Mathematics, 21.01.2021 21:00, kevinkingpin

An=−2+32(n−1)
What is the 21 term of the sequence?

Answers: 3

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answered: Guest

stethere all not eveanp-by-step explanation:

answered: Guest

step-by-step explanation:

a and d

answered: Guest

a) 40 more; b) old factory: 10%, new factory: 16%; c) week 4

explanation:

a) at week 0, we see in the graph that the new factory produces 190 specialty items.

using the function, substituting 0 in for w,

$p(w)=230(1.1)^w\\\\p(0)=230(1.1)^0\\\\p(0)=230(1)=230$

this is a difference of 230-190 = 40.

b) the function for the old factory is written in the form f(x) = a(1+r)ˣ, where a is the original amount, x is the amount of time and r is the growth rate. the equation for the old factory is $p(w)=230(1.1)^w$ ; 230 is in place of a and is the original amount; w is the amount of time; which means 1+r = 1.1. this means that r must be 0.1 or 10%.

for the new factory, we find the percent of increase to find the growth rate; the formula for this is

$\text{percent of change}=\frac{\text{amount of change}}{\text{original amount}}$

between the first two points, the amount of change is 220-190 = 30; this gives us

30/190 = 0.158 ≈ 0.16 = 16%

c) at week 0, the old factory has 230 while the new factory has 190.

at week 1, the old factory has 230(1.1) = 253 while the new factory has 220.

at week 2, the old factory has 230(1.1²) = 278.3 while the new factory has 252.

at week 3, the old factory has 230(1.1³) = 306.13 while the new factory has 290.

at week 4, the old factory has 230(1.1⁴) = 336.743 while the new factory has 337. this is the first week that the new factory surpasses the old.

answered: Guest

part a.

angle addition postulate:

if a point lies on the interior of an angle, that angle is the sum of two smaller angles with legs that go through the given point.

from the diagram you can see that point w lies on the interior of an angle, then

m∠uvx=m∠uvw+m∠wvx.

answer: correct choice is b.

part b.

substitution property of equality:

if x = y, then x can be substituted in for y in any equation, and y can be substituted for x in any equation.

given that xy≅yz and xy=4a+4, yz=20, you can substitute instead of xy the expression 4a+4 and instead of yz the expression 20 into the iquality xy≅yz and obtain

4a+4=20

answer: correct choice is a.

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