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1 year ago

consider the line 4x+9y=-8find the equation of the line that is perpendicular to this line and passes through the point (-2, -2)

find the equation of the line that is parallel of this line and passes through the point (-2, -2)

Mathematics

1 answer:

levacccp [35]1 year ago

8 0

$\begin{gathered} \text{The equation of the line is,} \\ 4x+9y=-8 \\ 9y=-4x-8 \\ y=-\frac{4}{9}x-\frac{8}{9} \\ \text{The slope is}\Rightarrow m=-\frac{4}{9} \\ perpendicular\text{ slope}\Rightarrow m^{\prime}=\frac{9}{4} \\ 1. \\ x_1=-2,y_1=-2 \\ So,\text{ the perpendicular equation of line is} \\ y-y_1=m^{\prime}(x-x_1) \\ y+2=\frac{9}{4}(x+2) \\ 4y+8=9x+18 \\ 4y=9x+10 \\ y=\frac{9}{4}x+\frac{5}{2}(\text{Ans)} \\ 2. \\ The\text{ parallel equation is,} \\ y-y_1=m(x-x_1) \\ y+2=-\frac{4}{9}(x+2) \\ 9y+18=-4x-8 \\ 9y=-4x-26 \\ y=-\frac{4}{9}x-\frac{26}{9}(\text{Ans)} \end{gathered}$

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Line 8x + 2y = 12 is parallel to the line 4x + y = 6.

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3 years ago

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3 years ago

Which of the sets of ordered pairs represents a function?

alexandr1967 [171]

Answer:

The correct option is 4. Neither A nor B represents a function.

Step-by-step explanation:

The given sets of ordered pairs are

$A=\{(1,-5), (8,-5), (8,7), (2,9)\}$

$B=\{(7,-4), (7,-2), (6,-3), (-9,5)\}$

A set of ordered pairs represents a function if there exist unique outputs for all inputs. It means for each values of x there exist, a unique value of y.

In set A the value of y-coordinates are -5 and 7 at $x=8$ .

At x=8, there exist more than one value of y, so the set A is not a function.

In set B the value of y-coordinates are -4 and -2 at $x=7$ .

At x=7, there exist more than one value of y, so the set B is not a function.

Therefore neither A nor B represents a function and option 4 is correct.

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3 years ago

Read 2 more answers

A food company sells salmon to various customers. The mean weight of the salmon is 37 lb with a standard deviation of 2 lbs. The

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Answer:

The standard deviation for the mean weigth of Salmon is 2/3 lbs for restaurants, 2/7 lbs for grocery stores and 1/4 lbs for discount order stores.

Step-by-step explanation:

The mean sample of the sum of n random variables is

$\overline{X} = \frac{X_1+X_2+...+X_n}{n}$

If $X_1, ..., X_n$ are indentically distributed and independent, like in the situation of the problem, then the variance of $X_1 + .... + X_n$ will be the sum of the variances, in other words, it will be n times the variance of $X_1$ .

However if we multiply this mean by 1/n (in other words, divide by n), then we have to divide the variance by 1/n², thus $\overkine{X} = \frac{V(X_1)}{n}$ and as a result, the standard deviation of $\overline{X}$ is the standard deviation of $X_1$ divided by $\sqrt{n}$ .

Since the standard deviation of the weigth of a Salmon is 2 lbs, then the standard deviations for the mean weigth will be:

Restaurants: We have boxes with 9 salmon each, so it will be $\frac{2}{\sqrt{9}} = \frac{2}{3}$
Grocery stores: Each carton has 49 salmon, thus the standard deviation is $\frac{2}{\sqrt{49}} = \frac{2}{7}$
Discount outlet stores: Each pallet has 64 salmon, as a result, the standard deviation is $\frac{2}{\sqrt{64}} = \frac{1}{4}$

We conclude that de standard deivation of the mean weigth of salmon of the types of shipment given is: 2/3 lbs for restaurants, 2/7 lbs for grocery stores and 1/4 lbs for discount outlet stores.

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3 years ago