In a fruit cocktail, for every 15 ml of orange juice you need 25 ml of apple juice and 10 ml of coconut milk. What proportion of the cocktail is orange juice?
Give your answer as a fraction in its simplest form.

Answer:

m = - 4

Slope of function = - 4

Step-by-step explanation:

m = slope of function

Two points on slope = ( - 4 , - 2 ) , ( - 2 , - 10 )

m = ( y1 - y2 ) / ( x1 - x2 )

y1 = - 2

y2 = - 10

x1 = - 4

x2 = - 2

m = [ ( - 2 ) - ( - 10 ) ] / [ ( - 4 ) - ( - 2 ) ]

m = ( - 2 + 10 ) / ( - 4 + 2 )

m = 8 / - 2

m = - 4

Therefore:

Slope of function = - 4

The slope of a line indicates how steep it is calculated mathematically as "rise overrun". It calculates the rate where the variable y changes when the relevant variable changes, and the further calculation can be defined as follows:

Given Points:

[tex]\bold{( - 4 , - 2 ) \ \ and \ \ ( - 2 , - 10 )}[/tex]

To find:

slope (m)=?

Solution:

[tex]\bold{( - 4 , - 2 ) \ \ and \ \ ( - 2 , - 10 )}[/tex]

[tex]\to \bold{x_1=-4}\\\\ \to \bold{y_1= -2}\\\\\to \bold{x_2= -2}\\\\\to \bold{y_2= -10}\\\\[/tex]

Using formula:

[tex]\bold{slope\ (m) = \frac{( y_2 - y_1 )}{( x_2 - x_1 )}}[/tex]

                 [tex]\bold{=\frac{-10-(-2)}{-2-(-4)}}\\\\\bold{=\frac{-10+2}{-2+4}}\\\\\bold{=\frac{-8}{2}}\\\\\bold{=-4}\\\\[/tex]

Therefore,  the slope is "- 4".

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Answer:

Easiest and fastest way is to graph both equations into a graphing calc and trace the graph to where they intersect.

Alternatively, you can use substitution to solve for your answer.

Step-by-step explanation:

Answer:

6[tex]\frac{1}{3}[/tex]

Step-by-step explanation:

4x-12 = x+7

4x-12+12 = x+7+12

4x = x+19

4x-x = x+19-x

3x=19

x = 6[tex]\frac{1}{3}[/tex]

And if we substitute the value of x into the equation 4x-12 = x+7,

we will get 13[tex]\frac{1}{3}[/tex] = 13[tex]\frac{1}{3}[/tex] in the end.

Hope this helps :)

Answer:

a₇ = - 0.4

Step-by-step explanation:

The n th term of a geometric progression is

[tex]a_{n}[/tex] = a₁ [tex](r)^{n-1}[/tex]

where a₁ is the first term and r the common ratio

Here a₁ = - 6250 and r = [tex]\frac{1250}{-6250}[/tex] = - [tex]\frac{1}{5}[/tex] , thus

a₇ = - 6250 × [tex](-\frac{1}{5}) ^{6}[/tex]

    = - 6250 × [tex]\frac{1}{15625}[/tex] = - [tex]\frac{6250}{15625}[/tex] = - 0.4

Answer:

The paint will not fill the tray by 5.22 in³.

Step-by-step explanation:

V = L × W × H

5 cm → in = 1.9685

V = 12 × 10 × 1.9685

V = 236.22 in³

Available Amount of Paint - 231 in³

236.22 in³ - 231 in³ = 5.22 in³

Hope this helps! :)

Answer:

We can call the numbers x and x + 1. Then we can write:

x + x + 1 = 113 which simplifies to 2x + 1 = 113.

Answer:

Hey there!

The correct answer would be x+x+1=113, or 2x+1=113.

Let the smaller number be x, then the larger number would be x+1

Thus, the sum of x and x+1 would be 2x+1.

We have that 2x+1=113.

Now, this is just a simple linear equation we have to solve.

Start by subtracting 1 to get 2x=112

Then, divide by 2 to get x=56

Since x=56, x+1 would be 57.

Thus, you would have the two numbers be 56 and 57, and use 2x+1 to solve.

Hope this helps :)

Answer:

Number 3 does not have a solution

Step-by-step explanation:

Answer:

  3 1/3 hours

Step-by-step explanation:

In 2 hours, the first guy did 2/6 = 1/3 of the job. Meanwhile, the new guy did 2/8 = 1/4 of the job. When the first guy left, the remaining amount of the job was ...

  1 - 1/3 - 1/4 = 12/12 -4/12 -3/12 = 5/12 . . . . . fraction of job remaining

So, completion of the remaining 5/12 of the job will take the new guy ...

  (5/12)(8 hours) = 10/3 hours = 3 1/3 hours

Answer:

Point M will be located between 0 and 1 at [tex]\frac{1}{13}[/tex].

Step-by-step explanation:

Two points A and B have been given on a number line.

Point A is at -3 and point B at 7.

Distance between these points AB = 7 - (-3)

                                                           = 7 + 3

                                                           = 10 units

Another point M divides the given segment AB in the ratio of 4 : 9.

Therefore, length of segment AM will be = [tex]\frac{4\times 10}{(4+9)}[/tex]

                                                                    = [tex]\frac{40}{13}[/tex]

                                                                    = [tex]3\frac{1}{13}[/tex] units

Now the position of point M will be at [tex](-3+3\frac{1}{13})[/tex] = [tex]\frac{1}{13}[/tex]

Therefore, point M will be located between 0 and 1 at [tex]\frac{1}{13}[/tex].

Answer:

18

Step-by-step explanation:

Plug in the values.

3(4) - 2(-3)

12 - - 6

12 + 6

= 18

Answer:

18

Step-by-step explanation:

[tex]3x - 2y \\ = 3 \times 4 - 2 \times (-3) \\ = 12 + 6 \\ = 18[/tex]

Answer:

The graph if h(x) =2x-3 will have the same slope, but placed lower on the graph, because it's y intercept is -3, while the y-int of f(x) is 0, which is higher up on the y axis

Answer:. An equation is a mathematical statement that shows the equal value of two expressions while an inequality is a mathematical statement that shows that an expression is lesser than or more than the other. 2. An equation shows the equality of two variables while an inequality shows the inequality of two variables.

Step-by-step explanation:

Answer:

left 1 unit, up 5 units

Step-by-step explanation:

First factor

g(x)=x^2+2x+6 = (x+1)^2+5

The standard transformation formula is

g(x) = a*f(bx-h) + k

which means

a=1, b=1,h=-1, k=5

or

h=-1 means translate left one unit

k=5 means translate up 5 units.  

Choose the first option: left 1 unit, up 5 units

Answer:

A

Step-by-step explanation:

Answer:

26) translation: (x - 4, y + 3)

27) see down below

Step-by-step explanation:

26) Its a translation since the shape isn't reflected nor rotated. To find the translation, you can see that the shape would move 4 to the left (- 4), and up 3 ( + 3), which gives you (x - 4, y + 3) (x determines left/right and y determines up/down).

27)

<1 = 135

<2 = 45

<3 = 45

<4 = x = 20

<5 = 135

<6 = 45

<8 = 135

Answer:

2.2

Step-by-step explanation:

2.2 units to the right of zero indicates that the integer is positive on a horizontal number line.

0 + 2.2 = 2.2

Answer:

5

Step-by-step explanation:

Number of players injured in a game count the other side

Complete Question:

To create a bulletin board, Maryann is planning to stretch fabric from burlap sacks over cardstock. She collects 6 kg of burlap sacks. The area density of the burlap is 0.4 kg/m².

Maryann's friends loved her bulletin board , and 4 of them asked her to make one for their homes. She offered to make each of her friends a replica of her bulletin board that measures 2 meters by 3 meters . How many kilograms of burlap should Maryann collect to complete the bulletin boards for her friends?

Answer:

To complete the bulletin boards for her friends, Maryanne should collect 6 kg of burlap more

Step-by-step explanation:

Mass of burlap sacks that Maryann collects = 6 kg

Area density of burlap = 0.4 kg/m²

Area Density = Mass / Area........(1)

The Area of bulletin board that can be made with the 6 kg of burlap sand can be calculated by using equation (1)

0.4 = 6 / Area

Area = 6/0.4

Area of bulletin board that can be made from 6 kg= 15 m² of bulletin board  

The area of bulletin board that Maryann made for herself = 2 * 3 = 6m²

To make similar bulletin boards for her four friends, the total area of bulletin board made for her 4 friends = 6 * 4 = 24m²

To calculate the mass of burlap required to make a 24m² bulletin board, use equation (1)

0.4 = Mass / 24

Mass = 0.4 * 24

Mass = 9.6 kg

The mass of burlap used to make Maryann's bulletin board alone:

0.4 = Mass/6

Mass = 2.4 kg

Out of the 6kg that she got, she has used 2.4 kg for herself

The remaining mass of burlap = 6 - 2.4 = 3.6 kg

Therefore, to complete the bulletin board for her friend, she should collect (9.6 - 3.6) = 6 kg of bulletin more

Answer:

y is equal to 50 degrees.

Step-by-step explanation:

The sum of the angles of a triangle is always 180 degrees.  To find what y is, subtract 80 from 180 and divide the difference by 2.  This will give you 50 degrees.

Answer:

y= 50°

Step-by-step explanation:

∠A =∠B = y. So, ΔABC is an isosceles triangle.

Sum of angles of triangle = 180

∠A + ∠B + ∠C = 180

y + y + 80 = 180   {add like terms}

2y + 80 = 180  {Subtract 80 from both sides}

2y + 80 - 80 = 180 - 80

2y = 100   {divide both sides by 2}

2y/2 = 100/2

y= 50°

Answer:

A.

Step-by-step explanation:

Since range is y-axis based, we are looking at the y-values. We see that the endpoints of the graphed segment are closed points, so they are included in the range. That eliminates B (exludes values) and C (Not infinity, it's a segment, not a line). Choice A is the best answer because when you identify the y-values, you get -8 to -3 included.

Answer:

given, triangle XYZ in which m of angle X=34°

angle Z= 26°

now,angle Y =?

we have,

AngleX + angle Y+ angle Z = 180°

or, 34°+angle Y +26°=180°

or, angle Y= 180°-60°

therefore, angle Y =120°.

hope it helped..

Answer:

Triangle X Y Z is shown.

If m∠X = 34° and m∠Z = 26°, what is m∠Y?

Answer:

m∠Y = 120°

Step-by-step explanation:

I just took the test and got 100% on Edge2021

Answer:

P=.14 or 1/7

Step-by-step explanation:

P(d)=3/35

P(f)=2/35

P( D or F) = 3/35 + 2/35=

1/7 or .14

Answer:

children take 3 pieces of candy are 6

Step-by-step explanation:

x+y=19-1          x+y=18

3x+5y=85-7    3x+5y=78

eliminate x by multiplying the first equation by 3:

3x+3y=54

3x+5y=85   subtract

(3x+3y)-(3x+6y)=54-78

3x-3y-3x-5y=-24

-2y=-24         y=-24/-2=12

y=12 , substitute for y:

x+y=18

x=18-12

x=6

check: 3x+5y=78

3(6)+5(12)=78

18+60=78 correct

Work Shown:

Josh:

1 room = m hours

1/m room = 1 hour

Kevin:

1 room = n hours

1/n room = 1 hour

We see that the rates for Josh and Kevin are 1/m and 1/n respectively. This is the amount of a room they paint in one hour. Combine the fractions

1/m + 1/n = n/(mn) + m/(mn) = (n+m)/(mn) = (m+n)/(mn)

The expression (m+n)/(mn) represents how much of the room they get painted in 1 hour. This is if they work together and it assumes neither worker slows the other one down.

Answer: D) y = -1/4x + 6

Step-by-step explanation:

First turn the equation into slope-intercept form: y = 4x + 6

For a line to be perpendicular to another line, it's slope must be the opposite reciprocal of the other perpendicular line.  Thus, the slope of the perpendicular line is -1/4.  As the y-intercept of the line is (0,6), the lines must intersect as (0,6).  Thus, the other line must also have a y-intercept of 6.  Thus, the answer is D.

Hope this helps <3

Answer:

Cost of staying hotel with fixed charge of 50 and $6 for each day stay

where d is number of days of stay

M is total money charged by hotel.

Step-by-step explanation:

We have to describe a situation to fit into the given model.

model is M = 50 + 6d

it consist of two part

constant part 50

and variable part 6d which depends on value of d,

Let take M as money

d as days

in hotel,  hotel service charge is fixed at 50

and for each day stay 6$ is charged.

Thus,

total money charged by hotel will be equal to sum of

fixed part 50

$6d for staying d days in the hotel

which can be modeled by given equation

M = 50 + 6d

Answer:

5d+4

Step-by-step explanation:

[tex]Total = d + (4d + 4)\\Total = 5d + 4[/tex]

Hope it helps ;P

Answer:

90 cm is submerged (depth of water)

Step-by-step explanation:

Refer to diagram attached.

Let

x = total length of the lotus stem

16 = exposed part of stem

56 = horizontal displacement.

Hence

depth of water = x-16

Using the Pythagorean theorem,

(x-16)^2 + 56^2 = x^2

Expand

x^2 -32x + 256 +3136 = x^2

Simplify

3392 = 32x

x = 3392/32 = 106

Depth of water = x-16 = 106 - 16 = 90 cm

Answer:

(C)51.4 degrees

Step-by-step explanation:

The sum of the exterior angle of a polygon is 360 degrees. (one complete revolution).

Given a regular polygon, the sum of each exterior angle is calculated using the formula:

[tex]\dfrac{360^\circ}{n}[/tex] where n is the number of sides.

The regular polygon shown made by the ant has 7 sides.

Therefore:

Each exterior angle [tex]=\dfrac{360^\circ}{7}=51.43^\circ[/tex]

Therefore:

The value of A correct to 1 decimal place is 51.4 degrees.

The correct option is C.

Answer:

The correct value of A to 1 decimal place is [tex]51.4^o[/tex].

Step-by-step explanation:

Given information:

The ant repeats the two steps 7 times going around the polygon

The sum of the exterior angle of polygon is [tex]360^o[/tex]

The formula for the exterior angle is

[tex]= 360/n[/tex]

Here,

[tex]n=7[/tex]

Hence, the Value of A will be

[tex]A=360/7\\A=51.4^o[/tex]

The correct value of A to 1 decimal place is [tex]51.4^o[/tex].

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Answer:

12

Step-by-step explanation:

2+2+1+1+6=12

Answer:

See below in bold.

Step-by-step explanation:

1. x^2 - 13x - 30

We need 2 numbers whose product is -30 and whose sum = -13.

They are  -15 and + 2:

Answer is (x - 15)(x + 2).

2.   2x^2 + 4x - 126

First we can take 2 out to give:

2(x^2 + 2x - 63)

Now we need 2 numbers whose product is - 63 and sum = +2.

These are +9 and - 7 so

Answer is  2(x - 7)(x + 9).

3. -30x^3 + 3x^2 + 9x

First we can take out -3x to give

-3x(10x^2 - x - 3)

Now we want  2 numbers whose product is 10*-3  = -30 and whose sum is -1. They are  -6 and +5 so we write the above as:

-3x(10x^2 + 5x - 6x - 3)

Now we factor the parentheses by grouping:

= -3x( 5x(2x + 1) - 3(2x + 1)

= -3x(2x + 1)(5x - 3)  Answer.

The answer to the second part is 12x^2 - 13x - 21.

Part 3

1, 18.

2. 6.

3. = 5(2(-3)^2 - 3*3*4 + 4^2) - 3)) - 2(-3)(-3 + 7(4) - 1) - 3*4^2

=  5*(67) - 2(72) - 48

= 143.

4.  (11m^2 - 7) - (6m^2 + 3m - 11) + (3m^2 - m - 9)

= 11m^2 - 7 - 6m^2 - 3m + 11 + 3m^2 - m - 9

=  8m^2 - 4m - 5

A = 8, B = 4 and C = 5.