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3 years ago

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Justity each step in solving the equation 4x = 7(x - 3) by writing a reason for each statement Answer Statement Reason 1. 4x7x3)

1. 2. 4x = 7x - 21 2. 3. 3x = 21 3. 4X=7 4.

1 answer:

NemiM [27]3 years ago

4 0

Answer:

2. 4x = 7x - 21

Step-by-step explanation:

$4x = 7(x - 3) \\ 4x = 7x - 21 \\ 21 = 7x - 4x \\ 21 = 3x \\ \frac{21}{3} = x \\ 7 = x \\$

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Find the sum of the first 25 terms in this geometric series:<br> 8 + 6 + 4.5...

Ksivusya [100]

Step-by-step explanation:

Given the geometric sequence

8 + 6 + 4.5...

A geometric sequence has a constant ratio and is defined by

$a_n=a_1\cdot r^{n-1}$

$\mathrm{Compute\:the\:ratios\:of\:all\:the\:adjacent\:terms}:\quad \:r=\frac{a_{n+1}}{a_n}$

$\frac{6}{8}=\frac{3}{4},\:\quad \frac{4.5}{6}=\frac{3}{4}$

$\mathrm{The\:ratio\:of\:all\:the\:adjacent\:terms\:is\:the\:same\:and\:equal\:to}$

$r=\frac{3}{4}$

$\mathrm{The\:first\:element\:of\:the\:sequence\:is}$

$a_1=8$

$\mathrm{Therefore,\:the\:}n\mathrm{th\:term\:is\:computed\:by}\:$

$a_n=8\left(\frac{3}{4}\right)^{n-1}$

$\mathrm{Geometric\:sequence\:sum\:formula:}$

$a_1\frac{1-r^n}{1-r}$

$\mathrm{Plug\:in\:the\:values:}$

$n=25,\:\spacea_1=8,\:\spacer=\frac{3}{4}$

$=8\cdot \frac{1-\left(\frac{3}{4}\right)^{25}}{1-\frac{3}{4}}$

$\mathrm{Multiply\:fractions}:\quad \:a\cdot \frac{b}{c}=\frac{a\:\cdot \:b}{c}$

$=\frac{\left(1-\left(\frac{3}{4}\right)^{25}\right)\cdot \:8}{1-\frac{3}{4}}$

$=\frac{8\left(-\left(\frac{3}{4}\right)^{25}+1\right)}{\frac{1}{4}}$

$\mathrm{Apply\:exponent\:rule}:\quad \left(\frac{a}{b}\right)^c=\frac{a^c}{b^c}$

$=\frac{8\left(-\frac{3^{25}}{4^{25}}+1\right)}{\frac{1}{4}}$

$\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{a}{\frac{b}{c}}=\frac{a\cdot \:c}{b}$

$=\frac{\left(1-\frac{3^{25}}{4^{25}}\right)\cdot \:8\cdot \:4}{1}$

$\mathrm{Multiply\:the\:numbers:}\:8\cdot \:4=32$

$=\frac{32\left(-\frac{3^{25}}{4^{25}}+1\right)}{1}$

$=\frac{32\cdot \frac{4^{25}-3^{25}}{4^{25}}}{1}$ ∵ $\mathrm{Join}\:1-\frac{3^{25}}{4^{25}}:\quad \frac{4^{25}-3^{25}}{4^{25}}$

$=32\cdot \frac{4^{25}-3^{25}}{4^{25}}$

$=\frac{\left(4^{25}-3^{25}\right)\cdot \:32}{4^{25}}$

$=\frac{2^5\left(4^{25}-3^{25}\right)}{2^{50}}$ ∵ $\mathrm{Factor}\:32:\ 2^5$ , $\mathrm{Factor}\:4^{25}:\ 2^{50}$

so

$=\frac{4^{25}-3^{25}}{2^{45}}$ ∵ $\mathrm{Cancel\:}\frac{\left(4^{25}-3^{25}\right)\cdot \:2^5}{2^{50}}:\quad \frac{4^{25}-3^{25}}{2^{45}}$

$\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{a\pm \:b}{c}=\frac{a}{c}\pm \frac{b}{c}$

$=\frac{4^{25}}{2^{45}}-\frac{3^{25}}{2^{45}}$

$=32-\frac{3^{25}}{2^{45}}$ ∵ $\frac{4^{25}}{2^{45}}=32$

$=32-0.024$ ∵ $\frac{3^{25}}{2^{45}}=0.024$

$=31.98$

Therefore, the sum of the first 25 terms in this geometric series: 31.98

3 0

3 years ago

EASY points here Solve for H; P=2L+2H

e-lub [12.9K]

P=2L+2H
First, isolate 2H:
2H=P-2L
Second, get a singular value of H (just H):
2H/2=(P-2L)/2

Final answer:

H= $\frac{P-2L}{2}$

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2 years ago

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How do I find the endpoint of a segment when given the first endpoint (-6, 5) and the midpoint(-1.5, 1)?

Anika [276]

Answer:

(3, -3)

Step-by-step explanation:

Use the midpoint formula.

x = (x₁ + x₂) / 2

-1.5 = (-6 + x) / 2

-3 = -6 + x

x = 3

y = (y₁ + y₂) / 2

1 = (5 + y) / 2

2 = 5 + y

y = -3

The other endpoint is (3, -3).

Graph: desmos.com/calculator/aze920ns2h

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3 years ago

A single hab can have a length that is below 17 cm, but it must be no less than 9 cm. Write the compound inequality that describ

Vinvika [58]

Answer: 17>x greater than or equal to symbol 9

Step-by-step explanation: if it must be less than 17 you put less than and it can be no less than 9 meaning it can be greater than or equal to 9

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3 years ago

What is this equation 41 > 6m - 7

malfutka [58]

Think of the greater than sign as an equals sign. Then, you solve for m

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3 years ago