Answers
The lengths of the sides of the triangles used for the building design, obtained using the relationships between similar triangles are;
1. \(\overline{AE}\) = 8 m
\(\overline{EI}\) = 6 m
\(\overline{AI}\) = 10 m
2. The appropriate measurement of the new triangle are;
Height = 16 m
Width = 12 m
Hypotenuse = 20 m
3. The new height of the palace would be 16 meters
What are similar triangles?Similar triangles has the same shape but their sizes may differ.
The design indicates that the height of the arches = Half the height of the palace
Therefore; \(\overline{DE}\) = (1/2) × \(\overline{AE}\)
\(\overline{AE}\) = 2 × \(\overline{DE}\)
\(\overline{DE}\) = 4 m, therefore;
\(\overline{AE}\) = 2 × 4 m = 8 m
\(\overline{AE}\) = 8 mThe location of the entry way to the palace = The middle of the palace
Width of the palace = \(\overline{EI}\)
The location of the entry way from a side of the palace = \(\overline{EF}\)
Therefore; \(\overline{EF}\) = (1/2) × \(\overline{EI}\)
\(\overline{EI}\) = 2 × \(\overline{EF}\)
\(\overline{EF}\) = 3 m, therefore;
\(\overline{EI}\) = 2 × 3 m = 6 m
\(\overline{EI}\) = 6 mThe ratio of the sides of the similar triangles indicates;
\(\overline{DE}\) = (1/2) × \(\overline{AI}\)
\(\overline{AI}\) = 2 × \(\overline{DE}\)
\(\overline{DE}\) = 5 m, therefore;
\(\overline{AI}\) = 2 × 5 m = 10 m
\(\overline{AI}\) = 10 mSimilarly using Pythagorean Theorem, we get;
\(\overline{AI}\)= √(\(\overline{AE}\)² + \(\overline{EI}\)²), therefore;
\(\overline{AI}\) = √(8² + 6²) = 10
\(\overline{AI}\) = 10 m
2. The points A and I in the triangle ΔAEI are the midpoints of the sides of the new (larger triangle), therefore;
\(\overline{AE}\) = (1/2) × The height of the new triangle
The height of the new triangle = 2 × \(\overline{AE}\)
The height of the new triangle = 2 × 8 m = 16 m\(\overline{EI}\) = (1/2) × The width of the new triangle
The width of the new triangle = 2 × \(\overline{EI}\)
The width of the new triangle = 2 × 6 m = 12 m\(\overline{AI}\) = (1/2) × The hypotenuse of the new triangle
The hypotenuse of the new triangle = 2 × \(\overline{AI}\)
The hypotenuse of the new triangle = 2 × 10 m = 20 m3. The new height of the palace if another level were to be added based on the calculations is 16 meters
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Related Questions
What percent of 175 is 50
Answers
Answer:
28.57
Step-by-step explanation:
hope this helps! :D
True or false. If false write the correct statement
1. The depreciation takes place by a specific rate for a specific time
Answers
helppppppppppppppppppppppppppp
Answers
3.
X=1
AB/DE=BC/EF
6/18=9/9(x+2)
1/3=1/(x+2)
(x+2)=3
X=3-2
x=1
What were the rental rates?
Answers
answer/explanation:
d = daily rental chargem = the charge per mileJon rented a car from a company that charged a daily rental fee and a mileage charge. He rented the car for 6 days and drove 300 miles and was charged $285.6d + 300m = 285His friend Amanda later rented the same car for 7 days and drove 260 miles and was charged $310.7d + 260m = 310by solving the system of equations6d + 300m = 2857d + 260m = 310we findd = $35m = $0.25the daily rental charge is $35.the company charge per mile is $0.25.hope this helps
Recall that Rn denotes the right-endpoint approximation using n rectangles, Ln denotes the left-endpoint approximation using n rectangles, and Mn denotes the midpoint approximation using n rectangles. Calculate the approximation for each of the given function and interval below. (a) R5, f(x) = x2 + x on the interval [−1,1]. (b) L6, f(x) = √6x + 2 on the interval [1,3]. (c) M4, f(x) = 1 x2 + 1 on the interval [1,5].
Answers
The approximation for each of the given function and interval below is 1.12
The term function refers the special relationship where each input has a single output.
Here we have given that (a) R5, f(x) = x2 + x on the interval [−1,1]
And we need to find the the approximation for each of the given function and interval
Here we want to to calculate the right-endpoint approximation (the right Riemann sum) for the function:
=> f(x) = x² + x
For the interval [-1, 1] using five equal rectangles.
Let us find the width of each rectangle:
=> Δx = (1 - (-1))/5 = 2/5
Now, we have to list the x-coordinates starting with -1 and ending with 1 with increments of 2/5:
=> -1, -3/5, -1/5, 1/5, 3/5, 1.
Here we are find the right-hand approximation, we use the five coordinates on the right.
Then we have to evaluate the function for each value. This is shown in the table below.
And then each area of each rectangle is its area (the y-value) times its width, which is a constant 2/5.
Therefore, the approximation for the area under the curve of the function f(x) over the interval [-1, 1] using five equal rectangles is:
=> R₅ = 2/5 [-0.24 - 0.16 + 0.24 + 0.96 + 2] = 1.12
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1.2.1
The winner of a 100 mile race drove his car to victory at a rate of 143.8683 mph. What was his time to the nearest thousandth of an hour)?
Answers
Answer:
I think its 0.69508 hours.
Step-by-step explanation:
NO LINKS OR ASSESSMENT!!
Graph the image of the figure using the transformation given. Don't forget to prime marks on your new image.
Answers
Answer:
See belowStep-by-step explanation:
Use points:
U(-1, -2), V(2, 0), W(3, -3)Apply the rule:
(x, y) → (x - 4, y + 4)New points are:
U'(-5, 2), V'(-2, 4), W'(-1, 1)
A Sumer job pays $5 per hour
b. After working 24 hours, do you have enough money to buy an MP3
player that costs $100? Explain your reasoning.
Answers
Answer:
Yes, since the total pay of $120 is more than the $100 cost of the MP3 player.
Step-by-step explanation:
hourly pay: $5/hour
number of hours: 24 hours
total pay = hourly pay × number of hours
total pay = $5/hour × 24 hours
total pay = $120
MP3 player costs $100.
Total pay is $120.
Answer: Yes, since the total pay of $120 is more than the $100 cost of the MP3 player.
6. True or false? Explain.
a. 5 days is * of a month.
Answers
Answer:
5 days is a sixth of a month
Step-by-step explanation:
1 month = 32 days
\(5 \: days = ( \frac{5}{30} ) \: months \\ \\ = \frac{1}{6} \)
Answer:
5 days is one sixth of a month
Step-by-step explanation:
there are 30 days in an average month and divide 30 by 5
Determine the equation of the circle with radius 9 and center ( − 1 , − 8 ).
Answers
The equation of the circle with radius 9 and center ( -1,-8 ) is( x + 1 )² + ( y + 8 )² = 81.
What is the equation of the circle?The standard form equation of a circle with center (h, k) and radius r is:
( x - h )² + ( y - k )² = r²
Given that the circle has a center of (-1, -8) and the radius is 9.
Hence; from the standard form of the equation of the circle:
Center ( h , k ) = ( -1, -8 )
h = -1
k = -8
And radius r = 9
Plug these values into the above formula and simplify.
( x - h )² + ( y - k )² = r²
( x - ( -1 ) )² + ( y - ( -8 ) )² = 9²
Simplify
( x + 1 )² + ( y + 8 )² = 81
Therefore, the equation of the circle is ( x + 1 )² + ( y + 8 )² = 81.
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a pyramid and a cone are both 10 centimeters tall and have the same volume what statement
Answers
Answer: "The pyramid and the cone have the same volume despite their different shapes."
Step-by-step explanation: If a pyramid and a cone are both 10 centimeters tall and have the same volume, then the statement that can be made is:
"The pyramid and the cone have the same volume despite their different shapes."
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How many numbers are there between 1 and 4?
Answers
Answer:
There are infinite numbers between one and four.
Step-by-step explanation:
There are whole, half, quarter, eighth and so many more numbers that the list is infinite. Hope this helps :)
Numbers are used to count and show measurement. There are infinite real numbers between 1 and 4 & there are 2 integers between 1 and 4.
Given
\(Min = 1\)
\(Max =4\)
The question can be interpreted in the following ways.
Interpretation 1: The number of integers/whole numbers/natural numbers between 1 and 4.
The category of numbers above do not have decimal points.
So: the solution to this interpretation is that there are 2 numbers between 1 and 4 and the numbers are 2 and 3.
Interpretation 2: The number of real numbers between 1 and 4.
The range of numbers between 1 and 4 is represented as:
\(Range = [1,4]\)
If the range is expanded, the numbers will be:
\(Numbers = \{1,1.000001,1.0000000000001,.....\}\)
This means that there can be as many numbers as possible between the interval.
Hence, the real numbers between 1 and 4 can not be counted i.e. infinity
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Whats 30 plus 10 and subtract thhe answer from 19 and multiply by two
Answers
Answer:
42
Step-by-step explanation:
Add 30+10=40
40-19=21
21x2=42
Who ever needs their hw done for cashapp hmu on insta kk_iwi
oh n btw the answer is 42
15x10^2 + 5.2x10^5 can you awnser this
Answers
Answer:
521,500 or 5.215 x 10^5
Step-by-step explanation:
A quick way to solve something that is multiplied by 10^n, simply move the decimal point the same number as n. (For example, 1.6 x 10^3 simply move the decimal to the right 3 times 1600.0)
Therefore,
15 x 10^2 = 1500
5.2 x 10^5 = 520000
1500 + 520000 = 521500 or 5.215 x 10^5
Answer:
521,500
Step-by-step explanation:
(15*(10^2)+(5.2*(10^))
1,500+520,000
521,500
Decide if each statement below is
true or false.
45 tens is equal to 450.
12.3 is equal to 123 ones.
80 tens is greater than 6 hundreds.
43,200 is less than 50 thousands.
60 hundreds = 6,000
Answers
(a) 45 tens is equal to 450. :- True
(b) 12.3 is equal to 123 ones. :- True
(c) 80 tens is greater than 6 hundreds. :- True
(d) 43,200 is less than 50 thousands. :- True
(e) 60 hundreds = 6,000 :- True
Consider the first statement,
45 tens are equal to 450
So, 45 tens mean 45 times 10 is written as:
45 × 10 = 450
Hence, it's true.
Consider the second statement,
12.3 is equal to 123 ones.
Now, 123 ones is equal to 123 times 1.
123 × 1 = 123
Hence, the statement is true.
Consider the third statement,
80 tens is greater than 6 hundreds.
Now 80 tens = 80 × 10 = 800
Now, 6 hundreds = 6 × 100 = 600
Now, 800 > 600
Hence, the statement is true.
Consider the fourth statement.
43,200 is less than 50 thousands.
Now, 50 thousands = 50 × 1000 = 50,000
We know,
50,000 > 43,200
Therefore, the statement is true.
Consider the fifth statement,
60 hundreds = 6000
Now, 60 hundreds = 60 × 100 = 6000
Therefore, the statement is true.
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Suppose that an individual has a body fat of 17.1% and weighs 128 pounds. How many pounds of his weight is made up of fat?
Answers
\(\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{17.1\% of 128}}{\left( \cfrac{17.1}{100} \right)128}\implies 21.888~~ \approx ~~22\)
CAN SOMEONE PLEASE HELP ME WITH MY MATH ASAP PLEASE!!!!
Answers
y-24=-7(x+4)
Answer:
y - 24 = - 7(x + 4)
Step-by-step explanation:
The equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b) a point on the line
Calculate m using the slope formula
m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)
with (x₁, y₁ ) = (- 4, 24) and (x₂, y₂ ) = (7, - 53)
m = \(\frac{-53-24}{7+4}\) = \(\frac{-77}{11}\) = - 7
Using m = - 7 and (a, b) = (- 4, 24) , then
y - 24 = - 7(x - (- 4) ) , that is
y - 24 = - 7(x + 4) ← equation in point- slope form
Consider the polynomial
(4mn^2n - 2mn + 6) + (6mn^2 - 1) - (mn^2 - 2 + 9mn)
Combine all like terms and enter the coefficients for each term into the blanks below
Answers
(4mn^2n - 2mn + 6) + (6mn^2 - 1) - (mn^2 - 2 + 9mn)
First, let's remove the parentheses:
4mn^2 - 2mn + 6 + 6mn^2 - 1 - mn^2 + 2 - 9mn
Next, let's combine like terms by adding or subtracting coefficients of the same variables:
(4mn^2 + 6mn^2 - mn^2) + (-2mn - 9mn) + (6 + 2 - 1)
Simplifying further:
9mn^2 - 11mn + 7
So, the coefficients for each term are:
9, -11, 7
If a wheelchair access ramp has to have an angle of elevation no more than 4.8 degrees and it has to rise 18 inches above the ground, how long must the ramp be?
Answers
The wheelchair access ramp must be 216.09 inches long.
To find the length of the wheelchair access ramp, we can use trigonometry.
The tangent function relates the angle of elevation to the ratio of the opposite side (height) to the adjacent side (length of the ramp).
Let's denote the length of the ramp as "x".
The height of the ramp is given as 18 inches.
Using the tangent function:
tan(angle of elevation) = height/length of the ramp
tan(4.8 degrees) = 18/x
To solve for x, we can rearrange the equation:
x = 18 / tan(4.8 degrees)
Using a calculator to evaluate the tangent of 4.8 degrees:
x = 18 / 0.08331
x= 216.09
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What is the slope of the line?
Answers
Answer:
2
Step-by-step explanation:
Every time the x value goes up one, the y value goes up 2.
pls help will give brainliest
Given f(x)=2/x^2+3x-10, which of the following is true?
A. f(x) is positive for all x<-5
B. f(x) is negative for all x<-5
C. f(x) is positive for all x<2
D. f(x) is positive for all x>2
Answers
The only true statement about the domain of the given function is:
B. f(x) is negative for all x < -5
How to solve for the domain of the function?The domain of a function is defined as the set of values that we can possibly plug into our function. This set is the x values in a function such as f(x).
Now, we are given the function as:
f(x) = \(\frac{2}{x^{2} } + 3x - 10\)
When x < -5, we have:
f(-4) = \(\frac{2}{(-4)^{2} } + 3(-4) - 10\)
f(-4) = -21.875
This suggests that for all values below x = -5 will result in negative values
When x > 2
f(3) = \(\frac{2}{3^{2} } + 3(3) - 10\)
f(3) = -0.78
Thus, it will get positive for higher values but it can also be negative as seen here.
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for every 3 racing computer games that joey owns, he had 5football games, he has 6 racing game. how many games does hehave in total
Answers
Answer:
He would have 16 because if you take 3 times 2 to get 6 then you have to ake 5 times 2 to get 10 then you add 6 and 10 to get 16
Step-by-step explanation:
PLEASE HELP- 25 points-what is the circumference of the circle. Diameter =9cm
Answers
Answer:
9π cm - exact value
28.26 cm - approximate value
Step-by-step explanation:
C = πd =9π cm - exact value
or
C=9π≈ 28.26 cm - approximate value
Find the Prime Factorization of 120.
A. 2x 32 x 5
B. 23 x 3 x 5
C. 4x6x5
D. 8 x3 x 5
Answers
Answer:
option (c)
Step-by-step explanation:
4*6*5
please mark as brainliest
A box contains 54 coins which are either 20-cent coins or 50-cent coins. If the total value of all the coins is $20.70, find the number of 20-cent coins in the box. LOF 1 11.
Answers
Number of 20-cent coins in the box are 33.
1. Let's assume the number of 20-cent coins to be x and the number of 50-cent coins to be y.
2. We can set up two equations based on the given information:
- x + y = 54 (since the total number of coins in the box is 54)
- 0.20x + 0.50y = 20.70 (since the total value of all the coins is $20.70)
3. We can multiply the second equation by 100 to get rid of the decimals:
- 20x + 50y = 2070
4. Now, we can use the first equation to express y in terms of x:
- y = 54 - x
5. Substitute the value of y in the second equation:
- 20x + 50(54 - x) = 2070
6. Simplify and solve for x:
- 20x + 2700 - 50x = 2070
- -30x = -630
- x = 21
7. Substituting the value of x back into the first equation:
- 21 + y = 54
- y = 33
8. Therefore, there are 21 20-cent coins and 33 50-cent coins in the box.
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What is the area of the region of points
satisfying the inequalities x ≤ 0, y ≤ 0, and
y ≥ |x + 4| − 5?
Answers
the area of the region of points satisfying the inequalities x ≤ 0, y ≤ 0, and y ≥ |x + 4| − 5 is 12.5 square units.
Which congruence theorems can be used to prove ΔABR ≅ ΔACR? Select three options. Triangles A B R and A C R share side A R. Angles A B R and A C R are right angles. Sides A B and A C are congruent. Sides B R and C R are congruent. HL SAS SSS ASA AAS
Answers
Answer:
A. HL
B. SAS
C. SSS
May I have brainliest please? :)
The triangles can be proved congruent by HL, SSS, and SAS congruence, the correct option is A, B, and C.
What is a Right Angled Triangle?A right triangle is a triangle in which the measure of one of the angles is 90 degrees.
The triangle given is are triangles ABR and ACR
They share a common side AR
∠ABR = ∠ACR = 90 degree.
AB ≅ AC
BR ≅ CR
The triangles can be proved congruent by,
HL- Height Length congruence for a right-angle triangle
SSS - All the sides are equal and,
SAS - The two sides and the included angle is equal.
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The theater sells two types of tickets: adult tickets for $6 and child tickets for $4.
Last night, the theater sold a total of 364 tickets for a total of $1930. How many adult tickets did the theater sell last night?
Answers
Answer:
237
Step-by-step explanation:
This is a system of equations.
The theater sold 364 adult and child tickets, so a + c = 364
They made a total of $1930. Each adult ticket was $6 & child tickets were $4. The second equation is 6a + 4c = 1930.
Let's line them up
a + c = 364
6a + 4c = 1930
Since we need to solve for the number of adult tickets, we want to get rid of the c variable. I'm going to multiply the entire first equation by -4 to do this. The second equation stays the same. Now, I have:
-4a - 4c = -1456
6a + 4c = 1930 Add them together
----------------------
2a = 474 Divide by 2 to solve for a
a = 237
There were 237 adult tickets sold
Suppose that the functions f and g are defined for all real numbers x as follows.5 (x) =3738 (x) =x?Write the expressions for (f+g) (x) and (f-g) (x) and evaluate (f-g)(-2).
Answers
Solution:
Given:
\(\begin{gathered} f(x)=3x^3 \\ g(x)=x^2 \end{gathered}\)Question 1:
\(\begin{gathered} (f+g)(x)=f(x)+g(x) \\ (f+g)(x)=3x^3+x^2 \end{gathered}\)Question 2:
\(\begin{gathered} (f\cdot g)(x)=f(x)\cdot g(x) \\ (f\cdot g)(x)=3x^3\cdot x^2 \\ (f\cdot g)(x)=3x^5 \end{gathered}\)Question 3:
\(\begin{gathered} (f-g)(x)=f(x)-g(x) \\ (f-g)(x)=3x^3-x^2 \\ (f-g)(-2)=3(-2)^3-(-2)^2 \\ (f-g)(-2)=-24-4 \\ (f-g)(-2)=-28 \end{gathered}\)Will give brain thingy lol I’m too lazy to use my brain and figure this out anyways.
Answers
Answer: C. 1/8
Step-by-step explanation:
2/16 were pepperoni at pizza hut the first time,
then simplifying 2/16 = 1/8 = 1/8 chance.
Answer:
1/8
Step-by-step explanation: