Answer:
57
Step-by-step explanation:
parentheses first then multiply by 3
Answer:
a type nut is 10 pounds
a different one is 14 pounds
Step-by-step explanation:
let a type of the nut be represented by t
Let a different one be represented by d
a type of nut cost $7 per pound
a different one cost $4.20 per pound
The cost of the mixture for 24 pounds = 5.37 * 24
= $128.88
t + d = 24 ........(1)
7t + 4.2d = 128.88 ..........(2)
From equation (1), t = 24 - d
Put t = 24 - d in equation 2
7(24 - d) + 4.2d = 128.88
168 - 7d + 4.2d = 128.88
168 - 2.8d = 128.88
-2.8d = 128.88 - 168
-2.8d = -39.12
d = -39.12 / -2.8
d= 13.97
d = 14 pounds
t = 24 - d
t = 24 - 14
t = 10 pounds
A type nut is 10 pounds. A different one is 14 pounds
By definition, two angles are supplementary if the sum of them is 180 degrees. In this case (see figure attached with the answer) the line AD is transversal to lines AB and DC. This is a proof of the Same-side interior angle theorem.
This theorem states that if we have two lines that are parallel and we intercept those two lines with a line that is transversal to both, same-side interior angles are formed, and also sum 180º, in other words, they are supplementary angles.
Then:
By the definition of a parallelogram, AB∥DC. AD is a transversal between these sides, so ∠A and ∠D are <em><u>same-side interior angles</u></em>. Because AB and DC are <em><u>parallel</u></em>, the same-side interior angles must be <em><u>supplementary</u></em> by the same-side interior angles theorem. Therefore, ∠A and ∠D are supplementary.
The figure consists of three objects, a rectangle, a trapezoid, a triangle
Find the area of the rectangle
The rectangle is 16 in long and 9 in wide
a₁ = l × w
a₁ = 16 × 9
a₁ = 144 in²
Find the area of the trapezoid
The base of trapezoid is 31 in and 16 in, and the height is 35 - 20 = 15 in.
a₂ = 1/2 × (a + b) × h
a₂ = 1/2 × (31 + 16) × 15
a₂ = 1/2 × 47 × 15
a₂ = 352.5 in²
Find the area of the triangle
The base of the triangle is 31 in, the height is 20 in
a₃ = 1/2 × b × h
a₃ = 1/2 × 31 × 20
a₃ = 310 in²
Add the area together
a = a₁ + a₂ + a₃
a = 144 + 352.5 + 310
a = 806.5
The answer is 806.5 in²
Answer:
40%
Step-by-step explanation:
i used a calculator
