Answer:
A Strawberries generally cost less.
D If the chef pays $6.00 for a pound of fruit, it is most likely cherries.
Step-by-step explanation:
A and D
Answer:
![(1-\sqrt{2})a^2](https://tex.z-dn.net/?f=%281-%5Csqrt%7B2%7D%29a%5E2)
Step-by-step explanation:
Consider irght triangle PRS. By the Pythagorean theorem,
![PS^2=PR^2+RS^2\\ \\PS^2=a^2+a^2\\ \\PS^2=2a^2\\ \\PS=\sqrt{2}a](https://tex.z-dn.net/?f=PS%5E2%3DPR%5E2%2BRS%5E2%5C%5C%20%5C%5CPS%5E2%3Da%5E2%2Ba%5E2%5C%5C%20%5C%5CPS%5E2%3D2a%5E2%5C%5C%20%5C%5CPS%3D%5Csqrt%7B2%7Da)
Thus,
![MS=PS-PM=\sqrt{2}a-a=(\sqrt{2}-1)a](https://tex.z-dn.net/?f=MS%3DPS-PM%3D%5Csqrt%7B2%7Da-a%3D%28%5Csqrt%7B2%7D-1%29a)
Consider isosceles triangle MSC. In this triangle
![MS=MC=(\sqrt{2}-1)a.](https://tex.z-dn.net/?f=MS%3DMC%3D%28%5Csqrt%7B2%7D-1%29a.)
The area of this triangle is
![A_{MSC}=\dfrac{1}{2}MS\cdot MC=\dfrac{1}{2}\cdot (\sqrt{2}-1)a\cdot (\sqrt{2}-1)a=\dfrac{(\sqrt{2}-1)^2a^2}{2}=\dfrac{(3-2\sqrt{2})a^2}{2}](https://tex.z-dn.net/?f=A_%7BMSC%7D%3D%5Cdfrac%7B1%7D%7B2%7DMS%5Ccdot%20MC%3D%5Cdfrac%7B1%7D%7B2%7D%5Ccdot%20%28%5Csqrt%7B2%7D-1%29a%5Ccdot%20%28%5Csqrt%7B2%7D-1%29a%3D%5Cdfrac%7B%28%5Csqrt%7B2%7D-1%29%5E2a%5E2%7D%7B2%7D%3D%5Cdfrac%7B%283-2%5Csqrt%7B2%7D%29a%5E2%7D%7B2%7D)
Consider right triangle PTS. The area of this triangle is
![A_{PTS}=\dfrac{1}{2}PT\cdot TS=\dfrac{1}{2}a\cdot a=\dfrac{a^2}{2}](https://tex.z-dn.net/?f=A_%7BPTS%7D%3D%5Cdfrac%7B1%7D%7B2%7DPT%5Ccdot%20TS%3D%5Cdfrac%7B1%7D%7B2%7Da%5Ccdot%20a%3D%5Cdfrac%7Ba%5E2%7D%7B2%7D)
The area of the quadrilateral PMCT is the difference in area of triangles PTS and MSC:
![A_{PMCT}=\dfrac{(3-2\sqrt{2})a^2}{2}-\dfrac{a^2}{2}=\dfrac{(2-2\sqrt{2})a^2}{2}=(1-\sqrt{2})a^2](https://tex.z-dn.net/?f=A_%7BPMCT%7D%3D%5Cdfrac%7B%283-2%5Csqrt%7B2%7D%29a%5E2%7D%7B2%7D-%5Cdfrac%7Ba%5E2%7D%7B2%7D%3D%5Cdfrac%7B%282-2%5Csqrt%7B2%7D%29a%5E2%7D%7B2%7D%3D%281-%5Csqrt%7B2%7D%29a%5E2)
Answer:
x^4
Step-by-step explanation:
Answer:
Longest side = 13 inches
Step-by-step explanation:
Perimeter of triangle = 30 inches
x + 4x - 8 + 2x +3 = 30
x + 4x + 2x - 8 + 3 = 30
7x - 5 = 30
7x = 30 + 5
7x = 35
x = 35/7
x = 5
Longest side is the hypotenuse.
Longest side = 2x + 3 = 2*5 + 3 = 10 + 3 = 13 inches
Answer:
40 inches
Step-by-step explanation:
We know that the height of water in a pool decreased 5 inches per week.
This means that we can form the equation
, since the amount of water remaining is proportionate to the amount of weeks that have passed.
We know
, since we need to find the change for 8 weeks.
![y = -5\cdot 8](https://tex.z-dn.net/?f=y%20%3D%20-5%5Ccdot%208)
![-5 \cdot 8 = -40](https://tex.z-dn.net/?f=-5%20%5Ccdot%208%20%3D%20-40)
![y=-40](https://tex.z-dn.net/?f=y%3D-40)
The change will be the absolute value of -40, which just makes it positive, so 40.
Hope this helped!