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3 years ago

Solve the system of linear equations by graphing y = -4x + 2 ; y = -x - 1 What is the solution?

Mathematics

1 answer:

elena-s [515]3 years ago

5 0

Answer:

Step-by-step explanation:

Easiest way would be to substitute points into the given equations and plot your answers.

E.g. if you substitute points into your first equation you get:

If x = 0, y = -4(0) +2 = 2

If x = 1, y = -4(1) +2 = -2

If x = -1, y = -4(-1) +2 = 6

Etc.

Second equation:

If x = 0, y= -(0) -1 = -1

If x = 1, y = -1 -1 = -2

If x = -1, y = -(-1) -1 = 0

Pretty much just plug in values for x into the equations to find y.

Once you have your points, draw a line :)

Where the two lines intercept would be the solution.

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Evaluate the function f(x) =-x/2 -7x -2 find f(-9)

NeX [460]

Answer:

$f(-9)=\frac{131}{2}$

Step-by-step explanation:

In order to evaluate a function at a given x-value, plug in that value into the actual function

$f(x)=-\frac{x}{2} -7x-2\\\\f(-9)=-\frac{9}{2} -7(-9)-2\\\\f(-9) = \frac{131}{2}$

3 0

2 years ago

What is the rate of change and initial value for the linear relation that includes the points shown in the table?

Wittaler [7]

Answer:

Initial value $12$ , rate of change: $-2$

Step-by-step explanation:

Step 1

Find the rate of change

we know that

In a linear equation the rate of change is equal to the slope

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

we have

$A(1,10)\ B(2,8)$

Substitute the values

$m=\frac{8-10}{2-1}$

$m=-2$ ----> rate of change

Step 2

Find the initial value

The equation of the line into slope-point form is equal to

$y-y1=m(x-x1)$

Substitute

$y-10=-2(x-1)$

$y=-2x+2+10$ $y=-2x+12$

The initial value is the value of y when the value of x is equal to zero (is the y-intercept)

$y=-2*0+12=12$ ----> initial value

7 0

2 years ago

Read 2 more answers

A line with a slope of -2 crosses the y-axis at (0, 3). The equation of the line is?

stepladder [879]

Y= -2x+3. This is the equation of the line.

3 0

2 years ago

How to construct a right scalene triangle using no given lengths with a ruler and a compass

11111nata11111 [884]

A scalene triangle contains three unequal in length sides. Therefore, a right scalene triangle can be constructed without the use of a ruler or compass. The 90-degree angle can be signified by a small box in the corner of the triangle that measures 90 degrees.

5 0

2 years ago

In the figure below, points M, P, H, J, and K lie in plane Z.

marishachu [46]

Answers:

(a) LN
(b) PHJ
(c) K
(d) HK

===================================================

Explanation:

Part (a)

Lines LN and PN have the point N in common. This is the intersection point.

-----------------

Part (b)

To name a plane, pick any three non-collinear points that are inside it. We cannot pick points H, J, K together because infinitely many planes pass through it. Imagine the piece of flat paper able to rotate around this axis (like a propeller). Having the points not all on the same line guarantees we form exactly one unique plane.

I'll pick the non-collinear points P, H and J to get the name Plane PHJ. Other answers are possible.

------------------

Part (c)

Points H, J and K are collinear as they are on the same line. Pick either H or K to fill out the answer box. I'll go with point K

------------------

Part (d)

Point P and line HK are coplanar. They exist in the same flat plane, or on the same sheet of flat paper together.

We can think of that flat plane as the ground level while something like point N is underground somewhere. So point N and anything on that ground plane wouldn't be coplanar.

Note: there are other possible names for line HK such as line JH or line JK. The order doesn't matter when it comes to naming lines.

4 0

2 years ago