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.
Answers
Answer:
Here's what I get
Step-by-step explanation:
a. Net of a cube
Fig. 1 is the net of a cube
b. Does the formula work?
Tony's formula works if you ignore dimensions.
There are six squares in the net of a cube.
If each side has a unit length s, the total area of the cube is 6s.
c. Will the formula work for any rectangular prism?
No, because a rectangular prism has sides of three different lengths — l, w, and h — as in Fig. 2.
d. Area of a rectangular prism
A rectangular prism has six faces.
A top (T) and a bottom (b) — A = 2×l×w
A left (L) and a right (R) — A = 2×l×h
A front (F) and a back (B) — A = 2×w×h
Total area = 2lw + 2lh + 2wh
If l = 5 m, w = 6 m and h = 8 m,
[tex]\begin{array}{rl}A &=& \text{2$\times$ 5 m $\times$ 6 m + 2$\times$ 5 m $\times$ 8 m + 2 $\times$ 6 m $\times$ 8 m}\\&=& \text{60 m}^{2} + \text{80 m}^{2} + \text{96 m}^{2}\\&=& \textbf{236 m}^{2}\\\end{array}[/tex]
Related Questions
Ebola has an Ro of 2. How
many third-wave cases can
doctors expect?
Answers
Answer:
4 I guess
Step-by-step explanation:
Because
3-1=2
2^2=2*2=4
Draw a line segment AB of length 6.6 cm. Bisect it perpendicularly at N using a
ruler and set squares
Answers
Step-by-step explanation:
If a line segment AB of length 6.6cm is drawn, bisecting it perpendicularly at N, we have two lines AN and NB of length 3.3cm each.
Because the line is bisected perpendicularly, the angles formed at the point of bisection are 90 degrees.
an equation uses the symbol
Answers
Answer:
The '=' sign.
Step-by-step explanation:
The equals sign ( = ). for example:
3x + 1 = 8.
The equals sign was invented by Robert Recorde of Tenby, South Wales, UK in the early part of the 16th century.
In the second raffle, winning tickets are prime numbers. Click on the winning tickets. 11 71 66 18 22 15 19 49 60 9 75 1 45 88 67 72 30 16 99 43
Answers
Answer:
11, 71, 19, 67, 43.
Step-by-step explanation:
Complete the table. At least the first few so I understand how to do it
Answers
Answer:
What we need to do is simply multiply the values in both columns e.g 4 * 3/36 = 12/36
Please check explanation for complete answer
Step-by-step explanation:
Here, we are concerned about filling the empty columns of the table.
What we want to do here is simply straightforward. All we need to do is to
multiply the values of x by the values of P(x) in each of the individual rows.
Also recall, we do not need to reduce the fractions.
So we have;
2. 3 * 2/36 = 6/36
3. 4 * 3/36 = 12/36
4. 5 * 4/36 = 20/36
5. 6 * 5/36 = 30/36
6. 7 * 6/36 = 42/36
7. 8 * 5/36 = 40/36
8. 9 * 4/36 = 36/36
9. 10 * 3/36 = 30/36
10. 11 * 2/36 = 22/36
11. 12 * 1/36 = 12/36
BRAINIEST!!! only answer if you know and can give an explanation, will report for non-sense answers
Answers
Answer:
Below
Step-by-step explanation:
For a given shape to be a rhombus, it should satisfy these conditions:
● The diagonals should intercept each others in the midpoint.
● The diagonals should be perpendicular.
● The sides should have the same length.
We will prove the conditions one by one.
■■■■■■■■■■■■■■■■■■■■■■■■■■
Let's prove that the diagonals are perpendicular:
To do that we will write express them as vectors
The two vectors are EG and DF.
The coordinates of the four points are:
● E(0,2c)
● G (0,0)
● F (a+b, c)
● D (-a-b, c)
Now the coordinates of the vectors:
● EG (0-0,0-2c) => EG(0,-2c)
● DF ( a+b-(-a-b),c-c) => DF (2a+2b,0)
For the diagonals to be perpendicular the scalar product of EG and DF should be null.
● EG.DF = 0*(2a+2b)+(-2c)*0 = 0
So the diagonals are perpendicular.
■■■■■■■■■■■■■■■■■■■■■■■■■■
Let's prove that the diagonals intercept each others at the midpoints.
The diagonals EG and DF should have the same midpoint.
● The midpoint of EG:
We can figure it out without calculations. Since G is located at (0,0) and E at (0,2c) then the distance between E and G is 2c.
Then the midpoint is located at (0,c)
● The midpoint of DF:
We will use the midpoint formula.
The coordinates of the two points are:
● F (a+b,c)
● D(-a-b,c)
Let M be the midpoint of DF
●M( (a+b-a-b,c+c)
● M (0,2c)
So EG and DF have the same midpoint.
■■■■■■■■■■■■■■■■■■■■■■■■■■
There is no need to prove the last condition, since the two above guarante it.
But we can prove it using the pythagorian theorem.
M1: L12a: Solving Equations Exit Ticket Determine which of the following equations have the same solution set. Must show work. 1. 3y + 8 = -10 - 3y 2. 6r+ 7 = 13 + 7r 3. 13 - 4m = 1 - m 4.-8-h=-3h 5. 38+7f=8f + 32 6. -6n + 20 = -14n - 4
determine which of the following has the same solution set must show work
Answers
Answer:
uhfcytuyyytt ryffffffffgtgghhh
The cost of milk is modeled by a linear equation where four quarts (one gallon) costs $3.09 while two quarts
(half-gallon) costs $1.65. Write the linear equation that expresses the price in terms of quarts. How much would
an eight-quart container of milk cost?
Answers
Answer:
linear equation to express the price is:
y=0.72x+0.21
An eight quarts will cost : $5.97
Step-by-step explanation:
linear equation represent y=mx+b
let x=quarts ( x=4, x=2)
y= price (3.09 and y=1.65 )
two points (4,3.09) and (2,1.65)
need to find the slope m:
y2-y1/x2-x1
(1.65-3.09)/(2-4) ⇒ m=0.72
y=0.72x+b find b at point (2,1.65)
1.65=0.72(2) +b ⇒ b=0.21
y=0.72x +0.21
check : point (4,3.09)
y=0.72(4) +0.21
y=3.09 ( correct)
An eight quarts will cost :
y=0.72(8)+0.21
y=5.97 dollars
idk know the answer i really need help
Answers
Answer:
37x - 13
Step-by-step explanation:
Hello!
The product of 37 and x mean multiply so we can write it as
37x
13 less means subtract so we put that at the end
37x - 13
The answer is 37x - 13
Hope this helps!
Answer:
37 * x - 13
This answer is here according to your question It said that 37*x - 13 Please mark this answer The brainliest one
What is the surface area of the sphere below?
Answers
Hey there! I'm happy to help!
To find the surface area of a sphere, here is what you do.
You square the radius.
4²=16
You multiply by 4.
16×4=64
And you multiply by pi!
64×π=64π
Therefore, the surface area of the sphere is A. 64π units². It's that easy!
Now you can find the surface area of a sphere! Have a wonderful day! :D
Question :-
What is the surface area of the sphere that has a radius of 4 units?Answer :-
The surface area of the sphere is 64π units².[tex] \rule{180pt}{3pt}[/tex]
Diagram :-
[tex]\setlength{\unitlength}{1.2cm}\begin{picture}(0,0)\thicklines\qbezier(2.3,0)(2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,-2.121)(0,-2.3)\qbezier(2.3,0)(2.121,-2.121)(-0,-2.3)\qbezier(-2.3,0)(0,-1)(2.3,0)\qbezier(-2.3,0)(0,1)(2.3,0)\thinlines\qbezier (0,0)(0,0)(0.2,0.3)\qbezier (0.3,0.4)(0.3,0.4)(0.5,0.7)\qbezier (0.6,0.8)(0.6,0.8)(0.8,1.1)\qbezier (0.9,1.2)(0.9,1.2)(1.1,1.5)\qbezier (1.2,1.6)(1.2,1.6)(1.38,1.9)\put(0.2,1){\bold{4 \: units}}\end{picture}[/tex]
Solution :-
As per the provided information in the given question, we have been given that the radius of the sphere is 4 units. We have been asked to find or calculate the surface area of the sphere.
To calculate the surface area of the sphere, we will use the formula below :-
[tex]\bigstar \:\:\:\boxed{\sf{\:\:Surface \: Area_{(Sphere)} = 4\pi r^2 \:\:}}[/tex]
Substitute the given values into the above formula and solve for surface area:
[tex]\sf:\implies Surface \: Area_{(Sphere)} = 4\pi r^2[/tex]
[tex]\sf:\implies Surface \: Area_{(Sphere)} = 4 \times \pi \times (4 \: units)^2[/tex]
[tex]\sf:\implies Surface \: Area_{(Sphere)} = (4 \: units)^2 \times 4 \times \pi[/tex]
[tex]\sf:\implies Surface \: Area_{(Sphere)} = 16 \: units^2 \times 4 \times \pi[/tex]
[tex]\sf:\implies \bold{Surface \: Area_{(Sphere)} = 64\pi \: units^2}[/tex]
Therefore :-
The surface area of the sphere is 64π units².[tex]\\[/tex]
Learn more about the surface area of the sphere at https://brainly.com/question/28988747
Have a great day! <33
A rectangular prism has a height of 12 centimeters and a square base with sides measuring 5 centimeters. A pyramid with the same base and half the height of the prism is placed inside the prism, as shown in the figure
Answers
The answer is 200 cm³
The volume of the rectangular prism (V1) is:
V1 = l · w · h (l - length, w - width, h - height)
It is given:
h = 12 cm
w = l = 5 cm (since it has a square base which all sides are the same size).
Thus: V1 = 12 · 5 · 5 = 300 cm³
The volume of pyramid (V2) is:
V2 = 1/3 · l · w · h (l - length, w - width, h - height)
It is given:
h = 12 cm
w = l = 5 cm (since it has a square base which all sides are the same size).
V2 = 1/3 · 12 · 5 · 5 = 1/3 · 300 = 100 cm³
The volume of the space outside the pyramid but inside the prism (V) is a difference between the volume of the rectangular prism (V1) and the volume of the pyramid (V2):
V = V1 - V2 = 300 cm³ - 100 cm³ = 200 cm³
Solve for y in the following system of equations: −x+y=0 −2x+y=−5 1. 5 2. 7 3. 6 4. 5
Answers
Answer:
y = 5
Step-by-step explanation:
−x+y=0 −2x+y=−5
Multiply the first equation by -2
-2(-x+y=0)
2x-2y =0
Add this to the second equation
2x-2y =0
−2x+y=−5
-------------------
0x -y = -5
-y =-5
Multiply by -1
y = 5
-14 = x - 12 pls answer this if I can and check answer
Answers
Answer:
x = -2
Step-by-step explanation:
-14 = x - 12
-14 + 12 = x
-2 = x
check:
-14 = -2 - 12
Point K on the number line shows Kelvin's score after the first round of a quiz: A number line is shown from negative 10 to 0 to positive 10. There are increments of 1 on either side of the number line. The even numbers are labeled on either side of the number line. Point K is shown on 3. In round 2, he lost 9 points. Which expression shows how many total points he has at the end of round 2? 3 + (−6) = −9, because −9 is 6 units to the left of 3 3 + 6 = −9, because −9 is 6 units to the left of 3 3 + (−9) = −6, because −6 is 9 units to the left of 3 3 + 9 = −6, because −6 is 9 units to the left of 3
Answers
Answer:
The correct option is;
3 + (-9) = -6, because -6 is 9 units to the left of 3
Step-by-step explanation:
The given information are;
Kelvin's score after the first round is shown at point K on the number line
The range of numbers on the number line = -10 to +10
The position of point K after the first round = +3
The number of points Kevin lost in the second round = 9 points
Therefore, Kevin's cumulative score = +3 - 9 = -6
Therefore, the expression that shows how many total points he has at the end is of round 2 = 3 + (-9) = -6, because -6 is 9 units to the left of 3.
At a school carnival is the diameter of the map of a trampoline has 12 feet and the diameter of the metal frame is 14 feet what is the length in feet of the metal frame that's around the trampoline use 3.14 for pie and round the answer to the nearest 10th
Answers
Answer:
The length of the steel frame will be approximately 44 feet
Step-by-step explanation:
We can solve this problem by calculating the circumference of the steel frame. We are working with the fact that the steel frame was welded into a circular shape.
The circumference of the steel frame can be calculated using
[tex]circumference = \pi \times d[/tex]
where d diameter of the steel frame = 14 feet
[tex]circumference = 3.14 \times 14=43.96ft[/tex]
Therefore, the length of the steel frame will be approximately 44 feet
What is the center of a circle with the equation (x - 6)2 + (y + 2)2 = 9?
A)
(6,2)
B)
(6,-2)
0)
(-6, 2)
D)
(-6, -2)
Answers
Answer:
B. (6,-2)
Step-by-step explanation:
The equation of a circle is (x-h)^2+(y-k)^2=r^2
The center of the circle is (h,k)
So, in this problem, h is 6 and k is -2, so the center of this circle is (6,-2).
Line m and point P are shown below. Part A: Using a compass and straightedge, construct line n parallel to line m and passing through point P. Leave all construction marks. Part B: Explain the process that you used to construct line n.
Answers
Answer:
The steps to construct a a line parallel to another line from a point includes
1) From the given line draw a transversal through the point
2) With the compass, copy the angle formed between the transversal and the given line to the point P
3) Draw a line through the intersection of the arcs of the angle construction to get the parallel line through the point P
Step-by-step explanation:
Brooke is evaluating her college credit hours. In order to graduate, Brooke must complete at least 132 credit hours. She has already completed 4 semesters, receiving 15 credit hours per semester. Which inequality could be used to find c, the number of credit hours that Brooke needs to complete in order to graduate college? A. 4(15) + 4c > 132 B. 4(15) + c > 132 C. 4(15) + c < 132 D. 4(15) + 4c < 132
Answers
Answer:
B. 4(15) + c > 132Step-by-step explanation:
We already establish an understand that, for Brooke to graduate she needs nothing less than 132 credit hours.
Now a semester has 15 credit hours, she has 4 semester completed already.
Hence 15*4= 60 credit hours done and dusted
This means that she has 132-60 = 72 credit hours to go
Since "c" is the number of credit hours that Brooke needs to complete in order to graduate college.
The inequality can be modeled as,
4(15) + c > 13260 + c > 132
c= 132-60
c= 72
If x = 7, what is the value of 4(x - 5)
Answers
Answer:
8
Step-by-step explanation:
Because if x=7 then it would be 7-5 which equals 2 then you would times 2 and 4 together which equals 8 then you would have your answer which is 8.
Answer:
its 8
Step-by-step explanation:
x= 7
so replace the x with the value of 7
4(7-5)
7 minus 5 is 2
4·2
4 multipied by 2 is 8
so the answer is 8
What is the domain of F(x) = In(x)?
Answers
Answer as an inequality: [tex]x > 0[/tex]
Answer in interval notation: [tex](0, \infty)[/tex]
Answer in words: Set of positive real numbers
All three represent the same idea, but in different forms.
======================================================
Explanation:
Any log is the inverse of an exponential equation. Consider a general base b such that f(x) = b^x. The inverse of this is [tex]f^{-1}(x) = \log_b(x)[/tex]
For the exponential b^x, we cannot have b^x = 0. We can get closer to it, but we can't actually get there. The horizontal asymptote is y = 0.
Because of this, [tex]\log_b(x)[/tex] has a vertical asymptote x = 0 (recall that x and y swap, so the asymptotes swap as well). This means we can get closer and closer to x = 0 from the positive side, but never reach x = 0 itself.
The domain of [tex]\log_b(x)[/tex] is x > 0 which in interval notation would be [tex](0, \infty)[/tex]. This is the interval from 0 to infinity, excluding both endpoints.
------------------------
The natural log function Ln(x) is a special type of log function where the base is b = e = 2.718 approximately.
So,
[tex]\log_e(x) = \text{Ln}(x)[/tex]
allowing all of what was discussed in the previous section to apply to this Ln(x) function as well.
------------------------
In short, the domain is the set of positive real numbers. We can't have x be 0 or negative.
Get this correct i will give u brainliest.
Answers
Answer:
x = - 2, y = - 8
Step-by-step explanation:
Given the 2 equations
13x - 6y = 22 → (1)
x = y + 6 → (2)
Substitute x = y + 6 into (1)
13(y + 6) - 6y = 22 ← distribute and simplify left side
13y + 78 - 6y = 22
7y + 78 = 22 ( subtract 78 from both sides )
7y = - 56 ( divide both sides by 7 )
y = - 8
Substitute y = - 8 into (2) and evaluate for x
x = - 8 + 6 = - 2
Thus x = - 2, y = - 8
What does 6x − 9 = 45 equal?
Answers
Answer:
9
Step-by-step explanation:
Add nine to both sides:
[tex]6x = 54[/tex]
Divide by six:
[tex] \frac{6x = 54}{6} [/tex]
[tex]x = 9[/tex]
Answer:
x = 9
Step-by-step explanation:
Add 9 to each side to begin simplifying. It should now look like this: 6x = 54Now, divide each side by 6 to find the value of x. It should look like this: x = 9I hope this helps!
There are several sets of different numbers which can be chosen from {0,1,2,3,4,5,6,7,8,9}. c How many of these sets contain any 4 numbers?
Answers
Answer: The number of sets contain any 4 numbers = 210
Step-by-step explanation:
Given: Universal set = {0,1,2,3,4,5,6,7,8,9}.
i.e. Total choices = Numbers in set = 10
By combinations, the number of sets contain any 4 numbers =[tex]^{10}C_4[/tex]
[tex]=\dfrac{10!}{4!6!}\ \ \ \ \ [^nC_r=\dfrac{n!}{r!(n-r)!}]\\\\=\dfrac{10\times9\times8\times7\times6!}{4\times3\times2\times1 \times6!}\\\\=210[/tex]
Hence, the number of sets contain any 4 numbers = 210
Use distributive property to simplify the following expression. 2(4+9w)
Answers
Answer:
18w+8
Step-by-step explanation:
[tex]2(4 + 9w) \\ = 2(4) + 2(9w) \\ 8 + 18w \\ = 18w + 8[/tex]
Answer:
8+18w [tex]\huge\checkmark[/tex]
Step-by-step explanation:
Hi! Hope you are having an amazing day! :)
Distribute 2 by multiplying everything inside the parentheses by 2:
[tex]\huge\mathrm{2(4+9w)}[/tex]
[tex]\huge\mathrm{8+18w}[/tex] (Answer)
Hope you find it helpful.
Feel free to ask if you have any doubts.
[tex]\bf{-MistySparkles^**^*}\star[/tex]
22.
A map has a scale of 1 inch : 20 miles. If two
cities are 240 miles apart, how far apart are
they on the map?
NEED HELP FAST!!
Answers
Answer:
12
Step-by-step explanation:
1 inch = 20 miles
240 miles ÷ 20 miles =
12 inches
Answer:
12 inches
Step-by-step explanation:
Hey there!
Well to solve the given question we need to use fractions,
if 1 inch is 20 milles, we can set up the following.
[tex]\frac{1}{20} = \frac{x}{240}[/tex]
Cross multiply
240 = 20x
Divide both sides by 20
x = 12
So it is 12 inches in the map.
Hope this helps :)
if one of the numbers 1 to 20 is chosen at random what is the probability that it is either a multiple of 3 or a multiple of 5 or both?
Answers
Answer:
45% that either would occur, or a 5% chance both would occur.
Step-by-step explanation:
There is one overlap, 15, so it must be subtracted from one of the number lists.
3 6 9 12 15 18
5 10 15 20
6/20 + 3/20 = 9/20 = 0.45 = 45%
15 is the ONLY overlap number, so 1/20 times both would occur.
1/20 = 0.05 = 5%
equation y = (2x)/(x-1), how do I get -0.5 as the x intercept ???
Answers
Answer:
( 0,0) is the x intercept
Step-by-step explanation:
y = (2x)/(x-1),
To find the x intercept set y = 0 and solve for x
0 = (2x)/(x-1)
Multiply by x-1 on each side assuming x does not equal 1
0 = 2x
x = 0
The x intercept is 0
( 0,0) is the x intercept
What is the slope of the line?
A) -1/3
B) 1/3
C) -3
D) 3
Answers
Answer:
Hey there!
A simple way to think about slope is rise over run. Between any two points on this line, the rise is 3, and the run is -1.
3/-1=-3, so the slope is -3.
Let me know if this helps :)
Find the value of x so that the function has the given value.
j(x)=−4/5x+7; j(x)=−5
x=
Answers
Answer:
x = 3
Step-by-step explanation:
j(x) = 4/5(-5) + 7
= -4 + 7
= 3
Answer:
15
Step-by-step explanation: -4/5 x has to be -12 because -12+7 equals 5. Since we want to figure out x, we have to flip -4/5 x to 4/5x which would change the -12 to 12. What is a fourth of 12? It is three. 12+3 equals 15. This is the first right answer on all of the internet for this question!
One type of fabric costs $31.25 for 5 square yards. Another type of fabric costs $71.50 for 11
square yards. Is the relationship between the number of square yards and the cost
proportional between the two types of fabric?
Answers
Answer:
as ratio of two type of fabric is different .
hence, the relationship between the number of square yards and the cost
is not proportional between the two types of fabric
Step-by-step explanation:
For a relation to be proportional
a:b = c:d
in other form
a/b = c/d
______________________________________________
Ratio for first type of fabric
cost of fabric/ area of fabric = 31.25/5 = 6.25
Ratio for other type of fabric
cost of fabric/ area of fabric = 71.50/11 = 6.5
as ratio of two type of fabric is different .
hence, the relationship between the number of square yards and the cost
is not proportional between the two types of fabric
