Find the value of In(-7).

Solve the equation by graphing. If exact roots cannot be found, state the consecutive integers between which the roots are locat

eimsori [14]

Answer:

There are NO real roots for this equation. The only roots have imaginary parts and therefore cannot be represented on the real x-axis.

Step-by-step explanation:

We notice that the expression on the left of the equation is a quadratic with leading term $2x^2$ , which means that its graph is that of a parabola with branches going up.

Therefore, there can be three different situations:

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

2) if its vertex is below the x-axis, the parabola's branches are 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 have NO 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 $a=2$ and $b=-3$ , we get that the x-position of the vertex is:

$x_v=\frac{-b}{2a}\\x_v=\frac{-(-3)}{2(2)}\\x_v=\frac{3}{4}$

Now we can find the y-value of the vertex by evaluating this quadratic expression for x = 3/4:

$y_v=f(\frac{3}{4})=2( \frac{3}{4})^2-3(\frac{3}{4})+4\\f(\frac{3}{4})=2( \frac{9}{16})-\frac{9}{4}+4\\f(\frac{3}{4})=\frac{9}{8}-\frac{9}{4}+4\\f(\frac{3}{4})=\frac{9}{8}-\frac{18}{8}+\frac{32}{8}\\f(\frac{3}{4})=\frac{23}{8}$

This is a positive value for y, therefore we are in the situation where there is NO x-axis crossing of the parabola's graph, and therefore no real roots.

We can though estimate a few more points of the parabola's graph in order to complete the graph as requested in the problem. For such we select a couple of x-values to the right of the vertex, and a couple to the right so we can draw the branches. For example: x = 1, and x = 2 to the right; and x = 0 and x = -1 to the left of the vertex:

$f(-1) = 2(-1)^2-3(-1)+4= 2+3+4=9\\f(0)=2(0)^2-3(0)+4=0+0+4=4\\f(1)=2(1)^2-3(-1)+4=2-3+4=3\\f(2)=2(2)^2-3(2)+4=8-6+4=6$

See the graph produced in the attached image.

4 0

3 years ago

josh is on his way home in his car. He has driven 18 miles so far,which is two- thirds of the way home, what is the total length

marta [7]

In order to do this problem:
Divide
18/(2/3)=
27
The answer is 27 miles

6 0

3 years ago

Let’s say the area of the map is 21 square inches. You want to make an enlarged map of Central Park to take with you on your jou

poizon [28]

Answer:

You could multiply 21*21=441 if its a square

Step-by-step explanation:

5 0

3 years ago

A particular brand of gasoline has a density of 0.737 g/ml at 25 ∘c. how many grams of this gasoline would fill a 13.4 gal tank

ruslelena [56]

Given, the density of a particular brand of gasoline = 0.737 g/ml.

13.4 gallon of tank given. We have to find the mass of gasoline to fill the tank.

First we will convert 13.4 gallon to ml.

We know that 1 gallon = 3.78541 litre

And 1 litre = 1000 ml

So we can write 1 gallon = $(3.78541)(1000) ml$ = 3785.41 ml.

13.4 gallon = $(3785.41)(13.4)$ ml = 50724.494 ml.

Let's take there is x grams of gasoline

We know that density = (mass/ volume) = $\frac{x}{50724.494}$

So we can write,

$0.737 =\frac{x}{50724.494}$

To find x we will multiply both sides by 50724.494. we will get,

$(0.737)(50724.494) =(\frac{x}{50724.494}) (50724.494)$

$(0.737)(50724.494) = x$

$37383.95 = x$

So we have got the required answer.

Mass of gasoline = 37383.95 grams.

5 0

4 years ago

Consider the statement: “In a triangle, the measure of an

Lerok [7]

Answer:

See the example given in the picture attached.

Step-by-step explanation:

No options are given, so I made my own example. In the picture attached, we can see that the measure of the exterior angle A is less than the measure of the adjacent interior angle B.

5 0

3 years ago