Answer:
<h2>x > -5</h2>
Step-by-step explanation:
-5(x + 7) < -10 <em>use the distributive property </em><em>a(b + c) = ab + ac</em>
(-5)(x) + (-5)(7) < -10
-5x - 35 < -10 <em>add 35 to both sides</em>
-5x < 25 <em>change the signs</em>
5x > - 25 <em>divide both sides by 5</em>
x > -5
If you decrease something by 4 percent,
you are keeping (100% - 4%) or 96% of the original
so multiply by the original amount by 96 percent or .96
If you have 100 pennies, and you give 4 away ( 4 percent decrease), you still have 96 pennies. You are keeping 96 percent of what you started with. This works no matter how much you start with.
Example:
you have 40 dollars
4% decrease
40 * .04 = 1.6 take this away
40 - 1.6 = 38.4 left
you keep 96 percent
40 * .96 = 38.4 left
Answer:
m
2
−2m+3
Step-by-step explanation:
<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>
Alrighty
squaer base so length=width, nice
v=lwh
but in this case, l=w, so replace l with w
V=w²h
and volume is 32000
32000=w²h
the amount of materials is the surface area
note that there is no top
so
SA=LW+2H(L+W)
L=W so
SA=W²+2H(2W)
SA=W²+4HW
alrighty
we gots
SA=W²+4HW and
32000=W²H
we want to minimize the square foottage
get rid of one of the variables
32000=W²H
solve for H
32000/W²=H
subsitute
SA=W²+4WH
SA=W²+4W(32000/W²)
SA=W²+128000/W
take derivitive to find the minimum
dSA/dW=2W-128000/W²
where does it equal 0?
0=2W-1280000/W²
128000/W²=2W
128000=2W³
64000=W³
40=W
so sub back
32000/W²=H
32000/(40)²=H
32000/(1600)=H
20=H
the box is 20cm height and the width and length are 40cm
