Answer: 4x2 + 32x − 80 = 0
Step-by-step explanation:
Area of a rectangle is given by
A = l*w
The length is (2x+10) and the width is (2x+6)
A = (2x+10)(2x+6)
FOIL
first 2x*2x = 4x^2
outer 2x*6 =12x
inner 2x*10 =20x
last 10*6=60
Add this together
4x^2 +12x+20x +60 = 4x^2 +32x+60
This must equal 140 inches
4x^2 +32x+60 = 140
Subtract 140 from each side
4x^2 +32x+60-140 = 140-140
4x^2 +32x -80=0
X*(1/5)=2 -- multiply by 5
x=10
He had 10 pounds.
Answer:
<h3>Question 1</h3>
<u>Function given:</u>
<u>In the vertex form:</u>
- y = x² + 4x + 4 - 8 = (x + 2)² - 8
Axis of symmetry is the vertical line passing through the vertex.
<u>The vertex is</u>
<u>Axis of symmetry is </u>
<u>y- intercept is </u>
- x = 0 ⇒ y = -4, so the point (0, -4)
<u>Two other points are</u>
- x = 1 ⇒ y = (1 + 2)² - 8 = 9 - 8 = 1, the point is (1, 1)
- x = -1 ⇒ y = (-1 + 2)² - 8 = 1 - 8 = -7, the point is (-1, -7)
<em>See the graph with all the points plotted</em>
<h3>Question 2</h3>
<u>Function given:</u>
<u>In standard form:</u>
<u>In vertex form:</u>
- y = - 2x² + 4x - 2 + 8 = -2(x - 1)² + 8
<u>The vertex:</u>
<u>Axis of symmetry is </u>
<u>y - intercept </u>
- x = 0 ⇒ y = -2(-1)² + 8 = -2 + 8 = 6, the point is (0, 6)
<u>Two other pints:</u>
- x = -1 ⇒ y = -2(-1 - 1)² + 8 = -8 + 8 = 0, the point is (-1, 0)
- x = 2 ⇒ y = -2(2 - 1)² + 8 = -2 + 8 = 6, the point is (2, 6)
<em>The graph is attached with the points plotted.</em>