Point b lies on the segment ac . Find the length of the segment ac, if ab=7.8 cm, bc=25mm. How many different solutions can this
1 answer:
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Vertex form is
y=a(x-h)^2+k
vertex is (h,k)
axis of symmetry is x=4, therfor h=4
y=a(x-4)^2+k
we have some points
(3,-2) and (6,-26)
input and solve for a and k
(3,-2)
-2=a(3-4)^2+k
-2=a(-1)^2+k
-2=a(1)+k
-2=a+k
(6,-26)
-26=a(6-4)^2+k
-26=a(2)^2+k
-26=a(4)+k
-26=4a+k
we have
-2=a+k
-26=4a+k
multiply first equation by -1 and add to second
2=-a-k
<u>-26=4a+k +</u>
-24=3a+0k
-24=3a
divide both sides by 3
-8=a
-2=a+k
-2=-8+k
add 8 to both sides
6=k
the equation is
y=a(x-h)^2+k
vertex is (h,k)
axis of symmetry is x=4, therfor h=4
y=a(x-4)^2+k
we have some points
(3,-2) and (6,-26)
input and solve for a and k
(3,-2)
-2=a(3-4)^2+k
-2=a(-1)^2+k
-2=a(1)+k
-2=a+k
(6,-26)
-26=a(6-4)^2+k
-26=a(2)^2+k
-26=a(4)+k
-26=4a+k
we have
-2=a+k
-26=4a+k
multiply first equation by -1 and add to second
2=-a-k
<u>-26=4a+k +</u>
-24=3a+0k
-24=3a
divide both sides by 3
-8=a
-2=a+k
-2=-8+k
add 8 to both sides
6=k
the equation is
Answer:
y = 11.84x - 32.71
Step-by-step explanation:
Here, the given data points,
(−3,−70),(−1,−42),(1,−21),(2,−9),(4,14),
Let x represents the input value and y represents the output value,
So, the table that represents the given situation is,
x -3 -1 1 2 4
y -70 -42 -21 -9 14
By the above table,
Let the equation of the line is,
y = bx + a
Where,
n = number of data points = 5,
By substituting the values we get,
a = - 32.70547945 ≈ - 32.71,
b = 11.84246575 ≈ 11.84,
Hence, the equation of line would be,
y = 11.84x - 32.71