All categories

3 years ago

Solve 9x^2 + 42x + 49 = 0

1 answer:

3 0

Because of the relatively large coefficients {9, 42, 49}, applying the quadratic formula would be a bit messy. Instead, I've chosen to "complete the square:"

9x^2 + 42x + 49 = 0 can be re-written as 9 [ x^2 + (42/9)x ] = -49

Dividing both sides by 9, we get [ x^2 + (42/9)x ] = - 49/9

Completing the square: [ x^2 + (42/9)x + (21/9)^2 - (21/9)^2 ] = -49/9

[ x + 21/9 ]^2 = 441/81 - 441/81 = 0

Then [ x + 21/9 ] = 0, and x = -21/9 (this is a double root).

You might be interested in

Mark bought a notebook for $1.45 and some pencils for $0.42 each. If the total cost was $6.91, how many pencils did he buy?

Lesechka [4]

B - 13

Okay, we know that Mark brought 1 notebook and the totally is 6.91 while one pencil costs $0.42.

x= number of pencils he brought.
we know the price of 1 notebook + the cost of pencils times the numbers of pencils he brought = total cost.

So the equation will be:

1.45 + 0.42x = 6.91 subtract 1.45 on both sides.
0.42x = 5.46 Then we solve for x by dividing both sides by 0.42
x= 13

So the number of pencils he brought is 13.

5 0

2 years ago

Read 2 more answers

A diagram of a small shed is shown below, find the volume of the composite figure. 3m 6m 5m 5m 8m

Novay_Z [31]

Answer:

Step-by-step explanation:

3 0

3 years ago

4(x−3)=1/2(x/2+5) how many solutions

charle [14.2K]

I think it might be six, sorry if its wrong, but I hope its right!!

Hope this helps!!!!

love: Deku <3

7 0

2 years ago

1.94x - 10/8x + 4.32 = [2(1.15x+8.5)]

kipiarov [429]

$1,94x-\frac{10}{8}x+4,32=[2(1,15x+8,5)]\\\\
1,94x-1,25x+4,32=2,3x+17\\\\
0,69x+4,32=2,3x+17\ \ \ |Subtract\ 2,3x\\\\
-1,61x+4,32=17\ \ \ |Subtract\ 4,32\\\\
-1,61x=12,68\ \ \ |Divide\ by\ -1,61\\\\\boxed{x\approx7,9}
$

8 0

3 years ago

PLEASE HELP ASAP!!! CORRECT ANSWERS ONLY PLEASE!!! Graph g(x) = 3x^2 - 12x - 3

Paul [167]

Answer: Vertex = (2, -15) 2nd point = (0, -3)

Step-by-step explanation:

g(x) = 3x² - 12x - 3

= 3(x² - 4x - 1)

a=1 b=-4 c=-1

Find the x-value of the vertex by using the formula for the axis of symmetry: $x = \dfrac{-b}{2a}$

$x = \dfrac{-(-4)}{2(1)}$

$= \dfrac{4}{2}$

= 2

Find the y-value of the vertex by plugging the x-value (above) into the given equation: g(x) = 3x² - 12x - 3

g(2) = 3(2)² - 12(2) - 3

= 12 - 24 - 3

= -15

So, the vertex is (2, -15) ← PLOT THIS COORDINATE

Now, choose a different x-value. Plug it into the equation and solve for y. I chose x = 0

g(0) = 3(0)² - 12(0) - 3

= 0 - 0 - 3

= -3

So, an additional point is (0, -3) ← PLOT THIS COORDINATE

5 0

3 years ago