The ball will be 73.5 meters above the ground after a time of 3 seconds. (Correct choice: A)
What is the height of the object after launch?
Herein we have an equation that models the height of the ball as function of time, we need to evaluate the expression for t = 3 s to find the required height:
s(3) = - 4.9 · (3 s)² + 19.6 · (3 s) + 58.8
s(3) = 73.5 m
The ball will be 73.5 meters above the ground after a time of 3 seconds. (Correct choice: A)
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Xin has $126 to purchase balloons for her friend's birthday. Each balloon costs $6. The function p= 126-6m represents the amount of
money Xin has after purchasing n balloons. What is the zero of the function?
So, on solving the question we can say that equation p= 126-6m ; p = 2 = -124 = -6m => m = 20.6666666667
What is equation?An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.
the equation is p= 126-6m
p = 2
-124 = -6m
m = 20.6666666667
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At a local pizza shop customers pay a set price for a large pizza plus an additional per topping ordered. A large pizza with 2 toppings would cost $13. 50, and a large pizza with 5 toppings would cost $15. 75
The cost price of large pizza is $12 and that of toppings is 0.75.
An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values. For example, 3x + 5 = 15. There are different types of equations like linear, quadratic, cubic, etc.
In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.
Let the cost of large pizza be x and that of toppings be y.
x + 2y = 13.50
x = 13.50 - 2y - (1)
x + 5y = 15.75 - (2)
substitute equation (1) in equation (2),
13.50 - 2y + 5y = 15.75
3y = 15.75 - 13.50
3y = 2.25
y = 2.25 / 3
y = 0.75
now, put the value of y = 0.75 in equation (1),
x = 13.50 - 2 × 0.75
x = 13.50 - 1.5
x = 12
Therefore, the cost price of large pizza is $12 and that of toppings is 0.75.
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Latisha is compiling a program for a video game.
For one part of the program they use the rule (x,y) → (x + 10, y - 6) to move a character on the screen.
(a) What output does the rule give when the input is (10,-5)? Show your work.
(b) What output does the rule give when the input is (-4,8)? Show your work.
The shifted coordinates for each of the following are (20,-11) and (6,2).
Coordinates are a pair of integers (Cartesian coordinates), or sporadically a letter and a number, that identify a certain place on a grid, also referred to as a coordinate plane. The x axis (horizontal) and y axis are the two axes that make up a coordinate plane (vertical).
Given, (x,y) → (x + 10, y - 6)
a) when the input is (10,-5) -
10 + 10 = 20
- 5 - 6 = - 11
(20,-11)
b) when the input is (-4,8) -
-4 + 10 = 6
8 - 6 = 2
(6,2)
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On one day at a local minigolf course, there were 320 customers who paid a total of $2,900. If the cost for a child is $7 per game and the cost for an adult is $10 per game, write a system of equations to model this scenario, where x represents the number of children and y represents the number of adults who played that day.
Answer: We can write a system of equations to model this scenario using the information given.
Let x represent the number of children who played minigolf that day, and let y represent the number of adults who played minigolf that day.
The first equation represents the total number of customers, which is the sum of the number of children and the number of adults.
x + y = 320
The second equation represents the total amount of money earned, which is the product of the number of children playing and the cost per child's game plus the product of the number of adults playing and the cost per adult's game.
7x + 10y = 2900
So the system of equations that models this scenario is:
x + y = 320
7x + 10y = 2900
We can use this system of equations to find the number of children and adults who played minigolf that day, given the total number of customers and total amount of money earned. By solving this system of equations we can find the values for x and y.
Step-by-step explanation:
Daniel and Elizabeth had to choose between making a 600-mile round trip by car or plane. Round-trip airfare was $260 for each of them and would take 2 hours. Round-trip cab fare to the airport would add $15. Driving their car would take 2 days each way and would add the cost of gas, food, and lodging. Elizabeth estimated that the whole trip would need $60 for gas, their combined food bill of $25 per day (4 days) , and that a room to share would be $48 for each night of the 4 total nights they would stay in a motel. Find the average cost per passenger-mile of driving.
The average cost per passenger - mile of driving is $0.503 per mile.
What is Average Cost?Average cost is calculated by dividing the total cost by the total output quantity.
There are two options for Daniel and Elizabeth, either by driving car or by plane.
We have to calculate the average cost per passenger - mile of driving in car.
Cost of gas = $60
Food bill for a day for two of them = $25
Food bill for a day for one = 25 / 2 = $12.5
Food bill for one passenger for 4 days = $12.5 × 4 = $50
Cost of room for 1 night = $48
Cost of room for 4 nights = $192
Total cost for 1 passenger = $60 + $50 + $192 = $302
Average cost per passenger - mile of driving = 302 / 600 = $0.503 per mile.
Hence the average cost per mile per passenger is $0.503 per mile.
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Find the length of side
x to the nearest tenth.
Answer:
Step-by-step explanation:
Isosceles triangle (Same angle) means both sides are the same length, triangle is also right meaning you can plug values into Pythagorean theorem ([tex]a^2 + b^2 = c^2[/tex])
[tex]x^2+x^2 = 1^2\\2x^2=1\\x = \sqrt{\frac{1}{2} }\\x = 0.707...\\x=0.7[/tex]
Assuming all my math is right, this is your answer
Limit of (t^4-1/t^3-1) as t approaches 1
ABDE is a cyclic quadrilateral.
ABC and EDC are straight lines.
Angle DBC = 60°.........................................................
The measurement of angle BCD is 30°
What is a cyclic quadrilateral?A cyclic quadrilateral is a four sided shape that can be inscribed into a circle. Each vertex of the quadrilateral lies on the circumference of the circle and is connected by four chords. The opposite angles of a cyclic quadrilateral have a total of 180°.
Given that, ABDE is a cyclic quadrilateral. ABC and EDC are straight lines. Angle DBC = 60°
According to the figure, BD║ AE
Therefore,
∠ DBC ≅ ∠ EAB (definition of corresponding angles)
∠ EAB = 60°
Since, ∠ EAB : ∠ BCD = 2:1
Therefore, ∠ BCD = 60 × 1/2 = 30°
Hence, the measurement of angle BCD is 30°
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Does 5 5 and 7 make a right triangle?
The base of the triangle 7 can be divided in half by a line of symmetry of the isosceles triangle, which will bisect the vertex angle. This creates two right triangles: Each with a base of 3.5 and a hypotenuse of 5.
What is meant by isosceles triangle?
A triangle with two equal sides is known as an isosceles triangle in geometry. Both having exactly two sides of equal length and having at least two sides of equal length are acceptable specifications, with the latter version containing the equilateral triangle as an exception.The faces of bipyramids, the golden triangle, the isosceles right triangle, and some Catalan solids are all examples of isosceles triangles.Isosceles triangles have been studied mathematically since the Babylonian and Egyptian periods.Isosceles triangles have been utilized as ornamentation since the dawn of time and are widely seen in architecture and design, such as in building pediments and gables.To learn more about isosceles triangle refer to
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The base of triangle 7 can be bisected by the line of symmetry of the isosceles triangle that bisects the apex angle. This creates two right triangles.
Each has a base of 3.5 and a hypotenuse of 5.
What does isosceles triangle mean?A triangle with two equal sides is called an isosceles triangle in geometry.
Both exactly 2 equal sides and at least 2 equal sides are permissible specifications, with the exception of equilateral triangles in the latter version. The bipyramid, the golden triangle, the isosceles right triangle, and the face of the Catalan solid are examples of isosceles triangles.
Isosceles triangles have been studied mathematically since Babylonian and Egyptian times.
Used as an ornament since the dawn of time, isosceles triangles are widely used in architecture and design, including in the construction of pediments and pediments.
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Do sides 5 cm 12cm and 13cm form a right angled triangle give reason?
Yes, the mentioned sides of triangle will be right angles triangle because they follow Pythagoras theorem.
A right angled triangle is characterized by presence of hypotenuse, perpendicular and base. The sides of right angled triangle are related through Pythagoras theorem, which is -
Perpendicular² = Base² + Hypotenuse²
As we know that hypotenuse is the longest side of triangle, hence, will be the 13 cm.
So, keeping the values in formula -
13² = 5² + 12²
Taking square on both the sides of equation
169 = 25 + 144
Performing addition on Right Hand Side of the equation
169 = 169
Since, LHS is equal to RHS, hence, it is right angled triangle.
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Can somebody help ASAP? I will give lots of points
Three-part question:
Answer:
A- NQ,
B- 24,
C- 14+10=24
Create math problems with the words : spent, difference, decreased, and dropped (temp) for subtraction
The math word problems with the given words is A has 52 marbles, B has 105 marbles, find the difference between the number of marbles between A and B.
What are word problems?A math word problem is a question that is written as one or more sentences and asks students to use their mathematical understanding to solve an issue from "real world."
1. A has 52 marbles, B has 105 marbles, find the difference between the number of marbles between A and B.
2. The temperature of city A is 35 degrees, on the second day the temperature decreased to 15 degrees. How much did the dropped (temp)?
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In the triangle below, with right angle I, suppose that m angle G = (4x-16)° and m angle H= (3x+15)°.
Find the degree measure of each angle in the triangle.
Therefore , the solution of the given problem of triangle comes out to be the measure of each angle is 36,54 and 90.
What is a triangle and some of its properties?A triangle is a three-sided polygon in geometry that has three edges and three vertices. The fact that the internal angles of a triangle add up to 180 degrees is the most crucial aspect of triangles. Angle sum property of a triangle is the name of this property.
Here,
Using the angle sum property of triangle,
90+4x-16+3x+15=180.( Since its a right angle triangle)
7x+89=180
7x=91
x=13
Therefore, ∠G=4X-16=36 and ∠H=3x+15=54.
Hence, the measure of each angle is triangle is 36,54 and 90.
Therefore , the solution of the given problem of triangle comes out to be the measure of each angle is 36,54 and 90.
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Find the distance between the points (8, 1) and (2, 9).
Round decimals to the nearest tenth.
Answer:
10
Step-by-step explanation:
using the distance formula
Pls the area of the figure.
Answer:
36
Step-by-step explanation:
4 x 4 = 16
2 x 10 = 20
You would have to separate the square and the rectangle.
The way you do this is by cut of the number and subtracting them, like 6 and 2 to get the square.
i need help please with this problem
Answer:
Pleae see the attached graph.
Step-by-step explanation:
The values of x are graphed for their respective valid regions, as defined in the question.
The measures of two supplementary angles total 180 degrees. The measure of angle y is 65 degrees less than the measure of angle x. What are the measures of the angles?
The measure of angle x is 122.5 degrees. The measure of angle y is 57.5 degrees.
The measure of angle x is 115 degrees. The measure of angle y is 65 degrees.
The measure of angle x is 57.5 degrees. The measure of angle y is 122.5 degrees.
The measure of angle x is 65 degrees. The measure of angle y is 115 degrees.
Based on the definition of supplementary angles, the measures of the angles are:
Angle x = 122.5°
Angle y = 57.5°
What are Supplementary Angles?When two angles gives a sum of 180 degrees when they are added together, then the two angles are referred to as supplementary angles.
For example, if angle x and angle y are supplementary angles, it means that:
Measure of angle x + measure of angle y = 180 degrees.'
Given the following:
The measure of angle x = x degrees
The measure of angle y = x - 65 degrees.
Therefore, we have:
x + x - 65 = 180
2x - 65 = 180
2x = 180 + 65
2x = 245
2x/2 = 245/2
x = 122.5
Thus:
Measure of angle x = 122.5°
Measure of angle y = 180 - 122.5 = 57.5°
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Answer:
A
Step-by-step explanation:
Challenge Emily and Andy each go to a hardware store to buy wire. The table shows the cost y in dollars for x of the wire they need. Emily needs 22 feet of wire. Andy needs 11 yards of the wire. How much will each of them spend on wire?? please answer quickly!!!
The amount of money each of them spends on the wire will be $23.76 and $35.64, respectively.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
Challenge Emily and Andy to each go to a home improvement shop to purchase wire. The table shows the expense y in dollars for x of the wire they need.
y = kx
9 = 100k
k = 0.09
Then the question is given as,
y = 0.09 · x
Emily needs 22 feet of wire. Then the cost is given as,
y = 0.09 · (22 × 12)
y = $23.76
Andy needs 11 yards of the wire. Then the cost is given as,
y = 0.09 · (11 × 3 × 12)
y = $35.64
The amount of money each of them spends on the wire will be $23.76 and $35.64, respectively.
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The complete question is given below.
What is the 2nd coordinate?
The second coordinate in a two-dimensional coordinate system is the y-coordinate, which indicates the vertical distance from the origin point (0, 0).
What is coordinates?Coordinate is a pair of numbers used to identify the position of a point in a plane or in space. It is mostly used in mathematics, science, and engineering. Coordinates are used to define locations on maps, to plot graphs, and to identify points on a two-dimensional plane. By knowing the coordinates of two points, one can calculate the distance between them.
The y-coordinate can be either positive, negative, or zero. The y-coordinate is also referred to as the “ordinate” or the “vertical coordinate”. The second coordinate is usually written as the number located at the top of the y-axis on a graph.
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A car traveled a distance of 192 miles from New York go a small town in Pennsylvania in 3 hours. Find the speed of the car.
Answer: 64 miles per hour
Step-by-step explanation: 192 divided by 3= 64
Quadrilateral JKLM is shown.
Suppose quadrilateral J´K´L´M´ is a reflection of JKLM in the line y = x. The coordinates of M´ would be : (_,_)
Suppose quadrilateral J''K''L''M'' is a rotation of JKLM 90° counterclockwise about the origin. The coordinates of J'' would be : (_,_)
The coordinates of M´ would be : (4, 1) after reflection across the line y = x.
The coordinates of J'' would be : (3, -1) after counterclockwise about the origin.
What is a transformation?A point is transformed when it is moved from where it was originally to a new location. Translation, rotation, reflection, and dilation are examples of different transformations.
The quadrilateral JKLM is shown in the given figure.
As per the given graph, we can see that
The coordinates of M would be : (4, 1)
Suppose quadrilateral J´K´L´M´ is a reflection of JKLM in the line y = x.
Then the coordinates of M´ would be : (4, 1)
The coordinates of J would be : (1, 3)
Suppose quadrilateral J''K''L''M'' is a rotation of JKLM 90° counterclockwise about the origin.
Under a counterclockwise rotation about the origin of 90 degrees
A coordinate ( x, y ) → ( y, - x ),
The coordinate J is (1, 3) and is translated using the rule
Then simply plug in the values of x and y which are x = 1 and y = 3
Thus (1, 3) → (3, -1)
Thus, the coordinates of J'' would be : (3, -1)
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How do you graph 2 3 on a number line?
We have plotted the point (2/3) on a number line and attached and explained it below.
A number line is one of the methods of visually representing any point that is a real number on a graduated straight line. This is made by marking graduations on a simple normal line and then marking whatever point we need on it.
The point (2/3) has been given in the problem which we need o plot on the number line. Since this point is a fraction, we need to divide/solve it first and then see where it will fit. On dividing the fraction, we find that the point is 0.66. Now, we find the graduations 0 and 1 since it lies between them. The image for this has been attached below.
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The upfront cost of a Porsche is 64K. At the end of 12 Years, the car is worth only $4000, Write a linear equation to represent the value of the car in terms of the year.
The linear equation to represent the value of the car in terms of the year will be c = 64000 - 5000y
How to illustrate the equation?An equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.
In this situation, the upfront cost of a Porsche is 64K and at the end of 12 Years, the car is worth only $4000.
The difference in amount will be:
= $64000 - $4000
= $60000
Number of years = 12
Amount in depreciation per year = $60000 / 12
= $5000 per year
The linear equation to represent the value of the car in terms of the year will be:
c = 64000 - 5000y
where c = value
y = number of years
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Anya is 3 years older than her brother,Cole. In 11 years,Cole will be twice Anya’s current age. Find their current age
By solving these equations, Cole is currently 27 years old, and Anya is 30 years old.
How does math work out age?A person's date of birth is compared to the date on which their age needs to be calculated as part of the age calculation process. The person's age is determined by deducting the person's birthdate from the given date. Age equals Given Date - Birthdate
Let x stand in for Anya's current age and y for Cole's present age.
Cole's older brother, Anya, is three years older. Hence:
x = y + 3
x - y = 3 (1) (1)
The total of their ages will be 79 in 11 years. Hence:
(x + 11) + (y + 11) = 79
x + y = 57 (2) (2)
Equations 1 and 2 are simultaneously solved to produce:
x = 30, y = 27
Cole is currently 27 years old, and Anya is 30 years old.
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ken added 5/8 cups more walnuts to the trail mix how many cups of Tremors does he have
Answer:
Please provide more information. Since you don't provide the original amount of walnuts used, we can't solve the problem.
Multiple Choice: Triangle ABC has been reduced to create triangle XYZ. By what ratio has it been reduced?
A
12
3/4
2/3
1/2
1.5
18
15
B
80
Y
XL
12
10
Answer:
2/3
Step-by-step explanation:
Choose any of the similar sides and set up the ratio, then reduce to the simplest fraction:
12/18 = 4/6 = 2/3
8/12 = 4/6 = 2/3
10/5 = 2/3
What is called a complex number?
A complex number is a number that can be expressed in the form a + bi, where a and b are real numbers, and i is the imaginary unit, which satisfies the equation i2 = -1.
What is complex number?
The number a is the real part of the complex number and b is the imaginary part. A complex number is said to be a sum of a real number and an imaginary number. Complex numbers are used in many branches of mathematics, including calculus, linear algebra, quantum mechanics, and electrical engineering.
They are also used in engineering, physics, chemistry, and other scientific fields. Complex numbers are useful in many real-world applications, such as finding the roots of a polynomial equation or solving systems of linear equations. Complex numbers can also be used to represent points in the plane and can be used to model phenomena in the physical world, such as electrical circuits and waveforms.
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kiran's Mother gets a resturant bill for $40. She has a coupon for 25% off. After the discount is applied, she adds 20% as a tip. What is the total after the discount and tip? Explain or show your reasoning.
Answer: $36
Step-by-step explanation:
Bill is $40, the 25% off coupon is used, and the 20% tip is left.
Step 1: Find 25% of 40
is/40=25/100 ------> 40(25)/100=10
Step 2: Find the new bill price after discount
40-10=30
Step 3: Find the 20% tip of 30
is/30=20/100 ---------> 30(20)/100=6
Step 4: Add the tip with the restaurant bill
30+6=$36
PLEASE HELP!!! I NEED HELP WITH MY HOMEWORK!!!!
(GEOMETRY)
WILL MARK BRAINLIEST!!!!
The right triangle in marked question number 3 have the value of u = 2 and v = √2 using the trigonometric ratio of sine and cosine of the angle 45°.
What are trigonometric ratiosThe trigonometric ratios involves the relationship of an angle of a right-angled triangle to ratios of two side lengths. Basic trigonometric ratios includes; sine cosine and tangent.
Considering the angle 45° for the right triangle, recall that sin 45° and cos 45° are generally both equal to √2/2
sin 45° = √2/u {opposite/hypotenuse}
√2/2 = √2/u
u = √2/√2 × 2 {cross multiplication}
u = 2
cos 45° = v/u {adjacent/hypotenuse}
√2/2 = v/2
v = 2/2 × √2
v = √2
Therefore, the value of u = 2 and that of n = 10, using the trigonometric ratio of sine and cosine of the angle 45° for the right triangle.
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]What is the first step in solving the quadratic equation -5x2+8=133?
taking the square root of both sides of the equation
subtracting 8 from both sides of the equation
squaring both sides of the equation
adding 8 to both sides of the equation
The first step in solving the quadratic equation is subtracting 8 from both sides.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 4 = 9 is an equation.
We have,
5x² + 8 = 133
Subtract 8 into both sides.
5x² = 133 - 8
5x² = 125
Divide both sides by 5.
x² = 125/5
x² = 25
x = √25
x = 5
Thus,
The root of the equation is 5.
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