0.15(34) = x......with x representing what they will save
The simplification form of the provided expression is 108 after applying the integer exponent properties.
<h3>What is integer exponent?</h3>
In mathematics, integer exponents are exponents that should be integers. It may be a positive or negative number. In this situation, the positive integer exponents determine the number of times the base number should be multiplied by itself.
We have an expression:
= 108
Thus, the simplification form of the provided expression is 108 after applying the integer exponent properties.
Learn more about the integer exponent here:
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Answer:
<h2>
b = -2</h2>
Step-by-step explanation:
The point-slope form of equation is: y - y₀ = m(x - x₀), where (x₀, y₀) is any point the line passes through and m is the slope.
m = 2
(4, 6) ⇒ x₀ = 4, y₀ = 6
So, the point-slope form of equation:
y - 6 = 2(x - 4)
Changing to the slope-intercept form of the equation of the line (y = mx + b, where m is the slope and b is the y-intercept of the line):
y - 6 = 2x - 8 {add 6 to both sides}
y = 2x - 2 ⇒ b = -2
Answer:
The new volume is 20litres
Step-by-step explanation:
This problem bothers on the expansion of gases
According to Boyle's law
The volume of a given mass of gas at constant temperature is inversely proportional to the pressure
P∝1/v
Pv= constant
Given data
P1= 1.5atm
v1 = 10 litter
P2=0.75atm
v2=?
Applying P1v1= P2v2
v2= P1v1/P2
v2= 1.5*10/0.75
v2= 15/0.75
v2= 20litres
Answer + Explanation + Theory
When a number is divided by a number it results in a quotient and a remainder
E.g. 9 / 4 = 2 remainder 1
9 is the dividend
4 is the divisor
2 is the quotient
1 is the remainder
Same way when a polynomial is divided by a linear expression
E.g.
Ax^2 + bx + c / (x-b) = (x+a) + r
Which can be rearranged to
ax^2 + bx + c = (x+a)(x-b) + r
When x = - a or b, only the remainder is left since either (x+a)(x-b) is 0.
If x = - a or b is substituted into the polynomial and the value is 0 then there is no remainder,
This would suggest (x+a) or (x-b) are factors of the polynomial.
Now apply this logic to these questions
1. Let’s assume (x-4) is a factor, this would mean that when x=4 is substituted into the polynomial the answer would be 0.
This is the case, therefore the remainder is 0.
2. Having seen the logic above (applied using the remainder and factor theorem) the linear expression is a factor of the polynomial.
