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2 years ago

Explain how slope is used to determine if a triangle is a right triangle.

2 answers:

5 0

A right triangle contains a right angle, so it must have two sides that are perpendicular. If the slopes of two sides can be shown to be negative reciprocals of each other, then it can be concluded that a right angle is formed. If a triangle contains a right angle, then it is a right triangle.

zysi [14]2 years ago

4 0

Do determine if a triangle is a right triangle using slopes, you have to understand perpendicular slopes/negative reciprocals.

You can calculate the slope of all 3 sides of the triangle and if two of the slopes are negative reciprocals, then those two lines intersect creating a right angle/right triangle.

Let's say there's triangle ABC.

If the slope of AB is 1/2
and the slope of BC is 2/5
and the slope of CA is -2/1
then AB and CA intersect resulting in a right angle (triangle).

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The net change in temperature from Neptune to Mars is

azamat

We know that the average temperature surface in neptune is : - 210 degree Celsius
Thee average temperature surface in mars is : -85 degree Celsius

The net change would be an increase in 125 degree celsius<span />

4 0

3 years ago

What is the median of the data displayed in this box-and-whisker plot? A.41 B.49 C.55 D.58

Likurg_2 [28]

The answer is A. 41 because it is in the middle of the box.

4 0

3 years ago

Read 2 more answers

Finding a polynomial of a given degree with given zeros

galben [10]

Since f(x) is a polynomial with 3rd degree, then it will have 3 roots (zeroes)

One of them is real and the other two are complex conjugate roots

Since the real root is 4, then

x = 4

Since the complex root is (1 - i), then

The other root will be the conjugate of it (1 + i)

x = (1 - i)

x = (1 + i)

To find f(x) we will multiply the three factors of it

We can get the factors from the zeroes

$x=4$

Subtract 4 from both sides

$\begin{gathered} x-4=4-4 \\ x-4=0 \end{gathered}$

The first factor is (x - 4)

$\begin{gathered} x=1-i \\ x-(1-i)=(1-i)-(1-i) \\ x-1+i=0 \end{gathered}$

The second factor is (x - 1 + i)

The third factor is (x - 1 - i)

$f(x)=(x-4)(x-1+i)(x-1-i)$

We will multiply them to find f(x)

$\begin{gathered} (x-1+i)(x-1-i)= \\ x^2-x-ix-x+1+i+ix-i-(i^2)= \\ x^2-2x+1-(-1)= \\ x^2-2x+1+1= \\ x^2-2x+2 \end{gathered}$

Multiply it by (x - 4)

$\begin{gathered} f(x)=(x-4)(x^2-2x+2) \\ f(x)=x^3-2x^2+2x-4x^2+8x-8 \\ f(x)=x^3-6x^2+10x-8 \end{gathered}$

The answer is

$f(x)=x^3-6x^2+10x-8$

5 0

1 year ago

3. Find the value of x. 4 3 6<br>

tester [92]

Answer:

Step-by-step explanation:

x in (-oo:+oo)

(x/4)/3 = 6 // - 6

(x/4)/3-6 = 0

1/12*x-6 = 0 // + 6

1/12*x = 6 // : 1/12

x = 6/1/12

x = 72

5 0

2 years ago

If a cup of coffee has temperature 97Â°C in a room where the ambient air temperature is 25Â°C, then, according to Newton's Law o

FinnZ [79.3K]

Answer:

The average temperature is $T_{a} = 81.95^oC$

Step-by-step explanation:

From the question we are told that

The temperature of the coffee after time t is $T(t) = 25 + 72 e^{[-\frac{t}{45} ]}$

Now the average temperature during the first 22 minutes i.e fro $0 \to 22$ minutes is mathematically evaluated as

$T_{a} = \frac{1}{22-0} \int\limits^{22}_{0} {25 +72 e^{[-\frac{t}{45} ]}} \, dx$

$T_{a} = \frac{1}{22} [25 t + 72 [\frac{e^{[-\frac{t}{45} ]}}{-\frac{1}{45} } ] ] \left| 22} \atop {0}} \right.$

$T_{a} = \frac{1}{22} [25 t - 3240e^{[-\frac{t}{45} ]} ] \left | 45} \atop {{0}} \right.$

$T_{a} = \frac{1}{22} [25 (22) - 3240e^{[-\frac{22}{45} ]} - (- 3240e^{0} )]$

$T_{a} = \frac{1}{22} [550 - 1987.12 + 3240]$

$T_{a} = 81.95^oC$

8 0

2 years ago