Rewrite the sentence with correct punctuation and capitalization.

Mathematics

1 answer:

Ludmilka [50]3 years ago

7 0

Matthew bought his cat, Filmore, at Mr. Macintosh’s pet store in Lincoln, Nebraska. (could do “!” at the end too)

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Albert receives $0.30 per pound for 1 to 49 pounds of glass bottles he recycles. He receives $0.40

Marina86 [1]

Answer:

Yes

Step-by-step explanation:

The amount of money Albert receives is described by the expression

$y = \begin{cases}0.30x & \quad \text{if } 0 \leq x \leq 49 \\0.40x & \quad \text{if } x > 50\\\end{cases}$

The graph is shown below.

To determine if the relation is a function, we can use the vertical line test:

If a vertical line crosses the graph more than once in any location, the relation is not a function.

We see that at no place will a vertical line intersect the graph more than once.

The relation is a function.

3 0

4 years ago

When does the value of f(x) = (1/2)x equal the value of g(x) =2x+8 ?

Zanzabum

Answer:

$\huge\boxed{f=g(x)\ \text{for}\ x=-\dfrac{16}{3}=-5\dfrac{1}{3}}$

Step-by-step explanation:

When does the value of f(x) = (1/2)x equal the value of g(x) =2x+8?

$f(x)=g(x)\iff\dfrac{1}{2}x=2x+8\qquad|\text{subtract}\ 2x\ \text{from bpoth sides}\\\\\dfrac{1}{2}x-2x=2x-2x+8\\\\-1\dfrac{1}{2}x=8\qquad|\text{convert the mixed number to the improper fraction}\\\\-\dfrac{2\cdot1+1}{2}x=8\\\\-\dfrac{3}{2}x=8\qquad\text{multiply both sides by}\ -\dfrac{2}{3}\\\\\left(-\dfrac{2\!\!\!\!\diagup}{3\!\!\!\!\diagup}\right)\left(-\dfrac{3\!\!\!\!\diagup}{2\!\!\!\!\diagup}x\right)=\left(-\dfrac{2}{3}\right)\cdot8\\\\x=-\dfrac{2\cdot8}{3}\\\\x=-\dfrac{16}{3}$