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Fed [463]
3 years ago
15

Find the minimum value of the function f(x) = x2 + 5x – 6

Mathematics
1 answer:
Klio2033 [76]3 years ago
6 0

So the easiest method to find the vertex (the minimum in this case) to do this is to find the axis of symmetry, then plug it into the function.

Firstly, the equation to find the axis of symmetry is x=\frac{-b}{2a} , with b = x coefficient and a = x^2 coefficient. The equation equation can be solved as such:

x=\frac{-5}{2*1}\\\\x=\frac{-5}{2}\\\\x=-2.5

Since the vertex falls on the axis of symmetry, we know that the x-coordinate of the vertex is -2.5. Now to solve for the y-coordinate, plug in x with -2.5 and solve as such:

f(-2.5)=(-2.5)^2+5*(-2.5)-6\\ f(-2.5)=6.25+(-12.5)-6\\ f(-2.5)=-12.25

Now putting it all together, our minimum value (vertex) is (-2.5,-12.25).

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What is the approximate value of b, rounded to the nearest tenth? Use the law of sines to find the answer.
vivado [14]

You can use the Law of Sines for this problem, but what makes it tough at first glance is that they put a step in before you can use it directly. That first step is to get m∠C. When solving a triangle, always get the third angle if you know the other two so that you can use the Law of Sines (or Law of Cosines) more directly.


The sum of the angles of any triangles is 180°. We know the measures of the two other angles. So we subtract them from 180° to find that third angle.


180° - 76° - 66° = 38°


Now we can use the proportion from the picture. Angle B measures 76°, side b is our unknown, Angle C measures 38°, and side c measures 3 units.


sin 76° sin 38°

----------- = -----------

b 3


Cross multiply to find b (the side). We carry out five places in these calculations to get more accuracy.


3 * sin 76° = b * sin 38°


b = 3 * sin 76° 3 * 0.56611 1.69832

--------------- = --------------- = ---------------- = 5.73044

sin 38° 0.29636 0.29636


To the nearest tenth, b - 5.7 units.

3 0
4 years ago
Read 2 more answers
The product of x and 8 is not less than 16
Marrrta [24]

Answer:

x ≥ 2

Step-by-step explanation:

The inequality would be: <em>x * 8 ≥ 16</em>

8x ≥ 16

x ≥ 16/8

<u>x ≥ 2</u>

Hope this helps!

5 0
3 years ago
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Which set of side lengths is a Pythagorean triple??? Please help
kodGreya [7K]

Answer:

C) 9,40,41

Step-by-step explanation:

Pythagorean triple is when a²+b²=c²

A) 1,3,10

  • 1+9=100 - incorrect

B) 4,5,9

  • 16+25=81- incorrect

C) 9,40,41

  • 81+1600= 1681- correct

D) 16,30,44

  • 256+900= 1936- incorrect
4 0
3 years ago
2 ( x-4 ) = 5/6 ( x+6 ) -6
givi [52]
Hopes this helps:

Answer: x = 6
3 0
3 years ago
What is the commutative, associative, and distributive property of 3a plus 5a plus 2b
anyanavicka [17]
Question: What is the commutative, associative, and distributive property of 3a plus 5a plus 2b0.


Answer:Defintion of  Commutative property holds for both addition and multiplication. That is: the operations addition and multiplication are commutative over the set of real numbers. That means, for any two real numbers x and. y, x + y = y + x and xy = yx. Definiton of associative In mathematics, the associative property is a property of some binary operations. In propositional logic, associativity is a valid rule of replacement for expressions in logical proofs and distrive property means The Distributive Property is an algebra property which is used to multiply a single term and two or more terms inside a set of parentheses. I really hope this helped thx for the question!
5 0
3 years ago
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