Answer:
13) 7 + x/2 = 10
14) 2x - 5 = 7
15) 4x - 1 = 11
16) 6x - 6 = 12
17) x/3 + 10 = 12
18) 2x + 7 = 1
19) 9 + x/7 = 11
20) 8(n - 3)
Step-by-step explanation:
The quotient of x and 2 = x ÷ 2 = x/2
The product is the result of multiplying two or more other numbers
The sum is the result of adding two or more numbers
The difference is the result of subtracting one number from another
13) 7 + x/2 = 10
14) 2x - 5 = 7
15) 4x - 1 = 11
16) 6x - 6 = 12
17) x/3 + 10 = 12
18) 2x + 7 = 1
19) 9 + x/7 = 11
20) 8(n - 3)
Answer:
Range: (2, 14)
General Formulas and Concepts:
<u>Algebra I</u>
- Range is the set of y-values that are outputted by function f(x)
Step-by-step explanation:
According to the graph, our line's y-values span from 2 to 14. Since both 2 and 14 are open dot, they are exclusive from the range:
Interval Notation: (2, 14)
Inequality Notation: 2 < y < 14
Answer:
He can make only one batch of cookies.
Step-by-step explanation:
Just by mental math you can say he can make maximum one batch of cookies.
Total sugar = 10 cups
sugar used for lemonade = 2 cups
leftover sugar = 8 cups
For 1 batch of cookie sugar needed = 11/2
which means 5 and 1/2 cups
And he's just left with 8 cups of sugar after lemonade
8 - 5 1/2 = 2 1/2 which is not enough for 2nd batch
That means the maximum number of cookies batches is 1.
Another way to solve it by inequality:
2+Il/2 X <u><</u> 10
11/2 X <u><</u> 8
11X <u><</u> 16
X <u><</u> 1 6/11
So he can make only one batch of cookies.
Answer:
Solutions are 2, -1 + 0.5 sqrt10 i and -1 - 0.5 sqrt10 i
or 2, -1 + 1.58 i and -1 - 1.58i
(where the last 2 are equal to nearest hundredth).
Step-by-step explanation:
The real solution is x = 2:-
x^3 - 8 = 0
x^3 = 8
x = cube root of 8 = 2
Note that a cubic equation must have a total of 3 roots ( real and complex in this case). We can find the 2 complex roots by using the following identity:-
a^3 - b^3 = (a - b)(a^2 + ab + b^2).
Here a = x and b = 2 so we have
(x - 2)(x^2 + 2x + 4) = 0
To find the complex roots we solve x^2 + 2x + 4 = 0:-
Using the quadratic formula x = [-2 +/- sqrt(2^2 - 4*1*4)] / 2
= -1 +/- (sqrt( -10)) / 2
= -1 + 0.5 sqrt10 i and -1 - 0.5 sqrt10 i
