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3 years ago

Determine the intercepts of the line that passes through the following points. (-15,5) (-9,10) (-3,15)

1 answer:

6 0

To find the x and y-intercept, we can write an equation in slope intercept form.
first, we need to find the slope
the formula for slope is
m= (y₂-y₁)/(x₂-x₁)

now just put any two points into the equation
m=(10-5)/(-9-(-15)
m=5/6

so now we can write the slope-intercept equation
y=5/6x + b

in a slope-intercept equation, b is equal to the y-intercept, so we can take one of our 3 pairs of points and put them into the equation to solve for b

15= 5/6(-3) +b
15=-2.5 + b
17.5 = b
so now we know the y-intercept is (0,17.5)

now we can write the equation as
y= 5/6x + 17.5

since the x intercept is when y=0, we can set y to 0 and then solve for x

0= 5/6x +17.5
-17.5 = 5/6x
-21 = x

by setting y to zero, we figured out that the x-intercept is (-21,0)

hope this helped!

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nataly862011 [7]

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4 years ago

6) (after 2.3) Consider the infinite system of linear equations in two variables given by ax + by = 0 where (a, b) moves along t

Paraphin [41]

Answer:

Step-by-step explanation:

Given infinite system of linear equations is ax + by = 0

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a) system having unique system (0, 0)

Since two of equation in thus system will be

$1.x+0.y=0\\x=0$

and

$0.x+1.y=0\\y=0$

It is clear that x = 0, y= 0 is the only solution

b) Linear independent solution in this system gives some set of solutions

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and

$0.x+1.y=0\\y=0$

Vector form is

$\left[\begin{array}{ccc}1&0\\0&1\end{array}\right] =I$

c) for this equation if add 0x +0y = 0 to system , Nothing will change

Because [0,0] satisfies that equation

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where 0.00001 is small positive number

so, the system will be inconsistent

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3 years ago

A sailor is 30m above the water in the crow's nest on a sailboat. The sailor encounters an orca surface at an angle of depressio

Natali [406]

Given :

A sailor is 30 m above the water in the crow's nest on a sailboat.

The sailor encounters an orca surface at an angle of depression of 15 degrees.

The crows nest is 20 m horizontally from the bow (front) of the boat.

To Find :

How far in front of the boat is the orca.

Solution :

Let, distance of boat front from the crow's nest is x.

So,

$\dfrac{30}{20+x}=tan \ 15^{\circ}\\\\x=\dfrac{30}{tan \ 15^{\circ}}-20\\\\x=111.94-20\\\\x=91.94\ m$

Hence, this is the required solution.

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3 years ago

Explain how to use a graph of the function f(x) to<br> find f(3).

Oksanka [162]

To find the value of f(3) we need to follow the below steps :

Step 1 : First plot the graph of f(x)

Step 2 : We need to find f(3) or the function value at x = 3 therefore, in the graph locate the point (3,0)

Step 3 : Draw a line parallel to Y-axis passing through the point (3,0) .

Step 4 : Now there exists two cases :

If the drawn line do not intersect the graph of f(x), then no value of f(3) exists for the given function of x

If the drawn line intersects the graph, then the intersection point is marked and a line parallel to x - axis is drawn passing through that marked or intersection point. And the line where it intersects the y - axis is our required value of f(3).

If this is wrong than I guess I wasn't smart enough :)

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2 years ago

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tankabanditka [31]

Answer:

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3 years ago