Answer:
Step-by-step explanation:
In order to determine the information you're being asked for, you need to complete the square on that quadratic. The first step is to move the constant over to the other side of the equals sign:
Here would be the step where, if the leading coefficient isn't a 1, you'd factor it out. But ours is a 1, so we're good there. Now take half the linear term (the term with the single x on it), square it, and add it to both sides. Our linear term is a -2. Half of -2 is -1, and -1 squared is +1. We add +1 to both sides giving us this:
Now we'll clean it up a bit. The right side becomes a 4, and the left side is written as its perfect square binomial, which is the whole reason we did this. That binomial is
(set equal to the 4 here). Now we'll move the 4 back over and set the whole thing back equal to y:
From this it's apparent what the vertex is: (1, -4),
the axis of symmetry is x = 1, and
the y-intercept is found by setting the x's equal to 0 in the original equation and solving for y. So the y-intercept is (0, -3).
Your choice for the correct answer is the very last one there.
Answer:
1. You would divide 30 by 3 which would be 10 bags of leaves per hour.
2. You would divide 34 by 17 which would be 2 quizzes per week.
3. You would have 7 people because it says Mrs. Sapanaro and the other 6. So you divide 245 by 7 which is 35$ per person.
Answer: The budget of Alexa is increased by $100.
Explanation:
It is given that the current income of Alexa is 3 times of her previous income.
Her previous salary was $800 and current salary was $2400.
Expenses = Rent + Utilities + Groceries + Savings + Bus
The sum of previous expenses is,
Previous expenses = $300 + $60 + $200 + $100 + $30 = $690
The sum of current expenses is,
Current expenses = $300 + $60 + $250 + $150+ $30 = $790
Effect of income on expenses is the difference of current expenses and previous expenses.
Effect of income on expenses = $790 - $690 = $100
Therefore, the budget of Alexa is increased by $100.
Jesse take 0.4 hours while Mark take 0.23 hours to reach back to home. The statements which should Jesse consider when solving this situation is statement 2.
<h3>What is Pythagoras theorem?</h3>
Pythagoras theorem says that in a right angle triangle, the square of the hypotenuse side is equal to the sum of the square of the other two legs of the right angle triangle.
Jesse and Mark are jogging along the route shown at a rate of 12 miles per hour.
- They start by jogging south along Capitol Street for 1 mile, then turn east on H Street and jog for 1.75 miles.
- At that point, Jesse is tired and decides to walk home along Florida Avenue at a rate of 5 miles per hour.
Here, Thus, Florida Avenue is hypotenuse triangular path and the other two sides are Capitol Street and H Street. The distance of Florida Avenue is,
Thus, Jesse walks 2.0156 with 5 miles per hour. Thus, the time taken by him is
Mark plans to jog back the way they came which is 2.75 miles (1+1.75) long with speed of 12 miles per hour. Thus, the time taken by him is
Thus, Jesse take 0.4 hours while Mark take 0.23 hours to reach back to home. The statements which should Jesse consider when solving this situation is statement 2.
Learn more about the Pythagoras theorem here;
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