Answer:
Given: 
, y =6
To prove: x =7
On substituting the value of y =6 in the equation 7y = 8x -14 to solve for x.
or
42 = 8x -14 ......[1]
Addition Property of equality states that you add the same number to both sides of an equation.
Add 14 to both sides in equation [1];
42+14 =8x -14+14
Simplify:
56 = 8x
or
8x =56 ......[2]
Division Property of equality states that you divide the same number to both sides of an equation.
Divide by 8 to both sides of an equation [2];
Simplify:
x =7 Hence proved!
A two Column proof:
Statement Reason
1. 7y = 8x -14 Given
y= 6
2. 7(6) = 8x -14 Substitution property
3. 42+14 = 8x Addition property of equality
4. 56 =8x Simplify
5. x =7 Division Property of equality
Answer:
B.
Step-by-step explanation:
B. The girl would have to use less force because she is using a simple machine, or a lever. The lever makes it easier to lift the rock because the rock is closer to the fulcrum.
Answer: P = $ 1,998.01
Step-by-step explanation:
First, converting R percent to r a decimal
r = R/100 = 24%/100 = 0.24 per year,
putting time into years for simplicity,
1 months ÷ 12 months/year = 0.083333 years,
then, solving our equation
P = 39.96 / ( 0.24 × 0.083333 ) = 1998.007992032
P = $ 1,998.01
The principal required to
accumulate interest of $ 39.96
on a rate of 24% per year for 0.083333 years (1 months) is $ 1,998.01.
Let Daniel's age be 'x' years , hence, Lisa's age is (x - 5) years. Let Grandma's age be 'y' = 54 years.
Hence,
x(x - 5) = 2/3 × y
x² - 5x = 2 × 54 years / 3
x² - 5x = 36 years
x² - 5x - 36 = 0
∆ = (-5)² - 4(1)(-36) = 25 + 144 = 169
√∆ = √169 = 13
x1 = (5+13)/2, x2 = (5-13)/2
x1 = 9, x2 = -4
Since, age can't be negative,
Daniel's age = x = 9 years.
Answer:
a) -3
b) 5
c) 7
d) 4
Step-by-step explanation:
We have the function 
a) We need to find the coefficient of 
.
This means that we need to find out what number is alongside the in this equation. From the function, we can find that it is -3
b) Now we need to find the degree of 
. Recall that the degree refers to the highest power of x that is present. As 
is the largest power, our degree would be 5.
c) The constant term refers to the number within the function that does not have any x's with it. In this function, that number would be 7.
d) Now we need to find the number of terms. For this one, we just need to count how many terms are separated by + or - signs. There are 4 in this function.
