum of 10 and a number": This can be expressed as \(10 + x\), where \(x\) is the unknown number.
  2. "half the sum": This means we take half of that sum, which can be represented as \(\frac{1}{2}(10 + x)\).

Therefore, the correct expression that represents the phrase is:

\(\frac{1}{2}(10 + x)\).

So, the answer is 1/2(10+x).

The Garza family drives to a state park. The remaining distance, in miles, to reach the state park is 315−55h, where h represents the number of driving hours.

What does each part of the expression represent?

The expression \( 315 - 55h \) represents the remaining distance in miles to reach the state park based on the number of driving hours \( h \). Each part of this expression has a specific meaning:

  1. 315: This number represents the total distance in miles from the starting point to the state park. It's the initial distance before any driving has occurred.

  2. 55h: This term represents the distance that the Garza family has already traveled after driving for \( h \) hours. The number 55 indicates the speed of the vehicle in miles per hour (mph), meaning for every hour of driving, they cover 55 miles. Hence, \( 55h \) calculates the total distance traveled after driving for \( h \) hours.

  3. \( 315 - 55h \): This overall expression shows the remaining distance to the park after subtracting the distance already traveled (\( 55h \)) from the total distance (315 miles).

To summarize:

  • 315: Total distance to the state park (miles)
  • 55h: Distance traveled after \( h \) hours (miles)
  • \( 315 - 55h \): Remaining distance to the state park (miles) after driving for \( h \) hours.
The length of a rectangle is 3 units shorter than one-third of the width, x.

Which expression represents the perimeter of the rectangle?

8/3x−2

2/3x−4

​2/3x−8​

8/3x−6

To find the expression representing the perimeter of the rectangle, we first need to express the length and width in terms of \( x \).

Given:

  • The width of the rectangle is \( x \).
  • The length is 3 units shorter than one-third of the width.

So, we can express the length \( L \) as: \[ L = \frac{1}{3}x - 3 \]

Now, we can use the formulas for the perimeter \( P \) of a rectangle, which is given by: \[ P = 2(\text{Length} + \text{Width}) = 2(L + W) = 2\left(\left(\frac{1}{3}x - 3\right) + x\right) \]

Now, let's simplify this expression step by step.

  1. Combine the length and width: \[ L + W = \left(\frac{1}{3}x - 3\right) + x = \frac{1}{3}x - 3 + \frac{3}{3}x = \left(\frac{1}{3}x + \frac{3}{3}x\right) - 3 = \frac{4}{3}x - 3 \]

  2. Now plug this back into the perimeter formula: \[ P = 2\left(\frac{4}{3}x - 3\right) \]

  3. Distribute the 2: \[ P = 2 \cdot \frac{4}{3}x - 2 \cdot 3 = \frac{8}{3}x - 6 \]

Thus, the expression that represents the perimeter of the rectangle is: \[ \frac{8}{3}x - 6 \]

So the correct answer is \(\frac{8}{3}x - 6\).

Cindy's age, x, is 3 times her age 6 years ago.
Which equation represents the statement?

A. x = 3x + 6

B. x=3(x−6)

C. x=3−6x

D. x=3x−6

To translate the statement "Cindy's age, \( x \), is 3 times her age 6 years ago" into an equation, we can break it down as follows:

  1. Cindy's current age is represented by \( x \).
  2. Cindy's age 6 years ago would be \( x - 6 \).
  3. The phrase "is 3 times" indicates that we should take 3 times her age 6 years ago.

Putting this all together, we can write the equation as: \[ x = 3(x - 6) \]

Thus, the correct option that represents this statement is B. \( x = 3(x - 6) \).

Eight times a number, x, is one-third the sum of the number and two.
Which answer represents this situation?

8x+1/3(x+2)

8x=1/3(x+2)

8x=1/3x+2

8x+1/3x+2

To represent the statement "Eight times a number, \( x \), is one-third the sum of the number and two" mathematically, we will break it down:

  1. Eight times a number, \( x \) can be expressed as \( 8x \).
  2. The sum of the number and two is represented as \( x + 2 \).
  3. One-third of this sum would be \(\frac{1}{3}(x + 2)\).

Putting it all together, the given statement can be represented as: \[ 8x = \frac{1}{3}(x + 2) \]

Thus, the correct representation of this situation is \( 8x = \frac{1}{3}(x + 2) \), which corresponds to option B. \( 8x = 1/3(x + 2) \).

A hummingbird can travel up to 15 meters per second.

What is the hummingbird's speed in miles per hour?

To convert the speed from meters per second (m/s) to miles per hour (mph), we can use the following conversion factors:

  1. There are 1609.34 meters in a mile.
  2. There are 3600 seconds in an hour.

The formula to convert from meters per second to miles per hour is: \[ \text{mph} = \text{m/s} \times \frac{3600 \text{ seconds}}{1 \text{ hour}} \times \frac{1 \text{ mile}}{1609.34 \text{ meters}} \]

Now, substituting 15 meters per second into the formula: \[ \text{mph} = 15 , \text{m/s} \times \frac{3600}{1609.34} \]

Calculating this step by step:

  1. First, calculate \(\frac{3600}{1609.34}\): \[ \frac{3600}{1609.34} \approx 2.237 \]

  2. Now multiply by 15: \[ \text{mph} \approx 15 \times 2.237 \approx 33.555 \]

Thus, the hummingbird's speed in miles per hour is approximately 33.56 mph when rounded to two decimal places.