The length of the diagonal is:
20.3147
Step-by-step explanation:We know that if we draw a diagonal in a rectangle such that the length and width of a rectangle are a and b then the length of the diagonal act as a hypotenuse of a right angled triangle with two sides of triangle as a and b.
Hence, we will use the Pythagorean Theorem to find the length of the hypotenuse (c) as follows:
[tex]c^2=a^2+b^2[/tex]
[tex]c^2=(15)^2+(13.7)^2\\\\c^2=225+187.69\\\\c^2=412.69\\\\c=\pm \sqrt{412.69}\\\\c=\pm 20.3147[/tex]
Since, length can't be negative.
Hence, we have:
[tex]c=20.3147[/tex]
Final answer:
Using the Pythagorean theorem, the length of the diagonal for a rectangular garden measuring 15 m by 13.7 m is approximately 20.31 meters.
Explanation:
The student is asking about finding the length of the diagonal of a rectangle. The rectangle has dimensions of 15 m (length) and 13.7 m (width). To find the diagonal, we can use the Pythagorean theorem, which is applicable in a right-angled triangle and states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). The diagonal of the rectangle can be considered as the hypotenuse (c) of a right-angled triangle with the other two sides being the lengths and the width of the rectangle.
Using the dimensions of the garden:
Length (a) = 15 m
Width (b) = 13.7 m
Diagonal (c) = ?
Applying the Pythagorean theorem:
c^2 = a^2 + b^2
c^2 = 15^2 + 13.7^2
c^2 = 225 + 187.69
c^2 = 412.69
c = [tex]\sqrt{412.69}[/tex]
c ≈ 20.31 m
So, the length of the diagonal from one corner of the garden to the other is approximately 20.31 meters.
A retiree invests $8,000 in a savings plan that pays 7% per year. What will the account balance be at the end of the first year?
Final answer:
To calculate the account balance at the end of the first year for an investment of $8,000 at 7% per year, the formula for simple interest is used. After applying the formula, the final account balance is determined to be $8,560.
Explanation:
The retiree invests $8,000 in a savings plan that pays 7% per year. To find out what the account balance will be at the end of the first year, we can use the formula for simple interest because it is only for one year. The formula is:
Final amount = Principal amount (1 + (Interest rate * Time))
Let's calculate:
Principal amount (P) = $8,000Interest rate (r) = 7% or 0.07Time (t) = 1 yearNow, substituting the values into the formula:
Final amount = $8,000 (1 + (0.07 * 1))
Final amount = $8,000 (1 + 0.07)
Final amount = $8,000 (1.07)
Final amount = $8,560
So, the account balance at the end of the first year will be $8,560.
Please help thanks very much!
What is the product of 1/2 times 2/3 times 3/4 .... times 1999/2000?
What is the answer to in a science class the girl to boy ratio is 3 to 7 out of 50 student how many are boys?
Cheryl Assembled 128 chairs in 16 hours. How many chairs per hour?
The points ( - 6, - 2) and ( - 4,6) fall on a particular line. what is its equation in point-slope form?
What is the function rule for the line?
f(x)=2/3x−2
f(x)=3/2x−2
f(x)=−2/3x−2
f(x)=3/2x+2
The function rule of the line is, f(x)=2/3x-2
What is a straight line?
A straight line is an endless one-dimensional figure that has no width. It is a combination of endless points joined both sides of a point and has no curve.
Here, we have to points (0,-2) and, (3,0)
So, by using the formula of equation of straight line of two-point form, we get,
(y-y_1)/(x-x_1 )=(y_2-y_1)/(x_2-x_1 )
=>(y+2)/(x-0)=(0+2)/(3-0)
=>3y+6=2x
=>y=2/3x-2
Let, y= f(x)
So, the required function rule of the line is f(x)=2/3x-2
Hence, the required function rule of the line is, f(x)=2/3x-2
To learn more on Equation 0f Straight-Line click:
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How much money will be in a bank account after 4 years if $8 is deposited at an interest rate of 5%?
A bathtub that holds 32 gallons of water contains 12 gallons of water. begin filling it, and after 5 minutes the tub is filled. write a standard equation
Answer:
In standard equation format, the condition can be written as [tex]V=5x+12[/tex].
Step-by-step explanation:
The capacity of the bathtub is 32 gallons.
The water already in the tub is 12 gallon.
It takes 5 minutes for the tub to be filled.
Let x be the flow rate of water through tap, in gallon per minutes.
Now, the water filled in the tank in 5 minutes will be [tex]5x[/tex] gallons.
So, in equation, the given condition can be written as,
[tex]V=5x+12\\32=5x+12[/tex]
here V represents the volume of the bathtub.
Therefore, in standard equation format, the condition can be written as [tex]V=5x+12[/tex].
For more details, refer the link:
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The standard equation for the volume of water in the bathtub at time t is V(t) = 12 + 4t, indicating the tub starts with 12 gallons and fills at a rate of 4 gallons per minute.
Explanation:To write a standard equation for filling a bathtub, we need to find the rate at which the tub fills. Since the tub starts with 12 gallons and ends up holding 32 gallons, it needs an additional 20 gallons to be filled. If it takes 5 minutes to fill these 20 gallons, then the fill rate is 20 gallons per 5 minutes.
The equation for the volume V of water in the tub at any given time t (in minutes) is:
V(t) = 12 + r × t
where r is the rate of filling the tub. We already calculated r to be 4 gallons per minute (20 gallons/5 minutes). Therefore, the equation becomes:
V(t) = 12 + 4t
This equation represents the amount of water in the bathtub at any given time t, assuming it starts with 12 gallons and fills at a rate of 4 gallons a minute.
The equation y=0.25x+50 models the cost y of renting a car if the car is driven x miles according to the model what is the best estimate of the cost for renting a car if you plan to drive 250 miles
Answer: $112.5
Step-by-step explanation:
Given : The equation [tex]y=0.25x+50[/tex] models the cost y of renting a car if the car is driven x miles according to the model .
To find the cost for renting a car if you plan to drive 250 miles, we substitute x= 250 in the given equation , we get
[tex]y=0.25(250)+50\\\\\Rightarrow\ y=62.5+50\\\\\Rightarrow\ y=112.5[/tex]
Hence, the cost for renting a car if you plan to drive 250 miles = $112.5
Thus , the best estimate of the cost for renting a car if you plan to drive 250 miles = $112.5
Twelve less than negative nine times a number is equal to 8 minus 4 times the number find the number
Final answer:
The number that satisfies the original equation is -4.
Explanation:
A student's question involves finding a number that satisfies the equation: 'Twelve less than negative nine times a number is equal to 8 minus 4 times the number'.
To solve this, we set up the equation -9x - 12 = 8 - 4x.
Solving for 'x' involves simple algebraic steps.
First, add 9x to both sides to get the variable terms on one side:
-9x - 12 + 9x = 8 - 4x + 9x-12 = 8 + 5xNext, subtract 8 from both sides to isolate the variable term:
-12 - 8 = 5x-20 = 5xFinally, divide both sides by 5 to find 'x':
-20 / 5 = 5x / 5-4 = xThe number that satisfies the original equation is -4.
Write a proof to show that a rectangle has congruent diagonals. Be sure to create and name the appropriate geometric figures. This figure does not need to be submitted.
Answer:
The diagonals intersect each other
Step-by-step explanation:
One of the distinguishing features of triangles is the congruency of the diagonals. The diagonals are bisected into two. Each perpendicular bisector gives a segment of the diagonal that is equal to the other.
Line segment JL is an altitude in triangle JKM. Which statement explains whether JKM is a right triangle? Round measures to the nearest tenth.
A) JKM is a right triangle because KM = 15.3.
B) JKM is a right triangle because KM = 18.2.
C) JKM is not a right triangle because KM ≠ 15.3.
D) JKM is not a right triangle because KM ≠ 18.2.
Answer:
C. JKM is not a right triangle because KM ≠ 15.3.
Step-by-step explanation:
We can see from our diagram that triangle JKM is divided into right triangles JLM and JLK.
In order to triangle JKM be a right triangle [tex]KM^{2}=JK^{2}+JM^{2}[/tex].
We will find length of side KM using our right triangles JLM and JLK as [tex]KM=KL+LM[/tex].
Using Pythagorean theorem in triangle JLM we will get,
[tex]LM=\sqrt{JM^{2}-JL^{2}}[/tex]
[tex]LM=\sqrt{8^{2}-5^{2}}[/tex]
[tex]LM=\sqrt{64-25}[/tex]
[tex]LM=\sqrt{39}=6.244997998\approx 6.24[/tex]
Now let us find length of side KL.
[tex]KL=\sqrt{JK^{2}-JL^{2}}[/tex]
[tex]KL=\sqrt{13^{2}-5^{2}}[/tex]
[tex]KL=\sqrt{169-25}[/tex]
[tex]KL=\sqrt{144}=12[/tex]
Now let us find length of KM by adding lengths of KL and LM.
[tex]KM=12+6.24=18.24[/tex]
Now let us find whether JKM is right triangle or not using Pythagorean theorem.
[tex]KM^{2}=JK^{2}+JM^{2}[/tex]
[tex]18.24^{2}=13^{2}+8^{2}[/tex]
[tex]18.24^{2}=169+64[/tex]
[tex]18.24^{2}=233[/tex]
Upon taking square root of both sides of equation we will get,
[tex]18.24\neq 15.264337522473748[/tex]
[tex]18.2\neq 15.3[/tex]
We have seen that KM equals 18.2 and in order to JKM be a right triangle KM must be equal to 15.3, therefore, JKM is not a right triangle and option C is the correct choice.
Answer:
I just took the test it is C
Patrick has seen 10 movies this year.what is the ratio of comedies to the toatal. 4 actions,1 animated,3 comedys,and 2 dramas
Compute the requested value. If the cost is $35.96 and the desired markup is 10%, what is the price after markup?
multiply the cost by 1.10 ( 10% plus cost price)
35.96 *1.10 = 39.556 rounded to $39.56
Alexia and Haley start out together to bike from Apple Valley to Hesperia, a distance of 15 miles.
Alexia bikes at 5 miles per hour.
Haley bikes at 7.5 miles per hour.
Which statement is true?
They arrive at the same time.
Alexia arrives 1 hour later than Haley.
Alexia arrives 2.5 hours later than Haley.
Haley arrives 37.5 hours earlier than Alexia.
50 42 32 35 41 44 24 46 31 47 36 32 30 44 22 47 31 56 28 37 49 28 42 38 45 mean and median
Where does the function f have a zero? (more than one can apply)
Explain in detail why the degree of the polynomial below is not 6.
3x^2+6xy-10x^5+y^6-10x^3y^5
Use volume and meniscus in the same sentence
The outdoor furniture buys wooden benches for $50 each. The furniture store owner adds 200% markup to the cost of the bench. After hearing from the costumers the selling cost of the bench is too high, the owner changes the markup to 120%. How much less per bench does the store owner make with the lower markup
Please help me
6 (d+1) - 2d = 54
6(d+1) -2d=54
distribute the 6
6d+6 -2d=54
subtract 2d from 6d
4d+6 =54
subtract 6 from each side
4d=48
divide both sides by 4 to get d
d=48/4
d=12
What is the solution of the system?
Use the elimination method.
4x + 2y = 18
2x + 3y = 15
Enter the answer in the boxes.
(__,__)
To solve this system of equations using the elimination method, we multiply one or both equations so that the coefficients of either x or y are the same or additive inverses. Then, we subtract one equation from the other to eliminate one variable. Finally, we solve for the remaining variable by substituting the value of the other variable.
Explanation:To solve the system of equations using the elimination method, we need to eliminate one variable by multiplying one or both equations so that the coefficients of either x or y are the same or additive inverses. In this case, we can multiply the first equation by 3 and the second equation by 2:
12x + 6y = 54
4x + 6y = 30
Next, we subtract the second equation from the first:
(12x + 6y) - (4x + 6y) = 54 - 30
8x = 24
Divide both sides by 8 to solve for x:
x = 3
To find the value of y, substitute the value of x into either of the original equations:
4(3) + 2y = 18
12 + 2y = 18
2y = 18 - 12
2y = 6
y = 6/2
y = 3
Factor this expression completely 9a4 - b2
to dilute a concentrated liquid fabric softener, the directions state to mix 3 cups of water with 1 cup of concentrated liquid. how many gallons of water will you need to make 6 gallons of diluted fabric softener?
In a proportional relationship, how can you determine the unit rate while looking at the graph?
In order for the data in the table to represent a linear function with a rate of change of –8, what must be the value of m?
m = 2
m = 3
m = 19
m = 35
Answer:
m= 19
Step-by-step explanation:
In a linear function the rate of change of y-variable respect x-variable must be constant. In mathematical terms:
Δy/Δx = constant
Given two points of the function: (x1, y1) and (x2, y2), Δy = (y2 -y1) and Δx = (x2 -x1). So,
Δy/Δx = (11 -27)/(12-10) = -8
(m -27)/(11-10) = -8
(m -27) = -8*(11-10)
m = -8 + 27
m = 19
range of 89,82,73,86,89,68,94
Louise used this figure to model the expression 20/4
What error did Louise make in her model?
The small arrows are pointed in the wrong direction.
The small arrows should all end in the same place as the large one.
The arrows should start at zero.
There should be one large arrow and 20 small arrows.
Answer:
The arrow should start at zero
Step-by-step explanation:
Because if it star any where else it would be incomplete
A club treasurer has $28.45 consisting of nickels, dimes, and quarters. she has 9 more nickels than dimes and three times as many dimes as quarters. how many does she have of each coin?