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
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find the value of unknowns in each of the following
chapter matrices
with full workings and explanations
The value of the unknowns are w = 5 , x = 12 , y = 1 and z = 15
What is a Matrix?
In mathematics, a matrix (plural matrices) is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns, which is used to represent a mathematical object or a property of such an object
A+B = B+A Commutative Law of Addition.
A+B+C = A +(B+C) = (A+B)+C Associative law of addition.
ABC = A(BC) = (AB)C Associative law of multiplication.
A(B+C) = AB + AC Distributive law of matrix algebra.
R(A+B) = RA + RB
Given data ,
Let the Matrix be A
Now , the given matrices are
[tex]2\left[\begin{array}{ccc}w&2\\5&z\\\end{array}\right] + 3\left[\begin{array}{ccc}2&x\\-2&-6\\\end{array}\right] =4\left[\begin{array}{ccc}4&7\\y&3\\\end{array}\right][/tex]
On simplifying the matrices , we get
[tex]\left[\begin{array}{ccc}2w&4\\10&2z\\\end{array}\right] + \left[\begin{array}{ccc}6&2x\\-6&-18\\\end{array}\right] =\left[\begin{array}{ccc}16&28\\4y&12\\\end{array}\right][/tex]
Now , from the distributive law of matrices ,
2w + 6 = 16 be equation (1)
4 + 2x = 28 be equation (2)
10 - 6 = 4y be equation (3)
2z - 18 = 12 be equation (4)
So on simplifying the equation , we get
2w + 6 = 16 be equation (1)
Subtracting 6 on both sides , we get
2w = 10
Divide by 2 on both sides , we get
w = 5
So on simplifying the equation , we get
4 + 2x = 28 be equation (2)
Subtracting 4 on both sides , we get
2x = 24
Divide by 2 on both sides , we get
x = 12
So on simplifying the equation , we get
10 - 6 = 4y be equation (3)
4y = 4
Divide by 4 on both sides , we get
y = 1
So on simplifying the equation , we get
2z - 18 = 12 be equation (4)
Adding 18 on both sides , we get
2z = 30
Divide by 2 on both sides , we get
z = 15
Therefore , the values are w = 5 , x = 12 , y = 1 and z = 15
Hence , The value of the unknowns are w = 5 , x = 12 , y = 1 and z = 15
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Solve this1
HURRY pleasee
Answer:
Part a
[tex]m = \dfrac{280-\boxed{140}}{\boxed{4} - 2} = \dfrac{\boxed{140}}{\boxed{2}}[/tex]
[tex]y = \boxed{70}x[/tex]
Part b.
The heart's resting rate is [tex]\boxed{70}[/tex] beats each minute
Step-by-step explanation:
Q6
Part a
The slope-intercept form of an equation is y = mx + b
where m is the slope and b the y-intercept ie the value of y when x is 0
Here we see when x = 0, y = 0 so the value of b is 0 and the equation is simply
y = mx
To compute m, all we have to do is take 2 points on the graph, find the difference in y values(called rise) and divide by the difference in x values(called run)
This would be [tex]\dfrac{y2-y1}{x2-x1}[/tex]
We are given y2 as 280(on the numerator). The corresponding x2 value from the graph is 4
We are given x1(on the denominator) as 2. The corresponding y1 value is 140 from the graph
So just fill in the missing values to get
[tex]m = \dfrac{280-\boxed{140}}{\boxed{4} - 2} = \dfrac{\boxed{140}}{\boxed{2}}[/tex]
The above simplifies to 70
So the equation is
[tex]y = \boxed{70}x[/tex]
Part b
The interpretation is:
The heart's resting rate is [tex]\boxed{70}[/tex] beats each minute
What are the values of x and y in the figure ?
Answer:
[tex]x=64, y=72[/tex]
Step-by-step explanation:
Using the angle sum of a triangle, [tex]x=180-57-59=64[/tex].
Thus, the left hand triangle has angles of 42°, 64° (using vertical angles), and y°. It follows that [tex]y=180-42-64=74[/tex].
Chloe's bedroom is rectangular. The length of one wall of Chloe's bedroom is 4 meters. The length from one corner of the bedroom to the diagonally opposite corner is 5 meters. What is the length of the other wall?
The length of the other wall is 3 meters, according to the declaration made.
What is the Pythagorean principle?Pythagoras' Theorem states that within a right-angled triangle, any square on the hypotenuse side is precisely equal to the sum of something like the squares on the other two sides. The Perpendicular, Base, as well as Hypotenuse are the names of the three sides of this triangle. The hypotenuse throughout this example is the longest side since it is located across from the 90° angle.
Pythagoras discovered what, exactly?The Pythagorean theorem, Pythagorean tuning, all five elements solids, ancient Theory and Proportions, understanding sphericity of the Earth, as well as the identification of the morning and evening luminaries and Venus are only a few of the the mathematical and scientific discoveries that Pythagoras gets attributed with in antiquity.
Briefing:According to Pythagoras theorem
[tex]c^2=a^2+b^2[/tex]
diagonal (c)= 5 m
length of one wall (a) = 4m
length of other wall (b)= ?
[tex]5^2=4^2+b^2\\25=16+b^2\\b^2=25-16\\b^2=9\\b=3[/tex]
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14. the absolute value of a correlation coefficient is:14. the absolute value of a correlation coefficient is:
The absolute value of a correlation coefficient is the strength of the relationship between two variables.
Hence, the answer is (a) the strength of the relationship between two variables.
Correlation coefficients helps to determine the degree of the relationship between two variables. It lies in a range of -1 to 1.
A positive correlation coefficient implies a positive relationship between the variables and a negative correlation coefficient implies an inverse relationship between the two variables. There is no linear link between the two variables if the correlation coefficient is zero.
--The question is incomplete, the correct question is as follows--
"14. The absolute value of a correlation coefficient is: a. The strength of the relationship between two variables. b. The direction of the relationship between two variables. c. The reliability of the relationship between two variables. d. The validity of the relationship between two variables."
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what is the slope and y-intercept of y= 7 over 5 x−5
A blimp is flying to cover a football game. The pilot sights the stadium at a 7° angle of depression. The blimp is flying at an altitude of 400 m. How many kilometers is the blimp from the point 400 m above the stadium?
To find the distance from the blimp to the stadium, we can use the tangent function and the information given in the problem. The tangent of an angle is defined as the ratio of the opposite side to the adjacent side in a right triangle. In this case, we can use the angle of depression to the stadium, the altitude of the blimp, and the distance from the blimp to the stadium to form a right triangle.
We can then use the tangent function to find the distance from the blimp to the stadium as follows:
tan(7°) = opposite/adjacent
opposite = tan(7°) * adjacent
opposite = tan(7°) * 400 m
opposite = 0.1214 * 400 m
opposite = 48.56 m
To convert this distance from meters to kilometers, we can divide the distance in meters by 1000, as follows:
Distance in kilometers = 48.56 m / 1000
Distance in kilometers = 0.0486 km
Therefore, the distance from the blimp to the stadium is approximately 0.0486 km.
The probability of winning a three-person game of rock paper scissors is 1/3. If you just
won the last 2 rounds, what is the probability you will win the next round?
a. 1/27
b. 1/9
c. 2/3
d. 1/3
e. 1/18
d
it's because it is 1 event
Please help and explain how to get the answer
Answer: 55
Step-by-step explanation:
7x+13=9x+1
-1 -1
7x+12=9x
-7x -7x
12=2x
12/2=6
x=6
7*6+13=55
9*6+1=55
which statement best explains why the sum of the areas of the two white squares in Figure 2 is the same as the area of the white square in figure 1?
From all the given statements, statement 1 is the best way to explain, the sum of the areas of the two white squares in figure 2 is the same as the area of the white square in figure 1.
What is an area of a triangle?
The area of a triangle is half the product of the base of the triangle and the height of the triangle.
Area = 1/2 * base * height
As given the Area of both the big squares of figure 1 and figure 2 are equal because the side of both the squares is equal, therefore, (a+b).
figure 1,
Big square = (a+b)²,
figure 2,
Big square = (a+b)²,
Also, the sides of the 4 triangles are also the same giving the same area for all 8 triangles from Figures 1 and 2.
Figure 1,
area for 1 triangle = ab/2
area for 4 triangle = 4*(ab/2)
area for white square = big square area - 4 triangles area
= (a+b)² - 4*(ab/2)
Figure 2,
area for 1 triangle = ab/2
area for 4 triangle = 4*(ab/2)
area for white square = big square area - 4 triangles area
= (a+b)² - 4*(ab/2)
Hence, the given statement, statement 1 is the best way to explain, the sum of the areas of the two white squares in figure 2 is the same as the area of the white square in figure 1.
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Merissa and mykuria are planning a trip to Orlando to celebrate graduation. They want to buy a three-day ticket to their favorite but the also need to find a place to stay during their trip. the theme park, which costs $299 per person but they also need to find a place to stay during their trip. They found a beautiful vacation rental in Orlando that has room for a number of guests and costs a total of $872.50. If Marissa and Mykuria are able to fill the room up to its maximum capacity with their friends, the price that each person would have to pay for the entire trip would be 361.25.
1. define a variable to represent the unknown.
2 write an expression for the 3-day ticket rate per person plus the total rental cost.
3 Write another expression for the total amount paid per person for the trip, assuming Marissa and mykuria are able to get enough friends to come on the trip so that the vacation rental house will be at maximum capacity.
Let x represent the number of people coming on the trip.
The 3-day ticket rate per person plus the total rental cost is 299 + 872.50 = $<<299+872.50=1171.50>>1171.50.
The total amount paid per person for the trip, assuming Marissa and Mykuria are able to get enough friends to come on the trip so that the vacation rental house will be at maximum capacity, is 361.25. This can be represented as an expression as follows:
(299 + 872.50)/x = 361.25
This equation can be rearranged to solve for the value of x, which represents the number of people coming on the trip.
Solve the equation. Show your work. Express your answer as both a simplified mixed number and as a decimal.
−4.75+0.8x=−3.7
Answer: x = 1.3125
Step-by-step explanation:
−4.75+0.8x=−3.7
First, add 4.75 to both sides
0.8x = 1.05
Then divide by 0.8 on both sides
x = 1.3125
Answer:
x = 1.3125
Step-by-step explanation:
At the gift shop, they sell small greeting cards and large greeting cards. The cost of a small greeting card is $1.20 and the cost of a large greeting card is $4.25. How much would it cost to get 5 small greeting cards and 4 large greeting cards? How much would it cost to get xx small greeting cards and yy large greeting cards?
Answer:
Q: How much are 5 small greeting cards?
A: $6
Q: How much are 4 large greeting cards?
A:$17
How much is it altogether? $23.
Step-by-step explanation:
Small greeting card cost: $1.20
Large greeting card cost: $4.25
Let's solve how much it would cost to get 5 small greeting cards.
5 (1.20)=6
So $6 for 5 small greeting cards
Let's solve how much it would cost for 4 large greeting cards
4 (4.25)= 17
So $17 for 4 large greeting cards.
I hope this helps!!! I didn't understand the question completely, so hopefully I added everything that you needed.
Fill in the table using this function rule y=-3x-3
After solving the equation using the function rule the values of y are [tex]9,3,-3,-9[/tex].
What is function rule?A function rule is an equation that describes a relationship between two variables, where one is a dependent variable, and the other is an independent variable. Function rules are used to determine the value of the dependent variable for any given value of the independent variable. Function rules can be written as a formula, a graph, or a table of values. Function rules are often used in mathematics, physics, and other sciences to describe the behavior of a system or process.
Given: Function [tex]y=-3x-3[/tex]
When we have a function, we just have to replace the x by the numbers on the table, in this case [tex]-4,-2,0,2[/tex].
Substituting the values of x we get,
y = -3 (-4) - 3 ⇒ 12 - 3 = 9
y = -3 (-2) - 3 ⇒ 6 - 3 = 3
y = -3 (0) - 3 ⇒ 0 - 3 = -3
y = -3 (2) - 3 ⇒ -6 - 3 = -9
Hence, the values of y are [tex]9,3,-3,-9[/tex].
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Find the circumference of a circular wimming pool with a radiu of 8. 5 yard. Ue 3. 14 a an approximation for pie
Answer:
53 if rounding to nearest 10
53.38 if not
Step-by-step explanation:
It's pretty simple actually, let's put vocabulary though
π = pie
r = radius C = circumference
ok now the formula for circumference is,
C = 2πr
because they gave you the radius, it is very simple
plug it in.
C = 2(3.14)(8.5)
3.14 x 2 = 6.28
8.5 x 6.28 = 53.38
if you're rounding to the nearest 10 it will be 53.
welcome:)
Please help question in photo
Is a = 9 a solution to the inequality below?
Answer:
No, 9 is not a solution to 12 [tex]\leq[/tex] a
Step-by-step explanation:
The expression 12 [tex]\leq[/tex] a states " 12 is less or equal to a." If a were 9, the statement would not be true, since 9 is less than 12. This contradicts the expression.
I’m having trouble and knowing what the name of the line is.
the name of the line is both XY and YX
One diamond in the safe deposit box is worth 12,000 if each of the other jewels are worth 2,160 how many total jewels are inside the box (including the diamond)
The total jewels that are inside the box will be 14160.
How to illustrate the expression?It should be noted that expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations.
Since one diamond in the safe deposit box is worth 12,000 if each of the other jewels are worth 2,160. The total jewels that are inside the box will be:
= 12000 + 2160
= 14160
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What is the simplest form of the expression (–11.7y – 3.3x) + 1.2x + (5.2y + x)?
–16.9y – 5.5x
–16.9y – 4.5x
–6.5y – 2.1x
–6.5y – 1.1x
Answer:
-6.5y - 1.1x
Step-by-step explanation:
Rearrange the problem to where like terms are closer together:
11.7y+5.2y + 1.2x + x - 3.3x
Simplify by adding the like terms and your final answer will be -6.5y -1.1x
5 scapulae (3 right and 2 left)
Axillary is 3 skulls.The remainder goes to the appendix.
Which of the bones in the collection belong to the axial skeleton?The bones could potentially represent up to 22 different people.This is due to the possibility that each bone comes from a different person.
There were only 3 skulls, leading some to first believe there would only be 3 persons. However, there were 4 right femurs, indicating that there is a missing skull to correspond with one of the right femurs.
In light of this, you can only conclude, until further proof, that each bone belongs to a different person.
Axillary =3 skulls.
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PLS HELP!!!
I attached the question in the picture below
0.85x18340 how do I solve this explain please
Answer:
Answer down below!
Step-by-step explanation:
Once you multiply 0.85 * 18340 you get
15589
2x - 3y = 9
x = 4 + y
Answer:
x = 3; y = -1
Step-by-step explanation:
2x - 3y = 9
x = 4 + y
Since the second equation is already solved for x, use the substitution method. Substitute 4 + y for x in the first equation and solve for y.
2x - 3y = 9
2(4 + y) - 3y = 9
8 + 2y - 3y = 9
-y = 1
y = -1
Now substitute -1 for y in the second original equation, and solve for x.
x = 4 + y
x = 4 + (-1)
x = 3
Answer: x = 3; y = -1
Write an equation of the line in point-slope form that passes through the given points.
(3,5) and (4,7)
Answer: y=2x - 1
Step-by-step explanation:
The point slope form equation is y=mx + b
m is the slope, to find slope we need to find the rise/run
We see that the y increase by 2 and x increase by 1, so the slope is 2.
The y-intercept is at (0,-1), so the b is -1
So we have the equation y=2x - 1
A line is defined by the equation y = two-thirds x minus 6. The line passes through a point whose y-coordinate is 0. What is the x-coordinate of this point?
The equation of a line is given by:
y = mx + c
where m is the slope of the line and c is the y-intercept.
The x-coordinate of the point is 9.
The equation of a line is given by:
y = mx + c
where m is the slope of the line and c is the y-intercept.
Example:
The slope of the line y = 2x + 3 is 2.
The slope of a line that passes through (1, 2) and (2, 3) is 1.
We have,
The equation of a line y = (2/3)x - 6 ______(1)
Now,
The line passes through a point (x, 0).
(x, 0) = (x, y) ______(2)
Now,
Putting (2) in (1) we get,
0 = (2/3)x - 6
6 = (2/3)x
x = 6 x 3 / 2
x = 9
Thus,
The x-coordinate of the point is 9.
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Which equations represent circles that have a diameter of 12 units and a center that lies on the y-axis? Select two options.
A. x2 + (y – 3)2 = 36
B. x2 + (y – 5)2 = 6
C. (x – 4)² + y² = 36
D. (x + 6)² + y² = 144
E. x2 + (y + 8)2 = 36
The equation represents a circle that has a diameter of 12 units will be x² + (y - 3)² = 36. Hence, option A is correct.
What is an equation?Equations are mathematical expressions that have two algebras on either side of an equal (=) sign. The expressions on the left and right are shown to be equal to one another, demonstrating this relationship. L.H.S. = R.H.S. (left-hand side = right side) is a fundamental simple equation.
As per the provided information in the question,
Use the equation of a circle,
(x -a)² + (y - b)² = r²
Here, a and b represent the center of the circle and r is the radius of the circle.
A center can be anywhere along the y-axis if it is (0, 3).
(x -0)² + (y - 3)² = 6²
x² + (y - 3)² = 36
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Find the values of the variable in the parallogram . please!
The values of the variables x, y, z in the parallelogram are x=31, y=153, z=96.
What is a parallelogram?In Euclidean geometry, a parallelogram is a simple (non-self-intersecting) quadrilateral with two sets of parallel sides. Both the congruence of opposite sides and the congruence of opposite angles require the Euclidean parallel postulate, or one of its equivalent formulations, and neither condition can be proved without it.
The values of the three supplied variables x, y, and z in the parallelogram are given to us.
Let's abbreviate the parallelogram, which is depicted in the attached image, ABCD.
Here,
m∠CAB = 31°, m∠ABC =96°.
Since CD and AB are parallel, AC is a transversal now. So,
m∠CAB =m∠ACD
m∠ACD=31°
x=31
From the ΔABC we have,
m∠ABC +m∠ACB+m∠BAC=180°
96°+Y+31°=180°
y+127°=180°
y=153°
y=153
And also we know that the measure of opposite angles in a parallelogram are always equal.
So, m∠ADC=m∠ABC
z=96°
z=96
Therefore, the required values of x, y, z are 31, 153, 96.
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Find the equation of the line passing through the points (-1,-1) and (3,5).
Answer:
y = 2/3x + 3
Step-by-step explanation:
(-1,-1) (3,5)
5+1/3+1
6/4
2/3
y = 2/3x + b
5 = (2/3)(3) + b
5 = 2 + b
b = 3
y = 2/3x + 3
Select the correct answer from each drop-down menu.
Consider the equation below.
x^3 - 3x^2 - 4 = 1/x-1 +5
The solutions to the equation are approximately x =
0.91 and x= *blank*
Graphing this equation x³ - 3x² - 4 = 1/(x - 1) + 5 we get one solution of approximately x = 0.91 and another one x = 3.689.
What is the graphical solution of a system of equations?Graphical solutions of a system of equations are a way of finding the intersection points of all the equations given.
A system with two or more than two equations has a solution only when they have a common intersection point.
Given, An equation of degree 3 which is,
x³ - 3x² - 4 = 1/(x - 1) + 5.
Now by graphing this equation we get one solution of approximately x =
0.91 and another one x = 3.689.
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He John Hancock Building in Chicago i 455 meter tall, which i about 1,400 feet, or about a quarter of a mile high. It ha one of the fatet elevator in the world, traveling at 20. 5 mile per hour, or about 5 meter per econd. How many econd woud it take to travel the the length of the building?
The required number of seconds would it take to travel the the length of the building is 91.
What is speed and its formula?The equation for speed is basic like distance partitioned by time. You take the distance voyaged (for instance 3 meters) and gap it when (three seconds) to get the speed (one meter each second) Thus, we can characterize Speed as the pace of progress of position of an article toward any path.
According to question:We have,
length of the building = 455 meter
speed of elevator = 5 m/s
We know,
speed = distance/time
5 = 455/time
Time = 455/5
Time = 91 seconds.
Thus,time take to travel the the length of the building is 91 seconds.
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