1848.24
You take the perimeter of the base and multiply it by the height of the prism.
This is a system of equations. We can solve it by recognizing the two linear equalities we've given to solve this equation.
First, let's start off by recognizing two variables: x and y. x will be our number of hard puzzles, and y will be our number of easy puzzles. We're given that the number of hard puzzles and easy puzzles sum to 50, so we can rewrite that as:
![x+y=50](https://tex.z-dn.net/?f=x%2By%3D50)
Next, we're given that the sum of the points gained from the hard puzzles (60x), and the number of points gained from the easy puzzles (30y), sum to 1950. We can rewrite that as:
![60x+30y=1950](https://tex.z-dn.net/?f=60x%2B30y%3D1950)
Now, we have our two linear equations, and we must solve for the hard puzzles, so x. Solving for the hard puzzles means eliminating the easy puzzles from our systems, so we can multiply our first equation by 30, and subtract it from the first equation. This is a technique called elimination.
![30x+30y=1500 \\ 60x+30y=1950 \\ 30x=450 \implies x=15](https://tex.z-dn.net/?f=30x%2B30y%3D1500%20%5C%5C%2060x%2B30y%3D1950%20%5C%5C%2030x%3D450%20%5Cimplies%20x%3D15%20)
Since x=15, Tina has solved 15 hard puzzles.
Answer:
Height = 25.46 inches
Width = 50.92 inches
Step-by-step explanation:
We can say area of a triangle is :
Area = 1/2 * length * height
The banner is twice as long and height, we can say:
length = 2*height
Since, area given as 648, we can write:
![Area=\frac{1}{2}*length*height\\Area = \frac{1}{2}*(2*height)(height)\\648=height^2\\height = \sqrt{648}\\ height=25.46](https://tex.z-dn.net/?f=Area%3D%5Cfrac%7B1%7D%7B2%7D%2Alength%2Aheight%5C%5CArea%20%3D%20%5Cfrac%7B1%7D%7B2%7D%2A%282%2Aheight%29%28height%29%5C%5C648%3Dheight%5E2%5C%5Cheight%20%3D%20%5Csqrt%7B648%7D%5C%5C%20height%3D25.46)
Height = 25.46 inches
Width = 2 * 25.46 = 50.92 inches
Answer:
9
Step-by-step explanation:
first you add up all the numbers 9+7+11+8+10=45
then you divide by the amount of numbers there are so in this case 5 so you would do 45÷5=9 hope this helps
Answer:
a
Step-by-step explanation: