answer:Extracellular signaling proteins, such as semaphorins and slits, play a crucial role in axon guidance during nervous system development. These proteins act as repulsive cues, directing axons away from certain areas and towards others. By creating gradients of these proteins, a path is established for axons to follow, ensuring the correct formation of neural connections. This process is essential for the proper functioning of the nervous system, allowing neurons to communicate effectively and coordinate complex behaviors.

answer:The new store's location can be found by identifying the centroid of the triangle formed by stores A, B, and C, as this point will be equidistant from all three vertices. The centroid, denoted by (X̄, Ȳ), of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3) is calculated as: {eq}(X̄, Ȳ) = left ( dfrac{x1 + x2 + x3}{3} text{ , } dfrac{y1 + y2 + y3}{3} right ) {/eq} For stores A(0, 0), B(8, 0), and C(4, 3), the centroid is: {eq}(X̄, Ȳ) = left ( dfrac{0 + 8 + 4}{3} text{ , } dfrac{0 + 0 + 3}{3} right ) {/eq} {eq}(X̄, Ȳ) = left ( dfrac{12}{3} text{ , } dfrac{3}{3} right ) {/eq} {eq}(X̄, Ȳ) = left ( 4 text{ , } 1 right ) {/eq} Thus, the coordinates of the new store's location are (4, 1).

answer:To solve the system of equations, we can use the method of substitution or elimination. Here, we will use the elimination method. First, we multiply the second equation by 5 to make the coefficients of x in both equations equal. This gives us: 15x + 10y + 6 = 0, -34x + 66y + 57 = 0. Next, we add the two equations together to eliminate x: (15x - 34x) + (10y + 66y) + (6 + 57) = 0, -19x + 76y + 63 = 0. Now, we can solve for y: -19x + 76y = -63, 76y = 63 + 19x, y = frac{63 + 19x}{76}. We can substitute this expression for y back into one of the original equations to solve for x. Let's use the first equation: 15x + 10left(frac{63 + 19x}{76}right) + 6 = 0, 15x + frac{630 + 190x}{76} + 6 = 0, 15x + frac{210 + 630 + 190x}{76} = 0, 15x + frac{840 + 190x}{76} = 0, 15x(76) + (840 + 190x) = 0, 1140x + 840 + 190x = 0, 1330x + 840 = 0, 1330x = -840, x = frac{-840}{1330}, x = frac{87}{665}. Now that we have the value of x, we can substitute it back into the expression for y to find the value of y: y = frac{63 + 19x}{76}, y = frac{63 + 19left(frac{87}{665}right)}{76}, y = frac{63 + frac{1653}{665}}{76}, y = frac{63(665) + 1653}{76(665)}, y = frac{41895 + 1653}{50860}, y = frac{43548}{50860}, y = -frac{1059}{1330}. Therefore, the solution to the given system of equations is x = frac{87}{665} and y = -frac{1059}{1330}. The solution to the given system of equations is x = frac{87}{665} and y = -frac{1059}{1330}.

answer:To simplify, we can break down each radical into its prime factors and then simplify. Here's the step-by-step simplification: 1. sqrt{48} = sqrt{16 cdot 3} = sqrt{16} cdot sqrt{3} = 4sqrt{3} 2. sqrt{57} remains as it is, as it cannot be simplified further. 3. sqrt{175} = sqrt{25 cdot 7} = sqrt{25} cdot sqrt{7} = 5sqrt{7} 4. sqrt{75} = sqrt{25 cdot 3} = sqrt{25} cdot sqrt{3} = 5sqrt{3} Now, substitute these simplified forms back into the expression: (4sqrt{3} - sqrt{57}) + (5sqrt{7} + 5sqrt{3}) Combine like terms: 4sqrt{3} + 5sqrt{3} - sqrt{57} + 5sqrt{7} = (4+5)sqrt{3} + 5sqrt{7} - sqrt{57} = 9sqrt{3} + 5sqrt{7} - sqrt{57} So, the simplified expression is 9sqrt{3} + 5sqrt{7} - sqrt{57}.