The 6th term of the geometric sequence is 3552
How to determine the 6th term of the geometric sequenceTo find the 6th term of a geometric sequence, we need to determine the common ratio (r) first.
Given that t3 = 444 and t7 = 7104, we can use these two terms to find the common ratio.
t3 = t1 * r^(3-1)
444 = t1 * r^2
t7 = t1 * r^(7-1)
7104 = t1 * r^6
Dividing the two equations, we get:
7104/444 = (t1 * r^6) / (t1 * r^2)
16 = r^4
Taking the fourth root of both sides, we find:
r = ∛16 = 2
Now that we have the common ratio (r = 2), we can find the first term (t1) by substituting the values of t3 and r into the equation t3 = t1 * r^(3-1):
444 = t1 * 2^2
444 = 4t1
t1 = 111
To find the 6th term (t6), we substitute the values of t1 and r into the general formula for the nth term of a geometric sequence:
t6 = t1 * r^(6-1)
t6 = 111 * 2^5
t6 = 111 * 32
t6 = 3552
Therefore, the 6th term of the geometric sequence is 3552.
Learn more about geometric sequence at https://brainly.com/question/1509142
#SPJ2
How do you solve all of these ?
Solve 4r2 – 7 = 29.
a. +-6
b. +-3
c. +-4
d. +-5
Calvin and hobbes are making snowballs to throw at suzi calvin made 3/7 of the snowballs and hobbes made 8/14 of the snowballs who mae more snowballs in fractions
recalculate 3/7 to have the same denominator as 8/14 ( 14)
so multiply both top and bottom by 2. 3/7 becomes 6/14
8/14 - 6/14 = 2/14 reduces to 1/7
Hobbes made more snowballs by 1/7
recalculate 3/7 to have the same denominator as 8/14 ( 14)
so multiply both top and bottom by 2. 3/7 becomes 6/14
8/14 - 6/14 = 2/14 reduces to 1/7
Hobbes made more snowballs by 1/7
Simplify the product using the distributive property. (-4h +2)(3h +7)
A.
-12h 2 - 22h + 14
B.
-12h 2 - 34h - 14
C.
-12h 2 + 34h - 14
D.
-12h 2 + 22h + 14
please help
Answer:
A. -12h² - 22h + 14
Step-by-step explanation:
(-4h +2)(3h +7) = -4h(3h +7) +2(3h +7) . . . . . . . (a +b)c = ac +bc
= (-4h)(3h) + (-4h)(7) + (2)(3h) + (2)(7) . . . . . . . a(b +c) = ab +ac . . . (twice)
= -12h² -28h +6h +14
= -12h² -22h +14 . . . . . . . . collect terms
If 300 cm^2 of material is available to make a box with a square base and an open top, find the maximum volume of the box in cubic centimeters. Answer to the nearest cubic centimeter without commas. For example, if the answer is 2,000 write 2000.
Use the discriminant of x^2+4x-32=0 to describe the roots
The formula for discriminant is:
discriminant = sqrt (b^2 – 4 a c)
Where,
a = 1
b = 4
c = -32
Therefore:
discriminant = sqrt (4^2 – 4 (1) (-32))
discriminant = sqrt 144
discriminant = 12
Since the discriminant is a positive real integer, then there are 2 unequal roots or 2 distinct real roots.
If k pencils cost c cents what is the cost in cents of p pencils
If k pencils cost c cents. Then the cost in cents of p pencils will be cp / k.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
If k pencils cost c cents. Then the cost of each pencil is given as,
⇒ c / k
Then the cost in cents of p pencils is given as,
⇒ (c / k) x p
⇒ (cp) / k
If k pencils cost c cents. Then the cost in cents of p pencils will be cp / k.
More about the Algebra link is given below.
https://brainly.com/question/953809
#SPJ5
A local carpet company has been hired to carpet a planetarium which is in the shape of a circle. If the radius of the planetarium is six yards, and the cost of the carpet is $14 per square yard, find the total cost to carpet the planetarium. (use 3.14 for π )
(06.01 LC)
What type of association does the graph show between x and y?
Linear positive association
Nonlinear positive association
Linear negative association
Nonlinear negative association
Answer:
b
im taking the same test 4 years later
How do I find ac in this problem
7 / x+4 = 5/x+1 =
5x+20 = 7x+7 =
20=2x+7
13=2x
x=13/2 = 6.5
6.5+4 = 10.5
6.5+1 =7.5
10.5+7.5 = 18
length of AC = 18
Select the inequality that corresponds to the given graph. graph of an inequality with a solid line through the points negative 8 comma 0 and 0 comma negative 4 and shading above the line A 4x − 3y > − 12 B x + 4y > 4 C 4x − 2y < − 8 D 2x + 4y ≥ − 16
Step-by-step explanation: In the given graph x-intercept is -8 and y-intercept is -4.
Also the graph is shaded up of the line for greater values of y's.
On the option 2x+4y ≥ -16 has x-intercept at -8 and y-intercept at -4.
Also all other inequalities has only less than or greater than sign.
In the given graph we have a solid line.
So, there should be greater than or equal to inequality sign for the inequality.
Only option 4 has greater than with equal to sign.
Therefore, correct option is 2x+4y ≥ -16
You have a total of 21 coins, all nickles and dimes. The total value is $1.70 Which of the following is the system of linear equations that represent this scenario? Let n= the number of nickles and let d= the number of dimes.
Which of these is NOT a part of formal proof? A.Reasons
b.statements
c. given
d. diagram
e.none of the above
The sum of three consecutive even integers is 288. find the three integers.
288/3 =96
96-2 = 94
96+2 = 98
94 +96 +98 = 288
Answer:
94, 96, 98
Step-by-step explanation:
Let the smallest integer is x,
So, second larger integer = x + 2 (Because integer are even and consecutive),
And, largest integer = x + 2 + 2 = x + 4,
So, the sum of these integers = x + x + 2 + x + 4 = 3x + 6
According to the question,
3x + 6 = 288
3x = 282
⇒ x = 94
Hence, the integers are,
94, 94+2, 94+4
= 94, 96, 98
The formula used to calculate simple interest is modeled by I=prt, where I=simple interest, p=principle, r=interest rate, and t=time, measured in years. Which of the following options represent(s) an alternative equivalent version of the simple interest formula? select all that apply....TY
I = trp
I = p + rt
I - rt = p
t= l/rp
p= l/rt
Step-by-step explanation:
The formula for simple interest is as follows.
I = prt
where, I = simple interest
p = principle
r = rate
t = time
This formula can be alternatively written by shifting I, r, t, and p either on the right or left side of equals sign.
Therefore, the formula can be rewritten as follows.
I = trp[tex]t = \frac{I}{rp}[/tex] [tex]p = \frac{I}{rt}[/tex]What are the solutions of the equation 2x2=2 use a graph of the related function
Answer:
[tex]x=-1\text{ or }x=1[/tex]
Step-by-step explanation:
We have been given an equation [tex]2x^2=2[/tex]. We are asked to find the solutions of our given equation.
First of all, let us divide both sides of our equation by 2.
[tex]\frac{2x^2}{2}=\frac{2}{2}[/tex]
[tex]x^2=1[/tex]
Upon taking square root of both sides of our equation we will get,
[tex]x=\sqrt{1}[/tex]
[tex]x=\pm 1[/tex]
[tex]x=-1\text{ or }x=1[/tex]
Therefore, [tex]x=-1\text{ or }x=1[/tex] are two solutions for our given function.
Find the height of the figure below if the volume is 480.66^3 cm.
volume = PI x r^2 x H
you know the volume and the radius ( 12/2 = 6)
480.66 =3.14 x 6^2 x H
480.66 = 113.04 x h
h = 480.66/113.04 = 4.252
round off as needed.
88 is the product of
8
and Jenny's score
product means multiplication
88 is the product of 8 multiplied by a number
so 88/8 =11
jenny's score is 11
An expression is shown below:
square root of 32 plus square root of 2
Which statement is true about the expression?
please help 25 points
A. It is rational and equal to 4
B. It is rational and equal to 5
C. It is rational and equal to 5√2
D. It is rational and equal to 4√2
What is the probability of flipping a penny and a nickel and obtaining one head and one tail?
Final answer:
The probability of flipping a penny and a nickel and obtaining one head and one tail is 0.25, or 25%.
Explanation:
The probability of flipping a penny and a nickel and obtaining one head and one tail can be calculated by multiplying the probabilities of getting a head on one coin and a tail on the other coin. Since the chance of getting a head on a fair coin is 0.5 and the chance of getting a tail is also 0.5, the probability of getting one head and one tail is:
Probability = (Probability of getting a head on the penny) × (Probability of getting a tail on the nickel)
Probability = 0.5 × 0.5 = 0.25, or 25%.
If x-5=2 then find the value of 6x-20
Work out problem in picture
for x multiply 6 by sin(45) = 3sqrt(2) = 4.2426
for y since it is a right triangle with 45 degree angle both legs are equal
so y = x
Find cos θ if sin θ = negative twelve divided by thirteen and tan θ > 0. negative five divided by twelve negative five divided by thirteen twelve divided by five negative thirteen divided by twelve
1. Find the coordinates of the circumcenter for ∆DEF with coordinates D(1,1) E (7,1) and F(1,5). Show your work.
2. What is the length of the 2nd base of a trapezoid if the length of one base is 24 and the length of the midsegment is 19? Show your work.
There were n balloons at the beginning of the party. By the end of the party, 5 of them had popped. Using n, write an expression for the number of balloons that were left
Answer:
The expression for the number of balloons that were left is [tex]n-5[/tex].
Step-by-step explanation:
There were n balloons at the beginning of the party.
By the end of the party, 5 of them had popped.
Let the remaining balloons be represented by x
So, x = total balloons minus 5
This gives: [tex]x=n-5[/tex]
Therefore, the expression for the number of balloons that were left is [tex]n-5[/tex].
which is enough information to prove that s||t
what is the domain and range of each function graohed below?
The scale on a map indicates that 1 in = 2.5mi. How far apart are two cities that measure 2.5 ft apart on the map? A. 60 miles B. 6.25 miles C. 75 miles D. 90 miles
Write the equation of a line that is perpendicular to the given line and that passes through the given point.
2x+9y=-30;(-8,0
Please help me and show work so I can understand worth 20 points!!!