Answer:
∠ 2 = 70°
Step-by-step explanation:
∠ 13 and ∠ 14 are adjacent angles and sum to 180° , then
12x - 22 + 9x - 29 = 180
21x - 51 = 180 ( add 51 to both sides )
21x = 231 ( divide both sides by 21 )
x = 11
Then
∠ 14 = 9x - 29 = 9(11) - 29 = 99 - 29 = 70°
∠ 7 = ∠ 14 = 70° ( Alternate angles )
∠ 2 = ∠ 7 = 70° ( Alternate angles )
Answer:
4.4
Step-by-step explanation:
Data set = 79, 93, 92, 86, 90
Xmean = (79 + 93 + 92 + 86 + 90)/5
= 440/5
Xmean = 88
MAD =
(79 - 88) + (93 - 88) + ( 92 - 88) + ( 86 - 88) + ( 90 - 88)/ 5
=
(9) + (5) + (4) + (2) + (2)/ 5
=
22/5
Mean Absolute Deviation = 4.4
Answer: B. 8x+3y=5
-8x - 4y= -6
Step-by-step explanation:
The given system of equations is expressed as
8x + 3y =5 - - - - - - - - -1
4x + 2y =3 - - - - - - - - - - 2
We would eliminate x by multiplying equation 1 by 4 and equation 2 by 8. It becomes
32x + 12y =20
32x + 16y = 24
Subtracting, it becomes
- 4y = - 4
y = - 4/ - 4
y = 1
Substituting y = 1 into equation 1. It becomes
8x + 3 × 1 =5
8x + 3 = 5 - 3 = 2
x = 2/8 = 1/4
Substituting x = 1/4 and y = 1 into the given options, it becomes
A. 8 × 1/4 + 3 × 1=5
2 + 3 = 5
- 8 × 1/4 +4 × 1 = 2
B. 8x+3y=5
-8x - 4y= -6
- 8 × 1/4 - 4 × 1 = -6
Therefore, the system of of equations that has the same solution as the given equation is
B. 8x+3y=5
-8x - 4y= -6
Answer:
$ 327.08
Step-by-step explanation:
Let x = width of the container,
Then Length of the container = 2x
Let h = height of the container,
volume of the container can be calculated as length × width × height
= 2x × x × h
= 2x² h
Then we can say Volume =
= 2x² h=10
If we simplify inorder to get h
We have h= 5/x²
Then the area= (2L×h) +(2xh)
Where L is lenght
x= wish
h= height
= 2× 2x × h+ x× h
= 4x× 5/x + 2x × 5/x
Area = 30/x
Now, the area of the base = length × width
But from question, for the base costs $20 per square meter. Material for the sides costs $12 per square meter
Then the cost C(x)= 2x²× 20+30/x ×12
C(x)= 40x²+35/x²
If we differenciate wrt x we have
C(x)= 80-360/x²
If we equate C(x)=0the
80=360/x²
x= 1.651
If substitute to C(x)= 40x²+35/x²
C(x) = 40(1.651)² + 35/(1.651)²
We have cost= 327.08
Answer:
A. He has $22 because he spends $2 on snacks each day.
B. He spends $2 a day, in the table we can see it decreases by $2 each day, so he spends $2 every day.
C. Yes because the cost evenly decreases by $2, therefore it is a linear relationship.
D. ?
E. X ÷ Y = Z
X being the money, $22
Y being the days, 6
Z being the leftover money, $8
