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3 years ago

What is the slope of a line that is perpendicular to the

Mathematics

1 answer:

alexgriva [62]3 years ago

5 0

Answer:

The slope of a line that is perpendicular to the line

shown in the graph is = 4

Hence, option 'd' is true.

Step-by-step explanation:

From the line equation, let us take two points

(0, 2)

(4, 1)

Finding the slope between two points

$\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}$

$\left(x_1,\:y_1\right)=\left(0,\:2\right),\:\left(x_2,\:y_2\right)=\left(4,\:1\right)$

$m=\frac{1-2}{4-0}$

$m=-\frac{1}{4}$

As we know that the slope of the perpendicular line is basically the negative reciprocal of the slope of the line, so

The slope of the perpendicular line will be:

$-\frac{1}{-\frac{1}{4}}=4$

Thus, the slope of a line that is perpendicular to the line

shown in the graph is = 4

Hence, option 'd' is true.

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Find the first three terms in the expansion , in ascending power of x , of (2+x)^6 and obtain the coefficient of x^2 in the expa

Nataly_w [17]

Answer:

The first 3 terms in the expansion of $(2 + x)^{6}$ , in ascending power of x are,

$64 , 192 \times x^{1} {\textrm{ and }}240 \times x^{2}$

coefficient of $x^{2}$ in the expansion of $(2+x - x^{2})^{6}$ = (240 - 192) = 48

Step-by-step explanation:

$(2+x)^{6}$

= $\sum_{k=0}^{6}(6_{C_{k}} \times x^{k} \times 2^{6 - k})$

= $6_{C_{0}} \times x^{0} \times 2^{6} + 6_{C_{1}} \times x^{1} \times 2^{5} + 6_{C_{2}} \times x^{2} \times 2^{4}$ + terms involving higher powers of x

= $64 + 192 \times x^{1} + 240 \times x^{2}$ + terms involving higher powers of x

so, the first 3 terms in the expansion of $(2 + x)^{6}$ , in ascending power of x are,

$64 , 192 \times x^{1} {\textrm{ and }}240 \times x^{2}$

Again,

$(2+x - x^{2})^{6}$

= $\sum_{k=0}^{6}(6_{C_{k}} \times (2 + x)^{k} \times (-x^{2})^{6 - k})$

Now, by inspection,

the term $x^{2}$ comes from k =5 and k = 6

for k = 5, the coefficient of $x^{2}$ is , $(-32) \times 6$ = -192

for k = 6 , the coefficient of $x^{2}$ is, $6_{C_{2}} \times 2^{4}$ = 240

so, coefficient of $x^{2}$ in the final expression = (240 - 192) = 48

3 0

2 years ago

How does the graph of g(x) = (x + 4)3 − 6 compare to the parent function f(x) = x3?

Solnce55 [7]

Answer:

g(x) is shifted 6 units to the left

Step-by-step explanation:

Lets try to simplify g(x) since has a few extra terms:

g(x)= 3x+12-6=3x+6

Now it is easier to compare the two functions.

We can tell that they both have the same slope, both differs on a extra term

This term tell us that the g(x) is shifted to the left (it is positive 6)

Another approach to the solution is to plot the two functions together by obtaining the crossing points with the 'y' axis and with the 'x' axis

the result is shown in the attached picture

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3 years ago

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stellarik [79]

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2 years ago

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Bezzdna [24]

Answer:

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Step-by-step explanation:

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Let c be the cost,

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c = 2 + 3d

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2 years ago

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egoroff_w [7]

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