Joaquin is constructing the perpendicular bisector of AB. He opens his

Answer:

The amount of wool required for a sweater was 400 grams.

A hat needed 80 grams of wool.

A scarf required 75 grams of wool.

Step-by-step explanation:

Let

x ------> grams of wool necessary for a sweater

y -----> grams of wool necessary for a hat

z -----> grams of wool necessary for a scarf

From the information given

x+y+z=555 -----> equation A

y=x/5 ----> x=5y -----> equation B

y=z+5 ---> z=y-5 ----> equation C

By substituting equations B and C into equation A, we can solve for y:

(5y)+y+(y-5)=555

7y=560

y=80 grams

Now, find x

x=5(80)=400 grams

Next, determine z

z=80-5=75 grams

In conclusion,

400 grams of wool was required for the sweater,

the hat needed 80 grams of wool, and

the scarf required 75 grams of wool.

The biggest cube has a volume of 64 cubic units, with sides measuring 4 units each.

Solution:

The lighthouse's actual height is 60 feet.

From measurement checks:

The ruler measures 3 inches.

Distance from eye to ruler equals 2 feet.

Let the distance from the lighthouse to the ruler be x feet.

Since the two triangles are similar by Angle-Angle (AA), their corresponding sides maintain proportionality, thus:

feet.

Therefore, the lighthouse is 40 feet away from the ruler.

Answer:

26

Step-by-step explanation:

Given that x is measured in hundreds, x equals 600 divided by 100.

Thus, x = 6.

This leads to 6x - 10.

If we substitute, we have:

6 * 6 - 10

Which simplifies to 36 - 10.

The result is 26.

Answer:

x > -1 or x < -1

Step-by-step explanation:

For the first inequality, 5x - 29 > -34:

Step 1: Add 29 to both sides to isolate the term with x

5x > -34 + 29

Step 2: Simplify the right side

5x > -5

Step 3: Divide both sides by 5

x > -1

Therefore, x must be greater than -1.

For the second inequality, 2x + 31 < 29:

Step 1: Subtract 31 from both sides

2x < 29 - 31

Step 2: Simplify the right side

2x < -2

Step 3: Divide both sides by 2

x < -1

Thus, x must be less than -1.