Answer:
Yes, if the first term of a geometric sequence is positive and r > 1, then the sequence increases
Step-by-step explanation:
* Lets talk about the geometric sequence
- There is a constant ratio between each two consecutive numbers
- Ex:
# 5 , 10 , 20 , 40 , 80 , ………………………. (×2)
# 5000 , 1000 , 200 , 40 , …………………………(÷5)
* General term (nth term) of a Geometric sequence:
# U1 = a , U2 = ar , U3 = ar2 , U4 = ar3 , U5 = ar4
# Un = ar^n-1, where a is the first term , r is the constant ratio
between each two consecutive terms, and n is the position of
the number in the sequence
- V.I.N: The position of the number means the place of the
number like first , second , third , .......... so n must be positive integer
* Lets talk about the ratio r
- If r greater than 1 and a is positive, the sequence increases lets
take some different examples to explain that
# If the first term is 2 and the ratio between the consecutive
terms is 3/2, then the first four terms in the sequence are
∵ a = 2
∵ r = 3/2 ⇒ greater than 1
∴ First = a = 2
∴ Second = ar = 2 × 3/2 = 3
∴ Third = ar² = 2 × (3/2)² = 2 × 9/4 = 9/2 4.5
∴ Fourth = ar³ = 2 × (3/2)³ = 2 × 27/8 = 27/4 = 6.75
- From the answers the sequence increases
# If the first term is 1/2 and the ratio between the consecutive
terms is 4/3, then the first four terms in the sequence are
∵ a = 1/2
∵ r = 4/3 ⇒ greater than 1
∴ First = a = 1/2
∴ Second = ar = 1/2 × 4/3 = 2/3 ⇒ 2nd > 1st
∴ Third = ar² = 1/2 × (4/3)² = 2 × 16/9 = 8/9 ⇒ 3rd > 2nd
∴ Fourth = ar³ = 1/2 × (4/3)³ = 2 × 64/27 = 32/27 ⇒ 4th > 3rd
- From the answers the sequence increases
* Now we are sure if the first term of a geometric sequence is
positive and r > 1, then the sequence increases
Answer:
The given statement is TRUE.
Step-by-step explanation:
We are given that if the first term of a geometric sequence is positive, and r>1, then the sequence increases which is true.
If the first term of any geometric sequence is positive and its common ratio ( r ) is greater than 1 then the sequence will always increase.
[tex] a _ n = a r ^ n - 1 [/tex]
Given the equation of a circle, determine the center and the radius.〖(x+5)〗2+〖(y-1)〗2=9.
The equation of a circle is (x-h)2 +(y-k)2 = r2
Answer:
The center is (-5,1)
and
the radius is 3
Step-by-step explanation:
The given equation of the circle is
[tex](x+5)^2+(y-1)^2=9[/tex]
We can rewrite this equation in the form;
[tex](x-h)^2+(y-1)^2=r^2[/tex]
This implies that;
[tex](x--5)^2+(y-1)^2=3^2[/tex]
When we compare, we get;
(h,k)=(-5,1) which is the center and r=3 the radius.
The answer is:
The center of the circle is located on the point (-5,1) and the radius is equal to 3 units.
Why?To determine the center and the radius of a circle from its equation, we need to look for "h" and "k", being "h" the x-coordinate of the center and "k" the y-coordinate the center, then, calculate the radius.
Since we are given the ordinary equation of the circle, we can find the radius and the center directly.
The ordinary equation is:
[tex](x-h)^{2} +(y-k)^{2} =r^{2}[/tex]
Where,
h is the x-coordinate of the center
y is the y-coordinate of the center
r is the radius.
So, we are given the circle:
[tex](x+5)^{2} +(y-1)^{2} =9[/tex]
Which is also equal to:
[tex](x-(-5))^{2} +(y-(1))^{2} =9[/tex]
Where,
[tex]h=-5\\k=1[/tex]
[tex]r^{2}=9\\\sqrt{r^{2}}=\sqrt{9} \\r=3units[/tex]
Hence, the center of the circle is located on the point (-5,1) and the radius is equal to 3 units.
Have a nice day!
Express 16=2x as a logarithmic equation
Convert the exponential equation to a logarithmic equation using the logarithm base
(
4
)
(
4
)
of the right side
(
16
)
(
16
)
equals the exponent
(
2
)
(
2
)
.
log
4
(
16
)
=
2
Anaba is stacking cereal boxes in a pyramid-shaped display. The bottom layer has 10 boxes. There are two fewer boxes in each layer than the layer below. How many boxes are in display.
Answer:
30 boxes
Step-by-step explanation:
~ You begin with the bottom row, which has 10 boxes.
~ You do 10 - 2 to get the number of boxes in the next layer, which is 8.
~ You then take 8 - 2, which is 6 for the next layer up.
~ Take 6 - 2, which is 4 for the next layer up.
~ Take away another two: 4 - 2 is 2.
~ When you take 2 away from 2, you get 0, so you have no more boxes.
~ Then, you add all the different amounts of boxes for each layer:
-> 10 + 8 + 6 + 4 + 2
-> Group smaller numbers together to get two bigger ones:
-> 18 + 12
= 30
The distance between points (3,7) and (x1,y1) is the square root of (x1 - 3)2 + (y1 - 7)2
True or False?
Answer : True
Explanation : It is according to distance formula.
The answer is True -Apex
mary has a total of 26 coins made up of quarters and nickles.the total value of mary's coins is $4.30 how many quarters does mary have
A.26 quarters
B.15 Quarters
C.11 Quarters
D.5 Quarters
help me out here asap
Answer:
d
Step-by-step explanation:
she has 16 quarters
1$=4 quarters
so 4$= 16 quarters
plus one more from the thirty cense
she could have 17 which is strange it’s not an option so go with B ig
How to do number 12
Answer:
To find the circumference of a circle you have to multiply Pi (3.14) with the diameter of the circle.
You need to find circumference of the circle first
help me pls asap i really need this
Answer:
26 degrees.
Step-by-step explanation:
180 - 154 = 26
Centennial park is evaluating
Answer:
270,000
Step-by-step explanation:
So, you have a number of people (15) that can stand comfortably within a certain area (5x8 ft = 40 sq feet). And you need to find out how many people can fit in the whole park area.
First step is to find out how big the park is, in square feet, so we can then evaluate the number of people that we can fit in.
You had the right number for calculating the area of the park:
A = 400 yards x 200 yards = 1,200 feet x 600 feet = 720,000 sq feet
Now, how many people can we fit in there? Let's use a simple cross-multiplication (x being the number of people fitting in the whole park, what we are looking for):
[tex]\frac{x}{720 000} = \frac{15}{40}[/tex]
By isolating x, we have x = (720,000 * 15) / 40 = 10,800,000 / 40 = 270,000
So, the park could accommodate 270,000 people.
That is of course if there are no trees, no benches, no kids playground or any other infrastructure in the park.
Which shows the correct substitution of the values a,b, and c from the equation 0=-3x^2-2x+6 into the quadratic formula ?
Answer:
a = -3
b = -2
c = 6
Step-by-step explanation:
The quadratic formula states that for an equation of the form:
[tex]ax^{2} + bx + c = 0[/tex]
The solution to that equation is:
[tex]\frac{-b±\sqrt{b^{2}-4ac}}{2a}[/tex]
In this case we have:
0=-3x^2-2x+6
Where:
a = -3
b = -2
c = 6
6 cm x 5cm x 4cm what is the volume of the prism in cubic centimeters
Answer:
120 [tex]cm^{3}[/tex]
Step-by-step explanation:
6 x 5 x 4 =120
Answer:
120 cm^3
Step-by-step explanation:
volume = length * width * height
volume = 6 cm * 5 cm * 4 cm
volume = 120 cm^3
4 times the sum of 1 plus a number equals 24. Find the number.
Answer:
the number is 5
Step-by-step explanation:
we can divide 24 by 4 in order to find the number
24/4 = 6
now we need to determine what number plus 1 equals 6 by subtracting 6 - 1
6 - 1 = 5
the answer is 5
we can check this by plugging 5 into the equation:
4(5+1) = 24
4(6) = 24
24 = 24
write the slope intercept equation. the graph of f passes through (-6,4) and is perpendicular to the line that has an x-intercept of 2 and a y intercept of -6
Answer:
y = [tex]-\frac{1}{3} x[/tex] + 2
Step-by-step explanation:
The slope of the line that has an x intercept of (2,0) and y-intercept of (0,-6) is:
Slope(s) = Change in y ÷ change in x
s = [tex]\frac{0 - -6}{2 - 0}[/tex] = 3
The slope of the perpendicular line to this line with slope of 3 has to have a slope of -1 ÷ 3 = [tex]-\frac{1}{3}[/tex]
Reason: The product of slopes of lines perpendicular to each other have to be -1
So the slope of the perpendicular line that passes through (-6,4) is [tex]-\frac{1}{3}[/tex]
As mentioned earlier, we derive a slope of a line by dividing the change in y by the change in x
Taking another point (x,y) on the line,
[tex]-\frac{1}{3}[/tex] = [tex]\frac{y - 4}{x - -6}[/tex]
[tex]-\frac{1}{3}[/tex] = [tex]\frac{y - 4}{x + 6}[/tex]
y - 4 = [tex]-\frac{1}{3}[/tex]x - 2
y = [tex]-\frac{1}{3}[/tex]x + 2
To find the slope-intercept equation of a line that passes through a given point and is perpendicular to another line, we can determine the slope of the given line and use it to find the equation.
To find the slope-intercept equation of a line, we need to know the slope and the y-intercept. Since the line that this problem is referring to is perpendicular to a line with an x-intercept of 2 and a y-intercept of -6, we can determine the slope of the line we are looking for by taking the negative reciprocal of the slope of the given line.
The slope of the given line is found using the formula: slope = (y2 - y1) / (x2 - x1)
Once we have the slope, we can use the point-slope form of a linear equation to find the equation of the line that passes through (-6,4) and has the determined slope. Finally, we can rearrange the equation to obtain the slope-intercept form, which is y = mx + b, where m represents the slope and b represents the y-intercept.
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simplify the following:a)12:18:36. b)320:480. c)16mm:480
Step-by-step explanation:
[tex]a)\ 12:18:36=\dfrac{12}{6}:\dfrac{18}{6}:\dfrac{36}{6}=2:3:6\\\\b)\ 320:480=32:48=\dfrac{32}{16}:\dfrac{48}{16}=2:3\\\\c)\ 16mm:480=\dfrac{16mm}{16}:\dfrac{480}{16}=1mm:30[/tex]
To simplify the given ratios, find the greatest common divisor (GCD) and divide all terms by the GCD. The simplified ratios are 2:3:6, 2:3, and 1:30. Refer to the solution for more details.
To simplify ratios, we divide both sides by their greatest common divisor (GCD).
a) 12:18:36
Find the GCD of 12, 18, and 36. It is 6.
Divide each number by 6:
12 ÷ 6 = 218 ÷ 6 = 336 ÷ 6 = 6The simplified ratio is 2:3:6.
b) 320:480
Find the GCD of 320 and 480. It is 160.
Divide both numbers by 160:
320 ÷ 160 = 2480 ÷ 160 = 3The simplified ratio is 2:3.
c) 16mm:480
Find the GCD of 16 and 480. It is 16.
Divide both numbers by 16:
16 ÷ 16 = 1480 ÷ 16 = 30The simplified ratio is 1mm:30. However, if there is no importance to specify units, simply 1:30 would be enough.
The RANGE of the function shown is
A) [4, 1]
B) [4, ∞)
C) [1, ∞)
D) [0, ∞)
Check the picture below.
recall that range is the interval over the y-axis for the graph of the function.
The range of the function shown is [4, ∝]
What is the range of the function?The collection of all a function's outputs constitutes its range. Example: Let's have a look at the function f: AB, where f(x) = 2x and A and B each represent a "collection of natural numbers." The domain in this instance is A, and the co-domain is B. The range then appears as the function's output. Set of even natural numbers is the range. The elements of the co-domain that are mapped are known as the pictures, while the elements of the domain are known as pre-images. The set of all images of the domain's elements in this case serves as the function's range, as does the set of all of its outputs.Here are the general formulas for calculating the range of various function types. The set of all real numbers is R in this instance.R is the range of a linear function.A quadratic function's range has the following values: y ≥ k if a > 0 and y ≤ k if a0A square root function's domain is y0.An exponential function has a range of y>0.R is the range of the logarithmic function.Solve the rational function y = f(x) for x and set the denominator to 0 to determine its range.To learn more about range of the function, refer to
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Which expression best represents the area of the rectangle?
Answer:
length×width
Step-by-step explanation:
Multiplying the length of a rectangle by the width will always give you the area. If one value is missing replace it with x.
Length x width should give you the answer your needing
Which list shows all the factors of 36? 1, 2, 3, 4, 6, 9, 12, 18, 36 1, 2, 3, 4, 8 , 9, 12, 18, 36 2, 3, 4, 6, 9, 12, 18 2, 4, 6, 8, 9, 12, 18 help fast
These are the factors of 36:
1, 2, 3, 4, 6, 9, 12, 18, 36
1, 2, 3, 4, 6, 9, 12, 18, 36
1 x 36 = 36
1, 2, 3, 4, 6, 9, 12, 18, 36
2 x 18 = 36
1, 2, 3, 4, 6, 9, 12, 18, 36
3 x 12 = 36
1, 2, 3, 4, 6, 9, 12, 18, 36
4 x 9 = 36
1, 2, 3, 4, 6, 9, 12, 18, 36
6 x 6 = 36
Hope this helped!
Answer:
1, 2, 3, 4, 6, 9, 12, 18, 36
Step-by-step explanation:
I took test on edge 2021
I’m hella confused on all this. What’s EF
rationalized form means that the number shoudnlt be a decimal that has never ending digits.
hope this answer to your question :)
Consider the equation y = -2x + 5. Create a table of five ordered pairs that satisfy the equation. What is the y-intercept of the equation? What is the x-intercept of the equation?
a.
y-intercept (5, 0); x-intercept (-5/2,0)
b.
y-intercept (0, 5); x-intercept (0,5/2)
c.
y-intercept (5, 0); x-intercept (5/2,0)
d.
y-intercept (0, 5); x-intercept (5/2,0)
Answer with step-by-step explanation:
Ordered pairs that satisfy the given equation:
x 0 1 2 3 4
y 5 3 1 -1 -3
To find the x-intercept, we will substitute y = 0 and solve for x to get:
[tex]0 = -2x + 5[/tex]
[tex] -2x = -5[/tex]
[tex]x = 5/2[/tex]
x-intercept = (5/2, 0)
To find the y-intercept, we will substitute x = 0 and solve for x to get:
[tex]y = -2(0) + 5[/tex]
[tex]y = 5[/tex]
y-intercept = (0, 5)
Answer: option d.
Step-by-step explanation:
To create a table of five ordered pairs that satisfy the equation, you need to give values to the variable "x" and substitute these into the function to find the corresponding value of "y":
For [tex]x=-2[/tex]
[tex]y = -2(-2) + 5=9[/tex]
For [tex]x=-1[/tex]
[tex]y = -2(-1) + 5=7[/tex]
For [tex]x=0[/tex]
[tex]y = -2(0) + 5=5[/tex]
For [tex]x=1[/tex]
[tex]y = -2(1) + 5=3[/tex]
For [tex]x=2[/tex]
[tex]y = -2(2) + 5=1[/tex]
Then, you can make the table:
x -2 -1 0 1 2
y 9 7 5 3 1
To find the x-intercept, substitute [tex]y=0[/tex] into the function and solve for "x". Then:
[tex]0 = -2x + 5\\\\x=\frac{-5}{-2}\\\\x=\frac{5}2}[/tex]
This is: ([tex]\frac{5}{2}[/tex], 0)
To find the y-intercept, substitute [tex]x=0[/tex] into the function and solve for "y". Then:
[tex]y= -2(0) + 5\\\\y=5[/tex]
This is: (0,5)
which of the following could be the graph of the line y=3x-2
Answer:
The graph in the attached figure
Step-by-step explanation:
we have
[tex]y=3x-2[/tex]
Plot the line
To plot the line find the intercepts
The y-intercept is the value of y when the value of x is equal to zero
so
For x=0
[tex]y=3(0)-2=-2[/tex]
The y-intercept is the point (0,-2)
The x-intercept is the value of x when the value of y is equal to zero
so
For y=0
[tex]0=3x-2[/tex]
[tex]x=2/3=0.667[/tex]
The x-intercept is the point (0.667,0)
Plot the intercepts and then draw the line
4 The pet store has 6 fish tanks.
Each tank has 7 goldfish and 5
Tetras. What is the total
number of fish (f) in the tanks?
x
= f
_= f
f
72 fish total. 12 fish in each tank.
_________________________
(g+t)n=f
g=Goldfish
t=Tetras
n=Number of fish tanks
*If I got it wrong, let me know*
Final answer:
The total number of fish in the tanks is 72.
Explanation:
To find the total number of fish in the tanks, we need to multiply the number of tanks by the sum of the goldfish and Tetras in each tank. Based on the information given, there are 6 tanks, and each tank has 7 goldfish and 5 Tetras.
So, the total number of fish (f) in the tanks can be calculated as:
f = (7 goldfish + 5 Tetras) * 6 tanks
f = (7 + 5) * 6
f = 12 * 6
f = 72
Therefore, the total number of fish in the tanks is 72.
Help me guys ....
1.What is the probability that a passenger is traveling for business ?
2.Given a passenger did not check their bag,what is the probability that the passenger is traveling for business ?
Answer:
1. .21
2. .79
Step-by-step explanation:
1. 103/490
2. 387/490
What is the volume of the cone pictured? (Use 3.14 for π.)
785 ft 3
104.67 ft 3
261.67 ft 3
314 ft 3
Answer:
261.67 [tex]ft^{3}[/tex]
Step-by-step explanation:
The formula is 1/3 [tex]\pi r^{2}h[/tex]
Answer:
261.67 ft^3
Step-by-step explanation:
mark me brainy plz!
Tina sells lampshades for $7 each and paper lanterns for $4 each at a one-day craft fair. She sells k lampshades and (k + 4) paper lanterns. The expression 7k + 4(k + 4) represents Tina’s total sales.
Select all the equivalent expressions for Tina’s total sales at the fair.
A 8k+16 B 11k+4
» 11k+16 D 7k+4k+4
» 7k+4k+16. How is it equivalent?
4xk = 4K 4x4= 16 +4K + 7k = 16+ 11k ( I would double check me
what is the relationship between the graphs of y=2^x and y=2^-x
One is rational and one is exponential.
Answer:
Step-by-step explanation:
the relationship between the graphs of y=2^x and y=2^-x is : symmetry by y-axis
Find the perimeter of a square that is 3 3/4 inches on a side. 7 inches 15 inches 12 inches 30 inches
Answer:
15 inches
Step-by-step explanation:
The perimeter of a polygon is the sum of the lengths of its sides. A square has 4 sides, all the same length. We can either add up the side lengths, or we can recognize that multiplication of one side's length by 4 is a useful alternative.
perimeter = 4 × (3 3/4 in)
= (4×3 +4×3/4) in
= 12 in + 3 in = 15 in
A die is tossed. Find p(less than 5/even)
Answer:6/36
Step-by-step explanation:
The probability of rolling a number less than 5 and even on a die is 1/2.
Explanation:To find the probability of rolling a number less than 5 and even, we need to determine the number of outcomes that satisfy both conditions and divide it by the total number of possible outcomes.
There are three outcomes that satisfy both conditions: {2, 4, 6}. The total number of possible outcomes is six since a die has six sides.
Therefore, the probability of rolling a number less than 5 and even is 3/6, which simplifies to 1/2.
Surface area
Math
Help
The answer for your question is d
Answer:
D)15+15+10+10+6+6
Step-by-step explanation:
the formula to find the SA of a rectangular prism is:
2(lw)+2(lh)+2(hw)
where
l=length
w=width
and
h=height
let's substitute the values,3,2,and 5 into the equation
2(5*3)+2(5*2)+2(3*2)=62
62 is the SA
from the options:
10+6=16
10+10+6+6=32
15+15+10+10+6=56
and
15+15+10+10+6+6=62
so option D is correct
George took a test with a certain number of questions. Each question had the same value. He answered 10 questions incorrectly, which resulted in an accuracy score of 60%. How many questions were on the test
10 questions = 40%
X question = 100%
40x = 1000
X = 25 questions
25 questions were on the test.
What is accuracy?There are two ways to assess observational error: accuracy and precision. Precision measures how closely spaced or widely separated a set of measurements are from one another, whereas accuracy measures how near or far off a given set of measurements are from their true value.
Given
60% accurate means 40% inaccurate.
10 inaccurate answers means 40% inaccurate
10/40 x 100 = 25
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Find the range of the data set represented by this box plot.
40
80
76
56
Answer:
56
Step-by-step explanation:
through estimation, you can see that the lowest value is 84 and the highest value is 140. in order to calculate the range, subtract the highest value from the lowest value. 140-84=56. The range is 56.
Answer:
56
Step-by-step explanation:
is -77 a rational or irrational number?
It’s a rational number.
Hope this helps!
Answer:
Rational
Step-by-step explanation:
Irrational numbers are numbers that are infinite and non- repeating numbers
irrational- pi, square root of 2, etc
rational- anything else.
rational- .333333..., 1/3, 2, 1, -5, .111..., .7171..., etc.