In geometry, Heron's formula (sometimes called Hero's formula), named after Hero of Alexandria, gives the area of a triangle by requiring no arbitrary choice of side as base or vertex as origin, contrary to other formulas for the area of a triangle, such as half the base times the height. Use Heron's formula to find the area, in square feet, of ΔABC.

Options:

A)

7.385

B)

8.270

C)

6.495

D)

5.591

In Geometry, Heron's Formula (sometimes Called Hero's Formula), Named After Hero Of Alexandria, Gives

Answers

Answer 1

Answer:

C) [tex] 6.495\: ft^2 [/tex]

Step-by-step explanation:

a = 7 ft, b = 3 ft, c = 5 ft (Given)

Therefore, a + b + c = 7 + 3 + 5 = 15 ft

Let's calculate semi Perimeter of the triangle which is given by s

[tex] s =\frac{a+b+c}{2}=\frac{15}{2} = 7.5 \: ft[/tex]

Now, by Heron's formula, area of triangle ABC is given as:

[tex] A(\triangle ABC) =\sqrt{s(s-a) (s-b)(s-c)} [/tex]

[tex]\therefore A(\triangle ABC) =\sqrt{7.5(7.5-7) (7.5-3)(7.5-5)} [/tex]

[tex]\therefore A(\triangle ABC) =\sqrt{7.5(0.5) (4.5)(2.5)} [/tex]

[tex]\therefore A(\triangle ABC) =\sqrt{42.1875} [/tex]

[tex]\therefore A(\triangle ABC) =6.49519053 [/tex]

[tex]\therefore A(\triangle ABC) =6.495\: ft^2 [/tex]


Related Questions

maths class 9
Multiply: 4√12 2√12

Answers

Answer:

[tex]4 \sqrt{122} \sqrt{12} \\ (4 \times 2) \times ( \sqrt{12} \times \sqrt{12} ) \\ (4 \times 2) \times 12 \\ 8 \times 12 \\ 96[/tex]

The answer:
48 the sign thing 16
Decimal form would be
117.57550765

There were 642 students enrolled in a freshman-level chemistry class. By the end of the semester, the number of students who passed was 5 times the number of students who failed. Find the number of students who passed and the number who failed.

Answers

Answer:

535 students passed and 107 students failed

Step-by-step explanation:

Create a system of equations where p is the number of students who passed and f is the number of students who failed:

p + f = 642

p = 5f

Solve by substitution by plugging in 5f as p into the first equation, then solving for f:

p + f = 642

5f + f = 642

6f = 642

f = 107

So, 107 students failed.

Find how many students passed by multiplying this by 5:

107(5)

= 535

535 students passed and 107 students failed.

Given the a center (-1, -2) and a radius r = 2. Identify the circle.

Answers

Answer:

1st option

1st graph has the centre on (-1,-2) and the distance of the circumference from the centre is 2

Answered by GAUTHMATH

Someone help please

Answers

Answer:  Choice A

[tex]\tan(\alpha)*\cot^2(\alpha)\\\\[/tex]

============================================================

Explanation:

Recall that [tex]\tan(x) = \frac{\sin(x)}{\cos(x)}[/tex] and [tex]\cot(x) = \frac{\cos(x)}{\sin(x)}[/tex]. The connection between tangent and cotangent is simply involving the reciprocal

From this, we can say,

[tex]\tan(\alpha)*\cot^2(\alpha)\\\\\\\frac{\sin(\alpha)}{\cos(\alpha)}*\left(\frac{\cos(\alpha)}{\sin(\alpha)}\right)^2\\\\\\\frac{\sin(\alpha)}{\cos(\alpha)}*\frac{\cos^2(\alpha)}{\sin^2(\alpha)}\\\\\\\frac{\sin(\alpha)*\cos^2(\alpha)}{\cos(\alpha)*\sin^2(\alpha)}\\\\\\\frac{\cos^2(\alpha)}{\cos(\alpha)*\sin(\alpha)}\\\\\\\frac{\cos(\alpha)}{\sin(\alpha)}\\\\[/tex]

In the second to last step, a pair of sine terms cancel. In the last step, a pair of cosine terms cancel.

All of this shows why [tex]\tan(\alpha)*\cot^2(\alpha)\\\\[/tex] is identical to [tex]\frac{\cos(\alpha)}{\sin(\alpha)}\\\\[/tex]

Therefore, [tex]\tan(\alpha)*\cot^2(\alpha)=\frac{\cos(\alpha)}{\sin(\alpha)}\\\\[/tex] is an identity. In mathematics, an identity is when both sides are the same thing for any allowed input in the domain.

You can visually confirm that [tex]\tan(\alpha)*\cot^2(\alpha)\\\\[/tex] is the same as [tex]\frac{\cos(\alpha)}{\sin(\alpha)}\\\\[/tex] by graphing each function (use x instead of alpha). You should note that both curves use the exact same set of points to form them. In other words, one curve is perfectly on top of the other. I recommend making the curves different colors so you can distinguish them a bit better.

Alex wants to test the reliability of “lie detector tests,” or polygraph tests. He performs a polygraph test on a random sample of 12 individuals. If there is more than a 50% chance that the tests result in no false positives (that is, the test does not result in a true statement being recorded as a lie), Alex will conclude that the tests are reliable. If the probability of a lie detector test resulting in a false positive is 5.5%, what will Alex conclude? Use Excel to find the probability, rounding to three decimal places.

Answers

The correct statement is test is reliable and authentic as the probability of no false positives is more than 0.5

Given that

[tex]H_o:P= 0.50\\\\H_1:P>0.50[/tex]

Now following calculations to be done to reach the conclusion:

There is no false positive as

= 100 - 5.5

= 94.5%

[tex]\hat P =0.945, n = 12[/tex]

Now

[tex]z = \frac{\hat P - P}{\sqrt\frac{P(1-P)}{n} }\\\\=\frac{0.945-0.5}{\sqrt\frac{0.5\times0.5}{12} } \\\\= 3.08[/tex]

So

P value = P(z >3.08) = 0.0010

Therefore we can conclude that test is reliable and authentic as the probability of no false positives is more than 0.5

Learn more about the polygraph test here:

brainly.com/question/3790493

What is 55 increased by 10%?

Answers

Answer:

10% of 55

=> 10/100 × 55

=> 1/10×55

=> 5.5

55 increased by 10% => 55 + 5.5

=> 60.5

hope that helps ✌

Answer:

Step-by-step explanation:

10% of 55

10/100*55

1/10*55

5.5 <--- That is 10% of 55

55+5.5 = 60.5

-1/4 (x+2)+5=-x I really need help

Answers

Answer:

x = -6

Step-by-step explanation:

Answer:

-6

Step-by-step explanation:

-1/4 (x+2)+5=-x

-1/4x-1/2+5=-x

-1/4x+4.5=-x

+1/4x          +1/4x

(4/3) 4.5=-3/4x (4/3)

6=x

x=6

√3 is a polynomial of degree ________.

Answers

Step-by-step explanation:

Therefore, the degree of polynomial √3 is zero.

[tex]\sf\huge\underline\color{pink}{༄Answer:}[/tex]

[tex]\tt{\sqrt{3}}[/tex] is a polynomial of degree 0

[tex]\sf\huge\underline\color{pinl}{༄Note:}[/tex]

The expression is constant, which means it can be rewritten with a factor of x^0. The degree is the largest exponent on the variable.

[tex]\color{pink}{==========================}[/tex]

-#CarryOnLearning

-Park Hana Moon

Chris drives 240 miles from his home in Atlanta, Georgia, at 60 miles per hour. How many minutes longer would the return trip take if he travels at 50 miles per hour

Answers

Answer:

48 minutes

240 at 60mph = 4 hrs.

240 at 50 mph = 4.8 hrs.

it would take an extra 60*.8 or 48 minutes

Step-by-step explanation:

The trip will be of 48 minutes longer when the speed is decreased by 10 miles per hour.

What is the formula for time?

The time is given by distance/speed. The unit of time is minutes or seconds.

What will be the time difference?

When distance of 240 miles is cover by the speed of 60 miles per hour then the time take to travel this distance will be 240/60=4 hours

When distance of 240 miles is cover by the speed of 50 miles per hour then the time take to travel this distance will be 240/50=4.8 hours

The difference between 4.8 hours and 4 hours is of 0.8 hours or 0.8*60=48 minutes.

Therefore, the trip will be of 48 minutes longer.

Learn more: brainly.com/question/21061928

#SPJ2

pls help me asap !!!!

Answers

Answer:

9--7

Step-by-step explanation:

Answer:

distance = √74

Step-by-step explanation:

d = √((x2 - x1)²+(y2 - y1)²)

Where the first point = (x1, y1) and the second point = (x2, y2)

First point: (2, -2)

Second point: (7, -9)

Step 1. Plug these points into the formula

d = √((7 - 2)² + (-9 - -2)²)

Step 2. Subtract

d=√(( 5 )² + ( -7 )²)

Step 3. Simplify the exponents

d=√(25) + (49)

Step 4. Add

d=√74


help me out .... I will mark u as brilliant students ​

Answers

oe which question are you figure it out

make a factor tree for 42

Answers

Answer:

The number 43 is a composite number because 42 can be divided by 1, by itself and at least by 2, 3, and 7. So it is possible to draw its prime tree. The prime factorization of 42=2*3*7

Step-by-step explanation:

hope this helps :)

Hope it helpppppssss !!!!

What is the shaded area of the figure?

Answers

Answer:

Step-by-step explanation:

The idea here is to find the area of the circle and then subtract from it the area of the triangle. That will give you the area of what's left in the circle (the shaded part). The area of a circle is:

[tex]A_c=\pi r^2[/tex] so

[tex]A_c=(3.14)(12.4)^2[/tex]   where 12.4 is the radius.

[tex]A_c=482.81[/tex] rounded to the nearest tenth. I used 3.14 for pi.

Now for the area of the triangle. The formula is

[tex]A_t=\frac{1}{2}bh[/tex] where h is the height of 12.4 and the base is the diameter which is 12.4 * 2 = 24.8

[tex]A_t=\frac{1}{2}(24.8)(12.4)[/tex] so

[tex]A_t=153.76[/tex]

Now subtract the triangle's area from the circle's area:

482.81 - 153.76 = 329.05 mm²

With the aid of an illustrative example, discuss the relationship between the area of a region and the definite integral. *​

Answers

Suppose there is a function f(x), the definite integral of the function is the difference between the upper and lower x-values.

There are three relationships between the definite integral and the area of the region. The relationships are:

Positive functionNegative functionRegion between two functions

Positive function

The area between the function itself and the x-axis represents the definite integral.

Negative function

The area between the function itself and the x-axis, multiplied by -1 represents the definite integral.

Region between two functions

The definite integral of the function is the difference between the region of both functions.

See attachment for further illustration

Learn more about area of a region and the definite integral at:

https://brainly.com/question/3471148

Write the ratio: 3 1/6 to 17/6
as a fraction in lowest terms.

Answers

Answer:  [tex]\frac{19}{6} : \frac{17}{6}[/tex]

Step-by-step explanation:

Let us first represent the ratio.

3[tex]\frac{1}{6} : \frac{17}{6}[/tex]

Now we need to convert 3[tex]\frac{1}{6}[/tex] into a improper fraction.

[tex]\frac{19}{6} : \frac{17}{6}[/tex]

Now it is in its simplest form.

The final answer is  [tex]\frac{19}{6} : \frac{17}{6}[/tex]

2t(t-1)-t+1 factorise​

Answers

Answer:

this is the answer of this question

hoping it will help u

answer please lol so uh yeah

Answers

The answer would be option A. If you substitute x for 4 that would be 5(4) which equals 20! you’re welcome

Answer:

5x=20

5x/5=20/5

x=4

Step-by-step explanation:

substitute the 5x

divide both sides by 5 it will be 20 divide by 5

answer is x =4

Equivalent expression -(-5.6m-n+9.9

Answers

Answer:

5.6m + n - 9.9

Step-by-step explanation:

-(-5.6m-n+9.9)

5.6m + n - 9.9

Help me quick i need helppp

Answers

[tex]\\ \sf\longmapsto (m-8)+(m-8)+(m-8)+(m-8)+(m-8)+(m-8)=12[/tex]

[tex]\\ \sf\longmapsto 6(m-8)=12[/tex]

[tex]\\ \sf\longmapsto 6m-48=12[/tex]

[tex]\\ \sf\longmapsto 6m=12+48[/tex]

[tex]\\ \sf\longmapsto 6m=60[/tex]

[tex]\\ \sf\longmapsto m=\dfrac{60}{6}[/tex]

[tex]\\ \sf\longmapsto m=10[/tex]

Answer:

M=14

Step-by-step explanation:

First make an equation - m÷6 =8Then shift 6 to 8 - m=6×8Answer - m=14

Determine the period

Answers

Answer:

16 units

Step-by-step explanation:

period = length of an interval that contains exactly one copy of the repeating pattern, so from one peak to another peak.

in this graph its the peaks are 1 and 17, hence the period is 16

If each side of a cube is doubled, its volume?​

Answers

If you double each side the volume is 8 times

Must click thanks and mark brainliest

Find the values of the missing sides. You must use exact answers! PLEASE HURRY AND HELP

Answers

Answer:

x=4sqrt3 a=4 b=3  ,y=8sqrt3 c=8 d=3

Step-by-step explanation:

because this is a 30-60-90 triangle, it is easy to find the side lengths. the longer leg is sqrt(3) times the shorter leg so x= 12/sqrt(3) or 4sqrt(3). the hypotenuse is 2 times the shorter leg so y= 8sqrt(3)

Please help solve for x

Answers

Answer:

8.49

Step-by-step explanation:

there is a little formula related to the famous formula of Pythagoras.

it says that the height of a triangle is the square root of the product of both segments of the baseline (the segments the height splits the baseline into).

so, x is actuality the height of the triangle.

x = sqrt(3×24) = sqrt(72) = 8.49

hlpppppppppppppppppppppppppppppppp

Answers

Answer:

c

Step-by-step explanation:

-7.5 is less than 6.5

An 8μC charge is moving through a 10T magnetic field at a speed of 2.5⋅107 m/s perpendicular to the direction of the field. What is the force on the charge

Answers

THIS IS YOUR ANSWER

HOPE IT HELPS YOU

What is the value of x?

Answers

Answer:

x = 54.6 m

Step-by-step explanation:

Δ MAB and Δ MNP are similar, then corresponding sides are in proportion, that is

[tex]\frac{MA}{MN}[/tex] = [tex]\frac{MB}{MP}[/tex] , substitute values

[tex]\frac{80.5-35}{80.5}[/tex] = [tex]\frac{x}{96.6}[/tex]

[tex]\frac{45.5}{80.5}[/tex] = [tex]\frac{x}{96.6}[/tex] ( cross- multiply )

80.5x = 4395.3 ( divide both sides by 80.5 )

x = 54.6

Answer:

Answer:

Answer:x = 25°

Answer:x = 25°Step-by-step explanation:

Answer:x = 25°Step-by-step explanation:The secant- secant angle FGE is one half the difference of the intercepted arcs, that is (135 - x) = 55 ( multiply both sides by 2 to clear the fraction )

Answer:x = 25°Step-by-step explanation:The secant- secant angle FGE is one half the difference of the intercepted arcs, that is (135 - x) = 55 ( multiply both sides by 2 to clear the fraction )135 - x = 110 ( subtract 135 from both sides )

Answer:x = 25°Step-by-step explanation:The secant- secant angle FGE is one half the difference of the intercepted arcs, that is (135 - x) = 55 ( multiply both sides by 2 to clear the fraction )135 - x = 110 ( subtract 135 from both sides )- x = - 25 ( multiply both sides by - 1 )

Answer:x = 25°Step-by-step explanation:The secant- secant angle FGE is one half the difference of the intercepted arcs, that is (135 - x) = 55 ( multiply both sides by 2 to clear the fraction )135 - x = 110 ( subtract 135 from both sides )- x = - 25 ( multiply both sides by - 1 )x = 25°

Hence the answer is 25.

Deion is saving up to buy a new phone. He already has $95 and can save an additional $7 per week using money from his after school job. How much total money would Deion have after 6 weeks of saving? Also, write an expression that represents the amount of money Deion would have saved in w weeks.

Answers

answer to part one of the question:
$95 + 7 x 6= 137

The expression that represents the amount of money Deion would have saved in w weeks is 95 + 7w and the total savings after 6 weeks will be $137.

What is an expression?

A statement expressing the equality of two mathematical expressions is known as an equation.

A mixture of variables, numbers, addition, subtraction, multiplication, and division are called expressions.

An expression is a mathematical proof of the equality of two mathematical expressions.

As per the given,

Initial fixed money = $95

Per week saving $7/week

Total money = fixed money + money in w weeks.

⇒ 95 + 7w

For 6 weeks, w = 6

⇒ 95 + 7× 6 = $137.

Hence "The expression that represents the amount of money Deion would have saved in w weeks is 95 + 7w and the total savings after 6 weeks will be $137".

To learn more about expression,

https://brainly.com/question/14083225

#SPJ3

 

Which of the following best describes the slope of the line below?
A. Zero
B. Negative
C. Positive
< PREVIOUS

Answers

Answer:

A. Zero.

Step-by-step explanation:

Technically, the correct answer is "undefined", as there will be infinite change in the slope amount. However, of all the given choices, Zero should be the best answer. However, if it is wrong, do ask your teacher, and state that undefined should be the answer choice, and that credit should be rewarded for such.

Select the equation written in slope intercept form that corresponds to the given slope y intercept

Answers

Answer:

[tex]y = -6x + 1[/tex]

[tex]y = 6x - 2[/tex]

[tex]y = -2x + 4[/tex]

[tex]y = x + 6[/tex]

Step-by-step explanation:

Given

See comment for missing part of the question

Required

The equation in slope intercept form

A linear equation is of the form:

[tex]y = mx + b[/tex]

(a) m = -6, b =1

Using the above format, we have:

[tex]y = -6x + 1[/tex]

(b) m =6, b = -2

[tex]y = 6x - 2[/tex]

(c) m = -2, b = 4

[tex]y = -2x + 4[/tex]

(d) m = 1, b = 6

[tex]y = x + 6[/tex]

Calculus!

The volume of a substance, A, measured in cubic centimeters increases according to the exponential growth model dA/dt = 0.3A, where t is measured in hours. The volume of another substance, B, also measured in cubic centimeters increases at a constant rate of 1 cm^3 per hour according to the linear model dB/dt = 1. At t = 0, substance A has a volume A(0) = 3 and substance B has size B(0) = 5. At what time will both substances have the same volume?

Would it be correct to write the growth model of substance B as x + 5? And how could I write the growth model of substance A? Thank you in advance, and sorry for the poor formatting.

Answers

Answer:

The two substances will have the same volume after approximately 3.453 hours.

Step-by-step explanation:

The volume of substance A (measured in cubic centimeters) increases at a rate represented by the equation:

[tex]\displaystyle \frac{dA}{dt} = 0.3 A[/tex]

Where t is measured in hours.

And substance B is represented by the equation:

[tex]\displaystyle \frac{dB}{dt} = 1[/tex]

We are also given that at t = 0, A(0) = 3 and B(0) = 5.

And we want to find the time(s) t for which both A and B will have the same volume.  

You are correct in that B(t) is indeed t + 5. The trick here is to multiply both sides by dt. This yields:

[tex]\displaystyle dB = 1 dt[/tex]

Now, we can take the integral of both sides:

[tex]\displaystyle \int 1 \, dB = \int 1 \, dt[/tex]

Integrate. Remember the constant of integration!

[tex]\displaystyle B(t) = t + C[/tex]

Since B(0) = 5:

[tex]\displaystyle B(0) = 5 = (0) + C \Rightarrow C = 5[/tex]

Hence:

[tex]B(t) = t + 5[/tex]

We can apply the same method to substance A. This yields:

[tex]\displaystyle dA = 0.3A \, dt[/tex]

We will have to divide both sides by A:

[tex]\displaystyle \frac{1}{A}\, dA = 0.3\, dt[/tex]

Now, we can take the integral of both sides:

[tex]\displaystyle \int \frac{1}{A} \, dA = \int 0.3\, dt[/tex]

Integrate:

[tex]\displaystyle \ln|A| = 0.3 t + C[/tex]

Raise both sides to e:

[tex]\displaystyle e^{\ln |A|} = e^{0.3t + C}[/tex]

Simplify:

[tex]\displaystyle |A| = e^{0.3t} \cdot e^C = Ce^{0.3t}[/tex]

Note that since C is an arbitrary constant, e raised to C will also be an arbitrary constant.

By definition:

[tex]\displaystyle A(t) = \pm C e^{0.3t} = Ce^{0.3t}[/tex]

Since A(0) = 3:

[tex]\displaystyle A(0) = 3 = Ce^{0.3(0)} \Rightarrow C = 3[/tex]

Therefore, the growth model of substance A is:

[tex]A(t) = 3e^{0.3t}[/tex]

To find the time(s) for which both substances will have the same volume, we can set the two functions equal to each other:

[tex]\displaystyle A(t) = B(t)[/tex]

Substitute:

[tex]\displaystyle 3e^{0.3t} = t + 5[/tex]

Using a graphing calculator, we can see that the intersect twice: at t ≈ -4.131 and again at t ≈ 3.453.

Since time cannot be negative, we can ignore the first solution.

In conclusion, the two substances will have the same volume after approximately 3.453 hours.

Other Questions
Monica: I was (be) in New York last week. Adam: Really? 2 Monica: Yes, I ^ 3 you _(love) it! (have) a good time? You ever 4 Adam: No, I haven't. I 5 few years ago, but I 6 What 7 (go) there? (visit) some friends in San Francisco a (not go) to the USA since then. (do) in New York? You Monica: I ^ 8 lots of souvenirs. (see) a show on Broadway, and I ^ 9 (buy) 10 Adam: Where you Monica: At a hotel in Manhattan. I 11 (stay)? (forget) its name. Adam: 12 (cost) a lot to stay there? 13 Monica: No, it was free. I (win) the holiday in a competition. Adam: You're lucky! I ^ 14 never (win) anything! Race relations were strained in the mid-1960s to such a large degree that even those who fought side by side for the passage of the Civil Rights Act of 1964 and the Voting Rights Act of 1965 abandoned each other. What was a primary source of animosity in race relations as the civil rights movement evolved in the 1960s Sammy and Hannah are finalists in a cooking competition. For the final round, each of them will randomly select a card without replacement that will reveal what their star ingredient must be. Here are the available cards:CabbageSpinachKaleLeeksCarrotsTurnipsCabbage Leeks Spinach Carrots Kale Turnips Sammy and Hannah both want to get leeks as their star ingredient. Sammy will draw first, followed by Hannah.What is the probability that NEITHER contestant draws leeks?Round your answer to two decimal places. 2 similar cardboards have areas of 24cm square and 150cm square. if the length of the bigger one is 10cm, what is the length of the smaller one Can someone find me the exact translation of each of the three sentences? (See picture below) 3T-2 + T -5T= -1 Solve it out please I really need an answer as soon as possible. 10 pts worth it WHO YOUR FATHER (GOD) OR (SAITAN) WHEN YOU CHOOSE GOD IT MEANS YOU LOVE HIM 15 POINTS WHEN YOU CHOOSE GOD Which of the following scenarios would not create a risk for a foodborne illness? A. Sofia prepares a plate of appetizers that includes mostly raw carrots, celery, and apples.B. Akito slices fresh vegetables on the same cutting board he just used for raw chicken.C. Dai enjoys eating oysters and clams but prefers to eat them raw instead of cooked.D. Francoise prefers for her chicken to be slightly undercooked so that it is juicer. What is the main idea of this text?A.Sojourner Truth feels that women's rights are areligious issue.B.Men should give women equal rights.C.Women can speak just as well as men.D.Sojourner Truth is a woman of great faith. 8x=3x-1 plz help me show your work HRH Collection Agency keeps a collection fee of 25% of any amounts collected. How much did the agency collect on a bad debt if the agency forwarded $2490 to a client? What happens when the density of a medium increases? Find the measure of the diagonal of a square is 50cm long. how long are the sides of the square? what Immigration events took place in the US during 1951-2000 Which of the following molecules does not have a permanent dipole?A CF4B CHF3C CH2F2 D CH3F Explain please Evaluate the expression: y y 1 + x Use x = 7 and y = 3 A ball of mass 0.50 kg is rolling across a table top with a speed of 5.0 m/s. When the ball reaches the edge of the table, it rolls down an incline onto the floor 1.0 meter below (without bouncing). What is the speed of the ball when it reaches the floor?PLEASE EXPLAIN HOW YOU GOT THE ANSWER THANK YOU SO MUCH Hello i need help with this question