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serg [7]
3 years ago
6

The graph below shows the numbers of cups of cherry juice that are mixed with different numbers of cups of lemon-lime soda to ma

ke servings of cherry soda: A graph is shown. The values on the x-axis are 0, 1, 2, 3, 4, 5. The values on the y-axis are 0, 5, 10, 15, 20, 25. Points are shown on ordered pairs 0, 0 and 1, 5 and 2, 10 and 3, 15 and 4, 20. These points are connected by a line. The label on the x-axis is Lemon-Lime Soda in cups. The title on the y-axis is Cherry Juice in cups. What is the ratio of the number of cups of cherry juice to the number of cups of lemon-lime soda? (1 point) 5:1 1:20 20:1 1:5
Mathematics
1 answer:
victus00 [196]3 years ago
7 0
Comment
Very well explained.

You can get the answer immediately by taking the y / x value of any one of the points. The slope of the line is also the answer. y/x isn't always possible. It is in this case because one of your points is 0,0

y/x = 20/4 = 5/1

The first choice is your answer.
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2x2 – 5x + 67 = 0<br> What would be your first step in completing the square for the equation above?
7nadin3 [17]

Answer:

The first step is to divide all the terms by the coefficient of x^{2} which is 2.

The solutions to the quadratic equation 2x^2\:-\:5x\:+\:67\:=\:0 are:

x=\frac{5}{4}+i\frac{\sqrt{511}}{4},\:x=\frac{5}{4}-i\frac{\sqrt{511}}{4}

Step-by-step explanation:

Considering the equation

2x^2\:-\:5x\:+\:67\:=\:0

The first step is to divide all the terms by the coefficient of x^{2} which is 2.

so

\frac{2x^2-5x}{2}=\frac{-67}{2}

x^2-\frac{5x}{2}=-\frac{67}{2}

Lets now solve the equation by completeing the remaining steps

Write equation in the form: x^2+2ax+a^2=\left(x+a\right)^2

Solving for a,

2ax=-\frac{5}{2}x

a=-\frac{5}{4}

\mathrm{Add\:}a^2=\left(-\frac{5}{4}\right)^2\mathrm{\:to\:both\:sides}

x^2-\frac{5x}{2}+\left(-\frac{5}{4}\right)^2=-\frac{67}{2}+\left(-\frac{5}{4}\right)^2

x^2-\frac{5x}{2}+\left(-\frac{5}{4}\right)^2=-\frac{511}{16}

Completing the square

\left(x-\frac{5}{4}\right)^2=-\frac{511}{16}

Since, you had required to know the first step in completing the square for the equation above, I hope you have got the point, but let me quickly solve the remaining solution.

For f^2\left(x\right)=a the solution are f\left(x\right)=\sqrt{a},\:-\sqrt{a}

Solving

x-\frac{5}{4}=\sqrt{-\frac{511}{16}}

x-\frac{5}{4}=\sqrt{-1}\sqrt{\frac{511}{16}}

x-\frac{5}{4}=i\sqrt{\frac{511}{16}}       ∵ Applying imaginary number rule \sqrt{-1}=i

x-\frac{5}{4}=i\frac{\sqrt{511}}{\sqrt{16}}

-\frac{5}{4}=i\frac{\sqrt{511}}{4}

x=\frac{5}{4}+i\frac{\sqrt{511}}{4}

Similarly, solving

x-\frac{5}{4}=-\sqrt{-\frac{511}{16}}

x-\frac{5}{4}=-i\frac{\sqrt{511}}{4}    ∵ Applying imaginary number rule  \sqrt{-1}=i

x=\frac{5}{4}-i\frac{\sqrt{511}}{4}

Therefore, the solutions to the quadratic equation are:

x=\frac{5}{4}+i\frac{\sqrt{511}}{4},\:x=\frac{5}{4}-i\frac{\sqrt{511}}{4}

4 0
3 years ago
Mark can paint a room in 3 hours, Frank can paint an identical room in 4 hours. How many hours would it take Mark and Frank to p
IRINA_888 [86]

All you have to do is find the LCD of the number of hours Mark and Frank uses to paint a room.

Mark - 3

Frank - 4

So list the numbers that are a result of a number and 3 and 4

(example: 4 x 1 = 4, 3 x 3 = 9)

3 - 3, 6, 9, 12, 15

4 - 4, 8, 12, 16

The list goes on and on but what we need to get is the LCD so it means it's the least number that 3 and 4 have in common.


3 and 4 both have 12 so The LCD of 3 and 4 is 12.

Another way of finding the LCD could be multiplying the numbers together, but it's not always gonna be the least number. Remember that LCD stands for Least Common Denominator.

How many hours would it take Mark and Frank to paint the room together at their respective rates?

The answer is - 12 hours

8 0
4 years ago
What’s are the answers for both?
nevsk [136]

Answer:

<h2>d = 8</h2><h2>g = 2</h2>

Step-by-step explanation:

8d + 4 = 5d + 28

Group like terms

That's

8d - 5d = 28 - 4

3d = 24

Divide both sides by 3

d = 8

\frac{7(7g + 8)}{4}  = 38.5

Cross multiply

we have

7(7g + 8) = 38.5(4)

49g + 56 = 154

49g = 154 - 56

49g = 98

Divide both sides by 49

g = 2

Hope this helps you

5 0
4 years ago
To determine the average number of hours that students study, members of the math club are polled. Identify the sample as biased
jeka94
The sample is biased, because the members of the math club are not the only people that study
6 0
3 years ago
What is the value of x? ​
atroni [7]

Answer: The value of x is 2

Step-by-step explanation:

x + 7 =3x + 3

-x        -x

7= 2x + 3

-3           -3

4= 2x

x= 2

5 0
4 years ago
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