Answer:
1p = r
Step-by-step explanation:
You are asking how many 1-foot pieces you can make out of a 5 foot piece of ribbon. You are asking for an equation.
p = the # of pieces
r = the amount of ribbon
So lets try the equation:
1p = r
1(4) = r
1*4 = 4
4 = r
<h2><u>
PLEASE MARK BRAINLIEST! </u></h2>
Step-by-step explanation:
1) 51
2)32
3) 18
4)9
5)12
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.
A. True. We see this by taking the highest order term in each factor:

B. True. Again we look at the leading term's degree and coefficient. f(x) behaves like -3x⁶ when x gets large. The degree is even, so as x goes to either ± ∞, x⁶ will make it positive, but multiplying by -3 will make it negative. So on both sides f(x) approaches -∞.
C. False. f(x) = 0 only for x=0, x = 5, and x = -2.
D. False. Part of this we know from the end behavior discussed in part B. On any closed interval, every polynomial is bounded, so that for any x in [-2, 5], f(x) cannot attain every positive real number.
E. True. x = 0 is a root, so f(0) = 0 and the graph of f(x) passes through (0, 0).
F. False. (0, 2) corresponds to x = 0 and f(x) = 2. But f(0) = 0 ≠ 2.
Answer: b=4(10)^1/2
Step-by-step explanation:
Distance Formula: a^2+b^2=c^2
6^2+b^2=14^2
36+b^2=196
b^2=160
b^2=10*16
b=(10*16)^1/2
b=4(10)^1/2