A rectangular pyramid is shown in the figure.
A rectangular pyramid with a base of dimensions 7 centimeters by 5 centimeters. The two large triangular faces have a height of 7.6 centimeters. The two small triangular faces have a height of 8 centimeters.
What is the surface area of the pyramid?
The surface area of the pyramid is 113 cm².
What is rectangular pyramid?A rectangular pyramid is a type of pyramid where the base is a rectangle and the triangular faces meet at a single point called the apex or vertex. It has five faces, including a rectangular base and four triangular faces, and it is a polyhedron with five vertices and eight edges.
The rectangular pyramid has a base of dimensions 7 cm by 5 cm, and the two large triangular faces have a height of 7.6 cm, while the two small triangular faces have a height of 8 cm.
To find the surface area of the pyramid, we need to find the area of each face and then add them up.
Area of the base:
The base of the pyramid is a rectangle with dimensions 7 cm by 5 cm, so its area is:
Area of base = length × width = 7 cm × 5 cm = 35 cm²
Area of the four triangular faces:
Each of the four triangular faces has a base of 5 cm (the width of the rectangle) and a height of either 7.6 cm or 8 cm. Using the formula for the area of a triangle, we can find the area of each face:
Area of each large triangular face = 1/2 × base × height = 1/2 × 5 cm × 7.6 cm = 19 cm²
Area of each small triangular face = 1/2 × base × height = 1/2 × 5 cm × 8 cm = 20 cm²
There are two large triangular faces and two small triangular faces, so the total area of the four triangular faces is:
Total area of four triangular faces = 2 × area of large triangular face + 2 × area of small triangular face
= 2 × 19 cm² + 2 × 20 cm²
= 78 cm²
Total surface area:
Finally, we can find the total surface area of the pyramid by adding the area of the base to the total area of the four triangular faces:
Total surface area = area of base + total area of four triangular faces
= 35 cm² + 78 cm²
= 113 cm²
Therefore, the surface area of the pyramid is 113 cm²
.
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what is a dynamic Rectangle ?
Answer:
A dynamic rectangle is a right-angled, four-sided figure (a rectangle) with dynamic symmetry.
Step-by-step explanation:
Aspect ratio (width divided by height) is a distinguished value in dynamic symmetry, a proportioning system and natural design methodology described in Jay Hambidge's books.
Answer:
A dynamic rectangle is a right angled four sided with dynamic symmetry
A discount of 10 percent was given. If a further discount of 10percent was given in the reduced price, calculate the total single discount given in the marked price .
Answer:
let marked price = x
on 10% discount, price= x-10%of x
=x-(10x/100)
=x-(x/10)
=9x/10
on further 10% discount, total discount = 10% of 9x/10
=10/100 * 9x/10
= 9x/100
= 9%of x
hence, the single discount given on marked price is 9%
Step-by-step explanation:
HELPP!!
Ryan collects rainwater in a barrel for his garden. The barrel is filled with 15 gallons of water. Ryan used 6.8 gallons to water his garden in June and 5 and one-eighth gallons in July. How much water is left in the barrel?
1.) 3.075 gallons
2.) 5.125 gallons
3.) 5.178 gallons
4.) 16.675 gallons
Subtracting the initial amount of water from the amount used, the remaining amount of water is given by:
1.) 3.075 gallons.
How to find the remaining amount of water in the barrel?
To find the remaining amount of water in the barrel, we have to subtract the initial amount by the amount used.
We have that:
The initial amount was of 15 gallons.The amount used was of: 6.8 + 5 + 1/8(relative to the one-eight) = 11.925 gallons.Hence the remaining amount is:
15 - 11.925 = 3.075 gallons.
Which means that option 1 is correct.
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Answer: 3.075 gallons
Step-by-step explanation:
i need help asap
than you!
The highest height for the daily rainfall were for 5 and 6 inches
How to Interpret Dot Plots?Dot plots are used to present data in the form of points or small circles. It is similar to a simplified histogram or bar graph in that the height of the bar made up of points represents the numerical value of each variable. Dot plots are used to represent small amounts of data.
From the given dot plot, we see the number of times for each height of rainfall.
Thus, we see that the highest number of times of rainfall height was from that of 5 and 6 inches.
Thus, we conclude those were the highest heights for the daily rainfall.
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PLZ HELL FAST WILL GIVE BRAINLIEST
Select all the correct equations.
Which equations have no real solution but have two complex solutions?
3x^2- 5x= -8
2x^2= 6x – 5
12x= 9x^2 + 4
-x^2– 10x = 34
\( {3x}^{2} - 5x = - 8 \\ {3x}^{2} - 5x + 8 = 0\)
This equation has the next form:
\( {ax}^{2} + bx + c = 0\)
To find if the equation has two complex solutions we have to check if the discriminant is negative, as follows:
\( {b}^{2} - 4ac \\ ( { - 5})^{2} - 4 \: . \: 3 \: . \: 8 = 25 - 96 = - 71 < 0\)
Then, the first case has two complex solutions.
In the second case,
\( {2x}^{2} = 6x - 5 \\ {2x}^{2} - 6x + 5 = 0\)
The discriminant in this case is:
\(( { - 6})^{2} - 4 \: . \: 2 \: . \: 5 = 36 - 40 = - 4 < 0\)
Then, the second case has two complex solutions.
In the third case,
\(12x = {9x}^{2} + 4 \\ { - 9x}^{2} + 12x - 4 = 0\)
The discriminant in this case is:
\( {12}^{2} - 4 \: . \: ( - 9) \: . \: ( - 4) = 144 - 144 = 0\)
Then, the third case has two real solutions.
In the fourth case,
\( { - x}^{2} - 10x = 34 \\ { - x}^{2} - 10x - 34 = 0\)
The discriminant in this case is:
\(( { - 10})^{2} - 4 \: . \: ( - 1) \: . \: ( - 34) = 100 - 136 = - 36 < 0\)
Then, the fourth case has two complex solutions.
Jill Janzen's gross weekly pay is $298. Her earnings to date for the year total $14,900. What amount is deducted from her pay each week for Social Security, which is taxed at 6.2%?
Jill's annual earnings can be calculated by multiplying her weekly pay by the number of weeks in a year: $298/week x 52 weeks/year = $15,496/year. Her earnings to date are $14,900, so she has earned an additional $596 in the current week.
Social Security is taxed at 6.2%, so the amount deducted from her pay each week is 6.2% of her gross weekly pay. That's 0.062 x $298 = $18.48.
Good morning! can somebody help me as soon as possible
it isn't a function tho..
but can you just send a picture attaching the options coming under " select "??
Problem ADr. Hong prescribed 0.019 liter moremedicine than Dr. Tannenbaum. Dr.Evans prescribed o.02 liter less thanDr. Hong. Who prescribed the mostmedicine? Who prescribed the least?1
Let say Dr. Hong = H
Dr. Tannenbaum = T
Dr. Evans = E
Now, Dr. Hong prescribed 0.019 liters more
medicine than Dr. Tannenbaum.
It means H = 0.019 + T
Also, Dr.Evans prescribed 0.02 liters less than
Dr. Hong.
It means E= 0.02 - H
With the information before, we replace the H value on the E equation:
E= 0.02 - H
E = 0.02- 0.019 + T
E = 0.001 + T
This means that Dr. Evans prescribed 0.001 more medicine than Dr.Tannenbaum
So:
E > T, H> T and E< H
Therefore:
-Who prescribed the most medicine? Dr. Hong prescribed more medicine than Dr. Evan and Dr.Tannenbaum
-Who prescribed the least? Dr.Tannenbaum prescirbed the least medicine
what is the greatest 3 digit number which is divisible by 3, 4 and 5 but not by 8
3*4*5= 60
1000/60 = 16.67
16 is a multiple of 2 so that's bad because it will make the number divisible by 8
so it's 15*60 = 900
The figure below has a volume of 60 cubic units. How many more cubes will it take to fill the figure?
1 cubic unit
5 cubic units
40 cubic units
55 cubic units
60 cubic units
Answer:
40 cubic units
Step-by-step explanation:
Question 1-1
A bike messenger earns $60 per day plus $12 per delivery. Today the messenger wants to earn at least $204.
Which inequality represents the number of deliveries, n, the bike messenger needs to make to earn at least $204?
A car can travel 45 miles on 2 gallons of gasoline. How far can it travel on 5.6
gallons?
Answer:
It can travel 45 / 2 = 22.5 miles per gallon so the answer is 22.5 * 5.6 = 126 miles.
Which graph represents the solution set to the system of inequalities?
{ Y ≤ 1/4X-2
Y ≥ −54X+2
ANSWER Down Below
The graph of the system of inequalities:
y ≤ (1/4)*x - 2
y ≥ −(5/4)x +2
Is in the image at the end.
Which is the graph of the system of inequalities?Here we have the system of inequalities:
y ≤ (1/4)*x - 2
y ≥ −(5/4)x +2
To graph this, we just need to graph both of the linear equations, and we need to shade the region below the first line (the one with positive slope) and the region above the second line, the one with negative slope.
Then the graph of the system of inequalities is the graph you can see in the image at the end of the answer.
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Colleen truman earns 5% commission on all sales in june her sales totaled 54,000$ how much did she earn in commission?
The amount earned as commission in the month of June is $2700
How to determine the amount earned as commission?From the question, we have the following parameters that can be used in our computation:
Commission percentage = 5%
Total sales in the month of June = $54000
The amount earned as commission in the month of June is then calculated as
Amount = Commission percentage x Total sales in the month of June
Substitute the known values in the above equation
So, we have
Amount = 5% x 54000
Evaluate
Amount = 2700
Hence, the commission amount is $2700
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Can the sides of a triangle have lengths 1, 1, and 2?
Answer:
Yes they can, but in an isosceles triangle.
hope that helps...
Helpme with this math
The Pink Party Punch has a stronger lemon-lime flavor because it has a higher volume of 6 liters.
What is volume?Volume can be defined as the total quantity of a substance that a container can hold at a given period of time. Also, the volume of a container is measured in:
LitersOunceCubic metersBased on the information provided in the table above, we can infer and logically deduce that the Pink Party Punch has a stronger lemon-lime flavor because it has a higher volume of 6 liters.
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I need help with these problems help me plsssss
Answer:
5. -(6/5)
6. 1/5
7. I think 4/25 but i am not full sure
8. 2
9. -(5/8)
Step-by-step explanation:
12. Sasha surveys students from her homeroom about the number of
siblings each student has. The results are 1, 0, 2, 2, 3, 0, 1, 1, 4,
and 5. What is the mode(s) of the data? (CC.6.SP.5c)
C 1
(D) 1 and 2
in
(A) 1.5
B 0 and 2
The calculated value of the mode(s) of the data is (a) 1
How to determine the mode(s) of the data?From the question, we have the following parameters that can be used in our computation:
1, 0, 2, 2, 3, 0, 1, 1, 4, and 5
By definition, the mode of a data is the data that has the highest frequency
Using the above as a guide, we have the following:
The data element 1 has the highest frequency of 3
Other data elements have lesser frequencies
Hence, the mode(s) of the data is (a) 1
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What is the equation of a parabola with a vertical axis, vertex (h, k), and directrix y = k – p, where p is a nonzero real number? How can the equation be simplified if the vertex is at the origin?
Note that equation of a parabola with a vertical axis, vertex (h, k), and directrix y = k – p, where p is a nonzero real number is (y-k)² = 4p(x-h).
How can the equation be simplified if the vertex is at the origin?The equation of a parabola with a vertical axis, vertex (h, k), and directrix y = k – p, where p is a nonzero real number, is:
(y - k)² = 4p( x - h)
If the vertex is at the origin (h = 0, k = 0 ), the equation an be simplified to....
y² = 4px
where p is still a nonzero real number.
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What is 924 \ 6
Please explain how you did it
( BTW / stands for “divided by”)
Tell me if I’m reading this incorrectly just in case. Thanks!
Answer:
154
Step-by-step explanation:
use the bus stop method so you divide each number separately, starting from the left.
9 divided by 6=1 with a remainder of 3 because 1x6=6 and 9-6=3. Then you move that 3 over to the next number, the 2, to make it 32.
32 divided by 6=5 with a remainder of 2 because 5 x 6=30 and 32-30=2. Then you move that 2 over to the next number, the 4, to make it 24.
24 divided by 6 is 4.
So if you put all of those numbers together, it makes 154.
i
You are given the difference of the numbers of boys and girls in a class and the ratio of boys to girls. How many boys
and how many girls are in the class?
4 more girls; 9 for every 13
There are
boys and
girls in the class.
Answer:
Maybe they are all 13s th am sure
what is:
k/3 + 17 = 12?
Answer:
-15
Step-by-step explanation:
yan po ang answer thank you na lang po
Write an equation that is parallel to the line y=3x-5 and passes through the point (-1,2)
Polly deposited $3,634 in an account earning 5% interest compounded annually.
To the nearest cent, how much will she have in 3 years?
Answer: $3,845.90
Step-by-step explanation:
What formula do I use for this? How do I get the points to graph?
The graph of the function y = 5|x - 4| is added as an attachment
Sketching the graph of the functionFrom the question, we have the following parameters that can be used in our computation:
y = 5|x - 4|
The above function is an absolute value function that has been transformed as follows
Vertically stretched by a factor of 5Shifted right by 4 unitsNext, we plot the graph using a graphing tool by taking not of the above transformations rules
The graph of the function is added as an attachment
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What is –6 9/16 written as a decimal?
Answer:
6.5625
Step-by-step explanation:
Welcome :)
Answer:
-6.5625
Step-by-step explanation:
Find the Interpret the mean absolute deviation of the data 1/4,5/8,3/8,3/4,1/2
The mean absolute deviation (MAD) for the given data is 1/20. This means that, on average, each data point in the set differs from the mean by 1/20.
To find the mean absolute deviation (MAD) of a set of data, we need to calculate the average difference between each data point and the mean of the data set. Here's how we can calculate it for the given data:
Step 1: Find the mean (average) of the data set.
Mean = (1/4 + 5/8 + 3/8 + 3/4 + 1/2) / 5 = 2/5
Step 2: Calculate the difference between each data point and the mean.
Differences: |1/4 - 2/5|, |5/8 - 2/5|, |3/8 - 2/5|, |3/4 - 2/5|, |1/2 - 2/5|
Step 3: Calculate the absolute value of each difference.
Absolute Differences: 1/20, 1/40, 1/40, 1/20, 1/10
Step 4: Find the average of the absolute differences.
MAD = (1/20 + 1/40 + 1/40 + 1/20 + 1/10) / 5 = 1/20
The MAD provides a measure of the average amount of variation or dispersion in the data set. In this case, a MAD of 1/20 indicates that the data points are relatively close to the mean, with most values falling within 1/20 of the mean value.
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The radius of a sphere is increasing at a rate of 5 mm/s. How fast is the volume increasing (in mm3/s) when the diameter is 60 mm
Answer:
The volume of the sphere is increasing at a rate of 56,549 cubic millimeters per second.
Step-by-step explanation:
Volume of a sphere:
The volume of a sphere is given by:
\(V = \frac{4\pi r^3}{3}\)
In which r is the radius.
Solving this question:
The first step do solve this question is derivating V implictly in function of t. So
\(\frac{dV}{dt} = 4\pi r^2 \frac{dr}{dt}\)
The radius of a sphere is increasing at a rate of 5 mm/s.
This means that \(\frac{dr}{dt} = 5\)
Diameter is 60 mm
This means that \(r = \frac{60}{2} = 30\)
How fast is the volume increasing (in mm3/s) when the diameter is 60 mm?
This is \(\frac{dV}{dt}\). So
\(\frac{dV}{dt} = 4\pi r^2 \frac{dr}{dt}\)
\(\frac{dV}{dt} = 4\pi*30^2*5 = 900*20\pi = 56549\)
The volume of the sphere is increasing at a rate of 56,549 cubic millimeters per second.
In an orchard 2/5 of the trees are banana trees, 1/4 of the trees are orange trees and the rest are apple trees. If there are 220 trees in all, find the number of each kind
Answer: banana- 88
Orange-55
Apple-143
Step-by-step explanation:
220 divided by 5, times 2,
that’s the banana trees
220 divided by 4, that’s the oranges
Add the answers together
Take the answer away from 220 that’s the apples