Given the following points on the graph determine the midpoint of the following segments

Andre45 [30]

Answer:

The length of the short side is 14.5 units, the length of the other short side is 18.5 units, and the length of the longest side is 23.5 units.

Step-by-step explanation:

The Pythagorean Theorem

<em> If a and b are the lengths of the legs of a right triangle and c is the length of the hypotenuse, then the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse. </em>

This relationship is represented by the formula:

$a^2+b^2=c^2$

Applying the Pythagorean Theorem to find the lengths of the three sides we get:

$(x)^2+(x+4)^2=(x+9)^2\\\\2x^2+8x+16=x^2+18x+81\\\\2x^2+8x-65=x^2+18x\\\\2x^2-10x-65=x^2\\\\x^2-10x-65=0$

Solve with the quadratic formula

$\mathrm{For\:a\:quadratic\:equation\:of\:the\:form\:}ax^2+bx+c=0\mathrm{\:the\:solutions\:are\:}$

$x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

$\mathrm{For\:}\quad a=1,\:b=-10,\:c=-65:\quad x_{1,\:2}=\frac{-\left(-10\right)\pm \sqrt{\left(-10\right)^2-4\cdot \:1\left(-65\right)}}{2\cdot \:1}\\\\x_{1}=\frac{-\left(-10\right)+ \sqrt{\left(-10\right)^2-4\cdot \:1\left(-65\right)}}{2\cdot \:1}=5+3\sqrt{10}\\\\x_{2}=\frac{-\left(-10\right)- \sqrt{\left(-10\right)^2-4\cdot \:1\left(-65\right)}}{2\cdot \:1}=5-3\sqrt{10}$

Because a length can only be positive, the only solution is

$x=5+3\sqrt{10}\approx 14.5$

The length of the short side is 14.5, the length of the other short side is $14.5+4=18.5$ , and the length of the longest side is $14.5+9=23.5$ .

3 0

3 years ago

The formula used to find the length of a line segment in space.

Zigmanuir [339]

It's the same formula as the one used on Earth. It is based on the Pythagorean theorem.

length = √((∆x)^2 +(∆y)^2 +(∆z)^2)
.. where ∆x, ∆y, ∆z are the differences between the end-point coordinates in the x-, y-, and z-directions, respectively.

4 0

4 years ago

Read 2 more answers

Please check all that apply.

liq [111]

Answer:

the answers should be the first, third, and fourth ones

Step-by-step explanation:

7 0

4 years ago

Read 2 more answers

Harco<br> Find the inverse function f-¹(x) for the given function f(x).<br> 5. f(x) = 4x-8

ipn [44]

The inverse function for the given function f(x) = 4x - 2 is x/4 + 2

or, f⁻¹(x) = x/4 + 2

Given function, f(x) = 4x-8

We have to find f⁻¹(x)

f(x) = 4x - 8

or, y = 4x - 8

Interchanging the x variable with y,

x = 4y - 8

Solving y,

x = 4(y - 2)

or, x/4 = y - 2

or, y = x/4 + 2

Now, replacing y with f⁻¹(x), we get;

f⁻¹(x) = x/4 + 2

For verifying, you can use

(f · f⁻¹ )(x) = x

Therefore, the inverse function of f(x) is x/4 + 2.

To learn more about the inverse functions, visit: brainly.com/question/14965513

#SPJ9

6 0

2 years ago

a marketing survey compiled data on the total number of televisions in households where k is a positie constant. What is the pro

MariettaO [177]

Hi, you have not provided the distribution, I'll solve the problem for a particular distribution and you can apply the same method for yours.

Answer:

0.39

Step-by-step explanation:

X is the random event and P(X) is the probability of the event X, therefore, X is the number of televisions

Distribution:

X 0 1 2 3 4 5

P(X) 0.24 0.37 0.20 0.11 0.05 0.03

When they ask for the probability of at least Two televisions, they are asking for the probability that the householder has two or more television or P(X>2). To calculate the probability we need to add the probability of each event in the range:

P(X>2) = P(2) + P(3) + P(4) + P(5) = 0.20 + 0.11 + 0.05 + 0.03 = 0.39

3 0

4 years ago