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postnew [5]
3 years ago
7

What are the intercepts of the graph of the equation 6 x − 1 . 5 y = 18?

Mathematics
1 answer:
WITCHER [35]3 years ago
3 0

For this case we have the following equation:

6x-1.5y = 18

We find the intersections with the axes:

  • Intersection with the x axis:

Makingy = 0 we have:

6x-1.5 (0) = 18\\6x = 18\\x = \frac {18} {6}\\x = 3

Thus, the intersection with the x-axis is:(3,0)

  • Intersection with the y axis:

Making x = 0 we have:

6 (0) -1.5y = 18\\-1.5y = 18\\y = \frac {18} {- 1.5}\\y = -12

Thus, the intersection with the y-axis is(0, -12)

Answer:

The intersection with the x axis is: (3,0)

The intersection with the y axis is: (0, -12)

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Which graph represents the solution to the system of inequalities? x + y ≥ 4 2x + 3y < 12
viktelen [127]
There are two inequality equations to be graphed:

<span>x + y ≥ 4
2x + 3y < 12

For the first step, let's disregard the inequality symbols and take it like any conventional algebraic equation. This is to be able to graph the lines on a Cartesian planes first.

For the first equation, x+y=4. To find the x- and y-intercepts, let the other variable be 0. For example,
x-intercept:
x+0=4
x=4
y-intercept:
0+y=4
y=4
Therefore, you can graph the equation line by plotting the intercepts (4,0) and (0,4) and connecting them together. The same thing is done to the second equation:
x-intercept: 
</span>2x + 0 = 12
x=12/2=6
y-intercept:
0 + 3y =12
y= 12/3 = 4
Therefore, you can graph the equation line by plotting the intercepts (6,0) and (0,4) and connecting them together. The graph is shown in the left side of the picture.

The next step would be testing the inequalities. Let's choose a point that does not coincide with the lines. That point could be (-5,-1). 

x + y ≥ 4
-5 + -1 ≥4
-6 ≥ 4 --> this is not true. Thus, the solution of the graph must not include the area of this point. It includes everything to the right of the line denoted by the blue-shaded region.

2x + 3y < 12
2(-5) + 3(-1) <12
-13 < 12 ---> this is true. Thus, the solution would include this point. That includes all points to the left of the orange line denoted by the orange-shaded the region.

The region where blue and orange overlap is the solution of the system of equations, denoted by the green-shaded region.

3 0
3 years ago
Evaluate the function.
Lunna [17]
20
...........................
7 0
3 years ago
Read 2 more answers
HELP PLS PLS PL SPLSLSSPPS
erma4kov [3.2K]

Answer:

x ≈ 73.3

Step-by-step explanation:

Using the cosine ratio in the right triangle

cos39° = \frac{adjacent}{hypotenuse} = \frac{57}{x} ( multiply both sides by x )

x × cos39° = 57 ( divide both sides by cos39° )

x = \frac{57}{cos39} ≈ 73.3 ( to the nearest tenth )

8 0
3 years ago
Evaluate the expression <br> [6+9 x (4-2)] ÷ 4+2
Sedaia [141]

Answer:

8

Step-by-step explanation:

4-2=2

2x9=18

18+6=24

24/4=6

6+2=8

=8

3 0
3 years ago
Read 2 more answers
If a fish ate a cow is it basically a whale at that point? ​
sammy [17]

Answer:

Shark ate fish, then whale eate shark.

Step-by-step explanation:

6 0
3 years ago
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