24. 11 - p
28. -54 = -9g 29. (\frac{x}{5} = 6)
in exercises 32–34, use an equation to solve the
32. insects the dragonfly is the fastest flying insect. it can move of about 50 feet per second. find the approximate time it takes a dragonfly to travel 400 feet.
33. computers from 2000 to 2001, annual worldwide sales of personal computers declined by about 6 million. in 2001, about 128 million personal computers were sold. find the approximate number of personal computers sold in 2000.
34. snacks you divide a bag of trail mix into 8 portions for you and your friends to have as snacks on a bike ride. each portion weighs 3 ounces. find the total weight of the trail mix originally in the bag.
35. geometry the perimeter of the... is 35 centimeters. diagram: a polygon with sides 9 cm, 8 cm, 5 cm, (x), ...

Question

24. 11 - p
28. -54 = -9g  29. (\frac{x}{5} = 6)
in exercises 32–34, use an equation to solve the
32. insects the dragonfly is the fastest flying insect. it can move of about 50 feet per second. find the approximate time it takes a dragonfly to travel 400 feet.
33. computers from 2000 to 2001, annual worldwide sales of personal computers declined by about 6 million. in 2001, about 128 million personal computers were sold. find the approximate number of personal computers sold in 2000.
34. snacks you divide a bag of trail mix into 8 portions for you and your friends to have as snacks on a bike ride. each portion weighs 3 ounces. find the total weight of the trail mix originally in the bag.
35. geometry the perimeter of the... is 35 centimeters. diagram: a polygon with sides 9 cm, 8 cm, 5 cm, (x), ...

Accepted Answer

Let's solve each problem one by one:

### Problem 28: $-54 = -9g$
# Explanation:
## Step 1: Isolate $g$
To solve for $g$, we divide both sides of the equation by $-9$.
$g=\frac{-54}{-9}$
## Step 2: Simplify the fraction
Dividing two negative numbers gives a positive result. $\frac{-54}{-9} = 6$
# Answer:
$g = 6$

### Problem 29: $\frac{x}{5}=6$
# Explanation:
## Step 1: Isolate $x$
To solve for $x$, we multiply both sides of the equation by $5$.
$x = 6\times5$
## Step 2: Calculate the product
$6\times5 = 30$
# Answer:
$x = 30$

### Problem 32: Insects - Dragonfly Time
# Explanation:
## Step 1: Recall the formula for time
The formula for time $t$ is $t=\frac{d}{v}$, where $d$ is distance and $v$ is velocity (speed).
Here, $d = 400$ feet and $v = 50$ feet per second.
## Step 2: Substitute the values
$t=\frac{400}{50}$
## Step 3: Simplify the fraction
$\frac{400}{50}=8$
# Answer:
The time taken is $8$ seconds.

### Problem 33: Computers - Sales in 2000
# Explanation:
## Step 1: Define the variables
Let $x$ be the number of personal computers sold in 2000 (in millions). In 2001, the number sold was $x - 6$ (since it declined by 6 million).
We know that in 2001, the number sold was 128 million. So we set up the equation:
$x-6 = 128$
## Step 2: Solve for $x$
Add 6 to both sides of the equation:
$x=128 + 6$
$x = 134$
# Answer:
The approximate number of personal computers sold in 2000 was 134 million.

### Problem 34: Snacks - Trail Mix Weight
# Explanation:
## Step 1: Define the variables
Let $w$ be the total weight of the trail mix (in ounces). The trail mix is divided into 8 portions, and each portion weighs 3 ounces. So we can set up the equation:
$\frac{w}{8}=3$
## Step 2: Solve for $w$
Multiply both sides of the equation by 8:
$w=3\times8$
$w = 24$
# Answer:
The total weight of the trail mix originally in the bag was 24 ounces.

### Problem 35: Geometry - Perimeter of the Pentagon
# Explanation:
## Step 1: Recall the formula for perimeter
The perimeter $P$ of a polygon is the sum of the lengths of its sides. For this pentagon, we know the perimeter is 35 cm, and three of the sides are 9 cm, 8 cm, and 5 cm, and one side is $x$ (we assume the fifth side is also $x$? Wait, looking at the diagram, it seems like a pentagon with sides $x$, $9$ cm, $8$ cm, $5$ cm, and $x$? Wait, maybe it's a symmetric pentagon? Wait, the perimeter is 35 cm. Let's assume the sides are $x$, $9$ cm, $8$ cm, $5$ cm, and $x$ (since it looks like a symmetric figure). So the perimeter $P=x + 9+8 + 5+x$
## Step 2: Simplify the perimeter formula
$P = 2x+22$
We know that $P = 35$ cm, so:
$2x+22 = 35$
## Step 3: Solve for $x$
Subtract 22 from both sides:
$2x=35 - 22$
$2x = 13$
Divide both sides by 2:
$x=\frac{13}{2}=6.5$
Wait, maybe the sides are $x$, $9$ cm, $8$ cm, $5$ cm, and another side? Wait, maybe I misread the diagram. Let's re - examine. If the perimeter is 35 cm, and the known sides are 9 cm, 8 cm, 5 cm, and we have two sides of length $x$ (assuming the pentagon has two equal sides). So:
$x + 9+8 + 5+x=35$
$2x+22 = 35$
$2x=35 - 22=13$
$x = 6.5$ cm.
# Answer:
The value of $x$ is $6.5$ cm.

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Problem 28: \(-54 = -9g\)

Step 1: Isolate \(g\)

Step 2: Simplify the fraction

Step 1: Isolate \(x\)

Step 2: Calculate the product

Step 1: Recall the formula for time

Step 2: Substitute the values

Step 3: Simplify the fraction

Answer:

Problem 29: \(\frac{x}{5}=6\)