Set up the ratio as fractions
(5/8) cup red / (2/5) cup yellow = r amount of red / 1 cup yellow
Then cross multiply the numbers and set up as a equation like this
(5/8) × 1 = (2/5) × r
(5/8) = (2/5)r
Multiply both sides of the equation by (5/2) to get rid of the fraction and solve for r
(5/2) × (5/8) = (2/5)r × <span>(5/2)
25/16 = r
Reduce down to 5/4 or change to a mixed number
1 and 1/4 cups = r</span>
Answer: H
Step-by-step explanation:
Answer:
Point-slope is the general form y-y₁=m(x-x₁) for linear equations. It emphasizes the slope of the line and a point on the line (that is not the y-intercept). Watch this video to learn more about it and see some examples. Created by Sal Khan.
Step-by-step explanation:
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Answer:
Step by step Explanation:
![\sin \theta = \dfrac{\text{Perpendicular} }{\text{Hypotenuse}} = \dfrac{12}{15}\\\\\\\cos \theta = \dfrac{\text{Base}}{\text{Hypotenuse}}= \dfrac{9}{15}\\\\\text{Now,}\\\\\tan \dfrac{\theta}2 = \dfrac{\sin \tfrac{\theta}2}{\cos \tfrac{\theta}2}\\\\\\~~~~~~~~=\dfrac{2\cos \tfrac{\theta}2 \sin \tfrac{\theta}2 }{2\cos^2 \tfrac{\theta}2}~~~~~~;\left[\text{Multiply by}~ 2\cos\tfrac{\theta}2 \right]](https://tex.z-dn.net/?f=%5Csin%20%5Ctheta%20%3D%20%5Cdfrac%7B%5Ctext%7BPerpendicular%7D%20%7D%7B%5Ctext%7BHypotenuse%7D%7D%20%3D%20%5Cdfrac%7B12%7D%7B15%7D%5C%5C%5C%5C%5C%5C%5Ccos%20%5Ctheta%20%3D%20%5Cdfrac%7B%5Ctext%7BBase%7D%7D%7B%5Ctext%7BHypotenuse%7D%7D%3D%20%5Cdfrac%7B9%7D%7B15%7D%5C%5C%5C%5C%5Ctext%7BNow%2C%7D%5C%5C%5C%5C%5Ctan%20%5Cdfrac%7B%5Ctheta%7D2%20%3D%20%5Cdfrac%7B%5Csin%20%5Ctfrac%7B%5Ctheta%7D2%7D%7B%5Ccos%20%5Ctfrac%7B%5Ctheta%7D2%7D%5C%5C%5C%5C%5C%5C~~~~~~~~%3D%5Cdfrac%7B2%5Ccos%20%5Ctfrac%7B%5Ctheta%7D2%20%5Csin%20%5Ctfrac%7B%5Ctheta%7D2%20%7D%7B2%5Ccos%5E2%20%5Ctfrac%7B%5Ctheta%7D2%7D~~~~~~%3B%5Cleft%5B%5Ctext%7BMultiply%20by%7D~%202%5Ccos%5Ctfrac%7B%5Ctheta%7D2%20%5Cright%5D)
![=\dfrac{\sin \theta}{1+ \cos \theta}~~~~~~~~~~~~;[2 \sin x \cos x = \sin 2x ~ \text{and}~ 2\cos^2 x =1+\cos 2x]\\\\\\=\dfrac{\tfrac{12}{15}}{1+ \tfrac{9}{15}}\\\\\\=\dfrac{\tfrac{12}{15}}{\tfrac{24}{15}}\\\\\\=\dfrac{12}{15}\times \dfrac{15}{24}\\\\\\=\dfrac{12}{24}\\\\\\=\dfrac{1}2](https://tex.z-dn.net/?f=%3D%5Cdfrac%7B%5Csin%20%5Ctheta%7D%7B1%2B%20%5Ccos%20%5Ctheta%7D~~~~~~~~~~~~%3B%5B2%20%5Csin%20x%20%5Ccos%20x%20%3D%20%5Csin%202x%20~%20%5Ctext%7Band%7D~%202%5Ccos%5E2%20x%20%3D1%2B%5Ccos%202x%5D%5C%5C%5C%5C%5C%5C%3D%5Cdfrac%7B%5Ctfrac%7B12%7D%7B15%7D%7D%7B1%2B%20%5Ctfrac%7B9%7D%7B15%7D%7D%5C%5C%5C%5C%5C%5C%3D%5Cdfrac%7B%5Ctfrac%7B12%7D%7B15%7D%7D%7B%5Ctfrac%7B24%7D%7B15%7D%7D%5C%5C%5C%5C%5C%5C%3D%5Cdfrac%7B12%7D%7B15%7D%5Ctimes%20%5Cdfrac%7B15%7D%7B24%7D%5C%5C%5C%5C%5C%5C%3D%5Cdfrac%7B12%7D%7B24%7D%5C%5C%5C%5C%5C%5C%3D%5Cdfrac%7B1%7D2)
