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Softa [21]
3 years ago
10

What is the length of line segment KJ?

Mathematics
1 answer:
expeople1 [14]3 years ago
4 0

Answer:

3 \sqrt{3}

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Which two tables represent the same function?
topjm [15]

Answer:

The 1st and the 5th tables represent the same function

Step-by-step explanation:

* Lets explain how to solve the problem

- There are five tables of functions, two of them are equal

- To find the two equal function lets find their equations

- The form of the equation of a line whose endpoints are (x1 , y1) and

  (x2 , y2) is \frac{y-y_{1}}{x-x_{1}}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}

* Lets make the equation of each table

# (x1 , y1) = (4 , 8) and (x2 , y2) = (6 , 7)

∵ x1 = 4 , x2 = 6 and y1 = 8 , y2 = 7

∴ \frac{y-8}{x-4}=\frac{7-8}{6-4}

∴ \frac{y-8}{x-4}=\frac{-1}{2}

- By using cross multiplication

∴ 2(y - 8) = -1(x - 4) ⇒ simplify

∴ 2y - 16 = -x + 4 ⇒ add x and 16 for two sides

∴ x + 2y = 20 ⇒ (1)

# (x1 , y1) = (4 , 5) and (x2 , y2) = (6 , 4)

∵ x1 = 4 , x2 = 6 and y1 = 5 , y2 = 4

∴ \frac{y-5}{x-4}=\frac{4-5}{6-4}

∴ \frac{y-5}{x-4}=\frac{-1}{2}

- By using cross multiplication

∴ 2(y - 5) = -1(x - 4) ⇒ simplify

∴ 2y - 10 = -x + 4 ⇒ add x and 10 for two sides

∴ x + 2y = 14 ⇒ (2)

# (x1 , y1) = (2 , 8) and (x2 , y2) = (8 , 5)

∵ x1 = 2 , x2 = 8 and y1 = 8 , y2 = 5

∴ \frac{y-8}{x-2}=\frac{5-8}{8-2}

∴ \frac{y-8}{x-2}=\frac{-3}{6}=====\frac{y-8}{x-2}=\frac{-1}{2}

- By using cross multiplication

∴ 2(y - 8) = -1(x - 2) ⇒ simplify

∴ 2y - 16 = -x + 2 ⇒ add x and 16 for two sides

∴ x + 2y = 18 ⇒ (3)

# (x1 , y1) = (2 , 10) and (x2 , y2) = (6 , 14)

∵ x1 = 2 , x2 = 6 and y1 = 10 , y2 = 14

∴ \frac{y-10}{x-2}=\frac{14-10}{6-2}

∴ \frac{y-10}{x-2}=\frac{4}{4}======\frac{y-10}{x-2}=1

- By using cross multiplication

∴ (y - 10) = (x - 2)

∴ y - 10 = x - 2 ⇒ add 2 and subtract y in the two sides

∴ -8 = x - y ⇒ switch the two sides

∴ x - y = -8 ⇒ (4)

# (x1 , y1) = (2 , 9) and (x2 , y2) = (8 , 6)

∵ x1 = 2 , x2 = 8 and y1 = 9 , y2 = 6

∴ \frac{y-9}{x-2}=\frac{6-9}{8-2}

∴ \frac{y-9}{x-2}=\frac{-3}{6}======\frac{y-9}{x-2}=\frac{-1}{2}

- By using cross multiplication

∴ 2(y - 9) = -1(x - 2) ⇒ simplify

∴ 2y - 18 = -x + 2 ⇒ add x and 18 for two sides

∴ x + 2y = 20 ⇒ (5)

- Equations (1) and (5) are the same

∴ The 1st and the 5th tables represent the same function

3 0
3 years ago
The sum of 6 consecutive even numbers is 270.What is the second number in this sequence?
Finger [1]

Answer: 42

Step-by-step explanation:

Let the six consecutive even numbers be x , x+2 , x+4 ,x+6 ,x+8 ,x+10.

Then According to the question , we have

x+(x+2)+(x+4)+(x+6)+(x+8)+(x+10)=270\\\\\Rightarrow\ x+x+2+x+4+x+6+x+8+x+10=270\\\\\Rightarrow\6x+30=270\\\\\Rightarrow\ 6x=270-30\\\\\Rightarrow\ 6x=240\\\\\Rightarrow\ x=40

Now, the second number from the above six consecutive even numbers  is x+2.

Substitute the value of x in it, we get

The second number in this sequence = x+2=40+2=42

3 0
3 years ago
Read 2 more answers
What operations are needed to solve this word problem? Joe has 8 Dalmatians. Sarah has 3 fewer Dalmatians than Joe. How many Dal
yan [13]
You take it like this=

8
-3
~~
3
+
3
+
3
-
1
~~
(4×2)
-
3
~~
[[5]]

《5+8》


/ \
| 13 |
\ /
3 0
2 years ago
Open furniture store has the following sale 1/2 off Mr. Davis bought 2 chairs during the sale the regular price of each chair wa
qwelly [4]
336 dollars for both chairs
4 0
3 years ago
Read 2 more answers
X/3 equals 1351 over seven
Fantom [35]
X/3=1351/7
cross multiply
7x=4053
divide by seven on both sides
x=579
5 0
3 years ago
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