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nasty-shy [4]
3 years ago
5

Line ℓ1 has the equation

Mathematics
1 answer:
aleksley [76]3 years ago
3 0

Answer:

\sqrt{2} units

Step-by-step explanation:

The Line 1 has equation x + y = 5 ....... (1) , and  

Line 2 has equation x + y = 3 .......... (2)

Now, we have to find the perpendicular distance between line 1 and line 2.

We can say that (3,0) is a point on line 2 as it satisfies the equation (2).

Now, the perpendicular distance from point (3,0) to the line 1 will be given by the formula

\frac{|3 + 0 - 5|}{\sqrt{1^{2}+ 1^{2}}} = \frac{2}{\sqrt{2}} = \sqrt{2} units (Answer)

We know that the perpendicular distance from any external point (x_{1},y_{1}) to a given straight line ax + by + c = 0 is given by the formula \frac{|ax_{1} + by_{1} + c|}{\sqrt{a^{2} + b^{2}}}.

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Quante’ had 15.3 feet of fishing line. He cut off a piece and had 3.2 inches left. How long was the piece he cut off?
Licemer1 [7]

Answer:

180.4 inches (15.033 feet)

Step-by-step explanation:

To solve this, we convert 15.3 feet to inches. We do this by multiplying 15.3 by 12. This gets us 183.6. Now, we subtract 3.2 from 183.6. This gets us 180.4. That means the piece cut off of 180.4 inches long. To convert this to feet, we divide by 12. That gets us 15.033. That means the piece cut off is 180.4 inches long, or 15.033 feet long.

6 0
3 years ago
Please help asap
Neko [114]
I believe it's 36. The vertices have the same x coordinate so I found the difference between the y coordinates.
7 0
3 years ago
If O is the center of the circle find x. ​
Over [174]

Answer:

x = 60°

Step-by-step explanation:

Angles on the circle formed by the same arc are congruent, then

∠ BDC = ∠ BAC = 50°

x = 180° - (70 + 50)° ← sum of angles in triangle = 180°

x = 180° - 120° = 60°

3 0
2 years ago
15. The solution to 2 × 27 will be what kind of number?
N76 [4]
2*27= 54 which is an even number, not a perfect square, odd or prime. The prime factorization would be 2*3^3
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3 0
3 years ago
The two-way table shows the medal count for the top-performing countries in the 2012 Summer Olympics. A 5-column table has 5 row
LUCKY_DIMON [66]

Which statement is true?

  • The probability that a randomly selected silver medal was awarded to Great Britain is StartFraction 17 Over 99 EndFraction.
  • The probability that a randomly selected medal won by Russia was a bronze medal is StartFraction 32 Over 103 EndFraction.
  • The probability that a randomly selected gold medal was awarded to China is StartFraction 88 Over 137 EndFraction.
  • The probability that a randomly selected medal won by the United States was a silver medal is StartFraction 104 Over 339 EndFraction.

Answer:

(A)The probability that a randomly selected silver medal was awarded to Great Britain is 17/99.

Step-by-step explanation:

The table is given below:

\left|\begin{array}{l|c|c|c|c|c}  &Gold&Silver          & Bronze       &Total\\United States    &46      &    29      &          29      &         104\\China             &     38     &     27       &         23        &         88\\Russia         &        24  &        26      &          32                 &82\\Great Britain   &    29   &        17        &        19        &         65\\&&&&&\\Total                    &137     &     99     &          103      &        339\end{array}\right

                         

We calculate the probabilities given in the statements.

(A) The probability that a randomly selected silver medal was awarded to Great Britain

= 17/99

(B)The probability that a randomly selected medal won by Russia was a bronze medal

=32/82

(C)The probability that a randomly selected gold medal was awarded to China

=38/137

(D)The probability that a randomly selected medal won by the United States was a silver medal

=29/104

We can see that only the first statement is true.

5 0
2 years ago
Read 2 more answers
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