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alexdok [17]
3 years ago
7

A graph creates a triangle with the x-axis, the line 3x-2y=0, and the line x+2y=10. Find the area of the triangle formed in squa

re units.
Mathematics
1 answer:
MariettaO [177]3 years ago
6 0

Answer:

18.75

Step-by-step explanation:

To identify the vertices of this triangle, you need to find the x intercepts of both lines, as where their solutions match. Let's start with setting them equal to each other. If you subtract 10 from both sides of the second equation, then both equations are left equaling zero.  You can also multiply both sides of the equation by -1 for easier solving later Now:

3x-2y=-2y-x+10

4x=10

x=2.5

y=3.75

This shows that the height of this triangle is 3.75. Now, to find the x intercepts of both equations, we simply have to plug in the y value as 0. For the first one, 3x-0=0, so x=0 as well and the coordinates are (0,0). For the second one, x+0=10, so x=10 and the coordinates are (10,0). This shows that the base is 10-0=10 units long. The formula for the area of a triangle is \frac{bh}{2}=\frac{10\cdot3.75}{2}=18.75. Hope this helps!

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Note that I made the probability of being defective as the probability of success = p

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\begin{gathered} P_x=^4C_2\times\lparen\frac{1}{6})^2\times\lparen\frac{5}{6})^{4-2} \\ P_x=6\times\frac{1}{36}\times\frac{25}{36} \\ P_x=\frac{25}{216} \\ =0.1157 \end{gathered}

Hence the answer is 0.1157

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\begin{gathered} \lparen\frac{5}{6})^4=\frac{625}{1296} \\ =0.4823 \end{gathered}

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(iii) All are defective

\begin{gathered} \lparen\frac{1}{6})^4=\frac{1}{1296} \\ =0.00077 \end{gathered}

(iv) At least one is defective

This is 1 - probability that none is defective

\begin{gathered} 1-\lparen\frac{5}{6})^4 \\ =1-\frac{625}{1296} \\ =\frac{671}{1296} \\ =0.5177 \end{gathered}

Hence the answer is 0.5177

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