Hi! I'm happy to help!
To solve this, we first need to find our what could give us 1/3. WE realize that the sequence is descending, so we must be dividing. We can then, from here, multiply our top number by 1/3, because that is our end number, and could possibly work for our common ratio. From this, we can check if this fits in our equation. (dividing by 3)
243×1/3=81
81×1/3=27
27×1/3=9
9×1/3=3
3×1/3=1
1×1/3=1/3
We can check if this is the correct amount of numbers that would fit into the geometric sequence. Let's see if this fits in:
243, 81, 27, 9, 3, 1, 1/3
This does fit into our geometric sequence. Our middle terms are underlined. (missing numbers)
Our common ratio is the number we multiply the previous number by to get our next, so our common ratio is 1/3.
So, our geometric sequence is 243, 81, 27, 9, 3, 1, 1/3, our middle terms are 81, 27, 9, 3, and 1. Our common ratio is 1/3.
I hope this was helpful, keep learning!
Answer:
Middle terms 81, 27, 9, 3, 1 or -81, 27, -9, 3, -1Common ratio 1/3 or -1/3Step-by-step explanation:
Given:
t₁ = 243, t₇ = 1/3To find the terms in between.
Find the common ratio first:
tₙ = t₁rⁿ⁻¹1/3 = 243*r⁶r⁶ = 1/729r = [tex]\sqrt[6]{1/729}[/tex]r = ± 1/3The terms in between are:
t₂ = 243*1/3 = 81 or -81t₃ = 81*1/3 = 27 t₄ = 27*1/3 = 9 or -9t₅ = 9*1/3 = 3t₆ = 3*1/3 = 1 or -1What is the quotient of 4.653 x 107 and 7.05 x 103 expressed in scientific
notation?
Which rule describes the pattern shown? 41, 54, 67, 80, 93, 106
Answer:
adding by 13
Step-by-step explanation:
subtract 54-41
Answer fast.
Which statement is not true?
A. All whole numbers and integers are
rational numbers.
B. All rational numbers can be written as a
fraction.
C. A whole number cannot be written as a
fraction.
D. All integers are whole numbers but not
all whole numbers are integers.
Answer:
C
Step-by-step explanation:
all whole numbers can be written as fractions that is over 1
Many doctors rely on the use of intravenous medication administration in order to achieve an immediate response of a particular drug's effects. The concentration, C, in mg/L, of a particular medication after being injected into a patient can be given by the function C of t is equal to the quantity negative 10 times t squared plus 50 times t end quantity over the quantity t squared plus 4 times t plus 3 end quantity comma where the time, t, is hours after injection. Part A: What is the domain of the function C(t) based on the context of the problem? Show all necessary calculations. (5 points) Part B: Graph the function to determine the greatest concentration of the medication that a patient will have in their body. (5 points)
Graphs are used to show the relationship between variables, where the variables are represented by a pair of axes.
The domain of the function is [tex]t \ge 0[/tex] The greatest concentration of the medication is 5mg/LGiven that:
[tex]C(t) = \frac{-10t^2 + 50t}{t^2 + 4t + 3 }[/tex]
(a): The domain of the function
Because the medication concentration C(t) is a function of time (t), the domain is the possible values t can take.
t, cannot take negative values (i.e. it is not possible to have a negative time).
The least possible value of t is 0
So, the domain of the function based on the context is:
[tex]t \ge 0[/tex]
(b) The greatest concentration of the medication
From the graph (see attachment), the maximum y-value is 5.
Hence, the greatest concentration of the medication is 5 mg/L
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A function assigns the values. The greatest concentration of the medication that a patient will have in their body is when the time is t=1.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
A.) Given the function of the concentration of medication in the body as to[tex]C(t)=\ \frac{\left(-10t^{2}+50t\right)}{t^{2}+4t+3}[/tex] where t is the time. Since the time can not be negative, therefore, the domain of the function is t≥0.
B.) The graph of the function can be plotted as shown below. Now, the greatest concentration of the medication that a patient will have in their body is when the time is t=1.
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Which equation represents a line which is perpendicular to the line y =
= -x - 72
6x - 5y = 30
Oby - 52 = 18
Submit Answer
O 6x + 5y = 20
O 5x + 6y = 42
PLS HELP ASAP
Answer:
[tex]5x + 6y = 42[/tex]
Step-by-step explanation:
Hope it is helpful....
Please find the value of x and y. It's in angle addition postulate so if you know how to solve these please help.
Answer:
see explanation
Step-by-step explanation:
(7)
(25x + 8) and (9x + 2) are adjacent angles and sum to 180° , then
25x + 8 + 9x + 2 = 180 , that is
34x + 10 = 180 ( subtract 10 from both sides )
34x = 170 ( divide both sides by 34 )
x = 5
Then
9x + 2 = 9(5) + 2 = 45 + 2 = 47
(7y + 5) and (9x + 2) are vertical angles and are congruent , so
7y + 5 = 47 ( subtract 5 from both sides )
7y = 42 ( divide both sides by 7 )
y = 6
------------------------------------------------------
(8)
(11x - 24) and (7x + 30) are vertical angles and are congruent, so
11x - 24 = 7x + 30 ( subtract 7x from both sides )
4x - 24 = 30 ( add 24 to both sides )
4x = 54 ( divide both sides by 4 )
x = 13.5
Similarly
(17y - 4) and (5y + 38) are vertical angles and congruent , then
17y - 4 = 5y + 38 ( subtract 5y from both sides )
12y - 4 = 38 ( add 4 to both sides )
12y = 42 ( divide both sides by 12 )
y = 3.5
Find the value of x (trig)
According to the figure:-
P=13H=25We know that Sin∅=P/H
Hence Sinx°=13/25
[tex] { \sin}^{ - 1} \frac{25}{13} = X°[/tex]
Be brainly8.
The
square of a number is always greater than the number.
Answer:
The above given statement is true
convert 0.2 kg into mg
Answer:
The answer is 200000 milligrams
Hope that helped you
This is finding the midpoint. Please help
Answer:
hence the required midpoint of the given line is (9,5)
Answer:
[tex]( \frac{6 + 2}{2} +\frac{12 + 8}{2}) = ( \frac{8}{2} + \frac{20}{2} ) = (4 \: comma10)[/tex]
The answer is :(4, 10)
which is the simplified form of the expression
please help!!
Answer:
A
Step-by-step explanation:
p^-8q^-20 * p^8q^-10
=q^-30
=1/q^30
Terminating Decimal between .5 and .6
The function y = f(x) is graphed below. What is the average rate of change of the function f(x) on the interval 1 < x < 2?
RS=3y+5, ST=2y+9, RT=54. what is the value of y?
Answer:
56
Step-by-step explanation:
show your work
Find three consecutive even integers such that five times the second is six more than twice the sum
of the first and third integers
Answer:
The first number = 4The second number = 6The third number = 8Step-by-step explanation:
Let all unknown numbers be represented by the variable x.So;x = first number
x + 2 = second number
x + 4 = third number
placing in a form as demanded by the question.5(x + 2) = 6 + 2x + 2 ( x + 4)
5x + 10 = 6 + 2x + 2x +8
5x - 4x = 14 - 10
x = 4
Therefore;The first number (x) = 4
The second number ( x + 2) = 4 + 2 = 6
The third number (x + 4) = 4 + 4 = 8
Answer:
2x + 2x +2 + 2x +4 = 6x +6 =Sum
5 * (2x +2) = 2 * (2x + 2x +4) +6
10x + 10 = 8x + 8 + 6
2x = 4
x = 2
So the numbers are:
2x or 4
2 x + 2 = 6
2x + 4 = 8
Double-Check
5 * 2nd integer = 30
2 * (1st + 3rd integers) = 24
30 is 6 more than 24
Success!!!
Step-by-step explanation:
Evaluate the expression. 0.3 = -5 - (-0.4 - -0.6) Write your answer as an integer or a decimal. Do not round.
Answer:
-20
Step-by-step explanation:
Hi
The value of the expression is a decimal -17.33.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
0.3x = -5 - (-0.4 - (-0.6))
0.3x = -5 - (-0.4 + 0.6)
0.3x = -5 - 0.2
0.3x = -5.2
x = -5.2/0.3
x = -17.33
Thus,
The value of x is -17.33.
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The gradient of the line joining (4, q) to (6, 5) is twice the gradient
of the line joining (0, 0) to (4, q). Find q.
Answer:
q is 4
Step-by-step explanation:
[tex]gradient = \frac{y_{2} - y_{1} }{x _{2} - x _{1} } \\ [/tex]
let gradient of the line joining (4, q) to (6, 5) be x
let gradient of the line joining (0, 0) to (4, q) be y
[tex]y = 2x[/tex]
therefore:
[tex]( \frac{q - 0}{4 - 0} ) = 2( \frac{5 - q}{6 - 4} ) \\ \\ \frac{q}{4} = \frac{2(5 - q)}{2} \\ \\ \frac{q}{4} = 5 - q \\ \\ q = 4(5 - q) \\ q = 20 - 4q[/tex]
collect like terms:
[tex]q + 4q = 20 \\ 5q = 20 \\ q = \frac{20}{5} \\ \\ q = 4[/tex]
Let,
The gradient of line joining (4, q) to (6, 5) be "x".The gradient of line joining (0, 0) to (4, q) be "y".As we know,
[tex]Gradient = \frac{y_2-y_1}{x_2-x_1}[/tex][tex]y = 2x[/tex]then,
→ [tex]\frac{q-0}{4-0} = 2(\frac{5-q}{6-4} )[/tex]
[tex]\frac{q}{4} = \frac{2(5-q)}{2}[/tex]
[tex]\frac{q}{4} = 5-q[/tex]
By applying cross-multiplication, we get
[tex]q = 4(5-q)[/tex]
[tex]q = 20-4q[/tex]
By adding "4q" both sides, we get
[tex]q+4q= 20-4q+4q[/tex]
[tex]5q = 20[/tex]
[tex]q = \frac{20}{5}[/tex]
[tex]q = 4[/tex]
Thus the above value is correct.
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(f×g) (x)
(4x+8)×(2x-12)
Answer:
[tex] = (4x + 8)(2x - 12) \\ = ( {8x}^{2} - 48x + 16x - 96) \\ = (8 {x}^{2} - 32x - 96) \\ = 8( {x}^{2} - 4x + 12)[/tex]
Answer:
\begin{gathered} = (4x + 8)(2x - 12) \\ = ( {8x}^{2} - 48x + 16x - 96) \\ = (8 {x}^{2} - 32x - 96) \\ = 8( {x}^{2} - 4x + 12)\end{gathered}
=(4x+8)(2x−12)
=(8x
2
−48x+16x−96)
=(8x
2
−32x−96)
=8(x
2
−4x+12)
What are the potential solutions of In(x2 - 25) = 0?
Ox= 113
O x= 15
x=+26
Ox=+10
Answer:
e^0=x^2-25=1
x^2=26
x=sqrt(26), pos and neg
The potential solution of the given equation is x=±√26. Therefore, option C is the correct answer.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.
The given equation is ln(x²-25)=0
x²-25>0
(x+5)(x-5)>0 (∵a²-b²=(a+b)(a-b))
x>-5 and x>5
Now, e⁰=x²-25
1=x²-25
x²=26
x=±√26
Therefore, option C is the correct answer.
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a man bought a 4 kg apples at the rate of rs 50 per kg he sold 3 kg apples at the rate of rs 65 and 1 kg apples at rs 40 find his profit or loss amount.
Answer:
35rs of profit
Step-by-step explanation:
4*50=200rs- he spent
3*65+1*40=195+40=235rs- he got
235-200=35rs of profit
3/2 x -6
hahshdnndndndjd
In the expression "4f + s", the letter "s" is: *
Answer:
Step-by-step explanation:
A variable
At a bake sale there were 52 items sold total. If 24 of the items sold were cookies and the rest were brownies what is the ratio of brownies sold to cookies sold?
Can someone help me on this?? Im really struggling
Benny thinks of a number, subtracts 18 from it, and divides the difference by 3, the result is (-4). What is the number?
Answer:
n=6
Step-by-step explanation:
(n-18)/3 = -4
multiply by 3
n-18 = -12
add 18
n = 6
any one solve these questions will mark brainliest the last three fast plz
(iii)
35+ x + 60 = 180
95 + x = 180
x = 180 – 95
x = 85
So; X = 85° ; < PON(iV)
x + 47 + 75 = 180
x + 122 = 180
x = 180 – 120
x = 58
So; x = 58° ; < COB(Vi)105 ° = 3 x° –> Opposite angles ,
x = 105 / 3
x = 35
3x = 3(35) = 105°
So; x = 35°Only the figure (V) I didn't know I'm sorry:(
I hope I helped you^_^
i don’t understand can someone please help me
Answer:
Answer:
Step-by-step explanation:
Answer as Photo
Evaluate \dfrac {9}m+4 m 9 +4start fraction, 9, divided by, m, end fraction, plus, 4 when m=3m=3m, equals, 3.
Fractions can be evaluated, same way non fractions are evaluated
The result of the fraction expression [tex]\mathbf{\dfrac {9}m+4}[/tex] is 7
The given parameters are:
[tex]\mathbf{\dfrac {9}m+4}[/tex]
[tex]\mathbf{m = 3}[/tex]
So, we have:
[tex]\mathbf{\dfrac {9}m+4}[/tex]
Substitute 3 for m
[tex]\mathbf{\dfrac {9}m+4 = \dfrac {9}3+4}[/tex]
Evaluate the division
[tex]\mathbf{\dfrac {9}m+4 = 3+4}[/tex]
Add 3 and 4
[tex]\mathbf{\dfrac {9}m+4 = 7}[/tex]
Hence, when m equals 3, the result of the fraction expression [tex]\mathbf{\dfrac {9}m+4}[/tex] is 7
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Help me pls ?? 1. Suppose there is a raffle with numbered tickets 1 - 150. One ticket is randomly
drawn from a hat. Find the following probabilities:
A. Drawing an even number
B. Drawing a number greater than 100
C. Drawing an even prime number
D. Drawing a negative number
Solve the equation for the specified variable.
Y = AD-5, for A
Help plzzzzz
Answer:
A = (Y + 5)/ D
Step-by-step explanation:
Y = AD - 5
Y + 5 = AD - 5 + 5
Y + 5 = AD
(Y + 5)/D = AD/D
(Y + 5)/ D = A
》A = (Y + 5)/ D
