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ira [324]
3 years ago
11

Cristine's middle school has a total of 900 students and 45 teachers. The local high school has 110 teachers and a student-teach

er ratio proportional to the middle school's. How many students will Cristine find when she gets to high school?
Mathematics
1 answer:
ozzi3 years ago
5 0
45/900=110/x
x=(110/45)*900=2200 students
Cristine will find 2200 students when she gets to high school.
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Maria buys 2 dozen pens at $7.20 a dozen. she then sells the pens at 80c each. calculate her profit​
Luda [366]
Her profit is $4.80 :)

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3 0
3 years ago
Identify the standard form of the equation by completing the square.
OLEGan [10]

Answer:

\dfrac{(x-1)^2}{9}-\dfrac{(y-2)^2}{4}=1

Step-by-step explanation:

<u>Given equation</u>:

4x^2-9y^2-8x+36y-68=0

This is an equation for a horizontal hyperbola.

<u>To complete the square for a hyperbola</u>

Arrange the equation so all the terms with variables are on the left side and the constant is on the right side.

\implies 4x^2-8x-9y^2+36y=68

Factor out the coefficient of the x² term and the y² term.

\implies 4(x^2-2x)-9(y^2-4y)=68

Add the square of half the coefficient of x and y inside the parentheses of the left side, and add the distributed values to the right side:

\implies 4\left(x^2-2x+\left(\dfrac{-2}{2}\right)^2\right)-9\left(y^2-4y+\left(\dfrac{-4}{2}\right)^2\right)=68+4\left(\dfrac{-2}{2}\right)^2-9\left(\dfrac{-4}{2}\right)^2

\implies 4\left(x^2-2x+1\right)-9\left(y^2-4y+4\right)=36

Factor the two perfect trinomials on the left side:

\implies 4(x-1)^2-9(y-2)^2=36

Divide both sides by the number of the right side so the right side equals 1:

\implies \dfrac{4(x-1)^2}{36}-\dfrac{9(y-2)^2}{36}=\dfrac{36}{36}

Simplify:

\implies \dfrac{(x-1)^2}{9}-\dfrac{(y-2)^2}{4}=1

Therefore, this is the standard equation for a horizontal hyperbola with:

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  • \textsf{Asymptotes}: \quad y = -\dfrac{2}{3}x+\dfrac{8}{3} \textsf{ and }y=\dfrac{2}{3}x+\dfrac{4}{3}
  • \textsf{Foci}: \quad  (1-\sqrt{13}, 2) \textsf{ and }(1+\sqrt{13}, 2)

4 0
2 years ago
Somebody please help. And be fr cause I’ll give that brainilest or whatever it’s called but please be the right answer.
bearhunter [10]
130 you multiply the left side by 13 to get the right side.
8 0
3 years ago
Please help anybody hm​
Ghella [55]

Answer:

The answer is 1

Step-by-step explanation:

8 0
3 years ago
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