Find the 6th term of a geometric sequence t3 = 444 and t7 = 7104.

Answers

Answer 1

Given the value of t3 and t7, and t7 = t3 * r^4, where r represents the geometric quotient.

So 7104 = 444 * r^4 -> solve for r, you will get r = 2 or -2

So, for r = 2, t6 = t7 / r = 7104 / 2 = 3552

For r = -2, t6 = -3552

Answer 2

The 6th term of the geometric sequence is 3552

How to determine the 6th term of the geometric sequence

To 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.

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Related Questions

Please help me and show work so I can understand worth 20 points!!!

Answers

The steps and final answer is shown in the attached image. I wrote it there so I could write out complex algebraic formulas. Let me know if you have any questions about any of the steps. Thank you.

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.

Answers

Hello,
Assume a the side of the base, b the height.

[tex]V=a^2*b\\ a^2+4ab=300==\ \textgreater \ b= \dfrac{300-a^2}{4a} \\ V=a^2*\dfrac{300-a^2}{4a}= \frac{1}{4} *(300a-a^3)\\ \dfrac{dV}{da} = \frac{1}{4} *(300-3*a^2)=0\\ ==\ \textgreater \ a=10 \ and\ b=5\\ V=10^2*5=500\\ [/tex]

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.

Answers

1. Draw an accurate drawing of the triangle in the coordinate axis, as shown in the picture.

FD and DE are perpendicular, because D and F have the same x coordinate, and D and E the same y coordinate.

Let A(4, 1) be the midpoint of DE and B(1, 3) be the midpoint of FD.

Draw the perpendiculars from A and B. They meet at O(4, 3), since AO is parallel to DF and BO is parallel to DE.

the point where the perpendicular bisectors of the sides meet is the circumcenter, so the circumcenter is O(4, 3)

2.

Let the length of the second base be x.

the length of the midsegment is the sum of the ases divided by 2.

[tex]19= \frac{x+24}{2} [/tex]

19*2=x+24

38=x+24

x=38-24=14

Answers:

1) O(4, 3)
2) length of second base = 14 units

(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

Answers

non-linear positive association

Answer:

im taking the same test 4 years later

The sum of three consecutive even integers is 288. find the three integers.

Answers

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

Work out problem in picture

Answers

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

Use the discriminant of x^2+4x-32=0 to describe the roots

Answers

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.

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

Answers

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

which is enough information to prove that s||t

Answers

The answer is: <2 = <8

It will be the second option

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

Answers

well by looking at the graph I can see that the equation for the line is y=-0.5x-4
rearranging I can get the answer.
y>=-0.5x-4
y+0.5x>=-4
2y+x>=-8

the answer is
2x+4y>=-16

Answer: 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

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

Answers

2x+9y=-30 subtract 2x from both sides

9y=-2x-30 divide both sides by 9

y=-2x/9-30/9

So the slope of the reference line is -2/9. For a line to be perpendicular to this line their slopes must be negative reciprocals of one another, mathematically:

m1*m2=-1 and in this case:

-2m/9=-1

m=9/2

m=4.5, so far we have:

y=4.5x+b, using point (-8, 0) we can solve for b

0=4.5(-8)+b

0=-36+b

36=b, so our line is:

y=4.5x+36

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

Answers

C) sqrt(32) = sqrt(2^5)=4sqrt(2), then + sqrt(2) = 5 * sqrt(2)

√(2^5)+√2

4√2+√2

(4+1)√2

5√2

There is a problem however...5√2 is IRRATIONAL because √2 is irrational, ie, it cannot be expressed as a ration of two integers...

So the problems simplified is certainly 5√2, but it is irrational.

Maybe there is a typo and should read:

C. It is IRrational and equal to 5√2

What is the probability of flipping a penny and a nickel and obtaining one head and one tail?

Answers

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%.

Solve 4r2 – 7 = 29.
a. +-6
b. +-3
c. +-4
d. +-5

Answers

4r^2-7=29
+7 both sides
4r^2=36
÷4 both sides
r^2=9
square root both sides
r=+/-3 B

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 )

Answers

This is the concept of application of geometry and financial mathematics; To calculate for the total cost of the carpet we proceed as follows;
Total cost=[area of the carpet]*[price per square yard]
area of carpet is given by:
Area=πr^2
where;
radius,r=6 yeards
=π*6^2
=113.1 square yards
therefore the price of the carpet will be:
113.1*14
=$1,583.4

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.

Answers

You need one equation for the physical nickels and dimes, which total to 21:

n+d=21

Secondly, you need one equation for the numerical value of those nickels and dimes. We know nickels are worth $0.05 and dime are worth $0.10:

.05n+.1d=1.70

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

Answers

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

Find the height of the figure below if the volume is 480.66^3 cm.

Answers

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.

If x-5=2 then find the value of 6x-20

Answers

First solve the first equation to find x.

x-5=2
x=7

Now plug it in to the other equation to get your answer.

6(7)-20
42-20
22

The answer is 22.

so x in the fist problem is 7. So the x is substituted be 7. guessing you want me to solve,
6x-20
=6(7)-20
=42-20
=22

88 is the product of
8
and Jenny's score

Answers

product means multiplication

88 is the product of 8 multiplied by a number

so 88/8 =11

jenny's score is 11

Which of these is NOT a part of formal proof? A.Reasons
b.statements
c. given
d. diagram
e.none of the above

Answers

the answer would be A. reasons

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

Answers

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].

What are the solutions of the equation 2x2=2 use a graph of the related function

Answers

The equation given is
2x² = 2
x² = 1
x = √1
x = 1

The solution is both -1 and 1 and the graph is shown below

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.

How do you solve all of these ?

Answers

5)

[tex]\bf \begin{array}{lllll} &x_1&y_1\\ % (a,b) &({{ 5}}\quad ,&{{ -3}})\quad % (c,d) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies -1 \\\\\\ % point-slope intercept y-{{ y_1}}={{ m}}(x-{{ x_1}})\implies y-(-3)=-1(x-5) \\ \left. \qquad \right. \uparrow\\ \textit{point-slope form} \\\\\\ y+3=-x+5\implies y=-x+2[/tex]

6)

[tex]\bf \begin{array}{lllll} &x_1&y_1\\ % (a,b) &({{ 2}}\quad ,&{{ 1}})\quad % (c,d) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies 3 \\\\\\ % point-slope intercept y-{{ y_1}}={{ m}}(x-{{ x_1}})\implies y-1=3(x-2) \\ \left. \qquad \right. \uparrow\\ \textit{point-slope form} \\\\\\ y-1=3x-6\implies y=3x-5[/tex]

7)

[tex]\bf \begin{array}{lllll} &x_1&y_1\\ % (a,b) &({{ 5}}\quad ,&{{ 2}})\quad % (c,d) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies 0 \\\\\\ % point-slope intercept y-{{ y_1}}={{ m}}(x-{{ x_1}})\implies y-2=0(x-5) \\ \left. \qquad \right. \uparrow\\ \textit{point-slope form} \\\\\\ y-2=0\implies y=2[/tex]

8)

[tex]\bf \begin{array}{lllll} &x_1&y_1\\ % (a,b) &({{ -2}}\quad ,&{{ 0}})\quad % (c,d) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{5}{2} \\\\\\ % point-slope intercept y-{{ y_1}}={{ m}}(x-{{ x_1}})\implies y-0=\cfrac{5}{2}(x-(-2)) \\ \left. \qquad \right. \uparrow\\ \textit{point-slope form} \\\\\\ y=\cfrac{5}{2}(x+2)\implies y=\cfrac{5}{2}x+5[/tex]

9)

[tex]\bf \begin{array}{lllll} &x_1&y_1\\ % (a,b) &({{ -2}}\quad ,&{{ 0}})\quad % (c,d) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{5}{2} \\\\\\ % point-slope intercept y-{{ y_1}}={{ m}}(x-{{ x_1}})\implies y-0=\cfrac{5}{2}(x-(-2)) \\ \left. \qquad \right. \uparrow\\ \textit{point-slope form} \\\\\\ y=\cfrac{5}{2}(x+2)\implies y=\cfrac{5}{2}x+5[/tex]

10)

[tex]\bf \begin{array}{lllll} &x_1&y_1\\ % (a,b) &({{-2}}\quad ,&{{ -2}})\quad % (c,d) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{3}{2} \\\\\\ % point-slope intercept y-{{ y_1}}={{ m}}(x-{{ x_1}})\implies y-(-2)=\cfrac{3}{2}(x-(-2)) \\ \left. \qquad \right. \uparrow\\ \textit{point-slope form} \\\\\\ y+2=\cfrac{3}{2}(x+2)\implies y+2=\cfrac{3}{2}x+3\implies y=\cfrac{3}{2}x+1[/tex]

How do I find ac in this problem

Answers

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

what is the domain and range of each function graohed below?

Answers

domain is the x values you can use
range is the y values

a.
the domain
hmm, seems to be all real numbers except for at x=0, it gets really close tho
so D=(-∞,0)U(0,∞)

range is all real numbers except for y=0, it gets really close tho
R=(-∞,0)U(0,∞)

b.
domain
that empty circle means something like < or >
goes from 5 to 6, not including 5
so domain is D=(5,6]

range is from -4 to 2, not including -4
range is R=(-4,2]

check the picture below.

notice the holes, the excluded values, on the first one,due to an asymptote, on the second one, is in the line itself.

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

Answers

The answer is C. 75 miles

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

Answers

An alternative equivalent versions are:

I = trp
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]

If k pencils cost c cents what is the cost in cents of p pencils

Answers

the cost in cents of 1 pencil = c/k

the cost in cents of p pencils = (c/k) * p

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.

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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

Answers

1.
Sin∅=opposite side / hypotenuse, in a right triangle, as shown in the figure.

In this triangle, the length of the hypotenuse is 13, the length of one side 12, and the other side can be found by the Pythagorean theorem to be:

[tex] \sqrt{13^{2} - 12^{2} }= \sqrt{169-144}= \sqrt{25}=5 [/tex]

2.
The value of the cosine is (adjacent side)/(hypotenuse)=5/13.

3.
The tangent is positive in the first and third quadrants.

Since Tan=Sine/Cosine, and Sine is negative, then cosine must be negative as well

Answer: -5/13

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