Determine if a triangle with the given dimensions is a right triangle. If it is, which angle is the right angle?

1 answer:

6 0

To determine if the triangle is a right triangle, we use the Pythagorean theorem to test or see if the data agrees. We do as follows:

c² = a² + b²
10² = (5√3)² + 5²
100 = 75 + 25
100 = 100

Therefore, the triangle with the given measurements is a right triangle. The angle that would have a right angle is angle BAC. Hope this answers the question. Have a nice day. Feel free to ask more questions.

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HELP ASAP PLEASE & SHOW UR WORK!! THANK YOU <333

alekssr [168]

Answer:

$\bold{x_1=-\dfrac{3+\sqrt{41}}{2}\approx-4.7\ ,\quad x_2=-\dfrac{3-\sqrt{41}}{2}\approx1.7}$

Step-by-step explanation:

$-2x^2-3x+4=0\\\\a=-2\,,\ b=-3\,,\ c=4\\\\\\x=\dfrac{-b-\sqrt{b^2\pm4ac}}{2a}=\dfrac{-(-3)\pm\sqrt{(-3)^2-4(-2)(4)}}{2(-1)}=\dfrac{3\pm\sqrt{9+32}}{-2}\\\\\\x_1=-\dfrac{3+\sqrt{41}}{2}\approx-4.7\ ,\qquad x_2=-\dfrac{3-\sqrt{41}}{2}\approx1.7$

4 0

2 years ago

PLEASE HELP!!!!

love history [14]

<h3>Answer is 1.5 square meters</h3>

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Work Shown:

The portion of the fabric that is laying across the ground is 2 meters. The portion of the fabric from the ground to the highest point (along the fabric's edge) is 1.5 meters, half of that is 0.75 meters and this is the length of the shadow. We can see this by forming a 30-60-90 triangle. The hypotenuse is 1.5 meters, the short leg is 0.75 meters. The short leg is always half of the hypotenuse of any 30-60-90 triangle, and the short leg is opposite the 30 degree angle.

So this shadow has length of 2 meters and 0.75 meters, making its area be 0.75*2 = 1.5 square meters when the sun is directly overhead at 12 noon

8 0

2 years ago

Determine whether the equation x^3 - 3x + 8 = 0 has any real root in the interval [0, 1]. Justify your answer.

nikdorinn [45]

Answer:

The equation does not have a real root in the interval $\rm [0,1]$

Step-by-step explanation:

We can make use of the intermediate value theorem.

The theorem states that if $f$ is a continuous function whose domain is the interval [a, b], then it takes on any value between f(a) and f(b) at some point within the interval. There are two corollaries:

If a continuous function has values of opposite sign inside an interval, then it has a root in that interval. This is also known as Bolzano's theorem.
The image of a continuous function over an interval is itself an interval.

Of course, in our case, we will make use of the first one.

First, we need to proof that our function is continues in $\rm [0,1]$ , which it is since every polynomial is a continuous function on the entire line of real numbers. Then, we can apply the first corollary to the interval $\rm [0,1]$ , which means to evaluate the equation in 0 and 1:

$f(x)=x^3-3x+8\\f(0)=8\\f(1)=6$

Since both values have the same sign, positive in this case, we can say that by virtue of the first corollary of the intermediate value theorem the equation does not have a real root in the interval $\rm [0,1]$ . I attached a plot of the equation in the interval $\rm [-2,2]$ where you can clearly observe how the graph does not cross the x-axis in the interval.