Step-by-step explanation:
-x+2y=-6
x-2y=6
x=2y+6
substitute in 2x-3y=11 gives us 2(2y+6)-3y=11
4y+12-3y=11
y=-1
-x+2(-1)=-6
-x=-4
x=4
Vertex form of an equation for a parabola looks like this:
f(x) = a(x-h)² + k
(h,k) is the vertex. Just plug in the values (3,-2)
f(x) = a(x-3)² - 2
Now use the point (5,-1) to find "a" so that the equation goes through that point.
-1 = a(5-3)² - 2
-1 = a(2)² - 2
-1 = 4a - 2
-1 + 2 = 4a
1 = 4a
1/4 = a
put that into the equation to get the answer
f(x) = (1/4)(x - 3)² - 2
I think for the question above, instead of 2 · 3^2 · 7 it is <span>2 · 3^2 · 5.
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Two numbers have prime factorizations of 2^2 • 3 • 5 and 2 • 3^2 • 5 (note 2 squared & 3 squared).
Now, to choose the GCF, you choose, for each base factor in either number, the least exponent-ed one; so the GCF needs a factor 2, a factor 3, and a factor 5. Thus the GCF is 30 (their product). [i.e,2 squared is not a common factor]
<span>To create the LCM, you choose, for each base factor in either number, the greatest exponented one. Thus, LCM needs a factor 2 squared, 3 squared, and 5, giving LCM = 4(9)(5) = 180.</span><span />
Answer:
Step-by-step explanation:
Sum of exterior angles of any Polygon = 360°
23. x + 65 + 106 + 78 = 360
x + 249 = 360
{To find the value of x, subtract 249 from both sides}
x = 360 - 249
x = 111°
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24. x + x + 59 + 48 + 50 + 39 + 58 = 360
2x + 254 = 360
2x = 360 - 254
2x = 106
x = 106 ÷ 2
x = 53°
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25. 2x + 3x + 44 +85 + 71 = 360
5x + 200 = 360
5x = 360 - 200
5x = 160
x = 160 ÷ 5
x = 32°
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26. x+ 2x + 77 + 40 + 45 = 360
3x + 162 = 360
3x = 360 - 162
3x = 198
x = 198 ÷ 3
x = 66°