Answer:
Value of LN = 19 units
Step-by-step explanation:
Given:
LN = 3 + 8x
Find:
Value of LN
Computation:
We know that LM + MN = LN
So,
8 + 6x - 1 = LN
So,
3 + 8x = 8 + 6x - 1
3 + 8x = 7 + 6x
8x - 6x = 7 - 3
2x = 4
x = 2
So,
LN = 3 + 8x
LN = 3 + 8(2)
LN = 3 + 16
LN = 19
Value of LN = 19 units
The answer would be <14 and <16
Answer:
A
35 60 65 70 90
Q1 = 60, Q3 = 70, Q3 - Q1 = 10
Low suspected outliers : 10 x 1.5 = 15
range, 60 -15 = 45
70 + 15 = 85
Hence, there are low suspected outliers i.e 35 and 90
X= shorter leg
x+6= longer leg
(x+6)+6= hypotenuse
Use the Pythagorean theorem to find the length of each side.
a= one leg
b= other leg
c= hypotenuse.
SHORTER LEG:
a^2 + b^2= c^2
substitute each length above
x^2 + (x+6)^2= [(x+6)+6]^2
square each set of parentheses; add inside right side parentheses before squaring
x^2 + (x+6)(x+6)= (x+12)(x+12)
squaring is multiplying each parentheses by itself one time; use the FOIL method: multiply first, multiply outside, multiply inside, multiply last
x^2 + x^2 + 6x + 6x + 36= x^2 + 12x + 12x + 144
combine like terms
2x^2 + 12x + 36= x^2 + 24x + 144
subtract x^2 from both sides
x^2 + 12x + 36= 24x + 144
subtract 24x from both sides
x^2 - 12x + 36= 144
subtract 144 from both sides
x^2 - 12x - 108= 0
factor
(x + 6)(x - 18)= 0
set each parentheses equal to 0
x + 6= 0
x= -6
x - 18= 0
x= 18 cm shorter leg
***Since a side cannot be a negative number, x= 18. Substitute x=18 to find the other sides.
LONGER LEG:
= x+6
= 18 + 6
= 24 cm longer leg
HYPOTENUSE:
= (x+6)+6
= 18 + 6 + 6
= 30 cm hypotenuse
CHECK:
18^2 + 24^2= 30^2
324 + 576= 900
900= 900
ANSWER:
x= 18 cm shorter leg
x+6= 24 cm longer leg
(x+6)+6= 30 cm hypotenuse
Hope this helps! :)
The value of x is 8.5.
Solution:
U is the mid-point of TV.
TU = 6
UV = 2x - 11
TU = UV
6 = 2x - 11
Add 11 on both sides.
6 + 11 = 2x - 11 + 11
17 = 2x
Divide by 2 on both sides.
8.5 = x
Switch the sides.
x = 8.5
Option B is the correct answer.
