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Lesechka [4]
2 years ago
14

(PLS HURRY I'LL MARK BRAINLIEST)

Mathematics
1 answer:
ch4aika [34]2 years ago
8 0

Answer:

<u>Answer</u><u>:</u><u> </u><u>(</u><u>0</u><u>,</u><u> </u><u>-</u><u>4</u><u>)</u><u> </u><u>and</u><u> </u><u>(</u><u>6</u><u>,</u><u> </u><u>1</u><u>)</u>

• x(t) = 6t --- equation (a)

• y(t) = 3t - 2 --- equation (b)

→ From equation (a), make t the subject:

→ \: { \tt{x(t) = 6t }} \\  \\ → \: { \tt{t =  \frac{x(t)}{6} }}

• substitute for t in equation (b)

→ \: { \tt{y(t) =  3(\frac{x(t)}{6}) - 2 }} \\  \\ → \: { \tt{y(t) =  \frac{x(t)}{2} - 2 }}

• Assume t is 1:

→ \: { \tt{y =  \frac{x}{2}  - 2}} \\  \\ → \: { \boxed{ \tt{2y = x - 4}}}

• when x is zero, y is -4

→ \: { \tt{2y = 0 - 4 =  - 4}} \\

• when x is 6, y is 1

→ \: { \tt{2y = 6 - 4 = 2 }} \\ { \tt{y = 1}}

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True. Because the you will get all the areas of those 6 congruent triangles equally and so summing up them will give you the area of the hexagon.
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3. Is the relationship shown by the data linear? If so, model the data with an equation X | Y 1 ,5| 5,10| 9,15| 13,20|
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Answer:

y=\frac{5}{4}x+\frac{15}{4}

Step-by-step explanation:

x | y

-------

1     5

5   10

9    15

13   20

This one is linear because as x goes up by the same number so does y. So the ratio of difference of y to difference of x is the same per pair of points.

So a linear equation in slope-intercept form is y=mx+b where m is the slope and b is the y-intercept.

To find the slope, I'm going to line up the points vertically and subtract, then put 2nd difference over 1st difference. Like so,

( 1    ,   5)

-( 5   ,  10)

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

-4          -5

So the slope is 5/4 which makes sense since the y's are going up by 5 each time and the x's are going up by 4 each time.

So we have m=5/4. Let's plug that into our y=mx+b.

y=5/4 x+b

To find b, we need to use y=5/4 x+b along with one of the given points.

Choose; it doesn't matter.  I like (1,5) I guess.

y=5/4 x +b with (1,5)

5=5/4 (1)+b

5=5/4    +b

Subtract 5/4 on both sides:

5-5/4=b

20/4-5/4=b  (Found a common denominator)

15/4=b

The y-intercept is 15/4 so b=15/4.

So the equation for the line in slope-intercept form is y=5/4 x +15/4.

y=\frac{5}{4}x+\frac{15}{4}

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