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3 years ago

Find the solutions to the equation below. Check all that apply. 4x2 + 4x + 1 = 0

Mathematics

1 answer:

Verizon [17]3 years ago

4 0

Answer:

The solution for the given polynomial $4x^2 + 4x+ 1 = 0$ is $x = (\frac{-1}{2})$

Step-by-step explanation:

Here, the given quadratic equation is : $4x^2 + 4x+ 1 = 0$

Now, here solving the given equation by SPLITTING THE MIDDLE TERM:

$4x^2 + 4x+ 1 = 0 = 4x^2 + 2x+ 2x + 1 = 0\\\implies 2x( 2x + 1) + 1(2x + 1) = 0\\\implies (2x +1)(2x +1) = 0\\$

⇒ either (2x+1) = 0, or ( 2x + 1) = 0

⇒ x = -1/2 or x = -1/2

Here, in both the cases, the value of x is equal i.e x = -1/2

So, the given function has TWO IDENTICAL ROOTS.

Hence the solution for the given polynomial $4x^2 + 4x+ 1 = 0$ is $x = (\frac{-1}{2})$

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Which equation shows the relationship between the volume, (V) of the prism and its height (h)?

denis-greek [22]

Answer:

h = V/lw

Step-by-step explanation:

We know the formula for the volume of a rectangular prism is V = lwh. We need to use this equation and solve for h by dividing lw on both sides.

V = lwh

V/lw = h

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3 years ago

M-3x=2x+p Solve for x

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3 years ago

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A student saves $3 dollars on August 1, $5 on August 2, $7 on August 3, and so on. How much will she save in August 20 ?

Delvig [45]

Here is your answer

Money saved on each successive day is-

$3, &5, $7....

Clearly it forms an AP,

where

a1= 3

common difference, d= 2

n=20

So,

using formula

Tn= a1+(n-1)d

T20= 3+(20-1)2

= 3+ 19×2

= 3+ 38

=41

So, money saved on August 20= $41

Sum of money saved upto August 20 =
n/2 (a1+T20)
= 20/2 (3+41)
= 10× 44
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3 years ago

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The relationship between V, the value of his car, in dollars, and t, the elapsed time, in years, since he

Sergio [31]

Answer:

t = -24*log(2/3)

Step-by-step explanation:

The expression is:

V = 22,500*10^(-t/12)

Replacing with V = 10,000 and isolating t, we get:

10,000 = 22,500*10^(-t/12)

10,000/22,500 = 10^(-t/12)

4/9 = 10^(-t/12)

(2/3)² = 10^(-t/12)

2*log(2/3) = -t/12

-12*2*log(2/3) = t

t = -24*log(2/3)

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2 years ago

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Compare the two graphs and explain the transformation that was applied to f(x) in order to look exactly like the graph of g(x).

Neporo4naja [7]

The two graphs are represented below.

Answer and Step-by-step explanation: One graph can "transform" into another through changes in the function.

There are 3 ways to change a function:

Shifting: it adds or subtracts a constant to one of the coordinates, thus changing the graph's location. When the y-coordinate is added or subtract and the x-coordinate is unchanged, there is a vertical shift. If it is the x-coordinate which changes and y-coordinate is kept the same, the shift is a horizontal shift;
Scaling: it multiplies or divides one of the coordinates by a constant, thus changing position and appearance of the graph. If the y-coordinate is multiplied or divided by a constant but x-coordinate is the same, it is a vertical scaling. If the x-coordinate is changed by a constant and y-coordinate is not, it is a horizontal scaling;
Reflecting: it's a special case of scaling, where you can multiply a coordinate per its opposite one;

Now, the points for f(x) are:

(-5,0) (0,6) (5,-4) (8,0)

And the points for g(x) are:

(-5,-3) (0,-9) (5,1) (8,-3)

Comparing points:

(-5,0) → (-5,-3)

(0,6) → (0,-9)

(5,-4) → (5,1)

(8,0) → (8,-3)

It can be noted that x-coordinate is kept the same; only y-coordinate is changing so we have a vertical change. Observing the points:

(-5,0-3) → (-5,-3)

(0,6-15) → (0,-9)

(5,-4+5) → (5,1)

(8,0-3) → (8,-3)

Then, the vertical change is a Vertical Shift.

Another observation is that y-coordinate of f(x) is the opposite of g(x). for example: At the second point, y-coordinate of f(x) is 6, while of g(x) is -9. So, this transformation is also a Reflection.

Range of a function is all the values y can assume after substituting the x-values.

Domain of a function is all the values x can assume.

Reflection doesn't change range nor domain of a function. However, vertical or horizontal translations do.

Any vertical translation will change the range of a function and keep domain intact.

Then, for f(x) and g(x):

graph translation domain range

f(x) none [-5,8] [-4,6]

g(x) vertical shift [-5,8] [-9,1]

In conclusion, this transformation (or translation) will affect the range of g(x)

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2 years ago