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3 years ago

5

In a school gym the ratio of the number of boys to the number of girls were 4:3. After 160 days boys left the gym, the ratio bec

ame 4:5. How many girls were there in the gym?

2 answers:

uysha [10]3 years ago

7 0

The Answer is 300 girls.

Allisa [31]3 years ago

4 0

<span>11/29/2017QQuiz 2: Supporting Speeches11/29/2017</span><span>QQuiz 2: Supporting Speeches11/29/2017</span><span>QQuiz 2: Supporting Speeches</span>

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NEED HELP PLEASE SOMEONE!!!!

weqwewe [10]

Let me work this out really quick and I'll get back to you

4 0

3 years ago

How to find the vertex calculus 2What is the vertex, focus and directrix of x^2 = 6y

son4ous [18]

Solution:

Given:

$x^2=6y$

Part A:

The vertex of an up-down facing parabola of the form;

$\begin{gathered} y=ax^2+bx+c \\ is \\ x_v=-\frac{b}{2a} \end{gathered}$

Rewriting the equation given;

$\begin{gathered} 6y=x^2 \\ y=\frac{1}{6}x^2 \\ \\ \text{Hence,} \\ a=\frac{1}{6} \\ b=0 \\ c=0 \\ \\ \text{Hence,} \\ x_v=-\frac{b}{2a} \\ x_v=-\frac{0}{2(\frac{1}{6})} \\ x_v=0 \\ \\ _{} \\ \text{Substituting the value of x into y,} \\ y=\frac{1}{6}x^2 \\ y_v=\frac{1}{6}(0^2) \\ y_v=0 \\ \\ \text{Hence, the vertex is;} \\ (x_v,y_v)=(h,k)=(0,0) \end{gathered}$

Therefore, the vertex is (0,0)

Part B:

A parabola is the locus of points such that the distance to a point (the focus) equals the distance to a line (directrix)

Using the standard equation of a parabola;

$\begin{gathered} 4p(y-k)=(x-h)^2 \\ \\ \text{Where;} \\ (h,k)\text{ is the vertex} \\ |p|\text{ is the focal length} \end{gathered}$

Rewriting the equation in standard form,

$\begin{gathered} x^2=6y \\ 6y=x^2 \\ 4(\frac{3}{2})(y-k)=(x-h)^2 \\ \text{putting (h,k)=(0,0)} \\ 4(\frac{3}{2})(y-0)=(x-0)^2 \\ Comparing\text{to the standard form;} \\ p=\frac{3}{2} \end{gathered}$

Since the parabola is symmetric around the y-axis, the focus is a distance p from the center (0,0)

Hence,

$\begin{gathered} Focus\text{ is;} \\ (0,0+p) \\ =(0,0+\frac{3}{2}) \\ =(0,\frac{3}{2}) \end{gathered}$

Therefore, the focus is;

$(0,\frac{3}{2})$

Part C:

A parabola is the locus of points such that the distance to a point (the focus) equals the distance to a line (directrix)

Using the standard equation of a parabola;

$\begin{gathered} 4p(y-k)=(x-h)^2 \\ \\ \text{Where;} \\ (h,k)\text{ is the vertex} \\ |p|\text{ is the focal length} \end{gathered}$

Rewriting the equation in standard form,

$\begin{gathered} x^2=6y \\ 6y=x^2 \\ 4(\frac{3}{2})(y-k)=(x-h)^2 \\ \text{putting (h,k)=(0,0)} \\ 4(\frac{3}{2})(y-0)=(x-0)^2 \\ Comparing\text{to the standard form;} \\ p=\frac{3}{2} \end{gathered}$

Since the parabola is symmetric around the y-axis, the directrix is a line parallel to the x-axis at a distance p from the center (0,0).

Hence,

$\begin{gathered} Directrix\text{ is;} \\ y=0-p \\ y=0-\frac{3}{2} \\ y=-\frac{3}{2} \end{gathered}$

Therefore, the directrix is;

$y=-\frac{3}{2}$

3 0

1 year ago

I need help please with theirs question

crimeas [40]

Answer:

A

Step-by-step explanation:

8 0

3 years ago

The parabola opens upward has x = 2 as an axis of symmetry and contains the non -vertex points (1, 9) and (4, 27) write the equa

Sedaia [141]

Answer:

<h3> f(x) = 6(x - 2)² + 3</h3>

Step-by-step explanation:

f(x) = a(x - h)² + k - vertex form of the equation of the parabola with vertex (h, k)

"the parabola opens upward" means: a>0

"the parabola has x = 2 as an axis of symmetry" means: h = 2

so f(x) = a(x - 2)² + k

"the parabola contains the point (1, 9)" means:

9 = a(1 - 2)² + k

9 = a(-1)² + k

9 = a + k

k = 9 - a

"the parabola contains the point (4, 27)" means:

27 = a(4 - 2)² + k

so:

27 = a(2)² + 9 - a

27 = 4a + 9 - a

3a = 18

a = 6

and k = 9 - 6 = 3

Therefore the vertex form for this parabola is:

<u> f(x) = 6(x - 2)² + 3</u>

4 0

3 years ago

I need help figuring out the steps to do this question

krok68 [10]

6x-18 14x+38

subtract the 6 from the 6 and the 14 which will give you: then add the 18 to the the 18 and the 38

8x = 56

then divide 8/8 which is zero and 8/56 which equals 7 so ur answer is x=7

3 0

3 years ago