Answer:
9.6 mi
Step-by-step explanation:
in right triangle ABC,
AC = 16 mi
BC = 24 mi
If AM is the median, then CM = MB = 12 mi
Consider triangles CAM and EBM. In these triangles,
- angles CMA and EMB are congruent as vertical angles;
- angles ACM and MEB are congruent as right angles.
So, triangles CAM and EBM are similar by AA postulate.
Similar triangles have proportional corresponding sides, so
![\dfrac{CA}{EB}=\dfrac{CM}{EM}\\ \\\dfrac{16}{EB}=\dfrac{12}{EM}\\ \\EM=\dfrac{3}{4}EB](https://tex.z-dn.net/?f=%5Cdfrac%7BCA%7D%7BEB%7D%3D%5Cdfrac%7BCM%7D%7BEM%7D%5C%5C%20%5C%5C%5Cdfrac%7B16%7D%7BEB%7D%3D%5Cdfrac%7B12%7D%7BEM%7D%5C%5C%20%5C%5CEM%3D%5Cdfrac%7B3%7D%7B4%7DEB)
By the Pythagorean theorem,
![MB^2=EB^2+EM^2\\ \\12^2=EB^2+\left(\dfrac{3}{4}EB\right)^2\\ \\144=EB^2+\dfrac{9}{16}EB^2\\ \\EB^2\left(1+\dfrac{9}{16}\right)=144\\ \\EB^2\cdot \dfrac{25}{16}=144\\ \\EB^2=144\cdot \dfrac{16}{25}\\ \\EB=12\cdot \dfrac{4}{5}\\ \\EB=\dfrac{48}{5}\\ \\EB=9.6\ mi](https://tex.z-dn.net/?f=MB%5E2%3DEB%5E2%2BEM%5E2%5C%5C%20%5C%5C12%5E2%3DEB%5E2%2B%5Cleft%28%5Cdfrac%7B3%7D%7B4%7DEB%5Cright%29%5E2%5C%5C%20%5C%5C144%3DEB%5E2%2B%5Cdfrac%7B9%7D%7B16%7DEB%5E2%5C%5C%20%5C%5CEB%5E2%5Cleft%281%2B%5Cdfrac%7B9%7D%7B16%7D%5Cright%29%3D144%5C%5C%20%5C%5CEB%5E2%5Ccdot%20%5Cdfrac%7B25%7D%7B16%7D%3D144%5C%5C%20%5C%5CEB%5E2%3D144%5Ccdot%20%5Cdfrac%7B16%7D%7B25%7D%5C%5C%20%5C%5CEB%3D12%5Ccdot%20%5Cdfrac%7B4%7D%7B5%7D%5C%5C%20%5C%5CEB%3D%5Cdfrac%7B48%7D%7B5%7D%5C%5C%20%5C%5CEB%3D9.6%5C%20mi)
4: Number of books: 9
Cost:6, 42, 60,24
5:idk
Answer:
(I'm assuming the "?" is a typo?)
Step-by-step explanation:
![(7p +18p-14p-5) + (p+3)\\(25p-14p-5)+(p+3)\\(11p-5)+(p+3)\\11p-5+p+3\\12p-2](https://tex.z-dn.net/?f=%287p%20%2B18p-14p-5%29%20%2B%20%28p%2B3%29%5C%5C%2825p-14p-5%29%2B%28p%2B3%29%5C%5C%2811p-5%29%2B%28p%2B3%29%5C%5C11p-5%2Bp%2B3%5C%5C12p-2)
Don't forget we can't add two different variables together (ex. we can't add
together because they're different variables).
I have no idea
I just need points for an answer sorry
111₂ = 1•2² + 1•2¹ + 1•2⁰
111₂ = 4 + 2 + 1
111₂ = 7