Answer:
O is in between m and p so it is 6
Step-by-step explanation:
In the figure below, O is between M and P, and N is the midpoint of MO. If =MP16 and =NO4, find OP.
1. The additive identity is 0. This is because adding 0 to anything leads to the same value. Example: 0+3 = 3.
2. An equation is where you have two expressions separated by an equal sign. In your case it would be "a mathematical sentence whose verb is 'equal' (=)"
3. The multiplicative identity is 1. Multiply 1 with any number and the result is that same number. Example: 1*7 = 7.
4. An open sentence is an equation that contains one or more variables. An example would be x+2 = 4. The reason why we call it open is because the true or false nature of the sentence is up in the air until we know what x is. If we knew that x = 3 for instance, then x+2 = 4 would be false since 3+2 = 4 is false. If we nailed down what x was then it would go from open to closed.
5. The symmetric property is that if a = b then b = a. Think of a mirror how the image reverses.
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)
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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.
9514 1404 393
Answer:
C. 78°
Step-by-step explanation:
The sum of angles in a triangle is 180°.
(7x-6)° +(4x+11)° +43° = 180°
11x +48 = 180 . . . . . divide by °, simplify
11x = 132 . . . . . . . subtract 48
x = 12 . . . . . . . divide by 11
Then the measure of angle T is ...
∠T = (7x -6)° = (7(12) -6)°
∠T = 78°
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The vertices of a polygon are given as follows: P(-2,4), Q(4,2), R(4,0); S(-12,0); k = 0.5 Find the coordinates of the vertex P' of the image after a dilation having the given scale factor. Type your answers as a coordinate pair in this format: (x,y)</span>
