To graphically solve a system of equations, we can plot the equations on a coordinate plane and find the point of intersection, which represents the solution to the system.
The first equation represents the total cost of the games, which is:
x(1.25) = 1.25x
The second equation represents the total cost of the rides, which is:
y(2.50) = 2.50y
The third equation represents the total cost of all games and rides, which is:
x(1.25) + y(2.50) = 12.50
We can also represent the fourth equation as the number of rides she went on is twice the number of games she played:
y = 2x
We can plot the first equation on the coordinate plane by treating x as the x-coordinate and 1.25x as the y-coordinate. We can plot the second equation in the same way, treating x as the x-coordinate and 2.5y as the y-coordinate.
We can plot the third equation as a line by treating x as the x-coordinate and 12.5-1.25x-2.5y as the y-coordinate.
Finally, we can plot the fourth equation as a line by treating x as the x-coordinate and 2x as the y-coordinate.
We can then find the point of intersection of the three lines, which represents the solution to the system of equations.
The point of intersection is the point (5,10) which means that Kaylee played 5 games and went on 10 rides.
How to solve triangles?.
There are several methods to solve a triangle such as SSS, SAS, ASA, and HL, using the Pythagorean theorem, the Law of Sines, and the Law of Cosines.
SSS (Side-Side-Side) Congruence: If the lengths of all three sides of one triangle are equal to the lengths of all three sides of another triangle, the two triangles are congruent.SAS (Side-Angle-Side) Congruence: If two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, the two triangles are congruent.ASA (Angle-Side-Angle) Congruence: If two angles and the included side of one triangle are equal to two angles and the included side of another triangle, the two triangles are congruent.HL (Hypotenuse-Leg) Congruence: If the hypotenuse and one leg of one right triangle are equal to the hypotenuse and one leg of another right triangle, the two triangles are congruent.Using the Pythagorean theorem: In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs.Law of Sines: states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all three sides of the triangle.Law of Cosines: states that the square of the length of the hypotenuse of a triangle is equal to the sum of the squares of the lengths of the legs, minus twice the product of the lengths of the legs and the cosine of the angle between them.To learn more about the triangle, visit:
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What is the distance between the origin and − 3 − 4 )?.
The distance between the origin and the point (3, 4) is 5 units.
The distance between the origin (0,0) and a point (x,y) in a two-dimensional coordinate system can be found using the distance formula, which is given by:
distance = √((x₂ - x₁)² + (y₂ - y₁)²)
In this case, the point is (3, 4) and the origin is (0, 0)
So, the distance between the origin and the point (3, 4) is:
distance = √((3 - 0)² + (4 - 0)²)
distance = √(3² + 4²)
distance = √(9 + 16)
distance = √(25)
distance = 5
So the distance between the origin (0,0) and the point (3,4) is 5
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Topic 6 Performance Task
Tomas and Emilio have a budget of $200 to plan their party at a movie theater. The party room at the theater costs $45.99 to rent and includes a free cake. Movie tickets cost $12.50
each, and a small bag of popcorn costs $4.50.
Seven friends accept the invitation to the twins' birthday party. At the last minute, Tomas and Emilio learn that their neighbor also wants to attend. The twins realize that they can stay
within their budget by buying different amounts of popcorn.
Small Popcorn
(serves 1)
$4.50
Medium Popcorn
(serves 2)
$5.75
Large Popcorn
(serves 2-3)
$6.50
Describe a different popcorn scenario that will allow the twins to bring 8 friends, including their neighbor, and still stay within their budget.
Small popcorn Scenario=Emilio is right.
Medium Popcorn Scenario=Tomas is right.
Large Popcorn Scenario=Tomas is right.
What is budget?A budget is a spending plan based on income and expenses. In other words, it’s an estimate of how much money you’ll make and spend over a certain period of time, such as a month or year.
1. Small popcorn Scenario.
Rent cost=46
Movie ticket cost + popcorn cost=17
For Tomas : 46+ (17*7)=46+119=$165
For Emilio : 46+(17*9)=46+153=$199
2.Medium Popcorn Scenario
Rent cost=46
Movie ticket cost + popcorn cost=?
For Tomas :46+ (18*7)=46+126=$172
For Emilio : 46+(18*9)=46+162=$208
3. Large Popcorn Scenario
Rent cost=46
Movie ticket cost + popcorn cost=?
For Tomas :46+ (19*7)=46+133=$179
For Emilio : 46+(19*9)=46+171=$217.
Small popcorn Scenario=Emilio is right.
Medium Popcorn Scenario=Tomas is right.
Large Popcorn Scenario=Tomas is right.
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A bag of Skittles has 3
green, 2 purple, 4 yellow, 6 red, and 5 orange candies.
If you pick one candy 10 times and replace it after each draw, how many times would you expect to get a candy that isn't green or purple?
Therefore , the solution of the given problem of probability comes out be probability of don't get green or purple candy = 0.75 .
What exactly does the probability process entail?Calculating the likelihood that a statement is true or that an event will occur is the focus of the branch of mathematics known as probability theory. Any number from range 0 to 1, where 1 represents certainty and 0 normally represents possibility, may be used to represent chance. The likelihood that a particular event will occur is depicted in a probability diagram.
Here,
Given :
there are 3 green, 2 purple, 4 yellow, 6 red, and 5 orange candies in the skittles.
total candies = 3 + 2 + 4 + 6 +5 =20
To find the probability that you don't get green or purple candy :
So , the probability of green candies is = 3/20 = 0.15
and the probability of purple candies is = 2/20 = 1/10 = 0.1
The probability of don't get green or purple candy
=> 0.15 + 0.1
=> 0.25
and 1 - 0.25 = 0.75
Therefore , the solution of the given problem of probability comes out be probability of don't get green or purple candy = 0.75 .
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Is an angle a defined term?.
The figure in which two rays intersect at a single location known as the vertex is referred to as an angle. The symbol "" is used to indicate an angle.
An angle is the figure formed when two rays cross at a common endpoint, according to the definition of angles. Simply put, an angle is a shape made up of two lines or rays that diverge from a central point (the vertex). The letter "a" stands for an angle.Vertex: The intersection of two angles is referred to as a vertex. It is the location where two rays converge. Arms: The two angle sides that are connected at a single endpoint. The initial side is also referred to as the reference line.
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What is the ratio of a 30 60 90 triangle?.
The angles of a 30-60-90 triangle are in the ratio 1: 2 : 3.
A triangle is a polygon with three edges and 3 vertices. The terminology for categorizing triangles is more than two thousand years vintage, having been defined on the first actual page of Euclid's elements.
In Euclidean geometry, any three factors, while non-collinear, decide a completely unique triangle and simultaneously, a unique plane (i.e. a -dimensional Euclidean space). In different words, there's best one plane that consists of that triangle, and every triangle is contained in some plane. If the entire geometry is only the Euclidean plane, there is the best one plane and all triangles are contained in it; however, in higher-dimensional Euclidean spaces, this is not real. this text is ready triangles in Euclidean geometry, and in particular, the Euclidean plane, except wherein otherwise stated.
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A small company has one manager and 5 other employees. The manager’s salary is 25% of the company’s salary budget. If the company’s salary budget is x dollars, which expressions represent the amount of money, in dollars, from the salary budget that is left for the 5 other employees?
The amount of money left for the 5 other employees is 0.75x dollars.
How to determine the amount of moneyFrom the question, we have the following parameters that can be used in our computation:
Employees = 5
Salary = 25%
If the manager's salary is 25% of the company's salary budget, and the company's salary budget is x dollars, we can represent the manager's salary as 0.25x.
To find the amount of money left for the 5 other employees, we need to subtract the manager's salary from the total salary budget.
We can represent this using the following expression: x - 0.25x
Simplifying this further, we get
x(1-0.25) = 0.75x dollars
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For what values of k will the system of equations KX 2y 5 3x Y 1 have a no unique solution?.
For k=6 the system of equations have a no unique solution
So,we have given 2 equations from the question:
kx+2y=5…(1)
3x+y=1 …(2)
First multiply the second equation by 2
We get:
6x+2y=2
Now subtracting (2) from (1), we get:
kx+2y−6x−2y=5−2
(k−6)x=3
x= 3/K-6
So, here if we put any value in k, then we will get a corresponding value of x but if we put k=6, then we will not get any value of x.
So, for k=6 this equation has no unique solution.
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Select the best Measures of Center for the data set:
4, 6, 9, 10, 6, 7
Question 3 options:
Either the Mean or the Median
The Median Only
The Mode Only
Answer:
either the mean or the median
A train travels at a constant speed during a portion of its cross county route the table shows the distance the train traveled over different intervals of time at this speed.
what is the Speed of the train in Miles per hour?
The Speed of the train in Miles per hour will be 105 miles per hour.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The slope of the line is given as,
m = (y₂ - y₁) / (x₂ - x₁)
A train travels at a constant speed during a portion of its cross-country route the table shows the distance the train traveled over different intervals of time at this speed.
The slope represents the speed of the train. Then we have
m = (157.5 - 131.25) / (1.50 - 1.25)
m = 26.25 / 0.25
m = 105 miles per hour
The Speed of the train in Miles per hour will be 105 miles per hour.
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lydia went on a trip with her family. for three hours they drove east and drove 40 miles per hour. then, they drove north for one hour and drove 50 miles. how far was lydia and her family from their home after 4 hours
Answer:
170 miles
Step-by-step explanation:
first, for 3 hours they drove 40 mph. this means you have to multiply 40 mph by the 3 hours.
40*3=120
then you have to add the extra 50 miles that they drive north because their speed changed.
120+50=170
No need to explain. check picture.
Answer: What you chose was correct :>
Why doesn’t 100% of the data fall within 3 standard deviations of the mean?
As per the Empirical Rule and the properties of a Normal distribution , 99.7% of the data lies within three standard deviation not 100%.
What is Empirical Rule?
According to the empirical rule, also known as the three-sigma rule or 68-95-99.7 rule, practically all observed data for a normal distribution will lie within three standard deviations of the mean or average.
In specifically, the empirical rule predicts that 68 percent of observations will fall within the first standard deviation, 95 percent will fall within the first two standard deviations, and 99.7 percent will fall within the first three standard deviations.
Hence, as per the Empirical Rule and the properties of a Normal distribution , 99.7% of the data lies within three standard deviation not 100%.
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How many types of polynomials are there in class 9?.
There are three types of polynomials in class 9 there are linear, quadratic, and cubic polynomials.
The words Nominal, which means "terms," and Poly, which means "many," are combined to make the word polynomial.
An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial (No division operation by a variable).
Linear polynomials are straightforward and simple to solve. Isolate the variable term first, then set the equation's solution equal to zero.
First, rewrite the expression using a quadratic polynomial in the order of decreasing degree. To find the equation's solution, equate the equation and use polynomial factorization.
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Find the length of the arc on a circle of radius r intercepted by a central angle θ?
A circle's arc length can be determined from its radius and central angle using the formula Length of an Arc = r, where is in radians.
How to Find Arc Length With the Radius and Central Angle?Length of an Arc = r, where is in radians, is a formula that may be used to calculate the arc length of a circle given its radius and central angle. A circle's length is equal to (r/180)r, where r is the radius and is the angle. The length of the arc on a circle of radius r intercepted by a central angle is S = r.
Multiply the radius (6 in) by the central angle's measurement in radians to determine the length of the arc. Remember that the angle must be expressed in radians in order to employ the calculation s = r.
Assuming that is measured in radians, the formula for the length s of the arc that is intercepted on a circle with radius r by a central angle is: s = r.
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What is the sum of the 2 solutions of the equation x^2-4x-45=0???
PLEASE HELP!!
Answer:
The first x is 9
The second x is -5
Step-by-step explanation:
The correct answer will get brainliest!!
Classify this triangle by its sides and angles.
A.) acute and isosceles, but not equilateral
B.) obtuse and isosceles, but not equilateral
C.) obtuse and equilateral
D.) acute and equilateral
[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
[tex] \textsf{As per the given figure, observations can be made} [/tex] [tex] \textsf{that : } [/tex]
[tex] \textbf{1.) Two sides of the given triangle are equal.} [/tex]
Conclusion : [tex] \textsf{It's an } [/tex][tex] \textbf{Isosceles} [/tex][tex] \textsf{triangle} [/tex][tex] \textbf{2.) All the three angles are less than 90° } [/tex]
Conclusion : [tex] \textsf{ it's an} [/tex][tex] \textbf{ acute } [/tex][tex] \textsf{angled triangle } [/tex][tex] \textsf{So, to sum it up, it can be said that the } [/tex][tex] \textsf{triangle is both Isosceles and acute } [/tex][tex] \textsf{angled triangle.} [/tex]
Answer : A.) acute and isosceles, but not equilateral
Answer:
Acute and Isosceles, but not equilateral.
Step-by-step explanation:
First, let us address equilateral. Equilateral triangles assumes by definition that all triangle sides are symmetrical (60° in measurement), and that all side lengths are congruent (the same length). As shown in the picture, it is not a equilateral triangle, as there is only a pair of congruent sides.
Therefore, the given triangle is a isosceles triangle, which by definition calls for having two sides of equal length, and two equal angles.
Next, we are solving for whether or not the triangle angles are obtuse or acute. Acute angles measure less than 90° (The measurement of a right angle). Obtuse angles, on the other hand, measure more than 90°. In this case, all sides are less than 90°, per definition of isosceles triangle.
Therefore, the given triangle is acute.
Your answer is Acute and isosceles, but not equilateral.
What are the 7 properties of equality?.
The 7 properties of equality are the following,
Reflexive SymmetricTransitiveSubstitutionAdditionDivisionMultiplicationThe properties of equality is used to represent the relation between the two sides of an equation and state that the two sides remain equal even after applying the same arithmetic operation on each side.
1) The Reflexive equality property : As per reflexive property, x = x ; x R
2) The Symmetric equality p : If x = y, then y = x .
3) The Transitive equality property : If x = y and y = z, then x = z.
4) The Addition equality Property :
If x = y, then x+z = y+p.
5) Subtraction equality property :
If x = y, and z = p, then x - z = y- p.
5) The Multiplication equialty Properties :
If x = y, then xc = ycIf x = y, and z = d, then xz = yd.6) The Division equaility properties : If x = y, and c≠ 0, then x/c = y/c. If x = y, and c = d ≠0, then x/c = y/d.
Consider the example : Assume the expression is 10 + x = 4(x - 2).
Solution: Solution of this using above properties, 10 + x = 4(x - 2)
=> 10 + x = 4x - 8
=> 10 = 3x - 8
=> 18= 3x
=> 6 = x
=> x = 6
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Which type of isometry is the equivalent of two reflections across parallel lines?
glide reflection
rotation
reflection
translation
The equivalent of two reflections across parallel lines is a glide reflection. Therefore, choice A is the best one.
What is isometry in a nutshell?d(f(x,y))=d(x,y) is a bijective map between two metric spaces that maintains distances, where f is the map and d(a,b) is the distance function. Congruence transformations are another name for isometries. Congruent refers to two figures that an isometry can change into one another (Coxeter and Greitzer 1967, p. 80). A linear transformation with length preservation is called an isometry of the plane. Rotation, translation, reflection, gliding, and the identity map are all examples of isometries. Geometrically congruent refers to two geometric figures that are connected by an isometry (Coxeter and Greitzer 1967, p. 80).
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The equivalent of two reflections across parallel lines is a glide reflection. Therefore, choice A is the best one.
What is isometry in a nutshell?A mapping of a metric space such that any two points' distances in the original space are equal to the distances between their images in the second space. d(f(x,y))=d(x,y) is a bijective map between two metric spaces that maintain distances, where f is the map and d(a,b) is the distance function. Congruence transformations are another name for isometries. Congruent refers to two figures that an isometry can change into one another. A linear transformation with length preservation is called an isometry of the plane. Rotation, translation, reflection, gliding, and the identity map are all examples of isometries.
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The arrows represent the forces acting on the object. Use the highlighter and draw an arrow to represent the direction that the object would be accelerating. Put an "X" if it is not accelerating.
Answer:
see attached
Step-by-step explanation:
You want the given diagram annotated with an arrow to show the direction of acceleration.
AccelerationAcceleration is a result of a net force on an object. It is in the direction of that net force.
ApplicationHere, the forces to the left and right are equal and opposite, so have a sum of zero.
The forces up and down are opposite, but unequal. The downward force is larger, so the direction of the net force is downward. (+5 +(-10) = -5)
The object will be accelerated downward in the direction of the 10 N force.
What is the formula of product in math?.
The multiplication formula in maths is given as follows Multiplier × Multiplicand = Product.
The product meaning in maths is a number you get to by multiplying two or more other numbers. For example, if you multiply 3 and 5 together, you get a product of 15.
Multiplication is an important part of maths. Learning and understanding how to find the product in maths is an important basis for developing their skills in maths.
You can help children learn the maths definition of the product by reminding them that it is produced when two or more numbers are multiplied together.
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Given:
R is the midpoint of QS
Prove: PRQ = TRS
Answer:
Step-by-step explanation: Hello!
I don't remember all of the postulates to these, but I hope this will help you! Vertical angles are congruent, so both angles SRT and PRQ are congruent. This also means that line segments PQ and ST are congruent. You also know that angles Q and S are congruent which is given. By the ASA Theorem, when two angles and a side are congruent, then the triangles are congruent.
Can you please answer the question o in this image ?
Answer:
Step-by-step explanation:
=([tex]\frac{24}{-6}[/tex])([tex]x^{6-3}[/tex])([tex]y^{3-1}[/tex])
=[tex]-4x^{3} y{2}[/tex]
Which of these expressions represents the sum of an irrational number and a rational number being irrational
The sum of an irrational number and a rational number can either be rational or irrational.
Depending on the specific numbers involved. There is no general expression for the sum of an irrational number and a rational number being irrational. If the sum of two numbers is irrational, it means that the result cannot be expressed as a simple fraction, and its decimal representation either goes on forever without repeating or repeats after a certain number of digits.
One example of the sum of an irrational number and a rational number being irrational is:
√2 + 1/2 = 1.732 + 0.5 = 2.232 (irrational)
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If 13 is added to a number and the sum is multiplied by 3, the result is 7 times the number decreased by 9. Find the number
Answer: 47/4
Step-by-step explanation:
Convert the words into math:
The number = x
( 13 + x ) * 3 = 7 * x - 9
Expand:
39 + 3x = 7x - 9
Subtract 3x from both sides:
38 = 4x - 9
Add 9 to both sides:
47 = 4x
x = 47/4
Please view the image and answer the questions.
On solving the provided question, we can say that the equation [tex]8x^3 - 1[/tex][tex]= (2x- I) (4x^2 + 2x + I)[/tex] so, a = 2 and b = 1
What is equation?A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.
here the equation is
[tex]8x^3 - 1[/tex]
[tex]= (2x- I) (4x^2 + 2x + I)[/tex]
so, a = 2 and b = 1
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Is this question right I just want to check?
Not quite, but really close. All you need to do is switch -4/3 and -0.2, because -4/3 is about -1.3, and negative numbers get greater as they get closer to 0
The box-and-whisker plot below represents some data set. What is the value of the upper quartile?
For the given figure, the value of upper quartile is 68.
When presented in increasing order, the value that 75% of data points fall within is known as the higher quartile, or third quartile (Q3). As the second quartile, the median is used (Q2).
The distance between the upper and lower quartiles is known as the interquartile range.
The median of a data set's upper half is the upper quartile.
To find this, divide the data set by the median, and then divide the remaining upper half by the median once more, with the higher quartile serving as the median.
Third or higher quartile is another name for the 75th percentile.
The value at which 25% of the answers are above that value and 75% of the answers are below that value is known as the 75th percentile.
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Which equation matches the graph? f( x) = ( x + 4) 2 – 2 f( x) = ( x – 2) 2 + 4 f( x) = ( x + 2) 2 + 4 f( x) = ( x – 4) 2 + 2 f( x) = ( x + 2) 2 – 4
The quadratic equation that matches the graph is f(x) = (x - 2)² + 4.
The correct option is B.
What is a quadratic equation?For variable x : ax² + bx + c = 0, where a≠0 is a standard quadratic equation, which is a second-order polynomial equation in a single variable. It has at least one solution since it is a second-order polynomial equation, which is guaranteed by the algebraic basic theorem.
Given:
The graph shows the function.
The graph is given in the attached image.
In the interval, [x = 0, x = 2],
we have a line that passes through the points (0, 8) and (2, 4).
That means, the points satisfies then function.
Let the f(x) = (x - 2)² + 4.
That means,
f(0) = 8
And f(2) = 4
Therefore, the quadratic function is f(x) = (x - 2)² + 4.
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Write a quadratic equation in x such that the sum of its roots is 9 and the product of its roots is −19.
x² - 9x-19=0 is a quadratic equation in x such that the sum of its roots is 9 and the product of its roots is −19.
What is quadratic equation?A quadratic equation is a second-order polynomial equation in a single variable x , ax²+bx+c=0. with a ≠ 0 .
If the Sum of zeroes and Product of the zeroes of a quadratic equation is given then the quadratic equation is
x² - sum of the zeroes x + Product of the zeros =0
In the given question sum of its roots is 9 and the product of its roots is −19.
So the equation will be x² - 9x-19=0
Hence, x² - 9x-19=0 is a quadratic equation in x such that the sum of its roots is 9 and the product of its roots is −19.
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