Isolate the variable by dividing each side by factors that don't contain the variable.
x = 1
-6+3x+4=2-4x+3
-8+7x+1=0
7x=7
x=1
Hello there.
<span>How many solutions does the system of equations have y=5x+7 and 3y-15x=18
</span><span>B two
</span>
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:
4320, I looked up 18% of 24000
Answer:
1. y = 14.718
2. ??
3. y = 39.794°
Step-by-step explanation:
<em>HINT the side we already know and the side we are trying to find, we use the first letters of their names and the phrase "SOHCAHTOA" to decide which function:
</em>
SOH...
Sine: sin(θ) = Opposite / Hypotenuse
...CAH...
Cosine: cos(θ) = Adjacent / Hypotenuse
...TOA
Tangent: tan(θ) = Opposite / Adjacent
1. Sine: sin(θ) = Opposite / Hypotenuse
sin(42°) = y / 22
so on your calculator enter 42 then sin = 0.669
0.669 = y/22 multiply both sides by 22 to get y
y = 14.718
2. is there any other information??
3. The two sides we know are Opposite 40 and Adjacent 48.
SOHCAHTOA tells us we must use Tangent.
Calculate Opposite/Adjacent = 40/48 = 0.833
Find the angle from your calculator using tan-1
Tan y° = opposite/adjacent = 40/48 = 0.833
tan-1 of 0.833 = 39.794°