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Pavel [41]
3 years ago
8

This season, Lisa's lacrosse team has won $\frac 23$ of their home games (games played at Lisa's school), but just $\frac 25$ of

their away games (games played at other schools). In total, Lisa's team has won $26$ games out of $49$ games they have played. How many home games has Lisa's team played? Explain how you solved the problem.
Mathematics
1 answer:
8090 [49]3 years ago
3 0
The team has played 24 home games.

Let h be the number of home games and a be the number of away games.  The total number of games is 49; this gives us
h+a=49

They won 2/3 of the home games and 2/5 of the away games; there were 26 games won.  This gives us
2/3h + 2/5a = 26

In the first equation we isolate h by subtracting a from both sides:
h+a-a=49-a
h=49-a

Substitute this into the second equation:
2/3(49-a)+2/5a = 26

Using the distributive property, we have
2/3*49 - 2/3*a + 2/5a = 26
98/3 - 2/3a + 2/5a = 26

Finding a common denominator to combine like terms, we have
98/3 - 10/15a + 6/15a = 26
98/3 - 4/15a = 26

We want to convert the whole number to thirds as well; 26 = 26*3/3 = 78/3:
98/3 - 4/15a = 78/3

Subtracting 98/3 from both sides:
98/3 - 4/15a - 98/3 = 78/3 - 98/3
-4/15a = -20/3

Divide both sides by -4/15:
a = -20/3 ÷ -4/15
a = -20/3 × - 15/4 = 300/12 = 25

There were 25 away games.

This means there were 49-25 = 24 home games.
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Find x 58 degrees and adjacent 4.0
PilotLPTM [1.2K]
A special kind of triangle is a right triangle whose definite characteristic is having a 90° angle. It is also special because there are derived trigonometric formulas/identities that can be applied to it. A right triangle has three sides: hypotenuse, adjacent side and opposite side. The hypotenuse is the longest side of the right triangle. You can determine this visually, if not, quantitatively. The other sides are with respect to a given angle.

For the problem, it might have asked for the opposite side or the hypotenuse. We use the cosine function to find the hypotenuse:

cos 58° = adjacent/hypotenuse = 4/hypotenuse
hypotenuse = 7.55 units

Then, we use the tangent function to find the opposite side.

tan 58° = opposite/adjacent = opposite/4
opposite = 6.4 units
4 0
3 years ago
Suppose that you currently own a clothes dryer that costs $25 per month to operate A new efficient dryer costs $590 and has esti
MArishka [77]

Answer:

After 59 months the new dryer will pay for itself.

Step-by-step explanation:

Let the new clothes dryer takes 'x' months to pay for itself.

Then the operating cost of the new dryer will be = 15x

Since cost of the new dryer = $590

So, total cost of the dryer in x months = $(590 + 15x)

Now we know old dryer's operating cost is = $25 per month

So, operating cost for x months = 25x

By the time when new dryer's total cost becomes equal to the old dryer's operational cost, the new dryer will pay for itself.

Now we can get the value of x by equating the old dryer's operational cost and the new dryer's total cost.

25x = 590 + 15x

25x - 15x = 590

10x = 590

x = \frac{590}{10}

x = '59 months'

6 0
3 years ago
There are 6 orange marbles, 2 red marbles, 3 white marbles, and 4 green marbles in a bag. Once a marble is drawn, it IS replaced
professor190 [17]

The probability of selecting two orange marbles with replacement is 36/169.

Data;

  • Orange= 6
  • Red = 2
  • Green = 4

<h3>Probability with replacement</h3>

Since after each draw, the orange marble is replaced.

The total number of marbles in the bag is

6+3+4 = 13

And the number of orange marbles is 6.

For the first selection, the probability of selecting one orange is

P = \frac{6}{13}

After drawn and replaced, the probability of selecting another marble is

P = \frac{6}{13}

And the probability of selecting two orange marbles with replacement is

P = \frac{6}{13} * \frac{6}{13} = \frac{36}{169}

The probability of selecting two orange marbles with replacement is 36/169.

Learn more on probability here;

brainly.com/question/24756209

4 0
2 years ago
Mr. Jensen said he would give as many kids as he could
sp2606 [1]

Answer:

30 kids with some candy left over

3 0
3 years ago
Help please!!!!! i don't understand, any help would be great!! thank you!!
Sergio039 [100]

Answer:

c

Step-by-step explanation:

just substitute a big number into x like 10^6 as it approaches

+  \infty

and a big negative number like -10^6 as it approaches

-  \infty

7 0
3 years ago
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