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1 year ago

Find the area of a triangle who's side lengths are 13, 14, and 15. (The questions doesn't tell the type of triangle.)

Mathematics

1 answer:

Y_Kistochka [10]1 year ago

5 0

Answer:

84 square units.

Step-by-step explanation:

<h2>Area of scalene triangle:</h2>

$\sf \boxed{\bf Area = \sqrt{s*(s-a)(s-b)*(s-c)}}$

Here, a, b and c are the sides of the triangle. s is the semi perimeter.

a = 13

b = 14

c = 15

$\sf s= \dfrac{a+b+c}{2}\\\\ =\dfrac{13+14+15}{2}\\\\=\dfrac{42}{2}\\\\s = 21$

s -a = 21 - 13 = 8

s -b = 21 - 14 = 7

s - c = 21 - 15 = 6

$\sf Area = \sqrt{21*8*7*6}$

$= \sqrt{ 7* 3 * 2 * 2 * 2 * 7 * 2 * 3}\\\\=7 * 3 *2*2\\\\= 84 \ square \ units$

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What value should be added to the expression to create a perfect square? x^2 - 20x

boyakko [2]

To complete the square:
we take the coefficient ox "x" (which in this problem is -20)
we divide it by 2
square that number
then add it to both sides of the equation

-20 / 2 = -10
-10^2 = 100
then we add 100 to both sides of the equation:
x^2 -20x
x^2 -20x +100 = 100
******************************************************
To get the roots of the equation, we take the square root of both sides:
(x -10) * (x-10) = 10
(x-10) = square root (10)
x-10 = 3.1622776602 
x1 = 13.1622776602 
and don't forget that square root of 10 also equals -3.1622776602 
x2 = 10 - 3.1622776602
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3 years ago

Which expression is equivalent to this expression? 3/4 (4h – 6)

sergij07 [2.7K]

Answer:
3h-9/2
Step-by-step explanation:
3/4(4h-6)=3h-18/4
simplify
3h-9/2

7 0

2 years ago

Vertically stretched by a factor of 2, then translated 4 units left and 1 unit down

drek231 [11]

A vertical stretch of scale factor 2, followed by a translation of 4 units left and 1 unit down is written as:

g(x) = 2*f(x + 4) - 1

<h3>How to write the given transformation?</h3>

For a general function f(x), a vertical stretch of scale factor K is written as:

g(x) = K*f(x).

Horizontal translation:

For a general function f(x), a horizontal translation of N units is written as:

g(x) = f(x + N).

If N is positive, the shift is to the left.
If N is negative, the shift is to the right.

Vertical translation:

For a general function f(x), a vertical translation of N units is written as:

g(x) = f(x) + N.

If N is positive, the shift is upwards.
If N is negative, the shift is downwards.

So, if we start with a function f(x) and we stretch it vertically with a scale factor of 2, we get:

g(x) = 2*f(x)

Then we translate it 4 units left:

g(x) = 2*f(x + 4)

Then we translate 1 unit down:

g(x) = 2*f(x + 4) - 1

This is the equation for the transformation.

If you want to learn more about transformations, you can read:

brainly.com/question/4289712

6 0

2 years ago

10 point to whoever know The CORRECT answer and who knows how to get good explanation

Nonamiya [84]

Answer:

30x^5 y^11 z^6

should be right

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2 years ago

In an analysis of healthcare data, ages have been rounded to the nearest multiple of 5 years. The difference between the true ag

Mars2501 [29]

Answer:

The approximate probability that the mean of the rounded ages within 0.25 years of the mean of the true ages is P=0.766.

Step-by-step explanation:

We have a uniform distribution from which we are taking a sample of size n=48. We have to determine the sampling distribution and calculate the probability of getting a sample within 0.25 years of the mean of the true ages.

The mean of the uniform distribution is:

$\mu=\dfrac{Max+Min}{2}=\dfrac{2.5+(-2.5)}{2}=0$

The standard deviation of the uniform distribution is:

$\sigma=\dfrac{Max-Min}{\sqrt{12}}=\dfrac{2.5-(-2.5)}{\sqrt{12}}=\dfrac{5}{3.46}=1.44$

The sampling distribution can be approximated as a normal distribution with the following parameters:

$\mu_s=\mu=0\\\\\sigma_s=\dfrac{\sigma}{\sqrt{n}}=\dfrac{1.44}{\sqrt{48}}=\dfrac{1.44}{6.93}=0.21$

We can now calculate the probability that the sample mean falls within 0.25 from the mean of the true ages using the z-score:

$z=\dfrac{X-\mu}{\sigma}=\dfrac{0.25-0}{0.21}=\dfrac{0.25}{0.21}=1.19\\\\\\P(|X_s-\mu|$

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3 years ago