In ΔHIJ, h = 33 cm, i = 61 cm and j=39 cm. Find the area of ΔHIJ to the nearest square centimeter.
Answers
Thus, the area of ΔHIJ using the Heron's formula is found as 580.47 square centimeter.
Explain about the Heron's formula:Heron of Alexandria (c. 62 ce) is credited with developing the Heron's formula, which determines the area of a triangle in regards of the lengths of its sides. If the side lengths are represented by the symbols a, b, and c: √s(s - a)(s - b)(s - c)
where s = half the perimeter,
s = (a + b + c)/2.
given data:
In ΔHIJ,
h = 33 cm, i = 61 cm and j =39 cm.semi -perimeter s = (i + j + h) / 2
s = (33 + 61 + 39) / 2
s = 66.5
Now,
s - h = 66.5 - 33 = 33.5
s - i = 66.5 - 61 = 5.5
s - j = 66.5 - 39 = 27.5
area of ΔHIJ = √s(s - h)(s - i)(s - j)
area of ΔHIJ = √66.5*33.5*5.5*27.5
area of ΔHIJ = √336947.1875
area of ΔHIJ = 580.47
Thus, the area of ΔHIJ using the Heron's formula is found as 580.47 square centimeter.
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Related Questions
A landscaping company charges $48 per cubic yard of mulch plus a delivery charge of $28. Find a linear function which computes the total cost C (in dollars) to deliver x cubic yards of mulch.
Answers
The linear function for the total cost C is:
\(\text{C} = 28 + 48\text{x}\)What is a function?A function is an expression, rule, or law that defines a relationship between one variable.
Example:
\(f(\text{x}) = 2\text{x} + 1\)
\(f(1) = 2 + 1 = 3\)
\(f(2) = 2 \times 2 + 1 = 4 + 1 = 5\)
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
Charge per cubic yard = $48Delivery charge = $28The total cost for x cubic yards.
\(\bold{C = 28 + 48x}\)
Thus, the function is C = 28 + 48x.
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Evaluate the piecewise function
Answers
The solution of the composite function fog(x) = 3x + 3 at x > 2.
What is composite function?Let the two function f(x) and g(x) generate a new function h(x) using an operation.
The operation is composition of functions and h(x) is a composite function.
We have three piecewise function.
First we have to show that,
the composite function,
fog(x) at x > 2.
For that,
g(x) at x > 2 is,
g(x) = 3x.
Now, f(g(x)),
= f(3x)
= 3x + 3 at x > 2.
Therefore, the function is fog(x) = 3x + 3.
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The complete question:
Find the fog(x) at x > 2
what is prime number
Answers
Answer:
a number that is divisible only by itself and 1 (e.g. 2, 3, 5, 7, 11).
Tìm số dư trong phép chia 3^{2020} chia cho 13
Answers
Your question translates to computing \(3^{2020} \pmod {13}\).
Recall Euler's theorem: if \(\gcd(a,n)=1\) (that is, \(a\) and \(n\) are relatively prime), then \(a^{\varphi(n)}\equiv1\pmod n\), where \(\varphi(n)\) denotes Euler's totient function, which counts the number of positive integers relatively prime to \(n\).
Since 13 is prime, we have \(\phi(13)=12\). Then by Euler's theorem,
\(3^{12} \equiv 1 \pmod{13}\)
Now, observe that 2020 = 168×12 + 4, so that
\(3^{2020} \equiv 3^{168\times12+4} \equiv \left(3^{12}\right)^{168} \times 3^4 \equiv 1^{168} \times 3^4 \equiv 3^4 \pmod{13}\)
and since 3⁴ = 81 = 6×13 + 3, we end up with
\(3^{2020} \equiv 81 \equiv 3 \pmod{13}\)
so the remainder upon dividing 3²⁰²⁰ by 13 is 3.
5. The sum
of K and L divided by
Sum of d
and e.
Answers
Answer:
(K+L) / (d+e)
Step-by-step explanation:
(K+L) / (d+e)
Fluency in the conversion of the metric system to the Imperial System is an essential skill in the nursing profession. Think of a situation in which negative effects have occurred due to incorrect dosage calculations? This situation could be a personal experience, the experience of someone you know, or a hypothetical. Explain how this error could have been avoided. How will you ensure that you avoid dosage errors due to metric conversions in your future career as a nurse?
Answers
In a hypothetical situation, an incorrect dosage calculation due to an error in metric system to Imperial System conversion could lead to potential harm to the patient. To avoid such errors, it is crucial to ensure accurate and precise conversions between the metric and Imperial systems. As a nurse, I will double-check my calculations, use reliable conversion charts or tools, and consult with colleagues or supervisors when in doubt. Additionally, ongoing education and training on dosage calculations and metric system conversions will be important to maintain proficiency and prevent errors in the future.
~~~Harsha~~~
PLEASE HELP!!!!!!!
The temperature is 56°F. The temperature decreases for 6 hours. Each hour, the temperature decreases by 3°F. Then the temperature rises 12°F in one hour. What is the temperature after 7 hours?
Answers
Answer:
50 degrees
Step-by-step explanation:
3 x 6 = 18
56 - 18 = 38
38 + 12 = 50
pls im not the brightest in math rn pls help!
Answers
Answer:
student 3
Step-by-step explanation:
How do I find out the check amount before the tip when the total amount was $55 with a 10% tip
Answers
Answer:$49.50
Step-by-step explanation:
First you have to find what 10% of 55 is. So if you times 10% by 55 you come out with $5.5. So after that you must subtract 5.5 from 55 which comes out to $49.50.
Mofor has homework assignments in five subjects. He only has time to do two of
them.
Answers
The decision of which two homework assignments to complete depends on Mofor's individual circumstances and priorities.
If Mofor only has time to do two homework assignments out of the five subjects, he will need to choose which subjects to prioritize. The specific subjects he chooses to work on will depend on various factors such as his strengths, weaknesses, upcoming deadlines, and personal preferences. Here are a few strategies he could consider:
1. Prioritize based on importance: Mofor can prioritize the homework assignments that carry more weight in terms of grades or have upcoming deadlines. This way, he ensures that he completes the assignments that have a higher impact on his overall academic performance.
2. Focus on challenging subjects: If Mofor finds certain subjects more difficult or time-consuming, he can prioritize those assignments to allocate more time and effort to them. This approach allows him to concentrate on improving his understanding and performance in subjects that require extra attention.
3. Balance workload: Mofor can choose to distribute his efforts evenly across subjects, selecting two assignments from different subjects. This strategy ensures that he maintains a balanced workload and avoids neglecting any particular subject.
The decision of which two homework assignments to complete depends on Mofor's individual circumstances and priorities. It is essential for him to consider his academic goals, time constraints, and personal strengths to make an informed decision.
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The sum of two numbers is 327. One of them is a 3-digit even number and the other is a 2-digit odd number. What is the largest possible difference between the two numbers?
Answers
Answer:
305
Step-by-step explanation:
let the numbers be x and y
let x be the 3 digit even number
let y be the 2 digit odd number
x+y = 327
According to the above sum, x will range from all even numbers between 300 to 316 if to be added to a 2 digit odd number y
y will range from all odd numbers between 11 to 27 if to be added to be added to a 3 digit even number x
To find the largest possible difference, we subtract 11 from 316
This will give us 305 which is the answer.
please help! I'm almost out of time on my assignment
Answers
Calcula el valor del lado "c" en el triángulo
rectángulo, que se proporciona en la figura;
aplicando las funciones trigonométricas:
Answers
Usando relaciones en un triángulo rectángulo, se encuentra que el valor del lado c es c = 35.5 unidades.
¿Cuáles son las relaciones en un triángulo rectángulo?Las relaciones en un triángulo rectángulo se dan de la siguiente manera:
El seno de un ángulo está dado por la longitud del lado opuesto al ángulo dividida por la longitud de la hipotenusa.El coseno de un ángulo está dado por la longitud del lado adyacente al ángulo dividido por la longitud de la hipotenusa.La tangente de un ángulo está dada por la longitud del lado opuesto al ángulo dividida por la longitud del lado adyacente al ángulo.El lado opuesto de el ángulo de 26º48' = 26.8º es de 16, de esa forma, puede-se encontrar el lado c de la siguiente manera:
\(\sin{(26.8^\circ)} = \frac{16}{c}\)
\(c = \frac{16}{\sin{(26.8^\circ)}}\)
c = 35.5º.
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The points R, S, T and U all lie on the same line segment, in that order, such that the ratio of RS:ST:TURS:ST:TU is equal to 1:1:4.1:1:4. If RU=54,RU=54, find RS.RS.
Answers
The segment RS has a length of 9 units
How to determine the length of the segment RS?From the question, the partition of the line segment is given as
RS : ST : TU = 1 : 1 : 4
Where the endpoints of the line segments are R and U
This means that the length RS can be calculated using the following equation
Length RS = Ratio of RS/Sum of the ratios x The length of RU
Substitute the known values in the above equation
So, we have
Length RS = 1/(1 + 1 + 4) x 54
Evaluate the sum
Length RS = 1/6 x 54
Evaluate the products
Length RS = 9
Hence, the length of the segment RS is 9 units
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the graph of a line is shown on the grid. the coordinates of both point indicated on the graph of the line are integer
Answers
Answer:
-5/6
Step-by-step explanation:
By the application of Analytical geometry the rate of change of y with respect to x is -5/6.
what is Analytical geometry?
Analytical geometry is a branch of mathematics that studies geometric shapes and figures using analytical methods. It is a branch of mathematics that uses algebraic techniques to describe geometric shapes and figures. It involves the use of analytical equations and formulas to study geometric concepts. Analytical geometry is used to study the properties of points, lines, angles, circles, and other geometric shapes. It can also be used to solve problems involving angles, distances, and areas of figures. In addition, analytical geometry can be used to find the intersection of two lines, calculate the area of a circle, and calculate the volume of a cylinder. Analytical geometry is a powerful tool used in many scientific and engineering fields.
The rate of change of y with respect to x for this line is -5/6
Therefore -5/6 is rate of change in this graph.
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expand or simplify
3c(5+c) -2(3c-7)
Answers
15c+3c^2-6c+14
9c+3c^2+14
Answer:
It is 3c² + 9c + 14
Step-by-step explanation:
\(3c(5 + c) - 2(3c - 7)\)
open the brackets:
\( = (15c + 3 {c}^{2} ) - (6c - 14) \\ = (15c + {3c}^{2} ) - 6c + 14\)
express in quadratic equation:
\(3 {c}^{2} + 9c + 14\)
Based on the information in the two-way table, what is the probability that a person
selected at random both bikes and runs?
Round your answer to the nearest tenth of a percent.
Answers
Answer:
Step-by-step explanation:
A ball is thrown in the air from the top of a building. Its height, in meters above ground, as a function of time, in seconds, is given by h(t)= −4.9t^2+11t+7. How many seconds does it take to reach maximum height? Enter the answer with at least 3 decimal places.
Answers
Given statement solution is :- It takes approximately 1.122 seconds for the ball to reach its maximum height.
To find the time it takes for the ball to reach its maximum height, we need to determine the vertex of the parabolic function given by the equation h(t) = \(-4.9t^2 + 11t + 7.\)
The vertex of a parabola in the form y = \(ax^2 + bx\) + c is given by the formula t = -b / (2a).
Comparing the equation h(t) = \(-4.9t^2 + 11t + 7\) to the standard form, we have:
a = -4.9
b = 11
Using the formula for the vertex, we can calculate the time it takes to reach the maximum height:
t = -11 / (2 * -4.9)
t = -11 / -9.8
t ≈ 1.122
Therefore, it takes approximately 1.122 seconds for the ball to reach its maximum height.
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during a single day at radio station WMZH,the probability that a particular song is played in 3/8.what is the probability that this thing will be played on exactly 2 days out of 3 days ?round to your nearest thousandth
Answers
The probability that the song will be played on exactly 2 days out of 5 days is approximately 0.164.
To find the probability that a particular song is played exactly 2 days out of 5 days at radio station WMZH, we can use the binomial probability formula.
The binomial probability formula is given by P(x) = C(n, x) * p^x * (1-p)^(n-x), where P(x) is the probability of x successful outcomes, n is the number of trials, p is the probability of a successful outcome on a single trial, and C(n, x) represents the binomial coefficient, which is the number of ways to choose x items from a set of n items.
In this case, we want to find the probability of the song being played exactly 2 days out of 5 days, so x = 2, n = 5, and p = 3/8.
Using the formula, we have:
P(2) = \(C(5, 2) * (3/8)^2 * (1 - 3/8)^(^5^-^2^)\)
C(5, 2) = 5! / (2! * (5-2)!) = 10
P(2) = 10 * (3/8)^2 * (5/8)^3
P(2) ≈ 0.164 (rounded to three decimal places)
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HELP WILL GIVE BRAINLIEST IF CORRECT
Answers
Answer:
B. No, the remainder is -50.
General Formulas and Concepts:
Algebra I
Roots are when the polynomial are equal to 0Algebra II
Synthetic DivisionStep-by-step explanation:
Step 1: Define
Function f(x) = x³ - 10x² + 27x - 12
Divisor/Root (x + 1)
Step 2: Synthetic Division
See Attachment.
To determine whether a given root is an actual root, the remainder must equal 0. Since we have a remainder of -50, the given root is not a factor of the polynomial.
Please excuse the bad handwriting. Hope this helped!
What is the volume of three cubes, each with a side length of fraction 1 over 3 foot? V = s3, where s is the side length.
fraction 1 over 3 ft3
fraction 1 over 2 ft3
fraction 1 over 9 ft3
fraction 1 over 27 f
Answers
Answer: A
Step-by-step explanation its easy
Answer:
C. fraction 1 over 9 ft3
Step-by-step explanation:
Hope I helped!!
. The population of a city decreased from 25,000 to 24,000. Find the decrease percentage. at to be paid
Answers
Answer:
4%
Step-by-step explanation:
1000 of 25000 is 4%
Part A Estimate 10/12 - 3/8 using benchmark values. Your equation must show the estimate for each fraction and the final estimate for the expression.Part BSolve 10/12 - 3/8Part Ccalculate the difference between your stimate in Part A and the actual value calculated in Part B.Show the solution as an equation Based on the results was your estimate in Part A reasonable?
Answers
Answer:
\(\begin{gathered} A\text{. 1/2} \\ B\text{. 11/24} \\ C\text{. }\frac{1}{24} \\ \end{gathered}\)Yes, the calculations in A were reasonable because the difference is pretty close to 0.
Step-by-step explanation:
For part A,
-estimate the fraction 10/12 using 1/2 as our benchmark
The lower range is 1/2 and the upper range is 1
The halfway point is:
\(\begin{gathered} \frac{1}{2}\cdot\frac{(1+2)}{2} \\ \frac{1}{2}\cdot\frac{3}{2}=\frac{3}{4} \end{gathered}\)Therefore, our range is 1/2 < 3/4 < 1
10/12 ≥ 3/4, we round up to 1
-estimate the fraction 3/8 using the 1/2 as our benchmark:
The lower range is 0 and the upper range is 1/2
The halfway point is:
\(\frac{1}{2}\cdot\frac{1}{2}=\frac{1}{4}\)Therefore, our range is 0 < 1/4 < 1/2
3/8 ≥ 1/4, we round up to 1/2
\(\frac{2}{2}-\frac{1}{2}=\frac{1}{2}\)For part B, the denominators are 12 and 8, so the LCM would be;
\(\text{LCM}=24\)Then, we make a common denominator and subtract the numerators
\(\begin{gathered} \frac{10}{12}-\frac{3}{8}=\frac{20}{24}-\frac{9}{24} \\ \frac{10}{12}-\frac{3}{8}=\frac{11}{24} \end{gathered}\)For part C, compute the difference between the two results from parts A and B:
\(\frac{1}{2}-\frac{11}{24}=\frac{1}{24}\)Yes, the calculations in A were reasonable because the difference is pretty close to 0.
herman bought a rug 2.5 meters in length. how many centimeters is the length
Answers
1 meter is equivalent to 100 centimeters.
Using this conversion factor we get:
\(2.5\text{ m}\cdot\frac{100\text{ cm}}{1\text{ m}}=2.5\cdot100\text{ cm =}250\text{ cm}\)The length is 250 centimeters
who was the first president in usa
Answers
George Kolinsky Washington
Answer:
George Washington
Step-by-step explanation:
On April 30, 1789, George Washington, standing on the balcony of Federal Hall on Wall Street in New York, took his oath of office as the first President of the United States.
Find k so that kx^2 - 12x + 9 is the square of a binomial
Answers
Answer:
k = 4
Step-by-step explanation:
Given polynomial is,
kx² - 12x + 9
We have to find the value of 'k' for which the given polynomial is a square of a binomial.
To find this we will use the formula,
(a - b)² = a² - 2ab + b²
kx² - 12x + 9 = kx² - 2(6x) + 3²
= kx² - 2(3)(2x) + 3²
By comparing this with the formula of (a - b)²,
b = 3
a = 2x
(2x)²- 2(2x)(3) + 3² = (2x - 3)²
4x² - 12x + 9 = (2x - 3)²
Therefore, k = 4 will make the polynomial a perfect square of a binomial.
Which of Earth's layers has the same chemical composition as the mesosphere? (1 point)
O inner core
O outer core
O asthenosphere
O lithosphere
Answers
Answer:
lithosphere
Explanation:Lithosphere is the Earth's layers has the same chemical composition as the mesosphere. The lithosphere has a rigid look and is locateed in the outer section of the Earth. It also consists of the Earth's crust and mantle.
What is the side length of y
Answers
Answer:
the side length of y is 6... sorry if that is incorrect
Determine the domain of which the following function is increasing
Answers
Answer:
domain : - ∞ < x < 1
Step-by-step explanation:
the function is increasing on the upward part of the curve. that is
from negative infinity to the vertex at (1, 3 )
domain : - ∞ < x < 1
A classroom has 30 seats arranged in 6 rows of 5 seats each. Each student is randomly assigned a seat.
What is the probability that the first student is placed in the first row?
a. 5/6
b. 1/5
c. 1/6
d. 1/30
Answers
Answer:
c. 1/6
Step-by-step explanation:
There are 6 rows.
The probability of sitting in any row is 1/6.
p(first row) = 1/6