Answer:
We conclude that 'A number t multiplied by -4 is at least −2/5' can be algebraically written as inequality such as:
Step-by-step explanation:
Given
A number t multiplied by -4 is at least −2/5
To determine
Write the sentence as an inequality.
For the inequalities, when we mention 'at least', we can term it as 'greater than or equal to' symbol such as '≥'.
It is stated that A number t multiplied by -4 is at least −2/5.
Let 't' be the number.
Multiplying t by -4 is: -4t
Thus, A number t multiplied by -4 is at least −2/5 will be written as:
-4t ≥ -2/5
Therefore, we conclude that 'A number t multiplied by -4 is at least −2/5' can be algebraically written as inequality such as:
Time it took runner A to complete the marathon = 26.2 / 5.6 = 4 hrs 41 mins
Time it took runner B to complete the marathon = 26.2 / 6.4 = 4 hrs 6 mins
Time it took runner B to complete the marathon relative to when runner A started = 30 mins + 4 hrs 6 mins = 4 hrs 36 mins
Therefore, runner B will finnish ahead of runner A.
Let x be the time the two runners are at the same point, then
5.6x + 5.6(0.5) = 6.4x
6.4x - 5.6x = 2.8
0.8x = 2.8
x = 2.8/0.8 = 3.5
Therefore, runner B will catch up with runner A 3.5 hours after runner A starts the race.
<span>Runner B; Runner B will catch up to Runner A 3.5 hours after Runner A crosses the starting line.</span>
Answer:
Step-by-step explanation:
Given
Required
Use the expression to prove a trigonometry identity
The given expression is not complete until it is written as:
Going by the Pythagoras theorem, we can assume the following.
- a = Opposite
- b = Adjacent
- r = Hypothenuse
So, we have:
Having said that:
The expression can be further simplified as:
Substitute values for sin and cos
becomes
Answer:
the answer is c 29.04 meters squared
Step-by-step explanation:
first you multiply 2.2 by 2.2 to get 4.84 then you multiply that by 6 to account for all of the faces
tis noteworthy that the segment contains endpoints of A and C and the point B is in between A and C cutting the segment in a 1:2 ratio,
![\bf \textit{internal division of a line segment using ratios} \\\\\\ A(-9,-7)\qquad C(x,y)\qquad \qquad \stackrel{\textit{ratio from A to C}}{1:2} \\\\\\ \cfrac{A\underline{B}}{\underline{B} C} = \cfrac{1}{2}\implies \cfrac{A}{C}=\cfrac{1}{2}\implies 2A=1C\implies 2(-9,-7)=1(x,y)\\\\[-0.35em] ~\dotfill\\\\ B=\left(\frac{\textit{sum of "x" values}}{\textit{sum of ratios}}\quad ,\quad \frac{\textit{sum of "y" values}}{\textit{sum of ratios}}\right)\\\\[-0.35em] ~\dotfill](https://tex.z-dn.net/?f=%5Cbf%20%5Ctextit%7Binternal%20division%20of%20a%20line%20segment%20using%20ratios%7D%20%5C%5C%5C%5C%5C%5C%20A%28-9%2C-7%29%5Cqquad%20C%28x%2Cy%29%5Cqquad%20%5Cqquad%20%5Cstackrel%7B%5Ctextit%7Bratio%20from%20A%20to%20C%7D%7D%7B1%3A2%7D%20%5C%5C%5C%5C%5C%5C%20%5Ccfrac%7BA%5Cunderline%7BB%7D%7D%7B%5Cunderline%7BB%7D%20C%7D%20%3D%20%5Ccfrac%7B1%7D%7B2%7D%5Cimplies%20%5Ccfrac%7BA%7D%7BC%7D%3D%5Ccfrac%7B1%7D%7B2%7D%5Cimplies%202A%3D1C%5Cimplies%202%28-9%2C-7%29%3D1%28x%2Cy%29%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20B%3D%5Cleft%28%5Cfrac%7B%5Ctextit%7Bsum%20of%20%22x%22%20values%7D%7D%7B%5Ctextit%7Bsum%20of%20ratios%7D%7D%5Cquad%20%2C%5Cquad%20%5Cfrac%7B%5Ctextit%7Bsum%20of%20%22y%22%20values%7D%7D%7B%5Ctextit%7Bsum%20of%20ratios%7D%7D%5Cright%29%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill)
![\bf B=\left(\cfrac{(2\cdot -9)+(1\cdot x)}{1+2}\quad ,\quad \cfrac{(2\cdot -7)+(1\cdot y)}{1+2}\right)~~=~~(-4,-6) \\\\[-0.35em] ~\dotfill\\\\ \cfrac{(2\cdot -9)+(1\cdot x)}{1+2}=-4\implies \cfrac{-18+x}{3}=-4 \\\\\\ -18+x=-12\implies \boxed{x=6} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{(2\cdot -7)+(1\cdot y)}{1+2}=-6\implies \cfrac{-14+y}{3}=-6 \\\\\\ -14+y=-18\implies \boxed{y=-4}](https://tex.z-dn.net/?f=%5Cbf%20B%3D%5Cleft%28%5Ccfrac%7B%282%5Ccdot%20-9%29%2B%281%5Ccdot%20x%29%7D%7B1%2B2%7D%5Cquad%20%2C%5Cquad%20%5Ccfrac%7B%282%5Ccdot%20-7%29%2B%281%5Ccdot%20y%29%7D%7B1%2B2%7D%5Cright%29~~%3D~~%28-4%2C-6%29%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20%5Ccfrac%7B%282%5Ccdot%20-9%29%2B%281%5Ccdot%20x%29%7D%7B1%2B2%7D%3D-4%5Cimplies%20%5Ccfrac%7B-18%2Bx%7D%7B3%7D%3D-4%20%5C%5C%5C%5C%5C%5C%20-18%2Bx%3D-12%5Cimplies%20%5Cboxed%7Bx%3D6%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20%5Ccfrac%7B%282%5Ccdot%20-7%29%2B%281%5Ccdot%20y%29%7D%7B1%2B2%7D%3D-6%5Cimplies%20%5Ccfrac%7B-14%2By%7D%7B3%7D%3D-6%20%5C%5C%5C%5C%5C%5C%20-14%2By%3D-18%5Cimplies%20%5Cboxed%7By%3D-4%7D)
