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35. For the following exercises, given each set of information, find a linear equation satisfying the conditions, if possible.

Montano1993 [528]

Answer:

The linear equation for the line which passes through the points given as (-2,8) and $(4,6), is written in the point-slope form as $y=-\frac{1}{3} x-\frac{26}{3}$ .

Step-by-step explanation:

A condition is given that a line passes through the points whose coordinates are (-2,8) and (4,6).

It is asked to find the linear equation which satisfies the given condition.

Step 1 of 3

Determine the slope of the line.

The points through which the line passes are given as (-2,8) and (4,6). Next, the formula for the slope is given as,

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

Substitute $6 \& 8$ for $y_{2}$ and $y_{1}$ respectively, and 4&-2 for $x_{2}$ and $x_{1}$ respectively in the above formula. Then simplify to get the slope as follows, $m=\frac{6-8}{4-(-2)}$

$\begin{aligned}&m=\frac{-2}{6} \\&m=-\frac{1}{3}\end{aligned}$

Step 2 of 3

Write the linear equation in point-slope form.

A linear equation in point slope form is given as,

$y-y_{1}=m\left(x-x_{1}\right)$

Substitute $-\frac{1}{3}$ for m,-2 for $x_{1}$ , and 8 for $y_{1}$ in the above equation and simplify using the distributive property as follows, $y-8=-\frac{1}{3}(x-(-2))$\\ $y-8=-\frac{1}{3}(x+2)$\\ $y-8=-\frac{1}{3} x-\frac{2}{3}$$

Step 3 of 3

Simplify the equation further.

Add 8 on each side of the equation $y-8=-\frac{1}{3} x-\frac{2}{3}$ , and simplify as follows, $y-8+8=-\frac{1}{3} x-\frac{2}{3}+8$

$y=-\frac{1}{3} x-\frac{2+24}{3}$$\\ $$y=-\frac{1}{3} x-\frac{26}{3}$$

This is the required linear equation.

6 0

2 years ago

Find the domain and the range of the relation. Determine whether the relation is a function.

andre [41]

Answer:

Domain: {-6, -1, 7}

Range: {-9, 0, 9}

The relation is not a function.

Step-by-step explanation:

Given the relation: t{(−1,0),(7,0),(−1,9),(−6,−9)}

In the ordered pairs:

The domain is the set of all "x" values
The range is set of all "y" values
We do not need to list any repeated value in the range/domain more than once.

Domain: {-6, -1, 7}

Range: {-9, 0, 9}

Next, we determine whether the relation is a function.

For a relation to be a function, each x must correspond with only one y value.

However, as is observed in the mapping attached below:

f(-1)=0
f(-1)=9

The x-value (-1) corresponds to two y-values (0 and 9)

Therefore, the relation is not a function.

8 0

3 years ago

24 + 28 as a product of two factors using the GCF and distributive property

Yakvenalex [24]

Answer:

52

Step-by-step explanation:

Using GCF:

The factors of 24 are; 1, 2, 3, 4, 6, 8, 12, 24

Factors of 28 are; 1, 2, 4, 7, 14, 28

The highest greatest common factor is 4.

Now, 4 × 6 gives 24

While 4 × 7 gives 28.

Thus, our original equation is now;

4(6 + 7)

Using distributive property, let's add the number in the bracket first to get;

4(13).

Now,we multiply out to get 52.

8 0

3 years ago

Find x I need help plz :( A. 6 B. 24 C. 12 D. 12 sqr root of 3 E. 36

Vera_Pavlovna [14]

Answer:

b

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

If 8 is an angle in standard position and its terminal side passes through the point (21,20), find the exact value of cos 0 in s

Sati [7]

Answer:

so x = 20 , y = -21 , which is in quad IV

r^2= 400+441 = 841

r = √841 = 29

then cos Ø = 20/29

sec Ø = 29/20 = 1.45

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8 0

3 years ago