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DIA [1.3K]
3 years ago
9

Indicate whether each statement about linear functions A and B shown below is true or false by checking the appropriate box in t

he table.
TRUE OR FALSE
The rates of change for both Function A and B are positive.

TRUE OR FALSE
The rate of change for Function A is 3 times the rate of change for Function B

TRUE OR FALSE
The y-intercepts for both Function A and Function B are positive.

Mathematics
1 answer:
Crank3 years ago
7 0
True because the rate and a and b are positive
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Answer:

17 ± sqrt(337)

 -----------------------

     2

Step-by-step explanation:

Let a = shorter leg

b= longer leg = a+7

c = hypotenuse = 2a-5

We can use the Pythagorean theorem

a^2+b^2 = c^2

a^2 + (a+7)^2 = (2a-5)^2

(a+7)^2 = a^2 +7a +7a+49 = a^2 +14a +49

(2a-5)^2 = 2a*2a -10a -10a +25 = 4a^2 -20a +25

Substituting these into the equation

a^2 + (a^2 +14a +49) = (4a^2 -20a +25)

Combine like terms

2a^2 +14a +49 = 4a^2 -20a +25

Subtracting 2a^2 from each side

2a^2 -2a^2 +14a +49 = 4a^2-2a^2 -20a +25

+14a +49 = 2a^2 -20a +25

Subtract 14a from each side

-14a+14a +49 = 2a^2 -20a -14a+25

+49 = 2a^2 -34a +25

Subtract 49 from each side

49-49 = 2a^2 -34a +25-49

0 =  2a^2 -34a -24

Divide each side by 2

0/2 =  2/2a^2 -34/2a -24/2

0 = a^2 -17a -12

Using the quadratic formula

a=1  b= -17  c = -12

17 ±sqrt( (-17)^2 - 4(1)(-12))

----------------------------------

2(1)

 17 ± sqrt(337)

 -----------------------

     2

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Answer:

see below

Step-by-step explanation:

First find the slope

m= ( y2-y1)/(x2-x1)

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  = 2.5 /5

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y = mx+b where m is the slope and b is the y intercept

y = 1/2x+b

Using a point from above

-5 = 1/2(2) +b

-5 =1+b

Subtract 1 from each side

-6 = b

We have the y intercept

y = 1/2x-6

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