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Leni [432]
4 years ago
11

A line passes through the point (-7,6) and has a slope of -2

Mathematics
2 answers:
faust18 [17]4 years ago
7 0

\bf (\stackrel{x_1}{-7}~,~\stackrel{y_1}{6})~\hspace{10em} slope = m\implies -2 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-6=-2[x-(-7)] \implies y-6=-2(x+7) \\\\\\ y-6=-2x-14\implies y=-2x-8

Aleks [24]4 years ago
6 0

y - 6 = -2(x + 7)

y - 6 = -2x - 14

y = -2x - 8       <---------------------equation in  slope intercept form

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Each polygon pair is similar. Find the missing side length
ohaa [14]

I'll do problem 1 to get you started.

The vertical sides are 3 and x for the left and right figures.

The horizontal sides are 15 and 60 for the left and right figures.

The corresponding sides form fractions which are equal (due to the nature of the similar polygons)

3/x = 15/60

3*60 = x*15 ... cross multiply

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15x = 180

x = 180/15 .... divide both sides by 15

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Another way you can see this is note how the jump from 15 to 60 is "times 4", so the jump from 3 to x must also be "times 4" to keep the same proportion

3 ---> x = 3*4 = 12

Or you could set up the proportion

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x = 12

-----------

<h3>Final Answer: 12</h3>
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Please help!
crimeas [40]

Answer:

The zeros are:

x =4, x=2, x = 5

  • The function has three distinct real zeros.

Hence, option (B) is true.

Step-by-step explanation:

Given the expression

h\left(x\right)=\left(x-4\right)^2\left(x^2-7x+\:10\right)

Let us determine the zeros of the function by putting h(x) = 0 and solving the expression

0=\left(x-4\right)^2\left(x^2-7x+10\right)

switch sides

\left(x-4\right)^2\left(x^2-7x+10\right)=0

as

x^2-7x+\:10=\left(x-2\right)\left(x-5\right)

so

\left(x-4\right)^2\left(x-2\right)\left(x-5\right)=0

Using the zero factor principle

  • \mathrm{If}\:ab=0\:\mathrm{then}\:a=0\:\mathrm{or}\:b=0\:\left(\mathrm{or\:both}\:a=0\:\mathrm{and}\:b=0\right)

so

x-4=0\quad \mathrm{or}\quad \:x-2=0\quad \mathrm{or}\quad \:x-5=0

x =4, x=2, x = 5

Thus, the zeros are:

x =4, x=2, x = 5

It is clear that there are three zeros and all the zeros are distinct real numbers.

Therefore,

  • The function has three distinct real zeros.

Hence, option (B) is true.

4 0
3 years ago
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