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2 years ago

write the equation of the line in either form (slope intercept or point slope form) that contains points (4,-5) (8,1)

Mathematics

1 answer:

lianna [129]2 years ago

7 0

Answer:

y = $\frac{3}{2}$ x - 11

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

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

with (x₁, y₁ ) = (4, - 5 ) and (x₂, y₂ ) = (8, 1 )

m = $\frac{1-(-5)}{8-4}$ = $\frac{1+5}{4}$ = $\frac{6}{4}$ = $\frac{3}{2}$ , then

y = $\frac{3}{2}$ x + c ← is the partial equation

To find c substitute either of the 2 points into the partial equation

Using (8, 1 ) , then

1 = 12 + c ⇒ c = 1 - 12 = - 11

y = $\frac{3}{2}$ x - 11 ← equation of line in slope- intercept form

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The function f(x) is a cubic function and the zeros of f(x) are -6, -3 and 1. The

jarptica [38.1K]

Answer:

$P(x)=-5x^3-40x^2-45x+90$

Step-by-step explanation:

<u>Equation of a Polynomial</u>

Given the roots x1, x2, and x3 of a cubic polynomial, the equation can be written as:

$P(x)=a(x-x1)(x-x2)(x-x3)$

Where a is the leading coefficient.

We know the three roots of the polynomial -6, -3, and 1, thus:

$P(x)=a(x+6)(x+3)(x-1)$

Since the y-intercept of the polynomial is y=90 when x=0:

90=a(0+6)(0+3)(0-1)

90=a(6)(3)(-1)=-18a

Thus

a = 90/(-18) = -5

The polynomial is:

$P(x)=-5(x+6)(x+3)(x-1)$

We must write it in standard form, so we have to multiply all of the factors as follows:

$P(x)=-5(x^2+6x+3x+18)(x-1)$

$P(x)=-5(x^2+9x+18)(x-1)$

$P(x)=-5(x^3-x^2+9x^2-9x+18x-18)$

$P(x)=-5(x^3+8x^2+9x-18)$

$\boxed{P(x)=-5x^3-40x^2-45x+90}$

3 0

2 years ago

Help pretty pretty please !!❤️

insens350 [35]

Answer:

HEYOOO

The answer must be that it has a MAX

Step-by-step explanation:

Its because the graph has a MAXIMUM "peak" of the line--the maximum point on the graph of which it reaches!

HOPE THIS HELPS!

4 0

3 years ago

Hello, just need the answer for this question. Thank you for your help if you do so.

musickatia [10]

Answer:

In the first one you are missing (x - 3) so it will be 4(x - 3) and if you factor it out it will be 4x - 12

In the second one you are missing a (x -5)which means 9x(x -5) or when you factor it out it will be 9x^2 - 45x

Step-by-step explanation:

3x^2 -23x + 40 = (3x - 8) (x - 5)

3x^2 -17x + 24 = (3x -8) ( x - 3)

7 0

2 years ago

5(x+3)-7(6-3)+29=50-3(8-x)

Sveta_85 [38]

Answer:

$\quad x=\frac{3}{2}$

Step-by-step explanation:

$7\left(6-3\right)=21$ , $\mathrm{Expand\:}5\left(x+3\right)-21+29:\quad5x+23$ , $\mathrm{Expand\:}50-3\left(8-x\right):\quad 3x+26$ , Subtract 23 and 3x from both sides and simplify: $2x=3$ , Divide both sides by 2 and simplify: $x=\frac{3}{2}$

<em>Hope this helps!!!</em>

6 0

3 years ago

A quadratic function is defined by

ella [17]

Answer:

1. The vertex of the graph of the function is (-4, 7)

2. The vertex represents a minimum value

3. The equation represented by the new graph is g(x) = (x + 4)² + 1

Step-by-step explanation:

The given quadratic function is given in vertex form, y = a·(x - h)² + k, as follows;

g(x) = (x + 4)² + 7

1. By comparing the given quadratic function and the vertex form of a quadratic equation, we have;

a = 1, h = -4, and k = 7

The vertex of the graph of the function, (h, k) = (-4, 7)

2. Given that a = 1 > 0, the graph of the quadratic function opens upwards and the vertex represents a minimum value

3. Shifting the graph 6 units down from where it is now will give;

The vertex = (h, k - 6) = (-4, 7 - 6) = (-4, 1)

h = -b/(2·a), k = (-b²/(4·a) + c = -a·h² + c

c = k + a·h²

Therefore, initial value of the constant term, c = -1×(-4)² + 7 = 23

After the shifting the graph 6 units down, c = 23 - 6 = 17

∴ k = 1 = -a·(-4)² + 17

∴ -16/16 = -1 = -a

a = 1

Therefore, the equation represented by the new graph is g(x) = (x + 4)² + 1.

5 0

3 years ago