The 17th term of the given geometric sequence, 3, 12, 48, 192, . . . , is 1.288490189 x 10^10.
A geometric sequence refers to a sequence of numbers, which the next term is obtained by multiplying the previous term with a constant, called a ratio.
a(n) = a r^(n-1)
Where:
a(n) = nth term
r = ratio
Given the geometric sequence 3, 12, 48, 192, . . .
Find the ratio,
r = a(n)/a(n-1)
r = a(2)/a(1)
r = 12/3
r = 4
Notice that the ratio between two succeeding terms is always 4.
Use the formula to find the 17th term of the geometric sequence.
a(n) = a r^(n-1)
a(17) = 3[4^(17-1)]
a(17) = 3(4^16)
a(17) = 1.288490189 x 10^10
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At the gift shop, they sell small greeting cards and large greeting cards. The cost of a small greeting card is $1.65 and the cost of a large greeting card is $5.40. How much would it cost to get 3 small greeting cards and 2 large greeting cards? How much would it cost to get xx small greeting cards and yy large greeting cards?
The cost to get 3 small greeting cards and 2 large greeting cards is $15.75 and the it cost to get xx small greeting cards and yy large greeting cards is equals to $1.65(xx) + $5.40(yy)
To find out the cost of three small greeting card we need to multiply the cost of one small greeting card with 3 which equals to $4.95
To find out the cost of two large greeting card we need to multiply the cost of large greeting card with two which equals to $10.80
To find out the cost to get 3 small greeting cards and 2 large greeting cards we need to add $4.95 and $10.80 which equals to $15.75
As explained above to find the cost to get xx small greeting cards and yy large greeting cards we need to multiply with their respective unit price which equals to $1.65(xx) + $5.40(yy)
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Find the value of c that completes the square.
r^2+21r+c
Answer: c=110.25
Step-by-step explanation:
[tex]r^2+21r+c\\r^2+(2)(r)(10.5)+(10.5)^2=\\(r+10,5)^2\\Hence,\\c=(10.5)^2\\c=(10.5)(10.5)\\c=110.25[/tex]
WILL GIVE BRAINLIEST :3 !
1.) 64 dollars
2.) 145 dollars
3.) -110 dollars?
4.) -50 solldars
54 + 10 = 64
60+85=145
-180+70=-110
37-87=-50
Answer:
Step-by-step explanation:
Okay so the first question you need to add because the store is giving a refund to Clare of $10. The second question you need to subtract $60 from $85. The third one you need to add again 180+ 70. The final problem you need to subtract 87 from 37 (Just know you will get a negative number) I hope this helps you! :D
Can you have a relation that is not, a function? Can you have a function that is not a relation? Explain.
If you consider the relationship between two quantities, an input/output machine can be used to represent this relationship. You have a function if there is only one output for each input. You have a relation if not.
Can a relationship exist that isn't a function?
A relation might translate inputs to numerous outputs. When it converts each input into exactly one output, something is a function. A subset of the set of all relations is the set of all functions. This implies that while all relations are functions, not all functions are relations.What is relation in math?
A collection of ordered pairs having one item from each set makes up a relation between two sets. If the ordered pair (x,y) is present in the relation and the objects x and y come from different sets, then the objects are said to be connected. One kind of relation is a function.Learn more about relation
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b. Is there a pattern in the table? Explain.
Answer:
no photo
Step-by-step explanation:
we need a photo to decide if answer is correct or not
I need help with this asap
Which of the following statements describe the steps to copy XY? Select all that apply.
X
OA. Use a ruler to draw line and label point M.
OB. Use a straightedge to draw line and label point M.
OC. Place a compass point at X and open the compass to length XY.
OD. Using the same setting, place the compass point at M, draw an arc through line , and mark point N as t
Solve 0.203 ÷ 7.
1.421
0.290
0.029
−6.797
Answer:
0.029
Step-by-step explanation:
The answer
The sum of four consecutive is 490. What are the four consecutive integers
The four consecutive integers are 121, 122, 123, 124.
We have the sum of four consecutive integers equals to 490
We have to determine those integers.
What are Integers?An integer is a number with no decimal or fractional part. It includes negative and positive numbers, including zero.
Assume the first integer is x. Then, the other integers will be -
x + 1 , x + 2 , x + 3.
Therefore -
x + (x + 1) + (x + 2) + (x + 3) = 490
4x + 6 = 490
4x = 484
x = 121
So -
x = 121
x + 1 = 122
x + 2 = 123
x + 3 = 124
Hence, the four consecutive integers are 121, 122, 123, 124.
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please help it’s urgent thank you!
this is a proportional relationship that can be written as:
P = 5,184*S
Could there be a realtionship?Top see this, just take the quotient between the number of pixels and the number of square inches of each screen, and let's see if we get the same value for the given rows.
31,104/6 = 5,184
For the next row we have:
373,248/72 = 5,184
And so on, you will get the same quotient for the 3 rows, then we can conclude that yes, this is a proportional relationship that can be written as:
P = 5,184*S
Where P is the number of pixels and S is the number of square inches.
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Rotation 90° counterclockwise around the
origin of the point (-8, 3)
(8,3)
(3,8)
(-8,-3)
(-3,-8)
The answer is (-3.-8)
When we rotate a point 90° counterclockwise around the origin, it's the same as rotating it 270° clockwise around the origin.
When we rotate something 270° clockwise around the origin, the original coordinates (x, y) becomes (-y, x).
Clockwise Rotations (CW) follow the path of the hands of a clock. These rotations are denoted by negative numbers. Counterclockwise Rotations (CCW) follow the path in the opposite direction of the hands of a clock. These rotations are denoted by positive numbers.
The angle of rotation between the two points or vertices is the number of central angles times the measure of a single central angle: angle of rotation =m×α = m × α .
y is 3, and -(3) is just -3, since multiplying negatives make a negative.
x just remains x, but it's in a different position.
This makes the new coordinate (-3, -8)
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Work out the value of the question mark in
the function machine below.
Input
-2→ ×?
Output
X-3-18
Answer:
output = -23
Step-by-step explanation:
if x = -2
output = x - 3 - 18 = -2 - 3 - 18 = -23
A clearance rack is marked as 35% off the regular price. a shirt on the clearance rack has a regular price of $45.99. if there is 7.25% sales tax, what will the shirt ring up for at the register? a. $17.26 b. $21.67 c. $29.89 d. $32.06 please select the best answer from the choices provided a b c d
According to the question, the given data for the clearance rack is as written below:
Regular price of the clearance rack = $[tex]$ 45.99[/tex]
Sales tax = [tex]7.25[/tex] percent
As per the question, multiply the given marked percentage with the regular price to get the exact value.
Therefore, Marked price(in $) = [tex]45.99X0.35 = 16.10[/tex]
Now, subtract the calculated price from the regular price:(in $)[tex]45.99-16.10 = 29.89[/tex]
Multiply the regular price with the sales tax: [tex]29.89X0.0725 = 2.17[/tex]
Add the tax price with the calculated regular price to know the register price: [tex]29.89+2.17=32.06[/tex]
Therefore, [tex]32.06[/tex] is the amount for the shirt ring up for at the register.
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the 4th and 5th terms of a GP are -13.5 and 40.5 find the first term and the sum of the first five terms
Answer:
First term: 0.5
Sum of the first give terms: 30.5
Step-by-step explanation:
General form of a geometric sequence:
[tex]a_n=ar^{n-1}[/tex]
where:
[tex]a_n[/tex] is the nth terma is the first termr is the common ratioGiven terms:
[tex]a_4=-13.5[/tex][tex]a_5=40.5[/tex]To find the common ratio r, divide consecutive terms:
[tex]\implies r=\dfrac{a_5}{a_4}=\dfrac{40.5}{-13.5}=-3[/tex]
To find the first term, substitute the found value of r and one of the terms into the general formula:
[tex]\begin{aligned}\implies a_5 =a(-3)^4 & = 40.5\\81a & = 40.5\\a & = \dfrac{40.5}{81}\\a & = 0.5 \end{aligned}[/tex]
Sum of the first n terms of a geometric series:
[tex]S_n=\dfrac{a(1-r^n)}{1-r}[/tex]
To find the sum of the first 5 terms of the geometric sequence, substitute n = 5 and the found values of a and r into the formula:
[tex]\begin{aligned}\implies S_5 & =\dfrac{0.5(1-(-3)^5)}{1-(-3)}\\\\& =\dfrac{0.5(1+243)}{1+3}\\\\& =\dfrac{0.5(244)}{4}\\\\& =\dfrac{122}{4}\\\\ & = 30.5\end{aligned}[/tex]
Therefore, the sum of the first 5 terms is 30.5.
What is the length of AB with endpoints A (-1,0) and B (4,-3)
Answer:
√34
Step-by-step explanation:
it would be radical 34.
What is the radius of a table with a circumference of 10 feet?
A. 1.6 ft B. 2.5 ft
C. 3.2 ft D. 5 ft
The radius of a table with a circumference of 10 feet is A. 1.6 ft .
What is circumference of circle?A circle's outside boundary is called the circumference and can be measured, or calculated, by using
Circumference = 2πr
where r is the radius of circle.
Now it is given that,
Circumference of table = 10 feet
Since, Circumference = 2πr
⇒ 2πr = 10
⇒ r = 10/2π
⇒ r = 10/6.28
⇒ r = 1.59
⇒ r ≈ 1.6 feet
Thus, the radius of a table with a circumference of 10 feet is A. 1.6 ft
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Solve each system.
5x + y = 0 , 5x + 2y = 30
After solving each system, 5x + y = 0, 5x + 2y = 30, the values of x and y are calculated to be -6 and 30 respectively.
The given equations are considered linear equations as the highest power of the variables in these equations is one.
By rearranging the first equation, the value of y can be found to be,
5x + y = 0
y = -5x
Putting the calculated value of y in the second equation,
5x + 2y = 30
5x + 2(-5x) = 30
5x - 10x = 30
-5x = 30
x = 30 / -5
x = -6
To solve for y, put x = -6 in the first equation as follows,
5x + y = 0
5(-6) + y = 0
-30 + y = 0
y = 30
Hence, the values of x and y in these systems are calculated to be -6 and 30 respectively.
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Function his a transformation of the parent exponential function, f(2)= 2º.
h(z)=-3-2²
Which statement is true?
A. Function h is a horizontal translation of function f
OB.
Function h is a reflection and a translation of function f
OC. Function h is a vertical translation of function f
OD. Function his a reflection and a dilation of function
According to the question, the true statement is the function 'h' is a vertical translation of a function ''f.
What is exponential function?
The exponential function can be defined as the base of two with the integer powers. The base can be represented as common factors as well as common multipliers. The graph representation of the exponential function can be called as "rate of change". It either increases or decreases or constant with respect to another functions.
The transformation of a function can be performed either with translation, reflection, vertical sliding or horizontal sliding. It can be done with the help of the calculated values known as asymptotic. And the end behavior of the function is always consistent.
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The midpoint of AB
is M(-3, 0)M(−3,0). If the coordinates of AA are (1, -4)(1,−4), what are the coordinates of BB?
The required coordinate of b is given as (-7, 4 ).
Given that,
To determine the coordinate of b if M is the midpoint of AB. A(1, -4) and M(-3 ,0).
What is the midpoint?The midpoint is that point the line whose distance from both the ends of the line is equal.
Here,
We have given two coordinates one of the endpoints of AB and the other is midpoint M i.e. A(1, -4) and M(-3, 0).
Definition of midpoint says,
x = [x₁ + x₂] / 2 ; y = [y₁ + y₂] / 2
x₁ = 1, x = -3 , y₁ = -4, y = 0
now,
-3 = [1 + x₂] / 2 ; 0 = [-4 + y₂] / 2
x₂ = -6 - 1 ; y₂ = 0 + 4
x₂ = -7 : y₂ = 4
Thus, the required coordinate of b is given as (-7, 4 ).
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1/2(12x+10)+2×
simplify
Mike sold 5,640 chickens and 5,732 ducks from his farm. He
made $79,696. If he sold 5,640 chickens and 5,640 ducks, he
would get $78,960. How much money did he make from
selling the 5,732 ducks?
$
The number of money farmers made by selling 5732 ducks will be $45856.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that Mike sold 5,640 chickens and 5,732 ducks from his farm. He made $79,696. If he sold 5,640 chickens and 5,640 ducks, he would get $78,960.
Form two equations to get the amount:-
5640c + 5732d = 79696
5640c + 5640d = 78960
Solve both the equations by elimination method:-
5640c -5640c + 5732d - 5640d = 79696 - 78960
92d = 736
d = 736 / 92
d = $8
Total amount = $8 x 5732 = $45856
Therefore, the money farmers made by selling 5732 ducks will be $45856.
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Find the coordinates of the midpoint of the line segment with endpoints (6, -2) and (-3, -2).
Answer: (3/2, -2)
Step-by-step explanation:
basically average of the x's and y's
6+-3/2 and -2+-2/2
which gives
(3/2, -2)
please help if you can, vv appreciated!!
Answer:
I believe 72
Step-by-step explanation:
Evaluate each expression 14^3
Line q has an equation of y = -10/9x+ 2. Line r includes the point (9, -3) and is parallel to
line q. What is the equation of line r?
Write the equation in slope-intercept form. Write the numbers in the equation as simplified
pro
fractiong imn
-fractions or intogoro
The equation of the line r is y = ₋(10/9)x ₊ 7.
Given, parallel lines have the same slope. Solve for the slope in the first line by converting the equation to slope intercept form
equation of line q is y = ₋10/9x ₊ 2
it's already in slope intercept form.
hence slope is:
m = (₋10/9) from the above the equation.
we know that the second line will also have a slope of ₋10/9 and we are given the point (9 , ₋3). We can setup an equation in slope intercept form and use these values to solve for the y inetrcept.
y = mx ₊ b
₋3 = ₋10/9 (9) ₊ b
₋3 = ₋10 ₊ b
b = 7
plug the y intercept back into the equation to get our final answer.
y = ₋(10/9)x ₊ 7
hence we get the equation of the line r as y = ₋(10/9)x ₊ 7.
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Let f(x)=2x-1, g(x)=3x, and h(x) = x² + 1. Compute the following:
f(g(-3)) =
Answer:
Step-by-step explanation:g(-3) = 3(-3) = -9
f(g(-3)) = f(-9) = 2(-9) -1 = -18 -1 = -19
Solve |2x - 3| ≤7.
OA.
2-2 and x ≤ 4
OB.
2-3 or x ≤ 2
OC. 2-2 and x ≤ 6
OD. 2-2 and x < 5
The solution of the inequality expression is -2 ≤ x ≤ 5
How to solve the inequality expression?The inequality expression is given as
|2x - 3| ≤7
Remove the absolute bracket
So, we have
2x - 3 ≤ 7 and 2x - 3 ≥ -7
Add 3 to both sides of the inequalities
2x ≤ 10 and 2x ≥ -4
Divide to both sides of the inequalities by 2
x ≤ 5 and x ≥ -2
Rewrite as
-2 ≤ x ≤ 5
Hence, the solution of the inequality expression is -2 ≤ x ≤ 5
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Djhsjsjakamakamsdgzhjshsbzjsjsn
10 less than 5 times a number is equal to 15.
05(2-n) = 15
5-10n = 15
10-5n = 15
5n-10 15
Answer:
5n - 10 = 15.
Step-by-step explanation:
If the number is n then 5 times it is 5n.
10 less than this is 5n - 10.
So, the equation is
5n - 10 = 15.
Three competing subcontractors are reporting their average work output to a large project leader for a new housing development.
Rosk Construction provided an equation, where w represents the number of full weeks of work and a represents the estimated area of vinyl siding that can be installed in 100 ft2 units.
Equation from Rosk Construction: a = 62w
Fosbert’s Contracting provided a table indicating similar data from two jobs that had recently been completed by its crew.
Durable B Construction provided a graph showing the results of three of its recently completed jobs.
The unit rate for Rosk Construction is
The unit rate for Fosbert's Contracting is
The unit rate for Durable B Construction is
Based on the construction information, the unit rates will be 62, 65, and 63.
What do we mean by unit rates?A unit rate is a price for one unit of something. This is written as a ratio with a denominator of one.For instance, if you ran 70 yards in 10 seconds, you averaged 7 yards per second. Both ratios, 70 yards in 10 seconds and 7 yards in 1 second, are rates, but only the latter is a unit rate.So, Rosk Construction's unit rate is 62. This is due to a=62w.
Fosbert's Construction has a unit rate of 65 because:
130/2 = 65260/4 = 65390/6 = 65Therefore the unit rate is 65
Then,
Durable B Construction will have a unit price of 63.
This is due to:
63/1 = 63126/2=63189/3=63Therefore, based on the construction information, the unit rates will be 62, 65, and 63.
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The correct question is given below:
Three competing subcontractors are reporting their average work output to a large project leader for a new housing development. Rosk Construction provided an equation, where w represents the number of full weeks of work and a represents the estimated area of vinyl siding that can be installed in 100 ft2 units. Equation from Rosk Construction: a=62w Fosbert’s Contracting provided a table indicating similar data from two jobs that had recently been completed by its crew. Forsbert's contracting Number of Full Weeks, w 2 4 6 Area (square feet), a 130 260 390
