Which expression is equivalent to -3.5(4x – 3)? A. -3.9x – 3.2 B. -3.9x + 3.2 C. -14x + 10.5 D. -14x – 10.5
2 answers:
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Answer:
5)
Line 1:
Line 2:
6)
Line 1:
Line 2:
7)
See below
Step-by-step explanation:
To write the system of equations on the graph, you just need to write the 2 equations of the 2 lines.
5)
The first thing to do is find the slope of the lines. Pick one of them, and start by finding 2 points on that line that land perfectly on the grid.
It's pretty hard to read that top graph in the photo, but I think I see these ones marked:
Line 1: (0, 3) and (3, 0)
Line 2: (0, -3) and (2, 3)
Make sure I got them correct, because the equations will be wrong otherwise. Same for problem 6. To find the slope, divide the change in y by the change in x. Starting with line 1, y went from 3 to 0, so a change of -3. x went from 0 to 3, so a change of 3.
Divide the change in y by the change in x:
The slope of line 1 is -1. That means every time x increases by 1, y decreases by 1. You can see that on the line.
Now for line 2:
When x increases by 1, y increases by 3.
The last thing to do is find the y-intercept of both lines. That's just where the line intersects the y-axis, at x = 0, and it's clearly visible on the graph so there isn't much to do.
Line 1: 3
Line 2: -3
Now, you can write the equations for these lines in slope intercept form:
where m is the slope and b is the y-intercept we found above.
Line 1:
Line 2:
In line 1, -1x can be simplified to just -x.
6)
I'll do the exact same process here, but with less explaining. Let me know if you have any questions.
Find 2 points:
Line 1: (0, -2) and (4, 0)
Line 2: (0, 6) and (4, -4)
Find the slope of line 1:
and line 2:
Now, the y-intercepts:
Line 1: -2
Line 2: 6
Write the equations:
Line 1:
Line 2:
7)
A system with 1 solution means 2 lines that intersect at 1 point. Problems 5 and 6 are both examples of this. A system with no solution means lines that never intersect, meaning that they have the same slope, they're parallel.
Example:
Those both have a slope of 2, and if you graph them, you'll see that they never intersect.
A system with infinitely many solutions means they intersect at every possible point. These would just be the same line.
Example:
That's what they are, graph them however you like.
Answer:
.
Step-by-step explanation:
Start by separating this decimal number into its integer part and its fraction part:
The most challenging task here is to express as a proper fraction. Once that fraction is found, expressing the original number
will be as simple as rewriting a mixed number as an improper fraction.
Let .
would then represent the original number.
Note that the repeating digits appear in groups of two. Therefore, if the digits in are shifted to the left by two places, the repeating part will continue to match:
.
Note, that this "shifting" is as simple as multiplying the initial number by (same as
raised to the power of the number of digits that needs to be shifted.)
Subtract the original number from the shifted number to eliminate the fraction part completely:
.
In other words:
.
.
Therefore, the original number would be:
.
Answer:
Step-by-step explanation:
The given pair of angles lie on a line, hence they are classified as linear angles. They possess the property by which their sum is equal to 180°.