Perimeter = sum of all the sides
let x = one side
longer side = x + 10
Perimeter = x + x + x + x + 10
62 = 4x + 10
4x = 52
x = 13
Longer side = 23
Area = (10+23)x2/10
= 6.6
Answer:
- addition property of equality
- integers are closed to addition
- identity element
- multiplication property of equality
- commutative property of multiplication; reals are closed to multiplication; identity element
Step-by-step explanation:
<u>Given</u>:
c/2 -5 = 7
Step 1: c/2 -5 +5 = 7 +5
Step 2: c/2 +0 = 12
Step 3: c/2 = 12
Step 4: 2(c/2) = 12(2)
Step 5: c = 24
<u>Find</u>:
The property that justifies each step of the solution.
<u>Solution</u>:
Step 1: addition property of equality (lets you add the same to both sides)
Step 2: integers are closed to addition
Step 3: identity property of addition (adding 0 changes nothing)
Step 4: multiplication property of equality
Step 5: closure of real numbers to multiplication; identity property of multiplication
_____
It is hard to say what "property" you want to claim when you simplify an arithmetic expression. Above, we have used the property that the sets of integers and real numbers are closed to addition and multiplication. That is, adding or multiplying real numbers gives a real number.
In Step 5, we can rearrange 2(c/2) to c(2/2) using the commutative property of multiplication. 2/2=1, and c×1 = c. The latter is due to the identity element for multiplication: multiplying by 1 changes nothing.
Apart from the arithmetic, the other properties used are properties of equality. Those let you perform any operation on an equation, as long as you do it to both sides of the equation. The operations we have performed in this fashion are adding 5 and multiplying by 2.
A dilation by a scale factor of 6 will cause the radius to increase by a factor of 6. So
. If we plug this value of r into the formula for the circumference of a circle we get
So basically N = 12r. You haven't given me any original radius, so I can't give you a constant for N, but if you do have that original radius you can just plug that into 12r.
Based on your comment, N = 12 * 9 = 108 inches
Answer:The amount of paint that was sold altogether is 173.36 litres
Step-by-step explanation:
The total amount of paint that the paint shop stocks is 1800 litres.
24% of the paint is white. It means that the amount of white paint would be
24/100 × 1800 = 0.24 × 1800 = 432 litres.
The amount of the remaining paint other than white would be
1800 - 432 = 1368 litres
The shops sells 18% of the white paint. This means that the amount of white paint sold by the shop will be
18/100 × 432 = 0.18 × 432 = 77.6 litres.
The shops sells 7% of the rest of the paint.
This means that the amount of the rest paint sold by the shop will be
7/100 × 1368 = 0.07 × 1368 = 95.76 litres.
The amount of paint that was sold altogether would be
77.6 + 95.76 = 173.36 litres
