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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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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Solve for m.D:
D (9x-44)
X =
(6x+7)
Answer:
m∠D = 109
Step-by-step explanation:
This is a parallelogram.
In parallelograms, the opposite interior angles are congruent, so we can write the following equation to find, first value x the measure of m∠D:
9x - 44 = 6x + 7
Transfer like terms to the same side of the equation.9x - 6x = 7 + 44
Add/subtract.3x = 51
Divide both sides by 3x = 17
Now we can calculate measure of m∠D:
m∠D = 9x - 44
Rewrite equation using the value we found for x.9×17 + 44 = 109
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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How many square inches of cloth are cut from the square (n = 3.14) if it’s 38inches
The number of square inches of cloth cut from the square will be 1,017.36 square inches. Then the correct option is A.
What is the area of the circle?It is the close curve of an equidistant point drawn from the center. The radius of a circle is the distance between the center and the circumference.
Let r be the radius of the circle. Then the area of the circle will be
A = πr² square units
The radius is given as,
r = 36 / 2
r = 18 inches
The area of the circle is given as,
A = π x (18)²
A = 3.14 x 324
A = 1,017.36 square inches
The number of square inches of cloth cut from the square will be 1,017.36 square inches. Then the correct option is A.
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The complete question is given below.
A circle is cut from a square piece of cloth, as shown:
A square, one side labeled as 36 inches, has a circle inside it. The circle touches all the sides of the square. The portion of the square outside the circle is shaded.
How many square inches of cloth is cut from the square?
(π = 3.14)
1,017.36 in2
1,489.24 in2
1,182.96 in2
1,276.00 in2
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
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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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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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
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]
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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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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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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Which is the equation of the axis of symmetry of the graph of y = –3(x – 6)2 + 5?
x = –6
x = –5
x = 5
x = 6
The equation that represents the axis of symmetry of the graph of the quadratic function is the line; x = 6
What is a quadratic function?A quadratic function is a function that has 2 as the highest exponent. The shape of the graph of a quadratic function is a parabola, which is U shaped.
The equation of the axis of symmetry of the graph of y = -3·(x - 6)² + 5 is obtained as follows.
The specified equation is in the vertex form of a quadratic function, which is; f(x) = a·(x - h)² + k
Where;
(h, k) = The coordinate of the vertex
The equation of the axis of symmetry is x = h
Comparison of the equation, y = -3·(x - 6)² + 5 and the vertex form of a quadratic equation, we get.
The vertex, (h, k) = (6, 5)
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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.
railroad crew can lay 5 miles of track each day. They need to lay 140 miles of track. The length, L (in miles), that is left to lay after d days is given by the following function.
Answer:
L = 140 - 5d
Step-by-step explanation:
To get the length left to lay you're going to have to multiply 5 and the number of days and further subtract it from 140
The lengths of the sides of a triangle are x, x + 11, and 2x + 5. a. Write a formula for the perimeter, simplifying your answer. b. If the perimeter is 72 cm, find the value of x.
Use the graph to write a linear function that relates y to x
The linear function of the graph is written as: y = 4/3x + 2.
How to Write a Linear Function that Relates y to x of a Graph?The most common form of a linear function is y = mx + b, where m is the slope of the line and b is the y-intercept.
To write a linear function in this form, you will need to find the slope and y-intercept of the line.
The slope is the ratio of the change in y to the change in x, and the y-intercept is the point at which the line crosses the y-axis. Once you have these two values, you can substitute them into the equation and write the linear function.
Using the given graph:
Slope (m) = rise/run = 8/6
Slope (m) = 4/3
The y-intercept (b) = 2.
To write the linear function, substitute m = 4/3 and b = 2 into y = mx + b:
y = 4/3x + 2
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A pizza delivery man makes $50.00 a shift. If he makes $3.00 on each shift he makes, how much money will he make if he makes 22 deliveries in one shift?
The total money to make 22 deliveries in one shift is, $116.
What is Addition?The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.
We have to given that;
A pizza delivery man makes $50.00 a shift.
And, He makes $3.00 on each shift.
Now, For the total money to make 22 deliveries in one shift is,
⇒ $50 + $3 × 22
⇒ $50 + $66
⇒ $116
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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:
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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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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How do you find the mean median and mode in class 9?.
To find the mean, median and mode add up the values and divide, the value of set in middle of the list and identify the most number of times a number is repeated.
The sum of all observations divided by the total number of observations yields the arithmetic mean of a set of data. For illustration, a cricketer's five ODI scores are as follows: 12, 34, 45, 50, 24. We compute the arithmetic mean of the data using the mean formula in order to get his typical score in a game:
Mean = Sum of all observations/Number of observations
Mean = (12 + 34 + 45 + 50 + 24)/5
Mean = 165/5 = 33
The median of the data is the value of the middle observation after the data have been arranged in either ascending or descending order.
Take these numbers as an example: 4, 4, 6, 3, 2. Let's organize these numbers ascending: 2, 3, 4, 4, 6.
Median = (n + 1)/2th observation
A data mode is the value that appears the most frequently in the provided data, or the observation with the highest frequency.
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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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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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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
Please help this question is on my test and if u help me and it’s right I will memorize the answer u gave me. Btw 20 points
Answer: a. w=3x+8 in b. P=24+6x in, c. P=27 in
Look at the Image Below for work.
Step-by-step explanation:
Circle X has a diameter of 5 inches. Circle Y has a diameter of 3 inches. Which measurement is the closest to the difference between the circumference of circle X and the circumference of Circle Y
The difference between the circumference of circle X and the circumference of Circle Y will be 6.28 inches.
What is the circumference of a circle?It is the close curve of an equidistant point drawn from the center. The radius of a circle is the distance between the center and the circumference. Let d be the diameter of the circle.
The circumference of the circle will be
C = πd units
Circle X has a diameter of 5 inches. Then the circumference is given as,
⇒ π x 5
⇒ 3.14 x 5
⇒ 15.7 inches
Circle Y has a diameter of 3 inches. Then the circumference is given as,
⇒ π x 3
⇒ 3.14 x 3
⇒ 9.42 inches
The difference is calculated as,
⇒ 15.70 - 9.42 inches
⇒ 6.28 inches
The difference between the circumference of circle X and the circumference of Circle Y will be 6.28 inches.
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At the beginning of the year, Gabriel had $25 in savings and saved an additional $14
each week thereafter. Adrian started the year with $80 and saved $9 every week. Let
G represent the amount of money Gabriel has saved t weeks after the beginning of
the year and let A represent the amount of money Adrian has saved t weeks after the
beginning of the year. Write an equation for each situation, in terms of t, and
determine the number of weeks after the beginning of the year until Gabriel and
Adrian have the same amount of money saved.
Answer: 11 weeks
Step-by-step explanation:
G(t) = 25 + 14t
A(t) = 80 + 9t
set G equal to A and find t
25 + 14t = 80 + 9t
5t = 55
t = 11
Question
Name the included angle between JK¯¯¯¯¯¯¯¯
and KL¯¯¯¯¯¯¯¯
.
Answer:
K is the angle between JK and KL. It is called the included angle of sides JK and KL.
