All the edges of a cube have the same length. Tony claims that the formula SA = 6s, where s is the length of
each side of the cube, can be used to calculate the surface area of a cube.
a. Draw the net of a cube to determine if Tony's formula is correct.
b. Why does this formula work for cubes?
Frances believes this formula can be applied to calculate the surface area of any rectangular prism. Is
she correct? Why or why not?
d. Using the dimensions of Length, Width and Height, create a formula that could be used to calculate the
surface area of any rectangular prism, and prove your formula by calculating the surface area of a
rectangular prism with dimensions L = 5m, W = 6m and H=8m.

Answer:

14.6

Step-by-step explanation:

It is given that,

The average weight of the top 5 fish caught at a fishing tournament was 12.3 pounds. From the attached figure, the weight of 5 fish are given. We need to find the weight of Wayne S. fish.

Average = sum of terms/no of terms

Let the weight of Wayne S. is x. So,

Here the sum of terms is x+12.8+12.6+11.8+9.7 and the number of terms is 5.

[tex]12.3=\dfrac{x+12.8+12.6+11.8+9.7}{5}\\\\61.5=x+12.8+12.6+11.8+9.7\\\\61.5=x+46.9\\\\x=14.6[/tex]

So, the weight of the heaviest fish is 14.6.

Answer:

[tex]\frac{x+5}{x-2}[/tex]

Step-by-step explanation:

Answer:

Step-by-step explanation:

Set this up as a ratio of number of cakes to cups of sugar, C:S

Then the ratio given is 1:2.5 which says 1 cake takes 2.5 cups of sugar. We want to know how many cakes, x, will be made with 37.75 ups of flour:

[tex]\frac{1}{2.5}=\frac{x}{37.75}[/tex] and cross multiply to solve:

2.5x = 37.75 so

x = 15.1 cakes or just 15 cakes (cuz you can't make one-tenth of a cake!)

Answer:

108 inches and 2160 inches

Step-by-step explanation:

108 inches = 274.32 cm

180 inches = 457.2 cm

The area of the mural, A1 = 274.32 X 457.2 = 125419.1 cm²

Let the area of the photograph = A2

The scale A1 to A2,

1/12 = A1/A2

1/12 = 125419.1/A2

∴ A2 = 12 X 125419.1 = 1505029.2 cm²

For their lenghs

1/12 = L1/L2

1/12 = 457.2/L2

L2 = 12 X 457.2 = 5486.4 cm (or 2160 inches)

The width of  the photograph

1505029.2/5486.4 = 274.3 cm ( 108 inches)

Answer:

3.625 gpm

Step-by-step explanation:

Answer:

It is over 7 days

hope it helps

Answer:

X=11/13

Step-by-step explanation:

First, convert the non-variable fractions to a common denominator.

1/4x+8/12=19/12

1/4x=19/12-8/12

1/4x=11/12

x=11/12*4/1

x=44/12

x=11/3

Answer:

aₙ = 30 - 5n

Step-by-step explanation:

25,20,15,10, ...

We see from the given series that it is AP with:

Then formula is:

Answer:

2304 cubic inches

Step-by-step explanation:

Volume = Width x length x height

Green cube:

[tex]12*12*6=864[/tex]

Blue cube:

[tex]10*18*8=1440[/tex]

Add them together:

[tex]1440+864=2304[/tex]

Answer:

Step-by-step explanation:

[tex](\sqrt{20} - 2\sqrt{45} +\sqrt{5} )*\sqrt{5}[/tex]

[tex] = \sqrt{20} \times \sqrt{5} - 2 \sqrt{45} \times \sqrt{5} + \sqrt{5} \times \sqrt{5} [/tex]

[tex] = \sqrt{100} - 2 \sqrt{225} + \sqrt{25} [/tex]

= 10 - 2 × 15 + 5

= 10 - 30 + 5

= 15 - 30

= -15 (Ans)

Answer:

A= 17 B= 19

Step-by-step explanation:

Answer:

a) 17 cups water

b) 19 cups rice

Step-by-step explanation:

w = 1.5r + 0.5

For 11 cups of rice, r = 11.

w = 1.5(11) + 0.5

w = 16.5 + 0.5

w = 17

For 11 cups of rice, 17 cups of water are needed.

With 29 cups of water, w = 29.

29 = 1.5r + 0.5

28.5 = 1.5r

r = 19

With 29 cups of water, 19 cups of rice can be cooked.

Answer:

68 ft³

Step-by-step explanation:

Take the above figure to be 2 rectangular prism. A smaller prism on top, and a bigger one under.

Volume of the smaller rectangular prism on top:

[tex] Volume = whl [/tex]

Where,

w = 2 ft

h = 4 ft

l = 4 ft

[tex] Volume = 2*4*4 = 32 ft^3 [/tex]

Volume of bigger Rectangle prism under:

w = 2 ft

h = 3 ft

l = 6 ft

[tex] Volume = 2*3*6 = 36 ft^3 [/tex]

Volume of composite figure = 32 + 36 = 68 ft³

Answer:

Step-by-step explanation:

The correct answer is 76

Big prism: 4x8x2=64

What's Left: (6-4)x2x3=12

64+12=76

Answer:

No Correlation

Step-by-step explanation

Simply because they are all spread out and you cant make a accurate line out of the points.

Answer:

Step-by-step explanation:

B

Answer:

The answer would be 30% (although I don't see that as an answer).

Step-by-step explanation:

This is because when you multiply the denominator times a number that makes the denominator 100 and multiply that same number by the numerator you get the percentage of the sample you are looking at on the numerator.

15/50 = (15*2)/(50*2) = 30/100 = 30%

Answer:

=X-2a

= 6- 2× (-7)

= 6 + 14

= 20

✌✌✌✌

Answer:

i. a = 7

ii. b = 7

iii. c = 14

Step-by-step explanation:

1. In a parallelogram, the pair of opposite sides are equal, thus;

6a + 10 = 8a -4

4 + 10 = 8a - 6a

14 = 2a

Divide both sides by 2,

a = 7

2. <SPQ + <PSR = [tex]180^{0}[/tex]

(18b - 11) + (9b + 2) =  [tex]180^{0}[/tex]

18b + 9b + 2 -11 =  [tex]180^{0}[/tex]

27b -9 =  [tex]180^{0}[/tex]

27b =  [tex]180^{0}[/tex] + [tex]9^{0}[/tex]

27b = [tex]189^{0}[/tex]

Divide both sides by 27,

b = 7

Therefore,

c = a + b

  = 7 + 7

  = 14

c = 14

Answer:

She is three years old.

Step-by-step explanation:

If she is 3, then six years from now she will be nine.

3 * 3 = 9

Answer:

I think E

Step-by-step explanation:

You know the shortest building is 25 m.

to find the rest, use trigo so Tan(20)=opposite/adjacent.

Adjacent is 50. Do the math and add the answer with 25.

Answer:

The answer would be E. 43.2

According to TOA, The opposite side is tan(20) x adjacent side( 50m)

the answer is 18.2( to 1 dp). Add the height of the second building together with 18.2 and you will get ur answer. HOpe this helps:)

Answer:

Vertex =(5,7)

Latus rectum = 2

Step-by-step explanation:

The general equation of a parabola can be expressed as x = a(y-h)²+k where 'a' is a constant and (h,k) is the vertex of the parabola.

Comparing the general equation with the given equation x= 1/2(y - 5)² + 7, it can be seen that a = 1/2, h = 5 and k = 7. Hence the vertex of the equation is (5,7) on comparison.

The length of the latus rectum of a parabola is 4a

On comparing the equation with the general equation, a = 1/2

Length of the latus rectum = 4(1/2)

Length of the latus rectum = 4/2 = 2

Hence the vertex is (5,7) and the length of latus rectum is 2

Answer:

The values of the angles are;

m∠DEA = 62°, m∠ADB = 45°

Step-by-step explanation:

Specify an arc or an angle three letters  

Angle opposite an arc on the circumference

m DA ≅ m CB = 62°  (Arc between parallel lines are congruent)

∠CAB = 1/2 × m CB = 1/2 × 62° = 31° (Angle at the center = 2 × Angle st the circumference)

∠DBA = 31° (Angle at the center m DA = 2 × Angle st the circumference)

m∠DAB = 104° (Given)

∠ADB = 180° - m∠DAB - ∠DBA = 180° - 104° - 31° = 45° (Interior angles of triangle ΔADB

m∠ADB = 45°

∠AEB = 180 - ∠CAB - ∠DBA = 180° - 31° - 31° = 118°

∠AEB ≅ ∠COD (Vertically opposite angles)

∠DEA ≅ ∠CEB (Vertically opposite angles)

∠AEB + ∠COD + ∠DEA + ∠CEB = 360° (Sum of angles at a point)

118° + 118° + ∠DEA + ∠CEB = 360°

∠DEA + ∠CEB = 360° - 118° - 118° = 124°

Given that ∠DEA = ∠CEB we have;

2 × ∠DEA = 124°

∠DEA = 124°/2 = 62°

m∠DEA = 62°.

Answer:

Step-by-step explanation:

If the password for a certain safe is indicated by multiplying (x^2-16)/(x-1) with 1 / ((x ^ 2 + 6x + 8) / (x ^ 2 + 2x-3))

Simplify the expression in its lowest term first

[tex]= \dfrac{x^2-16}{x-1} * \dfrac{1}{\dfrac{x ^ 2 + 6x + 8}{x ^ 2 + 2x-3} } \\\\= \dfrac{x^2-16}{x-1} * }{\dfrac{x ^ 2 + 2x - 3}{x ^ 2 + 6x + 8} }\\\\= \dfrac{ (x+4)(x-4)}{x-1} * \dfrac{(x+3)(x-1)}{(x+4)(x+2)}\\\\= \dfrac{x-4}{1} * \dfrac{x+3}{x+2}\\[/tex]

If the value of x = 9, to get the numeric value of the password, we will substitute x = 9 into the resulting function as shown;

[tex]= \dfrac{x-4}{1} * \dfrac{x+3}{x+2}\\\\= \dfrac{9-4}{1} * \dfrac{9+3}{9+2}\\\\= \frac{5}{1} * \frac{12}{11}\\\\= \frac{60}{11}\\ \\= 5.455[/tex]

Hence the numeric value of the password is 5.455

Answer:

64.5668 inches tall

Step-by-step explanation:

If you set up a proportion, you would have to do 1.64 times 39.37, which would equal 64.5668 inches.

X = 4×3 X + 7

Resultado

X = 12 X + 7

Forma alternativa

-11 X - 7 = 0

X = -7/11

Answer:

See below

Step-by-step explanation:

40% own neither, it means 100% - 40% = 60% own either a dog or a cat.

Since 45% own a dog, 60% - 45% = 15% own a cat but not a dog.

Since 25% own a cat and 15% own only a cat, 25% - 15% = 10% own a dog and a cat.

Now, 10% out of 45% own both pets, 45% - 10% = 35% own only a dog.

All the numbers reflected in the attached Venn diagram:

Answer:

1 2/3 = m

Step-by-step explanation:

2/3 = m+3/5 -8/5

Combine terms

2/3 = m-5/5

2/3 = m -1

Add 1 to each side

2/3 +1 = m-1+1

2/3 +3/3 = m

5/3 = m

1 2/3 = m

Answer:

[tex]\large \boxed{\sf m = \frac{5}{3} }}[/tex]

Step-by-step explanation:

2/3 = m + 3/5 - 8/5

Subtract the fractions since the denominators are same.

2/3 = m -5/5

Simplify the equation.

2/3 = m - 1

Add 1 to each side.

5/3 = m

Answer:

4.4

Step-by-step explanation:

Answer:

t = 4.4 seconds

Step-by-step explanation:

It hits the ground when the height is equal to zero

This occurs just before 4.5 seconds

t = 4.4 seconds

Answer:

see explanation

Step-by-step explanation:

Corresponding angles within the similar figures are congruent, thus

x = ∠ A = 52°

h = 7 × 1.5 = 10.5 cm

From B to A then divide by the scale factor, that is

w = 12 ÷ 1.5 = 8 cm

Step-by-step explanation:

A=3B

A+B=36

3B+B=36

4B=36

B=36/4

Step-by-step explanation:

let x represent the smaller number

3x is the second number

x+3x=36

4x=36

4x/4=36/4

x=9

the second number is 3(9)

=27

Answer:

y=-4x+1

Step-by-step explanation:

Equation: y=mx+b where m = slope and b= y intercept

TO find the slope, find the change in y over the change in x , or just to rise over run

From (-1,5) to (0,1), the y changes by -4 and the x changes by 1.

So the slope will be -4

To find the y intercept, find the point at which the line crosses the y-axis.

In this case, it is at (0, 1), so your y intercept will be 1

Plug all this info back into the equation and you get y=-4x+1

The y-intercept is 1 and that’s it sorry I can’t answer the rest.