x,y - the numbers
one positive number is 5 less than twice a second number
(1) x - 5 = 2y
their product is 117
(2) xy = 117
(1) x - 5 = 2y <em>add 5 to both sides</em>
x = 2y + 5 <em>substitute it to (2)</em>
(2y + 5)y = 117 <em>use distributive property</em>
(2y)(y) + (5)(y) = 117
2y² + 5y = 117 <em>subtract 117 from both sides</em>
2y² + 5y - 117 = 0
2y² + 18y - 13y - 117 = 0
2y(y + 9) - 13(y + 9) = 0
(y + 9)(2y - 13) = 0 ↔ y + 9 = 0 ∨ 2y - 13 = 0
y + 9 = 0 <em>subtract 9 from both sides</em>
y = -9
2y - 13 = 0 <em>add 13 to both sides</em>
2y = 13 <em>divide both sides by 2</em>
y = 6.5
<em>substitute the values of y to (1)</em>
x = 2(-9) + 5 = -18 + 5 = -13 < 0
x = 2(6.5) + 5 = 13 + 5 = 18
<h3>Answer: x = 18 and y = 6.5</h3>
Answer:
0.4 divided by 10
Step-by-step explanation:
Answer:
12m
Step-by-step explanation:
work out the area of the rectangle then times it by 2 because the parallelogram is twice the area of the rectangle. 8 × 4.5m = 36m². 36 ×2 = 72cm². Now you do 72 ÷ 6 = 12 . the answer is 12m.
Answer: Surface area = 29.32 inches²
Step-by-step explanation:
The surface area is the sum of areas of the faces. There are two triangular faces and three rectangular faces.
The formula for determining the area of a triangle is expressed as
Area = 1/2 × base × height
Base = 2 inches
Height = 2 inches
Area = 1/2 × 2 × 2 = 2 inches²
Area of the 2 triangular faces
= 2 × 2 = 4 inches²
The area of the two equal rectangles is
Area = 2 × 2 × 4 = 16 inches²
To determine the width, w of the rectangular base, we would apply Pythagoras theorem.
Hypotenuse ² = opposite side² + adjacent side²
w² = 2² + 2²
w² = 4 + 4 = 8
w = √8 = 2.83
Area of the rectangular base is
2.83 × 4 = 11.32 inches²
Surface area = 4 + 16 + 11.32 = 31.32 inches²
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