To solve for 'x' and the length of segment AB, we use the equation AB + BC = AC, which simplifies to (3x - 3) + (4x + 8) = 75, revealing that 'x' = 10 and the length of AB is 27 units.
Explanation:The question requires us to find the value of 'x' and the length of segment AB given that B is between A and C, with AB = 3x – 3, BC = 4x + 8, and the total length AC = 75. To solve this, we set up an equation using the given lengths of segments AB and BC to equal the total length AC. This gives us the equation AB + BC = AC, which simplifies to (3x – 3) + (4x + 8) = 75.
First, we simplify the equation: 3x + 4x – 3 + 8 = 75, which reduces to 7x + 5 = 75. Subtracting 5 from both sides gives us 7x = 70. Dividing both sides by 7, we find that x = 10. With the value of x, we can find AB by substituting x back into its equation: AB = 3(10) – 3 = 30 – 3 = 27.
Therefore, the value of 'x' is 10 and the length of segment AB is 27 units.
There are 5 red marbles four blue marbles and three yellow marbles in a bag what is the probability of a blue marble being randomly chosen
log(-2a+9)=log(7-4a)
please helpp!!
1. the temperature in Montreal was -8C in New York the temperature was 11C. How many degrees warmer was the temperature in New York?
2. mike deposited $200 in to his bank account. He then wrote checks for $20 and $30. The he deposited $40 dollars more. Which of the following represents the changes in the value of mike's account?
The number of tickets sold for a school event is 330. Let a represent the number of adult tickets sold and s represent the number of student tickets sold. The cost of a student ticket is $6 and the cost of an adult ticket is $10. In total, $2380 was taken in from ticket sales. Write a linear system to represent the information
The linear system is 6s+10a = 2380.
s represents student tickets and a represents adult tickets, and the total amount collected from the tickets is $2380.
What is the linear and non-linear system?Linear means something associated with a line. All the linear equations are used to construct a line. A non-linear equation is such that does no longer form a direct line. It looks as if a curve in a graph and has a variable slope price.
How do you realize a system is linear?If the connection between y and x is linear (instantly line) and crossing through starting place then the system is linear. If you locate any time t at which the system is not linear then the system is non-linear.
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Final answer:
To represent the ticket sales information as a linear system, we use two equations: a + s = 330 for the total number of tickets, and 10a + 6s = 2380 for the total revenue from ticket sales.
Explanation:
The question involves writing a linear system of equations based on the information provided about ticket sales for a school event. Given that 330 tickets were sold in total, comprising adult tickets (a) and student tickets (s), and that the total revenue from these tickets was $2380, with student tickets priced at $6 each and adult tickets at $10 each, we can represent this scenario with two equations.
The first equation represents the total number of tickets: a + s = 330.
The second equation represents the total revenue: 10a + 6s = 2380.
This linear system can be solved to find the values of a and s, which would give us the number of adult and student tickets sold, respectively.
The coordinate grid below shows triangle ABC and it's image after translation, triangle A'B'C':
Which of the following completes the rule for this translation, (x,y)>(x+4,__)?
y+4
y+2
y-4
y-2
Answer:
First option : y+4Step-by-step explanation:
Given triangle ABC and a translated triangle A'B'C'.
Coordinates of triangle ABC are
A(-1,-1)
B(-3,-3) and
C(2,-2).
Coordinates of triangle A'B'C' are
A'(3,3)
B'(1,1)
C'(6,2).
Let us check the translation is being applied there.
A(-1,-1) ---> A'(3,3)
We can see that A(-1,-1) ----> A'(-1+4, -1+4) to get (3,3).
Therefore, (x,y) ---> (x+4,y+4) rule is being applied there to get the translated triangle A'B'C'.
So, the correct option is first option:
y+4Molly walked 3.45 miles on a hike. Her sister walked 1.23 miles. Her brother walked 0.85 miles. How much farther did Molly walk than her brother and sister combined? 0.38 miles 1.37 miles 2.22 miles 5.53 miles
The distance walked together, is the sum of their distances.
Molly walked 1.37 miles farther than her brother and sister
The given parameters are:
[tex]\mathbf{Molly = 3.45\ miles}[/tex]
[tex]\mathbf{Sister = 1.23\ miles}[/tex]
[tex]\mathbf{Brother = 0.85\ miles}[/tex]
The combined distance walked by her brother and her sister is:
[tex]\mathbf{Both = Sister + Brother}[/tex]
Substitute known values
[tex]\mathbf{Both =1.23\ miles + 0.85\ miles}[/tex]
Evaluate like terms
[tex]\mathbf{Both =2.08\ miles}[/tex]
The distance Molly walked farther is calculated as follows:
[tex]\mathbf{Farther = Molly - Both}[/tex]
Substitute known values
[tex]\mathbf{Farther = 3.45\ miles - 2.08\ miles}[/tex]
Evaluate like terms
[tex]\mathbf{Farther = 1.37\ miles}[/tex]
Hence, Molly walked 1.37 miles farther than her brother and sister combined
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Calculate δe, if q= 0.769 kj and w= -860 j .
The change in internal energy (δe) of the system, calculated using the first law of thermodynamics, and considering that the heat and work quantities are converted to the same unit, is 1629 J.
Explanation:The query you've presented seems to be about the first law of thermodynamics, which states that the change in internal energy (ΔE or in your notation, δe) of a system is equal to the heat (q) added to the system minus the work (w) done by the system. Both heat and work quantities need to be in the same units for this calculation, whereas your values are given in different units: kJ for heat and J for work. To facilitate this calculation, let's first convert the heat quantity from kJ to J (1 kJ equals 1000 J).
So, q = 0.769 kJ = 0.769 * 1000 J = 769 J.
Given, w = -860 J.
Now, according to the first law of thermodynamics, δe = q - w.
Substituting the given values, we get δe = 769 J - (-860 J) = 769 J + 860 J = 1629 J.
Therefore, the change in internal energy, δe, is 1629 J.
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What is the value of x?
Enter your answer in the box.
Answer:
x = 9 and y = 5
Step-by-step explanation:
From the given figure :
In ΔLNM ,
LN = NM = LM
This shows that all the sides of the triangle are given to be equal.
And the triangle whose all sides are equal is called equilateral triangle and in an equilateral triangle the measure of its each angle is 60°
⇒ ∠L = ∠N = ∠M = 60°
Now, ∠N = 60°
⇒ 7x - 3 = 60
⇒ 7x = 63
⇒ x = 9
Also, ∠M = 60°
⇒ 11y + 5 = 60
⇒ 11y = 55
⇒ y = 5
Answer: x=9
Step-by-step explanation:
i did the test and got it right lol
Mariah has been hired as a receptionist. She is paid a flat rate of $225 each week and earns an additional $11.25 for every hour that she works. If her goal is to make $675 in one week, how many hours must Mariah work? 36 40 60 72
If a+bi is a zero of a function and the coefficients of the polynomial are real, what will be the other complex zero of the function?
1. -a + bi
2. a - bi
3. -a - bi
4. a
How many ways can six friends be arranged around a circular dinner table?
The surface area of a cone is given by the formula
S = πl + πr2. Solve the formula for l.
Answer:
l = (S - πr²) / π
Step-by-step explanation:
The problem gives us the formula for the surface area of a cone S, we will solve the formula for l.
The formula is
S = πl + πr²
If we take the πr² to the other side, we get:
S - πr² = πl
Now we divide by π, and we get:
(S - πr²) / π = l
Therefore solving for l, we get that
l = (S - πr²) / π.
Can I get some help on these please ?
What z-score values form the boundaries for the middle 60% of a normal distribution??
Mary has a total of 23 coins made up of nickels and quarters that made a sum of $3.15. How many more nickels than quarters does she have?
A) 10
B) 3
C) 8
D) 7
E) none of these
Find the GCF of the following monomials.
-50m⁴ n⁷ and 40m² n¹⁰
Answer: [tex]10\ m^2\ n^7[/tex]
Step-by-step explanation:
The given monomials : [tex]-50m^4n^7\text{ and }40 m^2 n^{10}[/tex]
The prime factorization of coefficients :-
[tex]50=5\times5\times2\\\\40=5\times2\times2[/tex]
GCF(50, 40)=[tex]2\times5=10[/tex]
The greatest common degree of m is 2
The greatest common degree of n is 7
So , the GCF of the given monomilas will be :-
[tex]10\ m^2\ n^7[/tex]
Line segments JK and JL in the xy-coordinate plane both have a common endpoint J (-4,11) and midpoints at M1 (2,16) and M2 (-3,5). What's the distance between M1 and M2?
Answer:
12.08 units.
Step-by-step explanation:
We have been given that line segments JK and JL in the xy-coordinate plane both have a common endpoint J (-4,11) and midpoints at [tex]M_1 (2,16)[/tex] and [tex]M_2 (-3,5)[/tex].
To find the distance between [tex]M_1[/tex] and [tex]M_2[/tex] we will use distance formula.
[tex]\text{Distance}=\sqrt{(x_2-x_1)^{2}+(y_2-y_1)^{2}}[/tex]
[tex]x_2[/tex] and [tex]x_1[/tex] are x-coordinates of two points.
[tex]y_2[/tex] and [tex]y_1[/tex] are corresponding y-coordinates of two points.
Let [tex]M_2[/tex] our first point, then [tex]x_1=-3[/tex] and [tex]y_1=5[/tex].
Let [tex]M_1[/tex] will be our second point, then [tex]x_2=2[/tex] and [tex]y_2=16[/tex]
Upon substituting coordinates of point [tex]M_1[/tex] and [tex]M_2[/tex] in distance formula we will get,
[tex]\text{Distance}=\sqrt{(2--3)^{2}+(16-5)^{2}}[/tex]
[tex]\text{Distance}=\sqrt{(2+3)^{2}+(11)^{2}}[/tex]
[tex]\text{Distance}=\sqrt{(5)^{2}+(11)^{2}}[/tex]
[tex]\text{Distance}=\sqrt{25+121}[/tex]
[tex]\text{Distance}=\sqrt{146}[/tex]
[tex]\text{Distance}=12.0830459735945721\approx 12.08[/tex]
Therefore, distance between [tex]M_1[/tex] and [tex]M_2[/tex] is 12.08 units.
Which does not describe the same situation?
Answer:
y = 3+6x
Step-by-step explanation:
Let us substitute x = 0, then we get
y = 3
This is not the case as the graph clearly shows that when x = 3, then y = 2
y = 2+6x
when x = 0 then y = 2 which valid from the graph
Now put x values from the table into the equation
y = 2+6×-1
⇒y = -4
x = 0 already solved
x = 2
y = 2+6×2
⇒y = 14
All the values fit in the equation. So, the bottom two options are valid.
Hence, the first equation is not valid.
You need to strengthen a 19% alcohol solution with pure alcohol solution to obtain 40% solution. How much pure alcohol should you add to 100 milliliters of the 19% solution.
Can anyone solve this problem???
graph y=4x please i need help
The original price of the DVD is nine dollars the sale price is 80% of the price what is the sale price of the DVD?
multiply $9 by 80%
80% = 0.80
9 * 0.8 = 7.20
subtract that from original price
9 - 7.20 = 1.80
Sale price is $1.80
The correct scientific notation for the number 0.00050210 is:
The correct scientific notation for the number 0.00050210 is 5.0210 x 10^(-4).
Explanation:The correct scientific notation for the number 0.00050210 is 5.0210 x 10-4. In scientific notation, the decimal point is moved to the right, and the number is multiplied by a power of 10. The exponent indicates how many places the decimal point was moved.
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When you are finding the slope of a line using two points, it doesn't matter which point you choose to be (x1,y1) and which point you choose to be (x2,y2)?
You have a $50 bill. you and your friend ordered two cheeseburgers for $4.25 each, two fries for $1.28 each, and two colas for $1.98 each. including 4% sales tax and 15% tip, what is the change you will receive from $50?
Answer: 32.13
Step-by-step explanation:
Answer:
The answer is: $32.13
Mr. furley has 27 coins that are all dimes and quarters. the value of the coins is 4.35. how many dimes and how many quarters does mr. furley have
Evaluate -8 × |2|.
-10
10
-16
16
A long piece of wood of length 2.0 m is broken into 4 pieces with two pieces of length a and the other two pieces of length
b. the four pieces are put together to form a rectangle. find b if your aim is to have a rectangle with the maximum area.
The value of b is 0.5 m if your aim is to have a rectangle with the maximum area.
What is the area of the rectangle?It is defined as the area occupied by the rectangle in two-dimensional planner geometry.
The area of a rectangle can be calculated using the following formula:
Rectangle area = length x width
It is defined as the two-dimensional geometry in which the angle between the adjacent sides are 90 degree. It is a type of quadrilateral.
It is given that:
A long piece of wood of length 2.0 m is broken into 4 pieces with two pieces of length a and the other two pieces of length b.
Total wooden length:
2a + 2b = 2
a + b = 1
Area = ab
A = a(1 - a)
dA/da = 0
1 - 2a = 0
a = 0.5 m
b = 0.5 m
Thus, the value of b is 0.5 m if your aim is to have a rectangle with the maximum area.
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What are the roots of the quadratic equation 0 = 2x^2 + 12x –14?
2, 12, –14
–7, 1
–1, 7
1, 6, –7
Can you explain what it is wanting or asking?
Answer:
-7, 1
Step-by-step explanation:
Given quadratic equation,
[tex]2x^2+12x-14=0[/tex]
By middle term splitting,
[tex]2x^2+(14-2)x-14=0[/tex]
[tex]2x^2+14x-2x-14=0[/tex]
[tex]2x(x+7)-2(x+7)=0[/tex]
[tex](2x-2)(x+7)=0[/tex]
By the zero product property,
[tex]2x-2=0\text{ or }x+7=0[/tex]
[tex]\implies x=1\text{ or }x=-7[/tex]
Hence, the roots of the given equation are -7 and 1.
Second option is correct.
Please help!!!!!!!!!
does x/x+6 simplify to 1/6 explain why or why not
No, it does not.
x and x + 6 are both prime and cannot be factored.
There are no common factors to divide out.
x over x + 6 is already simplified.
If you substitute in a value for x, the fraction will not be equal to 1/6.
The expression x/(x+6) does not simplify to 1/6 because there are no common factors in the numerator and denominator that can be canceled out.
The expression x/(x+6) does not simplify to 1/6. To understand this, we need to recognize that simplification involves reducing a fraction to its simplest form by factoring or canceling common factors in the numerator and the denominator.
If x were a factor in both the numerator and the denominator, then we could simplify by canceling out the x's.
However, in the expression x/(x+6), the term x+6 in the denominator cannot be simplified with x in the numerator because they are not factors of each other. They are connected by the addition of 6, which means that there are no common factors to cancel out.
The only way x/(x+6) would simplify to 1/6 is if 'x' were to be somehow removed from the denominator, leaving only the constant 6. But since this is not the case, the fraction cannot be simplified to 1/6. Therefore, the original expression is already at its simplest form unless a specific value is given for x, which may then allow further simplification.
One inlet pipe can fill an empty pool in 6 hours, and a drain can empty the pool in 9 hours. how long will it take the pipe to fill the pool if the drain is left open?