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3 years ago

10

Lauren made 15 cups of Juiceby mixing lemon juice and sugar water. The ratio of lemon juice to sugar water is 2:3. How many cups

of lemon juice are in the juice?

1 answer:

balandron [24]3 years ago

5 0

6 cups.
2/5 of the mixture would be lemon juice, and 2/5ths of 15 is 6

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There are 12 boys and 15 girls in your class for new students three boys and one girl join your class what is the ratio of the c

Finger [1]

Before the new kids the ratio of girls to boys is 15:12 because there are 15 girls and 12 boys now you can simplify by dividing 15 by 3 and 12 by 3 to get 5:4 as your simplified ratio. As far as after the new kids. Since there is 1 new girl you do 15+1 to get 16 and there are 3 new boys so you do 12+3 to get 15 now 16:15 is already in simplest form so your answer is:

Before: 15:12 simplified as 5:4
After 16:15

6 0

2 years ago

Read 2 more answers

On a coordinate plane, 2 straight lines are shown. The first solid line has a positive slope and goes through (0, negative 2) an

ExtremeBDS [4]

Answer:

$y\geq x-2$

$x+2y$

Step-by-step explanation:

step 1

<em>Find the equation of the first inequality</em>

Find the equation of the first solid line

we have the ordered pairs

(0,-2) and (2,0)

<u><em>Find the slope</em></u>

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

substitute the values

$m=\frac{0+2}{2-0}$

$m=\frac{2}{2}$

$m=1$

The equation in slope intercept form is equal to

$y=mx+b$

we have

$m=1$

$b=-2$ ---> the y-intercept is given

substitute

$y=x-2$

Remember that

Everything to the left of the solid line is shaded

so

The inequality is

$y\geq x-2$

step 2

<em>Find the equation of the second inequality</em>

Find the equation of the second dashed line

we have the ordered pairs

(0,2) and (4,0)

<u><em>Find the slope</em></u>

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

substitute the values

$m=\frac{0-2}{4-0}$

$m=\frac{-2}{4}$

$m=-\frac{1}{2}$

The equation in slope intercept form is equal to

$y=mx+b$

we have

$m=-\frac{1}{2}$

$b=2$ ---> the y-intercept is given

substitute

$y=-\frac{1}{2}x+2$

Remember that

Everything below and to the left of the line is shaded

so

The inequality is

$y$

Rewrite

Multiply by 2 both sides

$2y$

$x+2y$

therefore

The system of inequalities is

$y\geq x-2$

$x+2y$

see the attached figure to better understand the problem

5 0

3 years ago

Read 2 more answers

Need help on these !! 13 and 14! Please!!

katen-ka-za [31]

Question # 13

Answer:

The required equation for the given function is <em>y = 4sin(x/2+2π/3) -2 , as shown attached graph diagram.</em>

<em>Step-by-step explanation: </em>

As the general sine function is given by

$y=asin(bx+c)+d$ .......[A]

amplitude = a
period = 2π ÷ b
Phase shift = -c ÷ b
Vertical shift = d

As in the question,

amplitude = a = 4
period = 4π
phase shift = -4π/3
Vertical shift = d = -2

As

period = 2π ÷ b

b = 2π/period

b = 2π/4π ∵ period = 4π

b = 1/2

Also

Phase shift = -c/b

-4π/3 = -c/b ∵ phase shift = -4π/3

4π/3 = c/b

c = b × 4π/3

c = 1/2 × 4π/3

c = 4π/6

c = 2π/3

So, putting Amplitude ⇒ a = 4, Vertical shift ⇒ d = -2, b = 1/2 ,

and c = 2π/3 in Equation [A] would bring us the required equation for the given function.

$y=asin(bx+c)+d$

y = 4sin(x/2+2π/3)+(-2)

y = 4sin(x/2+2π/3) -2

<em>Note: The graph is also shown in attached diagram.</em>

Question # 14

<em>Answer:</em>

The required equation for the given function is y = cot(x+π/3)+2, as shown in attached graph diagram.

<em>Step-by-step explanation: </em>

As the general cotangent function is given by

$y=acot(bx+c)+d$ .......[A]

amplitude = a
period = π ÷ b
Phase shift = -c ÷ b
Vertical shift = d

As in the question,

period = π
phase shift = -π/3
Vertical shift = d = 2

As

period = π ÷ b

b = π/period

b = π/π ∵ period = 4π

b = 1

Also

Phase shift = -c/b

-π/3 = -c/b ∵ phase shift = -π/3

π/3 = c/b

c = b × π/3

c = 1 × π/3

c = π/3

So, putting vertical shift ⇒ d = 2, b = 1 and c = π/3 in Equation [A] would bring us the required equation for the given function.

$y=acot(bx+c)+d$

y = cot(x+π/3)+2

<em>Note: The graph is also shown in attached diagram.</em>

Keywords: amplitude, period , phase shift , vertical shift

Learn more about trigonometric functions of equations from brainly.com/question/2643311

#learnwithBrainly

7 0

3 years ago

Two buses leave Houston at the same time and travel in opposite directions. One bus averages 55 mi/h and the other bus averages

Veronika [31]

Well you can just keep adding 55 =1hr until you get to 400 the same with 45

6 0

3 years ago

Write an exponential

Alla [95]

Answer:

the answer is b? if wrong tell me. we may have different forms of the answers.

Step-by-step explanation:

3 0

2 years ago