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3 years ago

Which linear function represents the line given by the point-slope equation y + 1 = -3(x - 5)?

Mathematics

1 answer:

Anastaziya [24]3 years ago

5 0

Answer:

-3x + 14

Step-by-step explanation:

Expand -3(x-5)

. -3 * x = -3x

. -3 * -5 = 15

. y+1 = -3x + 15

Subtract 1 from both sides so that y is the subject

. y = -3x + 14

Now you can juse replace y with f(x) since theyre basically the same thing

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3 years ago

For a given geometric sequence, the 9th term, a9, is equal to 43/256 and the 14th term, a14, is equal to 172. Find the value of

EastWind [94]

Answer:

$18th=44032$

Step-by-step explanation:

From the question we are told that:

9th term $a9=\frac{43}{256}$

14th term $a14=172$

Generally the equation for Geometric sequence is mathematically given by

$a_n=a_1r^{n-1}$

For 9th term

$\frac{43}{256}=a_1r^{8}$

For 14th term

$172=a_1r^{13} \\a_1=\frac{172}{r^13}$

Substitute in 9th term

$\frac{43}{256}=\frac{172}{r^13}*r^{8}$

$\frac{43}{256*172}=r^{-5}$

$r=^5sqrt{\frac{44032}{43}}$

$r=4$

Therefore First term a is given as

$a_1=\frac{172}{4^13}$

$a_1=2.563*10^{-6}$

Generally the equation for the 18th term is mathematically given by

$18th=a_1r^{17}$

$18th=2.563*10^{-6}*4^{17}$

$18th=44032$

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3 years ago

What is the equation of the quadratic graph with a focus of (8, −8) and a directrix of y = −6?

yarga [219]

The vertex is exactly half way between directrix and focus. In this case the vertex is (8,-7)
(h,k)

P is the distance between the vertex and either the directrix or focus, in this case p = 1.

a = 1/(4p) or 1/(4*1) or 1/4

write the equation in vertex form

y = a(x-h)^2 + k

y = 1/4(x-8)^2 -7

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3 years ago