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3 years ago

Divide the following polynomial, then place the answer in the proper location on the grid.

Mathematics

2 answers:

podryga [215]3 years ago

4 0

So you are saying that you want to find out what it would be in simple from.
(a 2n-a n-6) (a n+8)
a²n²+2an-48

Lisa [10]3 years ago

4 0

Answer:

The two polynomials one of which is in Numerator and another one which is in Denominator

$\rightarrow \frac{a_{n}^2-a_{n}-6}{a_{n}+8}\\\\\text{Splitting the middle term}\\\\\rightarrow \frac{a_{n}^2-3a_{n}+2a_{n}-6}{a_{n}+8}\\\\\rightarrow \frac{a_{n}\times (a_{n}-3)+2\times(a_{n}-3)}{a_{n}+8}\\\\\rightarrow \frac{(a_{n}-3)(a_{n}+2)}{a_{n}+8}$

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The diagonals of a quadrilateral QRST intersect at P(-1,3). QRST has vertices at Q(3,6) and R(-4,5). What must be the coordinate

erica [24]

S = (-5,0)

T = (2,1)

Step-by-step explanation:

Step 1 :

Given

Q = (3,6) and R = (-4,5). P = (-1,3)

Let S be (a,b) and T be (c,d)

The diagonals of a parallelogram bisect each other. so in order to ensure that QRST is a parallelogram, P must be the mid point of the diagonals QS and RT.

Step 2 :

P is the midpoint of QS

So we have (3+a) ÷ 2 = -1 and (6 + b) ÷ 2 = 3

=> 3 + a = -2 and 6 + b = 6

=> a = -5 and b =0

So S should be (-5,0)

Step 3 :

P is the midpoint of RT

So we have (-4+c) ÷ 2 = -1 and (5 + d) ÷ 2 = 3

=> -4+ c = -2 and 5 + d = 6

=> c = 2 and d =1

So T should be (2,1)

Step 4 :

Answer :

S = (-5,0)

T = (2,1)

6 0

3 years ago

Solve the following quadratic equation by the square root method. (Y-9)^2=64

enot [183]

Hello!

To solve this, first perform the opposite operation for the last operation (on the left side) on both sides. The last operation of the left side is squaring. Therefore, square root both sides.

$(y - 9)^{2} = 64$

$y - 9 = ±\sqrt{64}$

$y - 9 = ±8$

Please note that you must include ±. This is because the square root of 64 can be either positive or negative, as a square of either a positive or negative number is positive.

Now, add 9 to both sides.

$y = 9±8$

There are 2 solutions from here. One comes from adding 8, and the other subtracting 8. Therefore, the two solutions are:

y = 9 + 8 = 17

y = 9 - 8 = 1

Therefore, your two solutions are 17 and 1.

Hope this helps!

8 0

3 years ago

The equation of function h is h... PLEASE HELP MATH

Flura [38]

Answer:

Part A: the value of h(4) - m(16) is -4

Part B: The y-intercepts are 4 units apart

Part C: m(x) can not exceed h(x) for any value of x

Step-by-step explanation:

Let us use the table to find the function m(x)

There is a constant difference between each two consecutive values of x and also in y, then the table represents a linear function

The form of the linear function is m(x) = a x + b, where

a is the slope of the function
b is the y-intercept

The slope = Δm(x)/Δx

∵ At x = 8, m(x) = 2

∵ At x = 10, m(x) = 3

∴ The slope = $\frac{3-2}{10-8}=\frac{1}{2}$

∴ a = $\frac{1}{2}$

- Substitute it in the form of the function

∴ m(x) = $\frac{1}{2}$ x + b

- To find b substitute x and m(x) in the function by (8 , 2)

∵ 2 = $\frac{1}{2}$ (8) + b

∴ 2 = 4 + b

- Subtract 4 from both sides

∴ -2 = b

∴ m(x) = $\frac{1}{2}$ x - 2

Now let us answer the questions

Part A:

∵ h(x) = $\frac{1}{2}$ (x - 2)²

∴ h(4) = $\frac{1}{2}$ (4 - 2)²

∴ h(4) = $\frac{1}{2}$ (2)²

∴ h(4) = $\frac{1}{2}$ (4)

∴ h(4) = 2

∵ m(x) = $\frac{1}{2}$ x - 2

∴ m(16) = $\frac{1}{2}$ (16) - 2

∴ m(16) = 8 - 2

∴ m(16) = 6

- Find now h(4) - m(16)

∵ h(4) - m(16) = 2 - 6

∴ h(4) - m(16) = -4

Part B:

The y-intercept is the value of h(x) at x = 0

∵ h(x) = $\frac{1}{2}$ (x - 2)²

∵ x = 0

∴ h(0) = $\frac{1}{2}$ (0 - 2)²

∴ h(0) = $\frac{1}{2}$ (-2)² =

∴ h(0) = 2

∴ The y-intercept of h(x) is 2

∵ m(x) = $\frac{1}{2}$ x - 2

∵ x = 0

∴ m(0) = $\frac{1}{2}$ (0) - 2 = 0 - 2

∴ m(0) = -2

∴ The y-intercept of m(x) is -2

- Find the distance between y = 2 and y = -2

∴ The difference between the y-intercepts of the graphs = 2 - (-2)

∴ The difference between the y-intercepts of the graphs = 4

∴ The y-intercepts are 4 units apart

Part C:

The minimum/maximum point of a quadratic function f(x) = a(x - h) + k is point (h , k)

Compare this form with the form of h(x)

∵ h = 2 and k = 0

∴ The minimum point of the graph of h(x) is (2 , 0)

∵ k is the minimum value of f(x)

∴ 0 is the minimum value of h(x)

∴ The domain of h(x) is all real numbers

∴ The range of h(x) is h(x) ≥ 2

∵ m(8) = 2

∵ m(14) = 5

∵ h(8) = $\frac{1}{2}$ (8 - 2)² = 18

∵ h(14) = $\frac{1}{2}$ (14 - 2)² = 72

∴ h(x) is always > m(x)

∴ m(x) can not exceed h(x) for any value of x

Look to the attached graph for more understand

The blue graph represents h(x)

The green graph represents m(x)

The blue graph is above the green graph for all values of x, then there is no value of x make m(x) exceeds h(x)

7 0

3 years ago

12 = -4(-6x -3) +24

Reil [10]

Answer:

x = -1

Step-by-step explanation:

Solve for x:

12 = 24 - 4 (-6 x - 3)

-4 (-6 x - 3) = 24 x + 12:

12 = 24 x + 12 + 24

Grouping like terms, 24 x + 12 + 24 = 24 x + (12 + 24):

12 = 24 x + (12 + 24)

12 + 24 = 36:

12 = 24 x + 36

12 = 24 x + 36 is equivalent to 24 x + 36 = 12:

24 x + 36 = 12

Subtract 36 from both sides:

24 x + (36 - 36) = 12 - 36

36 - 36 = 0:

24 x = 12 - 36

12 - 36 = -24:

24 x = -24

Divide both sides of 24 x = -24 by 24:

(24 x)/24 = (-24)/24

24/24 = 1:

x = (-24)/24

The gcd of -24 and 24 is 24, so (-24)/24 = (24 (-1))/(24×1) = 24/24×-1 = -1:

Answer: x = -1

8 0

2 years ago

Perform the Indicated operatlon. (-10) ÷ (-20) a)-2 b)2 c)1/2 d)-1/2

Nuetrik [128]

Answer:c

Step-by-step explanation of the

(-10)/(-20)

-1/(-2)

Negative sign result in positive result, so

1/2; c

4 0

3 years ago