As per the question each row must have 6 seats more than the row before it. And there are 11 seats in the first row.
So, the first row has 11 seats
2nd row has 11+6 seats
3rd row has 11+2*6=11+12=23
4th row has 11+3*6=11+18=29
and so on...
We know that the difference between any two consecutive integers in an arithmetic progression (AP) sequence of numbers is always the same amount. Arithmetic progression can be calculated as
aₙ = a₁ + (n - 1)d,
where aₙ is the nth and a₁ is the first term of this progression respectively and d is the common difference between terms.
So, we can observe the trend and develop the equation for the problem.
There are 11+(n-1)*6 seats in the n-th row.
So, there is 11+(18-1)*6=11+17*6=113 seats in the 18th row.
Therefore, there are 113 seats in the 18th row.
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what is the 10th term for sequence 4; 8; 13; 19; 26
Answer:
40
Step-by-step explanation:
35. Use the Change of Base Formula to evaluate logs 92. Then convert logs 92 to a logarithm in base 3. Round to the n
2.810; log3 55.2
2.810; log3 21.903
1.964, log3 55.2
4.522; log3 21.903
Russell has been offered positions by two cable companies. The first company pays a salary of $17,000 plus a commission of $20 for each cable package sold. The second pays a salary of $14,300 plus a commission of $30 for each cable package sold. How many cable packages would need to be sold to make the total pay the same?
Russell has to sell 270 cable packages to make the total pay of both the companies as same.
Suppose that Russell sells x cable packages such that the total pay of both the companies is the same.
Then the revenue Russell would make at the first company is $17000+20x
And, the revenue Russell would make at the second company is
$14300+30x
Since, the above two values are equal
so, 17000+20x=14300+30x
⇒17000-14300=30x-20x
⇒10x=2700
⇒x=270
The above problems are called mathematical modelling.
Mathematical modelling is the process of locating such equations to explain actual occurrences.
These formulae are referred to as mathematical models together with the definitions given to the variables.
Therefore, Russell has to sell 270 cable packages to make the total pay of both the companies as same.
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Which graph represents a reflection of f(x) = One-third(9)x across the x-axis?
On a coordinate plane, an exponential function approaches y = 0 in quadrant 2 and increases into quadrant 1. It goes through (1, 3) and increases to (1.25, 7).
On a coordinate plane, an exponential function approaches y = 0 in quadrant 1 and increases in quadrant 2. It goes through (negative 1, 3) and (negative 1.25, 7).
On a coordinate plane, an exponential function approaches y = 0 in quadrant 3 and decreases into quadrant 4. It goes through (1, negative 3) and (1.25, negative 7).
On a coordinate plane, an exponential function approaches y = 0 in quadrant 4 and decreases into quadrant 3. It goes through (negative 1, negative 3) and (negative 1.25, negative 7).
Using translation concepts, the graph that represents a reflection of [tex]f(x) = \frac{1}{3}(9)^x[/tex] across the x-axis is:
On a coordinate plane, an exponential function approaches y = 0 in quadrant 3 and decreases into quadrant 4. It goes through (1, - 3) and (1.25, -7).
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
In this problem, the function is:
[tex]f(x) = \frac{1}{3}(9)^x[/tex]
Which approaches y = 0 in quadrant 2 and increases into quadrant 1. For the reflection over the x-axis, the function assumes inverse(negative) values, that is, quadrant 2 -> quadrant 3 and then quadrant 1 -> quadrant 4, hence the correct statement is:
On a coordinate plane, an exponential function approaches y = 0 in quadrant 3 and decreases into quadrant 4. It goes through (1, - 3) and (1.25, -7).
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The graph which represents a reflection of f(x) = One-tenth(10)x across the y-axis is:
B. On a coordinate plane, an exponential function decreases from quadrant 2 to quadrant 1 and approaches y = 0 in quadrant 1. It goes through (negative 1, 1).
Coordinate Plane
This refers to the two-dimensional surface which is made up of two number lines, x and y.
With this in mind, we can see that from the complete text, we can see that the given graph on the function of x on the y-axis is on a coordinate plane.
Therefore, the correct answer is option B
If an investor invests $24,000 into two bonds, one that pays 4% in simple interest, and the other paying 2% simple
interest, and the investor earns $700 annual interest, how much was invested in each account?
Round your answers to the nearest dollar.
2% bond: $
4% bond: $
Answers:
2% bond: $11000
4% bond: $13000
========================================================
Explanation:
x = amount invested in the 4% bond
y = amount invested in the 2% bond
Amounts are in dollars
The two amounts add to $24,000 so
x+y = 24000
y = -x+24000 is one equation to set up
0.04x = interest earned from the 4% bond
0.02y = interest earned from the 2% bond
0.04x+0.02y = total interest earned = $700
0.04x+0.02y = 700 is another equation to set up
------------
The system of equations is
[tex]\begin{cases}y = -x+24000\\0.04x+0.02y = 700\end{cases}[/tex]
Apply substitution. Solve for x.
0.04x+0.02y = 700
0.04x+0.02(-x+24000) = 700
0.04x-0.02x+480 = 700
0.02x= 700-480
0.02x= 220
x= 220/(0.02)
x = 11000
Use this to find y
y = -x+24000
y = -11000+24000
y = 13000
D
4
3
2
1
-5 -4 -3 -2 -1 0
1
2
GO
-4
-5
A
1
2
3 4 5 Match the graph with its equation
This graph represents the equation y = -3
Need help with this geometry question
Answer: 10 inches
Step-by-step explanation:
Diagonals of a parallelogram bisect each other, so the top of the jack is 5(2)=10 inches off the ground.
Which of the following linear equations passes through points (-1,5) and (1,-5)?
Y=-5x
Y=5x+10
Y=-2x+3
Answer:
y = -5x
Step-by-step explanation:
gradient = delta y / delta x
gradient = -10 / 2
gradient = -5
y = mx + b
5 = -5(-1) + b
5 = 5 + b
b = 0
y = -5x
A rug is in the shape of a square. It measures 18 feet on each side. What is its perimeter?
Answer:
72ft²
Step-by-step explanation:
a square has 4 equal sides, when each one is 18ft, the total perimeter will be 18×4=72ft²
Hii!
_____________________________________________________
[tex]\stackrel\star{\rightsquigarrow\circ\boldsymbol{\underbrace{Answer}\circ\leftharpoonup}}[/tex]
Perimeter of the rug = 72 ft
[tex]\stackrel\star{\rightsquigarrow\circ\boldsymbol{\underbrace{Explanation}\circ\leftharpoonup}}}[/tex]
[tex]\bullet[/tex] Let's work out the perimeter
[tex]\twoheadrightarrow\sf P=4a[/tex] a=length of one side
[tex]\bullet[/tex] Stick in the values
[tex]\twoheadrightarrow\sf P=4\cdot18[/tex]
[tex]\bullet[/tex] Multiply
[tex]\twoheadrightarrow\sf P=72ft[/tex]
--
Hope that this helped! Best wishes.
[tex]\stackrel\star{\textsl{Reach far. Aim high. Dream big.}}[/tex]
--
What is the proper ordering (from least to greatest) of the
following numbers?
1.0.32
2.0.32%
3.3.2%
4. 3299
Answer:
.0032 .032 .32 3299
Step-by-step explanation:
0.32% =.0032
3.2% = .032
.32
3299
Simplify -2ab^3 (5a-4a^2 + 6ab^2 - 4b). ?
Answer:
10a^2b^3−8a^3b^3+12a^2b^5−8ab^4
Step-by-step explanation:
find the value of x y and z?
Answer:
Step-by-step explanation:
Solve for x in the triangle. Round your answer to the nearest tenth.
14
x
68
X
Answer:
x=15.1
Step-by-step explanation:
Side definitionsIn a right triangle, the side across from the right angle is always the hypotenuse.
The other two sides are termed "legs".
Once one of the other two angles is chosen as the angle to work from, then the two legs can be defined as the "opposite" and the "adjacent"
The leg touching the angle is the "adjacent" leg (or adjacent side), and the leg across from the angle is the "opposite" leg (or opposite side).
Trigonometric function definitions[tex]\sin(\theta)=\dfrac{\text{opposite side}}{\text{hypotenuse}}[/tex]
[tex]\cos(\theta)=\dfrac{\text{adjacent side}}{\text{hypotenuse}}[/tex]
[tex]\tan(\theta)=\dfrac{\text{opposite side}}{\text{adjacent side}}[/tex]
In this situation, the given angle is in the bottom right. A value is given for the side opposite the given angle, and the requested value is on the hypotenuse.
So, the two sides of interest are the "opposite" and the "hypotenuse". The trigonometric function that relates these two sides is the sine function.
Calculating x[tex]\sin(\theta)=\dfrac{\text{opposite side}}{\text{hypotenuse}}[/tex]
[tex]\sin(68^o)=\dfrac{(14)}{(x)}[/tex]
Evaluating the sine function in a calculator (in degree mode):
[tex]0.9271838546...=\dfrac{14}{x}[/tex]
Multiply both sides by x:
[tex](0.9271838546...)x=\left (\dfrac{14}{x} \right)x[/tex]
[tex](0.9271838546...)x=14[/tex]
Divide both sides by the decimal number:
[tex]\left (\dfrac{(0.9271838546...)x}{0.9271838546...} \right)=\dfrac{14}{0.9271838546...}[/tex]
[tex]x=15.0994864...[/tex]
Rounded to the nearest tenth, x=15.1
What is the range of the function represented by the following graph?
*
1 point
Captionless Image
A. all real numbers greater than 4
B. all real numbers less than - 1
C. all real numbers greater than - 6
D. all real numbers less than - 4
Answer:
C the prove is right there on the graph
Answer:
C
Step-by-step explanation:
The graph clearly shows that all the numbers are greater than -6
how to evaluate 16/81 1/2
An expression is defined as a set of numbers, variables, and mathematical operations. The value of (16/81)^(1/2) is 4/9.
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
The value of the given expression (16/81)^(1/2) can be calculated as shown below,
[tex](\dfrac{16}{81})^{\frac12}\\\\=\sqrt{\dfrac{16}{81}}\\\\= \dfrac49[/tex]
Hence, the value of (16/81)^(1/2) is 4/9.
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Answer:
★The square root of 16/81 = 4/9.
Reuben rented a truck for one day. There was a base fee of $14.95, and there was an additional charge of 80 cents for each mile driven. Reuben had to pay
$135.75 when he returned the truck. For how many miles did he drive the truck?
Answer:
hczgdjatulsfulsitsfisfula7tl7roa7pts
Solve for x : 2/5x -9 < 3/5x+3
X < 60
X > -60
-x < -60
-x < 60
Answer:
x>-60
Step-by-step explanation:
Combine multiplied terms into a single fraction
2/5x - 9 < 3/5x + 3
2x/5 - 9 < 3/5x + 3
Find common denominator
2x/5 - 9 < 3/5x + 3
2x/5 + 5(-9)/5 < 3/5x + 3
Combine fractions with the common denominator
2x + 5(-9)/5 < 3/5 + 3
I HOPE YOU GOT THE ANSWER JUST SIMPLIFY IT (2x + 5(-9)/5 < 3/5 + 3) AND YOU WILL GET THE ANSWER YOURSELF AS I HAVE GIVEN ABOVE PLS MARK ME AS THE BRAINLILEST IF YOU LIKE TO AND MY ANSWER HELPED YOU:)
Answer:
[tex]\boxed {x > -60}[/tex]
Step-by-step explanation:
2/5x - 9 < 3/5x + 3
-1/5x < 12
x > -12 x 5
x > -60
What is the product?
2 3
5 9 -1 -7
11 5 -3
10 15 20
45 -5 -35
55
10
4 2
55
7
14
25 -15
45 -1 -7
315
+7 9
CO
8
9
4 1-2
Answer:
A.
Step-by-step explanation:
Hello, this is what we call matrix. multiplication matrix to be precised.
so it is;
5×2=10
5×3=15
5×4=20
5×9=45
5×-1= -5.
5×-7= -35
5×11=55
5×5=25
5×-3= -15.
i hope you understand. That is matrix for you but it has different categories
A paint mix uses red and white paintin a ratio of 1:12.
a) How much white paint will be needed to mix with 1.4
litres of red paint ?
b) Ifatotalof15.5litresofpaintismixed,calculate
the amount of white paint and the amount of red paint used. Give your answers to the nearest 0.1 litre.
Answer:
(a).16.8 litres
(b).red-1.2 litres
white-14.3 litres
The scale on a map shows that 200 miles is represented by 5 inches on a map. Which proportion can be used to find the distance on the map, x, that represents 50 miles? StartFraction 5 over 200 EndFraction = StartFraction x over 50 EndFraction StartFraction 200 over 5 EndFraction = StartFraction x over 50 EndFraction StartFraction 50 over 200 EndFraction = StartFraction 5 over x EndFraction StartFraction 5 over 50 EndFraction = StartFraction x over 200 EndFraction
The proportion can be used to find the distance on the map (x) that represents 50 miles will be x/50 = 5 / 200. Then the correct option is A.
What are ratio and proportion?A ratio is a collection of ordered integers a and b represented as a/b, with b never equaling zero. A proportionate expression is one in which two items are equal.
The scale on a map shows that 200 miles is represented by 5 inches on a map.
Then the proportion can be used to find the distance on the map (x) that represents 50 miles will be
x/50 = 5 / 200
Then the correct option is A.
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Please help with this certain math problem
Answer: For this real-valued function;
[tex]fog = 2\sqrt{x-1} + 1\\ Domain = [1, )[/tex]
Step-by-step explanation:
COMPOSITE FUNCTIONIf f and g are functions, then the composite function or composition, of g and f is defined by
[tex]( f o g ) (x) = f(g(x))[/tex]
Given the functions [tex]f(x)=2x+1[/tex] , [tex]g(x)=\sqrt{x-1}[/tex],
Now composition for this;
[tex]fog = f(g(x))f(g(x)) = f(\sqrt{x-1} )[/tex]
[tex]f(\sqrt{x-1})[/tex]means we are to interchange variable x in [tex]f(x)[/tex] with the function [tex]\sqrt{x-1}[/tex]
[tex]f(\sqrt{x-1}) = 2(\sqrt{x-1})+1f(\sqrt{x+1}) = 2(\sqrt{x-1})+1fog = 2(\sqrt{x-1})+1[/tex]
The function inside the square root, x-1, must be more significant than or equal to zero (x-10), for the function to exist on any real-valued function.
[tex]if, x-1 \geq 0\\x\geq 0+1\\x \geq 1[/tex]
As a result, the range of the variable x must only include values that are larger than or equal to 1.
Hence, Domain = [1, )
DOMAIN = The domain of [tex]fog[/tex] is the set of all numbers [tex]x[/tex] in the domain of [tex]g[/tex] such that [tex]g(x)[/tex] is in the domain of [tex]f[/tex].Learn more about Composition and Domain here; https://brainly.com/question/6390405
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for the function f(x)=5(x+2) find f (2)
Answer:
20
Step-by-step explanation:
To calculate f(2), just replace x in the equation of f(x) with 2:
[tex]f(x) = 5(x + 2)\\\\f(2) = 5(2+2)\\\\f(2) = 5(4)\\\\f(2) = 20[/tex]
a + b = c
a + b + c =36
Given that a and b have the same value, work out the values of a,b and c
Answer:
a=9
b=9
c=18
Step-by-step explanation:
c(a+b)+a+b=36
2a+2b=36
a+b=18
c=18
2x+3y=9 -2x+2y=6 The y cordinate
Answer:
y = 3
Step-by-step explanation:
2x + 3y = 9
-2x + 2y = 6
We have to add these two equations which gives us 5y = 15. Now, if you divide by 5 on both sides you get y = 3.
Simplify that a chemical is mxing two acid solutions one of 45% concentration and the other of 55% cencetration which of the following concentration could not be obtained
47 49 53 59
The concentration could not be 59.
What is concentration?
The concentration of a solution is a measure of the amount of solute that has been dissolved in a given amount of solvent or solution.
Given:
solutions one of 45% concentration
other of 55% concentration.
The concentration should lie between 45 % to 55 %.
This is because it is not possible to get a mixture concentration which is lower than the lower concentrated acid or higher than the higher concentration acid.
Hence, Mixture concentration must be between 45% and 55%.
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look at the picture
5 hundreds minus 4 tens?*
Answer:
460
Step-by-step explanation:
4 tens is equivalent to 40, so 500-40 is = to 460.
Hope this helps! :D
hi brainly user! ૮₍ ˃ ⤙ ˂ ₎ა
⊱┈────────────────────────┈⊰
[tex]\large \bold {ANSWER}[/tex]
[tex]\large \boxed { \large \sf \green{460}}[/tex][tex]\large \bold {SOLUTION}[/tex]
5 hundreds is 5 multiplied by 100, so it equals 500. 4 tens is 4 times 10, so 40.
500 - 40 = 460So 5 hundreds minus 4 tens is 460.
Find f(g(x)) and g(f(x)).
f(x)=x²-2 and g(x)=√x+1
Answer:
1. x - 1
2. [tex]\sqrt{x^2-1}[/tex]
Step-by-step explanation:
[tex]f(g(x)) = \sqrt{x+1}^2 - 2\\ = x + 1 - 2\\= x - 1[/tex]
[tex]g(f(x)) =\sqrt{x^2-2+1}\\ = \sqrt{x^2-1}[/tex]
(-3,-2) (x,6) m=-8/5 solve for x
Answer:
-8
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
-8/5=(6-(-2))/(x-(-3))
-8/5=(6+2)/(x+3)
-8/5=8/(x+3)
5=-(x+3)
5=-x-3
-x=5+3
-x=8
x=-8
1532＝8467 4286＝5713 3059＝
Answer:
3059＝6940
Step-by-step explanation:
For the two examples given, we can see a consistency:
1 becomes 8 ; 8 becomes 1
5 becomes 4 ; 4 becomes 5
3 becomes 6 ; 6 becomes 3
2 becomes 7
because they are the only two digits left without a correlated pair, we can assume that 0 and 9 have the same relationship
So,
3 -> 6
0 -> 9
5 -> 4
9 -> 0
Meaning that 3059＝6940
hope this helps!! have a lovely day :)
