Jonah's swimming pool is 21 meters by 20 meters. He swam from one corner of the pool to the opposite corner. How far did Jonah swim?
Answers
Jonah swam a distance of 29 meters from one corner of the pool to the opposite corner.
To determine how far Jonah swam from one corner of the pool to the opposite corner, we can use the Pythagorean theorem. According to the theorem, in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, the two sides of the right-angled triangle are the length and width of the swimming pool, which are 21 meters and 20 meters respectively. The distance Jonah swam represents the hypotenuse of the triangle.
Using the Pythagorean theorem:
\(Hypotenuse^2 = Length^2 + Width^2\)
\(Hypotenuse^2\) =\(21^2 + 20^2\)
\(Hypotenuse^2\)= 441 + 400
\(Hypotenuse^2\)= 841
Taking the square root of both sides, we find:
Hypotenuse =\(\sqrt{841\)
Hypotenuse = 29
Jonah swam a distance of 29 meters from one corner of the pool to the opposite corner.
According to the Pythagorean theorem, in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.
The two sides of the right-angled triangle are the length and width of the swimming pool, which are 21 meters and 20 meters respectively. The distance Jonah swam represents the hypotenuse of the triangle.
Using the Pythagorean theorem:
\(Hypotenuse^2 = Length^2 + Width^2\\Hypotenuse^2 = 21^2 + 20^2\\Hypotenuse^2 = 441 + 400\\Hypotenuse^2 = 841\)
Taking the square root of both sides, we find:
Hypotenuse = \(\sqrt841\)
Hypotenuse = 29
Jonah swam a distance of 29 meters from one corner of the pool to the opposite corner.
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Related Questions
factor and solve
x^2-4x=5
Answers
Let’s solve the equation x^2 - 4x = 5 by factoring:
First, we’ll move all the terms to one side of the equation:
x^2 - 4x - 5 = 0
Now, we’ll factor the left side of the equation. We’re looking for two numbers that multiply to -5 and add to -4. Those numbers are -5 and 1. So we can write:
(x - 5) (x + 1) = 0
Now we’ll use the zero-product property to solve for x. This property states that if the product of two numbers is zero, then at least one of the numbers must be zero. So we have:
x - 5 = 0 or x + 1 = 0
Solving each equation separately, we find that x = 5 or x = -1.
So, the solutions to the equation x^2 - 4x = 5 are x = 5 and x = -1.
Marta just started a new job as an engineer. She is given a $9,000 sign on bonus and paid $4,500
per month. Write and solve an equation to determine the number of months that Marta must work
before she earns $27.000.
Answers
9000 + 4500 x n = 27000
4500 x n = 18000
n = 18000 : 4500
n = 4
4 months of work
Simplify 5^-2 x 5^5 x 5
Answers
Answer:
e
Step-by-step explanation:
2
8. Choose all decimals that are equivalent to (7 x 100) + (5 × 1) + (8 × 7) + X 10 (1 × 100). 75.081 705.810 705.801 75.810 705.81 705.081
Answers
Answer:
705.81 and 705.810
Step-by-step explanation:
700 + 5 + 0.8 + 0.01 = 705.81
Answers:
705.810
705.81
Evalúe the limit. Show steps
Answers
After evaluating the limit we have came to find that the limit of \(\lim_{x\rightarrow -\infty }\frac{x^2}{x^2\ +4}\) as x approaches ∞- is 1
What is limit?The value that a function, sequence, or index approaches as an input, or an index, approaches a particular value is known as a limit in mathematics. Limits, which are essential to calculus and mathematical analysis, are required by the definitions of continuity, derivatives, and integrals.
In addition to being closely related to the concepts of limit and direct limit in category theory, the idea of a limit of a sequence is further generalised to encompass the idea of a limit of a topological network.
A limit of a function is typically expressed in formulas as
\({\displaystyle \lim _{x\to c}f(x)=L,}\)
To find the limit we will use L'Hôpital's Rule
Find the derivative
⇒ \(\lim_{x\rightarrow -\infty }\frac{x^2}{x^2\ +4}\)
⇒ \(\lim_{x\rightarrow -\infty }\frac{2x}{2x +0}\)
⇒ \(\lim_{x\rightarrow -\infty }\frac{2x}{2x }\)
Evalue -∞ as x
⇒ \(\frac{2(-\infty)}{2(-\infty)} }\)
⇒ 1
Learn more about Limit
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How many ways to paint a house with 3 different colors from a pool of 12 distinct colors
Answers
6x + 45 is less than or equal to 240
Answers
Answer: neither
Step-by-step explanation:
To get rid of the fractions, we pick a useful number and multiply both sides of the equation by that number. The number is useful if multiplying eliminates all fractions.
Dana is making bean soup. The recipe she has makes 10 servings and uses
3/4
of a pound of beans. How many total pounds of beans does she need to make 5 servings of soup?
She has
1/16
of a pound of beans in one container and
1/4
of a pound of beans in another container. How many more pounds of beans does Dana need to make the 5 servings of soup? Show your work or explain your answer.
Answers
What is the average rate of change for this quadratic
function for the interval from x=2 to x = 4?
A. 12
B. -6
C. -12
D. 6
-10-
Click here for long description
SUBMIT
Answers
The average rate of change of the function over the interval is -6
Finding the average rate of changeFrom the question, we have the following parameters that can be used in our computation:
The graph
The interval is given as
From x = 2 to x = 4
The function is a quadratic function
This means that it does not have a constant average rate of change
So, we have
f(2) = -3
f(4) = -15
Next, we have
Rate = (-15 + 3)/(4 - 2)
Evaluate
Rate = -6
Hence, the rate is -6
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Given 7(x, y) = (x + 5, y + 4) and the point P (2, 3), what is 7(P)? please show work so sorry
Answers
Answer:
(7, 7)
Step-by-step explanation:
We are given the formula 7(x, y) = (x+5, y+4) for a pair of coordinates (x,y).
P is given as the coordinates: (2, 3), therefore if we substitute P into the equation, we can replace x and y in the given equation for the coordinates of P (2,3).
P is given as (2,3), so 7(P) = 7(2,3).
Using the given formula:
7(2,3) = (2+5, 3+4)
2+5 = 7, 3+4 = 7
Therefore 7(P) = (7, 7)
Hope this helped!
-6y-3x=-18 for x and y
Answers
The answer fam is..... X = 6 - 2y, Y = 3 - x/2
divide 7 by 12 to change 7/12 to a repeating decimal. 7/12 = 7 divided by 12 = ?
Answers
Answer:
0.58333333....
can i have brainliest plz
A triangle LMN with ln = 12 cm,Nm= x cm, Nk = 6cm and Km 8cm
Calculate the value of
(i) x
(ii) o
Answers
The value of x is 9 cm, and angle O is 0 degrees.
To solve the triangle LMN and find the values of x and angle O, we can use the Law of Cosines and the Law of Sines. Let's go step by step:
(i) To find the value of x, we can use the Law of Cosines. According to the Law of Cosines, in a triangle with sides a, b, and c, and angle C opposite to side c, the following equation holds:
c^2 = a^2 + b^2 - 2ab * cos(C)
In our case, we want to find side NM (x), which is opposite to angle N. The given sides and angles are:
LN = 12 cm
NK = 6 cm
KM = 8 cm
Let's denote angle N as angle C, side LN as side a, side NK as side b, and side KM as side c.
Using the Law of Cosines, we can write the equation for side NM (x):
x^2 = 12^2 + 6^2 - 2 * 12 * 6 * cos(N)
We don't know the value of angle N yet, so we need to find it using the Law of Sines.
(ii) To find angle O, we can use the Law of Sines. According to the Law of Sines, in a triangle with sides a, b, and c, and angles A, B, and C, the following equation holds:
sin(A) / a = sin(B) / b = sin(C) / c
In our case, we know angle N and side NK, and we want to find angle O. Let's denote angle O as angle A and side KM as side b.
We can write the equation for angle O:
sin(O) / 8 = sin(N) / 6
Now, let's solve these equations step by step to find the values of x and angle O.
To find angle N, we can use the Law of Sines:
sin(N) / 12 = sin(180 - N - O) / x
Since we know that the angles in a triangle add up to 180 degrees, we can rewrite the equation:
sin(N) / 12 = sin(O) / x
Now, we can substitute the equation for sin(O) from the Law of Sines into the equation for sin(N):
sin(N) / 12 = (6 / 8) * sin(N) / x
Now, we can solve this equation for x:
x = (12 * 6) / 8 = 9 cm
So, the value of x is 9 cm.
To find angle O, we can substitute the value of x into the equation for sin(O) from the Law of Sines:
sin(O) / 8 = sin(N) / 6
sin(O) / 8 = sin(O) / 9
9 * sin(O) = 8 * sin(O)
sin(O) = 0
This implies that angle O is 0 degrees.
Therefore, the value of x is 9 cm, and angle O is 0 degrees.
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The figure for the given question is provided here :
What is the solution set to the inequality (4x-3)(2x-1)>0?
Answers
Answer:
C
Step-by-step explanation:
Answer:
c
Step-by-step explanation:
A person walked diagonally across a square plot. Approximately, what was the percent saved by not walking along the edges? A. 35% B. 30 % C. 20 % D. None of the above
Answers
========================================
Explanation:
Consider a square with side length 1 unit.
Draw a diagonal and we have two congruent isosceles right triangles. Each triangle has a hypotenuse of sqrt(2) after using the pythagorean theorem.
If the person walks along the edges, then they walk 1+1 = 2 units.
If they walk along the diagonal, they walk roughly sqrt(2) = 1.4142 units.
They save roughly 2-1.4142 = 0.5858 units
which is roughly 0.5858/2 = 0.2929 = 29.29% of the walked distance along the edges. There's probably some slight rounding error going on, but it's fairly close to 30%, so that is likely the final answer.
how the number e was discover
Answers
Answer:
It was that great mathematician Leonhard Euler who discovered the number e and calculated its value to 23 decimal places. It is often called Euler's number and, like pi, is a transcendental number (this means it is not the root of any algebraic equation with integer coefficients
10-² =
Exponential form
Answers
Copy the base to the right side of the equality
10-^2=10
Rewrite the exponent -2 as the product of (-1) and 2
10-^2=10^(-1)x2
First, use the Power of a Power Property
10-^2=(10^(-1) ) ^2
Any number raised to the power of can be written as its reciprocal
10^-2=(1/10)^2
Next, use the Power of a Quotient Property
10^-2=1^2/10^2
1 raised to any power equals 1
10^-2=1/10^2
so the answer is 10^-2=1/10^2
Answer:
Step-by-step explanation:
the answer is 0.01
The base of the exponential form is 10 and the power is -2 therefore the answer is 0.01 if the power was 2 the answer would have been 100
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Which of the points shown below are on the line given by the equation y = 4x?
Check all that apply.
Answers
Answer:
its B and C
Step-by-step explanation:
why is the cutting edge of the knife made very thin ?
Answers
Due to the edge's significantly smaller surface area and increased pressure, it is simpler to force your palm through. You don't need to move the butter around as much because the edge is narrower.
What does a knife's cutting edge look like?The blade's edge is its cutting edge. It stretches all the way from the knife's tip to its heel. Heel: Opposite the tip, the heel is the back portion of the edge.
A knife's edge is how thick?Knives should have a thickness of between.013" and.25" to be considered optimum. Kitchen knives are typically slimmer, whereas survival blades are typically thicker.
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help 10 points to solve please
Answers
Answer:
A, B, & C are true.
Hope this helps & have a great rest of your day!
Answer:I believe the answer is A,B,C
Step-by-step explanation:
find the volume of each prism 2.7ft 3ft 2ft
Answers
Answer:
16.2 is the volume i hope i helped u
6(x+8)=-36 what does x equal
Answers
Answer:
Step-by-step explanation:
6(x+8) = -36
divide both sides by 6: x+8 = -6
subtract 8 from both sides: x = -14
Answer:
6(x+8)=-36
6x+48=-36
6x=84
x=14
Someone help ASAP PLEASE
Answers
Answer: 7 1/2 minutes
Answer:
7.5 mins.
Step-by-step explanation:
We know the unit rate is 1.5 mins for 1 km. So we can just multiply both numbers by 5.
1.5/1 = 7.5/5
It takes a shark 7.5 (7 1/2) minutes to swim 5 km.
Q. Pick out the most effective word from among the given words to fill in the blanks to make the sentence meaningfully complete.
On ____________ of his age he is ineligible for the examination.
1) Reason
2) Basis
3) Account
4) Purpose
Answers
Answer:4
Step-by-step explanation:
Answer:
4
Step-by-step explanation:
in triangle ABC, BC=10 and is the longest side of the triangle.
if AB^2 + AC^2 < 100 then triangle ABC is ______
A. right
B. obtuse
C. acute
Answers
Answer:
B. obtuse
Can't be right because 100 would have to = ab^2 + ac^2
to be acute, ab^2 + ac^2 would have to be greater than 100
Which expression is equivalent to the given expression? Give a step-by-step guide and explain how you got to your answer, so I can actually learn how to do this.
Answers
The Solution:
Given:
Required:
Find an equivalent expression of the given expression.
\(\begin{gathered} (2w^{-2})^3(8w^6) \\ \\ 2^3\times8\times w^{-2\times3}\times w^6 \end{gathered}\)\(\begin{gathered} 8\times8\times w^{-6}\times w^6 \\ \\ 64\times w^{-6+6} \\ 64\times w^0 \\ 64\times1 \\ 64 \end{gathered}\)Answer:
[option B]
Find the volume of a cone of radius 3.5cm and vertical height 12 cm.
Answers
Answer:
Volume ≈ 153.93804 cm^3
Rounded to the nearest whole number, the volume of the cone is approximately 154 cm^3.
Step-by-step explanation:
simplify [Xn (X'nY)]'.
Answers
Answer:
(X'U'Y) + (XUY')
Step-by-step explanation:
Starting with [Xn(X'nY)]', we can use De Morgan's laws to simplify the expression:
[Xn(X'nY)]' = (Xn)' + (X'nY)'
Recall that Xn represents the logical operator "and", while X' represents "not X". Using these definitions, we can expand the expression:
(Xn)' + (X'nY)' = (X'U'Y) + (XUY')
where U represents the logical operator "or".
Therefore, [Xn(X'nY)]' simplifies to (X'U'Y) + (XUY').
Hey guys are you available?
Answers
Answer:
c
Step-by-step explanation:
Answer:C
Step-by-step explanation:
A line intersects the points (3,-4) and
(1, 2). What is the slope-intercept
equation for this line?
y = -3x + [?]
Answers
2=-3(1)+?
2=-3+?, move the 3 to the other side by adding 3 to bothe sides,
?=5