Find the common ratio and write out the first four terms of the geometric sequence (1.06)n−1 Common ratio is a1= a2= a3= a4=
Answers
Solution
Step 1
Write the nth term ex[pression and the common ratio formula.
[tex]\begin{gathered} T_n\text{ = \lparen1.06\rparen}^{n-1} \\ Common\text{ ratio = }\frac{2^{nd}term}{1^{st}term} \end{gathered}[/tex]Step 2
[tex]\begin{gathered} T_1\text{ = \lparen1.06\rparen}^{1-1}\text{ = 1} \\ T_2\text{ = \lparen1.06\rparen}^{2-1}\text{ = 1.06} \\ T_3\text{ = \lparen1.06\rparen}^{3-1}\text{ = \lparen1.06\rparen}^2\text{ = 1.1236} \\ T_4\text{ = \lparen1.06\rparen}^{4-1}=\text{ \lparen1.06\rparen}^3\text{ = 1.191016} \end{gathered}[/tex]Step 3
[tex]Common\text{ ratio r = }\frac{1.06}{1}\text{ = 1.06}[/tex]Final answer
Related Questions
Solve:x + 2y + z = 82x + y - z = 1x + y – 2z = - 3
Answers
We are given the following system of equations:
[tex]\begin{gathered} x+2y+z=8,(1) \\ 2x+y-z=1,(2) \\ x+y-2z=-3,(3) \end{gathered}[/tex]To solve the system we will add equations (1) and (2):
[tex]x+2y+z+2x+y-z=8+1[/tex]Adding like terms:
[tex]\begin{gathered} 3x+3y=9 \\ x+y=3,(4) \end{gathered}[/tex]Now we multiply equation (2) by -2:
[tex]-4x-2y+2z=-2[/tex]Now we add this equation to equation (3):
[tex]x+y-2z-4x-2y+2z=-3-2[/tex]Adding like terms:
[tex]-3x-y=-5,(5)[/tex]Now we add equations (4) and (5):
[tex]x+y-3x-y=3-5[/tex]Adding like terms:
[tex]-2x=-2[/tex]Dividing both sides by -2:
[tex]x=-\frac{2}{-2}=1[/tex]Now we replace this value of "x" in equation (4):
[tex]\begin{gathered} x+y=3 \\ 1+y=3 \end{gathered}[/tex]Subtracting 1 to both sides:
[tex]\begin{gathered} 1-1+y=3-1 \\ y=2 \end{gathered}[/tex]Now we replace the values of "x" and "y" in equation (1):
[tex]\begin{gathered} x+2y+z=8 \\ 1+2(2)+z=8 \end{gathered}[/tex]Adding like terms:
[tex]\begin{gathered} 1+4+z=8 \\ 5+z=8 \end{gathered}[/tex]Subtracting 5 to both sides:
[tex]\begin{gathered} 5-5+z=8-5 \\ z=3 \end{gathered}[/tex]Therefore, the solution of the system is:
[tex]x=1,\text{ y=2, z=3}[/tex]What does the dashers part of the figure represent
Answers
The figure represents : Line
What is a Line?
A line is an object in geometry that is indefinitely long and has neither breadth nor depth nor curvature. Since lines can exist in two, three, or higher dimensional environments, they are one-dimensional things. The term "line" can also be used to describe a line segment in daily life that contains two locations that serve as its ends.
from the figure we have to find that whether its a line, line segment, vertex or ray
Line: A line is a perfectly straight, one-dimensional shape that extends infinitely in both directions and has no thickness. Sometimes a line is referred to as a straight line or, more formally, a right line.
Line segment: In other words, a line segment is a section or element of a line with two endpoints. A line segment, in contrast to a line, has a known length. A line segment's length can be calculated using either metric measurements like millimeters or centimeters or conventional measures like feet or inches.
Ray: A ray is a vector from a point to another point when seen as a vector. A ray is typically viewed in geometry as a half-infinite line, or half-line, with one of the two points and assumed to be at infinity.
Vertex: A vertex is a point on a polygon where two rays or line segments meet, the sides, or the edges of the object come together. Vertex is the plural form of vertices.
The figure represents a Line
Hence, The dashers part of the figure represent a Line
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which transformations had to occur for the blue triangle to become the purple triangle? [note: all rotations are about origin]
Answers
Let:
A = (-4,3)
B = (-1,3)
C = (-1,1)
after a 90 clockwise rotation:
A = (-4,3)--------->(y,-x)------->(3,4)
B = (-1,3)----------->(y,-x)------>(3,1)
C = (-1,1)------------>(y,-x)------>(1,1)
After a translation 3 units down and 2 units left:
(3,4)------>(x-2,y-3)------->(1,1)
(3,1)------>(x-2,y-3)------->(1,-2)
(1,1)------>(x-2,y-3)------->(-1,-2)
---------------------------
Therefore, the answer is D
The school record for the greatest number of jumping jacks in a row is 84 in 4 minutes. If the record for jumping jacks made is a constant ratio, how many jumping jacks did the record holder make in 1 minute?
Answers
The amount of jumping packs in 1 minute is 21
How to determine the amount of jumping packs in 1 minute?From the question, the given parameters are:
Number of jumping packs in a row = 84 packs
Number of minutes = 4 minutes
The amount of jumping packs in 1 minute is the quotient of the number of jumping packs in a row and the number of minutes
This is represented as
Jumping packs in 1 minute = Number of jumping packs in a row /Number of minutes
Substitute the known values in the above equation
Jumping packs in 1 minute = 84/4
Evaluate
Jumping packs in 1 minute = 21
Hence, the jumping packs in 1 minute is 21
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The record holder makes 21 jumping jacks in 1 minute which is the ratio of the number of jumping jacks performed in a row to the total number of minutes.
What is the ratio?A ratio is a relationship between two amounts that is represented by the division of one by the other.
The ratio of the total number of jumping jacks performed in a row to the total number of minutes determines how many jumping jacks should be performed in a minute.
No. of jumping packs in a row = 84 packs
No. of minutes = 4 minutes
So jumping packs in 1 minute = 84/4
Apply the division operation to get
Jumping packs in 1 minute = 21
Therefore, 21 jumping jacks should be performed in 1 minute.
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let f(x) =(4x"3+20)"2 and g(x) =4x"3+20.given that f(x)=(h°g)(x), find h(x)
Answers
Here, we want to find the function h(x)
From the question, we can see that the function f(x) is a composite function that was obtained by fitting g(x) into h(x)
What can we notice about g(x) and f(x)?
What we can see is that f(x) is the square of g(x)
Thus, what this mean is that h(x) = x^2
x + 3 = -7 Solve the inequality
Answers
The given inequality is expressed as
[tex]\begin{gathered} x\text{ + 3 }\leq\text{ - 7} \\ x\text{ }\leq\text{ - 7 - 3} \\ x\text{ }\leq\text{ - 10} \end{gathered}[/tex]PLEASE HELP!!!!!
Answer two questions about Equations AAA and BBB:
A. 4x+2=6-x
B. 5x+2=6
1) How can we get Equation BBB from Equation AAA?
Choose 1 answer:
(Choice A)
Add/subtract a quantity to/from only one side
(Choice B)
Add/subtract the same quantity to/from both sides
(Choice C)
Multiply/divide only one side by a non-zero constant
(Choice D)
Multiply/divide both sides by the same non-zero constant
Based on the previous answer, are the equations equivalent? In other words, do they have the same solution?
Choose 1 answer:
(Choice A)
Yes
(Choice B)
No
Answers
We can get equation B from equation A by Adding the same quantity to both sides. The equations are equivalent and have the same solution.
The equations are:
A : 4x+2 = 6-x
B : 5x+2 = 6
(1) We can get equation B from equation A by adding x to both sides of the equation.
We can verify this.
Add x to both sides of the equation A,
⇒ 4x+2 +x = 6-x+x
⇒ 5x+2 = 6
This is equation B.
So Add the same quantity to both sides of equation A to get equation B.
(2) We just added a same quantity on both sides of equation A. This will not change the equations. So equation A and equation B are equivalent. Also they have same solution.
Equation A: 4x+2=6-x
⇒ 4x+x = 6-2
⇒ 5x = 4
⇒ x = 4/5
Equation B: 5x+2 = 6
⇒ 5x = 6-2
⇒ 5x = 4
⇒ x = 4/5
So both have same solution.
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I think one is 10 I am just not sure though
Answers
Right Triangles
A right triangle is identified because it has an interior angle of 90° (right angle). The other two angles must be acute and add up to 90°.
In the special case that both acute angles have a measure of 45°, then we have an isosceles triangle, that is, both legs have the same length.
We can see one of the legs measures
[tex]L=5\sqrt[]{2}[/tex]Being this an isosceles triangle, the other leg (the base of the triangle) also measures L, thus you should drag
[tex]5\sqrt[]{2}[/tex]To the box at the bottom.
The other unknown length is the hypotenuse H. According to the Pythagorean's Theorem:
[tex]H^2=L^2+L^2=2L^2[/tex]Substituting:
[tex]\begin{gathered} H^2=2(5\sqrt[]{2}^{})^2 \\ \text{Operating:} \\ H^2=2\cdot50=10 \\ \text{Thus:} \\ H=\sqrt[]{100} \\ H=10 \end{gathered}[/tex]You should drag the length 10 to the hypotenuse.
A poster is 3 feet wide and 12 feet long. What are the dimensions if the poster is enlarged by a factor of 5/2?
Answers
To be able to get the enlarged dimensions, we will multiply the dimension of the poster by the given scale factor 5/2.
We get,
[tex]\text{Width = 3 ft. x }\frac{5}{2}\text{ = }\frac{15}{2}\text{ ft. or 7.5 ft.}[/tex][tex]\text{Length = 12 ft. x }\frac{5}{2}\text{ = }\frac{60}{2}\text{ ft. or 30 ft.}[/tex]Therefore, the enlarged dimension of the poster will be 7.5 ft. x 30 ft.
Is 24x equivalent to 3(2x + 6x)?YesNo
Answers
Answer
Yes
Step-by-step explanation
Given the expression:
[tex]3(2x+6x)[/tex]Combining similar terms:
[tex]3(8x)[/tex]Multiplying:
[tex](3\cdot8)x=24x[/tex]7. Solve for value of tan A 8. Solve for Cos Q
Answers
7. Tan A = opposite/adjecent
Therefore Tan A = 24/7
• Option number (2) is correct .
8. Cos Q = adjacent/hypotaneus
where hypotaneus side : r^2 = x^2+y^2
r^2 = 12^2 +5^2= 169
r =√169 = 13
Now Cos Q = 12/13
• Option 4 is correct .
ILL GIVE BRAINLIEST!!!!
Answers
Answer:
1 = yes
2 = no
3 = no
4 = yes
5 = yes
6 = no
7 = no
8 = no
Suppose f(x) = 3x² – 48. Solve f(x) = 0
Answers
ANSWER:
x = 4 and x = -4
STEP-BY-STEP EXPLANATION:
We have the following function:
[tex]f(x)\: =\: 3x^{2}\: -\: 48[/tex]We solve the values of x for when the function is equal to 0, as follows:
[tex]\begin{gathered} \: 3x^{2}\: -\: 48=0 \\ \: 3x^{2}\: -=48 \\ x^2=\frac{48}{3} \\ x=\sqrt[]{16} \\ x=\pm4 \end{gathered}[/tex]Select the correct answer. Which graph represents the solutions to this equation? x2 + 8x = -20 A. Linear-quadratic system graph shows upward parabola with vertex at (minus 2, 4) and passing through x and y-axis (minus 8, 0), and (0, 0) B. Linear-quadratic system graph shows upward parabola with vertex at (minus 4, 4) and passing through (minus 2, 8), and (minus 6, 8) C. Linear-quadratic system graph shows upward parabola with vertex at (4, 0) and passing through (1, 4), and (6, 4) D. Linear-quadratic system graph shows a downward parabola with vertex at (0, 8) which intercepts the x-axis at 3 and minus 3 units. Reset Next
Answers
A graph which represents the solutions to this quadratic equation (x² + 8x = -20) is: B. Linear-quadratic system graph shows upward parabola with vertex at (minus 4, 4) and passing through (minus 2, 8), and (minus 6, 8).
What is a graph?A graph can be defined as a type of chart that's commonly used to graphically represent data on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis.
In Mathematics, the graph of any quadratic function or equation always forms a parabola because it is a u-shaped curve.
In conclusion, we can reasonably infer and logically deduce that the given quadratic equation is modeled by an upward parabola with its vertex at (-4, 4) as shown in the graph attached below.
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4. (01.02 LC)
Brandi earned $59.00 in interest after one and one half years on an account that paid 5.5% simple interest annually. Use the formula / -Prt to find Brand's principal balance. Round to the nearest hundredth. (1
point)
O $486.75
$535.23
$617.98
O $715.15
Answers
Simple interest is a clear and simple method for computing financial interest. Simple Interest is the amount returned for using the borrowed funds over a predetermined amount of time.
What is meant by simple interest?Simple interest is, by definition, the amount of interest paid on a specific principal sum of money when an interest rate is applied. Compound interest, on the other hand, is the interest that is computed using both the principal and the interest that has accumulated over the preceding period.
Simple Interest is the amount returned for using the borrowed funds over a predetermined amount of time.
A = P(1 + rt)
Simple interest is a method for figuring out how much interest was paid on a sum of money during a specific time period at a specific rate. Simple interest has a constant principle amount. Simple interest is a clear and simple method for computing financial interest.
Therefore, the correct answer is option D. $715.15.
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Help me asp please!!
Answers
Every rhombus is a square 
Answers
Answer: False!
Step-by-step explanation:
Answer:
false
Step-by-step explanation:
Rhombus as a quadrilateral with equal sides. The angles may or may not be right-angled.
However, a square is a quadrilateral with equal sides and all angles are right angles.
Hence, every square is a rhombus but the opposite is not true.
make a 2 column proofplease make it simple like JK is parallel to NM(given)
Answers
Explanation:
Since L is the midpoint of JM, then JL = LM.
Therefore,
Statement: JL = LM
Reason: L is the midpoint of JM
The lines JK and NM are parrallel; therefore, by the alternate interior angles theorem,
[tex]\angle LJK=\angle LMN[/tex]Furthermore, since ∠JLK and ∠MLN are vertical angles,
[tex]∠JLK=∠MLN[/tex]Now since ∠JLK = ∠MLN, ∠LJK = ∠LMN, and JL = LM, then by ASA postulate
[tex]\boxed{△JKL=△MNL.}[/tex]Hence, our proof is complete!
How long ago, to the nearest year, was the artifact made?
Answers
Let's use the following formula:
[tex]A=A_0(0.5)^{\frac{t}{h}}[/tex]where:
Ao= Initial amount
t = time
h = half-life
[tex]\begin{gathered} A=0.2A_0 \\ so\colon \\ 0.2A_0=A_0(0.5)^{\frac{t}{5730}} \end{gathered}[/tex]solve for t:
[tex]\begin{gathered} 0.2=0.5^{\frac{t}{5730}} \\ \ln (0.2)=\frac{t}{5730}\ln (0.5) \\ t=5730\cdot\frac{\ln (0.2)}{\ln (0.5)} \\ t\approx13305 \end{gathered}[/tex]Write an equation for the line graphed below.
Answers
Answer:
y=-4/3x
Step-by-step explanation:
There is no b because it starts at the origin.
Answer:
-4/3x is the correct answer as provided by IceJadeKitsune
I am merely providing an explanation in case you are curious
Step-by-step explanation:
The equation for a line in slope-intercept form is
y = mx + b
where m is the slope and b the y-intercept
The slope of a line, m can be determined by what is called the rise/run ratio
The process is as follows
Take any two convenient points on the line and note their coordinatesLet's label the points as (x1, y1) and (x2, y2)The rise is the difference in the y values = y2 - y1 (The run is the difference in the x values = x2 - x1Divide this rise over run and you get the slope, mTo get b, find where the line crossed the y-axis and the value of b will be the value of y at that point.The value of x will be 0 at the y-intercept
From the graph choose points origin (0, 0) which is one point where the line crosses the y axis
From the graph we see that another distinct point where the line passes is at x = -3, y = 4 or the point(-3, 4)
Having got these two points we calculate
rise = 4 - 0 = 4
run = -3 - 0 = -3
Slope m = -4/3
Slope is negative because as y increases, x decreases
So the equation is y = -4/3x + b
Looking at the graph, we see that b = 0 since the graph passes through the origin as correctly stated by IceJadeKitsune
Therefore the equation of the line is [tex]\boxed{\bold{y = -\dfrac{4}{3}x}}[/tex]
What is the answer to this math problem which isn4/5+3/5=7/5=
Answers
Answer:
14/5 or, 2 4/5.
Step-by-step explanation:
4/5 + 3/5 = 7/5, 7/5 + 7/5 = 14/5
14/5 as a mixed number is 2 4/5.
I think you're talking about fractions so.
Find the present value given the following:Amount needed: $9,350Time in years: 3Interest: 5%Compounded: semiannually
Answers
Solution:
Amount needed (P): $9,350
Time in years (n): 3
Interest (r): 5%
Compounded: semiannually
To find the Amount (A).
we have the formula A, we get,
[tex]A=P(1+\frac{\frac{r}{2}}{100})^{2n}[/tex][tex]=9350(1+\frac{2.5}{100})^{2(3)}[/tex][tex]=9350(\frac{102.5}{100})^6[/tex][tex]=9350(1.025)^6[/tex][tex]=9350(1.15969)[/tex][tex]A=10,843.13[/tex]The present value is $10,843.133
How can you use the Power of a Quotient, Quotient of Powers, Zero Exponent Laws Identity Exponent and to evaluate numerical expressions with whole-number exponents?
Answers
Exponents and powers are terms that occasionally get used interchangeably, which can be confusing.
Mathematics uses expressions called powers, where n is the exponent and x is the base. When a number or variable is multiplied repeatedly, it is referred to as a power. The exponent of power tells us how many times to multiply the base by itself.
You can interpret the term as "x to the power." The exponent (n) is written smaller and at the head of the line using superscript, whereas the base (x) is printed in full size (if you are typing it on a computer). For instance, it is written as x squared or x to the second power, which in reality means that the value of x is multiplied by an amount equal to the exponent's value.
If the base is a number: In this situation, all you have to do to discover the solution is multiply the base by itself as many times as the exponent's value.
If the base is a variable, you must first replace the variable with a value before continuing.
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The pair of values below is form an inverse variation find the missing value (3,16) (10,y)
Answers
An inverse variation is represented as:
[tex]y=\frac{k}{x}[/tex]To find the missing value we need to find k first. Using the first pair we have:
[tex]\begin{gathered} 16=\frac{k}{3} \\ k=3\cdot16 \\ k=48 \end{gathered}[/tex]Now, we plug the value of k and use the second pair to find y:
[tex]\begin{gathered} y=\frac{48}{10} \\ y=\frac{24}{5} \end{gathered}[/tex]Therefore, y=24/5.
I need help with this!! 4. Ms. Ruggiero is rewarding her best class for doing outstanding on the final exam with a virtual pizza party. The pizzas are $8.75 each. On top of buying the pizza, she buys herself an order of wings for $4.25, pays 9.25% sales tax, and tips the clerk 15% after tax. How many pizzas can she buy with $50?
Answers
Let's use the variable x to represent the number of pizzas Ms. Ruggiero can buy.
If each pizza is $8.75, the wings are $4.25, the tax is 9.25% and the tip is 15%, and all this needs to be lesser than or equal 50, we have the inequality:
[tex]\begin{gathered} (8.75x+4.25)\cdot1.0925\cdot1.15\le50 \\ 10.99x+5.34\le50 \\ 10.99x\le50-5.34 \\ 10.99x\le44.66 \\ x\le\frac{44.66}{10.99} \\ x\le4.06 \end{gathered}[/tex]So Ms. Ruggiero can buy 4 pizzas with $50.
Mischa dives from a platform that is 5 meters above water. Her dive takes her 1.7 meters below the surface of the water. How
far does Mischa's dive take her?
Answers
Conditional equations - Mischa's dives take her 6.5 meter
What are conditional equations?
An equation that holds true for one or more values of the variable but holds false for other values of the variable is known as a conditional equation.
Explain the airthematic mathematical operations.
it deals with the study and use of numbers in all other branches of mathematics. Basic operations include +,-, x, and /.
We frequently employ these fundamental mathematical operations in our daily lives: +, -,x, and, /. For every such area of our lives, we apply mathematical operations, whether it be to figure out the annual budget or distribute things evenly to a lot of people.
Mischa dives from a platform that is 5 meters above the water.
Her dive take her 1.7 meters below the surface of the water.
The total distance of Mischa's dive take her will be,
5+1.7meters
=6.7 meter
thus Mischa's dives take her 6.5 meters far.
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Donny the Dot Dude is saving for a llama. He puts$3,000 in a savings account that earns 12% simpleannual interest. How many years it will it take forhim to have the $4,440 he needs ifhe makes no additional depositsor withdrawals?A) 4 yearsSOB) 5 yearsC) 6 yearseboD) 2 yearsх
Answers
The simple interest formula is:
A = P(1 + rt)
where A is the final amount, P is the princiapal, r is the annual interest rate (as a decimal), and t is time in years.
Substituting with A = $4,440, P = $3,000, and r = 0.12 (= 12/100), we get:
[tex]\begin{gathered} 4440=3000\cdot(1+0.12\cdot t) \\ \frac{4440}{3000}=1+0.12\cdot t \\ 1.48-1=0.12\cdot t \\ \frac{0.48}{0.12}=t \\ 4\text{ years = t} \end{gathered}[/tex]The students in my class watch less than 2 hours television at night. how can I decide what data to collect to test this statement, How can I design a suitable data collection instrument?
Answers
Solution
For this case we need to select a sample of students from the class
We can ask to each student how much time spend on average watching tv at night
From the results we can take the average and the standard deviation and we can use a t-test to test the statement
An artist is building a pedestal out of wood that
will be used to display a piece of sculpture. She
plans to cover the pedestal with tile.
10 cm
6 cm
10 cm
16 cm
30 cm
How much tile will it take to cover the pedestal,
including the bottom?
Answers
The area of tiles taken to cover the pedestal, including the bottom is 1176 cm².
What is the Total Surface Area of a Triangular Prism?A triangular prism's surface area is also referred to as its total surface area. A triangular prism's total surface area is the sum of the areas of all its faces. A triangular prism consists of two triangular faces and three rectangular faces.
Surface area = (Perimeter of the base × Length of the prism) + (2 × Base Area) = (S1 +S2 + S3)L + bh
where,
b is the base triangle's bottom edge, h is its height, L is its length, and S1, S2, and S3 are the three edges (sides) of the base triangle (bh).
[2 (1/2 bh)] = bh is the area of the two triangular faces
Given:
From the figure, we can say that the pedestal is in form of a triangular prism.
To find the area of the tile that it takes to cover the pedestal, including the bottom we have to determine the surface area of the pedestal.
So from the figure,
The side lengths of the triangular base are:
S1 = S2 = 10 cm
S3 = 16 cm
Base of prism = 16 cm
Height of prism = 6 cm
Length of prism = 30 cm
Surface area = (S1 +S2 + S3)L + bh
= (10+10+16)30 + 16×6
= 1176 cm²
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someone help please
Answers
Answer:
Angle 3 = 95° (vertically opposite angles)
Angle 2 and 4 = 180 - 95
= 85° (adjacent angles on straight line)
Angle 5 = 180 - 144
= 36° (adjacent angles on straight line)
Angle 6 = 180 - angle 3 - angle 5
= 180 - 95 - 36
= 49° (sum of angles in triangle=180)
Angle 1 = 180 - 90 - angle 6
= 180 - 90 - 49
= 41° (sum of angles in triangle=180)
Angle 7 = 180 - 38 - angle 5
= 180 - 38 - 36
= 106° (sum of angles in triangle=180)