Using a system of equations, it is found that:
The cost of an orchestra ticket is of $10.The cost of a balcony ticket is of $10.The quantities are equal.What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
In this problem, the variables are:
Variable a: Cost of an orchestra ticket.Variable b: Cost of a balcony ticket.Peter pays $50 for 1 orchestra and 4 balcony tickets, hence:
a + 4b = 50 -> a = 50 - 4b.
Justine pays $150 for 3 orchestra and 12 balcony tickets, hence:
3a + 12b = 150.
a + 4b = 50 -> a = 50 - 4b.
The equations are equal, hence we suppose that the costs are equal, that is:
a + 4b = 50 -> 5a = 50 -> a = 10.
Hence:
The cost of an orchestra ticket is of $10.The cost of a balcony ticket is of $10.The quantities are equal.More can be learned about a system of equations at https://brainly.com/question/24342899
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Which rules define the function graphed below?
65
4
3
32
(0.2)
-2
-3-
(3,5)
--3--2--11 1 2 3 4
O y=x; y = 5
O y = x + 2; y = 5
O y=x; x = 5
O y=x+2; x = 5
The rules that define the piecewise function graphed are as follows:
y = x + 2, y = 5.
What is a piecewise function?A piecewise function is a function that has different definitions, depending on the input.
In this problem, for x between 0 and 3, a linear function is given, with slope given as follows:
m = (5 - 2)/(3 - 0) = 1.
The y-intercept is of 2, as y = 2 when x = 0, hence the definition is:
[tex]y = x + 2, 0 \leq x \leq 3[/tex]
For x greater than 3, the function is constant at y = 5, hence the definition is:
y = 5, x > 3.
Hence, the rules that are used to define the piecewise function graphed are as follows:
y = x + 2, y = 5.
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– 42 – 54 + 96 =
what is the answer
Answer:
Answer:the answer is zero
Answer:the answer is zero Step-by-step explanation:
Answer:the answer is zero Step-by-step explanation:when we add -42 and -54 the answer we get is -96. -96and +96 cut each other and then the answer is zero
[tex] - 42 - 54 + 96 = 0[/tex]
The difference of the square of a number and 8 is equal to 8 times that number. Find the positive solution.
Answer:
[tex]2\sqrt{6} +4[/tex]
Step-by-step explanation:
Let x be that unknown number.
From the information given from the question, we can deduce:
[tex]x^{2} -8=8x[/tex]
From here, we can solve for x to find what is the number.
[tex]x^{2} -8=8x\\x^{2} -8x-8=0[/tex] (Quadratic Equation)
From here we can use the Quadratic Formula to solve for x.
[tex]x=\frac{-b+/-\sqrt{b^{2} -4ac} }{2a}[/tex]
In this case,
a = 1, b = -8 , c = -8
We substitute a, b and c to find x.
[tex]x=\frac{-(-8)+/-\sqrt{(-8)^{2}-4(1)(-8) } }{2(1)} \\= 2\sqrt{6} +4[/tex]
(Reject the negative solution)
What is
3/2^2 equal to
Answer: SQUARE ROOT OF 8
Step-by-step explanation: 2^3^1/2 is SQUARE ROOT OF 8. GOD BLESS
- FRIEND TO DINO
It rains 4 days in a week and is dry for 3 days. What fraction of the week is dry?
Answer:3/7
Step-by-step explanation:There are total 7 days in a week. 3 days were dry so the fraction is 3/7 . The dry days over the total days of the week
Simplify:
x² + 3x + 2 /x² - 4x - 5
x² + 7x + 12 / x²-3x - 28
[tex]\\ \rm\Rrightarrow \dfrac{x^2+3x+2}{x^2-4x-5}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{x^2+2x+x+2}{x^2-5x+x-5}[/tex]
[tex]\\ \rm\Rrightarrow {(x+2)(x+1)}{(x-5)(x+1)}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{x+2}{x-5}[/tex]
And
[tex]\\ \rm\Rrightarrow \dfrac{x^2+7x+12}{x^2-3x-28}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{x^2+4x+3x+12}{x^2-7x+4x-28}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{(x+4)(x+3)}{(x-7)(x+4)}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{x+3}{x-7}[/tex]
Use the drawing tool(s) to form the correct answer on the provided graph.
Graph the solution to this system of inequalities in the coordinate plane.
3y 2x+122x + y ≤5
The solution of the inequalities is (0.375, 4.25)
How to graph the inequalities?The system of inequalities is given as:
3y > 2x + 12
2x + y ≤ 5
Next, we plot the inequalities on a graph (see attachment)
From the graph, both inequalities intersect at
(x, y) = (0.375, 4.25)
This represents the solution of the inequalities
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Need an detailed step by step answer and solution again
Answer:
12u²
Step-by-step explanation:
area of a regular quadrilateral is always base x vertical height.
the base here is clearly 4 (just count the squares)
draw an imaginary line connecting the bottom right corner to the line before the top right corner (the line should be vertical)
count the squares here too and you get 3.
so the area = 3 x 4,
the area is 12u²
cual es la mitad de 980
Al aplicar operaciones de aritmética básica, tenemos que la mitad de 980 es igual a 490.
¿Cuál es la mitad de un número par?
En esta pregunta tenemos un número par de tres dígitos que termina en cero. De acuerdo con la teoría numérica, un número de base 10 de más de un dígito que tenga un número par relacionado con números impares como último dígito, tendrá un número impar si es dividido por 2.
Ahora bien, si tenemos un número par con más de un dígito que termina en cero, entonces tendrá un número par que termina en 0 si es dividido por 2.
Si dividimos 980 por 2, entonces tenemos 490 como resultado:
980/2 = 98/2 × 10 = 49 × 10 = 490
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The set of all three-digit binary numbers
The set of all three-digit binary numbers as required in the task content includes; 100,101,110,111.
What is the set of all three-digit binary numbers?A binary number by definition is one which is made of a combination of numbers 0 and 1.
On this note, it follows that the three digits binary numbers in discuss include; 100,101,110,111.
Binary numbers are most often used in computer programs to represent data.
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In the diagram above, angle 1=40. Find the measure of angle 4
Answer:
40
Step-by-step explanation:
angle 1 and 4 are vertical angles therefore they have the same measure of 40 degrees
Use the Associative Property to find the value of the variable.
(8 x 15) x s = 8 x (15 x 11)
Answer:
hey its me again so the answer is 11.
I'm sure because I did this.
Find an equation for the plane that contains the line
v=(-3,4,5)+t(3,2,4)
and is perpendicular to the plane
2x+y-3z+4=0
(Use symbolic notation and fractions where needed.)
The equation for the plane that contains the line and is perpendicular to the plane 2 · x + y - 3 · z = - 4 is - 10 · x + 17 · y - z = 76.
How to find the equation of a plane that contains a line and is perpendicular to another plane
From the equation of the plane 2 · x + y - 3 · z = - 4 we know that its normal vector is (2, 1, - 3). Hence, we have found two direction vectors and already know a point, which are part of this parametric equation:
(x, y, z) = (- 3, 4, 5) + t · (3, 2, 4) + u · (2, 1, - 3) (1)
The normal vector of the plane is equal to the cross product of the direction vectors of (1):
[tex]\vec n = (3, 2, 4) \,\times\,(2, 1, -3)[/tex]
[tex]\vec n = \left|\begin{array}{ccc}\hat{i}&\hat{j}&\hat{k}\\3&2&4\\2&1&-3\end{array}\right|[/tex]
[tex]\vec n = (-6-4,8+9, 3-4)[/tex]
[tex]\vec n = (-10, 17, -1)[/tex]
Since the plane contains the point (x, y, z) = (- 3, 4, 5), then we find that the independent constant of the equation of the plane is:
- 10 · x + 17 · y - z = k
- 10 · (- 3) + 17 · 4 - 5 = k
30 + 51 - 5 = k
k = 76
The equation for the plane that contains the line and is perpendicular to the plane 2 · x + y - 3 · z = - 4 is - 10 · x + 17 · y - z = 76.
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1376x13 please solve this equation and show work
The value of 1376 * 13 is 17888
How to solve the expression?The expression is given as:
1376 * 13
Express 1376 as 1300 + 76
(1300 + 76) * 13
Expand
1300 * 13 + 76 * 13
Evaluate the product
16900 + 988
Evaluate the sum
17888
Hence, the value of 1376 * 13 is 17888
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Find u. v.
U V=
(8, 2)
= (-6, 3)
U =
V =
Answer:
-42
Step-by-step explanation:
Assuming you want the dot product,
(8)(-6)+(2)(3)= -42
Zoya asked the students of her class their baseball scores and recorded the scores in the table shown below:
Baseball Scores
Score Number of Students
0 1
1 2
2 5
3 3
4 6
5 7
6 9
Based on the table, what is the mean baseball score?
2.5
2.9
3.5
4.1
Option D, 4.1 is the correct answer. The mean baseball score is 4.1 given the table of values of baseball scores and score number of students. This can be obtained by using the formula for mean.
Calculate mean for the data:Mean can be obtained by the formula,
Mean = [tex]\frac{sum\ of\ observations}{total\ number\ of\ observations}[/tex]
Sum of basketball scores = 0×1 + 1×2 + 2×5 + 3×3 + 4×6 + 5×7 + 6×9
= 0 + 2 + 10 + 9 + 24 + 35 + 54
total number of basketball scores = 1 + 2 + 5 + 3 + 6 + 7 + 9 = 33
Mean = [tex]\frac{0+2+10+9+24+35+54}{33}[/tex] = 4.06 ≈ 4.1
Hence the mean baseball score is 4.1 given the table of values of baseball scores and score number of students. Option D, 4.1 is the correct answer.
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average person burns approximately 221 calories per half-hour while bicycling. If a person does 2 hours of bicycling per day then how many calories will they burn in a week if they work out 5 days a week?
The amount of detergent dispensed into bottles of liquid laundry detergent bottles for a particular brand is normally distributed with a mean of 84.5 ounces with a standard deviation of 1.1 ounces. If seventeen bottles are randomly chosen from the factory, what is the probability that the mean fill is more than 84.8 ounces
The probability that the mean fill is more than 84.8 ounces is 0.39358
How to determine the probability that the mean fill is more than 84.8 ounces?From the question, the given parameters about the distribution are
Mean value of the set of data = 84.5Standard deviation value of the set of data = 1.1The actual data value = 84.8The z-score of the data value is calculated using the following formula
z = (x - mean value)/standard deviation
Substitute the given parameters in the above equation
z = (84.8 - 84.5)/1.1
Evaluate the difference of 84.8 and 84.5
z = 0.3/1.1
Evaluate the quotient of 0.3 and 1.1
z = 0.27
The probability that the mean fill is more than 84.8 ounces is then calculated as:
P(x > 84.8) = P(z > 0.27)
From the z table of probabilities, we have;
P(x > 84.8) = 0.39358
Hence, the probability that the mean fill is more than 84.8 ounces is 0.39358
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Multiply 3.4x and 1.2x.
4.08x2
4.6x2
4.08x
4.6x
Answer: 4.08x2
Step-by-step explanation:
Answer:
4.08x2
Step-by-step explanation:
Use the drawing tool(s) to form the correct answer on the provided graph.
Graph the solution to this system of inequalities in the coordinate plane.
3y 2x+122x + y ≤5
The plotting of the inequalities was done using geogebra online graphing calculator. The graph is attached.
What are inequalities?Inequalities are the mathematical expressions in which both sides are not equal. It should be noted that in inequality, unlike in equations, we compare two values.
The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign. Inequality is an expression used to show the nonequal comparison of numbers and variables.
Given the system of inequalities:
3y > 2x + 12
3y - 2x > 12 (1)
2x + y < -5 (2)
Plotting the inequalities using GeoGebra online graphing calculator. The graph is attached
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if a person invested half of her money at 11% and half at 10% and received $420 interest. find the total amount
The total amount invested was $4000. $2000 was invested at 11% while the remaining $2000 was invested at 10%.
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Let x represent the total amount of money invested, hence:
(0.5* x * 0.11) + (0.5 * x * 0.1) = 420
x = 4000
The total amount invested was $4000. $2000 was invested at 11% while the remaining $2000 was invested at 10%.
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Determine the output voltage of the op-amp circuit shown below:
The output voltage of the op-amp circuit shown is -5v.
What is voltage?It should be noted that voltage is the electric potential difference between two points l.
In this case, the output voltage will be:
= -5 × i
where I = 1.
Voltage = -5 × 1
= -5v
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Given the coordinates below, what is the midpoint of AB?
A(-6, -10)
B(2,5)
Given :
[tex] \: [/tex]
A(-6, -10)B( 2, 5)
[tex] \: [/tex]
[tex] \gray{ \frak{The \: given \: two \: \: points \: are(x_{1 },y_{1})=(−6 , -10)and(x_{ 2 },y_{2} )=( 2,5 )\:}}[/tex]
[tex] \: [/tex]
Let's solve by using midpoint formula :
[tex] \: [/tex]
[tex] \bf \boxed{\color{red}\frak{Midpoint \: \: Formula : {( \: x ,\:y \: ) = }( \frak{ \frac{x_{1 } + y_{1}}{2} , \frac{x_{2 } + y_{2}}{2} )}}}[/tex]
[tex] \: [/tex]
[tex] \large \gray{ \frak{( \: x ,\:y \: ) = }( \frak{ \frac{ -6 + 2}{2} , \frac{ - 10 + 5}{2} )}}[/tex]
[tex] \: [/tex]
[tex] \: \large \gray{ \frak{( \: x ,\:y \: ) = }( \frak{ \frac{ -4}{2} , \frac{ - 5}{2} )}}[/tex]
[tex] \: [/tex]
[tex]\large \gray{ \frak{( \: x ,\:y \: ) = }( \frak{ \cancel\frac{ -4}{2} , \cancel\frac{ - 5}{2} )}}[/tex]
[tex] \: \: [/tex]
[tex] \underline{ \boxed{ \large \red{ \frak{option \: d }( \frak{ - 2, - 2.5)}}}}✓[/tex]
Hope Helps! :)
Plug in different values of h and k to answer the following questions. What happens when h is positive? What happens when h is negative? What happens when k is positive? What happens when k is negative?
A logarithmic function is the inverse of an exponential function.
What is a logarithmic function?A logarithmic function is the inverse of an exponential function.
Now we have the function;
f(x) = log(x) and the translated function f(x) = log (x-h) + k.
When h is positive, the asymptote moves upwards by the stated amountWhen h is negative , the asymptote moves downwards by the stated amountSimilarly;
When k is positive, the entirety of the graph moves upwardsWhen k is negative , the entirety of the graph moves downwardsLearn more about logarithmic function:https://brainly.com/question/3181916
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Missing parts;
Use the graphing calculator to graph the parent function.
f(x) = log(x)
Add the translated function.
f(x) = log (x-h) + k
Plug in different values of h and k to answer the following questions.
What happens when h is positive?
What happens when h is negative?
What happens when k is positive?
What happens when k is negative?
Answer:
When h is positive: horizontal shift to the right
When h is negative: horizontal shift to the left
When k is positive: vertical shift up
When k is negative: vertical shift down
Step-by-step explanation:
got it right on Edge
could anyone help me with this?
Answer:
Step-by-step explanation:
A=6x²
[tex]\frac{dA}{dt} =6\times 2x \times \frac{dx}{dt} \\\frac{dA}{dt}=12x \frac{dx}{dt}[/tex]
there was 506 tickets sold for the school play they were either student tickets or adult tickets there was 56 more student tickets sold than adult tickets sold how many adult tickets were sold
Answer:
A = 228 tickets
Step-by-step explanation:
We need to set up a system of equation to find the number of adult tickets sold, where A represents the adult tickets and S represents the student tickets.
Because the number of adult and student tickets together equals 506, we have A + S = 506.
Because there are 56 more student tickets than adult tickets we have A + 56 = S
And the way the system is already set up allows us to use substitution.
Thus, we have:
[tex]A + S=506\\A+56 = S\\\\A+A+56 =506\\2A+56=506\\2A=456\\\\A=228\\228+56=S\\278=S[/tex]
The number of student tickets was not necessary to find in this problem, but I found anyway just in case you wanted check the work or wanted to prove the validity of the values.
which of the following regression equation best fits the data graphed below?
Answer:
D
Step-by-step explanation:
This is multiple choice pls help
Answer: b and e
Step-by-step explanation:
b - the slope is positive
the slope is 8 not negative 8 because, 4+4/2-1 = 8/1 = 8 since subtracting 4 and -4 makes it 4+4
e - it is possible for x to be positive and for y to be negative
Which of the following will form the composite function G(F(x)) shown
below?
G(F(x)) = x² + 4
OA. F(x) = x + 4 and G(x) = x²
OB. F(x)= x and G(x) = x²
O C. F(x)=x² and G(x) = 4
OD. F(x) = x² and G(x) = x + 4
The composite function G(F(x)) = x² + 4 is formed with these following original functions:
D. F(x) = x² and G(x) = x + 4.
How to find the composite function of f(x) and g(x)?The composite function of f(x) and g(x) is given as follows:
[tex](f \circ g)(x) = f(g(x))[/tex]
For g of f(x), we have that:
[tex](g \circ f)(x) = g(f(x))[/tex]
For this problem, we have that:
G(F(x)) = x² + 4.
Which is possible with option D, as:
[tex]G(F(x)) = G(x^2) = x^2 + 4[/tex]
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Match the expressions to their solutions or equivalents. (-3/8) + (-1/8)
Answer:
-1/2
Step-by-step explanation:
-3/8+-1/8=-4/8 which is equal to -1/2
Answer:
1/4
Step-by-step explanation:
(3/8)+(-1/8)
= (3/8) - (1/8)
= 2/8
= 1/4