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1 year ago

8 There are a combined 33 students who play a spring sport of track or

Mathematics

1 answer:

Rzqust [24]1 year ago

8 0

The number of students that are on the track team are 18.

The number of students that are on the baseball team are 15.

<h3>What are the linear equations that represent the question?</h3>

a + b = 33 equation 1

a - b = 3 equation 2

Where:

a = number of students that are on the track team
b = number of students that are on the baseball team

<h3>How many students that are on the baseball team?</h3>

Subtract equation 2 from equation 1

2b = 30

Divide both sides by 2

b = 30/2 = 15

<h3>How many students that are on the track team?</h3>

Subtract 15 from 33: 33 - 15 = 18

To learn more about simultaneous equations, please check: brainly.com/question/25875552

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1 year ago

Read 2 more answers

Write the equation for the hyperbola with foci (–12, 6), (6, 6) and vertices (–10, 6), (4, 6).

fomenos

Answer:

$\frac{(x--3)^2}{49} -\frac{(y-6)^2}{32}=1$

Step-by-step explanation:

The standard equation of a horizontal hyperbola with center (h,k) is

$\frac{(x-h)^2}{a^2}-\frac{(y-k)^2}{b^2}=1$

The given hyperbola has vertices at (–10, 6) and (4, 6).

The length of its major axis is $2a=|4--10|$ .

$\implies 2a=|14|$

$\implies 2a=14$

$\implies a=7$

The center is the midpoint of the vertices (–10, 6) and (4, 6).

The center is $(\frac{-10+4}{2},\frac{6+6}{2}=(-3,6)$

We need to use the relation $a^2+b^2=c^2$ to find $b^2$ .

The c-value is the distance from the center (-3,6) to one of the foci (6,6)

$c=|6--3|=9$

$\implies 7^2+b^2=9^2$

$\implies b^2=9^2-7^2$

$\implies b^2=81-49$

$\implies b^2=32$

We substitute these values into the standard equation of the hyperbola to obtain:

$\frac{(x--3)^2}{7^2} - \frac{(y-6)^2}{32}=1$

$\frac{(x+3)^2}{49} -\frac{(y-6)^2}{32}=1$

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2 years ago

X2 + 4x - 9 = 5x + 3<br> O A. 4<br> O B. -3<br> O C. -7<br> O D. 5<br> E. -2<br> F-4

elena-14-01-66 [18.8K]

Answer:

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2 years ago