Bruce has a bottle that contains 60% of lemon juice and the rest water. The bottle has 1 liter of water.Part A: Write an equation in one variable that can be used to find the total number of liters of lemon juice and water in the bottle. Define the variable used in the equation. (5 points)

Answers

Answer 1

Answer: Given:
lemon juice = 60% in the bottle
water = 1 liter.

Since lemon juice is 60% and the rest is water. Water is 40% of the bottle.

1 liter of water is equivalent to 40% of the bottle.

1/40% = 2.50 liters amount of total liquid in the water.

2.50 x 60% = 1.5 liters of lemon juice.

0.6x + 0.4x = 2.5

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B) y= -
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C) y= -
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D) y= -
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Answers

Answer:c

Step-by-step explanation:

In the standard (x, y) coordinate plane, what is the slope of the line joining the points (3,7) and (4,−8)?

Answers

$(3,7) \ and \ (4,-8)\n \n First \ find \ the \ slope \ of \ the \ line \ thru \ the \ points \: \n \n m= (y_(2)-y_(1))/(x_(2)-x_(1) ) \n \nm=(-8-7)/(4-3) = (-15)/(1)=-15 \n \nNow \ use \ y = mx + b \ with \ either \ point \ to \ find \ b, \ the \ y-intercept \ : \n \n y=mx+b \n \n7=-15*3+b\n \n7=-45 +b \n \nb=7+45\n \nb=52 \n \n y= - 5x+52 \ is \ the \ answer$

A recipe says to use 3.5 cups of flour to make 48 cookies. What is the constant of proportionality that relates the number of cookies made, y, to the number of cups of flour used, x. Round your answer to the nearest tenth.

Answers

Answer: 0.07 cups/cookie

Step-by-step explanation:

The Constant of proportionality is the measure by which the number of cookies made, y increases to the number of cups of flour used, x.

If 3.5 cups of flour makes 48 cookies then how many cookies does 1 cup make;

= 3.5/48

= 0.07 cups/cookie

The golfer hits the golf ball. The quadratic y=-8*x^2 +48*x gives the time x seconds when the golf ball is at height 0 feet. In total, how long is the golf ball in the air?

Answers

$y=-8\cdot x^2 +48\cdot x =-8x(x-6)\n \n-8x(x-6)=0\ \ \ \Leftrightarrow\ \ \ -8x=0\ \ \ \vee\ \ \ x-6=0\n \n.\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x=0\ \ \ \ \ \ \ \ \ \ \ \ \ \ x=6\n \n Ans.\ the\ golf\ ball\ is\ in\ the\ air\ 6\ seconds.$

There are nine balls. One is slightly lighter than the rest; the difference is small enough that you can't tell just by picking them up. Using a basic two-sided scale, what's the minimum number of times you'd need to weigh balls to guarantee you find the light one?

Answers

You will need to weight those balls only twice.You weight 6 balls, 3 on one side of weight and 3 on another, and other3 balls you have are in your hand.

Check picture bellow

just my thoughts:
this is assuming the rest of the balls are of equal weight.
put 4 and 4 on either side of the scale, if by some chance they end up equal then that means the one ball not on the scale is the lighter. (can switch out with another ball to confirm) and that will be 2 weighs by just luck.
systematically, the more likely case is that the lighter ball will be in the 8 you put on the scale, and it's lightness will cause one side to be higher. this means that the lighter ball is on the higher side.
then take the four balls from the higher side and put two and two back on the scale. again higher sides means lighter. then take those two and put one and one. you will then find the lightest ball.
this method will take 3 weighs

If (x1, y1) = (2, 3); x2= 3 and y3 = -2 and G is (0,0), Find y2 and x3.

Answers

Its very simple\

To find the values of x2 and y2 for point G(0,0) when you are given that G is the midpoint of points (x1, y1) and (x3, y3), you can use the midpoint formula:

Midpoint formula:

(x, y) = ((x1 + x3) / 2, (y1 + y3) / 2)

Given:

(x1, y1) = (2, 3)

G(0, 0)

Plug these values into the midpoint formula:

(0, 0) = ((2 + x3) / 2, (3 + y3) / 2)

Now, solve for x3 and y3:

For x3:

0 = (2 + x3) / 2

Multiply both sides by 2 to isolate x3:

0 = 2 + x3

Subtract 2 from both sides to find x3:

x3 = -2

For y3:

0 = (3 + y3) / 2

Multiply both sides by 2 to isolate y3:

0 = 3 + y3

Subtract 3 from both sides to find y3:

y3 = -3

So, the values are:

x3 = -2

y3 = -3

Therefore, the coordinates for point (x2, y2) are:

x2 = 3

y2 = -3

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