1. y = 4x + 9 ; m = 4 ; b = 9
the slope is 4 because there’s a pattern of +4 going down the function table in the “y” column
and b= 9 because at the number 0 on the x line has 9 in the y box
2. y = 3x - 1 ; m = 3 ; b = -1
basically the same thing as the first one just different numbers
Answer: the length is 6 feet. The width is 2 feet
Step-by-step explanation:
The garden pool is rectangular in shape.
Let L represent the length of the rectangular garden.
Let W represent the width of the rectangular garden.
The area of a rectangle is expressed as L× W. The area of the rectangular garden pond is 12ft^2. It means that
L× W = 12 - - - - - - - - - - 1
The length of the pool needs to be 2ft more than twice that width. This means that
L = 2W + 2 - - - - - - - - - - - 2
Substituting equation 2 into equation 1, it becomes
W(2W + 2) = 12
2W^2 + 2W = 12
2W^2 + 2W - 12 = 0
W^2 + W - 6 = 0
W^2 + 3W - 2W - 6 = 0
W(W + 3) - 2(W + 3) = 0
W - 2 = 0 or W + 3 = 0
W = 2 or W = - 3
Since the Width cannot be negative, then the width is 2 feet
Substituting W = 2 into equation 2. It becomes
L = 2×2 + 2 = 6 feet
All 3 of these would result in the same answer. You can see this by looking at the cross products that would be created for each of them.
In each proportion, you would get a variation of 37 times 7 = 4 times x, when you multiply the numerator of the first by the denominator of the second and the denominator of the first by the numerator of the second.
<span><span>2<span><span>(x+3)</span>2</span>+1</span><span>2<span><span>(x+3)</span>2</span>+1</span></span>Reorder the right side of the equation to match the vertex form of a parabola.<span><span>y=2<span><span>(x+3)</span>2</span>+1</span><span>y=2<span><span>(x+3)</span>2</span>+1</span></span>Use the vertex form, <span><span>y=a<span><span>(x−h)</span>2</span>+k</span><span>y=a<span><span>(x-h)</span>2</span>+k</span></span>, to determine the values of <span>aa</span>, <span>hh</span>, and <span>kk</span>.<span><span>a=2</span><span>a=2</span></span><span><span>h=−3</span><span>h=-3</span></span><span><span>k=1</span><span>k=1</span></span>Find the vertex <span><span>(h,k)</span><span>(h,k)</span></span>.<span>(−3,1<span>) ...................................</span></span>
Answer:
= 30x − 18
Step-by-step explanation:
