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Ksju [112]
3 years ago
6

Which expression is equivalent to the expression below? StartFraction 6 c squared 3 c Over negative 4 c 2 EndFraction divided by

StartFraction 2 c 1 Over 4 c minus 2 EndFraction.
Mathematics
1 answer:
Fudgin [204]3 years ago
7 0

The given equation (6c^2+3c)/(-4c+2)\div (2c+1)/(4c-2) is equivalent to the expression -3c.

Given that, the expression can be written as.

(6c^2+3c)/(-4c+2)\div (2c+1)/(4c-2)

By simplifying the above equation,

\dfrac{6c^2+3c}{-4c+2}\div \dfrac{2c+1}{4c-2}

By taking out the common terms from the equation,

\dfrac{3c(2c+1)}{2(-2c+1)}\div\dfrac{2c+1}{2(2c-1)}

By simplifying the above equation by cancel out the common factors.

\dfrac{3c}{-2c+1} \div \dfrac{1}{2c-1}

Now, by taking (-1) common from (-2c+1) we get,

\dfrac{3c}{-1(2c-1)} \div \dfrac{1}{2c-1}

By simplifying the above equation, we get the expression,

-3c

So the given equation (6c^2+3c)/(-4c+2)\div (2c+1)/(4c-2) is equivalent to the expression -3c.

For more details, follow the link given below.

brainly.com/question/1301963.

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Does anyone know this and if it is extraneous or not?
Anna11 [10]
Addd 4 to both sides
\sqrt{x+9}=5
sqare both sides
x+9=25
minus 9 both sides
x=16

plug it in for x and see
\sqrt{16+9}-4=1
\sqrt{25}-4=1
5-4=1
1=1
true

not extraneous
an extraneous root would be x=-34
5 0
3 years ago
Rectangle ABCD with coordinates A(1, 1), B(4, 1), C(4, 2), and D(1, 2) dilates with respect to the origin to give rectangle A'B'
Virty [35]

Scale factor is a ratio. The correct option is C.

<h3>How are scale drawings formed?</h3>

For a particular scale drawing, it is already specified that all the measurements' some constant scaled version will be taken. For example, let the scale be K feet to s inches.

Then it means

\rm 1\:  ft : \dfrac{s}{k}\:  in.

All feet measurements will then be multiplied by s/k to get the drawing's corresponding lengths.

The length of AB can be written as,

AB = √[(1-4)²+ (1-1)²]

AB = 3

Since the length A'B' is 6 units, therefore, the scale factor will be,

Scale factor = (Length after transformation)/(Length before transformation)

Scale factor = 6 /3 = 2

Hence, the correct option is C.

Learn more about Scale factors:

brainly.com/question/8765466

#SPJ1

8 0
2 years ago
Solve the equation by graphing. If exact roots cannot be found, state the consecutive integers between which the roots are locat
zavuch27 [327]

Answer:

The equation contains exact roots at x = -4 and x = -1.

See attached image for the graph.

Step-by-step explanation:

We start by noticing that the expression on the left of the equal sign is a quadratic with leading term x^2, which means that its graph shows branches going up. Therefore:

1) if its vertex is ON the x axis, there would be one solution (root) to the equation.

2) if its vertex is below the x-axis, it is forced to cross it at two locations, giving then two real solutions (roots) to the equation.

3) if its vertex is above the x-axis, it will not have real solutions (roots) but only non-real ones.

So we proceed to examine the vertex's location, which is also a great way to decide on which set of points to use in order to plot its graph efficiently:

We recall that the x-position of the vertex for a quadratic function of the form f(x)=ax^2+bx+c is given by the expression: x_v=\frac{-b}{2a}

Since in our case a=1 and b=5, we get that the x-position of the vertex is: x_v=\frac{-b}{2a} \\x_v=\frac{-5}{2(1)}\\x_v=-\frac{5}{2}

Now we can find the y-value of the vertex by evaluating this quadratic expression for x = -5/2:

y_v=f(-\frac{5}{2})\\y_v=(-\frac{5}{2} )^2+5(-\frac{5}{2} )+4\\y_v=\frac{25}{4} -\frac{25}{2} +4\\\\y_v=\frac{25}{4} -\frac{50}{4}+\frac{16}{4} \\y_v=-\frac{9}{4}

This is a negative value, which points us to the case in which there must be two real solutions to the equation (two x-axis crossings of the parabola's branches).

We can now continue plotting different parabola's points, by selecting x-values to the right and to the left of the x_v=-\frac{5}{2}. Like for example x = -2 and x = -1 (moving towards the right) , and x = -3 and x = -4 (moving towards the left.

When evaluating the function at these points, we notice that two of them render zero (which indicates they are the actual roots of the equation):

f(-1) = (-1)^2+5(-1)+4= 1-5+4 = 0\\f(-4)=(-4)^2+5(-4)_4=16-20+4=0

The actual graph we can complete with this info is shown in the image attached, where the actual roots (x-axis crossings) are pictured in red.

Then, the two roots are: x = -1 and x = -4.

5 0
3 years ago
Draw a line from each rectangular prism to its matching group of face shapes
IrinaK [193]
Can you put more information into this question
6 0
3 years ago
Read 2 more answers
Please help and thank you!
Stolb23 [73]

The conversion is

x =  r \cos \theta

y = r \sin \theta

So

\dfrac y x = \tan \theta

We're given the fairly unusual

\theta = -\frac 5 2

It's fairly unusual because usually an angle is given in degrees or radians, and typically the radians are a fraction times pi. We'll assume radians.

\dfrac y x = \tan \theta = \tan(-5/2) \approx 0.747

Ah, there's our .75. The approximate answer is

y = 0.75 x

Third choice.

The exact answer is

y = x \tan( -\frac 5 2)

also a line through the origin.

3 0
3 years ago
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