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7nadin3 [17]
3 years ago
14

find the numerical lengths of the diagonals of the parallelogram below where FB=4x-2 FD=3y-1 FC=3x and FA=3y-3. solve using a sy

stem of equations via substitution or elimination methods.

Mathematics
1 answer:
Andre45 [30]3 years ago
8 0

Answer:

BD = 28

AC = 24

Step-by-step explanation:

Diagonals of a parallelogram bisect each other.

4x − 2 = 3y − 1

3x = 3y − 3

Using elimination to solve the system of equations, subtract the second equation from the first.

(4x − 2) − 3x = (3y − 1) − (3y − 3)

4x − 2 − 3x = 3y − 1 − 3y + 3

x − 2 = 2

x = 4

Substitute into either equation to find y.

3(4) = 3y − 3

12 = 3y − 3

15 = 3y

y = 5

The length of BD is:

4(4) − 2 + 3(5) − 1 = 28

The length of AC is:

3(4) + 3(5) − 3 = 24

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4 0
2 years ago
James and Cameron are watching a film. They pause it with one fifth left to watch. What is the ratio of how much they have watch
goldenfox [79]

Answer:

The ratio of how much they have watched to how much they have left to see is 4 : 1.

Step-by-step explanation:

Consider that the total duration of the film is, 1.

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Compute the ratio of how much they have watched to how much they have left to see as follows:

\frac{\text{Duration Watched}}{\text{Duration Left}}=\frac{4/5}{1/5}=\frac{4}{1}=4:1

Thus, the ratio of how much they have watched to how much they have left to see is 4 : 1.

5 0
3 years ago
An open box is formed from a rectangular piece of cardboard whose length is 8cm more than its width by cutting squares of 2cm fr
Serggg [28]
If the width of the cardboard = x cm then its length is given by x + 8 cm.
Then the length of the box will be x + 8 - 2(2) =  x + 4
and the width = x - 2(2) = x - 4 cm The height is 2 cm 

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3 0
3 years ago
The U.S. Census Bureau announced that the median sales price in 2014 for new homes was $282,800 and the mean sales price was $34
victus00 [196]

Answer:

a) 0.9964

b) 0.3040

Step-by-step explanation:

Given data:

standard deviation =  $90,000

Mean sales price =$345,800

sample mean =  $370,000

Total number of sample = 100

calculate z score for [/tex](\bar x = 370000)[/tex]

z = \frac{\bar x - \mu}{\frac{\sigma}{\sqrt{n}}}

z = \frac{370000 - 345800}{\frac{90000}{\sqrt{100}}}

z = 2.689

P(x<370000) = P(Z<2.689)

FROM STANDARD NORMAL DISTRIBUTION TABLE FOR Z P(Z<2.689) = 0.9964

B)

calculate z score for (\bar x = 350000)

z = \frac{\bar x - \mu}{\frac{\sigma}{\sqrt{n}}}

z = \frac{350000 - 345800}{\frac{90000}{\sqrt{100}}}

z = 2.133

P(350000 \leq \bar x \leq 365000) = P(0.467 \leq Z\leq 2.133) = P(Z\leq 2.133) - P(Z\leq 0.467)

FROM NORMAL DISTRIBUTION TABLE Z VALUE FOR

P(Z\leq 2.133) = 0.9836

P(Z\leq 0.467) = 0.6796

SO,  = 0.9836 - 0.6796 = 0.3040

4 0
3 years ago
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