Step-by-step explanation:
The triangle is an Isosceles Right.
Answer:
c
Step-by-step explanation:
because it makes the most sense
<u>ANSWER: </u>
x-intercepts of ![\mathrm{x}^{2}+12 \mathrm{x}+24=0 \text { are }(-6+2 \sqrt{3}),(-6-2 \sqrt{3})](https://tex.z-dn.net/?f=%5Cmathrm%7Bx%7D%5E%7B2%7D%2B12%20%5Cmathrm%7Bx%7D%2B24%3D0%20%5Ctext%20%7B%20are%20%7D%28-6%2B2%20%5Csqrt%7B3%7D%29%2C%28-6-2%20%5Csqrt%7B3%7D%29)
<u>SOLUTION:</u>
Given,
-- eqn 1
x-intercepts of the function are the points where function touches the x-axis, which means they are zeroes of the function.
Now, let us find the zeroes using quadratic formula for f(x) = 0.
![X=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}](https://tex.z-dn.net/?f=X%3D%5Cfrac%7B-b%20%5Cpm%20%5Csqrt%7Bb%5E%7B2%7D-4%20a%20c%7D%7D%7B2%20a%7D)
Here, for (1) a = 1, b= 12 and c = 24
![X=\frac{-(12) \pm \sqrt{(12)^{2}-4 \times 1 \times 24}}{2 \times 1}](https://tex.z-dn.net/?f=X%3D%5Cfrac%7B-%2812%29%20%5Cpm%20%5Csqrt%7B%2812%29%5E%7B2%7D-4%20%5Ctimes%201%20%5Ctimes%2024%7D%7D%7B2%20%5Ctimes%201%7D)
![\begin{array}{l}{X=\frac{-12 \pm \sqrt{144-96}}{2}} \\\\ {X=\frac{-12 \pm \sqrt{48}}{2}} \\\\ {X=\frac{-12 \pm \sqrt{16 \times 3}}{2}} \\\\ {X=\frac{-12 \pm 4 \sqrt{3}}{2}} \\ {X=\frac{2(-6+2 \sqrt{3})}{2}, \frac{2(-6-2 \sqrt{3})}{2}} \\\\ {X=(-6+2 \sqrt{3}),(-6-2 \sqrt{3})}\end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Bl%7D%7BX%3D%5Cfrac%7B-12%20%5Cpm%20%5Csqrt%7B144-96%7D%7D%7B2%7D%7D%20%5C%5C%5C%5C%20%7BX%3D%5Cfrac%7B-12%20%5Cpm%20%5Csqrt%7B48%7D%7D%7B2%7D%7D%20%5C%5C%5C%5C%20%7BX%3D%5Cfrac%7B-12%20%5Cpm%20%5Csqrt%7B16%20%5Ctimes%203%7D%7D%7B2%7D%7D%20%5C%5C%5C%5C%20%7BX%3D%5Cfrac%7B-12%20%5Cpm%204%20%5Csqrt%7B3%7D%7D%7B2%7D%7D%20%5C%5C%20%7BX%3D%5Cfrac%7B2%28-6%2B2%20%5Csqrt%7B3%7D%29%7D%7B2%7D%2C%20%5Cfrac%7B2%28-6-2%20%5Csqrt%7B3%7D%29%7D%7B2%7D%7D%20%5C%5C%5C%5C%20%7BX%3D%28-6%2B2%20%5Csqrt%7B3%7D%29%2C%28-6-2%20%5Csqrt%7B3%7D%29%7D%5Cend%7Barray%7D)
Hence the x-intercepts of ![\mathrm{x}^{2}+12 \mathrm{x}+24=0 \text { are }(-6+2 \sqrt{3}),(-6-2 \sqrt{3})](https://tex.z-dn.net/?f=%5Cmathrm%7Bx%7D%5E%7B2%7D%2B12%20%5Cmathrm%7Bx%7D%2B24%3D0%20%5Ctext%20%7B%20are%20%7D%28-6%2B2%20%5Csqrt%7B3%7D%29%2C%28-6-2%20%5Csqrt%7B3%7D%29)
Answer:
120 degrees
Step-by-step explanation:
This is a quadrilateral, and by definition, the sum of all the interior angles is 360. So, we can just sum up all the expressions and set them equal to 360:
2x + x + 2x + x = 360
Combine like terms and solve for x:
6x = 360
x = 360/6 = 60
<BCD = 2x = 2 * 60 = 120
Thus, the answer is 120 degrees.
Hope this helps!
Answer:
Pierre has enough boards and nails to make 9 tables and 5 chairs.
Step-by-step explanation:
13T+8C ≤ 220
Let us substitute 9 for T and 5 for C and check.
13(9) + 8(5) = 117 + 40
= 157 < 220
So, 220 wooden boards are sufficient to make 9 tables and 5 chairs.
48T+37C ≤ 760
Substitute 9 for T and 5 for C.
48(9)+37(5) = 432 + 185
= 617 < 760
So, 760 nails are sufficient to make 9 tables and 5 chairs.
Hence, Pierre has enough boards and nails to make 9 tables and 5 chairs.