Answer:
120 in^2
Step-by-step explanation:
Area of shaded region
= 1/2 x 12 x 20
= 120 in^2
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:
1. g
2. a
3. d
4. b
Step-by-step explanation:
If you can't do these in you head or on a graph, you can always let your calculator do it.
When adding vectors put the tail of one at the nose of the other. When subtracting, add the opposite. When adding or subtracting a multiple, just do the repeated addition or subtraction.
Answer:
That's the exponential function.
Step-by-step explanation:
Simply just use a graphing calculator (there's plenty of apps and websites that are graphing calculators) and follow these steps.
1) Clear out calculator RAM
2) Press STAT button
3) Press ENTER on EDIT
4) Type the X's in L1 and type the Y's L2.
5) Press STAT again
6) Press the RIGHT ARROW once
7) Press 0
8) Press ENTER
9) There's your exponential function!
Answer:
CE= 32
QS= 14
Step-by-step explanation:
Since the C=R and the E=Q, and the RQ is 16, the CE is 2x that value. (Since the CDE is 2x bigger than RSQ)
You also want to flip the triangles until they are in the same positions as each other so you can analyze it easier