What is wrong in this

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

4. 46 is what percent of 69?

sergij07 [2.7K]

Answer:

66%(technically 0.66 repeating)

Step-by-step explanation:

We need to figure out what percentage of 69 equates to 46. In other words, we need to figure out what percentage <u>times</u> 69 equals 46:

$percentage*69 = 46$

Now that we formed this equation, we can solve for the percentage as if it was x.

First lets simplfy:

$percentage*69 = 46 -- > 69percentage = 46$

Now we can solve for x just by getting x alone, which means we must remove the coefficent. We can do this by dividing both sides of the equation by 69:

$percentage = \frac{46}{69}$

=

$percentage=0.66$

Putting this into the form of percentage, we must multiply by 100. Since, the percentage form of a decimal is 100 times bigger(moved up 2 decimal places):

$percentage = 0.66*100$

=

percentage = 66%

Hope this helps! :3

4 0

2 years ago

What is the explicit formula for this sequence?

ddd [48]

Answer:

$a_n=-7+4(n-1)$

or

$a_n=-7+(n-1)(4)$

Step-by-step explanation:

-7,-3,1,5,... is a arithmetic sequence.

Arithmetic sequences have a common difference. That is, it is going up by 4 each time.

When you see arithmetic sequence, you should think linear equation.

The point-slope form of a line is $y-y_1=m(x-x_1)$ .

m is the common difference, the slope.

Any they are using the point at x=1 in the point slope form. So they are using (1,-7).

So let's put this into our point-slope form:

$y-(-7)=4(x-1)$

$y+7=4(x-1)$

Subtract 7 on both sides:

$y=-7+4(x-1)$

So your answer is

$a_n=-7+4(n-1)$

6 0

3 years ago

Laura rents a movie for a flat fee of $2.00 plus an additional $0.50 for each night she keeps the movie. Choose the cost functio

daser333 [38]

Answer:

The cost function that represents this scenario is c(x) = 2 + 0.50x .

Option (b) is correct .

Step-by-step explanation:

As given

Laura rents a movie for a flat fee of $2.00 plus an additional $0.50 for each night she keeps the movie.

if x equals the number of nights Laura has the movie.

Than the cost function that represents this scenario .

c(x) = Flat fee + Cost for x equals the number of nights Laura has the movie.

c(x) = 2 + x × 0.50

c(x) = 2 + 0.50x

Therefore the cost function that represents this scenario is c (x) = 2 + 0.50x .

Option (b) is correct .

8 0

3 years ago

Read 2 more answers

Convert

ICE Princess25 [194]

Answer:

The correct option is A.

Step-by-step explanation:

The given number is

$\frac{5}{11}$

Where 5 is dividend and 11 is divisor.

Since dividend is less than divisor we add a decimal place and the first zero. Notice the decimal point which has appeared on the answer line and by the dividend. It does not appear anywhere else.

Now the dividend is 50. Divide the number by divisor.

$11\times 4=44$