Hey there! :)
To find the equation of a line that passes through (2, -4) & (5, 13), we must first find the slope.
To find the slope, we must use the slope equation, which is : m = (y₂-y₁) / (x₂-x₁)
So, let's plug everything in!
m = (y₂ - y₁) / (x₂ - x₁)
m = (13 - (-4)) / (5 - 2)
Simplify.
m = (13 + 4) / 3
Simplify.
m = 17/3
So, our slope is 17/3!
Now, let's find the equation of the line using slope-intercept form.
Remember that slope-intercept form is : y=mx+b where m=slope, b=y-intercept.
Since we already have the slope, all we need to do is find the y-intercept.
To find the y-intercept, let's plug all of our known variables into y-intercept form, using the points (2, 4) and the slope 17/3.
y = mx + b
(4) = (17/3)(2) + b
Simplify.
4 = 24/3 + b
Simplify.
4 = 8 + b
Subtract 8 from both sides.
4 - 8 = b
Simplify.
-4 = b
So, our y-intercept is b!
Using our known variables (slope, y-intercept), we can very easily plug it into a new slope-intercept equation!
y = mx + b
So, since our slope is 17/3 and our y-intercept is -4, let's plug and chug!
y = 17/3x - 4 → our final answer
~Hope I helped!~
Answer:
add the exponents
Step-by-step explanation:
when multiplying 2 powers that have the same base, you can add the exponents
<h3>
Answer:</h3>
6√2 ≈ 8.485 inches
<h3>
Step-by-step explanation:</h3>
The radii and the chord together make an isosceles right triangle with legs 6 inches long. The hypotenuse of such a triangle is √2 times the leg length. So, the chord will be 6√2 in long.
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<em>Comment on isosceles right triangle</em>
It is worth remembering that the hypotenuse of an isosceles right triangle is √2 times the leg length. This is easily found using the Pythagorean theorem:
... c² = a² + b²
... c² = 1² + 1² = 2 . . . . for legs of length 1
... c = √2 . . . . . . . . . . take the square root.
Scale this result as needed for any particular problem. Here, the scale factor is 6 inches.
Answer:
x² - x - 6
Step-by-step explanation:
Given
(x + 2)(x - 3)
Each term in the second factor is multiplied by each term in the first factor, that is
x(x - 3) + 2(x - 3) ← distribute parenthesis
= x² - 3x + 2x - 6 ← collect like terms
= x² - x - 6
