Hello,
The correct answer is C) 9 hours and 5 minutes.
Hope this helps!!!! :)
Answer:
I hope this helps
Step-by-step explanation:
So the way to handle a problem like this is to rewrite the three numbers in terms of their relationship to one of the three numbers. Let's call the numbers x, y, and z, where x is the first number, y is the second, and z is the third.
We know x + y + z = 83.
Since the third number is twice the second, we say that z = 2y.
Since the second number is seven less than the first, we say that y = x - 7. We can rewrite this as x = y + 7.
Now all three can be written in terms of y.
x + y + z = 83
(y + 7) + y + 2y = 83
4y + 7 = 83
4y = 76
y = 19
The second number is 19. The first is 19 + 7 or 26, and the third is 2 times 19 or 38.
A check reveals that 26 + 19 + 38 = 83.
Answer:
1, p = -0.5
Step-by-step explanation:
2(p+5) = 4 - 10p
2p+10 = 4 - 10p
2p + 10p = 4 - 10
12p = -6
p = -6/12
p = -0.5
2(-0.5+5) = 4 - 10(-0.5)
-1 + 10 = 4 + 5
9 = 9
<h3>
Answer: x-2y = -8</h3>
===========================================
Explanation:
Multiply both sides by 2 to clear out the fraction
y = (1/2)x+4
2y = 2[ (1/2)x + 4 ]
2y = 2*(1/2)x + 2*4
2y = x + 8
Then move the x term over to the left side
2y = x+8
2y-x = 8
-x+2y = 8
Optionally we can multiply both sides by -1
-x+2y = 8
-1*(-x+2y) = -1*8
x-2y = -8
This is in standard form Ax+By = C with A = 1, B = -2, C = -8
The reason why I multiplied both sides by -1 was to make A > 0 which is what some textbooks use as convention. Of course -x+2y = 8 is equally valid too.
Check the picture below.
you can pretty much just count off the grid the units for JK and MI.
now, let's check how long are KI and JM
![\bf \textit{distance between 2 points}\\ \quad \\ \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) K&({{ -4}}\quad ,&{{ 4}})\quad % (c,d) I&({{ -2}}\quad ,&{{ 3}}) \end{array}\qquad % distance value d = \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2} \\\\\\ KI=\sqrt{[-2-(-4)]^2+[3-4]^2}\implies KI=\sqrt{(-2+4)^2+(3-4)^2} \\\\\\ KI=\sqrt{2^2+(-1)^2}\implies KI=\sqrt{4+1}\implies \boxed{KI=\sqrt{5}}\\\\ -------------------------------](https://tex.z-dn.net/?f=%5Cbf%20%5Ctextit%7Bdistance%20between%202%20points%7D%5C%5C%20%5Cquad%20%5C%5C%0A%5Cbegin%7Barray%7D%7Blllll%7D%0A%26x_1%26y_1%26x_2%26y_2%5C%5C%0A%25%20%20%28a%2Cb%29%0AK%26%28%7B%7B%20-4%7D%7D%5Cquad%20%2C%26%7B%7B%204%7D%7D%29%5Cquad%20%0A%25%20%20%28c%2Cd%29%0AI%26%28%7B%7B%20-2%7D%7D%5Cquad%20%2C%26%7B%7B%203%7D%7D%29%0A%5Cend%7Barray%7D%5Cqquad%20%0A%25%20%20distance%20value%0Ad%20%3D%20%5Csqrt%7B%28%7B%7B%20x_2%7D%7D-%7B%7B%20x_1%7D%7D%29%5E2%20%2B%20%28%7B%7B%20y_2%7D%7D-%7B%7B%20y_1%7D%7D%29%5E2%7D%0A%5C%5C%5C%5C%5C%5C%0AKI%3D%5Csqrt%7B%5B-2-%28-4%29%5D%5E2%2B%5B3-4%5D%5E2%7D%5Cimplies%20KI%3D%5Csqrt%7B%28-2%2B4%29%5E2%2B%283-4%29%5E2%7D%0A%5C%5C%5C%5C%5C%5C%0AKI%3D%5Csqrt%7B2%5E2%2B%28-1%29%5E2%7D%5Cimplies%20KI%3D%5Csqrt%7B4%2B1%7D%5Cimplies%20%5Cboxed%7BKI%3D%5Csqrt%7B5%7D%7D%5C%5C%5C%5C%0A-------------------------------)
![\bf \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) J&({{ -7}}\quad ,&{{ 4}})\quad % (c,d) M&({{ -8}}\quad ,&{{ 3}}) \end{array}\qquad % distance value \\\\\\ JM=\sqrt{[-8-(-7)]^2+[3-4]^2}\implies JM=\sqrt{(-8+7)^2+(3-4)^2} \\\\\\ JM=\sqrt{(-1)^2+(-1)^2}\implies \boxed{JM=\sqrt{2}}](https://tex.z-dn.net/?f=%5Cbf%20%5Cbegin%7Barray%7D%7Blllll%7D%0A%26x_1%26y_1%26x_2%26y_2%5C%5C%0A%25%20%20%28a%2Cb%29%0AJ%26%28%7B%7B%20-7%7D%7D%5Cquad%20%2C%26%7B%7B%204%7D%7D%29%5Cquad%20%0A%25%20%20%28c%2Cd%29%0AM%26%28%7B%7B%20-8%7D%7D%5Cquad%20%2C%26%7B%7B%203%7D%7D%29%0A%5Cend%7Barray%7D%5Cqquad%20%0A%25%20%20distance%20value%0A%5C%5C%5C%5C%5C%5C%0AJM%3D%5Csqrt%7B%5B-8-%28-7%29%5D%5E2%2B%5B3-4%5D%5E2%7D%5Cimplies%20JM%3D%5Csqrt%7B%28-8%2B7%29%5E2%2B%283-4%29%5E2%7D%0A%5C%5C%5C%5C%5C%5C%0AJM%3D%5Csqrt%7B%28-1%29%5E2%2B%28-1%29%5E2%7D%5Cimplies%20%5Cboxed%7BJM%3D%5Csqrt%7B2%7D%7D)
so, add all sides, and that's the perimeter of the trapezoid.
