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blagie [28]
3 years ago
15

Translate the following algebraic inequality into a verbal inequality. 2x +6 > 20

Mathematics
1 answer:
Vera_Pavlovna [14]3 years ago
6 0
X >7. I hope this helps, happy learning.
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Find the solution to the linear system by using the x - and y -intercepts.
Elenna [48]

The solution to these equations is (x, y) = (2, 4).

We've not heard of a method of solving a linear system using the x- and y-intercepts. A Google search on the subject turns up this question, and no other information. However, there is information you can gain from the intercepts that can help you find a solution. (Your reference material may provide a better source of information on this subject.)

The <em>intercept form</em> of a linear equation is ...

... x/(x-intercept) + y/(y-intercept) = 1

Dividing the first equation by 4, you can rearrange it to ...

... x/(-2) +y/(2) = 1 . . . . . . the x-intercept is -2, the y-intercept is +2.

Dividing the second equation by -6, you can rearrange it to ...

... x/-6 +y/3 = 1 . . . . . . . . the x-intercept is -6, the y-intercept is +3.

_____

<em>What you can do with the intercepts</em>

The intercepts can be used to <em>graph the equations</em>. Plot each of the intercepts for a given equation, then draw a line through them. (See the attachment.)

Here, both lines have their intercepts on the negative x and positive y axes. The slopes and intercepts of the lines are such that they intersect in the 1st quadrant.

We can use the intercepts to <em>find the slope of the line</em>.

The slope of each line can be found from ...

... slope = -(y-intercept)/(x-intercept)

Then the slope of the first line is ...

... m1 = -2/-2 = 1

and the slope of the second line is ...

... m2 = -3/-6 = 1/2

The difference in slopes is ...

... m1 - m2 = 1 - 1/2 = 1/2

Using the slope and intercept we can <em>find the solution</em> by substitution or elimination.

For line 1 with slope m1 and y-intercept b1, the equation of the line in slope-intercept form is

... y = m1·x + b1 = x +2

For line 2 with slope m2 and y-intercept b2, the equation of the line in slope-intercept form is

... y = m2·x +b2 = (1/2)x +3

Subtracting the second equation from the first eliminates the y-variable and gives ...

... y - y = 0 = (x +2) -(1/2x +3) = 1/2x - 1

Adding 1 and multiplying by 2 gives the solution for x:

... x = 2

Then the first equation gives the solution for y:

... y = x + 2 = 2+2 = 4

The solution is (x, y) = (2, 4).

_____

<em>Comment on </em><em>find the solution</em>

Above, we subtracted one equation from the other to get ...

... y - y = 0 = x(m1 -m2) +(b1 -b2)

We could have simply equated the values of y to get ...

... m1·x +b1 = y = m2·x +b2

Either way you do this, you find the solution for x is ...

... x = (b2 -b1)/(m1 -m2)

4 0
3 years ago
Help due tonight.. *no links please*
elena-s [515]

Answer:

measure of angle 3= 109

angle 2=71

angle 1=109

Step-by-step explanation:

a straight line =180

7 0
3 years ago
Solve for m 0.6m +3=2m+0.2
DaniilM [7]
So in equations you want to do the same thing to both sides so that the equation will stay equal

when dealing with one unknown number (m) try to get them all on the same side

0.6m+3=2m+0.2
I usually like positive unknowns so
subtract 0.6m from both sides
3=1.4m+0.2
subtract 0.2 from both sides
2.8=1.4m
divide both sides by 1.4
2.8/1.4=2=x

if dividing by decimals move the decimal either round the decimals up or down then divide. or multiply them by the 10 to the same power then divide.

x=2
7 0
3 years ago
Read 2 more answers
Help Plzzz!<br> Convert 122lbs to Kilograms and plz show how you got the answer!!!!!!
PolarNik [594]

Answer:

55.83

Step-by-step explanation:

Divide the number of pounds by 2.2046 to use the standard equation.

4 0
3 years ago
Read 2 more answers
Find the distance between the points (0, 0) and (6, -8). 4 √28 10
kvasek [131]

Answer:

10

Step-by-step explanation:

The formula for finding the distance between 2 points (x1, y1) and (x2, y2) is

d = √[(x2 - x1)² + (y2 - y1)²]

Here (x2, y2) = (6, -8)  and (x1, y1) = (0, 0)

Plugging them gives us

d = √[(6 - 0)² + (-8 - 0)²]

     d = √[(6)² + (-8)²]

        d = √[36 + 64]

           d = √100

               d = 10

6 0
3 years ago
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