Answer:
The 10th term will be:
[tex]a_{10}=\frac{1}{512}[/tex]
Step-by-step explanation:
Considering the sequence
[tex]1,\:\frac{1}{2},\:\frac{1}{4}...[/tex]
A geometric sequence has a constant ratio r and is defined by
[tex]a_n=a_0\cdot r^{n-1}[/tex]
[tex]\mathrm{Compute\:the\:ratios\:of\:all\:the\:adjacent\:terms}:\quad \:r=\frac{a_{n+1}}{a_n}[/tex]
[tex]\frac{\frac{1}{2}}{1}=\frac{1}{2},\:\quad \frac{\frac{1}{4}}{\frac{1}{2}}=\frac{1}{2}[/tex]
[tex]\mathrm{The\:ratio\:of\:all\:the\:adjacent\:terms\:is\:the\:same\:and\:equal\:to}[/tex]
[tex]r=\frac{1}{2}[/tex]
[tex]\mathrm{The\:first\:element\:of\:the\:sequence\:is}[/tex]
[tex]a_1=1[/tex]
[tex]\mathrm{Therefore,\:the\:}n\mathrm{th\:term\:is\:computed\:by}\:[/tex]
[tex]a_n=\left(\frac{1}{2}\right)^{n-1}[/tex]
Putting n = 10 to determine in the nth term to determine the 10th term
[tex]a_{10}=\left(\frac{1}{2}\right)^{10-1}[/tex]
[tex]a_{10}=\left(\frac{1}{2}\right)^9[/tex]
[tex]\mathrm{Apply\:exponent\:rule}:\quad \left(\frac{a}{b}\right)^c=\frac{a^c}{b^c}[/tex]
[tex]a_{10}=\frac{1^9}{2^9}[/tex]
[tex]a_{10}=\frac{1}{2^9}[/tex] ∵ [tex]1^9=1[/tex]
[tex]a_{10}=\frac{1}{512}[/tex] ∵ [tex]2^9=512[/tex]
Therefore, the 10th term will be:
[tex]a_{10}=\frac{1}{512}[/tex]
2. need answer soon :) will give brainlyest
What number solves the equation 1/8 (x + 9) = 5?
Answer:
31
Step-by-step explanation:
Answer:
The number is 31
Step-by-step explanation:
Step 1: Distribute
1/8 (x + 9) = 5
1/8x + 9/8 = 5
Step 2: Subtract 9/8 from both sides
1/8x + 9/8 - 9/8 = 5 - 9/8
1/8x = 31/8
Step 3: Multiply both sides by 8
1/8x * 8 = 31/8 * 8
x = 31
Answer: The number is 31
Write the quadratic equation whose roots are −2 and 4, and whose leading coefficient is 5.
Answer:
10x2 + 30x - 40
Step-by-step explanation:
If the two roots are -2 and 4 then the factors shall be;
5(x+2)(x-4)
5 is the leading coefficient.
FOIL:
f(x) = 5(x2+4x+2x-8) =
f(x) = 5(x2+6x-8) =
f(x) = 10x2 + 30x - 40
Answer:5x^2-10x-40=0
Step-by-step explanation:
x=-2 or x=4
x+2=0 or x-4=0
(x+2)(x-4)=0
x^2-4x+2x-8=0
x^2-2x-8=0
Multiply the equation by 5
5x^2-10x-40=0
Find the lateral area for the pyramid with the equilateral base
A: 144 sq. units
B: 180 sq. units
C: 288 sq. units
Solution:
The given pyramid has 3 lateral triangular side
The figure is attached below
Base of triangle = 12 unit
Find the perpendicular
By Pythagoras theorem
[tex]hypotenuse^2 = opposite^2 + adjacent^2[/tex]
Therefore,
[tex]opposite^2 = 10^2 - 6^2\\\\opposite^2 = 100 - 36\\\\opposite^2 = 64\\\\opposite = 8[/tex]
Find the lateral surface area of 1 triangle
[tex]\text{ Area of 1 lateral triangle } = \frac{1}{2} \times opposite \times base[/tex]
[tex]\text{ Area of 1 lateral triangle } = \frac{1}{2} \times 8 \times 12\\\\\text{ Area of 1 lateral triangle } = 48[/tex]
Thus, lateral surface area of 3 triangle is:
3 x 48 = 144
Thus lateral area for the pyramid with the equilateral base is 144 square units
Find the slope of the line that passes through (9,3) and (6,3)
Answer:
0
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(3-3)/(6-9)
m=0/-3
m=0
what is 0.1 X 9670 equal to?
Answer:
967
Step-by-step explanation:
0.1 x 9670 = 967
Evaluate the expression. 33 + 6( 2 + 36 )
Answer: 261
Step-by-step explanation:
You use PEMDAS to solve this problem
you first do the Parenthesis (p)
33+6(2+36)
33+6 (38)
We then multiply first (M)
33 + 6(38) - we know that 8 times 6 is 48 ; 6 times 3 is 18 +4 because we brought down the 4 from 48 to 3. which will be equal to 228
33 + 228
261
1 point
9. The costs for going to a dog beach are $7 for 1 dog, and $2 for each
additional dog. Which equation shows this situation, where x is greater
than or equal 1? *
Solution:
Given that,
The costs for going to a dog beach are $7 for 1 dog, and $2 for each additional dog
Let "x" be the number of dogs
where x is greater than or equal 1
Cost y is $7 for the first dog and $2 for each of the other dogs
Therefore,
y = 7 + 2(x - 1)
x - 1 means the additional dogs
Therefore,
y = 7 + 2x - 2
y = 2x + 5
Thus the equation is found
A rectangular prism has a base that is 6 meters by 3.5 meters, and the prism is 9 meters high. What is the surface area of the prism?
Answer:
213 m^2
Step-by-step explanation:
The surface area for a rectangle prism is given by
A=2(wl+hl+hw)
We know the base is 6 meters by 3.5 m so l = 6 and width =3.5
The heigth is 9 m
A = 2 ( 6*3.5 + 9* 6 + 9* 3.5)
= 2 * (21 +54 +31.5)
= 2*(106.5)
=213 m^2
Answer:
213 square meters
Step-by-step explanation:
The surface area for a rectangle prism is given by
A=2(wl+hl+hw)
We know the base is 6 meters by 3.5 m so 6 * 3.5
The height is 9 m
A = 2 ( 6*3.5 + 9* 6 + 9* 3.5)
= 2 * (21 +54 +31.5)
= 2*(106.5)
=213 m^2
סוווטקיס
Find the length of the segment with endpoints (-9, -9) and (-4,3)
what’s the answer
Using distance formula we find that length is 13.
Hope this helps.
A movie theater charges $9.50 per movie ticket. If there is an average of 79
moviegoers a day, about how much money does the theater make in a week?
O A. $6000
O B. $3000
O C. $600
O D. -$600
Answer:
around $6000 the real answer is $5253.5
Step-by-step explanation:
.find the distance between the points (4, 3) and (0, 3).
a) 2
b) 4
c) 10
d) 12
Answer:The answer is 4
Step-by-step explanation:
12-4x-x=2 what is the Answers to this
Answer:
x = 2
Step-by-step explanation:
Answer:
x=2
Step-by-step explanation:
12-4x-x=2
Combine like terms
12 -5x =2
Subtract 12 from each side
12-5x-12 =2-12
-5x = -10
Divide each side by -5
-5x/-5 = -10/-5
x =2
Use the dot plot to answer questions.
Deanna's mean score is approximately
90
90.93
92
92.4
Amy's mean score is approximately
88.5
90
90.27
92.4
Answer:
90.93 and 90.27
Step-by-step explanation:
She took $20 with her to the movies. When she come back with $6. How much money did she spend
Answer:
$14
Step-by-step explanation:
$20 minus the $6 she came back with equals $14, which is what she spent.
(20-6=14)
Answer:
$14
Step-by-step explanation:
Take 6 away from 20
-5√112 radical expression
Answer:−
-20 √ 7
Step-by-step explanation:
steve deposits $1250 in an account paying 3.4% annual interest compounded continously. how long will it take for the account balance to reach $3150.50
Answer:
It will take 27.19 years
Step-by-step explanation:
Compound continuous interest can be calculated using the formula:
[tex]A=Pe^{rt}[/tex] , where
A = the future value of the investment, including interest P = the principal investment amount (the initial amount) r = the interest rate of interest in decimalt = the time the money is invested for∵ Steve deposits $1250 in an account
∴ P = 1250
∵ The account paying 3.4% annual interest compounded continuously
∴ r = 3.4%
- Change it to decimal by dividing it by 100
∴ r = 3.4 ÷ 100 = 0.034
∵ The account balance will reach to $3150.5
∴ A = 3150.5
- Substitute The values of A, P and r in the formula above to find t
∵ [tex]3150.5=1250e^{0.034t}[/tex]
- Divide both sides by 1250
∴ [tex]2.5204=e^{0.034t}[/tex]
- Insert ㏑ to both sides
∴ [tex]ln(2.5204)=ln[e^{0.034t}][/tex]
- Remember that [tex]ln(e^{n})=n[/tex]
∵ [tex]ln(e^{0.034t})=0.034t[/tex]
∴ ln(2.5204) = 0.034t
- Divide both sides by 0.034
∴ 27.18875 = t
∴ t ≅ 27.19
It will take 27.19 years
The formula f(x + 1) = Two-thirds(f(x)) defines a geometric sequence where f(1) = 18. Which explicit formula can be used to model the same sequence?
C. f (x) = 18 (2/3)x-1
Step-by-step explanation:
I got it right on edge. please mark brainliest!!
78 is the geometric mean of 30 and what number
Answer:
202.8
Step-by-step explanation:
The geometric mean of 2 numbers a and b is
[tex]\sqrt{ab}[/tex]
Here a = 30 and mean = 78, thus
[tex]\sqrt{30b}[/tex] = 78
To clear the radical square both sides
([tex]\sqrt{30b}[/tex] )² = 78², that is
30b = 6084 ( divide both sides by 30 )
b = [tex]\frac{6084}{30}[/tex] = 202.8
A wagon is on sale for 20% off. The sale price of the wagon is $114. What was the original price of the wagon assuming no sales tax is paid on the item? Report your answer to two decimal places. Do not include the dollar sign, $, in the answer box below.
To calculate the original price of a wagon on sale at 20% off, divide the sale price of $114 by 0.80, resulting in the original price of $142.50.
To find the original price of the wagon before the 20% sale, we have to determine what $114 represents after the discount has been applied. If $114 is 80% of the original price (100% - 20% = 80%), we need to find 100% by dividing $114 by 0.80:
Original Price = Sale Price / (1 - Discount Percentage)
Original Price = $114 / 0.80
Original Price = $142.50
So, the original price of the wagon before the sale was $142.50.
e:-6=3:9 what is the blank
Answer:
e=-2
Step-by-step explanation:
3*x=9
3*3=9
x=3
e*x=-6
e*3=-6
e=-6/3
e=-2
6/8=y/16 how do you find the proportion of value y
Katrine drinks 0.5 gallons of water per day. Which expression shows how to find the number of cups of water she drinks in a
There are 15 cups na gallion
Submit
Question:
Katrina drinks 0.5 gallons of water per day. Which expression shows how to find the number of cups of water she drinks in a week?
There are 15 cups in a gallon
Answer:
The expression to find the number of cups of water she drinks in a week is:
[tex]\frac{15\ cups}{1\ gallon} \times \frac{0.5\ gallons}{1\ day} \times \frac{7\ days}{1\ week}[/tex]
Solution:
Given that,
1 gallon = 15 cups
[tex]\frac{15\ cups}{1\ gallon}[/tex]
Katrina drinks 0.5 gallons of water per day
1 day = 0.5 gallons
[tex]\frac{0.5\ gallons}{1\ day}[/tex]
Find the number of cups of water she drinks in a week
1 week = 7 days
[tex]\frac{7\ days}{1\ week}[/tex]
Thus the expression to find the number of cups of water she drinks in a week is:
[tex]\frac{15\ cups}{1\ gallon} \times \frac{0.5\ gallons}{1\ day} \times \frac{7\ days}{1\ week}[/tex]
Graph a line that contains the point (-5,6) and has a slope of 2/3
Answer:
y= 2/3x + 28/3
Step-by-step explanation:
First, write your equation as y=2/3x+b. Plug in your coordinate into the equation, it should look like this: 6=2/3(-5)+b. Multiply 2/3 by -5 to get -10/3. It should look like this: 6= -10/3+b. Add 10/3 to both sides to get your y-intercept of 28/3. Go back to your original equation and plug 28/3 into b. This is your final equation: y= 2/3x + 28/3. Hope this helped!
A rectangle has a length of 7 units and a width of 4 units. One vertex of the rectangle is (0,0).
Use the segment tool to create a rectangle matching its description
The rectangle with a length of 7 units and a width of 4 units, and with one vertex at the origin (0,0), has been successfully created using the segment tool.
Open the drawing tool or any software that allows you to draw shapes and use the segment tool to begin the construction.
First, mark the origin (0,0) on the canvas as one of the vertices of the rectangle.
Now, move the cursor 7 units to the right from the origin along the x-axis and place a point. This point represents the opposite vertex of the rectangle on the right side.
Next, move the cursor 4 units up from the origin along the y-axis and place another point. This point represents the opposite vertex of the rectangle on the top side.
To complete the rectangle, draw straight lines connecting the following points: (0,0) with (7,0), (7,0) with (7,4), (7,4) with (0,4), and finally, (0,4) back to (0,0).
To know more about rectangle here
https://brainly.com/question/8663941
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Could a right triangle ever be an equilateral triangle?
Answer: An equilateral triangle can NOT be a right triangle.
Step-by-step explanation:
In a right triangle, however, the 3 angles can NOT be congruent. This is because in a right triangle, one angle equals 90 degrees. Therefore, you can't have 3 angles equal 90 degrees.
Answer:
n equilateral triangle can not be a right triangle. ... In a right triangle, however, the 3 angles can NOT be congruent. This is because in a right triangle, one angle equals 90 degrees. Therefore, you can't have 3 angles equal 90 degrees.
Step-by-step explanation:
Please mark me as brainliest... I really would appreciate that
what is the volume of a cube with sides 8.1
Answer:
531.441
Step-by-step explanation:
8.1*8.1*8.1 = Volume of a cube
jeds market has a total of 26 employees. Each full time employee makes $275/ week, and each part-time employee makes $140/ week. Jed pays a total of $5935 in wages each How many full-time and part-time employees does he have? Let f= number of fulltime employees, and p= number of part-time employees.
The number of full time employees is 17 and the number of part time employee is 9
Step-by-step explanation:
Step 1 :
Let f represent the number of full time employee and p represent the number of part time employee
Total number of employees = 26
Hence we have f + p = 26
Step 2 :
Wages of full time employee = $275
Wages of part time employee = $140
Total wages paid by Jeds = $ 5935
Hence we have 275 f + 140 p = 5935
Step 3:
Solving the equations obtained in step 1 and step 2 we have
f + p = 26, Multiplying by 275 = > 275 f + 275 p = 7150
275 f + 140 p = 5935
Subtracting equation 2 from 1 we have
135 p = 1215 => p = 9
Substituting this in f + p = 26 gives, f + 9 = 26
So f = 17
Step 4 :
Answer :
The number of full time employees is 17 and the number of part time employee is 9
Edmond is on the third day of his hike up Glacier Peak. The graph below shows his hiking time and altitude for the third day only.
What was his altitude at the beginning of the third day?
A. 5,000 feet
B.
3,500 feet
C. 3,000 feet
D 4,000 feet
Answer: 3,500 feet
Step-by-step explanation:
To determine the original altitude for the third day, identify the y-intercept of the graph.
Therefore, the original altitude was 3,500 feet.
Answer: my question was a little different but i posted an image of the correct answer.
Step-by-step explanation:
To determine the original altitude for the third day, identify the y-intercept of the graph.
Therefore, the original altitude was 4,000 feet.
In a survey of 300 house wires. It was discovered
that 150 had read magazine A, 200 had
read Magazine B and 156 had read
magazine C It was further discovered
that 48 had read A and B 60 had
read B and a while 52 hand read
A and a . Find
The number of housewives that had read.
all three magazine
Answer:
46 housewives read all three magazines.
Step-by-step explanation:
Given:
n(A) = 150
n(B) = 200
n(C) = 156
n(A∩B) = 48
n(B∩C) = 60
n(A∩C) = 52
n(A∪B∪C) = 300
so we know the relation as:
n(A∪B∪C) = n(A) + n(B) + n(C) - n(A∩B) - n(B∩C) - n(A∩C) + n(A∩B∩C)
∴ n(A∩B∩C) = n(A) + n(B) + n(C) - n(A∩B) - n(B∩C) - n(A∩C) - n(A∪B∪C)
= 150 + 200+ 156 - 48 - 60 - 52 - 300
= 46
Hence the number of housewives that had read all three magazine is 46.
Answer:
46 housewives read all three magazines.
Step-by-step explanation:
3. Triangle ABC has angle measures as shown.