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nataly862011 [7]
3 years ago
5

Write the equation of the line that passes through the points (−8,4) and (−3,7). Put your answer in fully reduced point-slope fo

rm, unless it is a vertical or horizontal line.
Mathematics
1 answer:
andreyandreev [35.5K]3 years ago
4 0

Answer:

y =  \frac{3}{5} x + 8 \frac{4}{5}

Step-by-step explanation:

<u>Point slope form</u>

y=mx +c, where m is the gradient and c is the y-intercept.

To find the gradient, use the formula below:

gradient =  \frac{y1 - y2}{x1 - x2}

m =  \frac{7 - 4}{ - 3 - ( - 8)}  \\ m =  \frac{3}{ - 3 + 8}  \\ m =  \frac{3}{5}

Substitute the value of m into the equation

y =  \frac{3}{5} x + c

To find c, substitute a coordinate into the equation.

When x= -3, y=7,

7 =  \frac{3}{5}( - 3) + c \\ 7 =  -  \frac{9}{5}  + c \\ c = 7 +  \frac{9}{5}  \\ c = 8 \frac{4}{5}

Thus, the equation of the line is y =  \frac{3}{5} x + 8 \frac{4}{5)

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Cindy plans to shop for her school supplies and wants to know how much money she would need to spend. from her friend she knows
vlabodo [156]

Let the cost of 1 notebook be x and the cost of 1 binder be y.

4 notebooks and 3 binders would cost 23.5

Therefore, 4x + 3y = 23.5     (1)

7 notebooks and 6 binders would cost 44.5

Therefore, 7x + 6y = 44.5     (2)

Multiply the first equation by 2.

8x + 6y = 47     (3)

(3) - (2) gives

x = 2.5

Substitute the value of x in (1), we get,

4(2.5) + 3y = 23.5

10 + 3y = 23.5

3y = 23.5 - 10

3y = 13.5

y = 13.5/3

y = 4.5

Hence, cost of 5 notebooks and 3 binders is:

5x + 3y = 5(2.5) + 3(4.5)

           = 12.5 + 13.5

           = 26

Hence, cost of 5 notebooks and 3 binders is $26.

4 0
3 years ago
What is the quotient and remainder of (4x^3-3x^2+x+7)/(x-2)
viva [34]

Answer:

4x^2+11x+23 r53

Step-by-step explanation:

4x^3-3x^2+x+7 / x-2

2 | 4 -3  1   7

        8 22 46

___________

    4 11 23 53

This means 4x^2+11x+23 with a remainder of 53

7 0
3 years ago
Item 15
Shtirlitz [24]

Answer:

28

Step-by-step explanation:

4*7= 28

when there is a variable (letter next to the number) next to the number like 4a it means 4 multiplied by a. since a is 7, 4 multiplied by 7 is 28.

8 0
3 years ago
If rx – st = r, which expression represents r.
statuscvo [17]

Answer:

{ \tt{rx - st = r}}

» Collect like terms, r terms on the left hand side by subtracting r from both sides and adding st to both sides

{ \tt{(rx - st) { \green{ - r + st }} = r{ \green{ - r + st}}}} \\ { \tt{rx - r = st}}

» On the left hand side, factorise out r

{ \tt{ \green{r(x - 1)} = st}} \\  \\ { \boxed{ \tt{ \blue{ \: r =  \frac{st}{x - 1} }}}}

5 0
2 years ago
6. A publisher requires 2⁄3 of a page of advertisements for every 5 pages in a magazine. If a magazine has 98 pages, to the near
earnstyle [38]

We have (2/3)÷5 = 2/15 advertisments for 1 page;

Then, we have 98 · (2/15) = 12.2(6) advertisments for 98 pages;

The nearest whole page is 12.

7 0
3 years ago
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