Answer:
(A) m = –3 and b = –3
Step-by-step explanation:
If m=–3 and b=–3
The system of linear equations:
y = –3x + 5
y = mx + b
Becomes
y = –3x + 5 ......(i)
y = –3x – 3 .......(ii)
Notice that 5 is added to -3x in (i) and -3 is added to -3x in (ii) and both equals y. This is impossible. Thus the system has no solution.
Using proportions, it is found that:
- In an 8-hour day, she keys 48 pages.
- For a day, her gross earnings are of $72.
- For a week, her gross earnings are of 72 x 7 = $504.
<h3>Proportions:</h3>
This question is solved using the proportions given, which are:
- Payment of $1.50 per page of 30 lines.
- Retha keys 6 pages per hour.
Hence, in an 8-hour day, she keys 6 x 8 = 48 pages.
Since she earns $1.50 per page, for a day, her gross earnings are of 48 x 1.5 = $72.
Considering a week has 7 days, for a week, her gross earnings are of 72 x 7 = $504.
To learn more about proportions, you can take a look at brainly.com/question/24372153
<span>The answers to this problem are:<span>(<span>±5</span></span>√3/8,±5/8)<span>Here is the solution:
Step 1: <span><span><span>x2</span>+<span>y2</span>=<span>2516</span>[2]</span><span><span>x2</span>+<span>y2</span>=<span>2516</span>[2]</span></span>
Step 2: Substitute:<span>
</span><span><span>8<span><span>(<span>25/16</span>)^</span>2</span>=25(<span>x^2</span>−<span>y^2</span>)
</span><span>8<span><span>(<span>25/16</span>)^</span>2</span>=25(<span>x^2</span>−<span>y^2</span>)</span></span>
</span><span>x^2</span>−<span>y^2</span>=<span>25/32</span><span>.
Add [2] and [3]:<span>
</span><span>2<span>x^2</span>=<span>75/32
</span><span>x^2</span>=<span>75/74</span></span>
<span>x=±5</span></span>√3/8<span>
Substitute into [2]:<span>
</span><span><span>75/64</span>+<span>y^2</span>=<span>50/32
</span><span>y^2</span>=<span>25/64</span></span>
<span>y=±<span>5/8</span></span>
</span>
</span>
Prime factorization of 5·2·5=5^2·2
