100 points
Find the Surface area of a right rectangular pyramid 50 points for explaining in full the equation of how.
L= 7
W= 5
H= 12
100 points explaining the equation for volume too.
Answers
Step-by-step explanation for Surface Area:
So, to find the surface area, you use the formula: [tex]A=lw+l\sqrt{(\frac{w}{2})^2 +h^2 } +w\sqrt{(\frac{l}{2})^2 +h^2 }[/tex]
I'll explain what each part means and why they are like that. (btw, it would help you more if you looked at a rectangular prism I added while you read the explanation :) )
First of all, you do lw because that is the base of the right rectangular pyramid (since you're finding the surface area, you need to find the area of all the surfaces on the pyramid)
You add [tex]l\sqrt{(\frac{w}{2})^2 +h^2 }[/tex] because now you're trying to find the triangular side with the length. You multiply the length, because that's how wide the "triangle" is. You do the square root because of the pythagorean theorem (since you're using the hypotenuse times the length to find that side). The width is divided by two, because as you can see in my attachments, that's how far away the height is from the length (if you look at the base, see where the height line drops in comparison to the length). (look at my second screenshot)
You add [tex]w\sqrt{(\frac{l}{2})^2 +h^2 }[/tex] for the same reason, except dealing with the width. You're finding the side with the width. You multiply the width by the hypotenuse of the right triangle (look at the third screenshot i attached). The length is divided by two because that's the distance between the bottom of the height line to the w.
I do believe that this should explain the meaning behind each piece of the formula (I'm not sure this is what you asked for lol but it does make understanding it a little easier, I think). To get the answer, you just substitute each variable with those values. So...
[tex]A=(7)(5)+(7)\sqrt{(\frac{(5)}{2})^2 +(12)^2 } +(5)\sqrt{(\frac{(7)}{2})^2 +(12)^2 }[/tex]
A ≈ 183.3
As for the Volume:
[tex]V=\frac{lwh}{3}[/tex]. I'm not 100% on why it's divided by three, but with any volume, you're always going to end up with an answer that is in cubed units. So that explains the three variables in the numerator. I'd like to think the three just has to do with the three variables, but I don't know. Give me the points if you'd like? I don't think this is a proper explanation though.
Good luck!
Answer:
volume = 140 cubic units
area = 183.3 square units
Step-by-step explanation:
I am going to assume we are dealing with a pyramid with a rectangular base. The rectangular base has length 7 units, width 5 units, and height 12 units.
Let's do the volume first since it's simpler.
Volume:
volume of pyramid = (1/3) * (area of base) * height
volume = (1/3) * 7 units * 5 units * 12 units
volume = 140 cubic units
Now we deal with the surface area.
The total surface area of a rectangular pyramid is the sum of the lateral area and the area of the base. The area of the base is the area of a rectangle. The lateral area is the sum of the areas of the 4 triangular sides. Each two opposite sides are congruent. For the base, we have the length and width of the rectangular base, so we can find the area easily.
For the 4 triangular sides, we need to find the the height of the triangles. Since each pair of opposite faces is congruent, we have two triangles we need to find the heights for. I'll call the heights "p" and "q". We use the Pythagorean theorem to find the heights of the triangular faces.
a^2 + b^2 = c^2
(3.5)^2 + (12)^2 = p^2
p^2 = 156.25
p = 12.5
(2.5)^2 + (12)^2 = q^2
q^2 = 150.25
q = 12.25765
Area of triangle = (1/2) * base * height
For two triangles, the base is 5 and the height is 12.5.
For the other two triangles, the base is 7 and the height is 12.25765.
total surface area = area of base + 2(area of triangle with base 5) + 2(area of triangle with base 7)
A = LW + 2(1/2)(base)(height) + 2(1/2)(base)(height)
A = 7(5) + 2(1/2)(5)(12.5) + 2(1/2)(7)(12.25765)
A = 183.3 square units
Related Questions
Robert wants to buy lights around the edge of his deck the deck is 49feet and 26feet wide how many yards of lights does he need
Answers
Answer:
150 feet
Step-by-step explanation:
Assuming the deck is a rectangle, you need to multiply each side by 2 and add them together.
Answer:
50 yards
Step-by-step explanation:
Let l = length, w = width, and P = perimeter in feet. Let x equal perimeter in yards.
To solve this problem, we first need to find the perimeter of the deck.
To do so, use the formula 2l + 2w = P.
Since the deck is 49 feet long and 26 feet wide, plug in 49 for l and 26 for w.
2(49) + 2(26) = P
Evaluating 2*49 and 2*26, the equation becomes 98 + 52 = P.
Evaluating 98 + 52, the equation becomes 150 = P.
The next step in this problem is to convert feet to yards. We know that Robert needs 150 feet of lights. Since there are three feet in a yard, we can use the formula P = 3x to find the amount of yards of lights Robert needs.
Plugging in 150 for P, the equation becomes 150 = 3x.
Dividing both sides by 3, the equation becomes 50 = x.
Therefore, the final answer is 50 yards.
Mathematical name of the shapes
Answers
Answer:
A: Triangular Prism B:Cuboid
Step-by-step explanation:
I hope this helps! ^_^
Rafael is ordering an ice cream dessert. He must order a size, a flavor of ice cream, and a topping. There are 3 sizes, 3 flavors, and 1 topping to choose from. How many different ice cream desserts could he order?
Answers
Answer:
9
Step-by-step explanation:
Multiply the number of sizes by flavors, the by toppings.
3*3*1
please give me a hand
Answers
Answer:
x=5? im not really sure what the question is its all fuzzy
Step-by-step explanation:
Your answer is x = 9.
To solve this equation we just need to expand the brackets and then rearrange the equation to have x on one side and the numbers on the other:
2(x + 5) - 7 = 3(x - 2)
2x + 10 - 7 = 3x - 6
2x + 3 = 3x - 6
- 2x
3 = x - 6
+ 6
9 = x
I hope this helps!
Drag numbers to the table so it shows a proportional relationship between x and y.
Answers
Answer:
0.8 4
3.2 16
12.8 64
Step-by-step explanation:
Proportional means that it will have a constant rate of change. If we divide 4/0.8 in the first example, we get 5. In the second example, we need to find x/3.2=5. 16/3.2=5. In the third example, we need to find 2 numbers divided by each other that equals 5. 64/12.8=5
Answer:
0.8 4
3.2 16
12.8 64
Step-by-step explanation:
A side of a square piece of cloth has a length of 12 inches what is the area of the piece of cloth
Answers
Answer:
144 inches squared
Step-by-step explanation:
multiply 12 by 12
Therefore, the answer is 144.
6. Find the lateral area and surface area of the
cylinder. Round to the nearest tenth.
12 cm
6 cm
Answers
Answer:
I don't know
Step-by-step explanation:
i don't know
i don't know
i don't know
i don't know
The results of a survey show that the percent of adults in a certain town who want to add bike lanes to a major roadway is in the interval (0.47, 0.63)
(a) What is the point estimate for the percent who want to add the bike lanes?
(b) What is the poll’s margin of error?
(c) If the town’s adult population is 75,783, what is the best estimate for the number of people who would support the bike lanes?
Answers
Answer:
a) [tex]\hat p =\frac{Upper+Lower}{2}= \frac{0.47+0.63}{2}= 0.55[/tex]
b) [tex] ME = \frac{Upper-Lower}{2}= \frac{0.63-0.47}{2}= 0.08[/tex]
c) For this case in order to find the number of people who would support the bike lanes we just need to multiply the estimated proportion by the total size and we got:
[tex] X = 0.55* 75783= 41680.65 \approx 41681[/tex]
Step-by-step explanation:
For this case we have an interval for the true proportion of adults in a certain town who want to add bike lanes to a major roadway:
[tex] 0.47 \leq p \leq 0.63[/tex]
Part a
For this case the point of estimate is given by:
[tex]\hat p =\frac{Upper+Lower}{2}= \frac{0.47+0.63}{2}= 0.55[/tex]
Part b
We can estimate the margin of error with this formula:
[tex] ME = \frac{Upper-Lower}{2}= \frac{0.63-0.47}{2}= 0.08[/tex]
Part c
For this case in order to find the number of people who would support the bike lanes we just need to multiply the estimated proportion by the total size and we got:
[tex] X = 0.55* 75783= 41680.65 \approx 41681[/tex]
A line graph has Number of Turns of a Large Tire on the x-axis, and Number of Turns of a Small Tire on the y-axis. For every 2 turns on a large tire, there are 10 turns on a small tire; 4, 20; 6, 30; 8, 40. Find the constant of proportionality from the proportional relationship shown on the graph.
Answers
Answer:
5
Step-by-step explanation:
PLZ HELP ME I WILL GIVE BRAINLIEST....
A scientist wants to find the average mass of fish living in a large pond. So she will use the masses of a sample of fish from the pond to find the average mass.
Answer the questions below.
(a) Which unit(s) could be used for the unit of measurement? Check all that apply.
1.) minutes
2.) kilograms
3.) grams
4.) milligrams
5.) seconds
(b) Which of the procedures below would be the best way to find the average mass?
1.) Pick 2 fish from a shallow region of the pond and weigh each of them.
2.) Pick 42 fish from a shallow region of the pond and estimate their masses.
3.) Randomly pick 2 fish from the entire pond and estimate their masses.
4.) Randomly pick 42 fish from the entire pond and weigh each of them.
Answers
Answer:
A. 2, 3, and 4
B: 4
Step-by-step explanation:
Average mass is defined as, adding masses of all bodies and then divide by number of bodies.
(a). Kilograms, grams and milligrams
(b) Randomly pick 42 fish from the entire pond and weigh each of them.
(a). Since we are interested in the masses of the fish and not the time
so that, only unit of mass is to be considered.
Therefore, Kilograms, grams and milligrams are used to find the average mass.
(b). Since, Random sampling is a part of the sampling technique in which each sample has an equal probability of being chosen
Therefore, Randomly pick 42 fish from the entire pond and measure their masses. This will provide a representative sample with no bias.
Learn more:
https://brainly.com/question/18060320
Evaluate
√18/30= what numders
Answers
Answer:
0.77745966692... (a repetitive decimal)
Rounded to the nearest hundredth is 0.78.
Step-by-step explanation:
Divide 18/30 which is 0.6.
You can use the calculator to square root 0.6.
The finalized answer is 0.777459666924...
Whether you decide to round it is up to you.
Analyze the set below and complete the instructions that follow.
C= {x|x<-42}
Use set-builder notation to define the complement of the set. U=R.
A. C^c=Ø
B. C^c={c|c<=-42}
C. C^c={x|x>=-42}
D. C^c={x|xeR}
Answers
Answer:
C
Step-by-step explanation:
Given: the set is defined as [tex]C=\left \{ x|x<-42 \right \}[/tex]
To find: Set builder form of the complement of the set C.
Solution:
A set is a well-defined collection of objects. Set-builder form is used to denote the elements of the set. This form can also be used to express sets using an interval or an equation.
Complement of set A refers to elements not in A.
For [tex]C=\left \{ x|x<-42 \right \}[/tex],
[tex]C^c=\left \{ x|x\geq -42 \right \}[/tex]
Option C is correct.
Which function best models the data?
y = 9,958(0.972)
y = 0.972(9,958)
y = 9,219x= 150
y = -150x + 9,219
Answers
Answer:
A. y= 9,958(0.972)
Step-by-step explanation:
Answer:
A. y= 9,958(0.972)
Step-by-step explanation:
Please help me with this question.
Answers
First, plug in the radius and height into the equation. V=1/3pi*4^2*9
Next solve. 3.14 x 16 x 9 = 452.16
Then you need to divide 452.16 by 3 to get 150.72
Answer:
150.72
Step-by-step explanation:
v=1/3 * 3.14 *4² * 9
v=1/3 * 3.14 * 16 * 9
v=1/3 * 50.24 * 9
v=1/3 * 452.16
v=150.72
What two geometric properties do all polygons share?
Answers
Answer:
all sides equal and.
all angles equal.
Which of the following people would be considered an American citizens by birth ?
Answers
What is the third term when you complete the square for the polynomial
x^2 + 8x?
4
8
16
64
Answers
Answer:
x^2 + 8x+16 is (x+4)^2
Step-by-step explanation:
Which equation demonstatres the distributive property?
A. 39 + 9 = 45
B. 39 + 3 = 39(12 + 3)
C. 36 times 9 = 9 times 36
D. (12 + 3)3 = 3(12 + 3)
Answers
Answer:
B
Step-by-step explanation:
The distributive property states that:
a(b + c) = ab + ac
Look at the choices:
A: 39 + 9 = 45
There's nothing of this form; in fact, there aren't even any parentheses, so eliminate A.
C: 36 times 9 = 9 times 36
This is saying 36 * 9 = 9 * 36. Again, there aren't any parentheses. Actually, this demonstrates the commutative property.
D: (12 + 3)3 = 3(12 + 3)
There are parentheses, but they're on both sides, so this can't be right, either. In fact, this is the associative property.
By elimination, the answer is thus B.
The rule of distributive property states that [ a(b + c) = ab + ac ].
So, we need to find an answer choice that contains that specific format.
Option A is incorrect because there is nothing to solve for on the right side.
Option B is correct because it contains the same format as the rule stated above.
Option C is incorrect because its the same as [ 36 * 9 = 9 * 36 ] and it's not in the same format as the rule.
Although Option D has half of the format in the rule, it doesn't have the other half containing what it looks like after the distributive property is appplied. So, this is incorrect as well.
Therefore, the answer is B.
Best of Luck!
Adam went on a 54 \text { km}54 km54, start text, space, k, m, end text hike. He divided the distance traveled evenly over 666 days. How many meters did Adam walk each day?
Answers
Answer:
9000 metres
Step-by-step explanation:
He went on a 54 km hike. First, we have to find this distance in metres.
1 km = 1000 m
54 km = 54 * 1000 = 54000 m
He divided the distance evenly over 6 days.
To find how many metres he walked each day, we divide the total distance he hiked by the number of days spent. That is:
54000 / 6 = 9000 metres
He walked 9000 metres each day.
Select the condition for which it is NOT possible to construct a triangle.
A triangle with side lengths 4 cm, 5 cm, and 6 cm
A triangle with side lengths 4 cm, 5 cm, and 15 cm
A triangle with side lengths 4 cm and 5 cm and an included 50°angle
A triangle with angle measures 30° and 60°, and an included 3 cm side length .
Answers
Answer:
A triangle with side lengths 4 cm, 5 cm, and 15 cm
Step-by-step explanation:
In order to form a triangle with given side lengths, sum of any two sides must always be greater than the third side.
[tex]4+5= 9\ngtr 15\\[/tex]
an event with a probability of 0 is called
A.certain
B.likely
C.impossible
Answers
Answer:
c
Step-by-step explanation:
it is impossible with a probability of 0
Answer:
Option C
Step-by-step explanation:
An event with a probability of 0 is impossible. There is no chance of the event happening. This makes A and B wrong.
The correct answer is C.
Brainilest Appreciated!
Anyone know the answer and explanation? thank you!!
Answers
Answer:
The answer is 10
Step-by-step explanation: So first we divided 15 by 3 which is 5. Then we times 4 and 5 which is 20. 10+x=20, so x = to 10
Answer:
x = 10
Step-by-step explanation:
4/3 = (x+10)/15
Using cross products
15*4 = 3*(x+10)
60 = 3(x+10)
Divide each side by 3
60/3 = 3/3(x+10)
20 = x+10
Subtract 10 from each side
20-10 = x+10-10
10 = x
An electric motor pumps water into a pool at a rate of 500 liters per hour. After a tune up, its rate increases by x liters per hour. If the motor now takes 3 hours to pump 1800 liters, in which equation does x represent the increase in speed after the tune up?
Answers
Answer: 3(500+x)=1800
A cyclist travels 45 miles in 3 hours. What is the cyclist's speed?
Hint: Use the formula: d = r x t (distance = rate x time)
Remember that division and multiplication are INVERSE operations. So, 45 = r x 3
so you will have to divide the distance by the time to get the rate.
45 ÷ 3 to find the rate
A: 15 miles per hour
B: 12 miles per hour
C: 16 miles per hour
Answers
Answer:
15
Step-by-step explanation:
you would divide 45 and 3 to get 15 miles per hour
Evaluate the expression when a=-15 and b=-5 .
b+14
----------
3
Answers
Step-by-step explanation:
I'm not 100% sure but I believe the answer is 6 and 1/3
If a question says an item is marked down by 35%
a) what percentage would you actually be paying of the original price
b) how would you write that as a decimal
**Both answer will be written as part of the answer part A/part B**
Answers
Answer:
a) 65%
b) .65
~ Please mark as brainliest :)
PLZ HELP ME!! I’m If you horizontally shift the absolute value parent function, F(x) = |xl, left three
units, what is the equation of the new function?
Answers
Answer:
g(x) = |x+3|
Step-by-step explanation:
Within the parentheses, it'll go left or right, outside of it, it'll go up or down
tell whether the events are independent or dependent.Then find P(A and B)...You roll a number cube two times.Event A:You roll an odd number on the first roll.Event B:You roll a 4 on the second roll.
Answers
Answer:
Some probability situations involve more than one event. When the events do not affect one another, they are known as independent events. Independent events can include repeating an action like rolling a die more than once, or using two different random elements, such as flipping a coin and spinning a spinner. Many other situations can involve independent events as well. In order to calculate probabilities accurately, we need to know if one event influences the outcome of other events.
Answer:
The outcome of the first roll does not affect the probabilities of the outcomes for the second roll. Therefore, these events are independent.
Step-by-Step Explanation:
The events are independent since the person rolling had rolled a number cube twice, not switching it for the two events.
3х +2y = 12 + у
4y — 7t = 10
Solving systems of equations
Answers
numbers 3x + 2y = 12
y = x + 1
Substitution Method
Since y is already isolated in the second equation we can use that value, to substitute for y in the first equation.
3x + 2 (x + 1) = 12
3x + 2x + 2 = 12
5x = 12 − 2
5x = 10
x = 2
Substitute the computed value of x to the second equation to determine the value of y.
y = 2 + 1
y = 3
Elimination Method
3x + 2y = 12
x − y = −1
Multiply the second equation by 2 to eliminate
x or you can also multiply the second equation by 3 to eliminate y. However since it is easier to multiply by 2, I will follow the first method.
3x + 2y = 12
2x − 2y = −2
Adding the two equations eliminates the y variable.
5x = 10
x = 2
Substitute the computed value of x to the second equation to determine the value of y.
y = 2 + 1
y = 3
Solution Set:
(2,3)
Graph the function and identify the domain and range. y=-4x^2
Algebra test unit:4 lesson:10
Quadratic Functions and Equations Unit Test Part 1
1.C, 2.B, 3.A, 4.C, 5.B, 6.A, 7.A, 8.B, 9.C, 10.B, 11.D, 12.A, 13.B, 14.B, 15.C, 16.C, 17.B, 18.C, 19.D, 20.B, 21.C,
Answers
Answer:
Domain: All real numbers, Range: All real numbers greater or equal to 0.
Step-by-step explanation:
A second order polynomial is a continuous function and therefore, domains is the set of all real numbers. Lastly, the range of the function according to the graph is all values of x greater or equal to 0. The positive leading coefficient of the polynomial indicates the existence of an absolute minimum.
The graph of function is attached below.
Domain of function is, (-∞ ,∞ )
Range of function is (-∞, 0)
Domain and range :The domain of function is defined as all input values to a function, for which function is defined.
Range of the function is output values to a particular input value.
Given function is,
[tex]y=-4x^{2}[/tex]
This open down parabola.
Domain of function is, (-∞ ,∞ )
Range of function is (-∞, 0)
The graph of function is attached below.
Learn more about the domain and range of function here:
https://brainly.com/question/1942755