Find the surface area of each figure to the nearest tenth. Show your work, please
Answers
Lateral surface area = [tex] \frac{2p*a}{2} [/tex] where p is the base perimeter and a the apothem.
The base is a sqaure so, find the area of the square.
Base Area = 16*16 = 256 in²
Calculate the perimeter = 16*4 = 64 in
LSA = (64*17)/2 = (64*17)/2 = 1088/2 = 544 in²
TSA = 544+256 = 800 in²
Total surface of cone: LSA + Base Area
LSA = πra
Let's find the apotheme. Apply Pitagora, again the hypothenuse is the apotheme. The legs are the radius and the height.
a = √8²+3² = √64+9 = √73 ≈ 8,5 in.
Base area (area of the circle) = πr² = 3²*π = 9π in²
LSA = 3*8,5*π = 25,5π in²
TSA = 25,5π+9π = 34,5π = 34,5*3,14 = 108,3 in²
Related Questions
Create a list of the odd numbers between 1 and n (include 1 as well as n -- if it's odd-- in the list). Associate the list with the variable odds.
Answers
Starting with 1 as the first odd number, you get 1, 3, 5, 7, 9, ...
A general formula to name the odd numbers is 2n + 1, where n can take any whole value.
Look:
n 2n + 1
0 0+1 = 1
1 2(1) + 1 = 2 + 1 = 3
2 2(2) + 1 = 4+1 = 5
3 3(2) + 1 = 6 + 1 = 7
4 4(2) + 1 = 8 + 1 = 9.
So, you now can use the general formula 2n + 1 to generate any odd number, starting with n = 0 to generate the first odd number, 1.
Identify the domain of the exponential function shown in the following graph: y=10x
Answers
We can replace x with any real number we want without worrying about restrictions. There won't be any issues such as dividing by zero or applying the square root to a negative number.
Find the measure of each interior angle
Decagon in which the measures of each interior angles are x + 5, x + 10, x + 20, x + 30, x + 35, x + 40, x + 60, x + 70, x + 80, and x + 90
Answers
To find each interior angle of a decagon given as expressions with x, we sum the expressions and set equal to 1440 degrees, the total sum of interior angles. Solving for x, we find x=100 and then substitute to find each angle.
To find the measure of each interior angle of a decagon where the angles are given as expressions involving x, we must use the fact that the sum of interior angles in a polygon is (n-2)180 degrees, where n is the number of sides in the polygon. For a decagon, which has 10 sides, the sum would be (10-2)180 = 1440 degrees.
x + 5 + x + 10 + x + 20 + x + 30 + x + 35 + x + 40 + x + 60 + x + 70 + x + 80 + x + 90 = 1440
Combining like terms, we find that:
10x + 5 + 10 + 20 + 30 + 35 + 40 + 60 + 70 + 80 + 90 = 1440
10x + 440 = 1440
10x = 1440 - 440
10x = 1000
x = 100
Once x is found, we substitute back into each angle expression to find the measure of each interior angle:
x + 5 = 105 degrees
x + 10 = 110 degrees
x + 20 = 120 degrees
x + 30 = 130 degrees
x + 35 = 135 degrees
x + 40 = 140 degrees
x + 60 = 160 degrees
x + 70 = 170 degrees
x + 80 = 180 degrees
x + 90 = 190 degrees
What is the area of a regular pentagon with an apothem of 14 inches long and a side 20 inches long?
Answers
Answer:
[tex]\text{Area of regular pentagon is }700 inches^2[/tex]
Step-by-step explanation:
Given that a regular pentagon with an apothem of 14 inches and a side of 20 inches.
we have to find the area of pentagon.
Apothem=a=14 inches
Side of pentagon= 20 inches
[tex]Perimeter=s=20\times 5=100 inches[/tex]
[tex]\text{Area of regular pentagon=}\frac{1}[2}\times perimeter \times apothem[/tex]
[tex]=\frac{1}{2}\times 100\times 14=700inches^2[/tex]
[tex]\text{Area of regular pentagon is }700 inches^2[/tex]
Answer:700in
Step-by-step explanation:
Solve the following system of equations algebraically. 2x = 5y + 8. 3x + 2y = 31
Answers
x=−12.301587 and y= 31/ 2
3x + 2y = 31 so 3x = -2y + 31 (2nd)
multiply (1st equation) by 3 and (2nd equation) by 2
6x = 15y + 24
6x = -4y + 62
-----------------------subtract
0 = 19y - 38
19y = 38
y = 2
2x = 5y + 8
2x = 5(2) + 8
2x = 18
x = 9
answer
solution (9, 2)
What is the slope of the line that contains the points (9, –4) and (1, –5)?
Answers
slope = (-5 - (-4) / (1 - 9) = -1 / -8 = 1/8 <==
The slope of the line that contains the given point is the rise/run, which is: 1/8.
How to Find the Slope of a Line?The slope of a line = rise / run = change in y / change in x.
Given the points on a line as (9, –4) and (1, –5):
Change in y = (-4 -(-5) = 1
Change in x = (9 - 1) = 8
Slope of the line = change in y/change in x = 1/8.
Learn more about the slope of a line on:
https://brainly.com/question/3493733
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There exists a similarity transformation that maps ΔABC to ΔA′B′C′. The measure of angle A is 68°, and the measure of angle B is 46°. What is the measure of angle C in degrees?
Answers
The answer is 66.
The measure of angle C in triangle ABC is 66 degrees, calculated by subtracting the sum of angles A and B from 180 degrees.
The measure of angle C can be determined by using the fact that the sum of angles in any triangle is always 180 degrees. Given that the measure of angle A is 68° and the measure of angle B is 46°, we can calculate the measure of angle C as follows:
C = 180° - A - B
C = 180° - 68° - 46°
C = 180° - 114°
C = 66°
Thus, the measure of angle C in ΔABC is 66 degrees.
Which number produces a rational number when added to 0.42?
Answers
A 12 foot rope is cut into two pieces so that one piece is 3 feet less than twice the length of the other piece. how long is each piece?
Answers
12 feet long
1st piece = x
2nd piece = 2x-3
3x-3 =12
3x=15
x = 5
1st piece = 5 feet
2nd piece = 2*5=10-3=7 feet
Is -1/2 rational or irrational
Answers
-1 and 2 are both integers because they are either whole numbers or of the opposite value (negative).
Find the range of the data. Scores: 81, 79, 80, 88, 72, 96, 86, 73, 79, 88 A) 22
B)24
C)28
D)23
Answers
96-72= 24
B.)24
Answer:
Option B - 24
Step-by-step explanation:
Given : Scores: 81, 79, 80, 88, 72, 96, 86, 73, 79, 88
To find : The range of the data?
Solution :
Range is defined as the difference between the smallest and the largest element of the data.
First we arrange the data into ascending order:
72,73,79,79,80,81,86,88,88,96
The smallest number is 72
The largest number is 96
The range of the data = largest number - smallest number
The range of the data = 96 - 72
The range of the data = 24
Therefore, Option B is correct.
Consider the function given by the graph. What are these values?
f(–2 ) =
f(0) =
f(4) =
Answers
The values of the function f(x) for the given graph are approximately -7, -18, and -29.
Explanation:The values of the function f(x) for the given graph can be found by looking at the corresponding points on the graph.
For f(-2), we look at the point on the graph where x = -2. From the graph, we can see that f(-2) is approximately -7.
Similarly, for f(0), we look at the point on the graph where x = 0. From the graph, we can see that f(0) is approximately -18.
For f(4), we look at the point on the graph where x = 4. From the graph, we can see that f(4) is approximately -29.
f(-2) = -1
- f(0) = 3
- f(4) = 0
The values of the function at different points on the graph can be found by looking at the corresponding coordinates on the graph.
To find f(-2), we look for the point on the graph where x = -2. From the graph, it appears that the y-coordinate of this point is -1. Therefore, f(-2) = -1.
To find f(0), we look for the point on the graph where x = 0. From the graph, it appears that the y-coordinate of this point is 3. Therefore, f(0) = 3.
To find f(4), we look for the point on the graph where x = 4. From the graph, it appears that the y-coordinate of this point is 0. Therefore, f(4) = 0.
It is important to note that the given information about the arrows and points (0,3) to (-6,0) and (0,1) to (6,-2) is unrelated to finding the values of the function at the given points. These arrows and points might represent something else in the context of the graph, but they do not affect the calculations of f(-2), f(0), and f(4).
If f(x) = 3x – 2 and g(x) = 6 – 4x, find f(x) + g(x). A. 7 + 4x B. 4 – x C. –x – 4 D. –4 – 7x
Answers
3x-2+6-4x
Then simplify
-x+4 = 4-x
The answer is B. 4-x
Which set of numbers can represent the side lengths, in centimeters, of a right triangle?
Answers
The sides should satisfy the equation (a^2)+(b^2)=(c^2).
Hope it helps
Answer:
Any set of numbers that fit in Pythagoras theorem will represent that set.
Step-by-step explanation:
Though options are not given, but there is a standard way to get such combinations of number.
As it is a right triangle, we have to work on Pythagoras theorem.
The sum of squares of two other sides is equal to square of the hypotenuse.
Like : [tex]3^{2} +4^{2} =5^{2}[/tex]
Using technology, we found that Juan’s investment account can be modeled by the function, c(x)=3x2-2x+10, in thousands of dollars. What was Juan’s initial investment?
A)$5
B)$10
C)$5,000
D)$10,000
Answers
Initial investment is given when [tex]x=0[/tex], so substituting this into [tex]c(x)[/tex] we have
[tex]c(0)=3 (0)^{2}-2(0)+10 [/tex]
[tex]c(0)=10[/tex]
Hence, correct answer is B $10
Answer:
D) $10,000.
Step-by-step explanation:
We have been given a function [tex]c(x)=3x^2-2x+10[/tex], which represents Juan’s investment account in thousands of dollars. We are asked to find Juan's initial investment.
To find Juan's initial investment, we will substitute [tex]x=0[/tex] in our given function.
[tex]c(0)=3(0)^2-2(0)+10[/tex]
[tex]c(0)=3*0-0+10[/tex]
[tex]c(0)=10[/tex]
Since the function gives Juan's investment in thousands of dollars, so Juan's initial investment would be [tex]10\times \$1,000=\$10,000[/tex], therefore, option D is the correct choice.
Angle 1 and angle 2 form a linear pair. if m angle 2 = 67. what is m angle 1
Answers
Final answer:
The measure of angle 1 can be found by using the fact that angle 1 and angle 2 form a linear pair. By setting up an equation and solving, we find that angle 1 measures 113 degrees.
Explanation:
To find the measure of angle 1, we need to understand that angle 1 and angle 2 form a linear pair. A linear pair of angles is formed when two adjacent angles are supplementary, meaning they add up to 180 degrees. So, angle 1 + angle 2 = 180 degrees. Given that angle 2 measures 67 degrees, we can substitute this value into the equation to find angle 1: angle 1 + 67 degrees = 180 degrees. Solving for angle 1, we get angle 1 = 180 degrees - 67 degrees = 113 degrees.
The adams family is remodeling their family room. the room measures 14 feet by 20 feet, and the contractor wants $35 per square foot to remodel it. how much will it cost to remodel?
Answers
$35 * 280 sq ft = $ 9,800
Answer:
It would cost $9800 to remodel the room.
Step-by-step explanation:
The Adams family is remodeling their family room.
Length of the room = 20 feet
Width of the room = 14 feet
To get area of the room we use the formula
Area = Length × Width
A = 20 × 14 = 280 feet²
The contractor wants $35 per square foot to remodel it.
So it would cost = 280 × 35 = $9800
It would cost $9800 to remodel the room.
The depth of the water at the end of a pier changes periodically along with the movement of tides. On a particular day, low tides occur at 12:00 am and 12:30 pm, with a depth of 2.5 m, while high tides occur at 6:15 am and 6:45 pm, with a depth of 5.5 m. Let t = 0 be 12:00 am. Write a cosine model, d = acos(bt) + k, for the depth as a function of time. This amplitude is meters. a =
Answers
Answers:
1.5, -1.5, 12.5, 4pi/25, 4, D
Step-by-step explanation:
Answer:
1.5 meters
a = -1.5
12.5 hours
b = 4 pi/25
k = 4 meters
last option is D
Step-by-step explanation:
edg 23'
Amy purchased 17 pencils and 18 pens for a fund-raiser at school and spent $61.50. Jocelyn purchased 10 pencils and 21 pens and spent $57. How much does each pencil cost?
Answers
17x + 18y = 61.50....multiply by 21
10x + 21y = 57 ....multiply by -18
------------------------
357x + 378y = 1291.5 (result of multiplying by 21)
-180x - 378y = - 1026 (result of multiplying by -18)
-----------------------add
177x = 265.5
x = 265.5 / 177
x = 1.50 <== cost for a pencil
pens(y) cost 2.00
Complete the statements about the key features of the graph of f(x) = x5 – 9x3. As x goes to negative infinity, f(x) goes to negative infinity, and as x goes to positive infinity, f(x) goes to positive infinity.
Choose all of the zeroes of f(x).
–3 with multiplicity 1
3 with multiplicity 1
0 with multiplicity 1
0 with multiplicity 3
3 with multiplicity 0
Answers
1. let's factorize the expression [tex]x^{5} -9x ^{3} [/tex]:
[tex]f(x)= x^{5} -9x ^{3}= x^{3} ( x^{2} -9)=x^{3}(x-3)(x+3)[/tex]
the zeros of f(x) are the values of x which make f(x) = 0.
from the factorized form of the function, we see that the roots are:
-3, multiplicity 1
3, multiplicity 1
0, multiplicity 3
(the multiplicity of the roots is the power of each factor of f(x) )
2.
The end behavior of f(x), whose term of largest degree is [tex] x^{5} [/tex], is the same as the end behavior of [tex] x^{3} [/tex], which has a well known graph. Check the picture attached.
(similarly the end behavior of an even degree polynomial, could be compared to the end behavior of [tex] x^{2} [/tex])
so, like the graph of [tex] x^{3} [/tex], the graph of [tex]f(x)= x^{5} -9x ^{3} [/tex] :
"As x goes to negative infinity, f(x) goes to negative infinity, and as x goes to positive infinity, f(x) goes to positive infinity. "
The end behavior of f(x) has the same end behavior of [tex]x^3[/tex] and all the zeroes of f(x) wiil be: -3 with multiplicity 1, 3 with multiplicity 1, 0 with multiplicity 3.
Given :
[tex]f(x) = x^5-9x^3[/tex] --- (1)
The value of x at which f(x) becomes zero can be determine by eqaution the equation (1) to zero.
[tex]x^5-9x^3=0[/tex]
[tex]x^3(x^2-9)=0[/tex]
[tex]x^3(x-3)(x+3)=0[/tex]
Therefore, all the zeroes of f(x) will be:
-3 with multiplicity 1,
3 with multiplicity 1,
0 with multiplicity 3.
The end behavior of f(x) has the same end behavior of [tex]x^3[/tex]. As x goes to negative infinity, f(x) goes to negative infinity, and as x goes to positive infinity, f(x) goes to positive infinity.The graph of f(x) is attached below.
For more information, refer the link given below:
https://brainly.com/question/24153248
Find the least common multiple of 8c4 and 6c2 .
Answers
Given: AC is the hypotenuse and BD is the altitude of △ABC. AD=27, CD=40, AB=e, BD=j, and BC=h
Find the value of e
How the literal devil am i supposed to do this, legit i've tried for hours first answer gets Brainliest
Answers
In triangle ABC:
m(B)=90°, let m(A)=α, and let m(C)=β
so m(B)+m(A)+m(C)=180°, so α+β=90°
In triangle ABD, m(A)=α, m(ADB)=90° so m(ABD) must be β, so that the sum completes to 180.
By the same logic, m(DBC)=α
so we have the following similarities of triangles: (let's go by the order α-β-90°):
ACB ≡ ABD ≡ BCD,
consider ABD ≡ BCD:
[tex] \frac{AB}{BC} = \frac{BD}{CD} = \frac{AD}{BD} [/tex]
substitute with the givens:
[tex] \frac{e}{h} = \frac{j}{40} = \frac{27}{j} [/tex]
from
[tex]\frac{j}{40} = \frac{27}{j}[/tex]
we have
[tex] j^{2}=40*27 =1080[/tex]
In triangle ABD, from the pythagorean theorem:
[tex] e^{2} = j^{2}+27^{2}=1080+729=1089[/tex]
so [tex]e= \sqrt{1089}= 42.53 (units)[/tex]
Remark: a direct solution can be given by Euclid's theorem, AB^2=AD*AC
[tex]AB^2=AD*AC[/tex] so
[tex] e^{2}=27*47[/tex], then take square root of e
Answer: 42.53 units
(4.4*10^6)*(3.9*10^4)
Scientific notation please help and explain
Answers
and
(3.9*10^4) = 39000
The exponents on top of the 10 tells you how many decimals you're supposed to move it to. If it's a negative number, you'll need to move the same amount of decimals, but to the left side instead.
for example: 4.3*10^-3 =0.0043
in this case, however, you should refer to the Laws of Exponents.
(4.4*10^6)*(3.9*10^4)
= 4.4 * 3.9 * 10^6 * 10^4
= 17.16 * 10^(6+4) <-- Law of Exponents say that when you multiply exponents with the same base, you add the exponents together.
= 17.16 * 10^10
Mr. Brown owned a house, which he rented for $60 a month. The house was assessed at $9000. In 1975 the rate of taxation was increased from $25 to $28 per $1000 assessed valuation. By what amount should the monthly rent have been raised to absorb the increase in that year's taxes?
Answers
Old value = 25×9 = 225 ⇒ The value 9 represents the 9 lots of thousands of the house's value
New value = 28×9 = 252
Increase in tax = 252 - 225 =27
Percentage increase = (27÷225) ×100 = 12%
The amount of yearly rent would be then increased by 12%
Monthly rent = $60
Yearly rent = 60×12 = $720
Increase by 12% = 720×1.12 = 806.4 ⇒ The value 1.12 is the multiplier, obtained from 100%+12%=112%=1.12
The monthly rent is 806.4÷12 = $67.20 which is an increase of $7.20 per month
In the above figure, find the measure of angle AEB + the measure of angle CED.
A. 75
B. 93
C. 112
D. 140
Answers
What is the area of the trapezoid?
Answers
Find the difference.
Correct and best explained answer gets brainliest.
Answers
9-5 =4
-4 +7=3
-1-6 =-7
so 4x^3+3x^2-7
A is the correct answer
How much money will be in a bank account after 9 years if $7 is deposited at an interest rate of 5% compounded annually?
Answers
A=p (1+r)^t
A future value?
P present value 7
R interest rate 0.05
T time 9 years
A=7×(1+0.05)^(9)
A=10.86
Help plz.. Evaluate this expression: -(-(-(-1)))?
Thanks.
Answers
every pair of negative cancel out
-(-a)=a
so we can just keep flipping the signs
go inside to out
-(-(-(-1)))=
-(-(1))=
-(-1)=
1
Using a calculator and the formula above, calculate the APR. Choose the correct answer.
Betty Buyer has a short term note at 16% interest per year.
To the nearest tenth, APR =
15.9
17.2
16.6
%.
Answers
APR=(1+0.16÷12)^(12)−1
APR=0.172×100
APR=17.2%