A rectangular patio is 10 feet by 13 feet. what is the length of the diagonal of the patio? (use pythagorean theorem: a² + b ²= c²)
Answers
The length of the diagonal is c = √269 feet.
To get the length of the diagonal of a rectangular patio, we can use the Pythagorean theorem, which states that for a right triangle with legs of length a and b, and hypotenuse of length c, a² + b² = c². In this case, the legs of the right triangle are the length and width of the rectangular patio, which are 10 feet and 13 feet, respectively. Let's use a and b to represent these lengths.
a = 10 feet
b = 13 feet
We want to find the length of the diagonal, which is the hypotenuse of the right triangle. Let's use c to represent this length.
a² + b² = c²
10² + 13² = c²
100 + 169 = c²
269 = c²
Now we need to find the square root of 269 to get the length of the diagonal.
c = √269
c ≈ 16.4 feet
So the length of the diagonal of the rectangular patio is approximately 16.4 feet. We can also find the ratio of the length, width, and diagonal of the rectangular patio.
length:width = 10:13
width:length = 13:10
length:diagonal = 10:√269
width:diagonal = 13:√269
diagonal:length = √269:10
diagonal:width = √269:13
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Related Questions
Need help ASAP. Please answer quick
Answers
Answer:
Energy used, input
Monthly bill, output
Step-by-step explanation:
the bill is affected by how much energy u use
HOPE THIS HELPS!
Brainliest?
I need to know how to do these and if I got the one right
Answers
23. The value for x in triangle is 11.14
24. The value for x in the triangle is 18.3
25. The value for x = 30.4
27 The value for x = 63.413 degrees
Sine, Cosine and Tangent23
Cos θ= adj/ hyp
cos 42= x/15
x = 15 cos 42
x = 11.14
24
tan θ= opp/ adj
tan 31= 11/ x
x(tan 31)= 11
x = 11/tan 31
x = 18.3
25
cos θ= adj/ hyp
cos 18= 29/x
x(cos 18) = 29
x = 29/ cos 18
x = 30.4
27
sin x = opp/ hyp
sin x = 17/19
sin x = 0.8947
x = 63.413 degrees
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What is the radius of a sphere with a volume of 41572 cm', to the nearest tenth of a
centimeter?
Answers
We know that,
Volume of sphere = 4/3πr³
41572 = 4/3 × 22/7 × r³
41573 × 21/88 = r³
³√9,920.82 = r
21.48 cm = r
:)
The radius of a sphere with a volume of 41572 cm³ is,
⇒ 21.4 cm
What is Multiplication?To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Now, To find the radius of a sphere with a volume of 41572 cm³, we can use the formula for the volume of a sphere as;
⇒ V = (4/3)πr³
where V is the volume and r is the radius.
Hence, We can rearrange this formula to solve for r:
⇒ r = ∛ (3V/4π)
Substituting the given volume, we have:
r = ∛ (3(41572)/4π)
r ≈ 21.4 cm
Therefore, the radius of the sphere to the nearest tenth of a centimeter is 21.4 cm.
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Joyce’s teacher asks her to write the sequence formed by the number of red squares in each picture for the first five pictures. What sequence should Joyce write?
Answers
Answer:
Joyce should write \(1,8,64,512,4096\)
Step-by-step explanation:
Let's analyze the procedure of how the pictures are formed.
Her teacher said the images were created by taking a red square, dividing it into 9 smaller squares, and removing the center square.
For the first two images we can see and count that there is 1 red square in the first picture and 8 red squares in the second picture.
For the third image, there are 8 squares formed by 8 red squares each one.
The number of red squares is 8 x 8 = 64
We can write the sequence as
1 , 8 , 64 ⇒ 1 , 8 , \(8^{2}\)
For the fourth picture we can do the same reasoning and figure out that there are 8 x 8 x 8 = 512 red squares in the fourth image.
The sequence so far is
1 , 8 , 64 , 512 ⇒ 1 , 8 , \(8^{2}\) , \(8^{3}\)
We can generalize the sequence and write that the sequence is :
\(8^{n}\) with \(n\) ∈ IN ⇒ The first five numbers will be
\(8^{0},8^{1},8^{2},8^{3},8^{4}\) = \(1,8,64,512,4096\)
Line m contains points a, b, and c, where a is (1, -3), b is (2,-6), and cis (-1,3). what is the slope of line m
Answers
The slope is the same between points a and b and between points b and c, we can conclude that the slope of line m is -3.
To find the slope of line m, we can use the formula:
slope = (change in y-coordinates) / (change in x-coordinates)
Given the coordinates of points a, b, and c:
Point a: (1, -3)
Point b: (2, -6)
Point c: (-1, 3)
The change in y-coordinates between points a and b is: -6 - (-3) = -3
The change in x-coordinates between points a and b is: 2 - 1 = 1
So, the slope between points a and b is: -3/1 = -3
Similarly, the change in y-coordinates between points b and c is: 3 - (-6) = 9
The change in x-coordinates between points b and c is: -1 - 2 = -3
So, the slope between points b and c is: 9/-3 = -3
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in the miss america pageant, 51 contestants must be narrowed down into 10 finalists. how many ways can this occur?
Answers
Total ways can occur is 19,653,800.
What is Combination?
Combinations are ways to choose elements from a larger set in mathematics where the order of the elements is irrelevant. Repetition is prohibited and the order of the elements does not matter in a combination, which is a subset of items.
The number of combinations of 51 things chosen 10 at a time, represented as C, determines the number of possibilities to choose 10 finalists from 51 contestants (51, 10).
Combinations are calculated as follows: C (n, k)=\(n! / (k! (n-k)!).\)
Consequently, there are three options to choose 10 finalists from the pool of 51 applicants:\(C(51, 10) = 51! / (10! (51-10)!) = 51! / (10! 41!) = 19,653,800.\\\)
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in the miss America pageant, 51 contestants must be narrowed down into 10 finalists. The total number of ways that can occur is 19,653,800.
What is Combination?
In mathematics, combinations are strategies to select components from a bigger set where the order of the elements is unimportant. In a combination, which is a subset of items, repetition is not permitted and the position of the parts is irrelevant.
The possibility of selecting 10 finalists from 51 contenders is determined by the number of combinations of 51 things picked 10 at a time, denoted as C. (51, 10).
Combinations are calculated as follows: C (n, k)= \(\frac{n!}{k!(n-k)!}\)
Consequently, there are three options to choose 10 finalists from the pool of 51 applicants: 19653800
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which of the following numbers is irrational
Answers
Answer:
E
Step-by-step explanation:
Irrational means cannot be put into a fraction. Or random repeating decimals is how I remember it.
√48 can be simplified to equal 4√3. √3 cannot be put into fraction form.
Bella has a cell phone plan in which she pays of each call minute and text message she sends. The total number of minutes used and text messages sent last month was 561. If call minutes cost 8€ each and text messages cost 5€ each and her pill was $34. 26, how many minutes did she use?
Answers
If the total number of minutes used and text messages sent last month was 561 , then the number of minutes she use is 207 minutes .
The total number of minutes used and text messages is = 561 ;
the cost for per minute cost is = 8 cents ;
the cost for per text message is = 5 cents ;
Bella's total bill amount is = $34.26 = 3426 cents
let the number of minutes used be = x minutes ; and
let the number of text messages be = y ;
So ,According to the question ,
the equations representing the situations are ,
\(x+y=561\) and \(8x+5y=3426\)
Substituting the values of \(y=561-x\) in the equation \(8x+5y=3426\) ,
we get ;
\(8x + 5(561-x)= 3426\)
On solving ,
we get ; x = 207 minutes ;
So , the number of text messages (y) = \(561-207\)
= 354 text messages.
Therefore , the number of minutes is = 207 minutes .
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if you subtract 1 by 2 from a number and multiply result 1by 2, you get 1by 8. what is the number
Answers
Answer:
the answer is 9/16 I hope this doesn't require step by step solve
Answer:
x = 4Step-by-step explanation:
x - 2 x 2 = 8
x times 2 = 8
x = 4
What is the quotient for 3 1/4 ÷ 2 3/8?
Answers
Answer:
26/16 or 1 7/19
which rule must be used to find the number of strings of four decimal digits that have exactly three digits that are 9s?
Answers
The product rule must be used to find the number of strings of four decimal digits, that have exactly three digits that are 9s.
What is product rule ?
The Product Rule says that the derivative of a product of two functions is the first function times the derivative of the second function plus the second function times the derivative of the first function.
To obtain the number of strings of 4 decimal digits that have exactly 3 digits that are 9s ; we use the product rule,
In first digit 1 possible way between 0 to 9
In second digit 1 possible way between 0 to 9
In third digit 1 possible way between 0 to 9
In fourth digit 9 possible ways between 0 to 9
That's mean 1 * 1* 1* 9* 4 = 36
Thus 36 possible ways.
The product rule must be used to find the number of strings of four decimal digits.
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figure b is a scaled copy of figure a. help?
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Gravetter/Wallnau/Forzano, Essentials - Chapter 12 - End-of-chapter question 17 Several factors influence the size of the F-ratio. For each of the following, indicate whether it would influence the numerator or denominator of the F- ratio, and indicate whether the size of the F-ratio would increase or decrease. Increasing the differences between the sample means: As the differences between sample means increase, Shewe also increases, and the F-ratio increases As the differences between sample means increase, Mbetween also increases, and the F-ratio decreases. As the differences between sample means increase, MSbor decreases, and the F-ratio decreases As the differences between sample means increase, MStarwe decreases, and the F-ratio increases Increasing the size of the sample variances: Increases in sample variability cause Mswibh to decrease and thereby decrease the F-ratio. Increases in sample variability cause Mouhinto decrease and, thereby, increase the F-ratio O Increases in sample variability cause MS within to increase and, thereby, increase the Fratio. Increases in sample variability cause MS in to increase and thereby decrease the F-ratio.
Answers
The size of the F-ratio value would increase as the numerator of the F-ratio (MS Between) increased and The size of the F-ratio value would increase as the numerator of the F-ratio (MSBetween) increased.
Given that,
The F ratio can be defined as,
F =Mean Sum of Squares of between treatments / Mean Sum of Squares of within treatments
F =MS Between /MS within
Increase the difference between the sample means.
As the difference between the sample means increases, between treatments has larger effect
(MS known ) . This affects the numerator of F-ratio.
Hence, As numerator of F-ratio ( MS Between ) increases, the size of the F-ratio value would increase.
Increase the size of sample variances.
As the size of sample variance increases, with treatments has larger effect ( MS within ). This
affects the denominator of F-ratio.
Hence, As the denominator of F-ratio (MS Within ) increases. The size of F-ratio will decrease.
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The distance between the school and the park is 6km. There is 1.6km in 1 mile. How many miles apart are the school and the park.
Answers
Answer:
3.75 miles
Step-by-step explanation:
You want to know the number of miles represented by 6 km, when the relationship is 1.6 km = 1 mile.
Conversion factorsAnytime measures are related by a constant conversion factor, the values of the measures in one unit are proportional to the values expressed in a different unit. That is, the ratio of km to miles is a constant.
ApplicationWe can let d represent the distance between the school and the park.
miles / km = (1 mi)/(1.6 km) = d/(6 km) . . . . miles and km are proportional
Multiplying by 6 km, we get ...
d = (6 km)(1 mi)/(1.6 km) = (6/1.6) mi ≈ 3.75 mi
The school and the park are 3.75 miles apart.
A rectangle's width is 2 meters shorter than its length, /. Its area is 168 square meters. Which equation can be used
to find the length of the rectangle?
Answers
Answer:
x(x-2)=168
x=14
Step-by-step explanation:
Let the length of the rectangle be x.
width=(x-2)
x(x-2)=168
x^2-2x=168
x=14, x=-12 (rejected)
Lines l and m are parallel.
Which statement is always true?
Group of answer choices
A 90° rotation will map line l onto line m.
Line l can be reflected over a horizontal line to map onto line m.
Line l can be reflected over a vertical line to map onto line m.
Line l can be translated to map onto line m.
Answers
Lines l and m are parallel; line l will map onto line m with a 90° rotation; line l can map onto line m with a vertical line of reflection.
Do you have any explanations as to why the lines L and m are parallel?L and m are not parallel because the sum of the co-interior angles on the same side of the transversal does not equal 180 degrees.In the event when two lines, l and m, are in the same plane but do not cross, they are said to be parallel.We are aware that the equivalent angles are equal if they are parallel and a transversal is drawn to intersect them both. Accordingly, these are x and y. As a result, we can conclude that x and y are equivalent if l and m are parallel.If two lines, l and m, are in the same plane and do not cross one another, then they are parallel.To learn more about Lines refer to:
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I
need the details why we choose answer c
109) Use the following random numbers to simulation crop yield for 10 years: 37, 23, 92, 01, 69, 50, 72, 12, 46, 81. What is the estimated crop yield from the simulation? A) 425 B) 442 C) 440 D) 475 A
Answers
The estimated crop yield from the simulation is 443 (option b).
To estimate the crop yield from the given random numbers, we need to assign a specific meaning to each random number. Let's assume that each random number represents the crop yield for a particular year.
Given random numbers: 37, 23, 92, 01, 69, 50, 72, 12, 46, 81
To find the estimated crop yield, we sum up all the random numbers:
37 + 23 + 92 + 01 + 69 + 50 + 72 + 12 + 46 + 81 = 443
Therefore, the estimated crop yield from the simulation is 443. The correct option is b.
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help plsssssssssssssss
Answers
What is GC?
A. 9
B. 12
C. 13
D. 14
Answers
Answer:
C 13
Step-by-step explanation:
i think answer its c
Answer:
nah man it's 12without a doubt look over at d a that's 13 if you compare the to gc is smaller in length so it is 12
If f(x) = sin x + 2x + 1 and g is the inverse function of f, what is the value of g'(1) ?.
Answers
Answer:
1/3
Step-by-step explanation:
\(g(f(x))=x \\ \\ g'(f(x))f'(x)=1 \\ \\ g'(f(x))=\frac{1}{f'(x)} \\ \\ g'(f(x))=\frac{1}{\cos x+2} \\ \\ g'(f(0))=\frac{1}{\cos(0)+2} \\ \\ g'(1)=\frac{1}{3}\)
are older men shorter than younger men? according to a national report, the mean height for u.s. men is 69.4 inches. in a sample of 170 men between the ages of 60 and 69, the mean height was x
Answers
If older men are shorter than younger men. However, we do have information about the mean height for U.S. men, which is 69.4 inches.
Additionally, we have a sample of 170 men between the ages of 60 and 69, but we do not have the value for the mean height of this sample (represented as "x" in the question).
If we were given the value of "x", we could compare it to the mean height for all U.S. men and potentially make conclusions about the height of older men compared to younger men.
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Use the distributive property to rewrite each expression in its equivalent form. -2×(3y + 9)
Answers
Answer:
-6y-18
Step-by-step explanation:
hope this helps :D
The answer is -6y-18
the question is on the image
(explain each step)
Answers
==========================================================
Explanation:
All three angles must add to 180. This is true for any triangle.
x+x+110 = 180
2x+110 = 180
2x = 180-110 ... subtract 110 from both sides
2x = 70
x = 70/2 .... divide both sides by 2
x = 35
As a check: 35+35+110 = 180 which helps confirm the answer.
Answer:
Step-by-step explanation:
x + x + 110 = 180 degree (sum of interior angles of a triangle)
2x + 110 = 180
2x = 180 - 110
x = 70/2
x = 35 degree
what is the perimeter of ABCD
Answers
The perimeter of triangle is 30. The perimeter of a shape is the entire distance enclosing it.
What is Perimeter?The whole length of any closed shape's boundary is known as its perimeter.
The whole distance encircling a shape is referred to as its perimeter.
It is the length of any two-dimensional geometric shape's boundary or outline.
Depending on the size, the perimeter of several figures can be the same. Consider a triangle built of an L-length wire, for instance.
If all the sides are the same length, the same wire can be used to create a square.
According to our question-
p = AB + AD + CD + BC
= 12 + 12 + 3 + 3
= 30
Hence, The perimeter of triangle = 30.
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Simplify.
(-2u?+u-3)+(4u²+7u+5)
Answers
Answer:
\(2u^2+8u+2\)
Step-by-step explanation:
\(\left(-2u^2+u-3\right)+\left(4u^2+7u+5\right)\)
\(\blacksquare\) Remove parentheses:
\(\longmapsto\) \(-2u^2+u-3+4u^2+7u+5\)
\(\blacksquare\) Combine like terms:
\(-2u^2+4u^2+u+7u-3+5\)
\(\longmapsto\) \(-2u^2+4u^2=2u^2\)
\(\longmapsto\)\(\:u+7u=8u\)
\(\longmapsto\) \(-3+5=2\)
\(\leadsto\) \(2u^2+8u+2\)
_______________________
Choose which statement is true about pi
Answers
I don’t see any statements?
QN is tangent to circle O at point I. IA is the circle's diameter. Find m/QIA.
N
€
E
E
C
3
R
3
C
Help I need help
Answers
The measure of tangent angle QIA is 180 degrees.
m/QIA = 180 degrees.
If IA is the diameter of the circle, it means that angle QIA is a right angle (90 degrees). Since QN is tangent to the circle at point I, it is perpendicular to the radius IA at that point.
Therefore, in triangle QIA, we have a right angle at Q and a right angle at I. This implies that angle IQA is also 90 degrees.
In a right triangle, the sum of the angles is 180 degrees. Since angles QIA and IQA are both right angles, the remaining angle in the triangle, angle QAI, must be:
180 degrees - 90 degrees - 90 degrees = 0 degrees
Angle QAI is a degenerate angle, which means it has a measure of 0 degrees. Therefore, the measure of tangent angle QIA is 180 degrees.
To summarize, m/QIA = 180 degrees.
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How does the volume of the larger cube compare to the volume of the smaller cube? Use pencil and
paper. Use this and other examples to describe what happens to the volume of a cube if you triple the length
of the edges.
Answers
Answer:
Option C, The volume of the length cube is 3 times the volume of the smaller cube
Step-by-step explanation:
21.8 / 7.8 = 2.8
the volume of the larger would be 21.8^3 = 10360.23
the volume of the larger would be 7.8^3 = 474.55
20 inch (diameter) bicycle wheel is spinning at a rate of 150 rpm. how fast is the bicycle moving (in mph)?
Answers
The bicycle is moving at a speed of 14,356 meters per hour.
Here, we are given that the wheel of a bicycle is spinning at the rate of 150 revolutions per minute.
The diameter of the wheel is 20 inches
⇒ radius = 10 inches
⇒ circumference of the wheel = 2 × π × 10
= 20π
Thus, the wheel will cover a distance of (20π × 150) inches in a minute
= 300π
now, we know that 1 inch = 0.254 meters
⇒ 300π inches = 300π × 0.254
= 76.2π
Thus, the bicycle covers 76.2π meters in a minute
⇒ it'll cover 76.2π × 60 meters in an hour
= 4572π
= 4572 × 3.14
= 14,356.08
Thus, the bicycle is moving at a speed of 14,356 meters per hour.
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Pls Help!!! Worth 99 Pts!!
Explain how to sketch a graph of the function f(x) = x3 + 2x2 – 8x. Be sure to include end-behavior, zeroes, and intervals where the function is positive and negative.
Answers
Answer:
First, for end behavior, the highest power of x is x^3 and it is positive. So towards infinity, the graph will be positive, and towards negative infinity the graph will be negative (because this is a cubic graph)
To find the zeros, you set the equation equal to 0 and solve for x
x^3+2x^2-8x=0
x(x^2+2x-8)=0
x(x+4)(x-2)=0
x=0 x=-4 x=2
So the zeros are at 0, -4, and 2. Therefore, you can plot the points (0,0), (-4,0) and (2,0)
And we can plug values into the original that are between each of the zeros to see which intervals are positive or negative.
Plugging in a -5 gets us -35
-1 gets us 9
1 gets us -5
3 gets us 21
So now you know end behavior, zeroes, and signs of intervals
Hope this helps
Answer:
The degree of the function is odd and the leading coefficient is positive – so the function goes to negative infinity as x goes to negative infinity and to positive infinity as x goes to positive infinity. The zeroes are –4, 0, and 2, all with multiplicity 1. The function is negative from negative infinity to –4 and from 0 to 2. The function is positive from –4 to 0 and from 2 to infinity.
Step-by-step explanation:
sample response on edge 2022