Answer:
length = 6 yards
width = 3.5 yards
Step-by-step explanation:
the length of a rectangle is 1 yard less than twice the width
LEt 'w' be the width of the rectangle
and 'l' be the length of the rectangle
length l = 2 times the width -1
so l = 2w -1
Area of the rectangle = length * width
Area = l * w
we know length is 2w-1 and given area = 21
21 = (2w-1) * w
subtract 21 on both sides
now solve for 'w'
0 = 2w(w+3)-7(w+3)
0= (2w-7)(w+3)
2w-7 = 0 and w+3 =0
w = 7/2 w=-3
width cannot be negative so we ignore w=-3
width w= 3.5
length = 2w-1= 2(3.5) - 1= 7-1=6
length = 6 yards
2x+y=8 is the equation perpendicular to x-2y=8.
Positive sine, negative tangent, means we have a negative cosine. We're talking about the second quadrant.
We know it's negative,
Answer: -(1/3)√5
Total: $125
The dance comitee could buy 75 balloons.
Answer: The height of the palm tree is 21 feet.
Step-by-step explanation:
We can use a ratio to solve this:
Actual height to shadow for both objects. The fraction equivalents must be equal.
6/8 = x/28 . Cross multiply
6(28) = 8x
168 = 8x Divide both sides by 8 (8's "cancel" on the right)
168/8 =8x/8
21 = x . This gives us the tree's height as 21 feet.
<em>Another way to solve this is to use the ratios, but simplify the first fraction</em>
<em>6/8 = 3/4</em>
<em>Then multiply the length of the shadow by 3/4</em>
<em>3/4 × 28 = height</em>
<em>28÷4 = 7 7 × 3 = 21</em>
<em>21 feet= the height of the palm tree.</em>
