The ratio between the hypotenuse of a right triangle and one of its legs is (13)/(12). The other leg is 15cm long. Find the perimeter of the triangle.
Answers
The perimeter of the triangle is 31.25 + 5√7 cm.
What is Perimeter?
Perimeter refers to the total length of the boundary or the outer edge of a two-dimensional shape. The perimeter of a polygon can be calculated by adding up the lengths of all its sides. For example, the perimeter of a rectangle with length L and width W can be calculated using the formula:
Perimeter = 2L + 2W
Let's denote the length of the hypotenuse by "x". According to the problem statement, the ratio between the hypotenuse and one of the legs is (13/12). Therefore, we can write:
x/15 = 13/12
To solve for "x", we can cross-multiply:
x = 15 × (13/12) = 65/4
Now we can use the Pythagorean theorem to find the length of the remaining leg:
a² + b² = c²
where "a" and "b" are the legs of the right triangle, and "c" is the hypotenuse. Substituting the given values, we get:
15² + b² = (65/4)²
225 + b² = 4225/16
b² = 4225/16 - 225 = 2800/16 = 175
b = √175 = 5√7
The perimeter of the triangle is the sum of the lengths of its three sides:
perimeter = a + b + c
where "a" and "b" are the legs, and "c" is the hypotenuse. Substituting the given values, we get:
perimeter = 15 + 5√7 + (65/4)
perimeter = 60/4 + 20√7 /4 + 65/4
perimeter = (60 + 20√7 + 65)/4
= (125 + 20√7 )/4
= 31.25 + 5√7
Therefore, the perimeter of the right triangle is 31.25 + 5√7 cm.
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Related Questions
Last season , the Roswell hornets out scored their opponents 5:2 if their opponents scored 28 points , how many points did the hornets score ?
Answers
The hornets scored 70 points if they scored 5:2 when their opponents scored 28 points.
Therefore the answer is 70.
If the Roswell hornets outscored their opponents 5:2, this means that for every 5 points the hornets scored, their opponents scored 2 points.
If we know that the opponents scored 28 points, we can use this information to find out how many points the hornets scored.
We can set up the equation:
x/28 = 5/2
Where x is the number of points the hornets scored.
On solving the equation we get:
x = (5 × 28)/2
x = 5 × 14
x = 70
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A simple random sample of 900 households is taken in a city. The average household size in the sample is 2. 2 people, with an sd of 2 people. True or false: approximately 95% of the households had sizes in the range 2. 07 to 2. 33 people
Answers
True. approximately 95% of the households had sizes in the range 2.07 to 2.33 people
To determine if approximately 95% of the households had sizes in the range of 2.07 to 2.33 people, we need to consider the concept of confidence intervals.
A confidence interval is a range of values that we can be reasonably confident contains the true population parameter. In this case, we are interested in the average household size.
Given that the sample size is large (900 households) and the standard deviation is known (2 people), we can use the Z-distribution to calculate the confidence interval.
For a 95% confidence interval, we consider the critical Z-value at the 2.5% and 97.5% percentiles (since we want to capture the middle 95% of the distribution).
Using a statistical table or software, the critical Z-value is approximately ±1.96.
The formula for the confidence interval is:
CI = X ± Z * (σ/√n)
where X is the sample mean, Z is the Z-value, σ is the population standard deviation, and n is the sample size.
Plugging in the given values, we have:
CI = 2.2 ± 1.96 * (2/√900)
Simplifying the equation, we get:
CI = 2.2 ± 1.96 * (2/30)
Calculating the values, we find:
CI ≈ 2.2 ± 0.271
CI ≈ (1.929, 2.471)
Since the range 2.07 to 2.33 falls within this confidence interval, it is true that approximately 95% of the households had sizes in that range.
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Alice and Bob the end the nice restaurant. At the end of the meal, Alice has eaten C_A dollars worth of food, and in her wallet a set of bills A = a_1, a_2 ..., a_n Similarly, Bob owes the restaurant c_B dollars and has bills B = {B_1, B_2, ....b_m}. Now, Alice and Bob are very calculating people, so they agree that each of them should pay their fair share (C_A and c_B, respectively). One thing they don't mind doing, however, is fairly trading bills. That is, Alice can exchange a subset A' subsetorequalto A of her bills for for a subset B' subsetorequalto B of Bob's bills, so long as sigma _a element A' a = sigma _b element B' b. Under the above EA' conditions, Alice and Bob wish to find, after trading as many times as desired, subsets of their bills A*, B* such that sigma _a element A* a = c_A and sigma _b element B* b = c_B. Show that FAIR DATE is NP-complete.
Answers
FAIR DATE is both in NP and NP-hard, we can conclude that FAIR DATE is NP-complete.
To prove that FAIR DATE is NP-complete, we need to show two things: (1) FAIR DATE is in NP, and (2) FAIR DATE is NP-hard.
1. FAIR DATE is in NP:
We can easily verify a potential solution for FAIR DATE in polynomial time. Given subsets A* and B*, we can check if the sum of the bills in A* equals c_A and the sum of the bills in B* equals c_B. This verification can be done in O(n) time for Alice's bills and O(m) time for Bob's bills, where n and m are the number of bills Alice and Bob have, respectively.
2. FAIR DATE is NP-hard:
To show that FAIR DATE is NP-hard, we need to reduce a known NP-complete problem to it. Let's choose the PARTITION problem for this reduction. In the PARTITION problem, given a set S of integers, we need to determine if there exists a subset S' of S such that the sum of the elements in S' is equal to half the sum of all elements in S.
Reduction: Given an instance of PARTITION, we can create an instance of FAIR DATE as follows:
- Let Alice's bill be the set A = S, and c_A = 1/2 * (sigma_a ∈ A, a).
- Let Bob's bill be the set B = {}, and c_B = 0.
Now, if there exists a subset A* of A such that sigma_a ∈ A* a = c_A, then this subset is the solution to the PARTITION problem as well. Conversely, if there is a solution to the PARTITION problem, then there exists a subset A* such that sigma_a ∈ A* a = c_A.
Since we can perform this reduction in polynomial time, FAIR DATE is NP-hard.
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Mrs. Pearl had $600. She spends half her money on clothes and gets $219 back from the cashier. Her brother gave her $637 and took away $230. How much money does she have?
Answers
Answer:
inthink its 627
Step-by-step explanation:
hope this helps
mrs. hansen asked eli to apply the distributive property to the expression, 2(7 3). which of the following should eli have not written?
A. 2(10)
B. 2(7) =2(3)
C. 2(3+7)
D. (7+3).2
Answers
Eli should not have written option D, (7+3).2, when applying the distributive property to the expression 2(7+3).
The distributive property states that when you multiply a number by a sum or difference inside parentheses, you need to multiply the number by each term inside the parentheses. In this case, Eli needs to multiply the number 2 by each term inside the parentheses (7 and 3). Let's analyze each option:
A. 2(10): Eli correctly applied the distributive property by multiplying 2 by 10, which is the result of adding 7 and 3.
B. 2(7) = 2(3): Eli correctly applied the distributive property by multiplying 2 by both 7 and 3 separately.
C. 2(3+7): Eli correctly applied the distributive property by multiplying 2 by the sum of 3 and 7.
D. (7+3).2: This expression does not apply the distributive property correctly. The parentheses indicate addition, not multiplication. Eli should have multiplied 2 by both 7 and 3, rather than adding them first.
Therefore, option D is the incorrect one, and Eli should not have written (7+3).2 when applying the distributive property to the given expression.
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The triangle PQT with RS ll QT is shown below.If PR=12,RQ=8,and PS=21,what is the length of PT?
Answers
Since the sides RS and QT are parallel, these triangles are similar by case AA.
So we can write the following proportion between corresponding sides:
\(\begin{gathered} \frac{PR}{PQ}=\frac{PS}{PT} \\ \frac{12}{12+8}=\frac{21}{PT} \\ PT=\frac{20\cdot21}{12} \\ PT=35 \end{gathered}\)So the length of PT is 35 units.
Give the equation of a line that has no x-intercepts no y-intercepts an infinite number of y-intercepts a point that is both the x-intercept and the y-intercept
Answers
Answer:
The x-intercept is (-2,0)
Step-by-step explanation:
Answer:
y = x
Step-by-step explanation:
Hey could you please help me with dis math
Answers
The solution to the inequality is x ≤ 14/3, which means option C) x ≤ 2 is the correct answer.
To solve the inequality 3x/4 - 2/3 ≤ 5/6, we can follow these steps:
First, let's simplify the left side of the inequality:
3x/4 - 2/3 = (3x - 8)/4 - 2/3
To combine the fractions, we need to find a common denominator, which in this case is 12. We can multiply the first fraction by 3/3 and the second fraction by 4/4:(3x - 8)/4 - 2/3 = (9x - 24)/12 - 8/12
Now, we can rewrite the inequality as:
(9x - 24)/12 - 8/12 ≤ 5/6
Next, we can combine the fractions on the left side:
(9x - 24 - 8)/12 ≤ 5/6
Simplifying the numerator:
(9x - 32)/12 ≤ 5/6
To get rid of the fraction, we can multiply both sides of the inequality by the least common denominator, which is 12:
12 * (9x - 32)/12 ≤ 12 * 5/6
This simplifies to:
9x - 32 ≤ 10
Next, let's isolate the x term by adding 32 to both sides:
9x ≤ 10 + 32
9x ≤ 42
Finally, divide both sides of the inequality by 9 to solve for x:
x ≤ 42/9
Simplifying the fraction:
x ≤ 14/3.
Option C
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Exterior Angles of A Triangle
Answers
Try doing this for the rest of them
Consider these two functions:
F(x)=2 cos(pix)
G(x) = 1/2cos(2x) What are the amplitudes of the two functions?
Answers
The amplitude of function F(x) is 2, and the amplitude of function G(x) is 1/2.
To determine the amplitudes of the given functions F(x) = 2cos(pix) and G(x) = 1/2cos(2x), we need to identify the coefficients in front of the cosine terms. The amplitude of a cosine function is the absolute value of the coefficient of the cosine term.
For function F(x) = 2cos(pix), the coefficient in front of the cosine term is 2. Thus, the amplitude of F(x) is |2|, which is equal to 2.
For function G(x) = 1/2cos(2x), the coefficient in front of the cosine term is 1/2. The amplitude is the absolute value of this coefficient, so the amplitude of G(x) is |1/2|, which simplifies to 1/2.
In summary, the amplitude of function F(x) is 2, and the amplitude of function G(x) is 1/2.
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What number makes the equation true? 35 + = 42
Answers
Answer:
7
Step-by-step explanation:
42 - 35 = 7
35+7=42
due now pls help!!!!!!!!!!!
Answers
Answer:
A and D
Step-by-step explanation:
so sorry im in school
x+y=4
-y. -y
x=4-y
4-y-y=2
4-2y=2
-4 -4
-2y= -2
/-2. /-2
y=1
x+1=4
-1 -1
x=3
so A and D is correct
tree that is 12 feet tall casts a shadow that is 6 feet long. What is the distance from the top of the tree to the tip of the shadow? Round to the nearest tenth.
Help
Answers
Answer:
13.4
Step-by-step explanation:
The tree to the shadow forms a right angle triangle, so to calculate the distance from the tree tip to the shadow tip we can use pythagoras.
a^2 +b^2 = c^2
12^2 +6^2 = 144 +36 = 180 =c^2
Square root of 180 is approx 13.42.
To the nearest 10th = 13.4
What is 68,500,000 written in scientific notation?
Answers
Write the relation as a set of ordered pairs.X333у- 102(2)
Answers
Solution
A relation can be thought of as a set of ordered pairs. We consider the first element of the ordered pair to be related to the second element of the ordered pair. Definition: A relation R from a set X to a set Y is a subset of the Cartesian Product X x Y, if (x, y) ∈ R, we write x R y and say that x is related to y.
The inputs ... the x values ... are on the left ...(from)
The outputs ... the y values ... are on the right ... (ro)
The coordinates are:
\(\begin{gathered} (3,-1) \\ (3,0) \\ (3,2) \end{gathered}\)
6. How do you find the slope of a line?
A Divide the difference of the y values by the differences of the x values.
B Divide the difference of the x values by the differences of the y values.
C Divide the rise of the line by the run of the line.
D Both A and C.
Answers
Answer:
D
Step-by-step explanation:
An investor purchased 100 shares of stock in a company for $20 per share. One year later, the investor sold all the shares for $1,950. What is the investor's rate of return?
A. -2.5%
B. -1.6%
C. 2.5%
D. 1.6%
Answers
The investor's rate of return is given as follows:
A. -2.5%.
How to obtain the rate of return?The rate of return is obtained applying the proportions in the context of the problem.
An investor purchased 100 shares of stock in a company for $20 per share, hence the total cost of the purchase was of:
20 x 100 = $2000.
One year later, the investor sold all the shares for $1,950, hence the return was of:
1950 - 2000 = -$50.
Then the rate of return is calculated as follows:
-50/2000 = -2.5%.
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Project p has an npv of $150,000; project q has an npv of $75,000. if you choose to work project p, what is the opportunity cost of not choosing project q?
Answers
The opportunity cost is merely the expense of not making a decision.
As a result, if you chose Project P placed above a white Project Q, the opportunity cost for such a decision is 75,000 times the estimated NPV of Project Q.
What is Net Present Value (NPV)?The distinction between current value of money over time value of cash outflows over time is defined as net present value (NPV).
Some key features regarding the Net Present Value (NPV) are-
To calculate NPV, approximate the amount and timing of future cash flow and choose a discount factor equal to a minimum standard rate of return.A discount rate may represent ones cost of capital or even the releasing on comparable risk investments.If a project's or investment's NPV is positive, this means it's own rate of return would be greater than the discount rate.NPV takes into account the time value of the money and may be used to compare this same rates of return of various projects or to compare a predicted rate of return with hurdle rate required to endorse an investment.The discount rate, which may be a hurdle rate for just a particular project on the a company's cost of capital, represents the time value of money in the NPV formula.To know more about the Net Present Value (NPV), here
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Renee bought 6 tickets to a football game. She paid a total of $216. Write an equation to represent the situation
Answers
Answer:
6 × 36 = 216
Step-by-step explanation:
one ticket price: 216 ÷ 6 = $36
Find the missing exponent: 5^11/5?=5^4
Answers
4. What are the coefficients in the polynomial 7x² - 4x + 6? (1 poin
O-7,4
07, 4, -6
07,-4, 6
07,-4
Add or subtract.
Answers
Answer:
D.) 7 and -4
Step-by-step explanation:
Coefficients are numbers placed directly before a variable.
(7) is a coefficient because it is placed before x².
(-4) is a coefficient because it is placed before x. The negative is included.
(6) is not a coefficient because it is not altering any variable through multiplication/division.
Chef Aaron Sanchez determined the annual profit in dollars from selling cakes using
p ( n ) = 62 n - 0.05 n 2 , where n is the number of cakes sold.
What is the annual profit if chef Aaron sells 500 cakes?
Answers:
15,575
16,800
18,500
18,975
Answers
Answer:
18,500
Step-by-step explanation:
h
5. Problem 5.15 (Present Value of an Annuity) Find the present values of these ordinary annuities. Discounting occurs once a year. Do not round intermediate calculations. Round your answers to the nearest cent. a. $400 per year for 14 years at 14%. $ b. $200 per year for 7 years at 7%. $ c. $400 per year for 7 years at 0%. $ d. Rework previous parts assuming they are annuities due. Present value of $400 per year for 14 years at 14%:$ Present value of $200 per year for 7 years at 7% : $ Present value of $400 per year for 7 years at 0% : $
Answers
a. Present value of $400 per year for 14 years at 14%: $2,702.83
b. Present value of $200 per year for 7 years at 7%: $1,155.54
c. Present value of $400 per year for 7 years at 0%: $2,800
d. Present value of $400 per year for 14 years at 14% (annuity due): $2,943.07
Present value of $200 per year for 7 years at 7% (annuity due): $1,233.24
Present value of $400 per year for 7 years at 0% (annuity due): $2,800
To find the present values of the ordinary annuities, we can use the formula for the present value of an annuity:
PV = PMT * [(1 - (1 + r)^(-n)) / r]
Where:
PV = Present value
PMT = Payment per period
r = Interest rate per period
n = Number of periods
a. $400 per year for 14 years at 14%:
PV = $400 * [(1 - (1 + 0.14)^(-14)) / 0.14]
≈ $2,702.83
b. $200 per year for 7 years at 7%:
PV = $200 * [(1 - (1 + 0.07)^(-7)) / 0.07]
≈ $1,155.54
c. $400 per year for 7 years at 0%:
Since the interest rate is 0%, the present value is simply the total amount of payments over the 7 years:
PV = $400 * 7
= $2,800
d. Reworking previous parts assuming they are annuities due:
For annuities due, we need to adjust the formula by multiplying it by (1 + r):
a. Present value of $400 per year for 14 years at 14%:
PV = $400 * [(1 - (1 + 0.14)^(-14)) / 0.14] * (1 + 0.14)
≈ $2,943.07
b. Present value of $200 per year for 7 years at 7%:
PV = $200 * [(1 - (1 + 0.07)^(-7)) / 0.07] * (1 + 0.07)
≈ $1,233.24
c. Present value of $400 per year for 7 years at 0%:
Since the interest rate is 0%, the present value remains the same:
PV = $400 * 7
= $2,800
In conclusion:
a. Present value of $400 per year for 14 years at 14%: $2,702.83
b. Present value of $200 per year for 7 years at 7%: $1,155.54
c. Present value of $400 per year for 7 years at 0%: $2,800
d. Present value of $400 per year for 14 years at 14% (annuity due): $2,943.07
Present value of $200 per year for 7 years at 7% (annuity due): $1,233.24
Present value of $400 per year for 7 years at 0% (annuity due): $2,800
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Pls help with questions
1. What is the volume of a cylinder that has a radius of 5 inches and height of 9 inches?
2. Mrs.vega brought a new aquarium for her turtles. How much space will the turtles have in the aquarium if the length is 5.2 ft, the width is 1.8 ft and the height is 2 ft?
Answers
Step-by-step explanation:
1. volume = πr²h
= π×(5²)×9
= π×225
= 225π
= 707.1 cubic inches
2. volume = lwh
= 5.2 × 1.8 × 2
= 18.72 square feets
You are given quadrilateral PQRS, such that
ABCD = T (0, -8)(Ro 180°(R y-axis (PQRS)))
What are the new coordinates for ABCD?
Answers
On solving the provided question, we can say that from the graphs
the new coordinates for ABCD (-1,-2),(2,-3),(-4,-6),(-3,8)
What is graphs?Mathematicians use graphs to logically convey facts or values using visual representations or charts. A graph point will typically reflect a relationship between two or more things. Nodes, or vertices, and edges make form a graph, a non-linear data structure. Glue together the nodes, often referred to as vertices. This graph has vertices V=1, 2, 3, 5, and edges E=1, 2, 1, 3, 2, 4, and (2.5), (3.5). (4.5). Statistical charts (bar charts, pie charts, line charts, etc.) graphical representations of exponential growth. a logarithmic graph in the shape of a triangle
here,
ABCD = T (0, -8)(Ro 180°(R y-axis (PQRS)))
from the graphs
the new coordinates for ABCD
(-1,-2),(2,-3),(-4,-6),(-3,8)
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S=26.32 E=55 t=3 standard diviation=60% 3-year r=2.4% 10-year
r=3.1%
What minimum value would you assign? What isthe maximum value
you would assign?
Answers
For the given standard deviation the minimum value we would assign is 22.the maximum value we would assign is 88.
To calculate the minimum and maximum values based on the given information, we need to consider the standard deviation and the respective interest rates for the 3-year and 10-year periods.
Given:
S = 26.32 (Initial value)
E = 55 (Expected value)
t = 3 (Years)
Standard deviation = 60% (of the expected value)
3-year interest rate = 2.4%
10-year interest rate = 3.1%
To find the minimum value, we will calculate the value at the end of the 3-year period using the lowest possible growth rate.
Minimum value calculation:
Minimum value = E - (Standard deviation * E) = 55 - (0.6 * 55) = 55 - 33 = 22
Therefore, the minimum value we would assign is 22.
To find the maximum value, we will calculate the value at the end of the 10-year period using the highest possible growth rate.
Maximum value calculation:
Maximum value = E + (Standard deviation * E) = 55 + (0.6 * 55) = 55 + 33 = 88
Therefore, the maximum value we would assign is 88.
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6,000 x ____ = 120,000
Answers
Answer:
6,000 * 20= 120,000
Step-by-step explanation:
A school librarian wanted to estimate the proportion of students in the school who had read a certain book. the librarian sampled 50 students from the senior english classes, and 35 of the students in the sample had read the book. have the conditions for creating a confidence interval for the population proportion been met?
Answers
All the conditions for creating a confidence interval for the population proportion been met.
The probability that a population parameter would fall between a set of values for a certain percentage of the time is described by a confidence interval in statistics. Analysts typically employ confidence intervals that cover 95% or 99% of predicted observations.
The prerequisites for establishing the confidence sampling are as follows:
Independent Random SamplingLarge SampleSuccess and Failure Conditionsuniformity of variationsThe requirements for establishing a confidence interval for the population proportion have been satisfied because all of the aforementioned requirements are satisfied.
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HELP!!!! 25 POINTS!!!! EXTREMELY EASY!!!!PLEASE HELP MEEEEE!!!!!!!
When finding the x-intercepts and relating them to graph....does the placement of the x-intercepts matter in the problem????
Answers
Answer:
The intercepts of a graph are points at which the graph crosses the axes. The x-intercept is the point at which the graph crosses the x-axis. At this point, the y-coordinate is zero. Yes it also matter because x axis go sideways and the y axis goes up and down. Hope this helps
Answer:
The intercepts of a graph are points at which the graph crosses the axes. The x-intercept is the point at which the graph crosses the x-axis. At this point, the y-coordinate is zero.
Step-by-step explanation:
A shop sells candles at Sx each and bath bombs at Sy each. (a) One day the shop sold 25 candles and 15 bath bombs. These sales totalled $680. Show that 5x + 3y = 136. (b) The next day the shop sold 16 candles and 18 bath bombs. These sales totalled $536. Show that 8x + 9y = 268. (c) Solve these simultaneous equations. 5x + 3y = 136 8x+9y = 268 (d) Calculate the difference in price between a candle and a bath bomb.
Answers
The most important details in this question are the three simultaneous equations: 5x + 3y = 136, 8x + 9y = 268, and the difference in price between a candle and a bath bomb. These equations can be solved by adding the equations together: 13x + 12y = 404, subtracting 5x and 8x from both sides of the equation:-3x/12 + y = 404/12, and substituting the values of x and y into the equation: Sx - Sy = -26.472.
What is a simultaneous equation?A simultaneous equation is a collection of two or more equations with two or more variables. Because they share variables, these equations must be solved together. In other words, the variables' values must fulfil all of the equations simultaneously.
(a) 5x + 3y = 136
Substitute the values given in the equation:
5(25) + 3(15) = 136
125 + 45 = 136
Simplify:
170 = 136
This equation is not true.
(b) 8x + 9y = 268
Substitute the values given in the equation:
8(16) + 9(18) = 268
128 + 162 = 268
Simplify:
290 = 268
This equation is not true.
(c) Solve these simultaneous equations.
5x + 3y = 136
8x + 9y = 268
Add the equations together:
13x + 12y = 404
Subtract 5x and 8x from both sides of the equation:
-3x + 12y = 404
Divide both sides of the equation by 12:
-3x/12 + y = 404/12
Simplify:
-1/4x + y = 33.67
Substitute this equation into the original equation:
5x + 3y = 136
5x + 3(33.67) = 136
Simplify:
5x + 100.01 = 136
Subtract 100.01 from both sides of the equation:
5x = 35.99
Divide both sides of the equation by 5:
x = 7.198
Substitute this value into one of the original equations:
5(7.198) + 3y = 136
Simplify:
35.99 + 3y = 136
Subtract 35.99 from both sides of the equation:
3y = 100.01
Divide both sides of the equation by 3:
y = 33.67
(d) Calculate the difference in price between a candle and a bath bomb.
Substitute the values of x and y into the equation:
Sx - Sy = 7.198 - 33.67
Simplify:
Sx - Sy = -26.472
Therefore, the difference in price between a candle and a bath bomb is Sx - Sy = -26.472.
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