Answer: Yes I agree with Jada. His approach is correct.
Step-by-step explanation: The question requires the student to write an equivalent equation with fewer terms. Nonetheless, this does not prevent applying a mathematically correct approach.
(1) Noah is wrong and the reason is that the initial step is mathematically incorrect. The expression on the right hand side reads 3(4 - 9x), therefore starting with "8 - 3" is very wrong. The right step was to take one side which is 8 and take the other side which is 3(4 - 9x).
(2) Lin is wrong and the reason is that she started inside the parenthesis and this also is mathematically incorrect. The digits inside the parenthesis are "not like terms" and hence calculating 4 - 9x = -5x is very incorrect (the same way you cannot correctly calculate 500 metres minus 200 inches. You must make sure they are both in meters or in inches, that is both must be like terms).
(3) Jada is very correct in using the distributive property and ended up with the only correct solution. The digits on the right hand side of the expression was solved first and that resulted in -12 + 27x. The reason being that the number outside the parenthesis which is -3, multiplied both digits inside the parenthesis. The minus sign had a major effect, and after simplifying the right hand side the expression now becomes;
8 - 12 + 27x
Since the like terms are 8 and 12, you can simplify further to become
- 4 + 27x OR the expression can be rearranged as 27x - 4
(4) Andre is not correct and the reason is that although he used the distributive property, he made a slight mistake while solving for the right side of the expression. What Andre did was
-3(4 - 9x)
-12 - 27x
Remember that when a negative value multiplies another negative value the answer is positive. Therefore -3 times -9x should have been +27x, just like Jada did as shown above.
From that point onward, his answer would be incorrect.
Answer:
I'm pretty sure A is the correct answer :)
(x-2)(x^4+3) is a polynomial
Answer:
6 and 10
Step-by-step explanation:
xy=60
2(x+y)=32
x+y=16
y=16-x
Substitute y into area equation
x(16-x)=60
16x-x^2=60
x^2-16x+60=0
(x-10)(x-6)=0
x=10, 6
y=6, 10
Answer:
Part A:
The graph passes through (0,2) (1,3) (2,4).
If the graph that passes through these points represents a linear function, then the slope must be the same for any two given points. Using (0,2) and (1,3). Write in slope-intercept form, y=mx+b. y=x+2
Using (0,2) and (2,4). Write in slope-intercept form, y=mx+b. y=x+2. They are the same and in graph form, it gives us a straight line.
Since the slope is constant (the same) everywhere, the function is linear.
Part B:
A linear function is of the form y=mx+b where m is the slope and b is the y-intercept.
An example is y=2x-3
A linear function can also be of the form ax+by=c where a, b and c are constants. An example is 2x + 4y= 3
A non-linear function contains at least one of the following,
*Product of x and y
*Trigonometric function
*Exponential functions
*Logarithmic functions
*A degree which is not equal to 1 or 0.
An example is...xy= 1 or y= sqrt. x
An example of a linear function is 1/3x = y - 3
An example of a non-linear function is y= 2/3x
Answer:
This table is a guess-and-check, which means that you input whatever number you think might work in this situation in “city gallons”
Step-by-step explanation:
After you just input that same number to wherever the “6” was in the first row...
E.g., if you put “7” for the next “city gallons”, then you’d put “10 - 7 = 3” in “freeway gal” and so on with ever different number you put in for “city gallons”.
That last part in the way bottom goes the same way! Except you input ”c” instead of a number, which is how you find the actual correct answer.
Hope this helps :)
