Find the remainder when x square-5x+3 is divided by x-3.

6.3.12

Semenov [28]

Answer:

$S = (4,-9)$

Step-by-step explanation:

Given

$T = (0,5)$

$Midpoint = (2,-2)$

Required

Find S

Midpoint is calculated as:

$Midpoint = 0.5(x_1 + x_2,y_1+y_2)$

So, we have:

$(2,-2)= 0.5(0+ x_2,5+y_2)$

<em>Where x2 and y2 are the coordinates of S</em>

Multiply through by 2

$2 * (2,-2)= 2 * 0.5(0+ x_2,5+y_2)$

$(4,-4)= (0+ x_2,5+y_2)$

$(4,-4)= (x_2,5+y_2)$

By comparison:

$x_2 = 4$

$5 + y_2 = -4$

$y_2 = -4-5$

$y_2 = -9$

So:

$S = (4,-9)$

7 0

3 years ago

An auditorium has rows of seats with 8 seats in each row. Kayla knows there are at least 70 seats but fewer than 340 seats in th

Vera_Pavlovna [14]

Answer:

The possible number of rows can be 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, or 42.

Step-by-step explanation:

First of all, if there are 70 seats, there should be 9 rows. (9*8 =72, which has 70 seats). And, 340 seats are there, so 340/8 = 42.5, i.e. 42 rows can be there at maximum. So, the actual number of rows can be between 9 and 42. Therefore the possible number of rows can be 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, or 42.

Hope this helps. :)

8 0

3 years ago

As x increases by 1 unit, what is the exponential growth factor??

san4es73 [151]

Given:

The graph of an exponential function.

To find:

The exponential growth factor as x increases by 1 unit.

Solution:

From the given graph, it is clear that the exponential function passes through the points (1,1) and (3,9). So, the equation of the exponential must must be satisfy by these points.

The general exponential function is:

$y=ab^x$ ...(i)

Where, a is the initial value and b is the growth factor.

Putting $x=1,y=1$ in (i), we get

$1=ab^1$ ...(ii)

Putting $x=3,y=9$ in (i), we get

$9=ab^3$ ...(iii)

Divide (iii) by (ii).

$\dfrac{9}{1}=\dfrac{ab^3}{ab}$

$9=b^2$

$3=b$

b is the the growth factor and the value of b is 3.

Therefore, the exponential growth factor is 3 as x increases by 1 unit.

7 0

3 years ago

162 water bottles in 9 cases=

marishachu [46]

162/9 = 18 water bottles per case

5 0

3 years ago

Line segments JK and JL in the xy-coordinate plane both have a common endpoint J (-4,11) and midpoints at M1 (2,16) and M2 (-3,5

lutik1710 [3]

Distance formula : sqrt ((x2 - x1)^2 + (y2 - y1)^2)
(2,16)...x1 = 2 and y1 = 16
(-3,5)...x2 = -3 and y2 = 5
time to sub and solve
d = sqrt ((-3 - 2)^2 + (5 - 16)^2)
d = sqrt ((-5^2) + (-11^2))
d = sqrt (25 + 121)
d = sqrt 146
d = 12.08 <=

4 0

3 years ago

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