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EleoNora [17]
3 years ago
9

Please help, will give brainliest!

Mathematics
1 answer:
12345 [234]3 years ago
6 0

Answer:

Step-by-step explanation:

In parallelogram, diagonals bisect each other

DP = IP

7x - 8 = 3x

7x       = 3x + 8

7x - 3x = 8

      4x = 8

       x = 8/4

     x = 2

NP = YP

3y = 7x - 2

3y = 7*2 - 2

3y = 14 - 2

3y = 12

y = 12/3

y = 4

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Loren drove 200 miles at a certain rate, and his wife, Lois, drove 100 miles at a rate 10 mph slower. If Loren had driven for th
NeX [460]

As long as Loren drove, the law of motion was

200 = st_1 \implies t_1 = \dfrac{200}{s}

As long as Loid drove, the law of motion was

100 = (s-10)t_2 \implies t_2 = \dfrac{100}{s-10}

So, the total time they took is

t_1+t_2=\dfrac{200}{s}+\dfrac{100}{s-10}

Had Loren driven the whole time, the law of motion would have been

300=st_3 \implies t_3 = \dfrac{300}{s}

And we know that this time would have been 30 minutes (i.e. 0.5 hours) faster. So, we have

t_3 = t_1+t_2-0.5

This translates into

\dfrac{300}{s}=\dfrac{200}{s}+\dfrac{100}{s-10}-\dfrac{1}{2}

If we subtract 200/s from both sides, we have

\dfrac{100}{s}=\dfrac{100}{s-10}-\dfrac{1}{2}

We can simplify the right hand side by summing the two fractions:

\dfrac{100}{s-10}-\dfrac{1}{2} = \dfrac{200-(s-10)}{2(s-10)}=\dfrac{210-s}{2(s-10)}

So, we have to solve

\dfrac{100}{s}=\dfrac{210-s}{2(s-10)}

If we cross multiply the denominators, we have

200(s-10)=s(210-s) \iff 200s-2000=210s-s^2 \iff s^2-10s-2000=0

Which yields the solutions

s=-40,\quad s=50

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3 years ago
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Solve for x. I need help with this problem. <br><br>​
Advocard [28]

Answer:

x = 9

Step-by-step explanation:

Rule: the two interior angles F and E when added, equal <FGH.

so

6x + 16 + 60 = 13x + 13  Combine the terms on the left.

6x + 76 = 13x + 13          Subtract 13 from both sides.

6x + 76-13 = 13x             Combine

6x + 63 = 13x                  Subtract 6x from both sides.

63 = 7x                            Divide by 7

63/7 = x

x = 9

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