Question:
Two rectangular picture frames have the same area of 45 square inches but have different side lengths. Frame A has a length of 6 3/4 inches, and Frame B has a length of 7 1/2 inches.
Answer:
1. the longer frame (B) has the shorter width
2. the shorter width is 6 3/7 inches, area divided by length
Step-by-step explanation:
The relation between area, length, and width is ...
A = LW
Then the width is ...
W = A/L . . . . . inversely proportional to length
1. Since length and width are inversely proportional (when area is constant), the shorter width will be associated with the longer length. Frame B will have the shorter width.__
2. The width of frame B is ...
W = A/L = (45 in²)/(7 in) = 45/7 in = 6 3/7 in
-Alan Becker
First find the area of the sector, which includes the shaded region's area and the area of the triangle JKL. Let be the area of the sector. This area occurs in a fixed ratio with the area of the entire circle based on the measure of the central angle subtended by the arc LK:
To get the area of the shaded region, subtract from the area of the triangle.
The area of a triangle is 1/2 the base times the height. If we bisect the central angle with a line segment that meets the side KL at its midpoint, then we get a right triangle with hypotenuse 27 and one angle of measure 27º (half of the central angle). This triangle has base and height such that
So the right triangle has area approximately 1/2*12.258*24.057, or about 147.443. Triangle JKL is made up of two of these right triangles, so it has area of 294.887.
Subtracting this from gives an area of the shaded region of about 48.472, which we round up to 48.5.
Answer:
B. 18/48 and 21/56
C. 20/28 and 15/18
Step-by-step explanation:
Simplifying 18/48 = 3/8
Simplifying 21/56 = 3/8
Simplifying 20/ 28= 5/7
Simplifying 15/18 = 5/7
<span><span>(<span><span>2x</span>−9</span>)</span><span>(<span><span>4x</span>+1</span>)</span></span><span> =<span><span>(<span><span>2x</span>+<span>−9</span></span>)</span><span>(<span><span>4x</span>+1</span>)</span></span></span><span> =<span><span><span><span><span>(<span>2x</span>)</span><span>(<span>4x</span>)</span></span>+<span><span>(<span>2x</span>)</span><span>(1)</span></span></span>+<span><span>(<span>−9</span>)</span><span>(<span>4x</span>)</span></span></span>+<span><span>(<span>−9</span>)</span><span>(1)</span></span></span></span><span> =<span><span><span><span>8<span>x^2</span></span>+<span>2x</span></span>−<span>36x</span></span>−9</span></span><span> Answer: <span><span><span>8<span>x^2</span></span>−<span>34x</span></span>−<span>9</span></span></span>
$70 for 5 hours = 70/5 for 1 hour.
70 / 5 = 14
That means $14 for 1 hour.
To find how much for 12 hours, multiply the price of 1 by 12 to get the price of 12 hours.
1 hour = $14
12 hours = 14 * 12
14 * 12 = 168.
That means the price of working for 12 hours is $168.
Hope this helped☺☺