Sorry about that, here's the answers.
1. expanded form
2. regroup
3. place value
4. A, C, D. The strategy I used was place value and regrouping. I chose these by using place value to help me understand how to regroup and what each option would sum to.
5. D. Ten thousands place
In this problem why is the easiest to substitute.
Just set the equations equal to each other because they both equal y
-x + 4 = 2x - 8
(You want to get all the x's to one side so add x to each side)
4 = 3x - 8
(next add 8 to both sides)
12 = 3x
(lastly divide 3 from both sides)
4 = x
You have got your x so now it is time to find that y just replace x to either of the two equations
y = 2(4) -8 or y = -(4) + 4
y = 8 - 8 y = 0
y = 0
Final Answer: y=0, x=4
The value maximizes angle APB.
In this question we need to determine the <em>maximum possible</em> angle APB, which can be determined by definition of dot product, that is to say:
(1)
Where:
- , - Magnitudes of and .
- - Internal angle, in sexagesimal degrees.
The magnitudes of each are respectively defined by line segment length formula: , ,
(2)
(3)
By (1), (2) and (3) we have the following expression:
(4)
From geometry we know that sum of internal angles in triangles equals 180°, which means that angle APB must meet this condition:
In addition, we know that <em>cosine</em> function is a bounded function between -1 and 1, where , ,
A quick approach consists in graphing (4) against x. Outcome is described in the second image attached. By direct inspection, we see that maximizes angle APB.
We kindly invite to check this question on optimization: brainly.com/question/4302495
No picture is shown can’t tell
B. 1/3 of the 24 problems remain. (8 is 1/3 of 24)