Answer:
71
Step-by-step explanation:
The question says we have 140 bags and we have 4 models
bags have buttons but no zips.
bags have zips but no buttons.
bags have neither zips nor buttons
bags have both zips and buttons
We don't know how many bags have zips and buttons but we know how many bags are produced. And other 3 types of bags number. So we can calculate
140-47-48-22=23
That means we have 23 bags that have zips and buttons
and
48 of the bags have zips too. that means we have 48+23=71 bags that have zips on them.
In general, the sum of the measures of the interior angles of a quadrilateral is 360. This is true for every quadrilateral. This does not help here, because there are two angles (angles B and D) we know nothing about. We only know about opposite angles A and C.
In this case, you can use another theorem.
Opposite angles of an inscribed quadrilateral are supplementary.
m<A + m<C = 180
3x + 6 + x + 2 = 180
4x + 8 = 180
4x = 172
x = 43
m<A = 3x + 6 = 3(43) + 6 = 135
Answer: 135 deg
The first option is correct. For the following question, the simplified expression for the volume is 8x3 + 14x2 + 3x.
Answer:
y = -⅔x + ²²/₃
Step-by-step explanation:
1. Calculate the slope of EF
Assume E is at (-2, 5) and F is at (1, 3).
m₁ = (y₂ - y₁)/(x₂ - x₁) = (3 - 5)/(1 -(-2)) = -⅔
2. Calculate the slope of the parallel line
m₂ = m₁ = -⅔
3. Calculate its y-intercept
y = mx + b
6 =-⅔(2) + b
Simplify
6 = -⁴/₃ + b
Add ⁴/₃ to each side
b = 6 + ⁴/₃ = ¹⁸/₃ + ⁴/₃ = ²²/₃
The y-intercept is at (0,²²/₃).
4. Write the equation for the line
y = -⅔x + ²²/₃
The diagram shows EF in red. The parallel line in black passes through (2, 6) with a y-intercept at (0,²²/₃).
Answer: 6 years
Step-by-step explanation:
Formula to calculate compound amount: 
, where P= Principal , r=rate of interest, t= time
Given: P = £400, r = 3% = 0.03 , A= 475
Required equation: 
Taking log on both sides , we get
Hence, he needs to invest the money for 6 years to get atleast £475.
