<span>All right triangles with the same acute angle θ are SIMILAR</span>
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
(-4,4),(0,-2)
slope = (-2 - 4) / (0 - (-4) = -6 / 4 = -3/2
y = mx + b
slope(m) = -3/2
use either of ur points...(0,-2)...x = 0 and y = -2
now sub and find b, the y int
-2 = 0(-3/2) + b
-2 = b
so ur equation for this line is : y = -3/2x - 2
to turn it to function notation, sub in f(x) for y
f(x) = -3/2x - 2 <=== ur answer
Answer:
a figure has a line symmetry if a line, called the <u>line of symmetry</u> divides the figure into two parts that are <u>mirror</u> of each.
Hey!! idk I wanted to help but I am not entirely sure, the second one I am more sure about tho ! Hope you have a great night/ day, wherever you are : )
Answer: x ≤ 120
Step-by-step explanation: To get <em>x</em> by itself in this inequality, since it's being divided by -6, we must multiply both sides by -6, just like we would if we were solving an equation, but here is the trick you have to watch out for with inequalities.
When you multiply or divide both sides of an inequality by a
negative, you <u>must</u> switch the direction of the inequality sign.
So our second step in this problem reads x ≤ 120.
<u>Please give this idea your full attention.</u>
<em>Even the most advanced algebra students will sometimes forget to switch the direction of the inequality sign when multiplying or dividing both sides of an inequality by a negative.</em>