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3 years ago

5

The Lakeside Legends, a broomball team, joined a 20-team league. They played each of their 19 opponents 3 times. Every broomball

game lasts for exactly 2 hours. At the end of the season, how many hours had the team spent playing games

1 answer:

SVEN [57.7K]3 years ago

4 0

Answer:

114 hours. 19 teams x 3 games = 57 games. 57 games x 2 hours = 114 hours. hope this helps

Step-by-step explanation:

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8.Find the value of c that makes the expression be a perfect square trinomial p^2-30p+c

Darina [25.2K]

Hope this is the right one.

Problem 8
p^2 - 30p + c
<em>Step One</em>
Take 1/2 of - 30
1/2 * -30 = - 15

<em>Step 2
</em>Square -15
(-15)^2 = 225
c = 225

Problem Nine
$\text{x = }\dfrac{ -b \pm \sqrt{b^{2} - 4ac } }{2a} 
$
a = 1
b = 4
c = -15
$\text{x = }\dfrac{ -4 \pm \sqrt{4^{2} - 4*1*(-15) } }{2*1}$
$\text{x = }\dfrac{ -4 \pm \sqrt{\text{16} + \text{60} } }{2}$

x = [-4 +/- sqrt(76)] / 2
x = [-4 +/- 2*sqrt19]/2
x = [-4/2 +/- 2/2 sqrt[19]
x = - 2 +/- sqrt(19)

x1 = - 2 + sqrt(19)
x2 = -2 - sqrt(19)

These two can be broken down more by finding the square root. I will leave them the way they are. It's just a calculator question if you want it to go into decimal form.

Problem Ten

a = 1
b = 4
c = -32

The discriminate is sqrt(b^2 - 4ac)
D = sqrt(b^2 - 4ac)
D = sqrt(4^2 - 4(1)(-32)
D = sqrt(16 - - 128)
D = sqrt(16 + 128)
D = sqrt(144)
D = +/- 12

Since D can equal + or minus 12 there must be 2 possible (and different) roots. As a matter of fact, this quadratic can be factored.
(x + 8)(x - 4) = y
But that' s not what you were asked for.
The discriminate is > 0 so the roots are going to be real.
<em>Answer; The discriminate is > 0 so there will be 2 real different roots.</em>

4 0

3 years ago

andy is 5 kilogram less than twice his brother's. together they weigh 100 kilograms what are they weights

Minchanka [31]

<span>Let x be the brother's weight.
Then 2x-5 is Andy's weight.
x+(2x-5)=100
3x-5=100
3x=105</span>

6 0

3 years ago

Read 2 more answers

Suppose the mean and standard deviation of the GPAs at Loyola are

Basile [38]

Answer:

Catherine's GPA is 2.48

Step-by-step explanation:

A z-score of 2.010 means that Catherine's GPA is 2.01 standard deviations above the mean. Therefore, Catherine's GPA is $\bar{x}+2.01\sigma=1.963+2.01(0.257)\approx2.48$

3 0

2 years ago

Find the solution of the following system of linear equations. x+y=6 -2x+y=0

andre [41]

Hope it helped you.

8 0

3 years ago

<img src="https://tex.z-dn.net/?f=f%28x%29%20-%20%5Cfrac%7Bx%5E%7B2%7D-4%20%7D%7Bx%5E%7B4%7D%20%2Bx%5E%7B3%7D%20-4x%5E%7B2%7D-4%

Llana [10]

a) The given function is

$f(x)=\frac{x^2-4}{x^4+x^3-4x^2-4}$

The domain refers to all values of x for which the function is defined.

The function is defined for

$x^4+x^3-4x^2-4\ne0$

This implies that;

$x\ne -2.69,x\ne 1.83$

b) The vertical asymptotes are x-values that makes the function undefined.

To find the vertical asymptote, equate the denominator to zero and solve for x.

$x^4+x^3-4x^2-4=0$

This implies that;

$x= -2.69,x=1.83$

c) The roots are the x-intercepts of the graph.

To find the roots, we equate the function to zero and solve for x.

$\frac{x^2-4}{x^4+x^3-4x^2-4}=0$

$\Rightarrow x^2-4=0$

$x^2=4$

$x=\pm \sqrt{4}$

$x=\pm2$

The roots are $x=-2,x=2$

d) The y-intercept is where the graph touches the y-axis.

To find the y-inter, we substitute;

$x=0$ into the function

$f(0)=\frac{0^2-4}{0^4+0^3-4(0)^2-4}$

$f(0)=\frac{-4}{-4}=1$

e) to find the horizontal asypmtote, we take limit to infinity

$lim_{x\to \infty}\frac{x^2-4}{x^4+x^3-4x^2-4}=0$

The horizontal asymtote is $y=0$

f) The greatest common divisor of both the numerator and the denominator is 1.

There is no common factor of the numerator and the denominator which is at least a linear factor.

Therefore the function has no holes.

g) The given function is a proper rational function.

There is no oblique asymptote.

See attachment for graph.

6 0

3 years ago