<span><span>y=<span><span>−<span>4x</span></span>+5</span></span>;<span>y=<span><span>−<span>2x</span></span>+1</span></span></span>Step: Solve<span>y=<span><span>−<span>4x</span></span>+5</span></span>for y:Step: Substitute<span><span>−<span>4x</span></span>+5</span>foryin<span><span>y=<span><span>−<span>2x</span></span>+1</span></span>:</span><span>y=<span><span>−<span>2x</span></span>+1</span></span><span><span><span>−<span>4x</span></span>+5</span>=<span><span>−<span>2x</span></span>+1</span></span><span><span><span><span>−<span>4x</span></span>+5</span>+<span>2x</span></span>=<span><span><span>−<span>2x</span></span>+1</span>+<span>2x</span></span></span>(Add 2x to both sides)<span><span><span>−<span>2x</span></span>+5</span>=1</span><span><span><span><span>−<span>2x</span></span>+5</span>+<span>−5</span></span>=<span>1+<span>−5</span></span></span>(Add -5 to both sides)<span><span>−<span>2x</span></span>=<span>−4</span></span><span><span><span>−<span>2x</span></span><span>−2</span></span>=<span><span>−4</span><span>−2</span></span></span>(Divide both sides by -2)<span>x=2</span>Step: Substitute2forxin<span><span>y=<span><span>−<span>4x</span></span>+5</span></span>:</span><span>y=<span><span>−<span>4x</span></span>+5</span></span><span>y=<span><span><span>(<span>−4</span>)</span><span>(2)</span></span>+5</span></span><span>y=<span>−3</span></span><span>(Simplify both sides of the equation)
</span><span><span>x=<span><span>2<span> and </span></span>y</span></span>=<span>−3</span></span>
"In partial-quotients division, it takes several steps to find the quotient. At each step, you find a partial answer (called a partial quotient); then you find the product of the partial quotientand divisor and subtract it from the dividend. Finally, you add all the partial quotients to find the final quotient" Hope this helps : )
Let's first establish what we already know for this problem.
x = total number of hotdogs sold
y = total profit from total sales of hotdogs
Let's also establish the other equations which we will require in order to solve this problem.
Equation No. 1 -
Profit for 40 hotdogs = $90 profit
Equation No. 2 -
Profit for 80 hotdogs = $210 profit
STEP-BY-STEP SOLUTION
From this, we can use the formula y = mx + b & substitute the values for x & y from one of the two previous equations into the formula in order to obtain the values of m & b for the final equation. Here is an example of the working out as displayed below:
Firstly, using the first or second equation, we make either m or b the subject. Here I have used the first equation and made m the subject:
Equation No. 1 -
y = mx + b
90 = m ( 40 ) + b
40m = 90 - b
m = ( 90 - b ) / 40
Now, make b the subject in the second equation as displayed below:
Equation No. 2 -
y = mx + b
210 = m ( 80 ) + b
210 = 80m + b
b = 210 - 80m
Then, substitute m from the first equation into the second equation.
Equation No. 2 -
b = 210 - 80m
b = 210 - 80 [ ( 90 - b ) / 40 ]
b = 210 - [ 80 ( 90 - b ) / 40 ]
b = 210 - 2 ( 90 - b )
b = 210 - 180 - 2b
b - 2b = 30
- b = 30
b = - 30
Now, substitute b from the second equation into the first equation.
Equation No. 1 -
m = ( 90 - b ) / 40
m = ( 90 - ( - 30 ) / 40
m = ( 90 + 30 ) / 40
m = 120 / 40
m = 3
Through this, we have established that:
m = 3
b = - 30
Therefore, the final equation to model the final profit, y, based on the number of hotdogs sold, x, is as follows:
y = mx + b
y = ( 3 )x + ( - 30 )
ANSWER:
y = 3x - 30
Answer:
Step-by-step explanation:
Put the numbers into the formula and do the arithmetic.
... A = P(1 +rt) = $4000(1 + 0.065·5) = $5300
Hi there! The answer is 30 hours.
Let the number of worked hours be represented by X.
The total earn of option 1, would then be 10X + 60
The total earn of option 2, would then be 12X
We end up with the following equation:
Subtract 10X from both sides.
Divide both sides by 2.
Therefore, after 30 hours of work Rebecca will earn the same amount of money.