Answer:
1. Base of pyramid; 6 in by 6 in
2. Base of prism; Its dimensions are also 6 in by 6 in, located at the bottom of the house and will not be seen, so it does not require painting.
3. twice the area of the square
4. Area = 228 inches squared
Step-by-step explanation:
For question 4, the area Molly needs to paint is found by adding all the surface areas and subtracting the 2 surfaces that will not be painted: base of pyramid and base of prism (outlined in red). According to the picture, these are both squares with 6 by 6 dimensions.
<h3>Step 1. Add all surface areas together</h3>
Prism: 6 surfaces
Surface area = 216 inches sq
- Front = 6 x 6 = 36
- Back = 6 x 6 = 36
- Top = 6 x 6 = 36
- Bottom (base) = 6 x 6 = 36
- Side = 6 x 6 = 36
- Other side = 6 x 6 = 36
Pyramid: 5 surfaces
Surface area = 84 inches sq
- Bottom (base) = 6 x 6 = 36
- Front triangle = (6 x 4)/2 = 12
- Back = (6 x 4)/2 = 12
- Side = (6 x 4)/2 = 12
- Other side = (6 x 4)/2 = 12
TOTAL surface area: 216 inches + 84 inches = 300 inches sq
<h3>Step 2. Subtract surfaces that are NOT being painted</h3>
300 - base of pyramid - base of prism
300 - 2(36)
300 - 72
<u>228 inches sq</u>
Hope this helps!
Let x represent the number of liters of 50% acid Theresa puts into the mix. The the number of liters of 30% acid will be (420-x). The total amount of acid in the final solution will be ...
0.50x + 0.30(420-x) = 0.45(420)
0.20x + 126 = 189 . . . . . . . . . . . . . . . simplify
0.20x = 63 . . . . . . . . . . . . . . . . . . . . . subtract 126
x = 63/0.20 = 315 . . . . . . . . . . . . . . . liters of 50% solution
(420-x) = 420-315 = 105 . . . . . . . . . liters of 30% solution
Theresa should mix ...
105 liters of 30% solution
315 liters of 50% solution
Multiply 3 * 1 1/2 to find how many miles she runs per hour
1 1/2 * 3
3/2 * 3
9/2
4 1/2 She will run 4 1/2 or 4.5 miles per hour.
Answer:
2; -2
Step-by-step explanation:
|7-9| = |-2| = 2
|7|-9= 7 - 9 = -2
Yes he did, the proof is in the context