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bija089 [108]
3 years ago
14

Question

Mathematics
1 answer:
Luden [163]3 years ago
3 0

Answer:

Step-by-step explanation:

2 units squared.

Explanation:

You can go about this in two ways: Algebra and Integrals.

Algebra

y = 2x-6 is linear, thus if we take the value over the x interval [2,4] we can use geometry to calculate the area.

graph{2x-6 [-2.27, 7.73, -2.18, 2.82]}

You can see two triangles in the graph (you could also find this algebraically). Thus, you can calculate the area.

=

2

⋅

(

1

2

⋅

b

⋅

h

)

=

2

⋅

(

1

2

⋅

1

⋅

2

)

=

2

square units

Integrals

An integral gives the area under the curve. Remember though that if a function goes below the X axis, the integral is negative Thus you have to do two separate integrals based on the X intercept.

finding the X intercept (that is where y = 0)

2

x

−

6

=

0

x

=

3

when

y

=

0

When

x

<

3

, then y is negative. Thus, we have to find the negative integral from 2 to 3 and the positive integral from 3 to 4

=

−

∫

3

2

2

x

−

6

d

x

+

∫

4

3

2

x

−

6

d

x

=

−

[

x

2

−

6

x

]

3

2

+

[

x

2

−

6

x

]

4

3

=

−

[

9

−

18

−

4

+

12

]

+

[

16

−

24

−

9

+

18

]

=

−

[

−

1

]

+

[

1

]

=

2

units squared. And Tada, that is the same as the other answer!

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const2013 [10]
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 This equation describes a parabola that opens up.
 When a is negative, the focus is on the negative y-axis, therefore, the parabola opens down.
 The answer is a. down.
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Mary is spending money at the average rate of $5 per day. After 14 days she has $68 left. The amount left depends on the number
Radda [10]

Answer:

A. Y-68=-5(x-14)

Step-by-step explanation:

Mary is spending money at the average rate of $5 per day. After 14 days she has $68 left. The amount left depends on the number of days that have passed. write an equation for the situation

We find the equation using the point slope equation of a line. This is given as:

y - y1 = m(x-x1)

The slope intercept form will be

y = -5x + b

since the amount decreases by $5 per day...

Our slope is -5 so m=-5

We have a point (x1,y1) = (14, 68)

Hence, we have:

y-68 = -5(x-14)

Option A is correct

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What is the probability of rolling a dice and getting either a 1 or 2 and flipping a coin and getting a heads?
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Answer:

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Step-by-step explanation:

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3 years ago
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The sum of two rational numbers of 63, and their difference is 12? What are the numbers?
VladimirAG [237]

Answer:

The two numbers are 37.5 and 25.5

Step-by-step explanation:

Comment

Let the two numbers be x and y

Equations

x + y = 63

x - y =  12

Solution

Add the two equations. The ys cancel out.

2x = 75               Divide by 2

2x/2 = 75/3         Do the division

x = 37.5

Now use one of the given equations to solve for y

x + y = 63

x = 37.5

37.5 + y = 63                     Subtract 37.5 from both sides

37.5-37.5+y= 63 - 37.5     Collect the like terms on both sides

y = 25.5

Check

x - y =? 12

37.5-25.5 =? 12

12 = 12      

3 0
4 years ago
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