3 years ago

The number of inches in any number of feet

Mathematics

2 answers:

GaryK [48]3 years ago

7 0

There is 12 inches in one foot, so 12 times however many feet.

BaLLatris [955]3 years ago

4 0

There are 12 inches in a foot.

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Point G is the centroid of triangle ABC. AG = (5x+4) units and GF= (3x-1) units. What is A F?

Vika [28.1K]

<span>Because G is the centroid of the triangle, therefore AG = 2GF
That is, 5x + 4 = 2(3x - 1)
5x + 4 = 6x - 2
4 + 2 = 6x - 5x
6 = x
Therefore AG = 5*6 + 4 = 34
GF = 3*6 - 1 = 17
A.F = AG + GF = 34 + 17 = 51
Answer: 51</span>

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3 years ago

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Which point is an x-intercept of the quadratic function<br> f(x) = (x + 6)(x – 3)?

Scilla [17]

Set each factor equal to zero and solve.
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3 years ago

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18. Determine the common difference, the fifth term, and the sum of the first 100 terms of the following sequence:

Ksenya-84 [330]

$a_1=1,\ a_2=2.5,\ a_3=4,\ a_4=5.5,\ ...\\\\a_2-a_1=2.5-1=1.5\\a_3-a_2=4-2.5=1.5\\a_4-a_3=5.5-4=1.5\\a_{n+1}-a_n=1.5=constans\\\\\text{It's an arithmetic sequence with}\\a_1=1,\ \boxed{d=1.5}\\\\a_n=a_1+(n-1)d\to a_n=1+(n-1)(1.5)=1+1.5n-1.5\\\\a_n=1.5n-0.5\\\\a_5=1.5(5)-0.5=7.5-0.5=7\\\boxed{a_5=7}\\\\\text{The formula of a Sum of the First n Terms of an Arithmetric Sequence:}\\\\S_n=\dfrac{2a_1+(n-1)d}{2}\cdot n\\\\\text{We have:}\\a_1=1,\ d=1.5,\ n=100\\\\\text{Substitute}$

$S_{100}=\dfrac{(2)(1)+(100-1)(1.5)}{2}\cdot100=\dfrac{2+(99)(1.5)}{1}\cdot50\\\\=(2+148.5)\cdot50=150.5\cdot50=7,525\\\\\boxed{S_{100}=7,525}\\\\Answer:\\the\ common\ difference:\ d=1.5\\the\ fifth\ term:\ a_5=7\\the\ sum\ of\ first\ 100\ terms:\ S_{100}=7,525$