Answer:
The lateral surface area of the rectangular pyramid is equal to sum of area of 4 lateral triangles.
Here, the base is square, then 4 lateral triangles have equal area.
=> Lateral surface area of this rectangular pyramid:
A = (area of lateral triangle) x 4
= (12 x 14 x 1/2) x 4 = 336 (ft2)
=> Option C is correct.
Hope this helps!
:)
The lateral surface area of the given rectangular pyramid is 336 ft²
What is lateral surface area?The lateral surface of an object is all the sides of the object, excluding its base and top.
The lateral surface area is the area of the lateral surface. This is to be distinguished from the total surface area, which is the lateral surface area together with the areas of the base and top.
Given that, a rectangular pyramid, we need to find the lateral surface area of the rectangular pyramid,
The lateral surface area of the rectangular pyramid is equal to the sum of area of 4 lateral triangles.
Here, the base is square, then 4 lateral triangles have equal area.
Therefore, the lateral surface area of this rectangular pyramid:
A = (area of lateral triangle) x 4
= (12 x 14 x 1/2) x 4
= 336 ft²
Hence, the lateral surface area of the given rectangular pyramid is 336 ft²
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Benjamin started her walk from the front door of her ground floor apartment. She walked 6 meters to the corner of the building and then turned the corner and walked 10 meters to her friend's apartment.
Answer:
4 meters.
Step-by-step explanation:
Benjamin has walked two legs of a right triangle, so you can connect her two movements with a line if you were sketching the situation.. The displacement is the objects overall change in position in relation to its origin, so in your case, Benjamin's apartment. While the total distance adds up regardless of her position.
So, the total distance Benjamin walked is 10m + 6m = 16m
Her displacement can be found by your best friends, the Pythagorean Theorem: 10m ^2 + 6m ^2 = delta x^2 (or displacement squared).. giving you a displacement of 11.66, or 12 m.
The difference between the distance she walked and her displacement is 4 meters.
I hope this helps. If you have any more questions, please feel free to post them and someone will be able to help you, whether it's myself or others. Please leave a like, rating, and if possible, Brainliest. Have a great day!
The owner of the Rancho Grande has 3,060 yd of fencing with which to enclose a rectangular piece of grazing land situated along the straight portion of a river. If fencing is not required along the river, what are the dimensions (in yd) of the largest area he can enclose?
Answer:
1170450 yd^2
Step-by-step explanation:
The first thing is to calculate the necessary perimeter, which would be like this:
2 * a + b = 3060
if we solve for b, we are left with:
b = 3060-2 * a
Now for the area it would be:
A = a * b = a * (3060-2 * a )
A = 3060 * a -2 * a ^ 2
To maximize the area, we calculate the derivative with respect to "a":
dA / da = d [3060 * a -2 * a ^ 2
]/gives
dA / day = 3060 - 4 * a
If we equal 0:
0 = 3060 - 4 * a
4 * a = 3060
a = 3060/4
a = 765 and d
Therefore b:
b = 3060 - 2 * a = 3060 - 1530 = 1530
A = a * b
A = 765 * 1530
A = 1170450 and d ^ 2
Final answer:
To find the largest area the owner of the Rancho Grande can enclose, we set up an equation using the perimeter of the rectangular land and the available fencing. By solving the equation and finding the maximum point of a quadratic equation, we determine that the dimensions of the largest area are L = 765 yd and W = 1,530 yd.
Explanation:
To find the dimensions of the largest area the owner of the Rancho Grande can enclose, we need to consider that the rectangular grazing land is situated along the straight portion of a river. Since fencing is not required along the river, the owner can use the available fencing to enclose the other three sides of the rectangular piece of land.
Let's assume the length of the rectangular piece of land is L and the width is W.
Since there are three sides that require fencing, the perimeter of the rectangular piece of land is given by:
P = L + W + L = 2L + W
According to the information provided, the owner has 3,060 yd of fencing available. Therefore, we can write the equation:
2L + W = 3,060
To maximize the area, we need to solve this equation for one variable and substitute it back into the area formula, A = L * W. Let's solve for L:
2L = 3,060 - W
L = (3,060 - W)/2
Substituting L in the area formula:
A = ((3,060 - W)/2) * W
Finally, we can maximize the area by finding the maximum point of the quadratic equation:
A = -0.5W^2 + 1,530W
The maximum point of a quadratic equation in the form A = ax^2 + bx + c occurs at x = -b/2a.
Comparing the quadratic equation to A = -0.5W^2 + 1,530W, we have:
a = -0.5
b = 1,530
Substituting these values into x = -b/2a:
W = -1,530 / (2 * -0.5)
Calculating W:
W = 1,530 / 1
W = 1,530
Now, substituting W back into the equation for L:
L = (3,060 - 1,530) / 2
L = 1,530 / 2
L = 765
Therefore, the dimensions of the largest area the owner of the Rancho Grande can enclose are L = 765 yd and W = 1,530 yd.
The list shows the number of contacts six people each have stored in the their cell phone: 68, 72, 77, 64, 69, 76. What is the mean absolute deviation for this set of data? will mark brainliest if correct
a- 71
b- 24
c- 4
d- 13
Final answer:
This answer explains how to calculate the Mean Absolute Deviation (MAD) for a given data set and determines the MAD for the provided set of numbers.
Explanation:
Mean Absolute Deviation (MAD) measures the average difference between each data point and the mean of the data set.
To calculate MAD:
Find the mean of the data set: (68 + 72 + 77 + 64 + 69 + 76) / 6 = 72.67
Find the absolute difference for each data point: |68 - 72.67|, |72 - 72.67|, |77 - 72.67|, |64 - 72.67|, |69 - 72.67|, |76 - 72.67|
Add up all the absolute differences and divide by the total number of data points: (4.67 + 0.67 + 4.33 + 8.67 + 3.67 + 3.33) / 6 = 4.67
The Mean Absolute Deviation for the given data set is 4.67. Therefore, option c- 4 is the correct answer.
Examine the diagram. It is not drawn to scale.
A triangle has angles A, C, 57 degrees. The exterior angle to angle A is B and the exterior angle to angle C is 118 degrees.
Use the measurements provided in the diagram to determine the measure of AngleB.
mAngleB =
°
E DGENUITY
Answer: 119
Step-by-step explanation: got it right
In the given figure, measure of angle A is 61°, measure of angle B is 119° and measure of angle C is 62°.
From the given triangle triangle, exterior angle to the angle C is 118°.
We know that, sum of two adjacent angles is 180°.
Here, ∠C+118°=180°
∠C=180°-118°
∠C=62°
By using exterior angle theorem of triangle, we get
∠A+57°=118°
∠A=118°-57°
∠A=61°
So, ∠A+∠B=180° (Adjacent angles)
61°+∠B=180°
∠B=180°-61°
∠B=119°
Therefore, in the given figure, measure of angle A is 61°, measure of angle B is 119° and measure of angle C is 62°.
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Which of the following is the coordinate for the image of point M(3, –7) after a 90° clockwise rotation? a.)M’(–7, –3) b.)M’(7, –3) c.)M’(7, 3) d.)M’(–7, 3)
M,(-7, -3)
Step-by-step explanation:
Answer:
M,(-7, -3) i took the quiz liker 5 seconds ago
The function f(x)=2.5x can be used to represent the curve through the points (1, 10), (2, 50), and (3, 250). What is the multiplicative rate of change of the function?
Answer:
The answer is 5.
Step-by-step explanation:
Multiplicative rate of change can be described as the rate change based on a original amount or point.
If we look at the given points for the function f(x) = 2.5x, we can see that the x coordinates increase by one while the y coordinate is increasing by 5 times it's value for the previous point.
So we can say that the multiplicative rate of change is 5 for the function f(x) = 2.5x.
I hope this answer helps.
the answer is(b) 5 got it right on the test
What is the scale factor in the dilation?
What is the area of the following circle?
Either enter an exact answer in terms of it or use 3.14 for IT and enter your answer as a decimal.
r = 7
Answer:
A =153.86
Step-by-step explanation:
The area of a circle is given by
A = pi r^2
We know pi = 3.14 and the radius is 7
A = 3.14 * 7^2
A =153.86
HELP PLZ I DONT GET THIS AGT ALL I SUCK AT MATH :( I REALLY NEED HELP CAN SOMEONE HELP PLZ
Answer:
£94
Step-by-step explanation:
Basically, we want to find the surface area of this cylinder.
The surface area of a cylinder is denoted by: A = 2πr² + 2πrh, where r is the radius and h is the height. However, note that the farmer only wants to paint the curved surface of the cylinder, so we don't want to include the 2πr² part that accounts for the two circular bases. Instead, we actually just want to find the value of 2πrh.
Here, we see that the diameter is 8 metres, so since the radius is half the diameter, we know that r = 8/2 = 4 metres.
We also see that the height is 6 metres, so h = 6.
Plug these numbers in:
2πrh
2π * 4 * 6 = 48π ≈ 150.8 m²
We see that each can of paint will cover 20 m², so divide 150.8 by 20 to find the number of cans we need:
150.8 ÷ 20 = 7.5 ≈ 8 cans
Each can costs £11.75, so multiply 8 by 11.75 to get the total cost:
11.75 * 8 = £94
The answer is £94.
Answer:
94 euros is the answer, plez mark as brainliest ty big brain man
Step-by-step explanation:
Can someone plz help ne
Answer:
38.5
Step-by-step explanation:
The perimeter is found by
P = 2( l+w)
We know the width is 23, we are looking for the length
P = 2 (23+l)
The perimeter is 123
123= 2 (23+l)
Divide each side by 2
123/2 = 23+l
61.5 = 23+l
Subtract 23 from each side
61.5 -23 = l
38.5 = l
The length of AB = 38.5
Answer the following questions about the problem above. Write in complete sentences to get full credit.
1. What is the slope for section "b" of Mrs. Washington's commute.
2. What is the slope for section "c" of Mrs Washington's commute?
3. Explain the difference in "b" and "c" in context of Mrs. Washing driving home.
4. How far does Mrs. Washington live from her work?
Answer:
1. -1
2. -1/4
3. As the line nears closer to y = 0, Mrs. Washington is getting closer to her house. As such, the line represents miles driven per minute, representing speed. As the slope of the line becomes steeper, as it does during section B of the commute, Mrs. Washington is driving one mile per minute, or 60 miles per hour. As she drives through section C, she only drove 1 mile after 4 minutes, or 15 miles per hour.
4. She lives 20 miles from her office.
Step-by-step explanation:
1. You can find the slope for section B of the commute by taking two points in section B and using them to find the slope.
I will take (10, 13) and (14, 9) as my points.
You can use [tex]\frac{y2-y1}{x2-x1}[/tex] to find the slope:
[tex]\frac{13-9}{10-14} \\\\\frac{4}{-4}[/tex]
The slope for section b is -1.
2. You can find the slope for section C using the same method.
I will use the points (16, 7) and (20, 6):
[tex]\frac{7-6}{16-20} \\\\\frac{1}{-4}[/tex]
The slope for section c is -1/4.
3. As the line nears closer to y = 0, Mrs. Washington is getting closer to her house. As such, the line represents miles driven per minute, representing speed. As the slope of the line becomes steeper, as it does during section B of the commute, Mrs. Washington is driving one mile per minute, or 60 miles per hour. As she drives through section C, she only drove 1 mile after 4 minutes, or 15 miles per hour.
4. She lives 20 miles from her office. This is stated in the question itself.
Answer:
1. Speed = 1 mph
2. ¼ mph
3. She's driving at 4 times faster speed in b than c
4. 20 miles
Step-by-step explanation:
1. Slope of a distance time graph is the speed
(15-7)/(16-8)
8/8
1 mph
2. Speed = (7-6)/(20-16)
1/4 mph
3. Speed in b is greater than c
1 = 4(¼)
4. Distance from 20 to 0, is 20 miles
The polynomial p(x)=x^3-7x-6 has a non-factor of (x+1) rewrite p(x) as a product of linear factors.
Answer:
Using synthetic division suffices to answer your question:
Step-by-step explanation:
Synthetic division is the process by one reduces a large polynomial in your case [tex]x^3-7x-6[/tex] by a binomial in your case [tex](x+1)[/tex].
To do so one does the following:
[tex]\begin{array}{cccccc}-1|& 1&0&-7&-6\\ & &-1&1&6 \\& 1&-1&-6&0 \end{array}[/tex]
Since we divided by a linear binomial it reduces the power by one which produces the following quadratic:
[tex](x^2-x-6)[/tex]
Which can be factored in the following, and I will provide the complete factorization as well:
[tex]p(x)=(x+1)(x-3)(x+2)[/tex]
m∠QPS=40
m∠RPS=8x+7
m∠QPR=9x+16
find m∠QPR
Answer:
25
Step-by-step explanation:
from the information given, we know that rps + qpr = qps.
so, (8x+7)+(9x+16) = 40.
simplify to get 17x + 23 = 40.
17x = 17.
x = 1.
plug in: 9+16 = 25.
which set is closed under subtraction?
Answer:
The rational numbers are "closed" under addition, subtraction, and multiplication. Under division, we run into the problem of division by 0, which makes the statement that "the rationals are closed under division" false.
Step-by-step explanation:
Anyone know how to go this ?
Answer:
the first one
P= 34
A= 66
----------------------------
the second one
P= 40
A= 120
----------------------------
the third one
P= 40
A= 81
the fourth one
if that's a 4
P= 12
if that's a 9
P=27
A=?
Which number is a common factor of 116 and 40
Answer:
4
Step-by-step explanation:
[tex]116 = 2 \times 2 \times 29 \\ 40 = 2 \times 2 \times 2 \times 5 \\ common \: factors = 2 \: \: 2 \\ common \: factors \: of \: 116 \: and \: 40 \\ = 2 \times 2 = 4[/tex]
The numbers 116 and 40 share common factors of 1, 2, and 4, with 4 being their greatest common factor.
The common factor of 116 and 40 can be found by identifying the numbers that divide both without leaving a remainder. To do so, we factorize both numbers:
116 = 2 x 2 x 29 = 2² x 2940 = 2 x 2 x 2 x 5 = 2³ x 5Next, we find the common factors by looking at the prime factors they share. Both numbers have the prime number 2 as a factor. The highest power of 2 that divides both numbers is 2², which is 4. Therefore, the greatest common factor (GCF) is 4. However, since we are looking for a common factor, not necessarily the greatest, 2 and 1 are also common factors of 116 and 40.
Audrey grabs a meal with her two co-workers. If everyone paid an equal amount of $8.50 then how much would the total be
Answer:
$25.50
Step-by-step explanation:
There three people- Audrey and two co-workers
Each pay $8.50
Then the total is:
$8.50*3 = $25.50How to round to the nearest degree
Answer:
to the nearest whole degree means that you look at the first decimal place. if it is less than 5, you keep the whole number and eliminate the decimal. if otherwise, the decimal is ≥5, you round up the whole number and eliminate the decimal.
Mr. John borrows $10,000 to remodel his kitchen; he borrows the money for 5 years, and has to pay a simple interest rate of 4.5% per year.
A) Since there are 12 months in the year, how many total months does Mr. John have to pay back this loan?
B) What will be the amount of Mr. john's monthly payment to the bank?
Answer:
A) 60
B)450
Step-by-step explanation:
A) you multiply 5x12
B)10,000(the whole) divided by 100(the 4.5% comes from 100%)is 100.Now instead of trying to divide the missing number,(you cant cause its not there) you instead multiply.You multiply 4.5% by the hundred that you got earlier.
The 53 students go to a nearby Italian restaurant for lunch. Each table holds 5 people. How many tables will the group need
Answer:
They will need 11 tables
Step-by-step explanation:
The first 10 will seat 5, the 11th will seat the final 3.
Answer:
The group will need 11 tables.
Step-by-step explanation:
Think: How many times does 5 go into 53?
We know that 5 goes into 50, 10 times. The extra 3 students must sit at a seperate table. That means they need 10 tables plus another. Therefore, the group will need 11 tables.
Simplify the following algebraic expression:
10xy - 5ab - 15yx + 9ba
Answer:
- 5xy + 4ab
Step-by-step explanation:
Allison's cinema has 100 seats. One day, Allison notices that her cinema is full, and she has taken exactly £100. The prices where: adult=£3.50, pensioner= £1, child=£0.85. she knows not everyone in the audience is a pensioner. Howmmany adults, children and pensioners where there?
Answer:
So starting with what we already know, £100 was paid in all, all 100 seats were taken. Adults pay £3.50, Children pay $0.85 and the Pensioners pay $1.00. I basicaly started off by trying it so all adults, children and pensioners are the exact same number. 33 adult tickets would cost them £115.50. Crossing that suggestion out; I tried again, but this time, with 3 adults, 50 children and the 47 that were left, i put as pensioners. So, now there is 100 people and this is kind of working out:
3 adults= £10.50, 50 children= £42.50, 47 pensioners= £47.00 Total £100
Step-by-step explanation:
As per the given data number of adults [tex]=3[/tex] , number of children [tex]= 50[/tex] and number of pensioner [tex]= 47[/tex].
What is number?" Number is defined as the count of the given quantity."
According to the question,
Total number of seats [tex]=100[/tex]
Total amount of full seats [tex]= \£100[/tex]
Price of adult ticket [tex]= \£ 3.50[/tex]
Price of children ticket [tex]= \£ .85[/tex]
Price of adult ticket [tex]= \£ 1[/tex]
[tex]'x'[/tex]represents the number of adults
[tex]'y'[/tex] reprsents the number of children
[tex]'z'[/tex] represents the number of pensioner
As per given condition we have,
[tex]x + y + z = 100\\\\\£3.50x + \£0.85y + \£1z = \£ 100[/tex]
Using trial and error method we get,
[tex]x = 3 ,\\\\y= 50\\\\z= 47[/tex]
For total number of tickets
[tex]3 + 50 + 47 = 100[/tex]
Left hand side = Right hand side
Substitute in left hand side of total cost we get,
[tex]\£3.50(3) + \£0.85(50) + \£1(47) \\\\= \£10.50 + \£42.50 + \£47[/tex]
[tex]= \£ 100[/tex]
= Right hand side
Hence, as per the given data number of adults [tex]=3[/tex] , number of children [tex]= 50[/tex] and number of pensioner [tex]= 47[/tex].
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Please answer i will mark brainliest Plato stores his Pokémon cards in a shoe box measuring eight inches by 14 inches by six
inches. Socrates stores his Magic cards in a cake box measuring one foot by one foot by
five inches. Whose container has the greater capacity?
Answer:
Socrates' box is 48 sq inches larger than Plato's.
Step-by-step explanation:
14x8x6=672
12x12x5=720
happy to help ya :)
Ned scored 84 points in the first 6 games of the basketball season . How many points per game has Ned scored ?
Answer:
he scored 14 points per game :)
Step-by-step explanation:
Consider the following figure and find the value of v
These are the vertical anvles, so v=50°
What is the size of the angle, below?
To find the size of an angle, one can use the small-angle approximation, which for small angles allows one to estimate the angle based on linear size and distance when measured in radians. The thumb method suggests a thumb at arm's length subtends an angle of 1 degree.
Explanation:To address the question about the size of a given angle, we must consider several mathematical concepts related to angles and their measurement. A key method of estimating angles involves using the small-angle approximation, which relates the linear size of an object to its angular size when viewed from a certain distance.
This approximation states that for small angles, the tangent of the angle is approximately equal to the angle itself when measured in radians. If we know the approximate width of an object, such as a thumb (1 cm) and use a comfortable viewing distance, Lo (\u2248 25 cm), we can estimate the angular size using this relationship.
The size of an angle can be described using different units, primarily degrees, arcminutes, and arcseconds, or radians. As part of learning about angles, students are taught to convert between these units. Given the question's context, if a thumb is estimated to subtend an angle of 1 degree at arm's length, we would have a straightforward method to approximate the angle's size through observation.
Write the next two numbers in the sequence: 1, 2, 4, 8, 16...
Answer:
32
Step-by-step explanation:
Answer:
Step-by-step explanation:
hello :
32 , 64 ( geometric-sequence) when the common ratio is : 2
URGENT!!!
Graph: -4x+2y=8
Answer:
Step-by-step explanation:
Popular culture may include changing trends in all of the following categories except __________. A. clothing styles B. history C. music D. art
Answer:
B. History
Step-by-step explanation:
Because cultures have certain clothing styles on cations, they listen to one or more types of music in certain lands, and they have art that is so pretty.
Popular culture may include changing trends in all of the following categories except history. Then the correct option is B.
What is history?History is the study of an event that is done in the past.
Examples - The British empire, Hitler's torture, world wars, political interference, etc.
Popular culture may include changing trends in all of the following categories except history.
Thus, the correct option is B.
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Write
44
51
in lowest terms
Answer:44=11/25 and 51=then its 51/100
Step-by-step explanation:if its frcations.hope it helps.
Answer:
44/51
Step-by-step explanation: