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3 years ago

The table shows the outputs, y, for different inputs, x:

1 answer:

3 0

<span>The table shows the outputs, y, for different inputs, x:

Input (x) 1 3 5 7
Output (y) 8 6 5 4

Part A: Do the data in this table represent a function? Justify your answer. (3 points)

Yes, the data in the table represent a function. The reason is that given an input (value of x), in the domain of the function (which is 1, 3, 5, 7), you can state the correspondant output (value of y) without ambiguity.

Part B: Compare the data in the table with the relation f(x) = 4x + 8. Which relation has a greater value when x = 3? (2 points)

x = 3 => f(3) = 4(3) + 8 = 12 + 8 = 20

While the image of 3 in the data is y = 6.

So, the function f(x) = 4x + 8 has a greater value when x = 3.

Part C: Using the relation in Part B, what is the value of x if f(x) = 76? Be sure to show all your work.

f(x) = 76 = 4x + 8 => 4x = 76 - 8 = 68

=> x = 68/4 = 17
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Find equations of the line that is parallel to the z-axis and passes through the midpoint between the two points (0, −3, 7) and

tia_tia [17]

Answer:

$\vec{r}(t)=\left$

In parametric form:

$x=-1, y=\displaystyle\frac{1}{2}, z=4+t$

Step-by-step explanation:

We first find the mid point:

$\displaystyle\left(\frac{0+(-2)}{2},\frac{-3+4}{2},\frac{7+1}{2}\right)=\left(-1,\frac{1}{2},4\right)$

Then, a vector parallel to the z-axis is:

$\vec{v}=\left< 0,0,1 \right>$

Then remember the equation of a line passing through point $(x_o,y_o,z_o)$ and parallel to the vector $\vec{v}=\left$ is:

$\vec{r}(t)=\left+t\left$

So, in this problem we get:

$\vec{r}(t)=\left+t\left$

After combining the two vectors:

$\vec{r}(t)=\left$

In parametric form:

$x=-1, y=\displaystyle\frac{1}{2}, z=4+t$

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3 years ago

Additive inverse of −11/ −13

g100num [7]

Answer: The additive inverse of -11/-13 is 11/13

Step-by-step explanation: The additive inverse is the opposite sign. (positive or negative). It's the amount that needs to be added or subtracted to get 0.

6 0

2 years ago

Which equations represent the line that is parallel to 3x – 4y = 7 and passes through the point (-4,-2)? Select two

seropon [69]

Answer:

4y = 3x + 4

3x-4y = -4 is correct

Step-by-step explanation:

This is what we do.

We first express the first equation in the form;

y = mx + c

where m represents the slope of the line

Thus we have;

4y = 3x -7

divide through by 4

y = 3/4x -7/4

Thus the slope here is the coefficient of x which is 3/4

Now, since the lines are parallel, it means that their slopes are equal

So the slope of the other line too is 3/4

We now use the point slope form to find the equation of this other line

Mathematically, that would be;

y-y1 = m(x-x1)

where (x1,y1) = (-4,-2)

Substituting this into the point slope equation, we have;

y-(-2) = 3/4(x-(-4))

y + 2 = 3/4(x + 4)

Cross multiply

4y + 8 = 3x + 12

4y = 3x + 12-8

4y = 3x + 4

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3 years ago

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jekas [21]

C is the answer of this problem

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3 years ago

Simplify: -1 | 2/3 - 4 | / 5/6

stealth61 [152]

Answer:

Step-by-step explanation:

$- 1 | \frac{2}{3} - 4| \div \frac{5}{6} \\ - 1 | \frac{2}{3} - \frac{4 \times 3}{1 \times 3} | \div \frac{5}{6} \\ - 1 | \frac{2 - 12}{3} | \div \frac{5}{6} \\ - 1 | \frac{ - 10}{3} | \div \frac{5}{6} \\ \frac{10}{3} \div \frac{5}{6} \\ \frac{10}{3} \times \frac{6}{5} \\ \frac{2}{1} \times \frac{2}{1} = 4$

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2 years ago