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:
It's B.
Step-by-step explanation:
Z=-3, z=6
It would be valid to <u>all the families in his neighborhood</u>.
Hello there!
Math is hard! So we as students, we need to play the smart game with Math in order to find the easiest way to solve the problems. What do I mean? Well as you can see they gave us Fraction which won't be easy! So we will transform the fractions into decimals. So let's get started.
Then a scale of 1/4. Transformed into decimal = Then a scale of 0.25
So instead of using the fraction 1/4, I used its decimal 0.25
So if:
48 feet ......> 12 inches
x feet ........> 0.25 inches
Cross multiply
12 * x = 0.25 * 48
12x = 12
Divide both sides by 12
12x/12 = 12/12
x = 1
The correct answer is option D, 1 foot
I hope this helps! Please let me know if you have any question.
Thanks!
<u>Answer</u>
3
<u>Explanation</u>
The two lines in the diagram are secants meeting outside the circle.
The products of a secant and the extension of the chord of one line is equal to the products of a secant and the extension of the chord of the other line.
∴ 4 × 9 = x × 12
36 = 12x
x = 36/12
= 3
