1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
zavuch27 [327]
3 years ago
5

Please help ASAP IM IN DESPREATE NEED OF HELP

Mathematics
1 answer:
Advocard [28]3 years ago
7 0

Answer:

See the attached image for the graph of the first system.

Step-by-step explanation:

Here's how to graph the first system.

Start with the inequality -y \le -2x-3.  You can make this easier to work with by multiplying through by -1.  Remember to switch the inequality sign when multiplying by a <u>negative</u> number.  OK, you get the inequality

y \ge 2x+3.

The graph will be a half-plane -- all the points on one side of a line.  The line that is the boundary of the half-plane has an equation:  y=2x+3 -- just use an  =  sign instead of the inequality sign.

Graph the line.

The equation of the line is in slope-intercept form:  y = mx + b, so you can tell the y-intercept is 3 and the slope is 2 (think of it as a fraction 2/1).  Graph the line by going to the point (0, 3) -- the y-intercept -- then use the slope 2/1 interpreted as "rise over run" to go up 2 units and right 1 unit, arriving at the point (1, 5).  Draw the line through those points, (0, 3) and (1, 5).

Now you have to decide which side of the line the inequality y \ge 2x+3 is describing. To do this, pick a point which is not on the line, plug its coordinates into the inequality; if the result is true, shade the side of the line the point you picked is on (if false, shade the <u>other</u> side!)

An easy point to pick in this case is the origin, (0, 0).  Put zeros in for x and y in the inequality, and you'll get the statement 0 \ge 2(0)+3 \, \Rightarrow \, 0 \ge 3.  That's <u>false</u>, so shade the side of the line <u>not</u> containing the origin.  In the image below, the shading is in purple.

All right, now for the other inequality, x+2\le 0.  Subtract 2 from both sides and the inequality becomes x \le -2.  This, too, graphs as a half-plane whose boundary line has equation x=-2.  Graph the line.  A line with an equation that has  x  in it but not  y is a vertical line with all its x-coordinates equal to the number on the right side of the equation.  This line is vertical and goes through points such as (-2, 0).

Pick a point <u>not</u> on the line (the origin works again).  Put the coordinates into the inequality to get 0\le -2 which is <u>false</u>.  Shade the side of the vertical line which does <u>not</u> contain the origin.  In the image below, the shading is in black.

Finally,  YAY!  \o/ ,  the solutions to the system are all the points in the plane that got shaded twice.  In the image, they are the cross-hatched points above the purple line and to left of the black line.

Note: If you get a system with three inequalities, you'll be graphing three half-planes and looking for points that got shaded three times!

Note: One of your questions has the inequalities x \ge 0 and y \ge 0 in it.  These two inequalities say that the x and y coordinates are both positive or zero, confining your attention to Quadrant I in the upper-right part of a graph, above the x-axis <u>and</u> to the right of the y-axis.

You might be interested in
What is the slope of у&gt;- 2х + 3
charle [14.2K]

Answer:

-2x

Step-by-step explanation:

Graph

y > −2x + 3

Use the slope-intercept form to find the slope and y-intercept.

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

y = mx + b

Find the values of m and b using the form y = mx + b. m = −2

b = 3

The slope of the line is the value of m, and the y-intercept is the value of b.

Slope: −2

intercept: (0, 3)

Graph a dashed line, then shade the area above the boundary line since y is greater than

−2x + 3.

y > −2x + 3

8 0
3 years ago
What is the percent increase if your salary went from $85 to $100 per week? Round your answer to the nearest percent, if necessa
slavikrds [6]
% increase  = 100 - 85
                        ---------     *  100
                          85

                  =   17.65 
                  = 18 % to nearest per cent
3 0
3 years ago
Read 2 more answers
Solve the simultaneous equation y-2x+1=0 and 4x^2+3y^2-2xy=7
Lapatulllka [165]

The first equation is y-2x+1=0

y=2x-1 (Equation 1)

The second equation is 4x^{2}+3y^{2}-2xy=7 (Equation 2)

Putting the value of x from equation 1 in equation 2.

we get,

4x^{2}+3(2x-1)^{2}-2x(2x-1)=7

4x^{2}+3(4x^{2}+1-4x)-4x^{2}+2x=7

by simplifying the given equation,

12x^{2}-10x-4=0

6x^{2}-5x-2=0

Using discriminant formula,

D=b^{2}-4ac

D=25-4 \times 6 \times -2 = 73

Now the formula for solution 'x' of quadratic equation is given by:

x=\frac{-b+\sqrt{D}}{2a}  and  x=\frac{-b-\sqrt{D}}{2a}

x=\frac{5+\sqrt{73}}{12}  and x=\frac{5-\sqrt{73}}{12}

Hence, these are the required solutions.

8 0
3 years ago
If a polynomial is divided by a binomial and the remainder is zero, what does that tell you about the relationship between the b
OleMash [197]

Answer:

Step-by-step explanation:

The binomial is a factor of the polynomial.

5 0
3 years ago
Pls pls answer this asap no wrong answers pls
klemol [59]

Answer:

20, increased, Bianca

Step-by-step explanation:

First one:

He is shown to have travelled 20km in 1 hour, so that's 20km/h.

Second:

The gradient is how steep the curve is, the steeper the faster the person is travelling. Due to the fact Bianca's curve becomes steeper, it shows she is travelling faster. Therefore, her running speed increases.

Third:

Bianca's line hits 50km before Alberto, so therefore she finished first.

Let me know if this makes sense, hope it helped! :D

6 0
2 years ago
Other questions:
  • Miss Honeypenny inherits £650. she decides to save some of the money and send the rest. The ratio of saving to spending money is
    8·1 answer
  • A major stadium has 45,000 seats. If baseball fans have bought 5/8 of the seats for the next game, how many seats are available?
    12·1 answer
  • nilai rata2 matematik dari 10 siswa adalah 55 jika digabungkan lagi dengan 5 siswa maka nilai rata2 menjadi 53tentukan nilai rat
    8·1 answer
  • 5/4v equal and less than 45
    5·1 answer
  • 1. Find the area of the following geometric figure.
    5·2 answers
  • Can somebody help me with the Math's questions with Forming and Solving Equations? Thanks
    9·1 answer
  • The library in Ben's town is 3 blocks east and 7 blocks north of his house. He finds a short cut by walking diagonally from his
    10·2 answers
  • The Earth is approximately 8.0 × 103 miles in diameter, from pole to pole. What number is the distance equivalent to?
    8·1 answer
  • Write the word sentence as an inequality
    9·1 answer
  • 1. Billy's plant is at least 2 inches tall. Graph all the possible heights of the plant.
    12·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!