2.5t = 11
Then you divide both sides by 2.5
t =11/2.5
t = 4.4
Answers:
1. b = - 6
2. z = -7.5
3. c = 5
4. s = -38
5. w = 12
6. m = -(12/7)
7. k = 88
8. x = -10
9. t = -7.5
10. d = 0.3
11. "a" can be any value (Infinite solutions)
12. No solution for "n"
Solution:
1. -7(b+16)=7(b-4)
Dividing both sides of the equation by 7:
-7(b+16)/7=7(b-4)/7
-(b+16)=b-4
-b-16=b-4
-b-16+b+4=b-4+b+4
-12=2b
2b=-12
2b/2=-12/2
b=-6
Checking the solution:
-7(b+16)=7(b-4)
-7(-6+16)=7(-6-4)
-7(10)=7(-10)
-70=-70 Ok
2. 9-z=3z+39
9-z+z-39=3z+39+z-39
-30=4z
4z=-30
4z/4=-30/4
z=-7.5
Checking the solution:
9-z=3z+39
9-(-7.5)=3(-7.5)+39
9+7.5=-22.5+39
16.5=16.5 Ok.
3. 12c-5c=4c+15
7c=4c+15
7c-4c=4c+15-4c
3c=15
3c/3=15/3
c=5
Checking the solution:
12c-5c=4c+15
12(5)-5(5)=4(5)+15
60-25=20+15
35=35 Ok
4. 40-5s=-2(-1+3s)
40-5s=(-2)(-1)+(-2)(3s)
40-5s=2-6s
40-5s-40+6s=2-6s-40+6s
s=-38
Checking the solution:
40-5s=-2(-1+3s)
40-5(-38)=-2(-1+3(-38))
40+190=-2(-1-114)
230=-2(-115)
230=230 Ok
5. 2.8w+5.3=3.3w-0.7
2.8w+5.3-2.8w+0.7=3.3w-0.7-2.8w+0.7
6=0.5w
0.5w=6
0.5w/0.5=6/0.5
w=12
Checking the solution:
2.8w+5.3=3.3w-0.7
2.8(12)+5.3=3.3(12)-0.7
33.6+5.3=39.6-0.7
38.9=38.9 Ok
6. 4(m+9)=3(8-m)
(4)(m)+(4)(9)=(3)(8)+(3)(-m)
4m+36=24-3m
4m+36-36+3m=24-3m-36+3m
7m=-12
7m/7=-12/7
m=-12/7
Checking the solution:
4(m+9)=3(8-m)
4(-12/7+9)=3(8-(-12/7))
4(-12+7(9))/7=3(8+12/7)
4(-12+63)/7=3(7(8)+12)/7
4(51)/7=3(56+12)/7
204/7=3(68)/7
204/7=204/7 Ok
7. (1/8)k+32=(1/2)k-1
(1/8)k+32-32-(1/2)k=(1/2)k-1-32-(1/2)k
(1/8-1/2)k=-33
[(1-4(1))/8]k=-33
[(1-4)/8]k=-33
[(-3)/8]k=-33
(-3/8)k=-33
(-1)(-3/8)k=(-1)(-33)
(3/8)k=33
k=8(33)/3
k=264/3
k=88
Checking the solution:
(1/8)k+32=(1/2)k-1
(1/8)(88)+32=(1/2)(88)-1
(1)(88)/8+32=(1)(88)/2-1
88/8+32=88/2-1
11+32=44-1
43=43 Ok
8. (3/4)x-x=-(1/4)(2x+10)
Multiplying both sides of the equation by 4:
4(3/4)x-4x=-(4/4)(2x+10)
3x-4x=-1(2x+10)
-x=(-1)(2x)+(-1)(10)
-x=-2x-10
-x+2x=-2x-10+2x
x=-10
Checking the solution:
(3/4)x-x=-(1/4)(2x+10)
(3/4)(-10)-(-10)=-(1/4)(2(-10)+10)
-30/4+10=-(1/4)(-20+10)
-7.5+10=-(1/4)(-10)
2.5=10/4
2.5=2.5 Ok
9. 9(t+1)=5(t-4)-1
(9)(t)+(9)(1)=(5)(t)+(5)(-4)-1
9t+9=5t-20-1
9t+9=5t-21
9t+9-9-5t=5t-21-9-5t
4t=-30
4t/4=-30/4
t=-7.5
Checking the solution:
9(t+1)=5(t-4)-1
9(-7.5+1)=5(-7.5-4)-1
9(-6.5)=5(-11.5)-1
-58.5=-57.5-1
-58.5=-58.5 Ok
10. 3d+1.1=2.3-d
3d+1.1-1.1+d=2.3-d-1.1+d
4d=1.2
4d/4=1.2/4
d=0.3
Checking the solution:
3d+1.1=2.3-d
3(0.3)+1.1=2.3-0.3
0.9+1.1=2.0
2.0=2.0 Ok
11. -7(a+2)+15=1-7a
(-7)(a)+(-7)(2)+15=1-7a
-7a-14+15=1-7a
-7a+1=1-7a
-7a+1-1+7a=1-7a-1+7a
0=0
"a" can be any value (Infinite solutions)
Checking the solution: For example a=0
-7(a+2)+15=1-7a
-7(0+2)+15=1-7(0)
-7(2)+15=1-0
-14+15=1
1=1 Ok
12. 6(3n-1)=2(9n+4)
(6)(3n)+(6)(-1)=(2)(9n)+(2)(4)
18n-6=18n+8
18n-6+6-18n=18n+8+6-18n
0=14 It's not possible, because 0 is different to 14, then there is no solution for "n".
Answer:
The shortest distance from A to C is 
Step-by-step explanation:
see the attached figure to better understand the problem
we know that
The shortest distance from A to C is the hypotenuse of the right triangle AYC
Applying the Pythagoras Theorem
step 1
Find the length YC (hypotenuse of the right triangle YBC)
Applying the Pythagoras Theorem
substitute the given values
step 2
Find the shortest distance from A to C
substitute the given values
In a parallelogram, the opposite angles are equal and the sum of the angles is 360 degrees.
W = Z and Y = X
3y = 3x
Y = X = y
3y + y + 3x + x = 360
3x + x + 3x + x = 360
8x = 360
x = 360/8 = 45
Therefore, x = 45; y = 45
