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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.

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.

Answer:

[tex]\boxed {\boxed {\sf x^2=-2y}}[/tex]

Step-by-step explanation:

First, plot the two points. We can see the focus is below the vertex. The result will be a vertical parabola. Since the parabola must contain the focus, it will have to open downward.

From this information, we know that the following equation must be used:

[tex](x-h)^2=-4p(y-k)[/tex]

where (h,k) is the vertex and p is the distance from the focus to the vertex.

Next, find p, the distance between the focus and vertex. We can use the distance formula.

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

The vertex is (0,0) and the focus is (0, -1/2). Therefore:

[tex]x_1=0\\y_1=0\\x_2=0\\y_2= -1/2[/tex]

[tex]d=\sqrt{(0-0)^2+(0--1/2)^2}[/tex]

[tex]d=\sqrt{(0)^2+(0+1/2)^2}[/tex]

[tex]d=\sqrt{0+(1/2)^2}[/tex]

[tex]d=\sqrt{0+1/4}[/tex]

[tex]d=\sqrt{1/4}[/tex]

[tex]d=1/2[/tex]

Now we know the distance and vertex. We can plug the values into the equation.

d=1/2 and (h,k)= (0,0)

[tex](x-0)^2=-4(1/2)(y-0)[/tex]

[tex](x)^2=-2(y)[/tex]

[tex]x^2=-2y[/tex]

The equation of the parabola is x²= -2y

9514 1404 393

Answer:

  B.  (4, 28)

Step-by-step explanation:

Substitute the value of x into the first equation. This gives you the value of y.

After substitution, we have ...

  y = 8(4) -4

  y = 28

Then the point is (x, y) = (4, 28).

Answer:

Step-by-step explanation:

Neither are a function because they do not pass the vertical line test.

Answer:

First collect like terms

4x-2x=7+3

6x=10

x=10/6

x=1.66666666667

x=1.67

Step-by-step explanation:

Please give me brainliest

Answer:

y = 30 - 5.30x

Step-by-step explanation:

y-intercept: 30

slope: 5.30x

Just plug in the amount of weeks on x, and then subtract from 30.

Answer:

m = -5/4

General Formulas and Concepts:

Algebra I

The slope of the perpendicular line is the negative reciprocal of the original slope.

Slope-Intercept Form: y = mx + b

Step-by-step explanation:

Step 1: Define

Slope-Intercept Form (Original):   y = 4/5x + 9

Step 2: Break Original Function

Slope m = 4/5

y-intercept b = 9

Step 3: Find slope of perpendicular line

Take the negative reciprocal.

Perpendicular Slope m = -5/4

Answer:

x=2

Step-by-step explanation:

3(7-2x)-19-5(4-x) = 3(8-6x)-9x+5(4-x)

or, 21-6x-19-20+5x = 24-18x-9x+20-5x

or, 21-19-20-6x+5x = 24+20-18x-9x-5x

or, -18-x = 44-32x

or, -x+32x = 44+18

or, 31x = 62

or, x = 62/31

or, x = 2

Answer:

Step-by-step explanation:

21-6x-19-20+5x=24-18x-9x+20-5x   distribution property

-x-18=44-32x              common factors

31x-18=44                   add 32x to both sides

31x=62                  add 18 to both sides

x=2                   divide 31 to both sides(equals 2) so x equals 2

Answer:

D

Step-by-step explanation:

A graph represents a function of x when it passes the vertical line test. That is, no x values map out to more than 1 y value.

Therefore, D is the only function of x.

Answer:

N + 7 = 12

Step-by-step explanation:

When you have a number minus a negative number, it's the same as addition.

Answer:

N=4

Step-by-step explanation:

or N- x -7=12   because

( ) means multiplication

Answer:

you need to shade 4/6

Step-by-step explanation:

Answer: t=12

Step-by-step explanation:

t-2=10

add 2 to both sides of the equation

t=12

Answer:

106°

Step-by-step explanation:

they are parallel to each other

Answer: 106

Step-by-step explanation:

Answer:

-3 is the solution set of the following equation

Answer:

Step-by-step explanation:

the answer is 25x^2-40x+16

25x^2-40x+16 is equivalent to (5x - 4)^2.

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

here, we have,

(5x - 4)^2

we know,

(a-b)^2= a^2-2ab+b^2

by using this, we get,

(5x - 4)^2

=5x*5x-2*5x*4+4*4

=25x^2-40x+16.

Hence, 25x^2-40x+16 is equivalent to (5x - 4)^2.

To learn more on multiplication click:

brainly.com/question/5992872

#SPJ2

Answer:

5

Step-by-step explanation:

55$-17.50=37.5

37.5/7.5=5

Answer:

x=3/12 or 1/4

Step-by-step explanation:

x + 1/6 = 5/12

x + 2/12 = 5/12

x = 3/12

converts to 1/4

Answer:

x= 1/4

Step-by-step explanation:

5/12- 1/6 = 1/4

Answer:

Actually, I didn't get your question, is it -3/8÷ -1/3 or -1/3÷ -3/8?

If it is -3/8÷ -1/3, the answer will be 9/8

But if is -1/3÷ -3/8, the answer will be 8/9

Step-by-step explanation:

-3/8÷ -1/3

= -3/8× 3/-1

= -9/-8

= 9/8

If your question is -1/3÷ -3/8, the answer is 8/9 in the same way.

Answer:

sin( 61) = x/55

55(sin(61)) = x

48.1 = x

Hope this helps!

Answer:

Break-even point in units= 334

Step-by-step explanation:

Giving the following information:

Desired profit= $500

Selling price= $2

Unitary variable cost= $0.5

To calculate the number of units to be sold, we need to use the following formula:

Break-even point in units= (fixed costs + desired profit) / contribution margin per unit

Break-even point in units= (0 + 500) / (2 - 0.5)

Break-even point in units= 334

Answer:

hi

Step-by-step explanation:

Answer:

4. CDB+DBE= CBE (55+35=90)

5. Definition of a right angle (90 degrees)

6. Linear pair postulate ( i think)

7. ABC and CBE are both 90 degrees

Step-by-step explanation:

Answer:

(5m+6) (5m-6)

Step-by-step explanation:

That's how you factor it since +30 and -30 cancel out

Answer:

orientation is preserved (stays the same)

Step-by-step explanation:

Answer: ab =6

have:

[tex]\frac{1}{a}+\frac{1}{b}+\frac{1}{ab}=1\\\\=>\frac{b}{ab}+\frac{a}{ab}+\frac{1}{ab}=1\\\\<=>\frac{a+b+1}{ab}=1[/tex]

=> a + b + 1 = ab

⇔ a + b + 1 - ab = 0

⇔ b - 1 - a(b - 1) + 2 = 0

⇔ (b - 1)(1 - a) = -2

because a and b are postive integers => (b - 1) and (1 - a) also are integers

=> (b - 1) ∈ {-1; 1; 2; -2;}

(1 -a) ∈  {-1; 1; 2; -2;}

because (b -1).(1-a) = -2 => we have the table:

b - 1        -1             1              2             -2

1 - a         2            -2            -1              1

a              -1            3             2              0

b              0            2             3              -1

a.b            0           6             6               0

because a and b  are postive integers

=> (a;b) = (3;2) or (a;b) = (2;3)

=> ab = 6

Step-by-step explanation:

Answer:

Step-by-step explanation:

i tride but it will be helpful if you give me brainlits

Step-by-step explanation:

h= 55/12 if thats what u askin for

5h – 15 + 7h = 40

value of h

[tex]:\implies \bold{5h – 15 + 7h = 40}[/tex]

[tex] :\implies \bold{5h + 7h = 40 + 15}[/tex]

[tex] :\implies \bold{12h= 55}[/tex]

[tex]:\implies \bold{h = \dfrac{55}{12} }[/tex]

[tex]:\implies\underline{\boxed{ \bold{h = 4.583}}}[/tex]

[tex]:\implies \bold{5h – 15 + 7h = 40}[/tex]

[tex]:\implies \bold{(5 \times 4.583) – 15 +( 7 \times 4.583)= 40}[/tex]

[tex]:\implies \bold{ 30– 15 + 32= 40}[/tex]

[tex]:\implies \bold{ 30– 15 + 32= 40}[/tex]

[tex]:\implies\underline{\boxed{ \bold{ 40= 40}}}[/tex]