<u>Sum of Cubes:</u>
a³ + b³ = (a + b)(a² - ab + b²)
Example: x³ + 8 → a=x, b=2
= (x + 2)(x² - 2x + 4)
<u>Difference of Cubes:</u>
a³ - b³ = (a - b)(a² + ab + b²)
Example: x³ - 27 → a=x, b=3
= (x - 3)(x² + 3x + 9)
<u>Difference of Squares:</u>
a² - b² = (a - b)(a + b)
Example: x² - 16 → a=x, b=4
= (x - 4)(x + 4)
The numeric values for the function are given as follows:
a) f(-5) = 14.
b) f(0) = 10.
c) f(5/2) = 8.
d) f(5a) = -4a + 10.
e) f(5a - 15) = -4a + 22.
<h3>How to find the numeric value of a function?</h3>
To find the numeric value of a function, we replace each instance of the variable by the desired value.
For this problem, the function is given by:
f(x) = -0.8x + 10.
Hence the numeric values are given as follows:
- f(-5) = -0.8(-5) + 10 = 14.
- f(0) = -0.8(0) + 10 = 10.
- f(5/2) = f(2.5) = -0.8(2.5) + 10 = 8.
- f(5a) = -0.8(5a) + 10 = -4a + 10.
- f(5a - 15) = -0.8(5a - 15) + 10 = -4a + 22.
More can be learned about the numeric value of a function at brainly.com/question/14556096
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Step-by-step explanation:
Flour needed to make birthday cakes = 2x
Flour needed to make holiday cakes = 1y = y
Maximum amount of Flour allowed = 20 (No more than 20)
Therefore
2x + y must not be more than 20

Here's one way to convert the number to the ratio of integers.
- Count the number of repeating digits. Call this number <em>n</em>. Here, only 5 has an overline, so there is only one repeating digit. That is, <em>n </em>= 1.
- Multiply the number by 10^(-n) and subtract that from the original number. Call the result <em>p</em>. Here, doing this gives

- Compute the value <em>q</em> = 1 - 10^(-n). The result of step 2 is <em>q</em> times the original number. Here, <em>q</em> = 1 - 10^-1 = 0.9.
- Create the fraction <em>p/q</em>. Note that both <em>p</em> and <em>q</em> have a finite number of decimal digits, so this is easily converted to the ratio of integers, by moving the decimal point an equal number of places in the numerator and denominator. Reduce the resulting fraction as may be required. This is the fraction you're looking for. Here, p/q = 3.23/0.9 = 323/90. No reduction of this fraction is possible.
The fraction you're looking for is ...

Answer: 10
Step-by-step explanation:
By the alternate interior angles theorem,
