Taking into account the definition of a system of linear equations, 240 stamps are in Will’s collection.
System of linear equationsA system of linear equations is a set of two or more equations of the first degree, in which two or more unknowns are related.
Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied. That is to say, the values of the unknowns must be sought, with which when replacing, they must give the solution proposed in both equations.
Number of stamps that are in Will’s collectionIn this case, a system of linear equations must be proposed taking into account that:
W: Number of stamps that are in Will’s collectionC: Number of stamps that are in Carlton’s collectionA: Number of stamps that are in Ashley’s collectionOn the other hand, you know that:
Ashley has 30 stamps and she has a third as many as Carlton has → A= [tex]\frac{1}{3}[/tex]C → 30= [tex]\frac{1}{3}[/tex]CWill has twice as many stamps in his collection as Carlton and Ashley do in their collections combined. → W= 2(C + A)So, the system of equations to be solved is
[tex]\left \{ {{30=\frac{1}{3}C } \atop {W=2(C+30)}} \right.[/tex]
There are several methods to solve a system of equations, it is decided to solve it using the substitution method, which consists of clearing one of the two variables in one of the equations of the system and substituting its value in the other equation.
Solving the first equation:
30= [tex]\frac{1}{3}[/tex]C
30÷[tex]\frac{1}{3}[/tex]= C
90= C
Substituting the value in the second equation:
W= 2(90 + 30)
W= 2×120
W=240
Finally, 240 stamps are in Will’s collection.
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At a concert for the band Algal Rhythms, 75% of the tickets were sold at the full price of 30. The remaining 25% of tickets were sold at a discounted price of $10. What was the average selling price of a ticket at the Algal Rhythms concert? Express your answer in dollars, rounded to the nearest cent.
Answer:
The average price of a ticket is $25.
Step-by-step explanation:
Lets us say 100% = 1
0.75 x 30 + 0.25 x 10 = 25
PLease helppppppppp!!!
Answer:
437.068 28.019
Step-by-step explanation:
Not sure how to explain this one....it is what it is
7 ones = 7
3 tens = 30
4 hundreds = 400 added = 437
No tenths = 0
6 hudredths = .06
8 thousandths = .008 added to = 437.068
280 tenths = 280 * 1/10 = 28
19 thousandths = .019 summed = 28.019
The base of each triangle varies inversely with the height. what are the possible base is 14 and height of a second triangle if the first triangle's base is 14 and its height 6 is ?
The possible base and height of a second triangle are:
B = 5 H = 12What is a triangle?A triangle is a three-edged polygon with three vertices. It is a fundamental shape in geometry. Triangle ABC denotes a triangle with vertices A, B, and C. In Euclidean geometry, any three non-collinear points define a unique triangle and, by extension, a unique plane.To find the base and height of the triangle:
First, we must find the constant of variation (k).
The problem indicates that the base of each triangle varies inversely with the height.
So, this can be represented as below:
B = k/H
B is the base of the triangle (B=10). H is the height of the triangle (H=6). k is the constant of variation.When we clear "k", we obtain:
B = k/H k = BxH k = 10x6 k = 60Now, we have:
B = 60/HWe can give any value to "H" and you will obtain the base of the second triangle.
If H = 12, then:
B = 60/H B = 60/12 B = 5Therefore, the possible base and height of a second triangle are:
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19/23 x 50
HELP ME Giving BRAINLIEST ALSO 30 POINTS
[tex]\boldsymbol{\sf{\dfrac{19}{23}\times50 }}[/tex]
We express 19/25 x 53, as a single fraction as follows:
[tex]\boldsymbol{\sf{\dfrac{19\times50}{23} \ \ \longmapsto \ \ \ [Multiply] }}[/tex]
[tex]\boldsymbol{\sf{\dfrac{950}{23} }}[/tex]
Like the fraction 950/23, it cannot be further simplified, so it remains that way, therefore
[tex]\red{\boxed{\boldsymbol{\sf{Answer \ \ \longmapsto \ \ \ \frac{950}{23} }}}}[/tex]
Membership to two different clubs are represented by the equations below. The x-value represents the number of months dues are paid. The y-value represents the total cost of dues over time. How many months will it take for the membership of both clubs to be the same?
y = 3x − 5
4x − 3y = 5
2 months
5 months
3 months
4 months
It would take 2 months for the membership of both clubs to be the same
What is an equation?An equation is an expression that shows the relationship between two numbers and variables.
The standard form of a linear equation is:
y = mx + b
Where m is the rate of change and b is the y intercept
Let y represent the total cost of dues over x months, hence given that:
y = 3x - 5 (1)
Also:
4x - 3y = 5
y = (4x - 5)/3 (2)
For the membership of both clubs to be the same:
3x - 5 = (4x - 5)/3
9x - 15 = 4x - 5
x = 2
It would take 2 months for the membership of both clubs to be the same
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2(x+1)=10 what's x please best example
Answer:
x = 4
Step-by-step explanation:
1.Distribute
2. Subtract 2 from both sides
3. Simplify
4. Divide both sides by same factor
5. Simplify
x = 4
Answer: 4
Step-by-step explanation:
We have to try getting x by itself to solve for it. Since we have two sides that are equal to each other, we can add, subtract, multiply, and divide anything on both sides to try to isolate x.
[tex]2(x+1)=10[/tex]
We can first divide the left side and the right side by 2. This would remove the 2 being multiplied on the outside.
[tex]\frac{2(x+1)}{2}=\frac{10}{2}\\x+1=10\div 2\\x+1=5[/tex]
Now, we have a + 1 on the left side that we need to remove to get x by itself. If we are adding something, we can remove that by subtracting the same thing. Hence, we can subtract 1 from both sides to remove the + 1.
[tex]x+1=5\\x+1-1=5-1\\x+0=4\\x=4[/tex]
After all that simplifying, we get that x equals 4.
Let a and b be 3 by 3 matrices with det (a) = 3 and det (b) = 5. find the value of det(ab).
If the value of determinant a is 3, determinant b is 5 then the value of determinant ab is 15.
Given that the value of determinant a is 3, determinant b is 5.
We are required to find the value of determinant ab.
Determinant of a matrix is the scalar value computed for a given square matrix.It means the matrix which is not square does not have a determinant value. It is denoted by IAI.
We know that,
IaI*IbI=IabI
So we have to just put the values in the above formula to get the determinant of ab.
IabI=3*5
=15
Hence if the value of determinant a is 3, determinant b is 5 then the value of determinant ab is 15.
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Solve for n.
7 + 2n
||
=
submit
Answer:
2
Step-by-step explanation:
7+2n = 11
2n = 11-7
2n = 4
n = 4/2
therefore n = 2
Alice and Bob are currently 1000 feet apart and are both running directly
toward each other at a constant speed of 10 feet per second. A bird starts in the same
position as Alice and flies directly toward Bob at a speed of 20 feet per second. When the
bird reaches Bob, it turns around immediately and starts flying toward Alice at the same
speed, turning around immediately when it reaches Alice, and repeating this procedure until
Alice and Bob meet. When Alice and Bob finally meet, what is the total distance that the
bird has flown, in feet?
The distance the bird has flown by the time Alice and Bob meet is 40 feet.
What is the distance?Distance is a measurement of time and speed.
The distance equals speed multiplied by time.
Data and Calculations:Distance between Alice and Bob = 1,000 feet
Distance between the bird and Bob = 1,000 feet
Speed of Alice and Bob = 10 feet per second, respectively
The combined speed of Alice and Bob = 20 feet per second
Since the two are running directly toward each other, the distance each will cover at the meeting point is 50 feet (1,000/20)
The time covered at the meeting point = 20 seconds (1,000/50)
Speed of the bird = 20 feet per second
The distance covered by the bird towards Bob at their meeting point is 40 feet (20 feet x 20 seconds)
Thus, the total distance covered by the bird at the meeting point is 40 feet.
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8x + 2y =16
standard form
1) m=
2 y - intercept x - intercept
Answer:
m=-4
y-intercept=8
x-intercept=2
Step-by-step explanation:
Please see attachment.
y-intercept=8
The y-intercept is where the line crosses the y-axis.
x-intercept=2
The x-intercept is where the line crosses the x-axis.
m=-4
If you do not know how to find slope by looking at graph, use slope formula.
(y2-y1)/(x2-x1)
Choose 2 points. You may use the x and y intercepts.
(2,0) and (0,8)
(8-0)/(0-2)=8/-2=-4
Hope this helps!
A bag contains 4 black tiles, 5 white tiles, and 6 blue tiles. event a is defined as drawing a black tile from the bag on the first draw, and event b is defined as drawing a white tile on the second draw. if two tiles are drawn from the bag, one after the other without replacement, what is p(a and b) expressed in simplest form?
P(A and B) expressed in the simplest form is (B) 2/21.
What is probability?Probability is an area of mathematics that deals with numerical descriptions of how probable an event is to occur or how likely a statement is to be true. The probability of an event is a number between 0 and 1, where 0 denotes the event's impossibility and 1 represents certainty.To express P(A and B) in the simplest form:
P(A and B) means that you need to multiply the two probabilities together since both A and B need to happen. The probability of drawing a black tile on the first draw is 4/15 since there are 15 total tiles and 4 of those are black. On the second draw, the bag is already missing a tile, and there are therefore 14 tiles remaining. For the second one, the probability is 5/14, since there are 14 total tiles and 5 of them are white. Multiplying these two together, we get 4/15 × 5/14 = 20 / 210 = 2/21.Therefore, P(A and B) expressed in the simplest form is (B) 2/21.
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The complete question is given below:
A bag contains 4 black tiles, 5 white tiles, and 6 blue tiles. Event A is defined as drawing a black tile from the bag on the first draw, and event B is defined as drawing a white tile on the second draw.
If two tiles are drawn from the bag, one after the other without replacement, what is P(A and B) expressed in the simplest form?
A. 4/45
B. 2/21
C. 4/15
D. 5/14
