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3 years ago

Factor x^2 + 12x + 36

Mathematics

2 answers:

larisa [96]3 years ago

8 0

Answer:

(x + 6 )(x + 6 )

2 numbers to add to 12 but also multiply to get 36

tatyana61 [14]3 years ago

5 0

Answer:

(x+6)(x+6)

Step-by-step explanation:

x^2 + 12x + 36

What 2 numbers multiply to 36 and add to 12

6*6 =36

6+6 =12

(x+6)(x+6)

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H=64t-32t^2 find the maximum height attained by the obiect

pshichka [43]

Check the picture below.

so if we just find its vertex, we know how many feet it went up by its y-coordinate.

$\bf h=64t-32t^2\implies h=-32t^2+64t+0 \\\\[-0.35em] ~\dotfill$

$\bf \textit{vertex of a vertical parabola, using coefficients} \\\\ h=\stackrel{\stackrel{a}{\downarrow }}{-32}t^2\stackrel{\stackrel{b}{\downarrow }}{+64}t\stackrel{\stackrel{c}{\downarrow }}{+0} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right) \\\\\\ \left(-\cfrac{64}{2(-32)}~~,~~0-\cfrac{64^2}{4(-32)} \right)\implies \left( \stackrel{\stackrel{\textit{how many}}{\textit{seconds}}}{1}~~,~~\stackrel{\stackrel{\textit{how many feet}}{\textit{it went up}}}{32} \right)$

5 0

3 years ago

What is the value of z so that-9 and 9 are both solutions of x^2+z=103?

notka56 [123]

If the sol'ns are -9 and 9, then we can use this to form our eq'n:
(x - 9)(x + 9) = 0
x^2 - 81 = 0
so...
x^2 + z - 103 = x^2 -81
z - 103 = -81
z = -81 + 103
z = 22

8 0

3 years ago

M(6,5) is the mid-point of the straight line joining A(2 , 3) to the

charle [14.2K]

Given :

M(6,5) is the mid-point of the straight line joining A(2 , 3) to the

point B.

To Find :

The coordinates of B.

Solution :

Let, coordinates of point B is ( h , k ) .

It is given that M is the mid - point of the straight line joining points A and B.

Coordinates of M is given by :

$M = (\dfrac{2+h}{2},\dfrac{3+k}{2})\\\\(6,5 ) = (\dfrac{2+h}{2},\dfrac{3+k}{2})\\\\\dfrac{2+h}{2} = 6 \ , \ \dfrac{3+k}{2} = 5\\\\h = 10 \ ,\ k = 7$

Therefore, coordinates of point B is ( 10 , 7 ).

7 0

3 years ago

M-9=21 <br> m=30 <br> is what i got

Stels [109]

That's correct! :) Well done! (M=30)
so M-9=21
would just be 30 - 9 = 21

5 0

3 years ago

Quadratics need help making parabola

timama [110]

Answer:

The equation of the parabola is $y = \frac{1}{3}\cdot x^{2}-\frac{4}{3}\cdot x -4$ , whose real vertex is $(x,y) = (2, -5.333)$ , not $(x,y) = (2, -5)$ .

Step-by-step explanation:

A parabola is a second order polynomial. By Fundamental Theorem of Algebra we know that a second order polynomial can be formed when three distinct points are known. From statement we have the following information:

$(x_{1}, y_{1}) = (-2, 0)$ , $(x_{2}, y_{2}) = (6, 0)$ , $(x_{3}, y_{3}) = (0, -4)$

From definition of second order polynomial and the three points described above, we have the following system of linear equations:

$4\cdot a -2\cdot b + c = 0$ (1)

$36\cdot a + 6\cdot b + c = 0$ (2)

$c = -4$ (3)

The solution of this system is: $a = \frac{1}{3}$ , $b = - \frac{4}{3}$ , $c = -4$ . Hence, the equation of the parabola is $y = \frac{1}{3}\cdot x^{2}-\frac{4}{3}\cdot x -4$ . Lastly, we must check if $(x,y) = (2, -5)$ belongs to the function. If we know that $x = 2$ , then the value of $y$ is:

$y = \frac{1}{3}\cdot (2)^{2}-\frac{4}{3}\cdot (2) - 4$

$y = -5.333$

$(x,y) = (2, -5)$ does not belong to the function, the real point is $(x,y) = (2, -5.333)$ .

5 0

3 years ago