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12345 [234]
3 years ago
9

The temperature of a point $(x,y)$ in the plane is given by the expression $x^2 + y^2 - 4x + 2y$. what is the temperature of the

coldest point in the plane?
Mathematics
1 answer:
ollegr [7]3 years ago
3 0
x^{2} + y^{2}-4x+2y

can be written as follows:

x^{2} -4x+ y^{2}+2y

(x^{2} -4x+4)-4+ (y^{2}+2y+1)-1

(x-2)^{2}+(y+1)^{2} -5

since (x-2)^{2} and (y+1)^{2} are always positive, except for x=2 and y=-1, when they become 0,

the minimum value of this expression is when x=2, and y=-1, that is -5



Answer: -5
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Peg and Larry purchased “no contract” cell phones. Pegs phone costs $25 plus $0.25 per minute. Larry’s phone cost $35 plus $0.20
marissa [1.9K]
Let x be the number of minutes Peg and Larry used their phones. So their costs can be written as:

Cost of Peg's Phone usage = 25 + 0.25x
Cost of Larry's Phone usage = 35 + 0.20x

We are to find when the Peg's phone will be more than Larry's phone. We can set up the inequality as:

25 + 0.25x > 35 + 0.20x

Re-arranging the inequality

0.25x - 0.20x > 35 - 25

0.05x > 10

x > 10/0.05

x > 200

Thus, Pag's phone will cost more if the number of minutes of phone usage is more than 200
5 0
3 years ago
A vet's office offers boarding for cats and dogs. boarding a cat cost$20 per night and a dog cost $25 per night if the vet's off
MAVERICK [17]

Answer:

b. x+y=18

20x+25y=400

Step-by-step explanation:

7 0
3 years ago
Audrey and Lauren began reading a novel on the same day. Audrey reads 15 pages a day and Lauren reads 5 pages a day. If Audrey i
mars1129 [50]
Lauren is on page 25. Since 75/15 is 5 that means she read fro 5 days. And they started at the same time so 5*5 is 25
4 0
3 years ago
Read 2 more answers
If a triangle has an area of 192 mm2, and the
Debora [2.8K]

Answer:32mm

Step-by-step explanation:

area of triangle = 1/2 *base * height

192mm2 = 1/2 *b* 12mm

192 =6b

base=192/6

base= 32mm

3 0
3 years ago
Solve for a: 5(a+5)-3=3(2-a)
ivann1987 [24]

Simplify:

5(a + 5) + -3 = 3(2 + -1a)

Reorder the terms:

5(5 + a) + -3 = 3(2 + -1a)

(5 * 5 + a * 5) + -3 = 3(2 + -1a)

(25 + 5a) + -3 = 3(2 + -1a)

Reorder the terms again:

25 + -3 + 5a = 3(2 + -1a)

Combine like terms:

]25 + -3 = 22

22 + 5a = 3(2 + -1a)

22 + 5a = (2 * 3 + -1a * 3)

22 + 5a = (6 + -3a)

Solve:

22 + 5a = 6 + -3a

To solve for variable 'a':

You have to move all terms containing A to the left, all other terms to the right.

Then add '3a' to each side of the equation:

22 + 5a + 3a = 6 + -3a + 3a

Combine like terms:

5a + 3a = 8a

22 + 8a = 6 + -3a + 3a

Combine like terms again:

-3a + 3a = 0

22 + 8a = 6 + 0

22 + 8a = 6

Add '-22' to each side of the equation.:

22 + -22 + 8a = 6 + -22

Combine like terms:

22 + -22 = 0

0 + 8a = 6 + -22

8a = 6 + -22

Combine like terms once more:

6 + -22 = -16

8a = -16

Divide each side by '8'.

a = -2

Simplify:

a = -2

Answer: a=-2

Hope I could help! :)

8 0
3 years ago
Read 2 more answers
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