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2 years ago

The perimeter of a triangle is 510 feet and the sides are in the ratio of 11:16:24. Find the area of the triangle

1 answer:

Nutka1998 [239]2 years ago

5 0

If the sides are in the ratio of 11:16:24, it means that they are all multiples of a same number x, according to these factors.

So, the shorter side is 11x feet long, the middle one is 16x feet long, and the longest side is 24x feet long.

This means that the perimeter is

$11x+16x+24x = 51x$ feet long. But we know that this is 510 feet, so we have

$51x = 510 \implies x = \cfrac{510}{51} = 10$ .

So, the three sides are 110, 160 and 240 feet long.

To find the area of a triangle knowing its three sides, you can use Heron's formula, which states that, if $s$ is half the perimeter of the triangle whose sides are $a,b,c$ , the area $A$ is given by

$A = \sqrt{s(s-a)(s-b)(s-c)}$

In our case, $s = 255, a = 110, b = 160, c = 240$ so the formula becomes

$A = \sqrt{255(255-110)(255-160)(255-240)} = \sqrt{255(145)(95)(15)} = \sqrt{52689375} \approx 7258.74$

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PLS HELP ASAP PLEASE Heidi and Andrew designed two raised flower beds for their garden. Heidi's flower bed was 5 feet long by 3

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First, find the area of both beds!
For Heidi: 5 x 3 = 15
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2 years ago

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A parabola, with its vertex at the origin, has a directrix at y = 3. Which statements about the parabola are true? Select two op

shutvik [7]

Answer:

Step-by-step explanation:

Let's answer these questions in an all-encompassing kind of explanation. If you plot the vertex and the directrix, you see that the vertex is below the directrix. Because of the fact that a parabola opens AWAY from the directrix, and wraps itself around the focus, we know it's an upside down parabola of the form

$4p(y-k)=-(x-h)^2$

The p value from the equation is a distance, specifically the distance between either the vertex and the directrix, or the vertex and the focus. The vertex is exactly in the middle of the directrix and the focus. So that tells us that the focus is 3 units below the vertex (because the directrix is 3 units above the vertex). We also know from this that p = 3.

Filling in the equation with a vertex of (0, 0) which is our h and k respectively:

$4(3)(y-0)=-(x-0)^2$ which simplifies to

$12y=-x^2$ and multiplying both sides by -1:

$-12y=x^2$ . This is not standard form, but it matches what your equation is in the choices. So to sum up:

The focus is located at (0, -3) and the first choice is true.

The parabola opens upside down and the second choice is not true.

The p value is found by counting the units between the vertex and the directrix, so the third choice is not true.

We solved the equation by filling in the values for h, k, and p and got that the equation in the fourth choice is true.

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2 years ago

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A study is being conducted in which the health of two independent groups of ten policyholders is being monitored over a one-year

uysha [10]

Answer:

46.91% probability that at least nine participants complete the study in one of the two groups, but not in both groups

Step-by-step explanation:

We use two binomial trials to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

Probability of at least nine participants finishing the study in a group.

0.2 probability of a students dropping out. So 1 - 0.2 = 0.8 probability of a student finishing the study. This means that $p = 0.8$ .

10 students, so $n = 10$

We have to find:

$P(X \geq 9) = P(X = 9) + P(X = 10)$

Then

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 9) = C_{10,9}.(0.8)^{9}.(0.2)^{1} = 0.2684$

$P(X = 10) = C_{10,10}.(0.8)^{10}.(0.2)^{0} = 0.1074$

$P(X \geq 9) = P(X = 9) + P(X = 10) = 0.2684 + 0.1074 = 0.3758$

0.3758 probability that at least nine participants complete the study in a group.

Calculate the probability that at least nine participants complete the study in one of the two groups, but not in both groups?

0.3758 probability that at least nine participants complete the study in a group. This means that $p = 0.3758$

Two groups, so $n = 2$

We have to find P(X = 1).

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 2) = C_{2,1}.(0.3758)^{1}.(0.6242)^{1} = 0.4691$

46.91% probability that at least nine participants complete the study in one of the two groups, but not in both groups

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Marizza181 [45]

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Use the Midpoint Formula three times to find the three points that divide the line segment joining (x1, y1) and (x2, y2) into fo

fredd [130]

We are given points $A(x_1,y_1)$ and $B(x_2,y_2)$ .

We first find the midpoint M, of AB, which divides the segment AB into 2 equal parts,

then we find the midpoint N of AM, and midpoint K of MB.

Thus each of the half parts is divided into 2 equal parts. The whole segment is divided into 4 equal parts.

The coordinates of M, N and K are found as follows:

the coordinates of M are: $( \frac{x_1+x_2}{2} , \frac{y_1+y_2}{2})$

the coordinates of N are:

$\displaystyle{( \frac{x_1+\frac{x_1+x_2}{2}}{2} , \frac{y_1+\frac{y_1+y_2}{2}}{2})=( \frac{\frac{2x_1+x_1+x_2}{2}}{2} , \frac{\frac{2y_1+y_1+y_2}{2}}{2})$

$=\displaystyle{(\frac{3x_1+x_2}{4}, \frac{3y_1+y_2}{4})}$

similarly, the coordinates of k are:

$=\displaystyle{(\frac{x_1+3x_2}{4}, \frac{y_1+3y_2}{4})}$

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2 years ago