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3 years ago

6

Jacques wants to fit a scale model of this room on an 8.5” by 11” paper. What scale factor should he use? He wants to make the s

cale model large enough to be visible and take up most of the sheet of paper?

1 answer:

AleksAgata [21]3 years ago

8 0

Answer:

1:20 scale should be perfect

Step-by-step explanation:

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(1/27)^x-6=27<br><br>Could I please have a step by step as well? Much appreciated!

Andrei [34K]

Answer:

$x = 7$

Step-by-step explanation:

1) Use Division Distributive Property: (x/y)^a = x^a/y^a.

$\frac{1}{ {27}^{x - 8} } = 27$

2) Multiply both sides by 27^x - 8.

$1 = {27} \times 27^{1 + x - 8}$

3) Use the product rule: x^a x^b = x^a+b.

$1 = {27}^{1 + x - 8}$

4) Simplify 1 + x - 8 to x - 7.

$1 = {27}^{x - 7}$

5) Use Definition of Common Logarithm: b^a = x if and only if log<u>b</u><u> </u>(x) = a.

$log_{27}1 = x - 7$

6) Use Change of Base Rule.

$\frac{ log_1 }{ log{27} } = x - 7$

7) Use rule of 1: log 1 = 0.

$\frac{0}{ log_{27}} = x - 7$

8) Simplify 0/log_27 to 0.

$0 = x - 7$

9) Add 7 to both sides.

$7 = x$

10) Switch sides.

$x = 7$

<u>Therefor</u><u>,</u><u> </u><u>the</u><u> </u><u>answer</u><u> </u><u>is</u><u> </u><u>x</u><u> </u><u>=</u><u> </u><u>7</u><u>.</u>

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3 years ago

1) State the amplitude, period, phase shift, vertical shift and graph

bogdanovich [222]

Answer:

See answers and explanations below (along with a visual graph)

Step-by-step explanation:

For the function $y=acos(b(x+c))+d$ :

Amplitude: $|a|$

Period: $\frac{2\pi}{|b|}$

Phase shift: $\frac{-c}{b}$

Vertical shift: $d$

Therefore, for $y=2cos(\frac{2}{3}(\theta+\pi))-1$ :

Amplitude: $|a|=|2|=2$ , which is 2 units above and below the midline (see d)

Period: $\frac{2\pi}{|b|}=\frac{2\pi}{|\frac{2}{3}|}=\frac{2\pi}{\frac{2}{3}}=3\pi$ , so the cycle will repeat every 3π units

Phase shift: $\frac{-c}{b}=\frac{-\frac{2\pi}{3} }{\frac{2}{3} }=-\pi$ , or π units to the left

Vertical shift: $d=-1$ , or 1 unit down

3 0

3 years ago

PLEASE PLEASE OLEASE HELP ME ASAP I WILL LOVE U FOREVER

vodomira [7]

Answer:

m=3/2

look how many units go up and to the side between 2 points

As seen here, we go up 3 units and over 2 units from (0, -3) to (2, 0.) Therefore, slope is 3/2

Step-by-step explanation:

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3 years ago

Andre types 208 words in 4 minutes. Noah types 342 words in 6 minutes. Who types faster?

Vesna [10]

Answer:

Noah types faster

Step-by-step explanation:

Andre's typing speed per minute - 52 words per minute

$\frac{208}{4}$ = 52

Noah's typing speed per minute - 57 words per minute

$\frac{342}{6}$ = 57

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3 years ago

Solve each inequality. Then compare the solutions.<br><br> 3x +4> 16<br> - 2x + 19< 11

Makovka662 [10]

Answer:

$3x + 4 > 16 \\ 3x > 16 - 4 \\ \frac{3x}{3} > \frac{12}{3} \\ x > 4 \\ \\ - 2x + 19 < 11 \\ - 2x < 11 - 19 \\ - 2x < - 8 \\ \frac{ - 2x}{ - 2} > \frac{ - 8}{ - 2} \\ x > 4 \\ \\ comparing \\ 4 < x > 4$

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3 years ago