All categories

2 years ago

Solve the system of equations algebraically. Verify your

Mathematics

2 answers:

xz_007 [3.2K]2 years ago

8 0

Answer:

The solution is the point (0.5,-3)

Step-by-step explanation:

we have

$y=4x-5$ ----> equation A

$y=-3$ ----> equation B

Solve the system by substitution

Substitute equation B in equation A

$-3=4x-5$

Solve for x

Adds 5 both sides

$-3+5=4x$

$2=4x$

Divide by 4 both sides

$x=0.5$

therefore

The solution is the point (0.5,-3)

<em>Verify your answer using the graph</em>

using a graphing tool

Remember that the solution of the system of equations is the intersection point both graphs

The intersection point is (0.5,-3)

therefore

The solution is the point (0.5,-3)

see the attached figure

Arada [10]2 years ago

8 0

Answer:

Since y= -3, just put that in the equation.

-3 = 4x - 5

+5 +5

2 = 4x

/4 /4

x=1/2

You might be interested in

A line has a slope of –3 and a y-intercept of (0, –1). What is the equation of the line that is parallel to the given line and p

givi [52]

Well, the first line has a slope of -3, and runs through 0, -1.

a line parallel to that one, will have the same exact slope of -3.

now, we know about this other parallel line that it runs through -3,1, and of course, since is parallel, it has a slope of -3

$\bf \begin{array}{ccccccccc}
&&x_1&&y_1\\
&&(~ -3 &,& 1~)
\end{array}
\\\\\\
% slope = m
slope = m\implies -3
\\\\\\
% point-slope intercept
\stackrel{\textit{point-slope form}}{y- y_1= m(x- x_1)}\implies y-1=-3[x-(-3)]
\\\\\\
y-1=-3(x+3)
\implies 
y-1=-3x-9\implies y=-3x-8$

6 0

2 years ago

Caculate the slope between the points <br> (9, 12) and (4, 17)

Scilla [17]

To calculate the slope you need to do (y2-y1)/(x2-x1). So you would get:
(17-12)/(4-9)
5/-5
=-1
Hope this helps.

3 0

2 years ago

A tetrahedron is a triangular pyramid with 4 equilateral faces. Han has a box of tetrahedrons with each of the 4 vertices marked

Daniel [21]

Theoretically, the number of the vertex comes at the top must be equal for infinitely many numbers of trials, but it's a tedious job to roll the dice for a large number of times. Rolling the tetrahedron only 10 times will not predict the correct result.

Han suspects that this tetrahedron is weighted in some way to make 1 appear more often than the other numbers.

So, check his suspect experimentally with the help of the concept of center of mass. A fair tetrahedron must have the center of mass at the center of the body.

The given tetrahedron has 4 equilateral triangular faces, so at first, measure all the sides of triangular faces and make sure that all are having the same length.

Then, conduct an experiment to check the location of the center of mass.

Hang the tetrahedron by attaching a thin string at the vertex 1 as shown in the figure and observe the base surface ( triangle 234) whether it is parallel to the ground or not.

Now, repeat the same by hanging it with vertices 2, 3, and 4 and observe the base surface.

For the center of mass to be located at the center of the tetrahedron, the base must be parallel to the ground (flat ground).i.e the hanging string must be perpendicular to the base for all the four cases.

If this is so, then the tetrahedron is a fair tetrahedron otherwise not.