Answer:
The explicit formula is [tex]a_n=15(\frac{4}{5})^{n-1}[/tex].
Step-by-step explanation:
First, we need to find the common ratio. We know this is a geometric sequence because the decrease from one term to the next is not a constant number.
To find the constant ratio, we can take the [tex]2^{nd}[/tex] term and divide by the [tex]1^{st}[/tex] term:
[tex]\frac{2nd}{1st}=\frac{12}{15}=\frac{4}{5}[/tex]
So, our common ratio is [tex]r=\frac{4}{5}[/tex].
We already know our initial term, [tex]a_0[/tex] is 15, so we get:
[tex]a_n=a_0(r)^{n-1}\\a_n=15(\frac{4}{5})^{n-1}[/tex]
on comparing the ratios a1/a2 b1/b2 and c1/c2 find out whether the pair of linear equations 2x -3y=8 and 4x-6y =9 are consistent or inconsistent
Answer:
The given linear equation are
⇒9x+3y+12=0....eq1
⇒a1 =9,b1 =3,c1 =12
⇒18x+6y+24...eq2
⇒a2 =18,b2 =6,c2 =24
⇒a1/a2 =9/18 =1/2
⇒ b1/b2= 3/6 = 1/2
⇒ c1/c2= 12/24= 1/2
comparing
⇒ a1/a2,b1/b2,c1/c2
⇒ a1/a2=b1/b2=c1/c2
Hence, the line represented by eq1 and eq2 are coincidents
Step-by-step explanation:
You are building a cube shaped box for your turtle to live in. You want to build your box with side lengths of 24 inches. However, when you finish the box, you find out that it has a volume of 27,000 cubic inches. How many more cubic inches is your box than you had planned? How much bigger are your side lengths than you had originally planned?
Answer: The box is 13,176 cubic inches larger than originally planned.
The side lengths turned out to be 6 inches longer than the 24 inches originally planned.
Step-by-step explanation:
To find the intended volume, "cube" 24 (24×24×24)
[tex]24^{3}= 13824[/tex]
To find the difference, subtract 13,824 from 27,000
27000 - 13824 = 13176
To find the actual side lengths of the box that was built take the cube root of 27000.
[tex]\sqrt[3]{27000}=30[/tex]
To find out how much longer, subtract 24 from 30.
30 - 24 = 6
you invest $2000 in an account that pays simple interest of 2% for twenty years. what amount of money will you have in 20 years
Answer:
$2971.9
Step-by-step explanation:
2000*(1+2%)^20 = 2971.895
what value is equivalent 8 x 9-2 x 5? HELP!!!!!!!!!!!
Answer:
62
Step-by-step explanation:
i hope it help
Answer:
350
Step-by-step explanation:
8*9-2*5=
72-2*5=
70*5=
350
(03.06 MC) What expression represents the value of y?
Answer:
[tex] y = \sqrt{wz} [/tex]
Step-by-step explanation:
The figure given shows the altitude (y) of a right triangle which is perpendicular to the hypotenuse (CA) of the triangle. The hypotenuse is divided by the altitude into two segments, w and z.
According to right triangle altitude theorem the relationship between y, w, and z is represented as follows:
[tex] y = \sqrt{wz} [/tex]
This expression represents the value of the altitude, y.
Answer:
y = wz with that check mark thingy over it
Step-by-step explanation:
i got the test
Since every square has 4 sides that are equal in the length, write an expression to determine the perimeter of a square in terms of the length of the squares sides?
9514 1404 393
Answer:
4s
Step-by-step explanation:
Let s represent the length of each of the four sides of the square. The perimeter is the sum of the lengths of the sides, so is ...
s + s + s + s
We use multiplication to signify repeated addition. So, this can be written more simply as ...
4s . . . . perimeter of a square of side length s
Which diagram has all the correct lines of reflectional symmetry for the rectangle?
A rectangle is folded diagonally on both corners.
A rectangle is folded by a vertical and horizontal line going through its center.
A rectangle is folded 4 ways. It is folded horizontally, vertically, and diagonally on both corners.
A rectangle is folded 4 ways. It is folded diagonally at each midpoint of every side.
Answer:
answer is b. a rectangle is folded by a vertical and horizontal line going through its center
Step-by-step explanation:
if you folded it along the lines of symmetry, the rectangle would line up with itself
A rectangle is folded by a vertical and horizontal line going through its center, has all the correct lines of reflectional symmetry for the rectangle.
What is reflectional symmetry?A well-balanced proportion in which two images or figures are the same size and shape is referred to as symmetry.
When the same figure is obtained following a transformation in geometry whether it be a reflection or a rotation symmetry has occurred.
An example of a shape with reflection symmetry is a rectangle. A line of reflection that passes through the center of two different sides will always be symmetrical.
There are two symmetry lines in a rectangle.
Each side of the rectangle would match up exactly if the rectangle were folded along each line of symmetry.
Keep in mind that a shape must possess at least one line of symmetry in order to qualify as having reflection symmetry.
learn more about reflectional symmetry here :
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4. The value of y is directly proportional to the value of x. If y = 45 when x = 180, what is the value of y when x = 80?
Answer:
y=8⇒8=24x
x=24/8=3
Step-by-step explanation:
The value of y when x = 80 is 20.
It is required to find the value of y.
What is arithmetic?Arithmetic is the branch of mathematics that deals with the study of numbers using various operations on them. Basic operations of math are addition, subtraction, multiplication and division. These operations are denoted by the given symbols.
Solution:
"Y is directly proportional to X" can be rewritten as a mathematical expression of the form Y = KX
"K" is the constant of proportionality and must be determined from the initial information.
According to given question we have,
If Y = 45 when X=180
It means
45 = 180K
K = 45/180
K = 0.25
Now that we know the value of K, we can use it to calculate the value of Y when X=80
Y = (0.25)(80)
Y=20
Therefore, the value of y when x = 80 is 20.
Learn more about arithmetic here:
brainly.com/question/18607551
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Estimate the product 4x279
Answer:
116
Step-by-step explanation:
es 116 porque lo cheque
Amir wants to buy a new MP3 player that costs $76.50. If he saves $8.50 each week, how many weeks will it take Amir to save enough money to buy the MP3 player? *
Answer:it would be ten weeks I think
Step-by-step explanation:
Each week he earns 8.50 so just take 8.50 times numbers until you get the closest answer to 76.50 and that’s ten
8.50 *10 = 85
Answer:
Answer:it would be ten weeks I think
Step-by-step explanation:
Each week he earns 8.50 so just take 8.50 times numbers until you get the closest answer to 76.50 and that’s ten
8.50 *10 = 85
The length of the top of a table is 4 m greater than the width. The area is 60m^2. Find the dimensions of the table
Answer:
Width = 6 m
Length = 10 m
Step-by-step explanation:
Let the width of the table be x meters.
Therefore, length of the table = (x + 4) meters.
[tex]length \times width = Area \\ \\ x(x + 4) = 60 \\ \\ {x}^{2} + 4x - 60 = 0 \\ \\ {x}^{2} + 10x - 6x - 60 = 0 \\ \\ x(x + 10) - 6(x + 10) = 0 \\ \\ (x + 10)(x - 6) = 0 \\ \\ x + 10 = 0 \: \: or \: \: x - 6 = 0 \\ \\ x = - 10 \: \: or \: \: x = 6 \\ \\ \because \: dimensions \: can \: not \: be \: negative \\ \therefore \: x \notin \: 10 \\ \implies \: x = 6 \\ x + 4 = 6 + 4 = 10 \\ width \: of \: table = 6 \: m \\ length \: of \: table = 10 \: m[/tex]
In which step was the subtraction property of equality applied?
A. Step 2
B. step 3
C.step 4
D. The subtraction property.of equality wasnot applied to solve this equatlon.
Answer
B.
Step 1: Calculate the price of 3 biscuits.
Step 2: Calculate the price of 3 sausages.
Step 3: Add the total amounts from Steps 1 and 2 to the amount of the tip.
Step 4: Subtract that total amount from $25.
Step-by-step explanation:
The total amount paid will be the price for 3 biscuits, 3 sausages, and the tip. The change will be the difference between this sum and $25. Choice B is an example of one way this calculation can be done.
What is the theoretical probability that you will roll a sum of 6?
A scanner scanned 56 photos in 7 minutes. If it scans photos at a constant rate, it can scan
photos in 27 minutes.
Answer:
56 photos-7 minutes
X photos-27 minutes
X=1 512 :7= A scanner will scan 216 photos
Step-by-step explanation:
What is 4/5 x 2/5? I need help
Answer:
8/25
Step-by-step explanation:
Please help this is my last question
Answer:
14(3x-1) / 5x^2 (3x+ 1)
Step-by-step explanation:
Please let me know if I gloss over something you don't understand
1) First simplify the complex fraction:
This can be written as
18x-6/ 15x + 5 * 21x^2 / 9x^5
which can be simplified to
18x-6/ 15x + 5 * 7/ 3x^3
which can be written as
(18x-6) * 7 / 3x^3 (15x+ 5)
2)
factor 3 from the top of the expression
3(6x-2) * 7 / 3x^3 (15x + 5)
3)
reduce the fraction with 3
3(6x-2) * 7 / 3x^3 (15x + 5)
(6x-2) * 7 / x^3 (15x + 5)
4)
Distribute 7 through the parenthesis on the top
42x-14/ x^ 3 (15x+ 5)
5)
Distribute x^3 through the parenthesis on the bottom
42x-14/ 15x^4 + 5x^3
6)
factor 14 from the top of the expression
14 (3x -1)/ 15x^4 + 5x^3
7)
factor 5x^3 from the bottom
14 (3x -1)/ 5x^3 (3x + 1)
The weight of one serving of goldfish is 0.5 ounces. How many servings are there in 7.5 ounces of goldfish? Write your answer as a decimal.
If 23 is subtracted from 8 times the number, the result is the square of 2 less than the number.
Please help me i need help!! How do you solve for M? Explain each step of the solution in a short paragraph
Answer:
M = 4pi²a³ / GT²
Step-by-step explanation:
Cross multiply: T² × GM = GMT²
1 × 4pi²a³ = 4pi²a³
It becomes: GMT² = 4pi²a³
Divide both sides by GT² to solve for M
We have : M = 4pi²a³ / GT²
PLZ HELP IM RUNNING OUT OF TIME!!! THIS IS A SIMPLE EXPLANATION PROBLEM PLEASE HELP!!!
The equation 7(x − 4) = 8(x + 8) has one solution. Which of the following best explains why?
A.
The x-terms are the same, but the constant terms are different.
B.
The x-terms are different, and the constant terms are different.
C.
The x-terms are the same, and the constant terms are the same.
D.
The x-terms are different, but the constant terms are the same.
Answer:
C. The x-terms are the same, and the constant terms are the same.
Step-by-step explanation:
Solve for x:
7 (x - 4) = 8 (x + 8)
Hint: | Write the linear polynomial on the left-hand side in standard form.
Expand out terms of the left hand side:
7 x - 28 = 8 (x + 8)
Hint: | Write the linear polynomial on the left-hand side in standard form.
Expand out terms of the right hand side:
7 x - 28 = 8 x + 64
Hint: | Move terms with x to the left-hand side.
Subtract 8 x from both sides:
(7 x - 8 x) - 28 = (8 x - 8 x) + 64
Hint: | Combine like terms in 7 x - 8 x.
7 x - 8 x = -x:
-x - 28 = (8 x - 8 x) + 64
Hint: | Look for the difference of two identical terms.
8 x - 8 x = 0:
-x - 28 = 64
Hint: | Isolate terms with x to the left-hand side.
Add 28 to both sides:
(28 - 28) - x = 28 + 64
Hint: | Look for the difference of two identical terms.
28 - 28 = 0:
-x = 64 + 28
Hint: | Evaluate 64 + 28.
64 + 28 = 92:
-x = 92
Hint: | Multiply both sides by a constant to simplify the equation.
Multiply both sides of -x = 92 by -1:
(-x)/(-1) = -92
Hint: | Any nonzero number divided by itself is one.
(-1)/(-1) = 1:
Answer: x = -92
I NEED SOME HELP
Bobby rich dude has $120,000 in his account that pays him 5.5% compounded daily. What amount and how much interest will his money earn in 30-days?
Answer:
Interest: Amount Gained: $198,000
Final Balance: Amount After 30 days of Interest: $318,000
Step-by-step explanation:
Equation Used to Solve:
120,000 · 0.055 = 120,000 + (xy)
Let x represent 5.5% of 120,000
Let y represent the number of days.
Solving the equation:
120,000 · 0.055 = 6,600
x = 6,600; y = 30
120,000 + (6,600 · 30) = 120,000 + 198,000
120,000 + 198,000 = 318,000
I need help with number 12 please. Thank you.
Step-by-step explanation:
The sides of a triangle have measures of 2x, 8, 12. If the measure of the longest side is 2x. What value of x makes the triangle a right triangle?
please answer !!!!...
Answer:
8+12= 2x
multiply all of them by power of 2
Step-by-step explanation:
so,
64+144 = 4x
208=4x
x = 52 what is the root of 52 the answer is
x = 7.188 or 3/16
the day Janella and her family left Hawaii, the temperature was 73°F above 0°F. what would a thermometer read at this temperature?
Please Answer
Answer:
73° F
Step-by-step explanation:
Add 73° F to 0° F
The answer is 73° F
Hope I helped :)
Please consider Brainliest :)
Answer:
I think it would be 0 because I devided but i'll try a nother way
Step-by-step explanation:
12)
0
1
1
В
у
3.5 4.5 5.5 6.5 7.5
equation:
Write down all the whole numbers between 1035 and 1041
Answer:
1035
1036
1037
1038
1039
1040
1041
Step-by-step explanation:
pls heart and brainliest
Answer:1036, 1037, 1038, 1039, 1040.
Step-by-step explanation:
What is the measure of the angle formed by the minute hand and hour hand of a clock in each case?
a)at 6 o’clock
b) at 4 o’clock
c) at 3o’clock
Answer:
a) 180 degrees
b) 120 degrees
c) 90 degrees
please help me!!! I am just a meme poster... :c
Which of polygons B, C, D, E, andF are similar to polygon A? Select All of
The answer is E bro bro
HELPPPPPP There are B giris and 5 boys on the math team Which ratio corroctly describos the rolotionship botvwoen boys ond gus on the math tearm? OThere are 5 boys for every 5 giris OThere are 5 boys for every 13 girfs O For every 5 boys there are B girls O For every B boys there are 5 giris
Answer:
for every 5 boys there are b girls
Step-by-step explanation:
that's how u read ratios, for every x there are y amount of something else. portions is how we'll describe it!!
Answer: C
Step-by-step explanation:
For every five (5) boys, there are eight (8) girls.
ℎ :)