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3 years ago

Factor the expression. 40z – 20

Mathematics

2 answers:

erik [133]3 years ago

7 0

$40z - 20$

$GCF=20
$

$20 ( \dfrac{40z}{20} - \dfrac{20}{20})$

$20(2z-1)$

artcher [175]3 years ago

5 0

Answer:

20(2z – 1)

TTM ;)

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3 years ago

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inna [77]

Find the decimal equivalent of each and then put in order.

Steve 130 5/6= 130.83333
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Now that they each have a decimal equivalent, we can put them in order from greatest to least.

Steve 130 5/6= 130.83333
Riley 130 2/3= 130.66666
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3 years ago

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2 years ago

Which of the following changes in the price index produces the greatest rate of inflation: 106 to 112, 112 to 118, or 118 to 124

boyakko [2]

Answer:

Step-by-step explanation:

firstly you have to find the rate of change of the various price index in percentage.

A, From 106 to 112:

we find the difference 112-106 = 6

then the rate of change = 6/106 * 100 = 5.66%.

B ,From 112 to 118:

we find the difference 118-112 = 6

then the rate of change = 6/118 * 100 = 5.36%.

C ,From 118 to 124:

we find the difference 124-118 = 6

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3 years ago

Solve the following ODE's: c) y* - 9y' + 18y = t^2

Nastasia [14]

Answer:

y = $C_1e^{3t}+C_2e^{6t}$ + $\dfrac{1}{18}(t^2+\frac{2t}{6} + \frac{2}{36}+\frac{2t}{3}+\frac{2}{18}+\frac{2}{9})$

Step-by-step explanation:

y''- 9 y' + 18 y = t²

solution of ordinary differential equation

using characteristics equation

m² - 9 m + 18 = 0

m² - 3 m - 6 m+ 18 = 0

(m-3)(m-6) = 0

m = 3,6

C.F. = $C_1e^{3t}+C_2e^{6t}$

now calculating P.I.

$P.I. = \frac{t^2}{D^2 - 9D +18}$

$P.I. = \dfrac{t^2}{(D-3)(D-6)}\\P.I. =\dfrac{1}{18}(1-\frac{D}{3})^{-1}(1-\frac{D}{6})^{-1}(t^2)\\P.I. =\dfrac{1}{18}(1-\frac{D}{3})^{-1}(1+\frac{D}{6}+\frac{D^2}{36}+....)(t^2)\\P.I. =\dfrac{1}{18}(1-\frac{D}{3})^{-1}(t^2+\frac{2t}{6} + \frac{2}{36})\\P.I. =\dfrac{1}{18}(1+\frac{D}{3}+\frac{D^2}{9}+....)(t^2+\frac{2t}{6} + \frac{2}{36})\\P.I. =\dfrac{1}{18}(t^2+\frac{2t}{6} + \frac{2}{36}+\frac{2t}{3}+\frac{2}{18}+\frac{2}{9})$

hence the complete solution

y = C.F. + P.I.

y = $C_1e^{3t}+C_2e^{6t}$ + $\dfrac{1}{18}(t^2+\frac{2t}{6} + \frac{2}{36}+\frac{2t}{3}+\frac{2}{18}+\frac{2}{9})$

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3 years ago