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3 years ago

I need an explanation for the problem 4v2=-12v-9. I don't understand why it factors into 4v+3 and 4v+3

Mathematics

1 answer:

kirza4 [7]3 years ago

7 0

Answer:

The factors are $2v+3,2v+3$ .

The factors are not $4v+3,4v+3$

Step-by-step explanation:

Equation is $4v^2=-12v-9$ .

This equation can be written as follows:

$4v^2+12v+9=0$

Here,

$12v=6v+6v$

Therefore,

$4v^2+6v+6v+9=0\\2v(2v+3)+3(2v+3)=0\\(2v+3)(2v+3)=0$

So, the factors are $2v+3,2v+3$ .

The factors are not $4v+3,4v+3$

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Which table represents a function? A 2-column table with 4 rows. The first column is labeled x with entries negative 3, 0, negat

tangare [24]

Answer:

This is a many-to-one function as the value of y = -1 corresponds to two values of x:

$\begin{array}{|c|c|}\cline{1-2} x & y\\\cline{1-2} -3 & -1\\\cline{1-2} 0 & 0\\\cline{1-2} -2 & -1\\\cline{1-2} 8 & 1\\\cline{1-2}\end{array}$

Step-by-step explanation:

Function

A special relationship where each input (x-value) has a single output (y-value).

A function is one-to-one if each value in the range (y-values) corresponds to exactly one value in the domain (x-values).

A function is many-to-one if some values in the range (y-values) correspond to more than one (many) value in the domain (x-values).

This is a many-to-one function as the value of y = -1 corresponds to two values of x:

$\begin{array}{|c|c|}\cline{1-2} x & y\\\cline{1-2} -3 & -1\\\cline{1-2} 0 & 0\\\cline{1-2} -2 & -1\\\cline{1-2} 8 & 1\\\cline{1-2}\end{array}$

This is not a function as the value of x = -5 corresponds to two values of y:

$\begin{array}{|c|c|}\cline{1-2} x & y\\\cline{1-2} -5 & -5\\\cline{1-2} 0 & 0\\\cline{1-2} -5 & 5\\\cline{1-2} 6 & -6\\\cline{1-2}\end{array}$

This is not a function as the value of x = -2 corresponds to two values of y:

$\begin{array}{|c|c|}\cline{1-2} x & y\\\cline{1-2} -4 & 8\\\cline{1-2} -2 & 2\\\cline{1-2} -2 & 4\\\cline{1-2} 0 & 2\\\cline{1-2}\end{array}$

This is not a function as the value of x = -4 corresponds to two values of y:

$\begin{array}{|c|c|}\cline{1-2} x & y\\\cline{1-2} -4 & 2\\\cline{1-2} 3 & 5\\\cline{1-2} 1 & 3\\\cline{1-2} -4 & 0\\\cline{1-2}\end{array}$

8 0

2 years ago

1. An account is opened with a balance of $2800earning 4.25% simple interest. What will be thebalance in the account in 30 years

JulijaS [17]

Answer:

$6370

Explanation:

The simple interest formula gives us the final amount A given the principal amount P:

$A=P(1+rt)$

where r is the interest rate and t is the time interval.

Now in our case we have

P = 2800

r = 4.25/100

t = 30 years

therefore, the above formula gives

$A=2800(1+\frac{4.25}{100}\cdot30)$

which simplifies to give

$\boxed{A=\$6370}$

Hence, the account balance after 30 years will be $6370.

7 0

1 year ago

The Morales family is remodeling their home. They want to remove the wall between the living room. and dining room to make one b

GuDViN [60]

Answer:

Area of living room

= 20(x+5)

= 20x +100

Area of dining room= 20x

Total area

= 20x +100 +20x

= 40x +100

Total perimeter (after wall is removed)

= 2(20) + 2( x+x+5)

= 40 + 2(2x+5)

= 40 +4x +10 (expand)

= 4x +50 (simplify)

Step-by-step explanation:

Area of rectangle= length × breadth

3 0

3 years ago

Help pleaseeeeeeeeeee

vova2212 [387]

Answer:

B & C

Step-by-step explanation:

The two binomials are equal to zero to find the roots.

Hope this helps

6 0

2 years ago

If the coordinates of the endpoints of a diameter of the circle are known, the equation of a circle can be found. First, find

Evgesh-ka [11]

Answer:

The equation of the circle is $(x+3)^2+(y-5)^2 = 17$

Step-by-step explanation:

The complete question is

If the coordinates of the endpoints of a diameter of the circle are known, the equation of a circle can be found. First, find the midpoint of the diameter, which is the center of the circle. Then find the radius, which is the distance from the center to either endpoint of the diameter. Finally use the center-radius form to find the equation.

Find the center-radius form of the circle having the points (1,4) and (-7,6) as the endpoints of a diameter.

Consider that, if both points are the endpoints of a diameter, the center of the circle is the point that is exactly in the middle of the two points (that is, the point whose distance to each point is equal). Given points (a,b) and (c,d), by using the distance formula, you can check that the middle point is the average of the coordinates. Hence, the center of the circle is given by

$(\frac{1-7}{2}, \frac{4+6}{2}) = (-3,5)$ .

We will find the radius. Recall that the radius of the circle is the distance from one point of the circle to the center. Recall that the distance between points (a,b) and (c,d) is given by $\sqrt[]{(a-c)^2+(b-d)^2}$ . So, let us use (1,4) to calculate the radius.

$r = \sqrt[]{(1-(-3))^2+(4-5)^2} = \sqrt[]{17}$ .

REcall that given a point $(x_0,y_0)$ . The equation of a circle centered at the point $(x_0,y_0)$ is

$(x-x_0)^2+(y-y_0)^2 = r^2$

In our case, $(x_0,y_0)=(-3,5)$ and $r=\sqrt[]{17}$ . Then, the equation is

$(x-(-3))^2+(y-5)^2 = (x+3)^2+(y-5)^2 = 17$

4 0

3 years ago