Answer:
the common ratio is either 2 or -2.
the sum of the first 7 terms is then either 765 or 255
Step-by-step explanation:
a geometric sequence or series of progression (these are the most common names for the same thing) means that every new term of the sequence is created by multiplying the previous term by a constant factor which is called the common ratio.
so,
a1
a2 = a1×f
a3 = a2×f = a1×f²
a4 = a3×f = a1×f³
the problem description here tells us
a3 = 4×a1
and from above we know a3 = a1×f².
so, f² = 4
and therefore the common ratio = f = 2 or -2 (we need to keep that in mind).
again, the problem description tells us
a2 + a4 = 30
a1×f + a1×f³ = 30
for f = 2
a1×2 + a1×2³ = 30
2a1 + 8a1 = 30
10a1 = 30
a1 = 3
for f = -2
a1×-2 + a1×(-2)³ = 30
-10a1 = 30
a1 = -3
the sum of the first n terms of a geometric sequence is
sn = a1×(1 - f^(n+1))/(1-f) for f <>1
so, for f = 2
s7 = 3×(1 - 2⁸)/(1-2) = 3×-255/-1 = 3×255 = 765
for f = -2
s7 = -3×(1 - (-2)⁸)/(1 - -2) = -3×(1-256)/3 = -3×-255/3 =
= -1×-255 = 255
!30 points! Which angle corresponds to angle N? (Photo attached)
A. N
B. O
C. O'
D. P'
Answer:
∠ N'
Step-by-step explanation:
Corresponding angles in the same position after the transformation.
∠ N' corresponds to ∠ N
Answer:
its A
Step-by-step explanation:
Help please and show me the steps on how u got the answers
What is
The midpoint between (8,3) and (12, -7) is,
Answer:
(10, -2)
Step-by-step explanation:
(8+12)/2 and (3+-7)/2
= (10, -2)
A sheet of paper is 0.00005 meter thick. One nanometer is 1 x 10-meter. How thick is a sheet of paper in nanometers?
O 50,000
O 500,000
O 50,000,000,000,000
O 500,000,000,000,000
The thickness of the sheet of paper in nanometre is 50,000
The sheet of paper is 0.00005 meter thick .
1 nanometre = 1 × 10⁻⁹ meters
1 × 10⁻⁹ meters = 1 nanometre
0.00005 meters = ?
cross multiply
Therefore,
Thickness of the paper (nanometre) = 0.00005/1 × 10⁻⁹
Thickness of the paper(nanometre) = 50,000
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Of the following, which is the first time after 11:30 that the minute and hour hands of my circular alarm clock no longer form an obtuse angle?
a. 11:40
b. 11:41
c. 11:42
d. 11:43
e. 11:44
f. 11:45
g. 11:46
If 3 cot ∅ = 4 , then (3 sin ∅ + 4 cos ∅)/(3 sin ∅ - 4 cos ∅) ?
Step-by-step explanation:
[tex]\large\underline{\sf{Solution-}}[/tex]
[tex]\rm \longmapsto\:3cot\theta = 4[/tex]
[tex]\rm\implies \:cot\theta = \dfrac{4}{3} [/tex]
Now, Consider
[tex]\rm \longmapsto\:\dfrac{3sin\theta + 4cos\theta }{3sin\theta - 4cos\theta } [/tex]
[tex]\rm \: = \: \dfrac{sin\theta \bigg[3 + 4\dfrac{cos\theta }{sin\theta } \bigg]}{sin\theta \bigg[3 - 4\dfrac{cos\theta }{sin\theta } \bigg]} [/tex]
[tex]\rm \: = \: \dfrac{3 + 4cot\theta }{3 - 4cot\theta } [/tex]
[tex]\rm \: = \: \dfrac{3 + 4 \times \dfrac{4}{3} }{3 - 4 \times \dfrac{4}{3} } [/tex]
[tex]\rm \: = \: \dfrac{3 + \dfrac{16}{3} }{3 - \dfrac{16}{3} } [/tex]
[tex]\rm \: = \: \dfrac{\dfrac{9 + 16}{3} }{ \dfrac{9 - 16}{3} } [/tex]
[tex]\rm \: = \: \dfrac{25}{ - 7} [/tex]
[tex]\rm \: = \: - \: \dfrac{25}{7} [/tex]
Hence,
[tex]\rm \longmapsto\:\boxed{\tt{ \dfrac{3sin\theta + 4cos\theta }{3sin\theta - 4cos\theta } = - \frac{25}{7} \: }} \\ [/tex]
Additional Information:-
Relationship between sides and T ratios
sin θ = Opposite Side/Hypotenuse
cos θ = Adjacent Side/Hypotenuse
tan θ = Opposite Side/Adjacent Side
sec θ = Hypotenuse/Adjacent Side
cosec θ = Hypotenuse/Opposite Side
cot θ = Adjacent Side/Opposite Side
Reciprocal Identities
cosec θ = 1/sin θ
sec θ = 1/cos θ
cot θ = 1/tan θ
sin θ = 1/cosec θ
cos θ = 1/sec θ
tan θ = 1/cot θ
Co-function Identities
sin (90°−x) = cos x
cos (90°−x) = sin x
tan (90°−x) = cot x
cot (90°−x) = tan x
sec (90°−x) = cosec x
cosec (90°−x) = sec x
Fundamental Trigonometric Identities
sin²θ + cos²θ = 1
sec²θ - tan²θ = 1
cosec²θ - cot²θ = 1
Clarise has $290 in her checking account. She writes checks for $102 and $75 and then makes a deposit of $170. Find the amount left in her account.
Answer:
$283
Step-by-step explanation:
Amount of money left in Clarise's account
= $290 - $102 - $75 + $170
= $283
Answer:
283
Step-by-step explanation:
100 Points And Brainlyest!! PLZ HELP
Answer:
741/10000
Step-by-step explanation:
please explain your answer
Answer:
51
Step-by-step explanation:
11+(-7)^2-9 - original
11+49-9 - square the -7, since its in brackets the negative applies too and a negative x a negative = positive, so it ends up as 7x7+49
60-9 - add both positives 11+49=60
51 - subtract 9 from 60, 60-9=51
Solve for xx. Express your answer as a proper or improper fraction in simplest terms.
-1/3= 5/12x-2/3
Answer:
4/5
Step-by-step explanation:
hope this helps :)
-1/3 = 5/12x - 2/3 Add 2/3 to both sides
1/3 = 5/12x Divide by 5/12
1/3 / 5/12 = x
x = 0.8 or 4/52 4/6 divided by 1 3/7 i will give brainlist and give a step by step
really need help with it to solve 34 and 35
Answer:
69
Step-by-step explanation:
funny number funny number
i need it asap answer
Answer:
D. As the number of students in a class increases, the average rating score of the class decreases.
Hope this helps!
Which is an obtuse angle?
1.
2.
3.
4.
Answer: 4. is an obtuse angle.
Step-by-step explanation: An obtuse angle is 180 degrees or more.
The product of three consecutive integers is 3360. What is the sum of the three integers?
Step-by-step explanation:
let the integer be x .
three consecutive integers : x, x+1, x+2.
according to the problem,.
Let the first of the 3 consecutive numbers be X.
Therefore the second number is (X + 1)
The third number is therefore (X + 2)
The product of the 3 consecutive numbers is:
( X )( X + 1 )( X + 2 ) = 3360 Equation( 1 )
Expanding Equation ( 1 ) gives
X³ + 3X² + 2X - 3360 = 0 Equation (2)
Solve Equation (2 ) which gives the following values for X
X1 = 14
X2 = - 8.5 + i (12.951834)
X3 = - 8.5 - i (12.951834).
the numbers are 14,15,16.
sum is 14+15+16 = 45.
hope this helps you.
find the volume of the solid
Answer:
The volume of the solid is 24 in^3
Step-by-step explanation:
The most general form of the equation of the volume of a pyramid is
V = (1/3)(base area)(height)
In this case,
V = (1/3)(18 in^2)(4 in) = 24 in^3
If triangle HBN is congruent to triangle LYR, find the value of x.
Answer:
Step-by-step explanation:
Ti piacciono i banane scimmia
At the fast food restaurant, an order of fries costs $0.96 and a drink costs $0.90. How
much would it cost to get 2 orders of fries and 5 drinks? How much would it cost to
get f orders of fries and d drinks?
ILL GIVE BRAINALIST IF YOU ANSWER CORRECTLY
If the two rays are perpendicular what is the value of m ?
Answer:no idea cause we can’t see what or where m is
Step-by-step explanation:but if two rays are perpendicular then they intersect at 90 degrees and the slope of ray1 =m1 and the slope or ray2 = m2 and m1 x m2 =-1
98% of 60??
Estimating with percents!
Answer:
58.8
Step-by-step explanation:98/100 *60
Answer:
58.8
Step-by-step explanation:
Fine the value of n
a.3 over 15 =n over 15
b. 20 over 45 = n over 9
Answer:
a) n = 3
b) n = 4
Step-by-step explanation:
a) Start off by multiplying each side by 15
[tex]\frac{15n}{15}=\frac{3(15)}{15}[/tex]
Then simplify the equation
[tex]n=3[/tex]
b) Start off by canceling the common factor of 5
[tex]\frac{n}{9} =\frac{4}{9}[/tex]
Then simplify the equation
[tex]n=4[/tex]
Which expression is negative?
a
b
+
+
-1
0
1
Choose 1 answer:
А
a +1
B
a -(-6)
None of the above
Answer:
I don’t understand
Step-by-step explanation:
i don’t understand
vă rog am nevoie de ajutor la ex 6 dacă il faceți dau corana ex este de clasa a 6
Answer:
sry but i can't help you with it bcz i don't understand spanish can u write it in clear english
Sry
Help my little brother
Answer:
1) 6
2) 9
3) 80
4) 10
5) 4
6) 4
Step-by-step explanation:
1) 36 / 6 = 6
2) 45 / 5 = 9
3) 10 * 8 = 80
4) 5 * 2 = 10
5) 16 / 4 = 4
6) 12 / 3 = 4
Hope this helped!
A meeting takes place between a diplomat
and fourteen government officials.
However, four of the officials are actually
spies. If the diplomat gives secret
information to ten of the attendees at
random, what is the probability that no
secret information was given to the spies?
Answer:
The number of ways to choose 10 people out of 14 people is given by 14C10 which is read "14 choose 10"
Only 1 of these combinations will result in no information being given to any of the 4 spies.
Can you figure out the probability from these 2 facts?
Step-by-step explanation:
Which list shows the fractions and decimals in order from least to greatest?
where's the list at ?
Answer:
Step-by-step explanation:
where is the list to give you the answer
Write and solve an inequality that represents the values of x for which the area of the rectangle will be at most 45 square meters. PLEASE SHOW WORK
will mark brainlist!!!!!!!!!!
what is 4+m/5=2
Answer:
-10
Step-by-step explanation:
Subtract 4 from both sides
m/5 = -2
Multiply by 5
m = -10
Step-by-step explanation:
4+m/5 = 2
4+m =2*5
4+m = 10
m= 10 -4
='6
Line B passes through the points (5, 10) and (0,0). What is the slope of the line
perpendicular to line B?
O 1
2
مسیر
1
2
o –
O2
None of the other answers are correct
1/2 DID THE TEST
Step-by-step explanation: