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2 years ago

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A line with a slope of -1/3 passes through the point (9,3). What is its equation in point-slope form?

1 answer:

amm18122 years ago

7 0

The point-slope form:

$y-y_1=m(x-x_1)$

We have:

$(9,\ 3)\to x_1=9,\ y_1=3\\\\m=-\dfrac{1}{3}$

Substitute

$y-3=-\dfrac{1}{3}(x-9)$

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In December yanni’s chocolate shop received 180 telephone orders. In January they received only 72 telephone orders. By what per

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2 years ago

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Audrey gave a 0.90 tip to a waitress for serving a meal costing $6.00. what percent of the bill was her tip?

maw [93]

Answer:

<u>15%</u> percent of the bill was her tip.

Step-by-step explanation:

Given:

Audrey gave a $0.90 tip to a waitress for serving a meal costing $6.00.

Now, to find the percent of the bill was her tip.

The bill was = $6.00.

The tip she gave = $0.90.

Now, to get the percent of the bill was her tip:

$\frac{The\ tip}{The\ bill}\times 100$

$=\frac{0.90}{6.00} \times 100$

$=0.15\times 100$

$=15\%.$

Therefore, 15% percent of the bill was her tip.

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3 years ago

The directions on a sewing pattern say to buy an extra 12.5% of fabric to account for error. Sam needs 2.75 yards of fabric to m

uranmaximum [27]

Answer:

Sam should have bought 3.09 yards of fabric instead of 2.4 yards

So, Option D is correct.

Step-by-step explanation:

Total fabric needed by Sam = 2.75

According to directions on a sewing pattern they say to buy an extra 12.5%

So, extra fabric would be: 12.5% of 2.75

Solving

$12.5\% \ of \ 2.75\\=\frac{12.5}{100}\times 2.75 \\=0.343$

Now adding 0.343 into 2.75 to get extra fabric quantity:

2.75+0.343

=3.09

Therefore Sam should have bought 3.09 yards of fabric instead of 2.4 yards

So, Option D is correct.

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2 years ago

Suppose that f : [a, b] → [a, b] is continuous. Prove that f has a fixed point. That is, prove that there exists c ∈ [a, b] such

nikklg [1K]

Answer:

Step-by-step explanation:

define the function:

$g(x) = f(x) -x$

As both $f(x)$ and x are continuous functions, $g(x)$ will also be continuous.

Now, what can we say about $g(a) = f(a) -a$ ?

we know that $a\leq f(a) \leq b$ , thus:

$a-a\leq f(a)-a \leq b-a\\0 \leq g(a) \leq b-a$

thus $g(a)$ is non-negative.

What about $g(b)$ ? Again we have:

$a\leq f(b) \leq b\\a-b \leq f(b) -b \leq 0\\a-b \leq g(b) \leq 0$

That means that $g(b)$ is not positive.

Now, we can imagine two cases, either one of $g(a)$ or $g(b)$ is equal to zero, or none of them is. If either of them is equal to zero, we have found a fixed point! In fact, any point $c$ for which $g(c)=0$ is a fixed point, because:

$g(c) = 0 \implies f(c) -c = 0 \implies f(c) = c$

Now, if $g(a) \neq 0$ and $g(b) \neq 0$ , then we have that

$g(a) >0$ and $g(b) < 0$ . And by Bolzano's theorem we can assert that there must exist a point c between a and b for which $g(c)=0$ . And as we have shown before that point would be a fixed point. This completes the proof.

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3 years ago