Let the amount invested at 4% be = x
Let the amount invested at 3% be = y
Given is:
or .... (1)
As, total income for the two investments is $194, so equation is:
....(2)
Putting value of x from (1) in (2)
And x=5200-y
Hence, money invested at 4% is $3800 and money invested at 3% is $1400
The lengths of the rectangles are 7 and 12 respectively. Form the ratio 7/12. The widths of the rects. are x and 5 respectively. Form the ratio x/5. Now equate these two ratios:
7 x
--- = ---
12 5
Solve this for x. One way to do this would be to cross-multiply, obtaining 12x = 35, and solving this result for x. x will be a fraction. Write the numerator and denominator in the boxes given.
Answer:
- dimensions: 12 ft by 5 ft
- area: 60 ft²
Step-by-step explanation:
Let x represent the shorter dimension in feet. Then the longer one is x+7 and the Pythagorean theorem tells us the relation of these to the diagonal is ...
x² + (x+7)² = 13²
2x² +14x + 49 = 169 . . . . eliminate parentheses
x² +7x -60 = 0 . . . . . subtract 169 and divide by 2
(x +12)(x -5) = 0 . . . . factor the equation
x = -12 or +5 . . . . . . . only the positive value of x is useful here.
The short dimension is 5 ft, so the long dimension is 12 ft. The area is their product, 60 ft².
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<em>Comment on finding the area</em>
The quadratic equation above can be rearranged and factored as ...
x(x +7) = 60
Since the dimensions of the garden are x and (x+7), this product is the garden's area. This equation tells us the area is 60. We don't actually have to find the dimensions.
Answer:
yes
Step-by-step explanation:
if it is a terminating decimal(a decimal that ends) it will be rational
A. -5x + 3y = 15 is your answer. this is because the slope is 5/3 and the y-intercept is 5 so you plot those onto the graph and this shows it.
hope this helps, God bless!