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3 years ago

Graph or explain how to graph on a coordinate plane: 4x + y ≥ 4

Mathematics

1 answer:

il63 [147K]3 years ago

6 0

We have been given the inequality

$4x + y \geq 4$

In order to graph this inequality, we will follow below mentioned steps:-

First of all we graph the equation $4x + y = 4$ . The x-intercept of the line is 1 and the y-intercept is 4. Hence, this line must pass through the point (1,0) and (0,4)

Now, since we have greater than equal to sign hence the line must be solid.

Now, we have to decide which region we need to shade and for this we apply the origin test.

Substituting x=0 and y=0 in the given inequality and check if the condition holds true or not.

$4 \cdot 0+0 \geq 4\\
\\ 0+0 \geq 4\\
\\
0 \geq 4\\$

Since 0 cannot be greater than 4. Hence, the condition is False.

Hence, we will shade away from origin.

Using all the above mentioned concepts, we can graph the inequality.

Attached is the graph of the inequality.

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1.In a class of 45 pupils ,21play chess and 23 play cards and 5play both games

Mumz [18]

Step-by-step explanation:

(a)

ii.

21 - 5 = 16 play only chess.

iii.

23 - 5 = 18 play only cards

5 play both.

that is 16+18+5 = 39 that play at least one of these games.

so, 45 - 39 = 6 don't play any of these games.

(b)

we have 16+18 = 34 pupils out of 45 that play exactly one game.

so the probabilty to pick one of them is as usual

desired cases / total cases = 34/45 =

= 0.755555555... ≈ 0.76

8 0

2 years ago

Ms. Turner is buying deli meat to make sandwiches for a class picnic. She buys 14 pounds of roast beef for $51.10. She also buys

Masja [62]

RB: $51.10/14=$3.65 per lb
Turkey: $42.60/12=$3.55 per lb
Ham: $3.80 per lb

Answer: Turkey is the LEAST expensive

8 0

3 years ago

Read 2 more answers

Graph a parabola whose vertex is at (3,5)(3,5)left parenthesis, 3, comma, 5, right parenthesis with yyy-intercept at y=1y=1y, eq

Rudik [331]

Using the given information we found that the equation of the parabola is:

y = (-4/9)*(x - 3)^2 + 5

And its graph is below.

<h3>How to get the equation of the parabola?</h3>

For a parabola with vertex (h, k), the equation is:

y = a*(x - h)^2 + k

Here the vertex is (3, 5), so the equation is:

y = a*(x - 3)^2 + 5

And the y-intercept is y = 1, this means that:

1 = a*(0 - 3)^2 + 5

1 = a*9 + 5

1 - 5 = a*9

-4/9 = a

So the parabola is:

y = (-4/9)*(x - 3)^2 + 5

And its graph is below.

If you want to learn more about parabolas, you can read:

brainly.com/question/1480401

4 0

2 years ago

Fins the zeroes of the quadratic equation : 4√ 5 x^ 2 - 24x - 9√ 5

liubo4ka [24]

Answer:

Step-by-step explanation:

Hello,

First of all, we know that the solution of the following equation

$ax^2+bx+c=0$

are

$\dfrac{-b\pm\sqrt{b^2-4ac}}{2a} \ \text{ when } \Delta=b^2-4ac \geq 0$

<em>I would suggest that you try to apply this formula first and check the solution only after you try.</em>

Let's apply it in this case, we have:

$a=4\sqrt{5} \\ \\ b=-24 \\ \\ c= -9\sqrt{5}$

$\Delta=b^2-4ac=24^2+4*9*5=1296 \\ \\ \sqrt{\Delta}=36 \ \text{ and the solutions are } \\ \\ \\ x_1=\dfrac{24-36}{8\sqrt{5}}=\dfrac{-12}{8\sqrt{5}}=\boxed{\dfrac{-3}{2\sqrt{5}}} \\ \\x_2=\dfrac{24+36}{8\sqrt{5}}=\dfrac{60}{8\sqrt{5}}=\boxed{\dfrac{15}{2\sqrt{5}}}$

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

5 0

3 years ago

What is the answer for 9-0-5-(-20)+(-13)?

Nitella [24]

The correct answer is: 11

Here’s how you solve it!

You can remove the 0 since when you add or subtract 0 it stays the same.

Then you would want to look at the first set of parentheses (-20)

Since it is -(-20) this changes the sign to a positive +20

9-5+20+(-13)

Now since the + is in front of the (-13) it remains the same.

Now you are left with this:

9-5+20-13

9-5=4

4+20=24

24-13=11

Then you are left with your answer: 11

Hope this helps! :3

4 0

3 years ago

Read 2 more answers