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mezya [45]
3 years ago
12

Question 2(Multiple Choice Worth 4 points) (08.02)A pair of equations is shown below. x + y = 5 y = one halfx + 2 If the two equ

ations are graphed, at what point do the lines representing the two equations intersect? (2, 5) (5, 2) (2, 3) (3, 2)

Mathematics
1 answer:
8_murik_8 [283]3 years ago
3 0

Answer:

(2,3)

Step-by-step explanation:

The first equation is  x+y=5

The second equation is y=\frac{1}{2}x+2

When we graph these two equations, <em>they will meet at a point which represent the solution of the two equations</em>.

We can solve the two equations simultaneously to determine their point of intersection.

Let us substitute the second equation into the first equation to get;

x+\frac{1}{2}x+2=5

Multiply through by 2 to get;

2x+x+4=10

Group similar terms to obtain;

2x+x=10-4

Simplify;

3x=6

Divide both sides by 3;

\Rightarrow x=2

Put x=2 into the second equation;

y=\frac{1}{2}(2)+2

\Rightarrow y=1+2

\Rightarrow y=3

Therefore the graphs of the two functions intersect at (2,3)

See graph in attachment.

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Use the given information to write the equation of the parabola.
m_a_m_a [10]

Answer:

x² = -2y

Step-by-step explanation:

The focus is p away from the vertex, and so is the directrix.

To find the equation of the parabola, we must first determine if the parabola is horizontal or vertical.

  • Horizontal parabola [Standard form]: (y – k)² = 4p(x – h)
  • Vertical parabola [Standard form]: (x – h)² = 4p(y – k)

If the parabola is vertical, the directrix, and focus will have the same x value but different y value compared to the vertex (h, k). You can also tell if the directrix in in the form y = k – p, and if the focus is in the form (h, k + p).

Likewise, if the parabola is horizontal, the directrix, and focus will have the same y value but different x value compared to the vertex (h,k) . You can also tell if the directrix is in the form x = h – p, and if the focus is in the form (h + p, k).

For this problem, given that the vertex is at the origin (0,0), and that the focus is at the point (0, -½).

You can tell that the x value is the same for the vertex, and focus so this must be a vertical parabola. Because this is a vertical parabola, we can use the form mentioned as earlier (x – h)² = 4p(y – k).

If h = 0, and k = 0, the p value must be the difference between the k of the vertex, and the k of the focus: -½ - 0 → -½.

Now we can just plug in our known information to derive the equation!

h = 0, k = 0, p = -½ → (x - h)² = 4p(y - k) →

(x - 0)² = 4(-½)(y - 0) → x² = -2(y - 0) →

x² = -2y.

Also p = 1/4a, if you are wondering.

So because this is a vertical parabola, x² = -2y is generally the same as y = -1/2x² in standard quadratic form. I just like to think of the horizontal parabola as an inverse quadratic because it is like reflecting over the line y = x.

8 0
3 years ago
Read 2 more answers
Write (2p)^4 without exponents.
Fed [463]

Answer:

= 8p

Step-by-step explanation:

Steps

2p · 4

Remove parentheses: (a) = a

= 2p · 4

Multiply the numbers: 2 · 4 = 8

= 8p

5 0
3 years ago
What is the value of x in the equation 1.5(x + 4) – 3 = 4.5(x – 2)?<br> a 3<br> b 4<br> c 5<br> d 9
Pepsi [2]
The answer would be B) x = 4.

1.5x + 6 - 3 = 4.5x - 9

1.5x + 3 = 4.5x - 9

3 = 4.5x - 9 - 1.5x

3 = 3x - 9

3 + 9 = 3x

12 = 3x

12/3 = x

4 = x

x = 4.
7 0
3 years ago
HELP ME HELP ME! I NEED HELP!!!!!!!!!!!
goldfiish [28.3K]

Answer

D.

Step-by-step explanation:

48/4=12

$12 for 1 adult

10-4=6

42/6=7

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6 0
3 years ago
Can i ask my parents<br><br> subject brainly.com
mestny [16]

Answer: You should ask your parents to subscribe! It'll help you so much - it helped me!

Step-by-step explanation:

8 0
3 years ago
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