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allsm [11]
2 years ago
7

HELLO AND HELP ASAP PLZ HELP

Mathematics
1 answer:
Anit [1.1K]2 years ago
3 0

21+31=52
180-52=128
So the answer is A
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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
3 years ago
Enter the correct value so that each expression is a perfect square trinomial
myrzilka [38]

Answer:

Step-by-step explanation:

1). x² - 10x + a²

  By using the formula of (a - b)² = a² - 2ab + b²

  x² - 2(5)x + a²

  Therefore, for a perfect square of the expression a should be equal to 5.

  Therefore, (x² - 10x + 25) will be the answer.

2). x² + 2ax + 36

  = x² + 2(a)x + 6²

  For a perfect square of the given expression value of a should be 6.

   x² + 2(a)x + 6² = x² + 2(6)x + 6²

                           = (x + 6)²

  Therefore, x² + 12x + 36 will be the answer.

3). x^{2}+\frac{1}{2}x+a^2

    x^{2}+2(\frac{1}{4})x+a^2

   To make this expression a perfect square,

   a² = (\frac{1}{4})^2

   x^{2}+2(\frac{1}{4})x+(\frac{1}{4})^2 = (x+\frac{1}{4})^2

  Therefore, the missing number will be \frac{1}{16}.

5 0
3 years ago
You are riding on a zip line. Your speed is 15 miles per hour. What is your speed in feet per second?
natima [27]

Answer:

22 feet per second

Step-by-step explanation:

Hope this helps and have a wonderful day!!!

8 0
2 years ago
Read 2 more answers
use the numbers 1,3,4,6 exactly once with any basic math operation(multiplication,division,addition and subtraction) to total 24
drek231 [11]

Step-by-step explanation:

It is 4*6! We have to play with these numbers (1,3, and 4) to create 4, or we have to play with these numbers (1,3, and 6) to create 6.

If you divide 6 by 1/4, you will get 24.

If you divide 4 by 1/6, you will get 24.

How to create 1/4 from 1,3, and 4?

How to create 1/6 from 1,3, and 6?

Creating 1/4 from 1,3, and 4 is possible by doing this: 1–3/4, it is =1/4!

So, the answer is 6/[1–3/4]=24.

3 0
2 years ago
Read 2 more answers
Which number is a FACTOR of both 12 and 24? A) 8 B) 10 C) 12 D) 18
timama [110]
A). 8 is a factor of 24 but not of12.

B). 10 is not a factor of 12 or 24.

C). Bingo.  12 is a factor of 12 and of 24.

D). 18 is not a factor of 12 or 24.
3 0
3 years ago
Read 2 more answers
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