What is the value of the expression |x| + |y + z| when x = –6, y = –3, and z = –5?

Answers

Answer 1

Answer:

x=-6, y=-3, z=-5

|x|+|y+z|=|-6|+|-3-5|=6+|-8|=6+8=14

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Rebecca buys some socks that cost $5.87 per pair and a t-shirt that cost $12.99. The cost of Rebecca’s total purchase is $87. What equation can be used to find n, the number of socks she purchased?

Answers

Answer:

$5.87n + 12.99 = 87$

There are 8 students in a small class. To make a team, the names of the 2 of them will be drawn from a hat. How many different teams of 2 students are

Answers

use slot method
2 slots

8 choices for first slot
7 choices for second (since 1 is in 1st slot)
8 times 7=56

56 ways to make 2 person teams

The first name can be any one of the 8.
   For each of those . . .
The second name can be any one of the remaining 7.

Total number of ways that 2 names can be drawn = (8 x 7) = 56 .

But . . .

Each team can be drawn in two different ways . . .
   -- Smith first, then Cohen
   -- Cohen first, then Smith.

So, among the 56 ways to draw 2 names, you will find
each possible pair of names drawn twice, in the opposite
order.

The number of different 2-member teams is (56 / 2) = 28 .

Rationalise:
(1) 4/(2+root3+root7)
(2) 4/(2root3+root5)

Answers

$(4)/(2+\sqrt3+\sqrt7)\cdot(2-(\sqrt3+\sqrt7))/(2-(\sqrt3+\sqrt7))=(8-4\sqrt3-4\sqrt7)/(2^2-(\sqrt3+\sqrt7)^2)=(8-4\sqrt3-4\sqrt7)/(4-3-2√(3\cdot7)-7)\n\n=(8-4\sqrt3-4\sqrt7)/(-6-2√(21))=(-2(2\sqrt3+2\sqrt7-4))/(-2(3+√(21)))=(2\sqrt3+2\sqrt7-4)/(3+√(21))\cdot(3-√(21))/(3-√(21))\n\n=(6\sqrt3-2√(63)+6\sqrt7-2√(147)-12+4√(21))/(3^2-(√(21))^2)=(6\sqrt3-2√(9\cdot7)+6\sqrt7-2√(49\cdot3)-12+4√(21))/(9-21)$

$=(6\sqrt3-6\sqrt7+6\sqrt7-14\sqrt3-12+4√(21))/(-12)=(-8\sqrt3+4√(21)-12)/(-12)=(-4(2\sqrt3-√(21)+3))/(-12)\n\n=(2\sqrt3-√(21)+3)/(3)$

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$(4)/(2\sqrt3+\sqrt5)\cdot(2\sqrt3-\sqrt5)/(2\sqrt3-\sqrt5)=(8\sqrt3-4\sqrt5)/((2\sqrt3)^2-(\sqrt5)^2)=(8\sqrt3-4\sqrt5)/(4\cdot3-5)=(8\sqrt3-4\sqrt5)/(12-5)\n\n=(8\sqrt3-4\sqrt5)/(7)$

$(1) (4)/(2+√(3) +√(7)) \n \n or, (4)/(2+√(3) +√(7)) * (2 - √(3) -√(7))/(2-√(3)-√(7)) \n \n => \frac{ \sqrt[2]{3} - √(21)+3}{3} \n \n \n (2) \frac{4}{\sqrt[2]{3} + √(5)} \n \n or, \frac{4}{\sqrt[2]{3} + √(5)} * \frac{\sqrt[2]{3}-√(5)}{\sqrt[2]{3}-√(5)} \n \n => \frac{\sqrt[8]{3}-\sqrt[4]{5}}{7}$

The total number of laps needed to complete a bike marathon is 75. Kayla completed at least 68 laps. How many possible complete laps could Kayla have completed. Please show work. I'm offering lots of points for this question. Thanks you guys.

Answers

well she needs to complete 75 laps to complete the race so 75 is the upper limit. She has completed at least 68 laps so the lower limit is 68. so the number of laps she could have completed could be from 68 to 75 so the number of laps (x) can be reprented by this inequallity 68 < x < 75

well, I'm not sure if this is correct, it probably isn't, and I'm sorry if it isn't, but i think kayla could have completed 75 laps because there was only 75 laps in the race.

Which relationship is always true for the angles x, y, and z of triangle MNP?

Answers

Answer:

Step-by-step explanation:

In every triangle, all the measures of the angles combined is 180 degrees.

So x + y + z = 180 degrees

Answer:

180 dg

Step-by-step explanation:

How would you write y = –3x2 + 12x – 21 in vertex form?

Answers

The vertex form of that expression would be y = 3 ( x +2 )squared - 25. This is done by transporting first the -21 to the other side then simplifying the 3(x2 + 4x). Then making the "x2 + 4x" a perfect binomial we need to add 4 and that makes it "x2 + 4x + 4". Then after that we now have the vertex form of y = 3 ( x +2 )squared - 25

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