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2 years ago

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Line bc is represented by 3x+2y=8 line ad is represented by -3x-2y=6 what is the relationship of line bc to line ad explain the

sum if the equations demonstrates the relationship

1 answer:

Bas_tet [7]2 years ago

8 0

Answer:

The answer is below

Step-by-step explanation:

The equation of a straight line is given by:

y = mx + b

where m is the slope of the line and b is the y intercept (value of y when x = 0).

Given the equation of two lines as $y=m_1x+b_1\ and\ y=m_2x+b_2$ , the two lines are parallel to each other if $m_1=m_2$ . Also the lines are perpendicular if

$m_1m_2=-1$

Given line BC:

3x + 2y = 8

2y = -3x + 8

y = -3x/2 + 4

Hence the slope of the line BC = -3/2

For line AD:

-3x - 2y = 6

-2y =3x + 6

y = -3x/2 - 3

Hence the slope of line AD is -3/2

Since both line BC and AD have equal slope (-3/2), hence both lines are parallel to each other

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What is a conversion factor that you an use to convert gallons to pints?how did you find it?

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Volume unit conversion. 1 gallon = 8 pints.

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3 years ago

1. an alloy contains zinc and copper in the ratio of 7:9 find weight of copper of it had 31.5 kgs of zinc.

m_a_m_a [10]

Answer:

Step-by-step explanation:

Question (1). An alloy contains zinc and copper in the ratio of 7 : 9.

If the weight of an alloy = x kgs

Then weight of copper = $\frac{9}{7+9}\times (x)$

= $\frac{9}{16}\times (x)$

And the weight of zinc = $\frac{7}{7+9}\times (x)$

= $\frac{7}{16}\times (x)$

If the weight of zinc = 31.5 kg

31.5 = $\frac{7}{16}\times (x)$

x = $\frac{16\times 31.5}{7}$

x = 72 kgs

Therefore, weight of copper = $\frac{9}{16}\times (72)$

= 40.5 kgs

2). i). 2 : 3 = $\frac{2}{3}$

4 : 5 = $\frac{4}{5}$

Now we will equalize the denominators of each fraction to compare the ratios.

$\frac{2}{3}\times \frac{5}{5}$ = $\frac{10}{15}$

$\frac{4}{5}\times \frac{3}{3}=\frac{12}{15}$

Since, $\frac{12}{15}>\frac{10}{15}$

Therefore, 4 : 5 > 2 : 3

ii). 11 : 19 = $\frac{11}{19}$

19 : 21 = $\frac{19}{21}$

By equalizing denominators of the given fractions,

$\frac{11}{19}\times \frac{21}{21}=\frac{231}{399}$

And $\frac{19}{21}\times \frac{19}{19}=\frac{361}{399}$

Since, $\frac{361}{399}>\frac{231}{399}$

Therefore, 19 : 21 > 11 : 19

iii). $\frac{1}{2}:\frac{1}{3}=\frac{1}{2}\times \frac{3}{1}$

$=\frac{3}{2}$

$\frac{1}{3}:\frac{1}{4}=\frac{1}{3}\times \frac{4}{1}$

= $\frac{4}{3}$

Now we equalize the denominators of the fractions,

$\frac{3}{2}\times \frac{3}{3}=\frac{9}{6}$

And $\frac{4}{3}\times \frac{2}{2}=\frac{8}{6}$

Since $\frac{9}{6}>\frac{8}{6}$

Therefore, $\frac{1}{2}:\frac{1}{3}>\frac{1}{3}:\frac{1}{4}$ will be the answer.

IV). $1\frac{1}{5}:1\frac{1}{3}=\frac{6}{5}:\frac{4}{3}$

$=\frac{6}{5}\times \frac{3}{4}$

$=\frac{18}{20}$

$=\frac{9}{10}$

Similarly, $\frac{2}{5}:\frac{3}{2}=\frac{2}{5}\times \frac{2}{3}$

$=\frac{4}{15}$

By equalizing the denominators,

$\frac{9}{10}\times \frac{30}{30}=\frac{270}{300}$

Similarly, $\frac{4}{15}\times \frac{20}{20}=\frac{80}{300}$

Since $\frac{270}{300}>\frac{80}{300}$

Therefore, $1\frac{1}{5}:1\frac{1}{3}>\frac{2}{5}:\frac{3}{2}$

V). If a : b = 6 : 5

$\frac{a}{b}=\frac{6}{5}$

$=\frac{6}{5}\times \frac{2}{2}$

$=\frac{12}{10}$

And b : c = 10 : 9

$\frac{b}{c}=\frac{10}{9}$

Since a : b = 12 : 10

And b : c = 10 : 9

Since b = 10 is common in both the ratios,

Therefore, combined form of the ratios will be,

a : b : c = 12 : 10 : 9

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2 years ago

The amount that Jimmy paid for his meals the four days, $6.45, $21.38, $1.99, $7.99, $16, $0, $7.99, $18.95, $4.30, $10.35, $18.

ella [17]

Answer:

$7.99

Step-by-step explanation:

Arrange numbers in numerical order: $0, $1.99, $4.30, $6.45, $7.99, $7.99, $10.35, $16, $18.20, $18.95, $21.38.

Count how many numbers you have, 11.

11 is an odd number so, the number in the middle of the data set is the median.

Final answer: $7.99 is the median.

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2 years ago

a woodworker wants to cut a board that is 8.225 feet long into 5 equal pieces. How long will each of the boards be?

jok3333 [9.3K]

Answer:

1.645 feet

Step-by-step explanation:

To solve this you must divide the total length by 5. 8.225/5=1.645. Each board will be 1.645 feet long

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