Answer:
4 hours. 1 3/4 is about 2, and 2 1/4 rounds to 2. 1/4 would round to 0, but it would not affect the estimate's accuracy much because we rounded up by 1/4 on 1 3/4 already. Philipe spent about 4 hours on activities.
Step-by-step explanation:
Answer:C
Step-by-step explanation: Divide the cost by the amount of pencils to find what each pencil cost. Choose the lowest cost per pencil.
The quadratic function given to us is:
![g(x)=2x^2+20x+49](https://tex.z-dn.net/?f=g%28x%29%3D2x%5E2%2B20x%2B49)
We are asked to find the vertex form of the function.
The general formula for the vertex form of a quadratic equation is:
![\begin{gathered} g(x)=a(x-h)^2+k \\ \text{where,} \\ (h,k)\text{ is the coordinate of the vertex} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20g%28x%29%3Da%28x-h%29%5E2%2Bk%20%5C%5C%20%5Ctext%7Bwhere%2C%7D%20%5C%5C%20%28h%2Ck%29%5Ctext%7B%20is%20the%20coordinate%20of%20the%20vertex%7D%20%5Cend%7Bgathered%7D)
In order to write the function in its vertex form, we need to perform a couple of operations on the function.
1. Add and subtract the square of the half of the coefficient of x to the function.
2. Factor out the function with its repeated roots and re-write the equation.
Now, let us solve.
1. Add and subtract the square of the half of the coefficient of x to the function.
![\begin{gathered} g(x)=2x^2+20x+49=2(x^2+10x+\frac{49}{2}) \\ \text{half of coefficient of x:} \\ \frac{10}{2}=5 \\ \text{square of the half of the coefficient of x:} \\ 5^2=25 \\ \\ \therefore g(x)=2(x^2+10x+25-25+\frac{49}{2}) \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20g%28x%29%3D2x%5E2%2B20x%2B49%3D2%28x%5E2%2B10x%2B%5Cfrac%7B49%7D%7B2%7D%29%20%5C%5C%20%5Ctext%7Bhalf%20of%20coefficient%20of%20x%3A%7D%20%5C%5C%20%5Cfrac%7B10%7D%7B2%7D%3D5%20%5C%5C%20%5Ctext%7Bsquare%20of%20the%20half%20of%20the%20coefficient%20of%20x%3A%7D%20%5C%5C%205%5E2%3D25%20%5C%5C%20%20%5C%5C%20%5Ctherefore%20g%28x%29%3D2%28x%5E2%2B10x%2B25-25%2B%5Cfrac%7B49%7D%7B2%7D%29%20%5Cend%7Bgathered%7D)
2. Factor out the function with its repeated roots and re-write the equation.
![\begin{gathered} g(x)=2(x^2+10x+25)-2(25+\frac{49}{2}) \\ re-\text{write the above function} \\ g(x)=2(x^2+10x+25)-1 \\ \text{Let us factorize this:} \\ g(x)=2(x+5)^2-1 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20g%28x%29%3D2%28x%5E2%2B10x%2B25%29-2%2825%2B%5Cfrac%7B49%7D%7B2%7D%29%20%5C%5C%20re-%5Ctext%7Bwrite%20the%20above%20function%7D%20%5C%5C%20g%28x%29%3D2%28x%5E2%2B10x%2B25%29-1%20%5C%5C%20%5Ctext%7BLet%20us%20factorize%20this%3A%7D%20%5C%5C%20g%28x%29%3D2%28x%2B5%29%5E2-1%20%5Cend%7Bgathered%7D)
Therefore, we can conclude that the Equation and vertex of the equation is:
Answer:
300
Step-by-step explanation:
Note the hundreds place value (bolded and underlined)
<u>2</u>87
Look at the place value directly next to it (the tens place value). It is an 8. Because 8 is greater than 5, round up:
287 rounded to the nearest hundreds is 300.
300 is your answer.
~
Answer:
x is less than or equal to 7
Step-by-step explanation: