X=one type that cost 9
y=one type that cost 8
total books=type1+type2
total books=13
x+y=13
the total cost=cost of each added together
cost of each=number of books times cost per book
total cost=108
9x+8y=108
we have
x+y=13
9x+8y=108
solve for x and y
multiply first equation by -8 and add to first equation
-8x-8y=-104
<u>9x+8y=108 +</u>
x+0y=4
x=4
subsitute
x+y=13
4+y=13
minus 4
y=9
4 of the $9
9 of the $8
thats how to solve
1 dm represents 100 m implies that 10 cm represents 100 m, so the scale is 1 : 10, that means that 1 cm is 10 m in the map.
Answer:
the awnser is A
Step-by-step explanation:
Answer:
- length: 14 feet , width: 43 feet, or
- length: 86 feet, width: 7 feet
Both solutions are valid.
Explanation:
1. First assumption is that the shape of the fence is <u>rectangular</u>.
2. Second, assum the length parallel to the wall measure y feet, so the other two lengths, y, together with x will add up 100 feet
3. The, the area of the fence will be:
- length × width = xy = 600
4. Now you have two equation with two variables which you can solveL
- Solve for y in the first equation: y = 100 - 2x
- Substitute the value of y into the second equation: x (100 - 2x) = 600
5. Solve the last equation by completing squares:
- Distributive property: 100x - 2x² = 600
- Divide both sides by - 1: 2x² - 100x = - 600
- Divide both sides by 2: x² - 50x = -300
- Add the sequare of the half of 50 to both sides: x² - 50x + 625 = 325
- Factor the left side: (x - 25)² = 325
- Square root both sides: x - 25 = ± 18.028
- Clear x: x = 25 ± 18.028
- x = 43.028 ≈ 43 or x = 6.972 ≈ 7
Both values are valid,
If x = 43 , then y = 600/43 = 14
If x = 7, then y = 600/7 = 86
Thus, the lenght and width of the fence may be:
- 43 feet (width) and 14 feet (length), or
- 7 feet (width) and 86 feet (length).
The correct question is
<span>Rui is a professional deep water free diver. His altitude (in meters relative to sea level), xxx seconds after diving, is modeled by: d(x)=1/2x^2 -10x What is the lowest altitude Rui will reach?
we have that
</span>d(x)=(1/2)x² -10x
we know that
the function is quadratic (a parabola)
so
<span>the lowest altitude (depth) is the vertex
</span>
using a graph tool
see the attached figure
the vertex is the point (10,-50)
that means
His altitude (in meters relative to sea level), 10 seconds after diving is 50 meters under the sea level
therefore
the answer is<span>
the lowest altitude is 50 meters under the sea level</span>