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ivanzaharov [21]

3 years ago

13

Mrs. Crews bought 4 pencils and 3 pens for $5.60. Miss Houston bought 2 pencils and 3 pens of the same kind for $4.60. What was

the price of each pencil and each pen?

1 answer:

dimulka [17.4K]3 years ago

3 0

The pencil is $1 and i do not know about the pen

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What is y in the first line if the line passing though (-1,y) and (1,0) perpendicular to the line passing (8,4) and (-1,1) ?

malfutka [58]

Answer:

$6$ .

Step-by-step explanation:

A line that goes through $(x_{0},\, y_{0})$ and $(x_{1},\, y_{1})$ where $x_{0} \ne x_{1}$ would have a slope of $m = (x_{1} - x_{0}) / (y_{1} - y_{0})$ .

The slope of the line that goes through $(8,\, 4)$ and $(-1,\, 1)$ would thus be:

$\begin{aligned}m_{2} &= \frac{1 - 4}{(-1) - 8} \\ &= \frac{(-3)}{(-9)} \\ &= \frac{1}{3}\end{aligned}$ .

Two lines in a cartesian plane are perpendicular to one another if and only if the product of their slopes is $(-1)$ .

Thus, if $m_{1}$ and $m_{2}$ denote the slope of the first and second lines in this question, $m_{1}\, m_{2} = (-1)$ since the two lines are perpendicular to one another. Since $m_{2} = (1/3)$ , the slope of the first line would be:

$\begin{aligned} m_{1} &= \frac{(-1)}{m_{2}} \\ &= \frac{(-1)}{(1/3)} \\ &= (-3)\end{aligned}$ .

Given that the first line goes through the point $(1,\, 0)$ , the point-slope equation of that line would be:

$(y - 0) = (-3)\, (x - 1)$ .

$y = -3\, x + 3$ .

Substitute in $x = (-1)$ to find the $y$ -coordinate of the point in question:

$y = -3\times (-1) + 3 = 6$ .

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Is Trazillion a number

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5-78 what does that give me

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Consider the arithmetic sequence:

Leona [35]

Answer:

If n is an integer, the function that generate the sequence 10, 12, 14, 16, ... is $\mathbf{d(n)=8+2n\:for\:n>1}$

Option D is correct option

Step-by-step explanation:

We are given the arithmetic sequence:

10, 12, 14, 16, ...

If n is an integer, which of these functions generate the sequence?

We need to find the nth term for the given sequence

The nth term for arithmetic sequence will be: $a_n=a_1+(n-1)d$

where aₙ is nth term, a₁ is first term and d is common difference

Looking at the sequence a₁ = 10 and d = 2

So, nth term will be:

$a_n=a_1+(n-1)d\\a_n=10+(n-1)2\\a_n=10+2n-2\\a_n=8+2n$

So, nth term is: $a_n=8+2n$

In the options below, the only correct answer is option D. so, we can write nth term as: $d(n) = 8 + 2n\: for\: n > 1$

So, If n is an integer, the function that generate the sequence 10, 12, 14, 16, ... is $\mathbf{d(n)=8+2n\:for\:n>1}$

Option D is correct option

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