MATHEMATICS HIGH SCHOOL

A student uses the substitution method to solve the system of equations below algebraically.2x - y = 5
3x + 2y = -3

Which equivalent equation could be used?

Answers

Answer 1
Answer: Solve the first equation for "y" and you get: y = 2x - 5.

That is the equivalent equation that answers the question.

To solve the system, you substitue it for "y" in the second equation and you obtain:

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

Now you have one equation with one single variable, "x" which you can solve easily.

Please, let me know if you could follow the explanation.

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John needs to make a scale drawing of his school building for art class. If the building is 256.25 meters long, and John scales it down using a ratio of 25 meters to 1 inch, how long will the building be in the sketch?

Answers

So we want to know how long will the scale drowing of the building be if the building is 265.25m long and the scale is 1 inch on the drawing is equal to 25 meters of the building. To find the answer lets scale the building. If the real length of the building is 256.25 meters, then the number of inches will be: 256.25/25=10.25 inches.

Kalinda buys x packs of currant buns and y boxes of iced buns

Answers

The whole word problem is:

Kalinda buys x packs of currant buns and y boxes of iced buns.
There are 6 currant buns in a pack of currant buns.
There are 8 iced buns in a box of iced buns.

Kalinda buys a total of T buns.
Write down a formula for T in terms of x and y.

T = 6x + 8y

There are 2,100 bacteria in a circular petri dish. The dish has a radius of 40 millimeters. What is the approximate population density? (Use 3.14 for π)

Answers

A petri dish is simply a circle; thus, we use the formula of the area of the circle which is πr^2. 
Given r = 40 mm
A = π(40)^2 = 5026.55 sq. mm

Population density = bacteria count / area
PD = 2,100 / 5026.55
PD = 0.417782 bacteria / mm sq.

Therefore, the answer is approximately 0.418 bacteria per square millimeter.
Determine the area of the circular petri dish through the equation, A = πr^2. Substituting the radius to the equation and solving for area gives, 5024 mm^2. The population density is obtained by dividing the population with the calculated area. Thus, the population density is approximately 0.418 bacteria per mm^2. 

Three balls are packaged in a cylindrical container as shown below. The balls just touch the top, bottom, and sides of the cylinder. The diameter of each ball is 13 cm. a. What is the volume of the cylinder? Explain your method for finding the volume.
b. What is the total volume of the three balls? Explain your method for finding the total volume.
c. What percent of the volume of the container is occupied by the three balls? Explain how you would find the percent.

Answers

We know the following:
Cylinder volume: V₁ = π r² h
Ball (sphere) volume:V₂ = (4)/(3) π r³
where:
V - volume
r - radius of base of cylinder and diameter of ball
h - height of cylinder.

R = 13 cm ⇒ r = 13 ÷ 2 = 6.5
π = 3.14

a) Since balls touch all sides of cylinder (as shown in image), it can be concluded that height of cylinder is equal to sum of diameters of 3 balls and that radius of base of cylinder is equal to radius of ball:
h = 3 × r = 3 × 13 cm = 39 cm
r = 6.5 cm
So,
V₁ = π r² h
V₁ = 3.14 × (6.5 cm)² × 39 cm
V₁ = 5,173.9 cm³

b. The total volume of three balls is the sum of volumes of each ball:
Vₐ = 3 × V₂ 
Vₐ = 3 × (4)/(3) π r³
Vₐ = 3 × (4)/(3) 3.14 (6.5 cm)³
Vₐ = 3,449.3 cm³

c. Percentage of the volume of the container occupied by three balls ould be expressed as ratio of volume of three balls and volume of cylinder:
V = ( V_(1))/( V_(a) ) ×100 
V = (3,449.3)/(5,173.9) ×100
V = 0.6666 ×100
V = 66.66%
A. The volume of the cylinder can be computed because the statement "The balls just touch the top, bottom, and sides of the cylinder" gives a clue of the height and radius of the cylinder. The height is equal to 3 times the diameter of the balls, and its radius is the same as the balls' radius.

Vcylinder = πr^2h = π(13/2)^2 (3*13) = 5176.56 cm^3

B. The volume of the three balls is computed using the equation of V for spheres:

Vball = 3*4*π*r^2/3 = 3451.05 cm^3

C. The answer is the equal to the total volume of the balls divided by the volume of the cylinder

3451.05(100%)/5176.56 = 66.67%

Prove: AABStep
Statement
Reason
Given
1
ABCD is a parallelogram
ABCD
Select a Reason!!
2
A
B
N

Answers

Hmmm… I wish I could help you with this one, sorry

-4(-2)+(-12)÷(+3)+-20+(+4)+(-6)​

Answers

Answer:

-18

Step-by-step explanation:

-4(-2)+(-12)÷(+3)+-20+(+4)+(-6). [B.E.D.M.A.Srule](Firstbracket)

= 8 - 12 ÷ 3 - 20 + 4 - 6. (Thendivision)

= 8 - 4 - 20 + 4 - 6. (Thenafteraddition)

= 8 + 4 - 4 - 20 - 6

= 12 - 30. (Atlastsubtraction)

= -18 (Ans)

Answer:

-18

Step-by-step explanation:

-4(-2)+((-12))/(+3)-20+(+4)+(-6)=8-(12)/(3)-20+4-6=8-4-20+4-6=-18
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