Answer:
30
Step-by-step explanation:
9 + 13 = 22
22 + 43 = 65
65 + 55 = 120
120 ÷ 4 = 30
hope this helps
Given the next quadratic function:
![y=2x^2+3x-2](https://tex.z-dn.net/?f=y%3D2x%5E2%2B3x-2)
to sketch its graph, first, we need to find its vertex. The x-coordinate of the vertex is found as follows:
![x_V=\frac{-b}{2a}](https://tex.z-dn.net/?f=x_V%3D%5Cfrac%7B-b%7D%7B2a%7D)
where <em>a</em> and <em>b</em> are the first two coefficients of the quadratic function. Substituting with a = 2 and b = 3, we get:
![\begin{gathered} x_V=\frac{-3}{2\cdot2} \\ x_V=-\frac{3}{4}=-0.75 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20x_V%3D%5Cfrac%7B-3%7D%7B2%5Ccdot2%7D%20%5C%5C%20x_V%3D-%5Cfrac%7B3%7D%7B4%7D%3D-0.75%20%5Cend%7Bgathered%7D)
The y-coordinate of the vertex is found by substituting the x-coordinate in the quadratic function, as follows:
![\begin{gathered} y_V=2x^2_V+3x_V-2 \\ y_V=2\cdot(-\frac{3}{4})^2+3\cdot(-\frac{3}{4})-2 \\ y_V=2\cdot\frac{9}{16}+3\cdot(-\frac{3}{4})-2 \\ y_V=\frac{9}{8}-\frac{9}{4}-2 \\ y_V=-\frac{25}{8}=-3.125 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20y_V%3D2x%5E2_V%2B3x_V-2%20%5C%5C%20y_V%3D2%5Ccdot%28-%5Cfrac%7B3%7D%7B4%7D%29%5E2%2B3%5Ccdot%28-%5Cfrac%7B3%7D%7B4%7D%29-2%20%5C%5C%20y_V%3D2%5Ccdot%5Cfrac%7B9%7D%7B16%7D%2B3%5Ccdot%28-%5Cfrac%7B3%7D%7B4%7D%29-2%20%5C%5C%20y_V%3D%5Cfrac%7B9%7D%7B8%7D-%5Cfrac%7B9%7D%7B4%7D-2%20%5C%5C%20y_V%3D-%5Cfrac%7B25%7D%7B8%7D%3D-3.125%20%5Cend%7Bgathered%7D)
The factorization indicates that the curve crosses the x-axis at the points (-2, 0) and (1/2, 0). We also know that the curve crosses the y-axis at (0,-2). Connecting these points and the vertex (-0.75, -3.125) with a U-shaped curve, we get:
The coordinates would be (2,4)
Hope This Helps!
Answer:
VW = 43.2
Step-by-step explanation:
First, we can see that VZ = 88 - 55 = 33.
Then by the Triangle Proportionality Theorem, we can write that:
![\displaystyle \frac{55}{33}=\frac{72}{VW}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7B55%7D%7B33%7D%3D%5Cfrac%7B72%7D%7BVW%7D)
Simplify:
![\displaystyle \frac{5}{3}=\frac{72}{VW}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7B5%7D%7B3%7D%3D%5Cfrac%7B72%7D%7BVW%7D)
Cross-multiply:
![216=5VW](https://tex.z-dn.net/?f=216%3D5VW)
So:
![\displaystyle V=\frac{216}{5}=43.2](https://tex.z-dn.net/?f=%5Cdisplaystyle%20V%3D%5Cfrac%7B216%7D%7B5%7D%3D43.2)