Find the 7th term of the geometric sequence show below
7x, -7x^5, 7x^9,…
Answer:
7x^25 :)
Step-by-step explanation:
1: 7x,
2. 7x^5,
3. 7x^9,
4. 7x^13,
5. 7x^17,
6. 7x^21,
7. 7x^25
Have an amazing day!!
Please rate and mark brainliest!!
Answer:
[tex]7x^{25}[/tex]
Step-by-step explanation:
Given sequence: [tex]7x, -7x^5, 7x^9[/tex]
General form of a geometric sequence: [tex]a_n=ar^{n-1}[/tex]
(where a is the first term and r is the common ratio)
[tex]a_1=7x[/tex]
[tex]a_2=-7x^5[/tex]
[tex]a_3=7x^9[/tex]
To find the common ratio, divide one term by the previous term:
[tex]r=\dfrac{a_2}{a_1}=\dfrac{-7x^5}{7x}=-x^4[/tex]
Therefore, substituting the found values of a and r into the formula:
[tex]\implies a_n=(7x)(-x^4)^{n-1}[/tex]
To find the 7th term, substitute n = 7 into the formula:
[tex]\begin{aligned}\implies a_7 & =(7x)(-x^4)^{7-1}\\ & = (7x)(-x^4)^6\\ & = (7x)(x^{24})\\ & = 7x^{25}\end{aligned}[/tex]
Suppose for some value of x the solution to the equation 2.5(y−x)=0 is y = 6. What must be true about x?
HELPPPPPPPPPP
The value of the expression inside the parentheses must be equal to
Step-by-step explanation:
In this case, you input the value of y (y = 6) into the equation ( 2.5(y-x)= 0)
2.5(6-x) = 0
Open the bracket,
(2.5×6)-2.5x= 0
Collect like terms.
2.5x= 2.5×6
Divide both sides by the coefficient of x (2.5)
x = 6
So,
x= 6 is true.
.
Substituting 6 for x in the equation,
2.5(6-6)= 0
2.5•0 = 0
0= 0
Which is also true.
Twenty less than thrice a number is 223
[tex]~~~~~~3x-20=223\\\\\implies 3x = 223+20\\\\\implies 3x = 243\\\\\implies x = \dfrac{243}{3}\\\\\implies x =81\\\\\text{The number is 81.}[/tex]
A 10-speed bike changes gears by moving the chain to different size sprockets on the front and back. The speed at which the bike goes varies directly with the number of revolutions per minute (rpm) you turn the pedals, directly with the number of teeth on the front sprocket, and inversely with the number of teeth on the back sprocket. A standard bike with 70 cm diameter wheels will go about 7.4 kilometers per hour if you pedal 40 rpm in the lowest gear (39-tooth front sprocket, 28-tooth back one). Write an equation expressing km/h in terms of the three independent variables.
The variation is a joint variation, and the equation that relates the three independent variables is [tex]s = 0.18\frac{rf}{b}[/tex]
How to determine the equation in terms of the variables?The direct and the inverse variations from the question can be represented using:
[tex]s = k\frac{rf}{b}[/tex]
Where:
s represents the speed; s = 10k represents the constant of variationr represents the number of revolutions per minutef represents the number of front sprocket teethb represents the number of back sprocket teethFrom the question, we have:
r = 40; f = 39; b = 28
So, we have:
[tex]s = k\frac{rf}{b}[/tex]
[tex]10 = k\frac{40 * 39}{28}[/tex]
Make k the subject
[tex]k = \frac{10 * 28}{40 * 39}[/tex]
Evaluate
k = 0.18
Substitute k = 0.18 in [tex]s = k\frac{rf}{b}[/tex]
[tex]s = 0.18\frac{rf}{b}[/tex]
Hence, the equation that relates the three independent variables is [tex]s = 0.18\frac{rf}{b}[/tex]
Read more about variation at:
https://brainly.com/question/6974617
#SPJ1
What is the answer to −6(x +2) − 2
Answer: hii <3
The Answer Is = −6x−14
Step-by-step explanation:
Simplify the expression.
Hopefully this helps you
- Matthew :)
Answer:
[tex]\Longrightarrow: \boxed{\sf{-6x-14}}[/tex]
Step-by-step explanation:
In order to solve this, you need to expand by the distributive property.
Distributive property:
[tex]\Longrightarrow: \sf{A(B+C)=AB+AC}[/tex]
[tex]\Longrightarrow: \sf{A(B-C)=AB-AC}[/tex]
-6(x+2)-2
Expand.
-6*x=-6x
-6*2=-12
Then, rewrite the expression down.
-6x-12
-6x-12-2
Subtract the numbers from left to right.
-12-2=-14
[tex]\Longrightarrow: \boxed{\sf{-6x-14}}[/tex]
Therefore, the correct answer is -6x-14.I hope this helps. Let me know if you have any questions.
Good luck with your assignment!
What is the area of each triangular base of the prism?
Each base: 12 ft^2
Surface Area: 48 ft^2
Explanation:Assuming it is a triangular prisim made of equilateral triangles, I would assume the formula would be 4 times the area of one triangular base, following the formula:
[tex]a = \frac{1}{2} bh \\ a = \frac{1}{2} (6)(4) \\ a = 12 \\ 4 \times 12 = 48[/tex]
I need help! This pattern repeats every 4 terms. The pattern is square, hexagon, trapezoid, triangle. What is the shape in the 7th term of this pattern?
==========================================================
Explanation:
There are two ways to do this problem.
Method 1 involves listing out the terms until we reach the seventh one.
squarehexagontrapezoidtrianglesquarehexagontrapezoidtriangleWe see that the trapezoid is term 7.
-------------
Method 2 is faster and the one I recommend.
Since the pattern repeats every 4 items, this means we divide by 4 and look at the remainder. Ignore the quotient entirely.
7/4 = 1 remainder 3
The remainder 3 means that the answer is found in term 3, which is the trapezoid.
A new car is purchased for 27,500 dollars. The value of the car depreciates at a rate of
9% per year. Which equation represents the value of the car after 2 years?
Answer:
A=27,500(1-.09)² or A=27,500(0.91)²
Write each fraction as a percentage
Answer:
answer below
Step-by-step explanation:
3/5=60%
1/50=2%
9/10=90%
9/5=180%
18/60=30%
find the circumference of the circle using 3.14 for pi
Answer: 34.54
Multiple 11 by 3.14 and you'll get 34.54
and if you need the radius just divide 11 by 2 and get 5.5
I hope this helps! :)
26) Anjali and Rob are selling cookie dough for a school fundraiser. Customers can buy packages of
sugar cookie dough and packages of oatmeal cookie dough. Anjali sold 6 packages of sugar cookie
dough and 2 packages of oatmeal cookie dough for a total of $116. Rob sold 9 packages of sugar
cookie dough and 12 packages of oatmeal cookie dough for a total of $318. Find the cost each of
one package of sugar cookie dough and one package of oatmeal cookie dough.
Answer:
Sugar cookie dough packages cost 14 dollars each, and oatmeal cookie dough packages cost 16 dollars each.
Step-by-step explanation:
Let s equal the cost of a sugar cookie dough package, and o equal the cost of oatmeal cookie dough packages.
6s + 2o = 116
9s+12o = 318
therefore,
18s+6o = 348
18s+24o = 636
Subtracting them, we get -18o = -288, or 18o = 288
Therefore, o = 16, and 6s+32=116, so 6s=84, so s = 14
A dental hygienist might pay about $20,000 for education beyond high school and expect to earn about $70,000 per year. A veterinarian might pay about $153,000 for education beyond high school and expect to earn about $84,000 per year. Compare the total earnings minus the costs of education for the careers in 10 years. Which career would you choose if salary was the most important factor? Explain
Answer:
$150,000.
Step-by-step explanation:
Identify the reflection of the figure with vertices T(−1,3), U(−3,−17), and V(12,−8) across the y-axis.
Answers:
T (−1, −3), U (−3, 17), V (12, 8)
T (1, −3), U (3, 17), V (−12, 8)
T (3, −1), U (−17, −3), V (−8, 12)
T (1, 3), U (3, −17), V (−12, −8)
Answer:Reflecting over the y-axis = (x,y) → (-x,y)
So T will be (1,3) , U (3,-17) and V (-12. -8)
So D
Step-by-step explanation:
Answer:
T (1, 3), U (3, −17), V (−12, −8)
Step-by-step explanation:
To find the image as it is reflected from the preimage across the y-axis, apply the transformation rule, (x,y)→(−x,y), to each of the preimage points.
T(−1,3)→T'(1,3)
U(−3,−17)→U'(3,−17)
V(12,−8)→V'(−12,−8)
Draw lines between the found vertices to construct the reflected figure.
Therefore, the reflection of the figure with vertices T(−1,3), U(−3,−17), and V(12,−8) across the y-axis is the figure with vertices T'(1,3), U'(3,−17), and V'(−12,−8).
A bucket contains 3 small red blocks, 5 small yellow blocks, 5 large yellow and 7 large red blocks. If a block is drawn randomly, what is the probability that the block is yellow, given that it is one of the large yellow blocks
Answer:
probability = favorable cases / true cases
p(A)=5/20 simplified by 5 = 1/4
answer : the probability that the block is one of the large yellow it's 1/4.
A team of researchers measured the length of 5 different rainbow trout pulled from different locations in a lake. length, in.: {18, 22, 15, 28, 17} what is the estimated mean absolute deviation of the lengths of rainbow trout in the lake? 1.3 in. 4 in. 20 in. 61 in.
4IN
Step-by-step explanation:
I took the test for k12 and got 100% hope it helps
Answer:
4 in
Step-by-step explanation:
18 + 22 + 15 + 28 + 17 = 100
100 / 5 = 20
So, the mean for the data set: 18, 22, 15, 28, 17 is 20.
18 - 20 = |2|
22 - 20 = |2|
15 - 20 = |5|
28 - 20 = |8|
17 - 20 = |3|
2 + 2 + 5 + 8 + 3 = 20
20 / 5 = 4
So, 4 in is the mean absolute deviation (MAD).
I also took the test.
Please show work y’all thank you!
Two yellow lines (one solid, another broken) in the center of a two-way road mean that vehicles traveling ___________.
Given m||n find the value of x (x+ 20) (4x-5)
Answer:
x² + 80x - 5
Step-by-step explanation:
x (x+ 20) (4x-5)x [tex]*[/tex] x = x² x [tex]*[/tex] 20 = 20xx² + 20x [tex]*[/tex] 4x - 5 20x [tex]*[/tex] 4x = 80xso in all = x² + 80x - 5A GIC pays 6% per annum. How long would it take $3000
to grow to $6000? (3 marks)
Answer:
180 weeks you have to convert the percentage to a decimal and multiple it to 3000
Judy simplified the expression (3x+1)(x-3) -( 2-2x^2-3x)
A piece of copper with a volume of 8.25 cubic centimeters has a mass of 73.92 grams. A piece of iron with a volume of 5 cubic centimeters has a mass of 39.35 grams. Which metal has the greater density?
PLEASE SHOW WORK, WILL MARK BRAINLIEST
A piece of copper with a volume of 8.25 cubic centimeters has a mass of 73.92 grams than has the greater density A piece of iron with a volume of 5 cubic centimeters has a mass of 39.35 grams.
How are density, volume and mass of a substance related?Suppose that a finite amount of substance is there having its properties as:
mass of substance = m kg
density of substance = d kg/m³
volume of that substance = v m³
Then, they are related as:
[tex]d = \dfrac{m}{v}[/tex]
A piece of copper with a volume of 8.25 cubic centimeters has a mass of 73.92 grams.
[tex]d = \dfrac{73.92}{8.25}\\d = 8.96[/tex]
A piece of iron with a volume of 5 cubic centimeters has a mass of 39.35 grams.
[tex]d = \dfrac{39.35}{5}\\\\d = 7.87[/tex]
Thus, A piece of copper with a volume of 8.25 cubic centimeters has a mass of 73.92 grams than has the greater density A piece of iron with a volume of 5 cubic centimeters has a mass of 39.35 grams.
Learn more about mass, volume and density relation here:
https://brainly.com/question/952755
#SPJ1
What is the standard deviation of the data? 0.5 1.5 2.0 2.5
Answer:
0.74
Step-by-step explanation:
The standard deviation of a data set is the sqaure root of the variance, so first we must find the variance. The equation for variance is:
σ² = [tex]\frac{{(x_{1}-[x bar] )}^{2}+...+{(x_{n}-[x bar]) }^{2}}{n}[/tex]
x = number in the data set
xbar = median of the data set
n = number of terms
Plugging in the given values, the equation for the variance of this number set is:
σ² = [tex]\frac{(0.5 - 1.625)^{2} + (1.5 - 1.625)^{2}+ (2.0 - 1.625)^{2}+(2.5 - 1.625)^{2} }{4}[/tex]
Solving:
= [tex]\frac{1.265625+0.015625+0.140625+0.765625}{4}[/tex]
= [tex]\frac{2.1875}{4}[/tex]
σ² = 0.546875
Since the standard devianation is the sqaure root of the variance, we'll sqaure 0.546875:
[tex]\sqrt{0.546875}[/tex]
= 0.73950997288745
= 0.74 (rounded)
hope this helps!
Answer:
0.5
Step-by-step explanation
Because it is a standar deviation
A certain number is subtracted from 20.the result multiplied by 3 is equal to 45. What is the number?
The product of two numbers is 26 and one of the numbers is one larger than six times the other number. find the numbers.
Answer:
(-13/6, -12)
&
(2, 13)
Step-by-step explanation:
x · y = 26 -------> x = 26/y
y = 1 + 6x
SUB for y
x(1 + 6x) = 26
x + 6x² = 26
SOLVE for x
6x² + x - 26 = 0
6x² + 13x - 12x - 26 = 0
6x(x - 2) 13(x - 2) = 0
(6x + 13)(x - 2) = 0
x = -13/6 or 2
Test x = -13/6 for both equations
Equation 1
-13/6 · y = 26
y = -156/13
y = -12
Equation 2
y = 1 + 6(-13/6)
y = 1 - 13
y = -12
-12 = -12 ✅
Test x = 2 for both equations
Equation 1
2 · y = 26
y = 26/2
y = 13
Equation 2
y = 1 + 6(2)
y = 1 + 12
y = 13
13 = 13 ✅
Hope this helps & God bless!
At what price should Nepali bags be sold in order to make a profit of 140% by selling 2000 bags in the USA which was purchased in Nepal for Rs. 800 each and after paying 15% export tax ? [Given that $1 = Rs. 105.00.]
The price at which the Nepali bags should be sold in order to make a profit of 140% is $21.02.
What is the price the bags should be sold ?Profit is total revenue less total cost.
The first step to convert Rs. 800 to US dollars: 800 / 105 = $7.62
The second step is to determine the total cost including taxes: 1.15 x 7.62 = $8.76
Selling price = (1 + 1.40) x 8.76 = $21.02
To learn more about percentages, please check: https://brainly.com/question/25764815
How many different vacation combinations do you have to choose from?
Answer:
12 different vacation caombinations
Step-by-step explanation:
has 3 options of Theme Park and 4 options of length of trip
[tex]C=(3)(4)=12[/tex]
Hope this helps
The perimeter of a rectangular poster is 14 feet and the length is 4 feet. Describe how to use the perimeter formula to find the width.
Answer:
solve the equation with known values filled in; width is 3 ft.
Step-by-step explanation:
The perimeter formula can be used to find a missing value by filling in all of the known values, and solving the resulting equation.
__
P = 2(L +W) . . . . . . perimeter formula
14 = 2(4 +W) . . . . . known values substituted
7 = 4 +W . . . . . . . divide by 2
3 = W . . . . . . . . . subtract 4
The width is found to be 3 feet using the perimeter formula.
Answer:
The width of rectangular poster is 3 feet.
Step-by-step explanation:
As per given question we have provided that :
→ Perimeter of rectangle = 14 feet→ Length of rectangle = 4 feetWe need to find the width of rectangle.
Here's the required formula to find the width :
[tex]{\underbrace{\sf{\small{ \: \: P = 2(L + W) \: \: }}}}[/tex]
➟ P = Perimeter ➟ L = Length ➟ W = WidthCalculating the width of rectangular poster by substituting the values in the formula :
[tex]\begin{gathered} \qquad{\twoheadrightarrow{\sf{\small{ \: \: P = 2(L + W) \: \: }}}} \\ \\ \qquad{\twoheadrightarrow{\sf{\small{ \: \: 14 = 2(4+ W) \: \: }}}} \\ \\ \qquad{\twoheadrightarrow{\sf{\small{ \: \: \dfrac{14}{2} = (4+ W) \: \: }}}} \\ \\ \qquad{\twoheadrightarrow{\sf{\small{ \: \: 7= (4+ W) \: \: }}}} \\ \\ \qquad{\twoheadrightarrow{\sf{\small{ \: \: W = 7 - 4\: \: }}}} \\ \\ \qquad{\twoheadrightarrow{\sf{\underline{\underline{\small{ \: \: W = 3\: \: }}}}}} \end{gathered}[/tex]
Hence, the width of rectangular poster is 3 feet.
[tex]\rule{200}2[/tex]
This question has two parts. Use the figure to answer Part A and Part B.
Angle ABC is a right angle.
a
Part A
Which equation could be used to correctly solve for X?
А
O A. 2x = 56
O B. 2x+56 = 90
OC. 2x + 56 = 180
Part B
What is the value of x? Enter the answer in the box.
56°
(2x)
B
C
X=
* not drown to scale
Answer:
Pt 1) B
Pt 2) 17
Step-by-step explanation:
a right angle is 90 so 56 plus 2x should equal 90. Subtract 56 from 90 and get 34, because it's 2x you divide by 2 and get 17
Many weather conditions need to be met before a space shuttle can launch. The temperature must be greater than 35°F and less than 100°F, and the wind speed cannot exceed 30 knots. A system of inequalities can be used to show these three conditions. Write a system for the above constraints.
Answer:
Launch may not occur if the temperature is 35° F or colder.
would be your answer.
Step-by-step explanation:
The temperature cannot exceed 99° F for 30 consecutive minutes. Peak wind speed is 30 knots. When the wind direction is between 100 degrees and 260 degrees, the maximum wind speed may be as low as 24 knots.
-121-1,649°C.
10 One of the legs of a right triangle has vertices with coordinates (-2,4) and (10,0).
What is the equation of the line of the other leg of the right triangle if it shares the vertice of (10,0)?
The equation of the line of the other leg of the right triangle if it shares the vertice of (10,0) is y = -1/3x + 10/3
How to find the equation of a line?The equation of a line in slope-intercept form is expressed as y = mx + b
where
m is the slope
b is the y-intercept
Given the coordinate points (-2, 4) and (10, 0)
Find the slope
Slope = -4/12
Slope = -1/3
Determine the y-intecept
0 = -1/3(10) + b
b = 10/3
Determine the equation
y = -1/3x + 10/3
Hence the equation of the line of the other leg of the right triangle if it shares the vertice of (10,0) is y = -1/3x + 10/3
Learn more on equation of a line here: https://brainly.com/question/13763238