The probability that both choose Black Panther as their favourite character is 189/3875.
How is the probability calculated?KHS students' list of their favourite Marvel comic character:
Spiderman - 45
Hulk - 30
Black panther - 28
Black widow - 17
Rocket raccoon - 5
Total = 125
The chances that two people can be drawn from a sample of 125 playing cards in 125[tex]C_{2}[/tex] ways.
[tex]125C_{2}=\frac{125*124}{1*2} \\\\125C_{2}=\frac{15500}{2}\\\\125C_{2}= 7750[/tex]
The event of choosing 2 Black Panthers from 28 can happen in 28 [tex]C_{2}[/tex] ways.[tex]28C_{2}=\frac{28* 27}{1*2} \\\\28C_{2}=\frac{756}{2}\\\\28C_{2}= 378[/tex]
The probability that both choose Black Panther as their favourite character is:[tex]P(BP) = \frac{28 C _{2}}{125C_{2}} \\\\P(BP) = \frac{378}{7750} \\\\P(BP) = \frac{189}{3875}[/tex] or 0.04877
So, option c is correct.
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty. The likelihood that an event will occur increases with its probability. Probability informs us of the likelihood that an event will occur given enough trials.Probabilities can be expressed numerically by the number of desired outcomes, divided by the total number of outcomes, when dealing with experiments that are random and well-defined in a purely theoretical context (like flipping a coin).To learn more about probability, refer:
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points
A right triangle has a hypotenuse of 10cm. If one angle is 40°, find the length of each leg. Round to the nearest whole number. Enter the smallest leg first. Do not enter units of measurement, only numbers.
Answer: 6 and 8
Step-by-step explanation: A right triangle is a triangle with one angle that measures 90 degrees. The side opposite the right angle is called the hypotenuse, and the other two sides are called the legs. In this case, the hypotenuse is 10cm long.
If one angle of the triangle is 40 degrees, then the other angle must be 90-40 = 50 degrees. The remaining two angles of a triangle must add up to 180 degrees, so the third angle is 180-40-50 = 90 degrees. This means that the triangle is a right triangle, and we can use the Pythagorean theorem to find the lengths of the legs.
The Pythagorean theorem states that 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. In this case, we have a2 + b2 = c2, where a and b are the lengths of the legs and c is the length of the hypotenuse.
Substituting the values from the problem, we have a2 + b2 = 102, which simplifies to a2 + b2 = 100. Since we don't know the values of a and b, we can't solve for them directly. However, we can use the fact that the angle opposite the longer leg is 50 degrees, and the angle opposite the shorter leg is 40 degrees. This means that the longer leg is the opposite side of the 50-degree angle, and the shorter leg is the opposite side of the 40-degree angle.
Since the longer leg is opposite the 50-degree angle, and the shorter leg is opposite the 40-degree angle, we can use the tangent function to find the ratio of the lengths of the legs. The tangent of an angle is defined as the ratio of the opposite side to the adjacent side, so we have tangent(50 degrees) = opposite side / adjacent side = a / b, and tangent(40 degrees) = opposite side / adjacent side = b / a.
Solving for a and b, we have a = b * tangent(50 degrees) and b = a * tangent(40 degrees). Since the legs are the opposite sides of the 40- and 50-degree angles, we can substitute the values from the problem to get a = b * tangent(50 degrees) = 100 * tangent(50 degrees) and b = a * tangent(40 degrees) = 100 * tangent(40 degrees).
To find the values of tangent(50 degrees) and tangent(40 degrees), we can use a calculator or look up the values in a table of trigonometric functions. We find that tangent(50 degrees) = 1.191753592594, and tangent(40 degrees) = 0.839099631177. Substituting these values into the equations for a and b, we have a = 100 * 1.191753592594 = 119.1753592594 and b = 100 * 0.839099631177 = 83.9099631177.
Rounding to the nearest whole number, we have a = 119 and b = 84. The lengths of the legs of the triangle are therefore 6 and 8.
A lifeguard recorded the daily average temperature in degrees Fahrenheit and the number of swimmers at the pool each day for 29 days. The scatterplot displays the data.
Complete the correct answers from each drop down menu to complete the statements.
As the x-values increase, the y-values decrease or increase?
This represents a negative or positive? linear or nonlinear? association between the daily average temperature and the number of swimmers at the pool.
For the given graph, As the x-values increase, the y-values also increase. This represent a positive graph. It is nonlinear function graph.
What is graph?In elementary mathematics, the term "graph" designates a plot or a function graph. A graph is, in the language of mathematicians, a set of points and the connections between some subset of those points (which may be empty). In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way. The relationships between two or more items are frequently represented by the points on a graph.
Here,
For the given graph, As the x-values increase, the y-values also increase.
This represent a positive graph.
It is nonlinear function graph.
As the x-values rise for the presented graph, the y-values rise as well. This graph shows a favorable trend. It is a graph of a nonlinear function.
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"9 less than a number is
zero."
I need help
Answer:9 less than 9 is 0
Step-by-step explanation:
9-9=0
Answer:
9
Step-by-step explanation:
Less means minus, so basically X ( something ) - 9 is 0
X - 9 = 0
You add 9 on each side
X = 0 + 9
X = 9
Basically, all you're doing is the reverse, you start with 0 and do the opposite of taking away 9 which is adding nine so that you get the number:
0 + 9 = 9
Hence the number is 9
:)
( sorry if I misunderstood )
1. Transform The equations into slope-intercept form: y mx+b
2. Graph the system of equations and find the solution
y=x+2
y=3x-2
The graph for system of the equation y = x + 2 and y = 3x - 2 are shown below and solution for the equations is x = 2 and y = 4.
What is the slope intercept form of an equation ?When any equation is represented in the y = mx +c form, it is called the slope intercept form of the equation.
Here m is slope and c is constant.
The given system of equations is,
y = x + 2 (1)
and y = 3x - 2 (2)
The given equations are already in slope intercept form and the slope of the equations are, m₁ = 1 and m₂ = 3.
The graph of the equations y = x + 2 and y = 3x - 2 are represented below.
To find the solutions, solve the equations (1) and (2),
x = 2 and y = 4.
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Given the equation 5y = 225, solve for y.
Answer: y = 45
Step-by-step explanation:
225/5 = 45
45·5 = 45
The sides of a hexagon are 2, 3, 2, 4, 7, and 6. Find the perimeter of a similar hexagon
with two sides of length 3.
The perimeter of hexagon is 24 unit. It is an irregular hexagon.
What is hexagon?A geometrical shape having six straight sides and six angles. The hexagon that has all six sides equal is called regular hexagon and if inequal lengths available is termed as irregular hexagon.
What is perimeter of hexagon?The term perimeter refers to the total length calculated along the boundary of a geometrical shape. Perimeter of a hexagon is six times of its length if it has similar six length. But the hexagon having variable side length is measured by adding the total six length.
we are given a hexagon that is irregular. sides are 2, 3, 2, 4, 7, 6 unit
now perimeter = 2+3+2+4+7+6
= 24 unit
hence, perimeter is 24 unit.
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Value of [ 1234568 * 198765432 + 98765432 * 98765432 ]^{1/4}
Answer: 10000
Step-by-step explanation:
((1234568)(198765432)+(98765432)(98765432))^1/4
=(245389441853376+(98765432)(98765432))^1/4
=(245389441853376+9754610558146624)^1/4
=10000000000000000^1/4
=10000
Hope this helps!!! :)
Landen had 2 3/4 king ize chocolate bar left formm halloween. He hare them between him and hi 4 friend. What fraction did they each get?
We can conclude that each one of them will get a fraction of 11/20 chocolate.
What are fractions?An element of a whole is a fraction.
The number is represented mathematically as a quotient, where the numerator and denominator are split.
Both are integers in a simple fraction.
A fraction appears in the numerator or denominator of a complex fraction.
So, the fraction of chocolate each friend gets is:
We know that Landen has: 2¾ of chocolate
She shares it with his 4 more friends.
So, we easily know that there will be 5 pieces of chocolate that are 4 friends, and 1 Landen.
Fraction of choclta eecah gets:
2¾ ÷ 5
8+3/4 ÷ 5
11/4 ÷ 5/1
11/4 * 1/5
11/20
Therefore, we can conclude that each one of them will get a fraction of 11/20 chocolate.
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The stem-and-leaf plot shows the ages of customers who were interviewed in a
survey by a store.
How many customers were older than 41?
Every time mary bakes a batch of brownies, she uses cup of chocolate. If she has cup(s) of chocolate remaining, how many batches of brownies can mary make? input your answer as a whole number.
Mary is capable of making 4 batches of brownies.
What is unitary method ?Area is the total amount of space that an object's shape or a flat (2-D) surface occupy.
Create a square on paper by using a pencil. Two dimensions make it up. A shape's area on paper is the space it takes up.
Imagine that your square is made up of smaller unit squares.
The area of a figure is equal to the number of unit squares required to completely cover the surface area of a particular 2-D shape. Square cms, square feet, square inches, square meters, etc. are a few common units for measuring area.
To get the area of the square figures presented below, draw unit squares with 1-centimeter sides. Therefore, the shape will be measured.
According to our question-
divide 8/10 by 1/5
4
Hence, Mary is capable of making 4 batches of brownies.
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The function f(x) = 150 - 8x represents the distance, in miles, remaining on a trip
x hours into the trip. What is the value of f(5)?
Subtracting a number is the same as adding its additive inverse. For which elevation do we need to find the additive inverse? What is the additive inverse of that elevation?
Yes subtracting a number is the same as adding its inverse. We have to find the additive inverse of a function.
What is additive inverse?The additive inverse of a number is the number which when we add to the number results zero.
How to find additive inverse?Complex numbers are made up of both real and fictitious numbers. A + iB, where A is the real number and B is the imaginary number, is a complex number.
The additive inverse of A + iB should now be a value that, when added to a given complex number, produces the result zero. It will therefore be -(A + iB).
Suppose we have to find additive inverse of 5.
Let the additive inverse of 5 be x.
So,5+x=0
x=-5
So the additive inverse of 5 is -5.
Hence to find additive inverse of a positive number we have to just put a negative mark and for a negative number we have put positive mark in front of the number.
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Triangle XYZ is taken by a dilation with center Y and scale factor 5/2 to Triangle XYZ.The measure of angle YXZ is 83 degrees and the measure of angle YXZ is 22 degrees.
Task 1:a) The measure of angle Y'Z'X'= 22 degrees
Task2:b) The measure of angle X'Y'Z'= 75 degrees.
What is meant by an angle?An angle is a figure in Euclidean geometry made up of two rays that share a terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are located in the plane where the rays are located. The meeting of two planes can also create an angle. Angle can also be used to describe the size of an angle or of a rotation. This metric represents the proportion of a circular arc's length to radius.
Angle Y'Z'X' = YZX = 22 degrees (in a triangle, angle dilation does not
modify angle size). Only the sides' length varies.
The sum of the triangle's angles for the XYZ angle is 180 - 83
-22 = 75 degrees. Since there are already two angles supplied, the third
angle is 75 degrees, so X'Y'Z' = XYZ = 75 degrees. The dilation angle size remains unchanged (for the same reason as in the previous challenge).
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The complete question is:
"Triangle XYZ is taken by a dilation with center Y and scale factor 5/2 to Triangle X’Y’Z’. The measure of angle YXZ is 83 degrees and the measure of angle YZX is 22 degrees.
Task 1: a) What is the measure of angle Y’Z’X’? Explain your reasoning.
Task 2: b) What is the measure of angle X’Y’Z’? Explain your reasoning."
A mall cube ha the volume hown. It ide length i 3. 5 in. Le than a econd, larger cube. What i the volume of the larger cube?
Volume:85 in^3
The large cube has a length of 7 inches each side and it's volume is 343 cubic inches.
Given,
The length of the small cube, a = 3.5 inch
The length of large cube = 2a = 2 × 3.5 = 7 inches
Now,
We have to find the volume of large cube
Volume;-
The space occupied within an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the object's capacity.
Here,
Volume of cube = a³
Volume = 7³ = 343 cubic inches
That is,
The length of side of the large cube is 7 inches and the volume of large cube is 343 cubic inches.
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Given question is incomplete. The completed question is;
A small cube has a length of 3.5 inch. The length of large cube is twice the small cube. Find the volume of the large cube.
The last time you went to the local market, you bought 17 pounds of rice for a community meal for $12.75. This week you have to prepare another community meal and need 38 pounds of rice.
Assuming the price is the same from the last purchase, what will the cost of the 38 pounds of rice be?
You bought 17 pounds of rice for a group lunch at the neighborhood market the last time you went there for $12.75. This week, you'll need 38 pounds of rice to prepare another shared meal.
How do you find original price ?Step 1: Divide the percent discount by 100% to convert it to a decimal. Step 2: Construct the equation P=(1d)x P = (1 d) x where P is the sale price, d is the discount expressed as a decimal, and x is the original price of the item to get its original price.
A linear demand equation is written as Q = a - bP in standard form. The price is treated as a function of quantity required in the inverse demand equation (also known as the pricing equation): P = f(Q) (Q).
When you most recently visited the neighborhood market, you spent $12.75 on 17 pounds of rice for a communal lunch. You need 38 pounds of rice this week to create another communal supper.
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it says i need the regression equation and the final answer
please help i dont understand this at all :(
A linear regression equation that represents the data set is y = -29.97x + 1048.80. Also, the number of new cases for 2026 is equal to 689 cases.
How to write the linear regression equation?In this scenario, the Year since 2014 (x) would be plotted on the x-axis of the scatterplot while the New cases (y) would be plotted on the x-axis of the scatterplot.
On the Excel sheet, you should right click on any data point on the scatterplot, select format trend line and then tick the box to display an equation for the linear regression (line of best fit) on the graph.
By critically observing the scatterplot (see attachment) which models the relationship given in the table, an equation for the linear regression is given by:
y = -29.97x + 1048.80
For 2026, the value of x is given by:
x = 2026 - 2014 = 12 years.
Now, we can determine the new cases for 2026:
y = -29.97(12) + 1048.80
y = -359.64 + 1048.80
y = 689.16 ≈ 689 cases.
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For a project in his Geometry class, Yusuf uses a mirror on the ground to measure the height of his school building. He walks a distance of 13.95 meters from the school, then places a mirror on flat on the ground, marked with an X at the center. He then steps 2.15 meters to the other side of the mirror, until he can see the top of the school clearly marked in the X. His partner measures the distance from his eyes to the ground to be 1.35 meters. How tall is the school? Round your answer to the nearest hundredth of a meter.
The height of the school is 9 meters.
What is proportion?
A proportion is an equation in which two ratios are set equal to each other. For example, if there is 1 boy and 3 girls you could write the ratio as 1 : 3 (for every one boy there are 3 girls) 1 / 4 are boys and 3 / 4 are girls. 0.25 are boys (by dividing 1 by 4).
Angle of incidence = Angle of reflection
As we can see in the picture attached, both the angles (θ) are equal.
m∠ACB = m∠ECD = 90° - θ
m∠ABC = m∠ADC = 90°
Therefore, both the triangles ΔABC and ΔEDC will be similar.
And by the property of similar triangles, their corresponding sides will be proportional.
AB/ED = CB/CD
1.35/ED = 2.15/13.95
ED = 8.75 meters
ED ≈ 9 m.
Hence, the height of the school is 9 meters.
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A 3 foot Gingerbread man i tanding 12 feet from the bae of the tallet candy cane he ha ever een. He i looking at the top of the candy cane at an angle of 35⁰. How tall i the candy cane?
The height of the candy cane is 11.4024 feet when the man is looking at the top of the candy cane at an angle of 35°.
We have the following information:
A 3 foot Gingerbread man is standing 12 feet from the base of the tall candy cane he has ever seen. He is looking at the top of the candy cane at an angle of 35⁰.
Now, we can find the height of the candy cane using the trigonometric function of tan.
Now, the base will be 12 feet and the height of the candy cane will be added to 3 feet to find the real height of the cane.
Tan 35 = height of the cane/base
0.7002 = Height of the cane/12
Height of the cane = 12*0.7002
Height of the cane = 8.4024 feet
Real height of the cane = 3+8.4024 feet
Real height = 11.4024 feet
Hence, the candy cane is 11.4024 feet when the man is looking at the top of the candy cane at an angle of 35°.
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what is the equation for the function (2,44) and (5,80)
Answer:
5, 80
Step-by-step explanation:
because 5b / 280 = c2 - b2
Answer: y= 12x +22
Step-by-step explanation:
Find the slope and y intercept
Mr. Potter's class will take a test for 1\dfrac121
2
1
1, start fraction, 1, divided by, 2, end fraction hours. They need to finish by half past 111111 to get to lunch on time.
90 minutes before 11:40.
= 10:10 + 90 minutes
= 10:10 + 1 hour + 30 minutes
= 11:40
The latest time the class can start the test to get to lunch on time is 10:10.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Time take to take the test = 1(1/2) hours = 1 hour and 30 minutes
The time the test needs to finished = 11:40
This means,
The test must start 90 minutes before 11:40.
1 hour = 60 minutes
1 hour and 30 minutes = (60 + 30) minutes
1 hour and 30 minutes = 90 minutes
Now,
90 minutes before 11:40.
= 10:10 + 90 minutes
= 10:10 + 1 hour + 30 minutes
= 11:40
Thus,
The latest time the class can start the test to get to lunch on time is 10:10.
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The complete question is:
Mr. Potter's class will take a test for 1 1/2 hours. They need to finish by 11:40 to get to lunch on time.
What is the latest time the class can start the test to get to lunch on time?
What system of linear inequalities is shown in the graph?
Answer:
y>x?
Step-by-step explanation:
The standard form of the equation of a parabola is y = -2x2 - 8x-13. What is the vertex form of the equation?
O A. y = -2(x-2)² - 5
OB. y = -2(x + 2)² - 5
O C. y = -2(x + 2)² -13
OD. y = -2(x-2)² - 13
In vertex form the equation of the parabola is [tex]y = -2(x+2)^{2} -5[/tex].
What is Vertex form if Parabola ?
When a graph crosses its symmetry axes, the vertex formula in mathematics may be used to get the vertex coordinate of a parabola. The vertex point is often represented by (h, k). We are aware that a parabola's conventional equation is y=ax2+bx+c. The vertex in this case should be near the base of the U-shaped curve if the coefficient of x2 is positive. The vertex should be at the peak of the U-shaped curve if the coefficient of x2 is negative. The standard form and vertex form of a parabola, as well as the vertex formula, will be covered in this article.
We are aware that the parabola's conventional form is y=ax2+bx+c.
So, y = a(x-h)2 + k is the vertex form of a parabola.
To determine a parabola's vertex, use the vertex formula. There are two methods for locating a parabola's vertex.
Vertex, (h, k) = (-b/2a, -D/4a)
Equation of the parabola,
y = [tex]-2x^{2} - 8x -13[/tex]
here ,
a = -2 , b = -8 and c = -13.
Therefore,
h = -b/2a = +8/-4 = -2 and,
k = -D/ 4a = [tex]-(b^{2} - 4ac)/4a[/tex] = -(64 - 104)/-8 = -40/8 = -5
So, the coordinate of vertex is (-2, -5)
So the vertex form of equation of parabola is
[tex]y = a(x-h)^{2} + k[/tex]
⇒ [tex]y = a(x+2)^{2} -5[/tex]
⇒ [tex]y = ax^{2} + 4ax +4a -5[/tex]
Equating this equation with equation pf parabola we get a = -2
So, in vertex form the equation of the parabola is [tex]y = -2(x+2)^{2} -5[/tex].
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Determine the point and slope from the equation
y-4-5(x + 7)
point (-7.4) slope: -5
point (7.4) slope: -5
point (7.-4) slope: -5
To determine the point and slope from the given equation, we can rewrite the equation in the standard form of a linear equation: y = mx + b, where m is the slope and b is the y-intercept (the point at which the line crosses the y-axis).
In this case, the equation is already in the standard form, so we can immediately see that the slope is -5 and the y-intercept is (0, 4). This means that the point at which the line crosses the y-axis is (0, 4), and the slope of the line is -5.
Therefore, the correct answer is:
Point: (0, 4)
Slope: -5
The angle of depression
from the top of a cliff to
a boat is 32°. If the cliff
is 600 feet tall, how far
is the boat from the base
of the cliff?
Round to the nearest hundredth.
i think it would be 200
Triangle a b c has centroid g. lines are drawn from each point through the centroid to the midpoint of the opposite side to form line segments a f, b d, and c e. the length of line segment a g is 19 x 14 and the length of line segment d g is 9 x 2. g is the centroid of triangle abc. what is the length of gf? units
For the given triangle abc, g is the centroid of and the length of line segment d g is 9 x 2 so the length of line segment gf is 133 units.
What is a triangle?A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. The specified object is a triangle having vertices A, B, and C. triangle with equal sides.
What are the 3 sides of triangle?There are three sides and three angles in every triangle, some of which may be the same. In the case of a right triangle, the three sides are given unique names: the hypotenuse, which is the side that faces the right angle, and the legs, which are the other two sides.
from given information;
2x = 19 * 14
Solving for value of x,
x = 19 * 14 / 2
x = 19 * 7
x = 133.
as both lines are same,
now we found that the length of line segment gf is 133 units.
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A school sold 461 tickets for the school play. Student tickets cost $3 and adult tickets cost $4. Ticket sales totaled $1624.
Part A. Write and solve a system of equations to model this situation.
Part B. Then explain the meaning of your solution.
Part A: A system of equations to model this situation includes:
Equation 1: x + y = 461
Equation 2: 3x + 4y = 1624.
Part B: The solutions of the equations show that 220 students bought tickets at $3 each, while 241 adults bought the tickets at $4 each to give the total sales revenue as $1,624.
What is a system of equations?A system of equations means simultaneous equations.
Simultaneous equations are two or more equations solved at the same time.
Simultaneous equations can be solved by graphing, substitution, and elimination methods.
In this situation, we decided to solve the equations by substitution after equating x = 461 - y from the first equation.
The total number of tickets sold for the school play = 461
The cost of student tickets per unit = $3
The cost of adult tickets per unit = $4
The total revenue raised = $1,624
Equations:Let the number of students = x
Let the number of adults = y
x + y = 461 ... Equation 1
3x + 4y = 1624 ... Equation 2
From Equation 1:
x = 461 - y ... Equation 3
Substitute x in Equation 2
3(461 - y) + 4y = 1624
1,383 - 3y + 4y = 1624
y = 241
From Equation 1:
x = 461 - y
= 461 - 241
= 220
Check:
3x + 4y = 1624
3(220) + 4(241) = 1624
660 + 964 = 1624
1624 = 1624
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Where do volcanoes come from 
Answer: Deep inside Earth, between the molten iron core and the thin crust at the surface, there is a solid body of rock called the mantle. When rock from the mantle melts, moves to the surface through the crust, and releases pent-up gases, volcanoes erupt. Extremely high temperatures and pressure cause the rock to melt and become liquid rock or magma. When a large body of magma has formed, it rises through the denser rock layers toward Earth's surface. Magma that has reached the surface is called lava.
Step-by-step explanation:
What is 3N?
Help please
The required matrix is obtained by scalar multiplication as [tex]\left[\begin{array}{ccc}-6&0\\9&15\\\end{array}\right][/tex].
What is a matrix?A matrix can be defined as a rectangular array of elements written in the form of rows and columns. For m rows and n columns the order of the matrix can be written as m × n.
The number of rows and columns for a square matrix are always equal.
Two matrix can only be added when their orders are equal.
The given matrix can be written as follows,
N = [tex]\left[\begin{array}{ccc}-2&0\\3&5\\\end{array}\right][/tex]
Where its elements are a₁₁ = -2, a₁₂ = 0, a₂₁ = 3 and a₂₂ = 5.
Since, the scalar multiplication of a matrix is equivalent to the matrix each of which elements are multiplied by that scalar.
As per the problem the matrix 3N can be evaluated as follows,
3N = [tex]\left[\begin{array}{ccc}-2\times3&0\times3\\3\times3&5\times3\\\end{array}\right][/tex]
= [tex]\left[\begin{array}{ccc}-6&0\\9&15\\\end{array}\right][/tex]
Hence, the matrix 3N is obtained by multiplying all of the terms of matrix by 3 as [tex]\left[\begin{array}{ccc}-6&0\\9&15\\\end{array}\right][/tex].
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A lake fishing map is laid out on a coordinate plane with each unit equal to 1 mille. The boat is launched from the point (7,0) and goes to point (7.-7) to fish. From there, the boat
travels to (0, -7) to fish and then goes back to the launch point.
Determine the total number of miles traveled. Round to the nearest whole number.
•10 miles
•12 miles
•14 miles
•24 miles
The total number of miles traveled by the boat, found using Pythagorean Theorem, rounded to the nearest whole number is about 24 miles
What does the Pythagorean Theorem state?Pythagoras theorem indicates that the square of the hypotenuse side of a right triangle is the same as the sum of the squares of the legs.
The coordinates of the location of the boat as goes to fish are;
The coordinate of the point at which the boat is launched = (7, 0)
The coordinate of the point at which the boat goes to fish = (7, -7)
The coordinate of the location the boat then travels to in order to fish = (0, -7)
Let A represent the point (7, 0), and let B represent the point (7, -7), and let C represent the point (0, -7), we get;
A(7, 0), B(7, -7), C(0, -7)The length of segment AB = 0 - (-7) = 7
Length of segment BC = 7 - 0 = 7
The x and y-coordinates of the points A and C are different therefore, the length of the segment AC can be found using the distance formula used for finding the distance between two points on the coordinate plane (a form of the Pythagorean Theorem) as follows;
d = √((x₂ - x₁)² + (y₂ - y₁)₂)
The distance between the points A(7, 0), and C(0, -7), is therefore;
Length of segment AC = √((0 - 7)² + (-7 - 0)²) = 7·√2
The total number of miles the boat traveled is therefore;
Total distance traveled = AB + BC + AC
Therefore;
Total distance traveled = 7 + 7 + 7·√2 ≈ 23.889 ≈ 24
The total distance the boat travels is about 24 milesLearn more about the Pythagorean Theorem in mathematics here:
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A two digit number is such that sum of the ones and tens digit is 10.If the digits are reversed, the new number formed exceeds the original number by 54. Find the new number
Let the tens digit of the original number be x and the ones digit be y. The original number is 10x + y, and the new number formed by reversing the digits is 10y + x.
Since the new number exceeds the original number by 54, we can set up the equation:
10y + x = 10x + y + 54
9x - 9y = 54
x - y = 6
Since x and y are both digits, they must both be integers. The only solution to this equation that satisfies this condition is x = 8 and y = 2.
Therefore, the original number is 82 and the new number formed by reversing the digits is 28. This is the new number.