Given that AC = 4x+5, and C is the midpoint of AB, meaning AC = CB, then AB = 2*(4x+5). Given that AB = 78, we can solve the equation 8x + 10 = 78 to find x = 8.5.
Explanation:The subject matter of this question is geometry, specifically concerning line segments and midpoints. If C is the midpoint of AB, then segments AC and CB are equal. This is a fundamental characteristic of midpoints.
Since AC = 4x + 5 and CB = AC, it also means that CB = 4x + 5. This implies that the total length of AB (which is the sum of AC and CB) equals 2 * (4x + 5). Therefore, AB equals 8x + 10.
We are given that AB = 78. So, we can set up and solve the equation 8x + 10 = 78. Subtracting 10 from both sides of the equation gives us 8x = 68. Dividing each side by 8 gives us x = 8.5. Therefore, the value of x that satisfies the given conditions is 8.5.
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A spinner has 4 equally-sized sections, labeled A, B, C, and D. It is spun and a fair coin is tossed. What is the denominator of the simplified fraction representing the probability of spinning “C” and flipping “heads”? P(spinning C and flipping heads) =
Answer:
1/8
Step-by-step explanation:
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.
graph y=4x please i need help
How many solutions are ther to this equation.
Sasha can mow 3/8 of an acre of grass in 45minutes.how many acres of grass does Sasha now per hour?
By graphing the system of constraints, find the values of x and y that maximize the objective function. 25<=x<=75 y<=110 8x+6y=>720 y=>0 minimum for c=8x+5y a. c=100 b. c=225 2/3 c. c=633 1/3 d. c=86 2/3
Solve the inequality 3(x + 1) + 2(x + 2) > 0. A. x < -7/5 B.x > -7/5 C. x < 7/5 D.x > 7/5
Answer:
3x+3+2x+4>0
5x>-7
x>-7/5
B
Step-by-step explanation:
What is the simplified form of the following expression? 7[6^2÷(5^2-4^2 )+8]
&
(3/4)^3
The weight of football players is normally distributed with a mean of 200 pounds and a standard deviation of 25 pounds. the probability of a player weighing less than 250 pounds is closest to:
Using the normal distribution, it is found that there is a 0.9772 = 97.72% probability of a player weighing less than 250 pounds.
Normal Probability DistributionIn a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It measures how many standard deviations the measure is from the mean. After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.In this problem:
The mean is of [tex]\mu = 200[/tex].The standard deviation is of [tex]\sigma = 25[/tex].The probability of a player weighing less than 250 pounds is the p-value of Z when X = 250, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{250 - 200}{25}[/tex]
[tex]Z = 2[/tex]
[tex]Z = 2[/tex] has a p-value of 0.9772.
0.9772 = 97.72% probability of a player weighing less than 250 pounds.
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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]
Plz help! True or False. The response variable is plotted along the y-axis.
Darryl has $5 left in his pocket. He spent $16 on a book, $20 on a compact disc, and $2 on a magazine. How much money did he have at the beginning of the day?
Darryl had $43 at the beginning of the day.
Let's denote the initial amount of money Darryl had as [tex]\( M \)[/tex].
He spent $16 on a book, which we can denote as [tex]\( S_{book} = \$16 \)[/tex].
He spent $20 on a compact disc, which we can denote as [tex]\( S_{CD} = \$20 \)[/tex].
He spent $2 on a magazine, which we can denote as [tex]\( S_{magazine} = \$2 \)[/tex].
He has $5 left at the end of the day, which we can denote as [tex]\( L = \$5 \)[/tex].
The total amount spent, [tex]\( S_{total} \)[/tex], is the sum of the amounts spent on the book, the compact disc, and the magazine:
[tex]\[ S_{total} = S_{book} + S_{CD} + S_{magazine} \][/tex]
[tex]\[ S_{total} = \$16 + \$20 + \$2 \][/tex]
[tex]\[ S_{total} = \$38 \][/tex]
The initial amount of money Darryl had, [tex]\( M \)[/tex], is the sum of the total amount spent and the amount left:
[tex]\[ M = S_{total} + L \][/tex]
[tex]\[ M = \$38 + \$5 \][/tex]
[tex]\[ M = \$43 \][/tex]
Molly 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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Which statement best describes how to determine whether f(x)=9-4x^2 is an odd function
If the slope and a point of a line are given, then the equation of the line can be written in point-slope form.
True
False
Evaluate the expression when x = -15
-4x -11
A. -71
B. -49
C. 49
D. 71
log(-2a+9)=log(7-4a)
please helpp!!
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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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.
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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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.
How many ways can six friends be arranged around a circular dinner table?
can somebody help me with these please ☺
Can somebody help me with this?
if (2x-3) and (x+5) are multiplied to form the trinomial ax^2 +bx+c, what is the value of b
After using the trinomial The required value of b is 7.
What is a trinomial?
An algebraic expression with three terms is called a trinomial. One or more terms in an algebraic expression each have variables and constants. These expressions use separators like +, -,, and that are symbols or operations. This algebraic expression encompasses polynomials, monomials, binomials, and trinomials. An algebraic expression that is created by squaring a binomial expression is known as a perfect square trinomial. It takes the shape of ax2 + bx + c. Real numbers a, b, and c are present here, and a 0. Take the binomial (x + 2), for instance, and multiply it by (x + 2). The outcome is equal to x2 + 4x + 4.
Given, [tex](2x-3)[/tex] and [tex](x+5)[/tex] are multiplied [tex]= (2x-3)(x+5)[/tex]
[tex]= 2x(x+5) -3(x+5)[/tex]
[tex]= 2x^{2} +10x -3x-15\\= 2x^{2} +7x-15[/tex]
Now, comparing the calculated expression [tex]2x^{2} +7x-15[/tex] with the given equation [tex]ax^{2} +bx+c[/tex] , then we get, [tex]b=7[/tex]
Therefore, the required value [tex]b[/tex] is 7.
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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.
Grandpa schmidt is 75 years old. this is 9 years less than seven times the age of junior schmidt. how old is junior
The sum of two consecutive odd integers is 24. find the integers. which equation can be used to find the first integer n
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
I can't figure this out I need helppp!!!!