Consider the function f(x) = -4x²-9x+20. Determine f(-2)=

Mathematics

1 answer:

hoa [83]3 years ago

3 0

Step-by-step explanation:

you just substitute (-2) into the x values of the above function

$f( - 2) = - 4( - 2)^{2} - 9( - 2) + 20 \\ f( - 2) = 22$

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If F(x) = 7x - 6, which of the following is the inverse of F(x)?

Alex777 [14]

Answer:

$f^{-1} (x)=\frac{x+6}{7}$

Step-by-step explanation:

To find the inverse of a function, we must substitute in y for f(x), swap the locations of y and x, and then solve for y

$y=7x-6\\\\x=7y-6\\\\x+6=7y\\\\y=\frac{x+6}{7} \\\\f^{-1} (x)=\frac{x+6}{7}$

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3 years ago

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IRISSAK [1]

The wording of this question is a bit confusing... You can't write a sequence in sigma notation, but rather a series or sum. I think the question is asking you to write the sum of the sequence,

$\dfrac12,\dfrac14,\dfrac18,\ldots,\dfrac1{64}$

which would be

$\dfrac12+\dfrac14+\dfrac18+\cdots+\dfrac1{64}$

in sigma notation.

To do this, notice that the denominator in each term is a power of 2, starting with $2^1=2$ and ending with $2^6=64$ . So in sigma notation, this series is

$\displaystyle\sum_{n=1}^6\frac1{2^n}$

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3 years ago

Triangle ABC

Virty [35]

Answer:

15 cm

Step-by-step explanation:

Similar triangles are triangles which have the same shape but not the same size. This means their angle measures are equal but their side lengths are not instead they are proportional. To solve, we will set up a proportion and solve.

A proportion is two equal ratios set equal to each other. We form the ratios by finding corresponding sides (sides which match to each other on both triangles by their position). Out ratios will be one side of the small triangle over the corresponding side on the big triangle as shown below:

$\frac{BC}{EF} =\frac{AC}{DF}$ .