Answer:
A worked 20 hours and B worked 15 hours.
Step-by-step explanation:
Given:
Mechanic A hourly rate = $55
Mechanic B hourly rate = $45
Total charged = $1775
Let's assume Mechanic A worked 'A' amount of hours and Mechanic B worked 'B' amount of hours, then
Step 1:
First equation: A + B = 35
Second equation: 55xA + 45xB = 1775
Step 2:
First equation can be written as: A = 35 - B
Step 3: Replace value of A in second equation
Second equation: 55x(35-B) + 45B = 1775
: 1925 - 55B + 45B = 1775
: (1925 - 1775 )/10 = B
: B = 15 hours
A worked = 35 - 15
= 20 hours
Answer:
3+2c
Step-by-step explanation:
To translate the phrase into an algebraic expression, you have to analyze the information provided. Three dollars more than twice the cost of a bowl of soups means that given that c is the costs of a bowl of soup, you have to multiply c for 2 as the phrase says twice the cost. Also, it says three dollars more which means that you have to add 3. According to this, the expression is: 3+2c.
18 1/2 :)
Explanation: Leave the 18 as it is then split 5 in half =2.5
1) An operator is missing in your statement. Most likely the right expression is:
2x
f(x) = -------------
3x^2 - 3
So, I will work with it and find the result of each one of the statements given to determine their validiy.
2) Statement 1: <span>The
graph approaches 0 as x approaches infinity.
Find the limit of the function as x approaches infinity:
2x
Limit when x →∞ of ------------
3x^2 - 3
Start by dividing numerator and denominator by x^2 =>
2x / x^2 2/x
--------------------------- = ---------------
3x^2 / x^2 - 3 / x^2 3 - 3/x^2
2/∞ 0 0
Replace x with ∞ => ------------ = ------- = ---- = 0
3 - 3/∞ 3 - 0 3
Therefore the statement is TRUE.
3) Statement 2: The graph approaches 0 as x
approaches negative infinity.
</span><span><span>Find the limit of the function as x approaches negative infinity:
2x
Limit when x → - ∞ of ------------
3x^2 - 3
Start by dividing numerator and denominator by x^2 =>
2x / x^2 2/x
--------------------------- = ---------------
3x^2 / x^2 - 3 / x^2 3 - 3/x^2
2/(-∞) 0 0
Replace x with - ∞ => ------------ = ---------- = ---- = 0
3 - 3/(-∞) 3 - 0 3
Therefore, the statement is TRUE.</span>
4) Statement 3: The graph approaches 2/3 as x approaches
infinity.
FALSE, as we already found that the graph approaches 0 when x approaches infinity.
5) Statement 4: The graph approaches –1 as x approaches negative infinity.
</span>
FALSE, as we already found the graph approaches 0 when x approaches negative infinity.
<u>Missing part of the question</u>
Hayley bakes zucchini bread and banana bread. Some ingredients Hayley uses for each type of bread are shown in the tables
Zucchini Bread
2 eggs 2 cups of flour 1.5 cups of sugar 0.5 stick of butter
Banana Bread
1 egg 3 cups of flour 2 cups of sugar 0.25 stick of butter
Answer:
Step-by-step explanation:
Given
Since there are enough of other ingredients, we will only consider the amount of eggs and cups of flour.
So, we have:
Zucchini Bread
Banana Bread
<u>For the eggs</u>
The ratio of eggs to use in the Zucchini bread to Banana bread is:
(z) : (b)
This gives:
The total number of eggs cannot exceed 9.
So, the inequality is:
<u>For the flours</u>
The ratio of flours to use in the Zucchini bread to Banana bread is:
(z) : (b)
This gives:
The total cups of flours cannot exceed 15.
So, the inequality is:
Hence:
The system of inequalities is:
