Write the standard form of the line that passes through the given points.
1 answer:
First of all, remember what the equation of a line is:
<span>y = mx+b</span>First, let's find what <span>m:
m = 1-(-3) / 2-(-1)
m = 4/3
</span>
so: y = 4/3x + b
Now, what about b, or the y-intercept?<span>To find b, think about what your (x,y) points mean:
<span><span>(-1,-3).
When x of the line is -1, y of the line must be -3.
</span><span>(2,1).
When x of the line is 2, y of the line must be 1.
</span></span>
Now, look at our line's equation so far: <span>y=4/3x+b</span>.
You can plug either (x,y) point you want into the x and y variables..the answer will be the same:
<span><span>(-1,-3)
-3=4/3 × -1+b,
b=-3-(4/3)(-1)
b=-5/3
</span><span>
(2,1)
1=4/3 × 2+b
b=1-(4/3)(2).
b=-5/3.
</span></span>In both cases we got the same value for b.
</span>
So we have y = 4/3x -(5/3).
In standard form it would be:
(4/3)x - y = (5/3)
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See attached picture for better understanding of the problem. In the problem, the given values are the following:
hypotenuse = length of the ladder
adjacent = base of the ladder to base of the wall
Solving the angle x, we have the solution as below:
cos x = adjacent / hypotenuse
cos x = 91 / 350
x = 74.93°
The answer is 74.93°.
hypotenuse = length of the ladder
adjacent = base of the ladder to base of the wall
Solving the angle x, we have the solution as below:
cos x = adjacent / hypotenuse
cos x = 91 / 350
x = 74.93°
The answer is 74.93°.
Using the Factor Theorem, the polynomials are given as follows:
1.
2.
3. P(x) = -0.1(x³ - 4x² - 3x + 18)
<h3>What is the Factor Theorem?</h3>The Factor Theorem states that a polynomial function with roots is given by:
In which a is the leading coefficient.
Item a:
The parameters are:
Hence the equation is:
P(x) = (x - 1)²x²(x + 4)
P(x) = (x² - 2x + 1)(x + 4)x²
P(x) = (x³ + 2x² - 7x + 1)x²
Item b:
The roots are:
Hence:
P(x) = a(x - 4)²x(x + 4)
P(x) = a(x² - 16)x(x - 4)
P(x) = a(x³ - 16x)(x - 4)
It passes through the point x = 5, P(x) = 36, hence:
45a = 36.
a = 4/5
a = 0.8
Hence:
Item 3:
The roots are:
Hence:
P(x) = a(x - 3)²(x + 2)
P(x) = a(x² - 6x + 9)(x + 2)
P(x) = a(x³ - 4x² - 3x + 18)
For the y-intercept, x = 0, y = -1.8, hence:
18a = -1.8 -> a = -0.1
Thus the function is:
P(x) = -0.1(x³ - 4x² - 3x + 18)
More can be learned about the Factor Theorem at brainly.com/question/24380382
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