Answer:
x = 16
Step-by-step explanation:
(x +4) : (x +12) :: (x-1)(x +5)
As they are in proportion,
Product of means = Product of extremes
(x + 4)* (x +5) = (x + 12)(x - 1) {Use FOIL method}
x*x +x*5 +4*x + 4*5 = x *x + x*(-1) +12*x + 12*(-1)
x² + <u>5x + 4x</u> + 20 = x² <u>- x +12x</u> - 12 {Now combine like terms}
x² + 9x + 20 = x² + 11x -12
x² + 9x +20 - x² - 11x = -12
x² - x² + 9x - 11x = -12 - 20
0 - 2x = - 32
-2x = -32 {Divide both sides by -2}
x = -32/-2
x = 16
Let the length of second side be x" ,
So,
Length of first side = 2" shorter than second = ( x - 2 )"
Length of third side = 5" longer than second = ( x + 5 )"
=×=×=×=×=×=×=×=×=×=×=×=×=×=×=×=×=

Given, perimeter = 33"
= > first side + second side + third side = 33"
= > ( x - 2 ) + x + ( x + 5 ) = 33
= > x - 2 + x + x + 5 = 33
= > 3x + 3 = 33
= > 3x = 30

= > x = 10
Hence, length of each side is
First side = ( x - 2 )" = ( 10 - 2 )" = 8 inches
Second side = x " = 10 inches
Third side = ( x + 5 )" = ( 10 + 5 )" = 15 inches
The probability of winning when betting on two lines that touch each other on the table is 6/38
<h3>How to determine the probability?</h3>
The sample size is given as:
n = 38
The numbers on the range 1-2-3-4-5-6 is:
Range = 6
So, the probability is calculated as:
P = Range/n
This gives
P = 6/38
Hence, the probability of winning is 6/38
Read more about probability at:
brainly.com/question/251701
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Answer:
x=55
a=11.47
Step-by-step explanation:
To find x we add all the angles in the triangle. The three angles in a triangle add to 180 degrees
35+x+90 = 180
Combine like terms
125+x=180
Subtract 125 from each side
125-125+x=180-125
x= 55
To find a
sin 35 = opposite side/ hypotenuse
sin 35 =a/20
Multiply each side by 20
20sin35 =a
11.47152873 =a
Set up as for portion with X as unknown number of gray cats. So 1/3=x/9. Cross multiply. 3X=9. Divide both sides by 3. X=3.