1. 42.3
When x=3 and y=7, the expression becomes
[tex]3.6 x+4.5y =\\3.6\cdot (3) + 4.5\cdot (7) =\\10.8+31.5=42.3[/tex]
2. 32.6
When r=12 and s=4, the expression becomes
[tex]5.5r-8.35 s=\\5.5\cdot (12)-8.35 \cdot (4)=\\(66)-(33.4)=32.6[/tex]
3. [tex]x(m)=12+0.5 m[/tex]
We can call [tex]x_0=12[/tex] the initial weight of the object, and its weight increases by 0.5 for each month, so must add [tex]0.5\cdot m[/tex]. Therefore, the expression for the weight will be
[tex]x(m)=12+0.5 m[/tex]
4. -11
For c = -2:
[tex]4c-3 =\\4\cdot (-2)-3=\\(-8)-3=-11[/tex]
5. +3
For x = -6:
[tex]\frac{1}{3}x+5=\\\frac{1}{3}\cdot (-6)+5=\\\frac{-6}{3}+5=\\-2+5=+3[/tex]
6. 14
For k = 20 and m = -2:
[tex]0.3 k - 4 m=\\0.3 \cdot (20)-4 \cdot (-2)=\\(6)+(8)=14[/tex]
7. -60
For p = -26:
[tex]-50+\frac{5}{13}p=\\-50 + \frac{5}{13}\cdot (-26)=\\-50 +\frac{5\cdot (-26)}{13}=\\-50 - (5\cdot 2)=-50-10=-60[/tex]
8. [tex]5.25b+6.5s[/tex]
In fact, b represents the number of baseballs, while s represents the number of softballs. Each ball weights 5.25 ounces, so the total weigth of the baseballs is [tex]5.25 \cdot b[/tex]. Similarly, each softball weighs 6.5 ounces, so the total weight of the softballs will be [tex]6.5 \cdot s[/tex]
9. B. 157.5 pounds
The weight of the crate is 22.5 pounds.
The weight of each box is 11.25 pounds, and we have n=12 boxes, so the expression for the total weight will be
[tex]w=22.5+ 11.25 n=\\22.5+11.25 \cdot 12=\\22.5+135=157.5[/tex]
10. [tex]34 - 1.5 d[/tex]
We can assume that the initial amount of water in the container is 34 ounces. Every day, 1.5 ounces of water are lost: calling d the number of days, this means that after d days, we will have lost [tex]1.5\cdot d[/tex] ounces of water. Therefore, we must use a negative sign, and the final expression will be
[tex]34 - 1.5 d[/tex]
11. 3.75 miles from the destination
The initial distance from the destination is d = 60. At each hour, the freigth covers a distance of 22.5 miles. Calling h the number of hours, the distance from the destination can be expressed as
[tex]60-22.5 h[/tex]
And substituting h = 2.5 (number of hours), we find the distance from the destination after 2.5 hours:
[tex]60-22.5 \cdot (2.5)=\\60-56.25=3.75[/tex]
12. 107.5 feet
The initial elevation of the elevator is 85.5 feet. At each second, the elevation increases by 2.75 feet: if we call t the number of seconds passed, the elevation of the elevator can be expressed as
[tex]85.5+2.75 t[/tex]
And substituting t=8 (number of seconds), we find the elevation after 8 seconds:
[tex]85.5 + 2.75 \cdot (8)=\\85.5+22=107.5[/tex]
