Answer:
The total number of marbles in the set is 107 marbles
Step-by-step explanation:
The parameters given are;
Let the size of the marbles be 1 unit
The marbles are arranged to form the equilateral triangle as follows;
1st row = 1 marble
2nd row = 2 marbles and so on so that the total number of marbles for an arithmetic series as follows;
Total number of marbles, t = 1 + 2 + 3 + ... + n
Therefore;
[tex]t = \dfrac{1 + n}{2} \times n[/tex]
Since there are 2 marbles left in forming the first equilateral triangle, we have the total number of marbles in the set, t₁, is given as follows;
[tex]t_1 = \dfrac{1 + n}{2} \times n + 2[/tex]
When the same marble set are arranged into a triangle in which each side has one more marble than in the first arrangement, there where 13 marble shortage, hence, the total number of marbles is given as follows;
[tex]t_1 = \dfrac{1 + (n+1)}{2} \times (n+1) -13[/tex]
We therefore have;
[tex]t_1 = \dfrac{1 + n}{2} \times n + 2 = \dfrac{1 + (n+1)}{2} \times (n+1) -13[/tex]
Which gives;
[tex]\dfrac{n^{2}+n+4}{2}=\dfrac{n^{2}+3\cdot n-24}{2}[/tex]
Therefore;
n² + n + 4 = n² + 3·n - 24
2·n = 24 + 4 = 28
n = 14
From which we have;
[tex]t_1 = \dfrac{1 + 14}{2} \times 14 + 2 = 107[/tex]
Therefore, the total number of marbles in the set, t₁ = 107 marbles.
The number of marbles in the set would be as follows:
[tex]107[/tex] marbles
Arrangement
Given that,
After arranging the marbles in an equilateral Δ, 2 marbles would be left
The size of marble being 1 unit,
So,
The first row of the equilateral Δ will consist of 1 marble,
while
The second row comprises of 2 marbles.
The process goes so on and on.
Therefore,
Total marbles [tex]t = 1 + 2 + 3 + ... + n[/tex]
Hence,
[tex]t = (1 + n)/2[/tex] × n
Because 2 marbles are extra,
[tex]t = (1 + n)/2[/tex] × n [tex]+ 2[/tex]
In case,
The same marble set are framed into a triangle, every side would contain 1 marble exceeding the previous one where 13 marbles would be felt short.
Thus,
Total marbles = [tex]\frac{1 + (n + 1)}{2}[/tex] × [tex](n + 1) - 13[/tex]
by putting the values, we get
[tex]n^2 + n + 4 = n^2 + 3n - 24\\2n = 24 + 4 = 28\\n = 14[/tex]
∵ Total marbles [tex]= (1+ 14)/2[/tex] × [tex]14 + 2[/tex]
[tex]= 107[/tex]
Thus, 107 marbles are the correct answer.
Learn more about "Probability" here:
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Based on an architectural drawing, a roof slopes to a drain
along the function represented in the table that defines the
edge of slope, where x is the horizontal distance in feet and
f(x) is the vertical distance in feet.
If the drain is at the minimum point, how far is it from the wall
defined by the y-axis?
0 feet
8 feet
80 feet
160 feet
Answer:
80 feet
Step-by-step explanation:
The smallest value of f(x) in the table is f(x) = 0. It occurs where x = 80.
Since x is the horizontal distance in feet from the wall, the minimum point (drain) is 80 feet from the wall.
Answer:
c
Step-by-step explanation:
edge2020
HELPPPPP
What are the coordinates of the hole in the graph of the function?
f(x)=x^2−3x−10/x−5
Enter your answer in the boxes.
Answer: If the function is: f(x) = (x^2−3x−10)/(x−5) The function has no holes.
If the function is f(x) = x^2−3x−10/x−5 then the hole is at x = 0 (the left side goes up, and the right side goes down, as the numerator is a negative number)
Step-by-step explanation:
I am not shure of what is the function, as you used no parentheses in it, so i will solve it for two different functions:
We have the function:
f(x) = (x^2−3x−10)/(x−5)
We want to find the "hole", this means that we want to find the value of x where the denominator is equal to zero.
If you look at the function, is easy to think that in x = 5 the denominator will be equal to zero, but we need to prove it.
First, we need to see if the numerator part is also zero when x = 5.
so
5^2 - 3*x - 10 = 25 -15 - 10 = 0
Ok, let's find the other root of the quadratic function:
x^2 - 3*x - 10 = (x - 5)*(x - b) = x^2 - (b + 5)*x + (b*5)
then we have: (b + 5) = 3 and b*5 = -10
then b = -2, this means that we can write the numerator part as:
x^2 - 3*x - 10 = (x - 5)*(x + 2)
then our function is:
f(x) = (x - 5)*(x + 2)/(x - 5) = x + 2
This function has no holes.
Now, if the function actually is:
f(x) = x^2−3x−10/x−5
Then we have an x on the denominator of the third term of the equation, this denominator is 0 only when x = 0
Carolyn is searching online for tickets to a concert. Two weeks ago, the cost was $50. Now the cost is $59. What is the percent increase
Answer: 18%
Step-by-step explanation: Percentage of 9 in 50=
9/50 × 100= 0.18×100= 18%
PLEASE RATE 5 STARS AND VOTE AS BRAINLIEST:)
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Write an equation for the line that is parallel to the given line and that passes through the given point. y= 1/2x - 8; (-6,-17)
Answer:
y = x/2 -14
Step-by-step explanation:
Since the lines are parallel, their slopes are equal
For the first line, we have
y = 0.5x -8
so comparing this with the standard form y = mx + c
Our m is the slope which is 0.5 here
kindly recall that 1/2 is same as 0.5
so the slope of the line we want to form also is 0.5
Now, we use the point slope form to find the equation of this new line
Mathematically that would be;
y-y1 = m(x-x1)
So;
y-(-17) = 0.5(x-(-6)
y + 17 = 0.5(x + 6)
y + 17 = 0.5x + 3
y = 0.5x + 3-17
y = 0.5x -14
or y = x/2 -14
What is the following product? Assume x greater-than-or-equal-to 0 and y greater-than-or-equal-to 0
StartRoot 5 x Superscript 8 Baseline y squared EndRoot times StartRoot 10 x cubed EndRoot times StartRoot 12 y EndRoot
3 x Superscript 5 Baseline y StartRoot 3 x y EndRoot
10 x Superscript 5 Baseline y StartRoot 6 x y EndRoot
3 x cubed y StartRoot 3 x squared y squared EndRoot
10 x cubed y StartRoot 6 x squared y squared EndRoot
[tex]answer \\ = 10 {x}^{5} y \sqrt{6xy} \\ please \: see \: the \: attached \: picture \: for \\ full \: solution \\ hope \: it \: helps[/tex]
The product of the given expression is;
B: 10x^(5) • y√(6xy)
Laws of ExponentsWe are given the expression;
√(5x^(8) • y²) × √(10x³) × √(12y)
Now, according to laws of exponents, we know that; √(a⁴) × √(b³) = √(a⁴ × b³)
Thus, our given expression will be;
√(5x^(8) • y²) × √(10x³) × √(12y) = √[(5x^(8) • y²) × (10x³) × (12y)]
Collecting like terms, we will have;√[(5x^(8) × 10x³) × (y² × 12y)]
This now gives;√(50x¹¹ × 12y³)
>> √(600x¹¹y³)
Now, further break down of this gives;
10x^(5) • y√(6xy)
Read more about Laws of exponents at; https://brainly.com/question/11761858
In the given figure, values of x and y, are 1. 40°, 25° 2. 30°, 40° 3. 30°, 20° 4. 40°, 35°
Answer:
1. 40°, 25°
Step-by-step explanation:
The sum of opposite angles of a quadrilateral inscribed in a circle is 180°.
2x + 4 + 4y - 4 = 180
x+ 10 + 5y + 5 = 180
2x + 4y = 180
x +5y + 15 = 180
x + 2y = 90
x + 5y = 165
x = 90 - 2y
x = 165 - 5y
90 - 2y = 165 - 5y
5y - 2y = 165 - 90
3y = 75
y = 25
x = 90- 2y = 90 - 2*25 = 40
x= 40, y = 25
Please I need help
With this question thank you for your help me
Answer:
Using CPCTC we can derive that WM = 8 and OL = 10.
4. Al restar 5 x ᶺ 2 – 8 x + 9 con – 9 + 16 x – 25 x ᶺ 2 se obtiene como resultado (Procedimiento)
Step-by-step explanation:
SE RESTAN ENTRE LOS NÚMEROS QUE TIENEN LA MISMA VARIAVLE.
[tex](5x^{2} + 25x^{2})[/tex] - (8x - 16x) + (9 + 9) = [tex]30x^{2}[/tex] - 24x + 18
What is the base of a triangle that has an area of 60 square centimeters and a height of 8 centimeters?
A 7.5 cm
B 30 cm
C 52 cm
D 15 cm
Answer:
I think its (A)
Step-by-step explanation:
To find the area you have to multiply (b*w)*h
and if the area is 60 you just have to divide by the height to get the base area.
60/8=7.5
Hope this helps :3
Jasmine is traveling at 45 miles per hour. At that same rate, how long will it take her to travel 135 miles?
1. 1/3 hours
2. 3 hours
3. 3.5 hours
4. 5 hours
Answer:the answer is 2 it will take jasmine 3hrs to travel 135 miles
Step-by-step explanation:
−38d−57≥−19d+76 i need this asap
Eduardo had 18 candies. 2/3 of the candies were butterscotch discs. How many were butterscotch discs?
Answer:
is 12
Step-by-step explanation:
2/3=18
18:3= 6
6 x 2=12
[tex]answer \\12 \\ solution \\ \\ \frac{2}{3} \times 18 \\ = 12 \\ \\ hope \: it \: helps \\ good \: luck \: on \: your \: assignment[/tex]
anyone can help me figure this out ?
Answer:
The inverse is 1/4x
Step-by-step explanation:
f(x) = 4x
y = 4x
Exchange x and y
x = 4y
Solve for y
Divide each side by 4
1/4x = 4y/4
1/4x = y
The inverse is 1/4x
Answer:
y=(1/4)*x
Step-by-step explanation:
to inverse set f(x)=4x
as y=4x
next, change places y and x
4y=x
now, solve for y
4y=x
y=(1/4)*x
Triangle P Q R is shown. Angle R P Q is 99 degrees and angle P Q R is 31 degrees. The length of Q R is 11. Determine the measures of all unknown angles and side lengths of ΔPQR. Round side lengths to the nearest hundredth.
Answer:
[tex]\angle PRQ = 50^\circ[/tex]
PR = 5.74 units and
PQ = 8.53 units
Step-by-step explanation:
We are given the following details:
[tex]\angle RPQ =99^\circ[/tex]
[tex]\angle PQR =31^\circ\\\text{Side QR} = 11\ units[/tex]
To find:
[tex]\angle PRQ =?\\Side\ PR = ?\\Side\ PQ = ?[/tex]
We know that the sum of all the angles of a triangle is equal to [tex]180^\circ[/tex]
i.e.
[tex]\angle PQR +\angle PRQ +\angle RPQ =180^\circ\\\Rightarrow 31^\circ +\angle PRQ +99^\circ =180^\circ\\\Rightarrow \angle PRQ = 180-130\\\Rightarrow \angle PRQ = 50^\circ[/tex]
To find the sides, we can use Sine rule:
As per Sine rule:
[tex]\dfrac{a}{sin A} =\dfrac{b}{sin B} =\dfrac{c}{sin C}[/tex]
Where a, b and c are the sides opposite to [tex]\angle A,\angle B,\angle C[/tex] respectively.
Using Sine rule in given triangle:
[tex]\dfrac{11}{sin 99} =\dfrac{b}{sin 31} =\dfrac{c}{sin 50}\\\\\text{Solving }\dfrac{11}{sin 99} =\dfrac{b}{sin 31} \\\Rightarrow b = \dfrac{11}{sin 99} \times sin31\\\Rightarrow b =5.74\ units\\\\\text{Now, Solving }\dfrac{11}{sin 99} =\dfrac{c}{sin 50} \\\Rightarrow c = \dfrac{11}{sin 99} \times sin50\\\Rightarrow c =8.53\ units[/tex]
So, sides are
PR = 5.74 units and
PQ = 8.53 units
Answer:
Answer:
PR = 5.74 units and
PQ = 8.53 units
Step-by-step explanation:
We are given the following details:
To find:
We know that the sum of all the angles of a triangle is equal to
i.e.
To find the sides, we can use Sine rule:
As per Sine rule:
Where a, b and c are the sides opposite to respectively.
Using Sine rule in given triangle:
So, sides are
PR = 5.74 units and
PQ = 8.53 units
Step-by-step explanation:
Investigate the relationship between the T-total and the T-number.
Answer:
feed me brainly points
Step-by-step explanation:
brainliest?
is (1,8) a solution of the equation 3x + 5 = y ?
A True
B False
Answer:
A.
Step-by-step explanation:
Plug it in:
3 + 5 = 8
TRUE
Solve for x in the diagram below.
3a
80°
2z
د 2
Answer:
[tex]x = 20[/tex]
Step-by-step explanation:
[tex]3x + 2x + 80 = 180 \\ 5x + 80 = 180 \\ 5x = 180 - 80 \\ 5x = 100 \\ \\ x = \frac{100}{5} \\ \\ x = 20[/tex]
Answer:
x=20
Step-by-step explanation:
The 3 angles are on a straight line together. Therefore, they are supplementary. This means they must add to 180 degrees.
Therefore,
3x+80+2x=180
Combine like terms by adding 3x and 2x
(3x+2x)+80=180
5x+80=180
We want to find out what x is. In order to do this, we have to get x by itself. Perform the opposite of what is being done to the equation. Keep in mind, everything done to one side, has to be done to the other.
80 is being added to 5x. The opposite of addition is subtraction, so subtract 80 from both sides.
5x+80-80=180-80
5x=180-80
5x=100
x is being multiplied by 5. The opposite of multiplication is division, so divide both sides by 5.
5x/5=100/5
x=100/5
x=20
x is equal to 20.
Which function is graphed on the right? y = 2x+3 – 2 y = 2x–3 + 2 y = 2x–2 + 3 y = 2x–2 – 3
Answer:
y=2x-2-3
Step-by-step explanation:
First you will need graphing paper. Go ahead and locate the y intercept on each of these equations. Then locate the slope. (y=mx+b). If the slope is positive count the amount of blocks up the slope's value is. And if negative count down. Then count to the right depending on the denominator. (2/1) You will make a triangle draw the line on the hypotenuse of the triangle. Then you have the line. You can also just use desmos.
The equation of the graphed function is [tex]y = 2^{x-2} + 3[/tex]
What are functions?Functions are used to represent equation, graphs and tables
The parent function of the graph is an exponential function represented by
[tex]y = 2^x[/tex]
First, the function is shifted 2 units right.
So, we have:
[tex]y = 2^{x - 2}[/tex]
Next, the function is shifted 3 units up.
This is represented as:
[tex]y = 2^{x - 2} + 3[/tex]
Hence, the equation of the graphed function is [tex]y = 2^{x-2} + 3[/tex]
Read more about exponential functions at:
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NO ONE HELPED ME WITH MY LAST QUESTION PLS HELP WITH THISSSS, I DONT WANNA GET A BAD GRADE AND I HAVE 2 MINUTES LEFTT!!
Answer:
Step 2.
-11/12 > -1.5
1.6 > 5/4
1 < 5/4
Step-by-step explanation:
Eval should have swapped the numerator and denominator of 4/9 when she replaced division by multiplication.
I dont understand B and C in this question so there are a deck of cards 1-10 i already got A right but B and C i dont understand
B: what is the probability of choosing a card that has a digit 1 on it
C: what is the probability that does not have a digit 1 on it? give both answers as a fraction here are the numbers to help
1 2 3 4 5 6 7 8 9 10
Answer:
see below
Step-by-step explanation:
1 2 3 4 5 6 7 8 9 10 = 10 cards
9 of them have 1 digit on them ( 10 has 2 digits)
P( 1 digit) = number with 1 digit) / total = 9/10
P( not have 1 digit)= number not with 1 digit) / total = 1/10
I'm in summer school and need help. The situation that is best modeled by a discrete graph is
the daily records of the distance of each hotel from home during a cross-country trip.
the height of a wave over time.
the speed of a motorcycle over the distance it travels.
the body temperature of an athlete during a workout.
Answer:
A. The daily records of the distance of each hotel from home during a cross country trip.
Step-by-step explanation:
A discreet graph is one that is composed of unconnected, "scattered" points. The best option is A because B,C and D would all be graphed to show the increase or decrease in values, (function) while the distances of the hotels are not something that you would have to measure!
Answer:
A
Step-by-step explanation:
Because I have big brain and also y’all know what edge is I got it correct
find the volume of prism
pls!! show how you got the volume
Answer:
7.5
Step-by-step explanation:
Add each number then divide at the end
The radius of a circle is 7.1 cm. Find the circumference to the nearest tenth.
Answer:44.61?
Step-by-step explanation:
which graph shows the line y=-3x+1? graph a graph b
The graph of y = - 3x + 1 has a slope of -3 and a y-intercept of 1
How to determine the graph?The equation is given as:
y = - 3x + 1
The above equation is a linear function
A linear function is represented as:
y = mx + c
Where m represents the slope and c represents the y-intercept
This means that the graph of y = - 3x + 1 has a slope of -3 and a y-intercept of 1
Read more about linear equations at:
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A flow chart has 4 boxes. The top box is labeled given and contains angle A is-congruent-to angle B, angle C is congruent to angle B. The second box is labeled symmetric property and contains angle B is-congruent-to angle C. The third box is labeled question mark and contains angle A is congruent to angle C. The fourth box is labeled definition of congruent to angle x and contains m angle A = m angle C. What is the missing justification? transitive property reflexive property symmetric property substitution property
Answer:
transitive property
Step-by-step explanation:
The transitive property tells you that ...
∠A ≅ ∠B and ∠B ≅ ∠C
means you can conclude ...
∠A ≅ ∠C . . . . transitive property of congruence
Answer:
transitive property
Step-by-step explanation:
on Edguenity quiz
Using the midpoint method (show your work), calculate the price elasticity of demand when the price of a barrel of gosum berries rises from $10 to $20. What kind of elasticity is this value that you computed for the price elasticity of demand and what does it mean for how demand will change based on a change in price within this price range?
Answer:
0.18
Step-by-step explanation:
Given that:
P₁ = $10, P₂ = $20
From the tables Q₁ = 900, Q₂ = 800
Using midpoint method:
Percentage change in quantity = [tex]\frac{Q_2-Q_1}{(Q_1+Q_2)/2} *100\%=\frac{800-900}{(900+800)/2}*100\%= -11.76\%\\[/tex]
Percentage change in price =
[tex]\frac{P_2-P_1}{(P_1+P_2)/2} *100\%=\frac{20-10}{(20+10)/2}*100\%= 66.67\%\\[/tex]
Price of elastic demand = Percentage change in quantity/ Percentage change in price = -11.76% / 66.67% = 0.18
The Price of elastic demand is positive because we took the absolute value and elasticity are always positive
Therefore since Price of elastic demand < 1, the demand is inelastic in this interval.
This means that, along the demand curve between $10 to $20, if the price changes by 1%, the quantity demanded will change by 0.18%. A change in the price will result in a smaller percentage change in the quantity demanded. For example, a 10% increase in the price will result in only a 1.8% decrease in quantity demanded and a 10% decrease in the price will result in only a 1.8% increase in the quantity demanded
Convert the fraction
103
7497
to an equivalent percentage.
Report your answer accurate to one decimal place.
Answer:
1.4
Step-by-step explanation:
We need to convert 103/7497 into a percentage.
All we have to do is multiply the fraction by 100:
103/7497 * 100 = 1.37
To one decimal place, the equivalent fraction is 1.4
Please help! Correct answer only, please!
Given matrix A and B both have dimensions 2 x 2 and are the inverse of one another what should be the following product?
A · B
A.
B.
C.
D.
Answer:
B)
Step-by-step explanation:
If two square matrix, with same dimensions, are inverse of one another, their product will always be the identity matrix with the same dimensions.
The matrix A and B are 2x2, so the result of the product A * B is a 2x2 identity matrix, that is represented as follows:
I = [1 0 ; 0 1]
(First line: 1 0, second line: 0 1)
So the correct option is B)
This is a continuous set of points in the coordinate plane. It can be, but is not always, straight.
Answer:
Linear. While all linear equations produce straight lines when graphed, not all linear equations produce linear functions. In order to be a linear function, a graph must be both linear (a straight line) and a function (matching each x-value to only one y-value).
Solve the proportion 4/x=8/(x-3)
Answer:
x=-3
Step-by-step explanation:
4/x=8/(x-3)
We can solve this using cross products
4 ( x-3) = 8x
Distribute
4x -12 = 8x
Subtract 4x from each side
4x-4x-12 = 8x-12-4x
-12 =4x
Divide each side by 4
-12/4 = 4x/4
-3 =x
Answer:
X=-3
Step-by-step explanation:
Solve it like any other two step equation.
But first we have to have x on its own to get what the x value is