Answer: the first term of the series is 128
Step-by-step explanation:
In a geometric sequence, the consecutive terms differ by a common ratio. The formula for determining the sum of n terms, Sn of a geometric sequence is expressed as
Sn = a(1 - r^n)/(1 - r)
Where
n represents the number of term in the sequence.
a represents the first term in the sequence.
r represents the common ratio.
From the information given,
r = 1/4 = 0.25
n = 4
S4 = 170
Therefore, the expression for the sum of the 4 terms, S4 is
170 = a(1 - 0.25^4)/(1 - 0.25)
170 = a(1 - 0.00390625)/(1 - 0.25)
170 = a(0.99609375)/(0.75)
170 = 1.328125a
a = 170/1.328125
a = 128
Answer: SAS
Step-by-step explanation:
AC = AC (reflexive property)
So we know that AC = AC
Angle 1 = Angle 2 (given)
And AC = BC (given)
They are similar by SAS
By the Pythagorean theorem
.. 15^2 = 10^2 +a^2
.. 225 = 100 +a^2
.. 125 = a^2
.. √125 = a
.. 5√5 = a ≈ 11.18
The missing side length is 5√5 cm.
Answer:
453.75 sq. feet
Step-by-step explanation:
In this question, we are going to calculate the area of a room given the blue print measurement and the actual measurements with the answer being in the actual measurement.
To correctly do this, it is best if the measurements are converted to the actual.
The measurements we’ll be trying to convert is 5 inches by 3 inches with a scale of 2in to 11ft ( same as 1 in to 5.5 ft)
The 5 inches blueprint measurement will be 5 * 5.5 = 27.5 ft
The 3 inches blueprint measurement will be 3 * 5.5 = 16.5 ft
The area in sq. feet will be length * width = 27.5 * 16.5 = 453.75 sq feet
