Answer:
a)1400 + 300x ≤ 5000
b) x ≤ 12 days
Step-by-step explanation:
a) Since the grocery store owner wants to stay within budget then, this means he would be spending at most $5,000
The word at most is represented by the inequality sign ≤ = Less than or equal to
Let x = Number of days
Hence,
Our inequality equation is
$1400 + 300× x ≤ $5000
1400 + 300x ≤ 5000
b) Solving for x
1400 + 300x ≤ 5000
300x ≤ 5000 - 1400
300x ≤ 3600
x ≤ 3600/300
x ≤ 12 days
Find <span>tan<span>(<span><span>5π</span>12</span>)</span></span> and sin ((5pi)/12)
Answer: <span>±<span>(2±<span>√3</span>)</span>and±<span><span>√<span>2+<span>√3</span></span></span>2</span></span>
Explanation:
Call tan ((5pi/12) = t.
Use trig identity: <span><span>tan2</span>a=<span><span>2<span>tana</span></span><span>1−<span><span>tan2</span>a</span></span></span></span>
<span><span>tan<span>(<span><span>10π</span>12</span>)</span></span>=<span>tan<span>(<span><span>5π</span>6</span>)</span></span>=−<span>1<span>√3</span></span>=<span><span>2t</span><span>1−<span>t2</span></span></span></span>
<span><span>t2</span>−2<span>√3</span>t−1=0</span>
<span>D=<span>d2</span>=<span>b2</span>−4ac=12+4=16</span>--> <span>d=±4</span>
<span>t=<span>tan<span>(<span><span>5π</span>12</span>)</span></span>=<span><span>2<span>√3</span></span>2</span>±<span>42</span>=2±<span>√3</span></span>
Call <span><span>sin<span>(<span><span>5π</span>12</span>)</span></span>=<span>siny</span></span>
Use trig identity: <span><span>cos2</span>a=1−2<span><span>sin2</span>a</span></span>
<span><span>cos<span>(<span><span>10π</span>12</span>)</span></span>=<span>cos<span>(<span><span>5π</span>6</span>)</span></span>=<span><span>−<span>√3</span></span>2</span>=1−2<span><span>sin2</span>y</span></span>
<span><span><span>sin2</span>y</span>=<span><span>2+<span>√3</span></span>4</span></span>
<span><span>siny</span>=<span>sin<span>(<span><span>5π</span>12</span>)</span></span>=±<span><span><span>√<span>2+<span>√3</span></span></span>2</span></span></span>
Answer:
Step-by-step explanation:
2) let the two numbers be x and y
x-y =15
(taking x to be big)
x = 3 (y)+1
i.e. x-3y =1
Subtracting we get
2y =14 or y =7
x =15+7 =22
Larger number is 22 and smaller number is 7
-----------------------------------
Alysha is 2 years younger than Bryce/
Let Alysha be x years old then Bryce would be x+2
Sum of their ages
=x+x+2 =28
2x+2 =28
2x=26
x=13
Hence Alysha is 13 years old and Bryce 14 years old.
<h3>
Answer: 95 degrees</h3>
=======================================================
Explanation:
I recommend drawing it out to see what's going on. See the drawing below.
In the diagram, both angles are in the northeast corner of their four-corner configurations. They are both congruent corresponding angles. So that's why the second angle is also 95 degrees.
Side note: we could replace "northeast" with any of the other directions on the compass (such as southwest). All that matters is that they are in the same configuration.
