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Anton [14]
3 years ago
12

What is the slope of the line that contains the point (2,6) and (3,10)?

Mathematics
1 answer:
irina1246 [14]3 years ago
7 0
Work:

Slope: m= y1-y2/x1-x2
Points: (2,6) & (3,10)

m= 6-10/2-3
m= -4/-1
m= 4

The slope of the line that contains the point (2,6) and (3,10) is 4.
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D) left a units, down b units

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The length plus the width of a rectangle is 10. Let x represent the length. The equation for the area y of the
yuradex [85]

Answer:

length of rectangle = 5

width of rectangle = 5

Area of rectangle = 25

Step-by-step explanation:

Since the length of the rectangle is "x", and the value of the area is given by the product of the length "x" times the width "10-x", indeed, the area "y" of the rectangle is given by the equation:

y=x\,(10-x)=10x-x^2

Now, they tell us that the area of the rectangle is such that coincides with the maximum (vertex) of the parabola this quadratic expression represents. So in order to find the dimensions of the rectangle and therefore its area, we find the x-coordinate for the vertex, and from it, the y-coordinate of the vertex, which is the rectangle's actual area.

Recall that the formula for the x of the vertex of a quadratic of the form :

y=ax^2+bx+c

is given by the formula:

x_{vertex}=-\frac{b}{2\,a}

which in our case gives:

x_{vertex}=-\frac{b}{2\,a}\\x_{vertex}=-\frac{10}{2\,(-1)}\\x_{vertex}=5

Therefore, the length of the rectangle is 5, and its width (10-x) is also 5.

The area of the rectangle is therefore the product of these two values: 5 * 5 = 25

Which should coincide with the value we obtain when we replace x by 5 in the area formula:

y=10x-x^2\\y=50-(5)^2\\y=50-25\\y=25

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Which point is on the graph of f(x) = 2*5^x
vodomira [7]

Answer:

Option B (1,10)

Step-by-step explanation:

we have

f(x)=2(5^x)

we know that

If a ordered pair is on the graph of f(x) then the ordered pair must satisfy the function f(x)

<u><em>Verify each case</em></u>

case A) (0,0)

For x=0

f(x)=2(5^0)\\f(x)=2(1)=2

Compare the value of f(x) with the y-coordinate of the ordered pair

2\neq 0

therefore

The ordered pair is not on the graph of f(x)

case B) (1,10)

For x=1

f(x)=2(5^1)\\f(x)=2(5)=10    

Compare the value of f(x) with the y-coordinate of the ordered pair

10=10

therefore

The ordered pair is on the graph of f(x)

case C) (0,10)

For x=0

f(x)=2(5^0)\\f(x)=2(1)=2

Compare the value of f(x) with the y-coordinate of the ordered pair

2\neq 10

therefore

The ordered pair is not on the graph of f(x)

case D) (10,1)

For x=10

f(x)=2(5^{10})\\f(x)=2(9,765,625)=19,531,250

Compare the value of f(x) with the y-coordinate of the ordered pair

19,531,250\neq 1

therefore

The ordered pair is not on the graph of f(x)

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4 years ago
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