A line is graphed in the xy-plane shown at left. Which of the following is an equation of the line?

The ratio of the amount of juice to the amount of ginger ale is 3 : 8

Step-by-step explanation:

Fruit punch = amount of juice + amount of gingle ale

(convert the mixed fraction into proper fraction)

Ratio of the amount of juice to the amount of ginger ale = (5/2) / (20/3)

⇒ (5/2)[tex]\times[/tex](3/20)

⇒ (1/2)[tex]\times[/tex](3/4)

⇒(3/8)

∴ The ratio of juice to ginger ale is 3 : 8

Answer:

x=3 y=1

Step-by-step explanation:

x+y=4

y=-x+4

plug in the y

2x-(-x+4)=5

2x+x-4=5

3x=9

x=3

plug in x=3 into first equation to find y

y=-(3)+4

y=-3+4

y=1

Answer:

Step-by-step explanation:

x + y = 4   equation 1

2x - y = 5  equation 2

using substitution method,

x= 4 - y  equation 3

substitute equation 3 into equation 2

2(4-y) -y = 5

8 - 2y - y = 5

8 - 3y = 5

-3y = 5 - 8

-3y = -3

divide through by -3

-3y/-3 = -3/-3

y = 1

substitue the value of y into equation 1

x + y = 4

x + 1 = 4

x = 4 - 1

x = 3

Hence, x = 3 and y = 1

Answer:

each box contained 18

Step-by-step explanation:

because 108 divided by the total number of boxes = 18

Final answer:

To determine how many cupcakes were in each of the 6 boxes for John's party with a total of 108 cupcakes, simply divide 108 by 6, resulting in 18 cupcakes per box.

Explanation:

The question asks us to determine how many cupcakes each box contained if there were a total of 108 cupcakes for John's birthday party, and 6 similar boxes were ordered in total. To find the answer, we divide the total number of cupcakes by the total number of boxes.

First, we know that the mother ordered 4 boxes initially and then ordered 2 more boxes, which gives us a total of 4 + 2 = 6 boxes. Then, we are given the total number of cupcakes, which is 108. To find out how many cupcakes each box contained, we divide the total number of cupcakes by the number of boxes:

108 cupcakes ÷ 6 boxes = 18 cupcakes per box

Therefore, each box contained 18 cupcakes.

Answer:

Ten added to the difference of six and four. Or, the difference of six and four added to ten.

Step-by-step explanation:

The word phrase for the mathematical expression 10+(6-4) is 'Ten plus the difference of six and four'. It is the representation of the arithmetic operation in a sentence format.

The word phrase for the mathematical expression 10+(6-4) is 'Ten plus the difference of six and four'. In this phrase, 'Ten plus' corresponds to the 10+ part of the expression. 'The difference of six and four' means you subtract 4 from 6, which corresponds to the (6-4) part of the expression.

The expression 10+(6-4) can be simplified using the order of operations. First, we need to subtract 4 from 6, which equals 2. Then, we add the result 2 to 10, which equals 12. Therefore, the word phrase for the expression 10+(6-4) is "Ten plus the difference of six and four."

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Answer:

  the number is -1/3

Step-by-step explanation:

The given statement can be written in math terms as ...

  (1/5)(n -3) = 2n . . . the problem statement, using n to represent the number

  n -3 = 10n . . . . . . . . . multiply by 5

  -3 = 9n . . . . . . . . . . . subtract n

  -1/3 = n . . . . . . . . . . . divide by 9 and reduce the fraction

The number is -1/3.

_____

Check

  -1/3 -3 = -3 1/3 = -10/3

  1/5 of -10/3 = -2/3

  -2/3 is twice the number -1/3 . . . . . answer checks OK

Answer:

First batch: 12 - 9 1/4 = 2 3/4 cups

Second batch: 9 1/4 - 6 1/2 = 2 3/4 cups

(2 batches)(2 3/4 cups per batch) =

2(11/4) = 11/2 = 5 1/2 cups

6 1/2 - 5 1/2 = 1 cup of flour left

Answer:

point b

Step-by-step explanation:

i did it on imagine math

Answer:

point b is the correct answer

Step-by-step explanation:

cs it correct

Answer:

There is no numbers shown

Step-by-step explanation:

No numbers shown

Answer:

you don't have a pic to show me... what numbers...???

Step-by-step explanation:

BOI

Answer:

a the answer is a

Step-by-step explanation:

Answer:

$16.40

Step-by-step explanation:

First we find the how much the discount takes off

$20 × .18 = $3.60

So, the discount takes off $3.60, we then subtract that from $20

$20 - $3.60 = $16.40

Which then gives the price of the shirt as $16.40

Answer:

1st three months are January, February and March.

Add all values of each month together.

16+10=26

26-8=18

$18,000,000 in earnings

Step-by-step explanation:

Answer:

The height of triangle EFG is 9 units

Step-by-step explanation:

see the attached figure to better understand the problem

step 1

Find the area of a square ABCD

The area of a square is equal to

[tex]A=b^2[/tex]

where

b is the length side of the square

we have

[tex]b=AB=6\ units[/tex]

substitute

[tex]A=6^2=36\ units^2[/tex]

step 2

Find the height of triangle EFG

The area of triangle EFG is equal to

[tex]A=\frac{1}{2}(b)(h)[/tex]

where

b is the base of triangle

h is the height of triangle

we have

[tex]b=EG=8\ units[/tex]

[tex]A=36\ units^2[/tex] ---> area of triangle EFG is the same that the area of square ABCD

substitute the given values in the formula

[tex]36=\frac{1}{2}(8)(h)[/tex]

solve for h

[tex]36=4h\\h=9\ units[/tex]

therefore

The height of triangle EFG is 9 units

Answer:

The rise would be 4 the run would be 5.

Answer: Rise = 4, Run = 5

Step-by-step explanation:

Rise is how many it goes up

Run is how many is goes right

Answer:

x=72.6

Step-by-step explanation:

use inverse trig because your finding a missing angle. use tan because you haved opp/adj

tan-1=(16/5)

x=tan-1(16/5)

*use a calculator

x=72.6

The the angle of elevation from the point the dog is standing on the ground to the cat is 72.6 degrees

We have given that a dog is standing 5 feet from the base of a tree, looking up at a cat that has climbed 16 feet up the tree

We have to find the angle of elevation

We can see in a figure.

The angle between the horizontal line of sight and the object.

use inverse trig because we are finding a missing angle.

use tan because we have given height of tree (one side) and a distance between dog and tree(second side)

[tex]tab(\theta)}= opp/adj[/tex]

Apply [tex]tan^-1[/tex] on both side we get,

[tex]\theta=tan-1(16/5)[/tex]

[tex]\theta=tan-1(16/5)[/tex]

[tex]\theta=72.6[/tex]

Therefore,the the angle of elevation from the point the dog is standing on the ground to the cat is 72.6 degrees

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Answer:

9 feet

Step-by-step explanation:

Given:

A prism with a triangular base has a volume of 432 cubic feet.

The height of the prism is 8.

The triangle base has a base of 12 feet.

Question asked:

The height of the triangular base of the prism = ?

solution:

Volume of  triangular prism = [tex]Area of triangle \times height[/tex]

[tex]432 = Area of triangle \times8[/tex]

Dividing both side by 8

[tex]54 = Area of triangle[/tex]

[tex]54 =[/tex]  [tex]\frac{1}{2} \times base \times height[/tex]

[tex]54 = \frac{1}{2} \times12\times height\\54 = \frac{12}{2} \times height[/tex]

Multiplying both side by 2

[tex]108 = 12 \times height[/tex]

Dividing both side by 12

[tex]9 = height[/tex]

Thus, height of the triangular base of the prism is 9

Answer:

a=0

Step-by-step explanation:

Solve for a

4a + 12 = 2a +12

4a-2a=12-12

2a=0

a=0/2

a=0

Answer:

1/12

Step-by-step explanation:

There are 3 ways to get two numbers whose sum is 4:

1 and 3, 2 and 2, and 3 and 1

So the probability is 3/36 = 1/12.

Answer:

%40

Step-by-step explanation:

Step 1:  Divide 2/5

2/5 = 0.4

Step 2:  Convert to Decimal by multiplying by 100

0.4 * 100 = %40

Answer:  %40

Answer: 0.025%

Step-by-step explanation:

Answer:

What is the best definition of a biohazard?

Step-by-step explanation:

Answer:  

1.5g

you need to find out how many miligrams (mg) are in a gram (g).

1mg = .001g   therefore move the decimal point over three times to the left

Step-by-step explanation:

Answer:

i) b = 9

ii) m = -3/2

iii) another two ordered pairs on the graph can be (2, 6) and (8, -3).

Step-by-step explanation:

i.) equation of the line is y = mx + b

ii)  x  = number of letters in my first name  = 6 is the x-intercept

iii) y = number of letters in my last name = 9 is the y-intercept

iv) if x  = 0 then y-intercept is b. then 9 = (0 [tex]\times[/tex] m) + b. Therefore b = 9

v) if y = 0 then x -intercept is given by 0 = (6 [tex]\times[/tex] m) + 9.

Therefore 0 = 6m + 9   [tex]\Rightarrow[/tex]   6m = -9,   m = -3/2

vi) another two ordered pairs on the graph can be (2, 6) and (8, -3).

The formula for the volume of a prism is V=Bh , where B is the base area and h is the height. The base of the prism is a rectangle. The length of the rectangle is 9 cm and the width is 7 cm. The area A of a rectangle with length l and width w is A=lw EXAMPLE

put that into a formula.... and boom solved just comment on this for the answer

Answer:

attached below

Step-by-step explanation:

Answer:

C.

Step-by-step explanation:

Final answer:

To solve the system of equations x + 14y = 38 and x + 2y = 5, we used the elimination method to find x = -0.5 and y = 2.75.

Explanation:

Solving the System of Equations

The question requires solving a system of linear equations. The given equations are:

x + 14y = 38 (Equation 1)

x + 2y = 5 (Equation 2)

We can solve this system using the substitution method or elimination method. Let's use the elimination method:

Multiply Equation 2 by 7 to make the coefficient of x the same in both equations:

7x + 14y = 35 (Equation 3)

Subtract Equation 3 from Equation 1 to eliminate x:

(x + 14y) - (7x + 14y) = 38 - 35

-6x = 3

x = -0.5

Substitute x = -0.5 in Equation 2 to find y:

-0.5 + 2y = 5

2y = 5.5

y = 2.75

The solution to the system of equations is x = -0.5 and y = 2.75.

Answer:

  B)  No line of symmetry is drawn,

Step-by-step explanation:

RW is the only line of symmetry. It in not drawn, and is not among the answer choices.

No line of symmetry is drawn.

208.81 square centimeters of aluminium are needed

Solution:

Given that,

Radius = 3.5 cm

Height = 6 cm

We have to find the square centimeters of aluminum needed

So we have to find the surface area of cylinder

The surface area of cylinder is given by formula:

[tex]A = 2 \pi r(h+r)[/tex]

Where "r" is the radius and "h" is the height of cylinder

Substituting the values we get,

[tex]A = 2 \times 3.14 \times 3.5 \times (6+3.5)\\\\A = 21.98 \times 9.5\\\\A = 208.81[/tex]

Thus 208.81 square centimeters of aluminium are needed

The soda can requires approximately 208.51 square centimeters of aluminum.

To determine the amount of aluminum needed to make the soda can, we need to calculate the surface area of the cylinder. The formula for the surface area of a cylinder is:

Surface Area = 2πr(h + r)

Given the radius (r) = 3.5 cm and the height (h) = 6 cm, we substitute these values into the formula:

Surface Area = 2 * 3.14 * 3.5 * (6 + 3.5)

First, calculate the term inside the parentheses:

6 + 3.5 = 9.5

Next, multiply by the radius:

3.5 * 9.5 = 33.25

Finally, multiply by 2π:

2 * 3.14 * 33.25 ≈ 208.51

So, the total surface area of the soda can is approximately 208.51 square centimeters of aluminum.

Answer:

34cm3

Step-by-step explanation:

Volume of sphere = 4/3 pi x cube of radius

Radius =2cm , pi = 3.142

Volume = 4/3 x 3.142 x 2 x 2 x 2

Volume = 1.3333 x 3.142 x 8

Volume = 33.5cm3

Volume = 34cm3 to the nearest whole number

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Final answer:

The simplified form of the expression (x-y)/(x+y) - (x+y)/(x-y) is -4xy / (x²-y²).

Explanation:

To simplify the expression (x-y)/(x+y) - (x+y)/(x-y), we need to find a common denominator and then combine the terms.

The common denominator for the fractions is (x+y)(x-y), which is the product of both denominators and simplifies to x²-y² due to the difference of squares.

Let's go ahead and combine the fractions over this common denominator:
 ((x-y)² - (x+y)²) / (x²-y²)

Expanding the numerators gives:
 (x² - 2xy + y²) - (x² + 2xy - y²) / (x²-y²)

Now, simplify by combining like terms:
 (x² - x² - 2xy - 2xy + y² - y²) / (x²-y²)

Cancelling out the x² and y² terms, we are left with:
 -4xy / (x²-y²)

Thus, the simplified form of the given expression is:
 -4xy / (x²-y²)

Answer:

William will make 12 bags of food and each of the bag will contains 2 cans of fruit and 5 cans of vegetables.

Step-by-step explanation:

Given:

Number of fruits cans = 24

Number of veggies cans = 60

William will have to distribute them in equal bags with equal cans of fruits and vegetables respectively.

For this:

We have to find the GCF (greatest common factor) of 24 and 60.

GCF by listing out the factors method.

Factors of 24  : [tex]1,2,3,4,6,8,12,24[/tex]

Factors of 60 : [tex]1,2,3,4,5,6,10,12,15,20,30,60[/tex]

So,

The greatest common factor of [tex]24[/tex] and [tex]60[/tex] is [tex]12[/tex].

The number of bags William will used for equal distribution = [tex]12[/tex]

Now,

We have to distribute the veggies and fruits in equal number of cans to these [tex]12[/tex]bags.

Number of fruits cans used in each bag = [tex]\frac{24}{12} = 2[/tex]

Number of vegetables can used in each bag = [tex]\frac{60}{12} =5[/tex]

We can say that:

William will make 12 bags of food and each of the bag will contains 2 cans of fruit and 5 cans of vegetables.

Final answer:

By computing the greatest common divisor (GCD) of 24 and 60, it is determined that William can create 12 equal bags with each bag having 2 cans of fruit and 5 cans of vegetables.

Explanation:

The student is asking how to divide 24 cans of fruit and 60 cans of vegetables into bags such that each bag contains the same number of cans without any leftovers. This requires finding the greatest common divisor (GCD) of 24 and 60, which is 12. Therefore, William can make 12 bags, with each bag containing 2 cans of fruit and 5 cans of vegetables.

Answer:

Step-by-step explanation:

100CM equal 1m

Therefore

39.4*100=3940cm

Answer:

The volume of the  cylinder is

 [tex]V=99\ in^3[/tex]

Step-by-step explanation:

we know that

The volume of the cone is equal to

[tex]V=\frac{1}{3}\pi r^{2}h[/tex]

[tex]V=33\ in^3[/tex]

so

[tex]33=\frac{1}{3}\pi r^{2}h[/tex]

Multiply by 3 both sides

[tex]99=\pi r^{2}h[/tex] ----> equation A

Remember that

The volume of a cylinder is equal to

[tex]V=\pi r^{2}h[/tex]

The cylinder has the same height and the same  radius as the cone

so

Equate the volume of cylinder to equation A

[tex]V=99\ in^3[/tex]

The volume of the cylinder is 99 cubic inches and this can be determined by using the formula of the volume of the cylinder and the volume of the cone.

Given :

The formula of the volume of a cone is given by:

[tex]\rm V = \dfrac{1}{3}\pi r^2h[/tex]

[tex]\rm 3V = \pi r^2h[/tex]   --- (1)

The formula of the volume of the cylinder is given by:

[tex]\rm V' = \pi (r')^2 h'[/tex]  --- (2)

According to the given data, the cylinder has the same height and the same  radius as the cone. That is:

h' = h

r' = r

So, from equations (1) and (2):

V' = 3V

According to the given data, V = 33 cubic inches.

V' = 3(33)

V' = 99 cubic inches

So, the volume of the cylinder is 99 cubic inches.

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