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mestny [16]
3 years ago
14

HELP 40 POINTS

Mathematics
1 answer:
Tom [10]3 years ago
7 0
Answer: the function g(x) has the smallest minimum y-value.


Explanation:


1) The function f(x) = 3x² + 12x + 16 is a parabola.


The vertex of the parabola is the minimum or maximum on the parabola.


If the parabola open down then the vertex is a maximum, and if the parabola open upward the vertex is a minimum.


The sign of the coefficient of the quadratic term tells whether the parabola opens upward or downward.


When such coefficient is positive, the parabola opens upward (so it has a minimum); when the coefficient is negative the parabola opens downward (so it has a maximum).


Here the coefficient is positive (3), which tells that the vertex of the parabola is a miimum.


Then, finding the minimum value of the function is done by finding the vertex.

I will change the form of the function to the vertex form by completing squares:

Given: 3x² + 12x + 16

Group: (3x² + 12x) + 16
Common factor: 3 [x² + 4x ] + 16
Complete squares: 3[ ( x² + 4x + 4) - 4] + 16
Factor the trinomial: 3 [(x + 2)² - 4] + 16
Distributive property: 3 (x + 2)² - 12 + 16
Combine like terms: 3 (x + 2)² + 4

That is the vertex form: A(x - h)² + k, whch means that the vertex is (h,k) = (-2, 4).


Then the minimum value is 4 (when x = - 2).


2) The othe function is <span>g(x)= 2 *sin(x-pi)
</span>

The sine function goes from -1 to + 1, so the minimum value of sin(x - pi) is - 1.


When you multiply by 2, you just increased the amplitude of the function and obtain the new minimum value is 2 (-1) = - 2


Comparing the two minima, you have 4 vs - 2, and so the function g(x) has the smallest minimum y-value.

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Nadusha1986 [10]

Answer:

The system has one solution.

Both lines have the same y-intercept.

The solution is the intersection of the 2 lines.

Step-by-step explanation:

Lines are

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       slope = 0.5

       y intercept(put x =0) =5

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      slope = 1

       y intercept(put x =0 ) =5

Both are linear equation thus they have only one solution. Also two non parallel lines meet only at one point.

If you solve these linear equation coordinate of  point of intersection of line on graph will come.

4 0
3 years ago
Simplify the square root of 10000 using powers of 10.
Alexxandr [17]

Answer:

square 10 to the 4th power but you have to divide it into 2 so it will be 10 to the 2nd power

hope this helps

4 0
2 years ago
What is the equation of the line that passes through the given points in slope-intercept form? (-2,3) and (-3,-4)
Orlov [11]

Step-by-step explanation:

The equation of a line is typically written as y=mx+b where m is the slope and b is the y-intercept. If you know two points that a line passes through, this page will show you how to find the equation of the line.

6 0
2 years ago
Write 0.00000000018 in a scientific notation
Ugo [173]

Answer:

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Step-by-step explanation:

To find the number in scientific notation you want to find how many times you have to move the decimal to get the decimal to be right after the first non-zero number. If you move to the left the exponent is positive and if you move it to the right the exponent is negative. The answer would be 1.8*10^{-10}.

6 0
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How do you find the size of angle B?
Vitek1552 [10]

the sum of the interior angles is 180° (triangles)

it's isosceles, 2 equal sides and 2 equal angles.

you take away the given angle from 360° and you will find the sum of the 2 equal sides, you divide by 2 and you have the angle b (equal to angle C).


(180 - 72) : 2  =

108 : 2 = 54° (your answer)

-----------------------

72 + 54 + 54 = 180°

The answer is good.

6 0
3 years ago
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