Simplify -15+33-12+(-12)
2 answers:
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Matt earns $4 and $3 for 1 load of laundry and 1 load of dishes respectively
<u>Solution:</u>
Given, Matt gets paid at home for doing extra chores.
We have to find How much does Matt earn for completing each type of chore?
Let the amount for 1 load of laundry be m and amount for 1 load of dish be n.
Now, last week, he did 6 loads of laundry and 1 load of dishes, and his parents paid him $27.
Then, 6 amount for 1 load of laundry + 1
amount for 1 load of dish = 27
The week before, he finished 1 load of laundry and 9 loads of dishes, earning a total of $31
Then, 1 amount for 1 load of laundry + 9
amount for 1 load of laundry = 31 ⇒m + 9n = 31 ⇒ (2)
Now let us solve equations (1) and (2)
0 – 53n = - 159
-53n = -159
53n = 159
n = 3
Now, substitute n value in (1) ⇒ 6m + 3 = 27 ⇒ 6m = 24 ⇒ m = 4
Hence, matt earns $4 and $3 for 1 load of laundry and 1 load of dishes respectively.
Answer:
A. The length of the second leg is 8.5 inches
B. The length of the three-dimensional diagonal is 9.9 inches
Step-by-step explanation:
Let us revise the relation between the hypotenuse and the two legs of a right triangle
(hypotenuse)² = (vertical leg)² + (horizontal leg)²
∵ The length of the rectangular box = 8 inches
∵ The width of the rectangular box = 3 inches
∵ The height of the rectangular box = 5 inches
∵ Length and width are perpendicular to each other
∴ The Δ whose legs are 3 and 8 is a right triangle
In the right Δ whose legs are 3 and 8
∵ (hypotenuse)² = (3)² + (8)²
∴ (hypotenuse)² = 9 + 64
∴ (hypotenuse)² = 73
- Take √ for both sides
∴ hypotenuse = = 8.544003745
- Round it to the nearest tenth of one inch
∴ hypotenuse = 8.5 inches
A.
The 3-dimensional diagonal is the hypotenuse of a right triangle whose legs are the vertical edge and the hypotenuse of the right triangle whose legs are 3 and 8
∵ The hypotenuse of the right triangle whose legs are 3 and
8 is 8.5 inches
∴ The length of the second leg is 8.5 inches
B.
In the right triangle whose hypotenuse is the 3-dimensional diagonal and legs are the vertical edge , the hypotenuse of the right triangle whose legs are 3 and 8
∵ (3-dimensional diagonal)² = (5)² + (73)²
∴ (3-dimensional diagonal)² = 25 + 73
∴ (3-dimensional diagonal)² = 98
- Take √ for both sides
∴ 3-dimensional diagonal = = 9.899494937
- Round it to the nearest tenth of an inch
∴ 3-dimensional diagonal = 9.9 inches
∴ The length of the three-dimensional diagonal is 9.9 inches
<em>V.I.N: you can find the length of the three-dimensional diagonal by using this rule → </em><em> </em>