Which shows the expressions in the order they would appear on a number line from least to greatest?
1 answer:
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Answer:
The equation of the line is:
Step-by-step explanation:
Given the points
- (-2, -5)
- (1, 1)
Finding the slope between the points
We know the slope-intercept form of the line equation
where m is the slope and b is the slope-intercept form
substituting the value m=2 and the point (-2, -5) to find the b-intercept
-5 = 2(-2) + b
b = -5+4
b = -1
Now, substituting m=2 and b=-1 in the slope-intercept form to get the equation of a line
y=mx+b
y=2x+(-1)
y=2x-1
Thus, the equation of the line is:
<h3>Answer: As a fraction, HC is 21/4 units long</h3><h3>In decimal form, HC is 5.25 units long.</h3>
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Work Shown:
Let x = HC and y = BH
AH = 12-x since AH = 12-HC and x = HC
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See the attached drawing below. The altitude BH forms three similar triangles which makes the proportion below possible
HC/BH = BH/AH
x/y = y/(12-x) ... substitution
x(12-x) = y^2 ... cross multiply
y^2 = -x^2+12x
note how I isolated y^2 instead of y. We will use this equation later.
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Focus on triangle AHB. Use the pythagorean theorem
(BH)^2 + (AH)^2 = (AB)^2
(y)^2 + (12-x)^2 = (9)^2
y^2 + 144-24x+x^2 = 81
-x^2+12x + 144-24x+x^2 = 81 ... replace y^2 with -x^2+12x
-x^2+12x + 144-24x+x^2-81 = 0
-12x + 63 = 0
-12x = -63
x = -63/(-12)
x = 5.25 <<-- answer in decimal form
x = 5 + 0.25
x = 5 + 1/4
x = 20/4 + 1/4
x = 21/4 <<-- answer as a fraction