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Anna [14]
3 years ago
11

The distance between the two points is (2,-3)and (k,9) is 13 units find k​

Mathematics
1 answer:
docker41 [41]3 years ago
8 0

Step-by-step explanation:

\sqrt{(k - 2)^{2}  +  {(9 + 3)}^{2} }  = 13 \\  \\  \therefore \:  \sqrt{k^{2} - 2 \times 2k + 2^{2}  +  {(12)}^{2} }  = 13 \\  \\ \therefore \:  \sqrt{k^{2} - 4k + 4 +  144 }  = 13\\  \\ \therefore \:  \sqrt{k^{2} - 4k + 148 }  = 13 \:  \\  \:  \:  \:  \:  \:  \: squaring \: both \: sides \\  \\ k^{2} - 4k + 148  = 169 \\  \\ \therefore \:  k^{2} - 4k + 148   -  169  = 0\\  \\ \therefore \:  k^{2} - 4k  - 21  = 0\\  \\ \therefore \:  k^{2} - 7k  + 3k - 21  = 0\\  \\ \therefore \:  k(k - 7) + 3(k - 7)  = 0 \\  \\ \therefore \:  (k - 7) (k+ 3)  = 0 \\  \\ \therefore \:  (k - 7) = 0 \: or \:  (k+ 3)  = 0 \\  \\ \therefore \: k = 7 \: or \: k =  - 3 \\  \\  \huge \purple{ \boxed{\therefore \:k =  \{ - 3, \:  \: 7 \}}}

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A half-dollar coin issued by the United States Mint measures 30.61 millimeters across. Nick has 9 half dollars. He lines them up
Paraphin [41]

Answer:

Step-by-step explanation:

137,745 mm

Becouse the diamter of the Half dollar is 2 double Than a raggio becoise u must moltiplicate it for Hal of the moneu u have... 4.5 x 30.61

6 0
2 years ago
A bag contains purple marbles and yellow marbles, 52 in total. The number of purple marbles is 4 more than 3 times the number of
Masja [62]

Answer:

16

Step-by-step explanation:

This question can be modeled using the equation 3x+4=52 (x is the purple marbles). To solve this equation subtract 4 from both sides, making it 3x=48. divide both by three showing x=16. This shows that 16 is the answer.

5 0
3 years ago
If 5 choc ices cost 330p how much do 9 cost?
borishaifa [10]


use unitary method

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so for 1 choc it will cost 330/5

to get 9,

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8 0
3 years ago
Read 2 more answers
Which of these problem situations could best be modeled by the equation below? 52(18) + x = 1200 Debbie sold 52 boxes of fruit f
kirill [66]

Answer:

a) Debbie sold 52 boxes of fruit for $18 each plus a bonus x, for selling the boxes quickly. Find x, the bonus if Debbie sold the fruit quickly and earned $1200.

Step-by-step explanation:

The model equation is given as:

52(18) + x = 1200

a) Debbie sold 52 boxes of fruit for $18 each plus a bonus x, for selling the boxes quickly. Find x, the bonus if Debbie sold the fruit quickly and earned $1200.

52($18) + x = $1200

52(18) + x = $1200

Option a is correct

b) Katrina earned $18 plus a weekly bonus x, for managing her money wisely each week for 52 weeks. Find x, if Katrina earned $1200.

x = weekly bonus, hence, we have the equation:

$18 + (x)52 = $1200

Option b is wrong

c) Marissa has $52 in her savings account. She earns $18 for each lawn she mows. Find x, the number of weeks she needs to mow lawns in order to have a total of $1200.

This is represented as:

$52 + $18(x) = $1200

Option c is wrong

d) Edward had a balance of $52 in the bank. He added x dollars to his account last month. This week he deposited another $18. Find x, the amount Edward deposited in the bank last month if his total savings is now $1200.

This is represented as :

$52+ $x + $18 = $1200

Option d is wrong.

Therefore, the correct statement that modelled the equation is option a

5 0
3 years ago
Write 2.63 as a mixed number in simplest form.
Sedaia [141]

Answer:

263100=2.63

Step-by-step explanation:

263100 is already in the simplest form. It can be written as 2.63 in decimal form (rounded to 6 decimal places).

6 0
2 years ago
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