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sveta [45]
2 years ago
7

Help...(MATH).......

Mathematics
1 answer:
Hitman42 [59]2 years ago
7 0

If f(x) = √x and g(x) = 7x + b, then

f(g(x)) = f(7x + b) = √(7x + b)

If the plot of f(g(x)) passes through (4, 6), then

f(g(4)) = √(7•4 + b) = √(28 + b) = 6

Solve for b :

√(28 + b) = 6

(√(28 + b))² = 6²

28 + b = 36

b = 36 - 28

b = 8

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Answer:

d_{AB}\ne d_{JK}

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Therefore,

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Option (B) is false

Option (C) is false

Step-by-step explanation:

Considering the graph

Given the vertices of the segment AB

  • A(-4, 4)
  • B(2, 5)

Finding the length of AB using the formula

d_{AB}\:=\:\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}

        =\sqrt{\left(2-\left(-4\right)\right)^2+\left(5-4\right)^2}

         =\sqrt{\left(2+4\right)^2+\left(5-4\right)^2}

         =\sqrt{6^2+1}

         =\sqrt{36+1}

        =\sqrt{37}

d_{AB}\:=\sqrt{37}

d_{AB}=6.08 units        

Given the vertices of the segment JK

  • J(2, 2)
  • K(7, 2)

From the graph, it is clear that the length of JK = 5 units

so

d_{JK}=5 units

Given the vertices of the segment GH

  • G(-5, -2)
  • H(-2, -2)

Finding the length of GH using the formula

d_{GH}\:=\:\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}

         =\sqrt{\left(-2-\left(-5\right)\right)^2+\left(-2-\left(-2\right)\right)^2}

          =\sqrt{\left(5-2\right)^2+\left(2-2\right)^2}

          =\sqrt{3^2+0}

           =\sqrt{3^2}

\mathrm{Apply\:radical\:rule\:}\sqrt[n]{a^n}=a,\:\quad \mathrm{\:assuming\:}a\ge 0

d_{GH}\:=\:3 units

Thus, from the calculations, it is clear that:

d_{AB}=6.08  

d_{JK}=5

d_{GH}\:=\:3

Thus,

d_{AB}\ne d_{JK}

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d_{GH}\ne \:d_{JK}

Therefore,

Option (A) is false

Option (B) is false

Option (C) is false

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