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tatuchka [14]
3 years ago
8

PLEASE HELP ME SOON!

Mathematics
2 answers:
exis [7]3 years ago
5 0
The answer is D. <1 and <5
timama [110]3 years ago
4 0
The answer is C angle 1 and 4 
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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
2 years ago
What is this equation written in slope-intercept form (y=mx+b)?
LuckyWell [14K]

Answer:

Y=2/3 -3

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
Hey guys how do I stop crying my favorite teacher left yesterday for five months for the military he always is by my side and he
NeX [460]

Answer:

Step-by-step explanation:

I understand you hardships your going through. I believe you feel like you've lost your best friend, and I have gone through a similar experience when I was in 7th grade.

What I did was I wrote a journal everyday to let my teachers see my English improving day by day (he was my English teacher), because I wanted him to be proud of my progress once he came back.

This made me motivated to see how much time was left for my to see him coming back! I hope this helps.

6 0
3 years ago
Which certificate does Jenny require?
Airida [17]
Can you give some more details please thank you
7 0
3 years ago
3. Hi
butalik [34]

Answer:

D. linear; y = – 3x –6

Step-by-step explanation:

Answer:

Option (2).

Step-by-step explanation:

From the figure attached,

Since there is a common difference in each successive term and previous term of y,

y_{2}-y_{1}=-9-(-6)

          = -3

y_{3}-y_{2}=-12-(-9)

          = -3

Therefore, this data represents a linear equation.

Now we choose two points from the table given.

Let the points are (0, -6) and (1, -9)

Slope of this line 'm' = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}

m = \frac{-9+6}{1-0} = -3

Y-intercept 'b' = -6

Equation of the line will be,

y = -3x - 6

Option (2) will be the answer.

Answer: The correct answer is c

Step-by-step explanation: you would have to plot your graph and the put the answer in slop intercept for y=mx+b or y=-3x-6

Answer:

exponential; y = –6 • 1.5x

Step-by-step explanation:

1.5 x 1 = 1.5

1.5x-6= -9

5 0
2 years ago
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