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4 years ago

Multiply or divide as indicated. Y^-9•y^-8•y^10

Mathematics

1 answer:

BabaBlast [244]4 years ago

8 0

Answer:

1 / y^7

Step-by-step explanation:

Y^-9•y^-8•y^10

= y^10 / y^9•y^8

= y^10 / y^17

= 1 / y^7

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Find the value of x that makes def ~ xyz<br>x=

Neporo4naja [7]

Answer:

x = 3.5

Step-by-step explanation:

$\triangle DEF \sim \triangle XYZ\\\\\therefore \frac{DE}{XY} =\frac{DF}{XZ} \\\\\therefore \frac{5}{7.5} =\frac{7}{3x} \\\\\therefore 3x = \frac{7.5\times 7}{5} \\\\\therefore x = \frac{7.5\times 7}{3\times 5} \\\\\therefore x = \frac{52.5\times 7}{15} \\\\\therefore x = 3.5$

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4 years ago

Write an equation of the line passing through the point (5, 1) that is perpendicular to the line 5x+3y=15. An equation of the li

pochemuha

Answer:

$\displaystyle y = \frac{3}{5}\, x + (-2)$ .

Step-by-step explanation:

The slope of a line in a plane would be $m$ if the equation of that line could be written in the slope-intercept form $y = m\, x + b$ for some constant $b$ .

Find the slope of the given line by rearranging its equation into the slope-intercept form.

$3\, y = (-5)\, x + 15$ .

$\displaystyle y = \frac{(-5)}{3} \, x + 5$ .

Thus, the slope of the given line would be $(-5) / 3$ .

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

Let $m_{1}$ and $m_{2}$ denote the slope of the given line and the slope of the line in question, respectively.

Since the two lines are perpendicular to each other, $m_{1}\, m_{2} = (-1)$ . Apply the fact that the slope of the given line is $m_{1} = (-5) / 3$ and solve for $m_{2}$ , the slope of the line in question.

$\begin{aligned}m_{2} &= \frac{(-1)}{m_{1}} \\ &= \frac{(-1)}{(-5) / 3} = \frac{3}{5}\end{aligned}$ .

In other words, the slope of the line perpendicular to $5\, x + 3\, y = 15$ would be $(3 / 5)$ .

If the slope of a line in a plane is $m$ , and that line goes through the point $(x_{0},\, y_{0})$ , the equation of that line in point-slope form would be:

$(y - y_{0}) = m\, (x - x_{0})$ .

Since the slope of the line in question is $(3 / 5)$ and that line goes through the point $(5,\, 1)$ , the equation of that line in point-slope form would be: