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tresset_1 [31]
2 years ago
14

Carla’s team won 3 of its 5 games played. Elena’s team won games at the same rate. How many games were played if Elena’s team wo

n 12 games?
Mathematics
2 answers:
garik1379 [7]2 years ago
8 0

3/5=12/x

reciprical of both sides

5/3=x/12

times twelve on both sides

x=20

Anna007 [38]2 years ago
6 0

Answer:

7.2 games, 2.4 times rate.

Step-by-step explanation:

Carla's team won 3 of 5 games which is 3/5 aka 60%.

Elena's team won games at the same rate which means Elena's team won about 7 games since it's 7.2/12 (60%). They won at the rate of 2.4 times while Carla wins at 3/5 rate.

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A hotel rents 210 rooms at a rate of $ 60 per day. For each $ 2 increase in the rate, three fewer rooms are rented. Find the roo
lidiya [134]

Answer:

r=$14,400

The hotel should charge $120

Step-by-step explanation:

Revenue (r)= p * n

where,

p = price per item

n = number of items sold

A change in price leads to a change in number sold

A variable to measure the change in p and n needs to be introduced

Let the variable=x

Such that

p + x means a one dollar price increase

p - x means a one dollar price decrease

n + x means a one item number-sold increase

n - x means a one item number-sold decrease

for each $2 price increase (p + 2x) there are 3 fewer rooms are rented (n-3x)

know that at $60 per room, the hotel rents 210 rooms

r = (60 + 2x) * (210 - 3x)

=12,600-180x+420x-6x^2

=12,600+240x-6x^2

r=2100+40x-x^2

= -x^2 +40x+2100=0

Solve the quadratic equation

x= -b +or- √b^2-4ac / 2a

a= -1

b=40

c=2100

x= -b +or- √b^2-4ac / 2a

= -40 +or- √(40)^2 - (4)(-1)(2100) / (2)(-1)

= -40 +or- √1600-(-8400) / -2

= -40 +or- √ 1600+8400 / -2

= -40 +or- √10,000 / -2

= -40 +or- 100 / -2

x= -40+100/-2 OR -40-100/-2

=60/-2 OR -140/-2

= -30 OR 70

x=70

The quadratic equation has a maximum at x=70

p+2x

=60+2(30)

=60+60

=$120

r= (60 + 2x) * (210 - 3x)

={60+2(30)}*{(210-3(30)}

r=(60+60)*(210-90)

=120*120

=$14,400

7 0
3 years ago
Christy is doing her homework. After every 15 minutes of studying, she gets up and takes a 5 minutes break. If she has 2 hours i
gavmur [86]
2 hours is also 120 minutes

120/15=8

8 x 5=40

120+40=160

It will take her 160 minutes to finish, or 2 hours and 40 minutes
3 0
3 years ago
Ac method for x^2+20x-8=0
yanalaym [24]
<h2>Explanation:</h2><h2></h2>

By using quadratic formula:

x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}

\quad a=1,\:b=20,\:c=-8

x_{1,\:2}=\frac{-20\pm \sqrt{20^2-4\cdot \:1\left(-8\right)}}{2\cdot \:1}

x=\frac{-20+\sqrt{20^2-4\cdot \:1\left(-8\right)}}{2\cdot \:1}:\quad 2\left(3\sqrt{3}-5\right)

x=\frac{-20-\sqrt{20^2-4\cdot \:1\left(-8\right)}}{2\cdot \:1}:\quad -2\left(5+3\sqrt{3}\right)

So the solutions are:

\boxed{x=2\left(3\sqrt{3}-5\right),\:x=-2\left(5+3\sqrt{3}\right)}

5 0
3 years ago
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