Answer:
It would take 4 weeks
Step-by-step explanation:
We can solve this problem most easily by forming it into an equation. We could represent weeks as <em>w.</em>
Since you train 5 more minutes every week, we could represent that as 5<em>w</em>, showing that you work 5 minutes times the number of weeks you worked out.
The constant would be adding 10, since you started out working 10 minutes a day. Now lets just write the equation!
10+5<em>w</em>=30
All we have to do is solve.
Subtract 10 on both sides to cancel out the positive 10.
5<em>w</em>=20
Now just divide both sides by 5 to isolate the <em>w</em>.
w=4
It would take him 4 weeks
Hope this helps!
Answer:
Step-by-step explanation:
1. 6
2. 6
3. 374
4. -72
5. -231
Answer:
16 ft by 22 ft
Step-by-step explanation:
The Area of the carpeting she must have = 352 ft²
To solve for this, we have:
Length × Width = Area of a rectangle
352ft² = Length × Width
352ft² = (20 - x) (26 - x)
352 = 520 - 20x - 26x + x²
352 = 520 - 46x + x²
Collect like terms
x² - 46x + 520 - 352
x² - 46x + 168
We factorise
x² - 4x - 42x + 106
(x² - 4x) -(42x + 106)
x(x - 4) -42(x - 4)
(x - 4)(x - 42)
x - 4 = 0, x = 4
x - 42 = 0, x = 42
We choose the least value for x
Hence, x = 4
Length = 20 - 4 = 16ft
Width = 22- 4= 22ft
The dimensions the rug should have is 16ft by 22 ft, meaning 16ft wide and 22ft long
Recuerda que
• |<em>x</em>| = <em>x</em> si <em>x</em> ≥ 0
• |<em>x</em>| = -<em>x</em> si <em>x</em> < 0
Necesitas considerar dos casos:
• si <em>x</em> - 3 ≥ 0,
|<em>x</em> - 3| < 1 ⇒ <em>x</em> - 3 < 1 ⇒ <em>x</em> < 4
• si <em>x</em> - 3 < 0,
|<em>x</em> - 3| < 1 ⇒ -(<em>x</em> - 3) = 3 - <em>x</em> < 1 ⇒ -<em>x</em> < -2 ⇒ <em>x</em> > 2
Entonces la solución consta de todos los números reales <em>x</em> tales que <em>x</em> > 2 y <em>x</em> < 4, o simplemente 2 < <em>x</em> < 4.
El método para resolver las otras desigualdades es el mismo.
|4<em>x</em> + 1| > 0 ⇒ 4<em>x</em> + 1 > 0 o -(4<em>x</em> + 1) > 0
… ⇒ 4<em>x</em> + 1 > 0 o -4<em>x</em> - 1 > 0
… ⇒ 4<em>x</em> > -1 o -4<em>x</em> > 1
… ⇒ <em>x</em> > -1/4 o <em>x</em> < -1/4
⇒ <em>x</em> ≠ -1/4
|<em>x</em> - 1| < 5 ⇒ <em>x</em> - 1 < 5 o -(<em>x</em> - 1) < 5
… ⇒ <em>x</em> - 1 < 5 o -<em>x</em> + 1 < 5
… ⇒ <em>x</em> < 6 o -<em>x</em> < 4
… ⇒ <em>x</em> < 6 o <em>x</em> > -4
⇒ -4 < <em>x</em> < 6
