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3 years ago

Two sidewalks in a park are represented by lines on a coordinate grid. Two points on each of the lines are shown in the tables.

1 answer:

3 0

Thank you for posting your question here at brainly. I hope the answer will help you. Feel free to ask more questions.
Slope of the first is chg y/chg x or 4/2=2
now use point slope formula y-y1=m(x-x1), where m is the slope and (x1,y1) is the point.
y-3=2(x-0)
y=2x+3

The other
slope is 2/-2=-1
y-5=-1(x-1)
y-5=-x+1
y=-x+6

Slopes aren't the same or a negative reciprocal, so they intersect. Coincident.
substitute the second into the first
-x+6=2x+3
3x=3
x=1
Therefore, y=2(1)+3=5. The point is (1,5) where they intersect.
Check with the second
5=-1+6, check

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2 years ago

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Anettt [7]

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3 years ago

[25 POINTS] The approximate change in the value of f(x) = sqrt(2(x-1)) at x = 3 using differentials with dx = 0.01 is

otez555 [7]

Answer:

$\frac{1}{200}$

Step-by-step explanation:

Find the derivative of the function when x=3

$y=\sqrt{2(x-1)}$

$\frac{dy}{dx}=\frac{1}{\sqrt{2(x-1)}}$

$\frac{dy}{dx}=\frac{1}{\sqrt{2(3-1)}}$

$\frac{dy}{dx}=\frac{1}{\sqrt{2(2)}}$

$\frac{dy}{dx}=\frac{1}{\sqrt{4}}$

$\frac{dy}{dx}=\frac{1}{2}$

Since the change in the value of the function is $dy$ and we know that the change in x is $dx=0.01$ , then we have:

$\frac{dy}{dx}=\frac{1}{2}$

$dy=\frac{1}{2}dx$

$dy=\frac{1}{2}(0.01)$

$dy=\frac{1}{200}$

Therefore, the 2nd option is correct

8 0

2 years ago

The area of a circular fountain is 121pi square feet. What is the diameter of the fountain?

Alla [95]

Answer:

22 feet

Step-by-step explanation:

Area of circle = pi(r²)

the square root of 121 is 11, so r = 11

d = 2r

d = 22

7 0

2 years ago

HELP ME Using the following equation, complete the square and find the center and radius of the circle:

IrinaK [193]

Answer: $(-2,3)$ , $r=5\ \text{units}$

Step-by-step explanation:

Given

the equation is $x^2+y^2+4x-6y-12=0$

completing the square

$\Rightarrow (x^2+2\times 2\times x+4-4)+(y^2-2\times3\times y+9-9)-12=0\\\Rightarrow (x^2+2\times 2\times x+4)+(y^2-2\times3\times y+9)-12-4-9=0\\\Rightarrow (x+2)^2+(y-3)^2=25\\\Rightarrow (x+2)^2+(y-3)^2=5^2\\\Rightarrow (x-(-2))^2+(y-3)^2=5^2$

Thus, the center of the circle is $(-2,3)$ and radius is $r=5\ \text{units}$

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3 years ago