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Marina86 [1]
3 years ago
6

Explain how you used mental math

Mathematics
2 answers:
andriy [413]3 years ago
4 0
Addition, I would use the principles of addition. 
DIA [1.3K]3 years ago
4 0
Addition is the correct answer
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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
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
From the top of a building 42 feet high, the angle of depression to a car stopped on the ground is 27 degrees. What is the dista
lions [1.4K]

Answer: it equals to 82

Step-by-step explanation:

3 0
3 years ago
Can you help me plz i will give you brainly its
hodyreva [135]
The answer is 3.5 + 1.5x = 12.5. So the answer would be C.
4 0
2 years ago
How do you write 3x to the -5 power using only positive exponents?
Inga [223]
Negative:

(3x)^-5

Positive:

(1/3x)^5



4 0
2 years ago
What is the area? <br> Possible Answers: 24m^2, 30m^2, 20m^2, 120m^2
attashe74 [19]

Answer:

24m^2, I think.

Step-by-step explanation:

Well the area is Base times Height, so 6 times 4, the squared is just showing that its the area.

8 0
3 years ago
Read 2 more answers
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