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A cafeteria serves lemonade that is made from a powdered drink mix. There is a proportional relationship between the number of s

Vitek1552 [10]

All the answers to the given parts are mentioned below -

<h3>What is the general equation of a Straight line? How it represents a proportional relationship?</h3>

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.

y = mx also represents direct proportionality. We can write [m] as -

m = y/x

OR

y₁/x₁ = y₂/x₂

We have a cafeteria serves lemonade that is made from a powdered drink mix. There is a proportional relationship between the number of scoops of powdered drink mix and the amount of water needed to make it. For every 2 scoops of mix, one-half gallon of water is needed, and for every 6 scoops of mix, one and one-half gallons of water are needed.

We can write the proportional relationship as -

y = kx

Now, from the given information, we can write -

2 scoops need 0.5 gallon of water

6 scoops need 1.5 gallon of water

So -

k = 2/0.5

k = 2/(1/2)

k = 2 x 2 = 4

Equations that represents the relationship can be written as -

y = 4x + c

Now, 2 scoops need 0.5 gallon of water.

2 = 4 x 1/2 + c

2 = 2 + c

c = 0

So, the equation will be y = 4x.

Graph of y = 4x is attached at the end.

For 10 scoops of water -

10 = 4x

x = 2.5 gallons of water is needed.

Therefore, all the answers to the given parts are mentioned above.

To solve more questions on proportional relationship, visit the link below-

brainly.com/question/12917806

#SPJ1

5 0

1 year ago

I have no idea!! Please help!!!

Ber [7]

The area of a traingle is $\frac{1}{2}bh$
So we need to know the base and the height
To work out the sides of a right angle triangle we can use a²+b²=c
c is the hypotenuse and a and b are the other sides
Because this triangle is isoceles we know that a and b are the same

a²+b²=c²
a²+a²=c²
2a²=c²
2a²=(x√6)²
2a²=(x√6)(x√6)
2a²=x²+x√6+x√6+6
2a²=x²+x√6+x√6+6
a²= $\frac{x^{2}+x \sqrt{6}+x \sqrt{6}+6 }{2}$
a= $\sqrt{\frac{x^{2}+x\sqrt{6}+x\sqrt{6}+6}{2}}$

A= $\frac{1}{2}bh$
A= $\frac{1}{2}a*a$
A= $\frac{1}{2}$ × $\sqrt{\frac{x^{2}+x\sqrt{6}+x\sqrt{6}+6}{2}}$ × $\sqrt{\frac{x^{2}+x\sqrt{6}+x\sqrt{6}+6}{2}}$
A= $\frac{1}{2}$ × $\frac{x^{2}+x \sqrt{6}+x \sqrt{6}+6 }{2}$
A= $\frac{x^{2}+x \sqrt{6}+x \sqrt{6}+6 }{4}$

8 0

2 years ago

What is the factor to this as a expression?

kotegsom [21]

Answer:

The expression is not factorable with rational numbers

Step-by-step explanation:

7 0

2 years ago

Could some one plz help me with this question

zhuklara [117]

Answer:

A

Step-by-step explanation:

The formula for this type of interest is $A=P(1+\frac{r}{n})^{nt}$ , where A is the total amount, P is the initial investment, x is the interest rate, n is the amount of times that the investment is compounded a year, and t is the amount of years. Plugging in the numbers given, you get: