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Select all of the true statements. $\newline$ Multi-select Choices: $\newline$ (A) $6 \times 10^5$ is $20$ times as much as $3 \times 10^4$ . $\newline$ (B) $7 \times 10^3$ is $100,000$ times as much as $7 \times 10^{-3}$ . $\newline$ (C) $9 \times 10^{-5}$ is $0.01$ times as much as $9 \times 10^{-3}$ . $\newline$ (D) $3 \times 10^4$ is $20$ $0$ times as much as $20$ $1$ .

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Transformations of functions

Full solution

Q. Select all of the true statements.

\newline

Multi-select Choices:

\newline

(A)

6 \times 10^5

is

20

times as much as

3 \times 10^4

.

\newline

(B)

7 \times 10^3

is

100,000

times as much as

7 \times 10^{-3}

.

\newline

(C)

9 \times 10^{-5}

is

0.01

times as much as

9 \times 10^{-3}

.

\newline

(D)

3 \times 10^4

is

20

0

times as much as

20

1

.

Calculate Comparison Result: Calculate if $6 \times 10^5$ is $20$ times as much as $3 \times 10^4$ . $\newline$ $6 \times 10^5 = 600,000$ $\newline$ $3 \times 10^4 = 30,000$ $\newline$ $20 \times 30,000 = 600,000$ $\newline$ So, $6 \times 10^5$ is indeed $20$ times as much as $3 \times 10^4$ .
Check Multiplication Result: Check if $7 \times 10^3$ is $100,000$ times as much as $7 \times 10^{-3}$ .
$7 \times 10^3 = 7,000$
$7 \times 10^{-3} = 0.007$
$100,000 \times 0.007 = 700$ , not $7,000$ .
So, this statement is incorrect.
Determine Proportion: Determine if $9 \times 10^{-5}$ is $0.01$ times as much as $9 \times 10^{-3}$ . $\newline$ $9 \times 10^{-5} = 0.00009$ $\newline$ $9 \times 10^{-3} = 0.009$ $\newline$ $0.01 \times 0.009 = 0.00009$ $\newline$ So, $9 \times 10^{-5}$ is indeed $0.01$ times as much as $9 \times 10^{-3}$ .
Figure Out Multiplication: Figure out if $3 \times 10^4$ is $5$ times as much as $6 \times 10^3$ .
$3 \times 10^4 = 30,000$
$6 \times 10^3 = 6,000$
$5 \times 6,000 = 30,000$
So, $3 \times 10^4$ is indeed $5$ times as much as $6 \times 10^3$ .

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What kind of transformation converts the graph of

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\newline

\newline

\text{[A]translation 10 units left}

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\newline

\newline

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\newline

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Question

\lim _{x \rightarrow \frac{\pi}{4}} \cos (x)=?

\newline

1

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Tess tried to solve the differential equation

\frac{d y}{d x}=2 x y-6 x

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\newline

\frac{d y}{d x}=2 x y-6 x

\newline

1

\quad \frac{d y}{d x}=(y-3) 2 x

\newline

2

\quad \int \frac{1}{y-3} d y=\int 2 x d x

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3

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4

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5

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\newline

6

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7

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1

\newline

(A) Tess's work is correct.

\newline

1

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\newline

4

is incorrect. The right-hand side of the equation should be

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\newline

7

is incorrect. Tess didn't account for adding

3

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Question

Aditya tried to solve the differential equation

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\newline

\frac{d y}{d x}=6 x-30

\newline

1

\quad \int 30 d y=\int 6 x d x

\newline

2

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3

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1

\newline

(A) Aditya's work is correct.

\newline

1

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\newline

2

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\newline

3

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2

of the following expressions represents the distance between the sandbag and the target?

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2

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|250+75|

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\newline

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\newline

1

\newline

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\newline

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\newline

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