What is the value of x in the geometric sequence x,3,−1/3
Answers
Answer:
x=27
Step-by-step explanation:
the answer is proved in the diagram above
The value of x is 27
What is Geometric progression?A geometric progression is a special type of progression where the successive terms bear a constant ratio known as a common ratio. It is also known as GP. The GP is generally represented in form a, ar, ar2.... where a is the first term and r is the common ratio of the progression. The common ratio can have both negative as well as positive values. To find the terms of a geometric series, we only need the first term and the constant ratio.
The geometric progression is of two types. They are
finite geometric progression andinfinite geometric progression.Given:
x,3,−1/3
First term, a
second term
ar= 3
a= 3/r
third term
ar² = -1/3
a= -1/3r²
So,
3/r= - 1/3r²
9r= 1
r= 1/9
So,
ar= 3
a= 27.
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Related Questions
Corinne solved the equation below:
5x = 95
5x − 5 = 95 − 5
x = 90
Is Corinne's solution correct? If the solution is incorrect, explain why it is incorrect and show the correct steps to solve the equation.
Answers
Answer:
The solution is incorrect
Step-by-step explanation:
5x = 95
We need to do the opposite
We are multiplying x by 5 so we need to divide by 5
5x/5 = 95/5
x = 19
Corinne's solution is incorrect.
The mistake occurred when she subtracted 5 from both sides of the equation.
We have,
To solve the equation correctly, we need to isolate the variable x. Here are the correct steps:
Starting with the equation:
5x = 95
To isolate x, we divide both sides of the equation by 5:
(5x) / 5 = 95 / 5
x = 19
Thus,
The correct solution to the equation is x = 19.
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The sum of 2 times a number and 4 equals 9
Answers
Answer:
2x +4 = 9
x = 5/2
Step-by-step explanation:
Let x = number
2x +4 = 9
Subtract 4 from each side
2x+4-4 = 9-4
2x = 5
Divide by 2
2x/2 =5/2
x = 5/2
2x + 4 = 9
Step-by-step explanation:
If you’re looking for this answer to be written in mathematical form, the answer would be 2x + 4 = 9
Explanation: sum means addition obviously and the sum of 2 times a number would best represent 2 times x. The 4 is being added to the sum of 2 times a number and equals to 9.
We are given both the slope and y-intercept so writing the equation in slope-intercept form is a breeze! Label both the slope and y-intercept and them substitute them into the general form of slope-intercept form. So, y=4x−3.
Answers
Answer:
below
Step-by-step explanation:
hope it is well understood?
The slope is 4 and y- intercept is 13
What is slope?A number that describes a line's direction and steepness is known as the slope or gradient of a line in mathematics.
A slope exists Numerical calculation of a line's inclination relative to the horizontal. In analytic geometry, the slope of any line, ray, or line segment stands as the proportion of the vertical to the horizontal distance between any two points on it (“slope equals rise over run”).
Given
Slope
y = 4x-3
dy/dx = 4
slope = 4
intercepts y = 4(4) 3
y = 16-3
y = 13
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A 9.85 m ladder is placed against a wall. The height to the top of the ladder is 5 m more than the distance between the wall and the foot of the ladder. Find the height to the top and the distance between the wall and the foot of the ladder. find base and height
base...... m
height.....m
Answers
Given:
Length of the ladder = 9.85 m
The height to the top of the ladder is 5 m more than the distance between the wall and the foot of the ladder.
To find:
The height to the top and the distance between the wall and the foot of the ladder.
Solution:
let x be the distance between the wall and the foot of the ladder. Then the height to the top of the ladder is (x+5).
Pythagoras theorem: In a right angle triangle,
[tex]Hypotenuse^2=Base^2+Perpendicular^2[/tex]
In the given situation, hypotenuse is the length of ladder, i.e., 9.85 m. The base is x m and the height is (x+5) m.
Using the Pythagoras theorem, we get
[tex](9.85)^2=x^2+(x+5)^2[/tex]
[tex]97.0225=x^2+x^2+10x+25[/tex]
[tex]0=2x^2+10x+25-97.0225[/tex]
[tex]0=2x^2+10x-72.0225[/tex]
Here, [tex]a=2, b=10,c=-72.0225[/tex]. Using the quadratic formula, we get
[tex]x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
[tex]x=\dfrac{-10\pm \sqrt{(10)^2-4(2)(-72.0225)}}{2(2)}[/tex]
[tex]x=\dfrac{-10\pm \sqrt{676.18}}{4}[/tex]
Approximating the value, we get
[tex]x=\dfrac{-10\pm 26}{4}[/tex]
[tex]x=\dfrac{-10+26}{4},\dfrac{-10-26}{4}[/tex]
[tex]x=\dfrac{16}{4},\dfrac{-36}{4}[/tex]
[tex]x=4,-9[/tex]
Distance cannot be negative so [tex]x\neq -9.[/tex]
Now we have [tex]x=4[/tex]
[tex]x+5=4+5[/tex]
[tex]x+5=9[/tex]
Therefore, the base is 4 m and the height is 9 m.
The base, height to the top of the ladder and height of the ladder when connected together we will get a triangle and then apply Pythagoras theorem we get base 4.0 m and height 9 m.
What is Pythagoras theorem?According to this theorem, the hypotenuse l, base b and opposite side a are connected by the equation written as follows:
hypotenuse² = base² + opposite side²
l² = a² + b².
Thus if we know either two sides or the triangle we can calculate the length of the unknown side of the triangle. It is given that the length of ladder is 9.85 m. It is placed against a wall and the base that is distance between foot and wall is 5 m less than the height to the top.
Assuming a triangle connecting these three points, the hypotenuse is the length of the ladder 9.85 m and let x be the base and opposite side that is the height to the top be x + 5. Now apply Pythagoras theorem.
9.85² = (x+5)² + x²
97.02 = 2 x² + 10x + 25
2 x² + 10x -72.02 = 0
Now solve for x using quadratic equation we get x = 4.00. The base of the triangle is 4 m and opposite side that is the height = x +5 = 4 +5 = 9m.
Therefore, base is 4 m and height to the top of the ladder is 9 m.
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Given the functions below, find f(x) - g(x) f(x) = 2x + 5 g(x) = x^2 - 3x + 1
Answers
Answer:
One of these
Step-by-step explanation:
The length of a rectangle is increasing at a rate of 7 cm/s and its width is increasing at a rate of 6 cm/s. When the length is 12 cm and the width is 8 cm, how fast is the area of the rectangle increasing
Answers
Answer:
Step-by-step explanation:
This is a super simple problem. I'm going to walk through it as I do when I teach this to my students for the first time.
We are given a rectangle. We are told to find how fast the area is changing under certain conditions. That tells us that the main equation for this problem is the area formula for a rectangle which is
[tex]A=lw[/tex]. If we are looking for the rate at which the rectangle's area is changing, that means that we need to find the derivative of the area implicitly. This derivative is found using the product rule because the length is being multiplied by the width:
[tex]\frac{dA}{dt}=l\frac{dw}{dt}+w\frac{dl}{dt}[/tex] . If our unknown is the rate at which the area is changing, [tex]\frac{dA}{dt}[/tex], that means that everything else has to have a value (because you can only have one unknown in an equation). Here's what we're told:
The length of the rectangle is increasing at a rate of 7 cm/s, so that satisfies our [tex]\frac{dl}{dt}[/tex];
the width is increasing at a rate of 6 cm/s, so that satisfies our [tex]\frac{dw}{dt}[/tex];
and all of this is going on when the length = 12 and the width = 8. It looks like everything will have a value except for our unknown. Filling in:
[tex]\frac{dA}{dt}=12(6)+8(7)[/tex] and
[tex]\frac{dA}{dt}=72+56[/tex] so
[tex]\frac{dA}{dt}=128\frac{cm^2}{s}[/tex]
Translate the following word phrase into an algebraic expression nine times the difference of five and y
Answers
nine times is 9* and the difference of 5 and y is 5-y
convert the following decimals to a simplified fraction, showing all wok
Answers
Answer:
[tex]\frac{4}{3}[/tex]
Step-by-step explanation:
Have a nice day
Answer:
first let y=1.33 (with a _ on top of the threes after the decimal) then let 100y=133.33( with a _on top of the threes after the decimal)then subtract eq(ii) -eq(I) which is left side 100y-y= 99yright side 133.33-1.33=132then 99y=132then y=132/99 hence converted to fractionComplete the square to solve the equation below.
Check all that apply.
x^2-10x-4=10
Answers
1. Move terms to the left side
2.Subtract the numbers
3.Use the quadratic formula
4.Simplify
5.Separate the equations
6.Solve
Rearrange and isolate the variable to find each solution.
Solution,
Solution
x=5±√39
Graph the function h(x) = -2x– 3.
Answers
Answer:
look below
Step-by-step explanation:
To graph the function h(x) = -2x - 3, we can plot points on a coordinate plane using the equation and then connect the points to form the graph.
To find the points, we can choose different values of x and substitute them into the equation to calculate the corresponding values of h(x). Let's select a few values for x:
When x = -2:
h(-2) = -2(-2) - 3 = 4 - 3 = 1
So we have the point (-2, 1).
When x = 0:
h(0) = -2(0) - 3 = 0 - 3 = -3
So we have the point (0, -3).
When x = 2:
h(2) = -2(2) - 3 = -4 - 3 = -7
So we have the point (2, -7).
Now, we can plot these points on a coordinate plane and connect them to form the graph of the function h(x) = -2x - 3.
The graph will show a straight line that passes through the points (-2, 1), (0, -3), and (2, -7). The line will have a negative slope of -2, meaning it slopes downward from left to right.
Here's a rough representation of the graph:
|
|
-7 | .
|
-3 |
| .
1 |
|____________________
-2 0 2
Please note that this graph is just an approximation, and for a more accurate graph, you may use graphing software or a graphing calculator.
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if D is the center of the circle below and AC measures 48, what is the mesure of ABC
Answers
Answer:
A. 24
Step-by-step explanation:
48/2=24. Hope this helps:)
what are the value of m and o in the diagram below?
Answers
m = [tex]\frac{\sqrt{3}}{2}[/tex]
theta = 60 degrees or pi/3
The best way to figure these sorts of questions out is memorizing the unit circle. There are many tricks that can help! For example, from (0,1) to the left and right, the x-values of the points go from sqrt(3) to sqrt(2) to 1.
Hope this helps!
Your help would be very much appreciated I will mark you brainliest as well! :D
Answers
4/3 pi r ^3
4/3 pi (3,375)
4,500pi = 14,137.17
A data set is summarized in the frequency table below. The data set contains a total of 50 data values. What is the missing frequency?
Value Frequency
1 5
2 6
3 5
4 6
5 □
6 5
7 8
8 4
9 4
10 3
Answers
Answer:
4
Step-by-step explanation:
Add up all the frequencies given
5+6+5+6+5+8+4+4+3 = 46
The total frequencies with the missing data value should add up to 50
50 = 46 + x
x = 50 - 46
x = 4
Answer:
4
Step-by-step explanation:
The nine given values add to 5+6+5+6+5+8+4+4+3=46, so the missing frequency is 50−46=4.
A manufacturer of golf equipment wishes to estimate the number of left-handed golfers. A previous study indicates that the proportion of left-handed golfers is 8%. How large a sample is needed in order to be 98% confident that the sample proportion will not differ from the true proportion by more than 2%?
Answers
Answer:
A sample of 997 is needed.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
The margin of error is of:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
A previous study indicates that the proportion of left-handed golfers is 8%.
This means that [tex]\pi = 0.08[/tex]
98% confidence level
So [tex]\alpha = 0.02[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.02}{2} = 0.99[/tex], so [tex]Z = 2.327[/tex].
How large a sample is needed in order to be 98% confident that the sample proportion will not differ from the true proportion by more than 2%?
This is n for which M = 0.02. So
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.02 = 2.327\sqrt{\frac{0.08*0.92}{n}}[/tex]
[tex]0.02\sqrt{n} = 2.327\sqrt{0.08*0.92}[/tex]
[tex]\sqrt{n} = \frac{2.327\sqrt{0.08*0.92}}{0.02}[/tex]
[tex](\sqrt{n})^2 = (\frac{2.327\sqrt{0.08*0.92}}{0.02})^2[/tex]
[tex]n = 996.3[/tex]
Rounding up:
A sample of 997 is needed.
For the parallelogram, if m∠2=4x+30 and m∠4=2x+70, find m∠3.
Answers
Hope that helped
20 points & Mark brainliest
Help me with steps
Answers
9414 1404 393
Answer:
A. 3.46
Step-by-step explanation:
The side ratios of a 30°-60°-90° triangle are 1 : √3 : 2. You are given the short side GF of this triangle, so its long side is GH = GF·3.
Then the area of ΔGFH is ...
A = 1/2(GF)(GH) = 1/2(4)(4√3) = 8√3 ≈ 13.86 . . . . square units
__
Segment GI divides the area of ΔGFH in half, so that ΔGFI is half the above area. Segments GF, FI, IH, GI are all congruent, so segment GJ divides isosceles triangle GFI in half. That is. ΔGJI is half the area of ΔGFI, so is 1/4 the area of GFH.
Area of ΔGJI = (8√3)/4 = 2√3 ≈ 3.46 . . . square units
PLZZZZ HELPPP!!!
What is the value of x?
12 units
15 units
20 units
24 units
Answers
Answer: I believe that the value of x is 15 units.
Solve for x.
A. 8
B. 4
C. 10
D. 7
Answers
Answer:
D. 7
Step-by-step explanation:
Apply the secant-scant product theorem. Thus, based on the theorem, we have the following equation:
6(4 + 6) = 5(x + 5)
6(10) = 5x + 25
60 = 5x + 25
Subtract 30 from each side
60 - 25 = 5x + 25 - 30
35 = 5x
Divide both sides by 5
35/5 = 5x/5
7 = x
x = 7
Given the similarity statement
AJKL ANOP, what's the
corresponding side of ON ?
Answers
Answer:
ON = KJ
Step-by-step explanation:
JKL = NOP
We know the angles match
<J = <N
<K = <O
< L = <P
And we know
JK = NO
KL = OP
JL = NP
We are looking for ON = KJ
9514 1404 393
Answer:
(d) KJ
Step-by-step explanation:
The segment of interest is named using the 2nd and 1st letters of the right side of the similarity statement.
The corresponding segment will be named using the 2nd and 1st letters of the left side of the similarity statement: KJ.
Select the correct answer from each drop-down menu?
Answers
9514 1404 393
Answer:
second3firstisStep-by-step explanation:
We observe that the second equation of System B has had the x-term eliminated. That can be accomplished by adding 3 times the first equation to the second.
"To get System B, the second equation in System A was replaced by the sum of that equation and 3 times the first equation. The solution is the same as the solution to System A."
The angles in a triangle represented by x, 3x, and 6x. What is the value of x?
A.20
B.30
C.18
D.36
Answers
Answer:
18
Step-by-step explanation:
The sum of the angles of a triangle is 180
x+3x+6x = 180
10x = 180
Divide by 10
10x/10 =180/10
x = 18
The soil samples for the next field indicate that fertilizer coverage needs to be
greater. To achieve this, you need to increase flow rate. How would you achieve
this?
A. Increase speed to approximately 7.1 mph so that you cover the field more
quickly
B. Increase the engine speed to approximately 2,000 rpm
C. Decrease speed to approximately 6.0 mph so that you cover the field more
slowly
D. Shift to second gear so that the engine speed slows
Answers
Answer:
A. Increase speed to approximately 7.1 mph so that you cover the field more.
Step-by-step explanation:
The soil samples for the next field require more fertilizer coverage therefore there is need for more field coverage by the equipment. The speed of the tractor will be increase to 7.1 mph so that greater area can be covered in lesser time.
Help me please
I’m in need of help
Answers
So the answer should be C
Wish u the best !!
What is the solution to 2x-8<12?
Answers
Answer:
X=10
Step-by-step explanation:
2x-,8<12
2x>12+ 8
2x>20
x>10
In 2013, selected automobiles had an average cost of $16,000. The average cost of those same automobiles is now $20,000. What was the rate of increase for these automobiles between the two time periods
Answers
Answer:
25%
Step-by-step explanation:
The average cost of the automobile in 2013 is $16,000
The present cost now is $20,000
Therefore the rate of increase between the two automobiles can be calculated as follows
= 20,000-16,000/16,000
= 4,000/16,000
= 0.25×100
= 25%
Hence the rate of increase is 25%
Triangle A”B”C is formed using the translation (x+1,y+1) and the dilation by a scale factor of 3 from the origin. Which equation explains the relationship of BC and B”C? PLEASE HELP
Answers
9514 1404 393
Answer:
(b) BC = B"C"/3
Step-by-step explanation:
Choices A, C, D are all different ways of expressing the same relationship, and they are all incorrect.
B"C" is segment BC after dilation by a factor of 3, so it is 3 times as long as BC. That is, BC is 1/3 the length of B"C", choice B.
help.........................................................
Answers
Answer:
C and D have the same slope of 1
If f(x) is an exponential function where f(-3.5) = 25 and
f(6)
= 33, then find the value of f (6.5), to the nearest hundredth.
Answers
Answer:
f(x)=27.63(1.03)^x
Step-by-step explanation:
[tex]\sqrt{x} 3500[/tex]
Answers
Step-by-step explanation:
Download gauthmath it will help
