X is zero for sure because 0=0. It can’t be anything else. For example, simply take away the Xs. 5 does not equal 6. Neither can 5•-1=6•-1. Or 5•2=6•2.
hope that’s helpful!
Distribute the 5 into the polynomial to get 5a + 5b - a - b. Combine like terms to get 4a + 4b, your answer.
Answer:
see explanation
Step-by-step explanation:
This is an example of the Altitude - on - Hypotenuse theorem.
The altitude that is perpendicular to the hypotenuse of a right triangle.
The two triangles formed are similar to the given triangle and to each other.
x² = (smaller part) × (larger part) of main hypotenuse
x² = 6 + 19 = 114 ( square root both sides )
x ≈ 10.68 ( nearest hundredth )
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y² = ( smaller part) × (whole part) of main hypotenuse
y² = 6 × 25 = 150 ( square root both sides )
y ≈ 12.25 ( nearest hundredth )
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z² = ( larger part) × (whole part) of main diagonal
z² = 19 × 25 = 475 ( square root both sides )
z ≈ 21.79 ( nearest hundredth )
Answer:
0
Step-by-step explanation:
27+(-15)+(-12)=
= 27-15-12=
=0
Answer:
32.55 cm
Step-by-step explanation:
Let x = the length of wire that becomes a circle.
Then 74 - x = the length of wire that becomes a square
Circumference of circle + perimeter of square = 74
1. Expression for the side of the square
P = 4s = 74 - x
s = ¼(74 - x)
2. Expression for the radius of the circle
C = 2πr = x
r = x/(2π)
3. Expression for the total area
![\begin{array}{rcl}\text{Total area} & = &\text{area of circle+ area of square}\\A & = & \pi r^{2} + s^{2}\\& = &\pi \left(\dfrac{x}{2 \pi}\right)^{2} + \left (\dfrac{1}{4}(74 - x)\right)^{2}\\\\ & = & \dfrac{x^{2}}{4 \pi} + \dfrac{1}{16}(5476 - 148x + x^{2})\\\\ & = & 0.07958x^{2} + 342.25 - 9.25x + 0.0625x^{2}\\A & = & 0.1421x^{2} -9.25x + 342.25 \\ \end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Brcl%7D%5Ctext%7BTotal%20area%7D%20%26%20%3D%20%26%5Ctext%7Barea%20of%20circle%2B%20area%20of%20square%7D%5C%5CA%20%26%20%3D%20%26%20%5Cpi%20r%5E%7B2%7D%20%2B%20s%5E%7B2%7D%5C%5C%26%20%3D%20%26%5Cpi%20%5Cleft%28%5Cdfrac%7Bx%7D%7B2%20%5Cpi%7D%5Cright%29%5E%7B2%7D%20%2B%20%5Cleft%20%28%5Cdfrac%7B1%7D%7B4%7D%2874%20-%20x%29%5Cright%29%5E%7B2%7D%5C%5C%5C%5C%20%26%20%3D%20%26%20%5Cdfrac%7Bx%5E%7B2%7D%7D%7B4%20%5Cpi%7D%20%2B%20%5Cdfrac%7B1%7D%7B16%7D%285476%20-%20148x%20%2B%20x%5E%7B2%7D%29%5C%5C%5C%5C%20%26%20%3D%20%26%200.07958x%5E%7B2%7D%20%2B%20342.25%20-%209.25x%20%2B%200.0625x%5E%7B2%7D%5C%5CA%20%26%20%3D%20%26%200.1421x%5E%7B2%7D%20-9.25x%20%2B%20342.25%20%5C%5C%20%5Cend%7Barray%7D)
This is the equation of a parabola.
In standard form,
ƒ(x) = 0.1421x² -9.25x + 342.24
a = 0.1421; b = -9.25; c = 342.24
The parabola opens upwards, because a > 0. Therefore, the vertex is a minimum.
The vertex of a parabola occurs at
x = -b/(2a) = 9.25/(2 × 0.1421) = 9.25/(0.2842) = 32.55
The circumference of the circle is 32.55 cm.
The graph below shows that the area of the circle is a minimum when x = 32.55 cm