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ruslelena [56]
3 years ago
5

What is an equation of the line that passes through the points ( 3 , 1 ) and ( − 3 , − 7 ) ?

Mathematics
1 answer:
Vladimir79 [104]3 years ago
7 0

Answer:

y = 4/3x - 3

Step-by-step explanation:

Use this formula to find the slope first.

(y2 - y1) / (x2 - x1)

(x2, y2) --> (-3, -7)

(x1, y1) ---> (3, 1)

Now plug in:

(-7 - 1) / (-3 - 3)  =  -8 / -6  =  4/3

Now find the y intercept by plugging any points to y= 4/3x + b

I will use (3, 1).

1 = 4/3(3) + b  

1 = 4 + b  (subtract 4 on both sides)

-3 = b

So the formula is

y = 4/3x - 3

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What are the ratios for sin A and cos A? The triangle is not drawn to scale.
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Answer:

SinA = \frac{84}{85}  and  CosA=\frac{13}{85}

Step-by-step explanation:

The ratios of sine and cos are defined as follows:

Sin A = \frac{Opposite}{Hypotenuse} , and

CosA = \frac{Adjacent}{Hypotenuse}

The hypotenuse is always the side opposite of the 90 degree angle (for the given triangle, the hypotenuse is 85)

Since we are looking at the angle A, the opposite side with respect to A would be the side length of 84. That leaves the side 13 as the adjacent side.

Thus, we can now write:

Sin A = \frac{Opposite}{Hypotenuse}\\SinA = \frac{84}{85}

CosA = \frac{Adjacent}{Hypotenuse}\\CosA=\frac{13}{85}

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4 years ago
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An Easter basket contains eggs of three different colors. Find the total number of eggs in the basket if 2 7 of all eggs are gre
mrs_skeptik [129]

Answer:

Total number of eggs in basket = 56

Step-by-step explanation:

Let z be the total number of eggs

Green eggs = \frac{2}{7} × z   ........1

Blue eggs =  \frac{1}{4} × z    .......2

Rest of eggs = 26  ........3

The addition of 1, 2 and 3 is equal to z  

\frac{2}{7} × z + \frac{1}{4} + 26 = z

\frac{8z + 7 z}{28} + 26 = z                        ∵GCF for 4 and 7 is 28  

\frac{15z}{28}  + 26 = z

15z + (26 × 28) = 28z                ∵ multiply both sides by 28

15z + 728 = 28z

28z - 15z = 728     .......... rearranging above equation

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Total number of eggs = z = 56

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3 years ago
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