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Paha777 [63]
3 years ago
8

A lighthouse casts a 128-ft shadow. A nearby lamppost that measures 5

Mathematics
1 answer:
Yakvenalex [24]3 years ago
5 0

Answer:

80 ft

Step-by-step explanation:

Let the height of the light house be x feet.

\therefore \:  \frac{128}{8}  =  \frac{x}{5}  \\  \\ x =  \frac{128 \times 5}{8}  \\  \\ x =  \frac{640}{8}  \\  \\ x = 80 \: feet

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Can someone please help!!!
RideAnS [48]

Answers:

  • System 1:  x = 3 and y = -5
  • System 2: x = 1 and y = 2

==========================================================

Explanation:

For now, let's focus on system 1.

We have identical copies of "2y" in each equation, which means that if we were to subtract the equations straight down, then the y terms cancel out. That allows us to solve for x.

  • The x terms subtract to 7x-x = 6x
  • The y terms subtract to 0 and go away
  • The right hand sides subtract to 11 minus (-7) = 11-(-7) = 11+7 = 18

After doing those subtractions, we have the new equation 6x = 18 which solves to x = 3. Divide both sides by 6 to isolate x.

Once we know x, we can find out y.

7x+2y = 11

7(3)+2y = 11

21+2y = 11

2y = 11-21

2y = -10

y = -10/2

y = -5

or we can say

x+2y = -7

3+2y = -7

2y = -7-3

2y = -10

y = -10/2

y = -5

We should lead to the same y value either way. This helps confirm we have the correct x value.

Overall, the solution to system 1 is (x,y) = (3, -5)

----------------------------

Now onto system 2.

Unfortunately, we don't have identical y terms this time. But what we can do is double everything in the second equation to go from -x+y = 1 to -2x+2y = 2.

The new equivalent system is

\begin{cases}7x+2y = 11\\-2x+2y = 2\end{cases}

Now we have the same situation as before: Subtract straight down, solve for x.

  • The x terms subtract to 7x-(-2x) = 7x+2x = 9x
  • The y terms go away when subtracting
  • The right hand sides subtract to 11-2 = 9

So we have 9x = 9 and that solves to x = 1.

We'll use this x to find the y value.

7x+2y = 11

7(1)+2y = 11

7+2y = 11

2y = 11-7

2y = 4

y = 4/2

y = 2

Or you could pick on the second equation

-x+y = 1

-1+y = 1

y = 1+1

y = 2

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mina [271]
Answer: 75

h23 means we look at the 2nd row and 3rd column of matrix H. The value found here is 75
3 0
3 years ago
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in order to receive a B grade in a college course, it is necessary to have an overall average of 80% correct on two 1-hour exams
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Since 80% of the 300 total points is 240, and we have 127 so far, 240-127=113 as a minimum
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Answer:

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