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3 years ago

Line segments AB and CD are

Mathematics

1 answer:

dalvyx [7]3 years ago

8 0

Answer:

x = 16 or -2

Step-by-step explanation:

If both lines are congruent, their magnitudes are equal.

To find the magnitude of a line, the equation to use is;

D = √(x2-x1)^2 + (y2-y1)^2

So for AB, we have

D = √(-2 + 11)^2 + (5 + 3)^2

D = √81 + 64 = √145

For the second line

The distance would be;

D = √x-7)^2 + (9-1)^2

D = √(x-7)^2 + 8^2

Equate both magnitude

√145 = √(x-7)^2 + 64)

Simply remove the square roots on both sides

145 = 64 + (x - 7)^2

145 -64 = (x -7)^2

81 = (x-7)^2

Thaw the square root of both sides

x - 7 = 9

or x -7 = -9

x = 9 + 7 or x = -9 + 7

x = 16 or -2

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pogonyaev

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2 years ago

Change 3240 degrees/second to radians/second

Sergeu [11.5K]

Using the formula 1° × π/180 = 0.01745rad,

3240 degrees/second = 56.54867 radians/seconds

4 0

3 years ago

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mel-nik [20]

Answer:

40 students

Step-by-step explanation:

In this problem, one is given the ratio ( 8 : 3 ), since a ratio is another way of writing a fraction one can rewrite it as; $\frac{8}{3}$ (8) represent the number of students who want to learn about magnets, and (3) represents the number of students who want to learn about magic tricks.

In the problem, it is also given that 25 more students wanted to learn about magnets compared to magic tricks. If one uses the parameter (x) to represent the factor by which the fraction $\frac{8}{3}$ is reduced, then one can get the equation;

8x = 3x + 25

Use inverse operations to solve,

8x = 3x + 25

-3x

5x = 25

x = 5

Substitute back in to find out how many students want to learn about magnets,

= 8(5)

= 40

3 0

3 years ago

3.50 rounded to the nearest whole ounce

Maslowich

Answer:

Step-by-step explanation:

Look at the tenths place to round.

4 and below, round down.

5 and above, round up.

In this case, it’s 5 so round up.

3.50 -> 4

5 0

3 years ago

In analyzing the city and highway fuel efficiencies of many cars and trucks, the mean difference in fuel efficiencies for the 60

Olegator [25]

Answer:

$7.38-1.96\frac{2.51}{\sqrt{601}}=7.18$

$7.38+1.96\frac{2.51}{\sqrt{601}}=7.58$

For this case the confidence interval is given by :

$7.18 \leq \mu \leq 7.58$

Step-by-step explanation:

Data provided

$\bar X=7.38$ represent the sample mean for the fuel efficiencies

$\mu$ population mean

s=2.51 represent the sample standard deviation

n=601 represent the sample size

Confidence interval

The formula for the confidence interval of the true mean is given by:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

The degrees of freedom for this case is given by:

$df=n-1=601-1=600$

The Confidence level for this case is 0.95 or 95%, and the significance level $\alpha=0.05$ and $\alpha/2 =0.025$ and the critical value is given by $t_{\alpha/2}=1.96$

Replcing into the formula for the confidence interval is given by:

$7.38-1.96\frac{2.51}{\sqrt{601}}=7.18$

$7.38+1.96\frac{2.51}{\sqrt{601}}=7.58$

For this case the confidence interval is given by :

$7.18 \leq \mu \leq 7.58$

8 0

3 years ago