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disa [49]
3 years ago
11

Find x and y so that the quadrilateral is a parallelogram.

Mathematics
1 answer:
sergiy2304 [10]3 years ago
3 0

Answer:

Result:

  • The value of x = 12
  • The value of y = 21

Step-by-step explanation:

Given

The parallelogram DEFG

DE = 6x-12

FG = 2x+36

EF = 4y

DG = 6y-42

We know that the opposite sides of a parallelogram are equal.  

As DE and FG are opposite sides, so

DE = FG

substituting DE = 6x-12 and FG = 2x+36 in the equation

6x-12 = 2x+36

6x-2x = 36+12

simplifying

4x = 48

dividing both sides by 4

4x/4 = 48/4

x = 12

Therefore,

The value of x = 12

Also, EF and DG are opposite sides, so

EF = DG

substituting EF = 4y and DG = 6y-42 in the equation

4y = 6y-42

switching sides

6y-42 = 4y

6y-4y = 42

2y = 42

dividing both sides by 2

2y/2 = 42/2

y = 21

Therefore,

The value of y = 21

Result:

  • The value of x = 12
  • The value of y = 21
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Angelina_Jolie [31]
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The equation we have is:
5,249 = 29d
If they read 5,249 <em>pages</em>, then we can include the unit for pages in the equation.
Since we also know that <em>d</em> is the number of days it took, you can replace <em>d</em> with days.
The equation becomes:
5,249\ pages=29*(x\days)
Now that we have one variable, we can solve for <em>p/d</em>:
\frac{5,249\ pages}{29}=x\ days\\\\181 = x
Thus it took them 181 days to read it all.

If Johnny read 5,249 pages over 181 days and the unit rate is pages per day(p/d), then the equation for finding <em>p/d</em> is:
\frac{p\ pages}{d\ days}=\frac{5,249\ pages}{181\ days}=\frac{29\ pages}{1\ day}\\\\29\ \frac{pages}{day}
Johnny read 29 pages per day.
8 0
3 years ago
Given that g(x) = 2x ^ 2 - 2x + 8 , find each of the following. a) g(0) b) g(- 2) C) g(3) d) g(- x) e) g(1 - t)
raketka [301]

Answer:

g(-2)=20

Step-by-step explanation:

Given g(x)=2x^2-2x+8, substitute what is in the parentheses for x to find an output.

For g(-2), the term -2 is in the parentheses. Thus, substitute x=-2 into 2x^2-2x+8 to find g(-2):

g(-2)=2(-2)^2-2(-2)+8,\\g(-2)=2\cdot 4+4+8,\\g(-2)=8+4+8,\\g(-2)=\boxed{20}

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I hope this helps!

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A new American graduate is contemplating buying a Japanese, German, or an American car. No matter the type of car, he plans to b
Svetach [21]

Answer:

The best option is to buy Japanese Car.

Step-by-step explanation:

Fuel usage per year is 150000/ 8 = 18750 miles per year

Fuel cost (year 1 -8) = $3.0, $3.06, $3.12, $3.18, $3.25, $3.312, $3.38, $3.5

Japanese Car:

Fuel usage 18750 / 23 = 815 * $3 = $2446  

Fuel charges (year 1 -8) = $2445, $2494, $2623, $2758. $2900, $3050, $3207, $3372

Repair Cost (year 1 - 8) = $700, $721, $742, $764, $787, $811, $835, $860

Insurance cost (Year 1 - 8) = $700, $714, $728, $742, $757, $772, $788, $804

Present value of cost at 5% = 24674.07

Cost of car is $30,000

Total cost = $54674.07

Amercian Car:

Cost $35,000

Fuel usage 18750/20 = 937.5 * $3 per gallon = $2812.5.

Fuel charges (year 1 -8) = $2812, $2913, $2986, $3011. $3098, $3124, $3176, $3208

Repair Cost (year 1 - 8) = $800, $894, $921, $978, $1109, $1176, $1207, $1301

Insurance cost (Year 1 - 8) = $800, $827, $876, $898, $908, $932, $954, $934

Present value of cost at 5% = 25302.18

Cost of car is $35,000

Total cost = $60302.

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Cost = $45,000

Fuel usage 18750 / 21 = 892 * $3 = $2678  

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Present value of cost at 5% = 27105.73

Cost of car is $45,000

Total cost = $72105.

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