Point P is the orthocenter of the triangle.
Answer:
x=36
Step-by-step explanation:
First rewrite equation then multiply each side by 36. 9x-36=4x+144.
then move the variable 9x-4x+36=144. Next subtract 9x and 4x ...5x=144+36.... 5x=180. Lastly you divide 180÷5 this your answer x=36
The highest common factor of the numbers 210 and 308 is 4.
<h3>What is the highest common factor?</h3>
The highest factor of the two numbers which divides both the numbers is called as greatest common factor or HCF.
The highest common factor will be calculated by finding the factors of the two numbers. The factors of the two numbers are as follows:-
308 = 2 x 2 x 7 x 11
210 = 2 x 2 x 3 x 17
We can see that the 2 x 2 = 4 is the highest factor which is common between the two numbers 210 and 308. So 4 is the HCF which can divide both the numbers 210 and 308.
Therefore the highest common factor of the numbers 210 and 308 is 4.
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Domain means the values of independent variable(input) which will give defined output to the function.
Given:
The height h of a projectile is a function of the time t it is in the air. The height in feet for t seconds is given by the function
Solution:
To get defined output, the height h(t) need to be greater than or equal to zero. We need to set up an inequality and solve it to find the domain values.
![To \; find \; domain:\\\\h(t) \geq0\\\\-16t^2+96t \geq 0\\Factoring \; -16t \; in \; the \; left \; side \; of \; the \; inequality\\\\-16t(t-6) \geq 0\\Step \; 1: Find \; Boundary \; Points \; by \; setting \; up \; above \; inequality \; to \; zero.\\\\t(t-6)=0\\Use \; zero \; factor \; property \; to \; solve\\\\t=0 \; (or) \; t = 6\\\\Step \; 2: \; List \; the \; possible \; solution \; interval \; using \; boundary \; points\\(- \infty,0], \; [0, 6], \& [6, \infty)](https://tex.z-dn.net/?f=%20To%20%5C%3B%20find%20%5C%3B%20domain%3A%5C%5C%5C%5Ch%28t%29%20%5Cgeq0%5C%5C%5C%5C-16t%5E2%2B96t%20%5Cgeq%20%200%5C%5CFactoring%20%5C%3B%20-16t%20%5C%3B%20in%20%5C%3B%20the%20%5C%3B%20left%20%5C%3B%20side%20%5C%3B%20of%20%5C%3B%20the%20%5C%3B%20inequality%5C%5C%5C%5C-16t%28t-6%29%20%5Cgeq%20%200%5C%5CStep%20%5C%3B%201%3A%20Find%20%5C%3B%20Boundary%20%5C%3B%20Points%20%5C%3B%20by%20%5C%3B%20setting%20%5C%3B%20up%20%5C%3B%20above%20%5C%3B%20inequality%20%5C%3B%20to%20%5C%3B%20zero.%5C%5C%5C%5Ct%28t-6%29%3D0%5C%5CUse%20%5C%3B%20zero%20%5C%3B%20factor%20%5C%3B%20property%20%5C%3B%20to%20%5C%3B%20solve%5C%5C%5C%5Ct%3D0%20%5C%3B%20%28or%29%20%5C%3B%20t%20%3D%206%5C%5C%5C%5CStep%20%5C%3B%202%3A%20%5C%3B%20List%20%5C%3B%20the%20%5C%3B%20possible%20%20%5C%3B%20solution%20%5C%3B%20interval%20%5C%3B%20using%20%5C%3B%20boundary%20%5C%3B%20points%5C%5C%28-%20%5Cinfty%2C0%5D%2C%20%5C%3B%20%5B0%2C%206%5D%2C%20%5C%26%20%5B6%2C%20%5Cinfty%29%20)
![Step \; 3:Pick \; test \; point \; from \; each \; interval \; to \; check \; whether \\\; makes \; the \; inequality \; TRUE \; or \; FALSE\\\\When \; t = -1\\-16(-1)(-1-6) \geq 0\\-112 \geq 0 \; FALSE\\(-\infty, 0] \; is \; not \; solution\\Also \; Logically \; time \; t \; cannot \; be \; negative\\\\When \; t = 1\\-16(1)(1-6) \geq 0\\80 \geq 0 \; TRUE\\ \; [0, 6] \; is \; a \; solution\\\\When \; t = 7\\-16(7)(7-6) \geq 0\\-112 \geq 0 \; FALSE\\ \; [6, -\infty) \; is \; not \; solution](https://tex.z-dn.net/?f=%20Step%20%5C%3B%203%3APick%20%5C%3B%20test%20%5C%3B%20point%20%5C%3B%20from%20%5C%3B%20each%20%5C%3B%20interval%20%5C%3B%20to%20%5C%3B%20check%20%5C%3B%20whether%20%5C%5C%5C%3B%20makes%20%5C%3B%20the%20%5C%3B%20inequality%20%5C%3B%20TRUE%20%5C%3B%20or%20%5C%3B%20FALSE%5C%5C%5C%5CWhen%20%5C%3B%20t%20%3D%20-1%5C%5C-16%28-1%29%28-1-6%29%20%5Cgeq%20%200%5C%5C-112%20%5Cgeq%20%200%20%5C%3B%20FALSE%5C%5C%28-%5Cinfty%2C%200%5D%20%5C%3B%20is%20%5C%3B%20not%20%5C%3B%20solution%5C%5CAlso%20%5C%3B%20Logically%20%5C%3B%20time%20%5C%3B%20t%20%5C%3B%20cannot%20%5C%3B%20be%20%5C%3B%20negative%5C%5C%5C%5CWhen%20%5C%3B%20t%20%3D%201%5C%5C-16%281%29%281-6%29%20%5Cgeq%20%200%5C%5C80%20%5Cgeq%20%200%20%5C%3B%20TRUE%5C%5C%20%5C%3B%20%5B0%2C%206%5D%20%5C%3B%20is%20%5C%3B%20a%20%5C%3B%20solution%5C%5C%5C%5CWhen%20%5C%3B%20t%20%3D%207%5C%5C-16%287%29%287-6%29%20%5Cgeq%20%200%5C%5C-112%20%5Cgeq%20%200%20%5C%3B%20FALSE%5C%5C%20%5C%3B%20%5B6%2C%20-%5Cinfty%29%20%5C%3B%20is%20%5C%3B%20not%20%5C%3B%20solution%20)
Conclusion:
The domain of the function is the time in between 0 to 6 seconds
The height will be positive in the above interval.
Answer:
0.97 per ball
Step-by-step explanation:
Take the total cost and divide by the number of items
8.74 /9
0.97111
Rounding to the nearest cent
0.97
