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san4es73 [151]
3 years ago
9

What is the value of x? Enter your answer in the box. x =

Mathematics
1 answer:
Zinaida [17]3 years ago
3 0

Answer:

x = 5

Step-by-step explanation:

Remember the rule: 5, 12, 13

To prove this rule: Use the equation a² + b² = c²; where as a & b = shorter side, and c is the hypotenuse (longest).

Solve. Let a = x, b = 12, c = 13

a² + b² = c²

(x)² + (12)² = (13)²

Simplify

x² + 144 = 169

Isolate the x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.

x² + 144 (-144) = 169 (-144)

x² = 169 - 144

x² = 25

Isolate the x. Root both sides

x² = 25

√(x²) = √(25)

x = √25 = √(5 * 5) = 5

5 is your answer for x

~

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TiliK225 [7]

Answer:

Step-by-step explanation:

5 and 6 are the same, so I will do one of those and you can use the example to do the other one.  

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Using our points in question 5:  (2, 4) (5, 4)

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For question 7 they want the line parallel to y = 3x + 6 that goes through (-10, 2.5).  For a line to be parallel to another line, their slopes have to be identical.  The slope in y = 3x + 6 is 3.  So the slope of the "new" line is going to be 3 as well.  Now we will use that slope and the given point to solve for b, just like in #5:

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Now we will fill in:

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For question 8 they want the line perpendicular to y = -4x - 2 that goes through (-16, -11).  For a line to be perpendicular to another line, their slopes have to be opposite reciprocals.  Opposite meaning the sign is opposite (positive becomes negative and negative becomes positive), and reciprocal meaning the fraction is flipped upside down.  The slope in our line is -4.  That means that the perpendicular slope is positive 1/4.  Using that along with our point, we will again solve for b:

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For question 8, in order to find the line parallel to the given line, you need to know the slope.  In the form it is currently in, we do not know the slope.  We need to put it into slope-intercept form to find the slope, then we will proceeed as above.  If

x + 4y = 6, then

4y = -x + 6 and, dividing by 4,

y=-\frac{1}{4}x+\frac{3}{2}

(The 3/2 is reduced from 6/4)

Now we can see the slope is -1/4.  We use that along with the point (-8, 5) to solve for b:

5=(-\frac{1}{4})(-8)+b which simplifies to

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