Answer:
The nth term Tn = -8(-1/4)^(n-1) or Tn = 6(1/3)^(n-1) can be used to find all geometric sequencesStep-by-step explanation:
Let the first three terms be a/r, a, ar... where a is the first term and r is the common ratio of the geometric sequence.
If the sum of the first two term is 24, then a/r + a = 24...(1)
and the sum of the first three terms is 26.. then a/r+a+ar = 26...(2)
Substtituting equation 1 into 2 we have;
24+ar = 26
ar = 2
a = 2/r ...(3)
Substituting a = 2/r into equation 1 will give;
(2/r))/r+2/r = 24
2/r²+2/r = 24
(2+2r)/r² = 24
2+2r = 24r²
1+r = 12r²
12r²-r-1 = 0
12r²-4r+3r -1 = 0
4r(3r-1)+1(3r-1) = 0
(4r+1)(3r-1) = 0
r = -1/4 0r 1/3
Since a= 2/r then a = 2/(-1/4)or a = 2/(1/3)
a = -8 or 6
All the geometric sequence can be found by simply knowing the formula for heir nth term. nth term of a geometric sequence is expressed as
if r = -1/4 and a = -8
Tn = -8(-1/4)^(n-1)
if r = 1/3 and a = 6
Tn = 6(1/3)^(n-1)
The nth term of the sequence above can be used to find all the geometric sequence where n is the number of terms
What is the decay factor in y = 760(0.75)3?
Answer:
Decay factor is 0.75.
Step-by-step explanation:
The given function is
[tex]y=760(0.75)^3[/tex] ...(1)
The general form of exponential decay function is
[tex]y=a(1-r)^t[/tex] ...(2)
where, a is initial amount, t is the time period, r is decay rate and (1-r) is the decay factor.
On comparing (1) and (2), we get
[tex]a=760, t=3, (1-r)=0.75[/tex]
Therefore, the decay factor is 0.75.
Find the volume of prism
Pls!! Show how you got the volume
Answer:
The original or the Bigger prism's volume would be 15 x 6 x 10= 900 cubic centimetres given that the smaller prism has not been cut out.
the volume of the cut-out cube would be 6 x 4 x 6= 144 cubic centimetres
so the original volume of the prism is 900 - 144= 756 cubic centimetres
What is the slope?
Simplify your answer and write it as a proper fraction, improper fraction, or integ
Simplify the question in the picture
Answer:
B.3^9
Step-by-step explanation:
3^5•3^4=3^5+4=3^9
What is the radius of the garden?
Step-by-step explanation:
Area of circle= Πr²
Πr² = 132² m
r²=132²/Π m
=5546.23m
r =√5546.23
=74.473 m
Use the grouping method to factor the polynomial below x^3 -4x^2+3x-12
Answer:
x^2(x-4) + 3(x-4)
(x^2 + 3)(x-4)
Step-by-step explanation:
Please help me. I don't understand how to work it out.
[tex]answer \\ = 60 \: meters \\ please \: see \: the \: attached \: picture \: for \\ full \: solution \\ hope \: it \: helps[/tex]
Find the volume of a cone with a radius of 20cm and a height of 15cm.
Answer:6283.19 cm cubed, assuming pi is 3.14 or it's 2000 pi
Step-by-step explanation:
V=pi r squared times h over 3
Answer:
The answer is around 6283.19
Step-by-step explanation:
I know this because the formula of the cone is V=πr^2h/3 so substituded the known value to get this answer.
Pi equal 3.14
The table shows the amount of flour needed for six cookie recipes.
Recipe
Amount of Flour
(in cups)
Chocolate Chip Cookies
Sugar Cookies
2
Gingerbread Men
1.5
Peanut Butter Cookies
2.25
Oatmeal Cookies
2
Iced Pumpkin Cookies
23
21
What is the total amount of flour needed for all six cookie recipes?
Answer:
A. 15.5
Step-by-step explanation:
What epuation correctly shows how to determine the distance between points 9,-2 6,3
[tex]d = \sqrt{(x_2 - x_1)^2 + (y_2-y_1)^2}[/tex]
This is the distance formula. To find the distance, solve as shown:
[tex]d=\sqrt{(6-9)^{2}+(3-(-2))^{2} } \\d=\sqrt{(6-9)^{2}+(3+2)^{2} } \\d=\sqrt{(-3)^{2}+(5)^{2} } \\d=\sqrt{9 +25 } \\d=\sqrt{34 }[/tex]
PLZ PLZ PLZ PLZ HELP HELP HELP HELPFind the area of the shape.
Either enter an exact answer in terms of
π
πpi or use
3.14
3.143, point, 14 for
π
πpi and enter your answer as a decimal.
Answer:
3.14
Step-by-step explanation:
The formula for the area of a circle is [tex]\pi r^2[/tex], where r is the radius. In this circle, the area would therefore be [tex]3.14\cdot 2^2=12.56[/tex]. However, since this is only a quarter circle, you need to divide the area by 4, meaning that the area of this shape is 3.14 square units. Hope this helps!
Answer:
π
Step-by-step explanation:
calculate the the full circle: A = π*[tex]r^{2}[/tex] = π*[tex]2^{2}[/tex] = π*4 (the area of the full circle)
you've got 1/4 or the circle according to the picture, so divide the area of the full circle with 4:
(π*4)/4 = π
(4+7+5+5+2)+( 12 5/8+ 12 3/4+ 12 7/8+ 13+ 13 1/8)=???
please help asp I will give ya 30 points
Answer:
87.375
Step-by-step explanation:
Answer:
699/8 or 87.375
Step-by-step explanation:
Assuming 12 5/8+ 12 3/4+ 12 7/8+ 13+ 13 1/8 are mixed numbers.
In △XYZ, m∠X = 27° and m∠Y = 48°. Which gives the sides of the triangle in order from shortest to longest?
Answer:
z, y and x
Step-by-step explanation:
Now, to answer this question, what we must know is that the side facing the largest angle is the largest while the side facing the smallest is the smallest.
What i’m saying in essence is that the bigger the angle faced, the larger the side.
Now since we have 3 angles in a triangle that adds up to 180
we have 27 and 48 already, the third side would be 180-27-48 = 105
So which side faces which angle?
Let’s have a diagrammatic representation of the said triangle.
Check this in the attachment please
The longest side is thus z, followed by y and lastly x
The measure of the angle from shortest to longest will be ∠z, ∠y, and ∠x.
What is angle measurement?An angle measure is the measurement of the angle created by two rays or arms at a shared vertex in geometry. A protractor is used to measure angles in degrees (°).
Given data;
m∠X = 27°
m∠Y = 48°
The sum of the angle of the triangle is 180°
m∠X+m∠Y+m∠Z = 180°
27° +48° + m∠Z = 180°
m∠Z = 105°
The order of the angle measurement;
m∠Z > m∠Y > m∠X
Hence, the measure of the angle from shortest to longest will be ∠z, ∠y, and ∠x.
To learn more about the angle measurement, refer to the link;
https://brainly.com/question/14684647
#SPJ5
Using the order of operations, what is the last calculation that should be done to evaluate 4(8 − 6)52 − 6 ÷ (−3)?
4(8 − 6)52 − 6 ÷ (−3)
4(2)52 − 6 ÷ (−3)
4(2)(25) − 6 ÷ (−3)
200 − 6 ÷ (−3)
200 − (−2)
Answer & Step-by-step explanation:
4(8 - 6)52 - 6 ÷ (-3)
First, subtract 6 from 8
4(2)52 - 6 ÷ (-3)
4(2)(52) - 6 ÷ (-3)
Multiply 2 by 52
416 - 6 ÷ (-3)
Divide -6 by -3.
416 + 2
Add 2 to 416
418
So, your evaluated answer would be 418.
Answer:
its 200+2
So addition is the last calculation to be done.
Step-by-step explanation:
Two distinct number cubes are rolled together. Each number cube has sides numbered 1 through 6.
What is the probability that the outcome of the roll is an even sum or a sum that is a multiple of 3?
Enter your answer, in simplest fraction form, in the box.
Answer:
2/3
Step-by-step explanation:
If karri takes a 7 question true false test and guess on every question, what is the probability that she gets all 7 questions correct? Answer in decimal form to 4 decimal places.
part 2. Find the missing sides for each 30 60 90 triangles. Show work please.
5. tan(30) =4/g
g = 4/tan(30)
g = 4√3
sin(30) = 4/h
h = 4/sin(30)
h = 8
6.
tan(30) = 14/l
l = 14/tan(30)
l = 14√3
sin(30) = 14/m
m = 14/sin(30)
m = 28
7.
sin(30) = j/50
j = 50 x sin(30)
j = 25
cos(30) = k/50
k = 50 x cos(30)
k = 25√3
Which is the first step in simplifying the expression 2(x + 3) + 5?
Answer:
Step-by-step explanation:
Feel pleasure to help you.
Write each polynomial in standard form. What is the name of the polynomial based on its degree and number of terms?
a. 3 + 5x − 4x2
b. 8x + x + 5 + x3
Answer:
Step-by-step explanation:
(a) 3 + 5x − 4x^2 should be written as −4x2 + 5x + 3. This is a QUADRATIC function.
(b) 8x + x + 5 + x^3 should be re-written first as 9x + 5 + x^3 and then as
x^3 + 9x + 5. This is a CUBING function.
Find the distance between (-3, 3) and (-3, -3).
Answer:
6
Step-by-step explanation:
Since they have the same x - value, just find the distance between the y - values.
6
Examine the following gizmo problem and choose the best answer
Answer:
C. The answer is correct
Step-by-step Explanation:
One of the rules that applies when simplifying radical expressions, is that, only like radicals can be added together or subtracted from each other. In other words, the radicand, which is the number inside the "√" must be the same for two or more radicals to be added together or subtracted from each other.
In the expression given in the question, step 1 and step 2 are correct, as well as the final answer.
The final answer is correct because only like radicals can be added as 3√19 and 8√38 are unlike radicals. Their radicands, √19 and √38, are not the same, hence, the radicals do not need to be added.
The answer "3√19 + 8√38" is correct.
The number 72 lies between the perfect squares blank, and blank . So, the square root of 72 lies between the numbers blank, and blank , which means the square root of 72 is blank number.
Answer:
The perfect squares it lies between are 64 and 81
The answer is 6√2
And it lies between the numbers 8 and 9
Hope this helps.
Answer:
the real answer is 64 -75 8-9
72 is a rational number
Step-by-step explanation:
I need help with this question pls
Answer:
2^-2Step-by-step explanation:
2^(3-5)
=2^-2
Answer:
[tex] \frac{ {2}^{4 + 3} }{2^{5 + 4} } [/tex]
[tex] \frac{ {2}^{7} }{2^{9} } [/tex]
= 2^7-9
= 2^-2
C. 0.045
What is the length of line DE in the figure
bellow?
20cm
cm
13cm
D
21cm
9cm
racing car Covered
B. 16cm
D. 11cm
d:
Answer:
can you please give a correct question next time or please make the question clear for the answerer.
thank you
A painted water tower is shown. What percent of the surface area of the water tower (not including the surface underneath the tower) is green? Round your answer to the nearest tenth of a percent.
Answer:
43.6%
Step-by-step explanation:
curved surface area (green) is found by circumference multiply by height
[tex]\pi[/tex] x d x h = [tex]\pi[/tex] x (15 x 2) x 12 = 360[tex]\pi[/tex]
total surface area is
blue circle + total curved surface area (blue + green)
= [tex]\pi[/tex][tex]r^{2}[/tex] + 15(2)(8)[tex]\pi[/tex] + 360[tex]\pi[/tex]
= [tex]15^{2}[/tex][tex]\pi[/tex] + 240[tex]\pi[/tex] + 360[tex]\pi[/tex]
= 825[tex]\pi[/tex]
percentage = 360[tex]\pi[/tex]/825[tex]\pi[/tex] x 100%= 22/55 x 100% = 43.63
Given the statement:
Little sisters are annoying.
If you are a little sister, then you are annoying. This is the_
converse
original statement
contrapositive
inverse
Hypothesis
conclusion
Answer:
conclusion
Step-by-step explanation:
We are given a single statement:
"Little sisters are annoying."
A hypothesis regarding that statement is then proposed:
You are a little sister.
The only two possible interpretations from the information given are that you either are annoying or not. Since little sisters are annoying, if you are a little sister, the only possible logical conclusion is that you are annoying.
The answer is conclusion.
It would be conclusion
“Little sisters is annoying”
Helpppppp meeeee please URGENT
True or False
Answer:
false
Step-by-step explanation:
you cant have same size without congruent
Wright (3+4i)+(8+2i) as a complex number in standard form
Answer:
11 +6i
Step-by-step explanation:
(3+4i)+(8+2i)
Add the real portions
3+8 = 11
Add the imaginary portions
4i+2i = 6i
The complex number in a+bi form is
11 +6i
Answer:
[tex] = 11 + 6i[/tex]
Step-by-step explanation:
[tex](3 + 4i) + (8 + 2i) \\ 3 + 4i + 8 + 2i \\ = 11 + 6i[/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
The function in the table below shows the relationship between the total number of houses built in an area and the number of months that passed. A two column table with five rows. The first column, Months Passed, has the entries, 0, 3, 4, 8. The second column, Total Houses Built, has the entries 0, 33, 46, 108. Which best describes the data set? It is nonlinear because the “Total Houses Built” column does not increase at a constant additive rate. It is nonlinear because the “Months Passed” column does not increase at a constant additive rate. It is nonlinear because the increase in the “Total Houses Built” compared to the increase in the “Months Passed” does not show a constant rate of change. It is linear because the increase in the “Total Houses Built” compared to the increase in the “Months Passed” shows a constant rate of change.
Answer: C. I hope this helps ❤️.
Answer:
the correct answer is c
Step-by-step explanation:
A new lawn has a perimeter of 278 ft. and a width of 64 ft. A bag of grass seed will cover 384 ft 2of ground. How many bags of grass seed are needed to seed the new lawn? A. 4.34 B. 6 C. 10.25 D. 12.5
Answer:
12.5 bagsStep-by-step explanation:
This problem is on the mensuration of flat shapes
Given
perimeter of lawn = 278 ft
width of lawn = 64 ft
1. we need to solve for the length of the lawn
2. we also we need to solve for the area of the lawn
perimeter of lawn= 2(width) + 2(length)
substituting our data we have
let the length be x
[tex]= 278= 2(64) + 2(x)\\\=278= 128+2x\\\=278-128= 2x\\\=150=2x\\\\\x=\frac{150}{2} \\\x= 75ft[/tex]
the length is 75 ft
the area of the lawn is [tex]75*64= 4800ft^2[/tex]
if a bag will cover[tex]384ft^2[/tex]
to cover the lawn we will need
[tex]\frac{4800}{384} \\=12.5 bags[/tex]
