Answer:
The airplane flies 95 miles.
Step-by-step explanation:
First we need to find the distance for the first segment using the formula for distance [tex]D=\sqrt{(x_{2}-x_{1})^2 + (y_{2}-y_{1})^2}[/tex]. Let's say [tex](x_{1},y_{1})[/tex] is (0, 0) and [tex](x_{2},y_{2})[/tex] is (33, 56). This gets us that the length of this segment is 65 miles.Next, we need to find the distance for the second segment. Using the same formula for distance [tex]D=\sqrt{(x_{2}-x_{1})^2 + (y_{2}-y_{1})^2}[/tex], we can say [tex](x_{1},y_{1})[/tex] is now (33, 56) and [tex](x_{2},y_{2})[/tex] is now (23, 32). This gets us that the length of this segment is 26 miles.To get the total distance traveled, add the length of these two segments together (65 miles + 26 miles) to get 91 total miles traveled.Question:
An airplane flies from City 1 at (0, 0) to City 2 at (33, 56) and then to City 3 at (23, 32). What is the total number of miles it flies? Each unit represents 1 mile.
Answer:
The plane flew 91 miles.
Step-by-step explanation:
City 1 - City 2
---------------------------------------------------------------------------------------------------------
[tex]d_{1}[/tex] = [tex]\sqrt{(33 - 0)^{2} + (56 - 0)^{2}[/tex]
[tex]d_{1}[/tex] = [tex]\sqrt{33^{2} + 56^{2}[/tex]
[tex]d_{1[/tex] = [tex]\sqrt{1089 + 3136[/tex]
[tex]d_{1}[/tex] = [tex]\sqrt{4225}[/tex]
[tex]d_1[/tex] = [tex]65[/tex]
---------------------------------------------------------------------------------------------------------
City 2 - City 3
[tex]d_2[/tex] = [tex]\sqrt{(33 - 23)^2 + (56 - 32)^2[/tex]
[tex]d_2[/tex] = [tex]\sqrt {10^2 + 24^2}[/tex]
[tex]d_2[/tex] = [tex]\sqrt{676}[/tex]
[tex]d_2[/tex] = 26
---------------------------------------------------------------------------------------------------------
[tex]d_1 + d_2 = 65 + 26[/tex]
[tex]d_1 + d_2 = 91[/tex]
---------------------------------------------------------------------------------------------------------
Therefore, the airplane flew a total of 91 miles through every city
---------------------------------------------------------------------------------------------------------
Key words: the airplane, 91 miles, through, every, city, flies, City 1, City 2, City 3, total, number, unit, represent, mile.
<3 Lots of love!
-The Book Worm.
There are 13 different bags of candy for a party. Susan randomly selects 7 bags. How many different combinations are there?
There are 1716 different combinations of the bags
How to determine the number of combination?The given parameters are:
Total, n = 13
Bags to select, r = 7
The number of combination is calculated using:
[tex]Total = ^{13}C_7[/tex]
Evaluate the combination expression
Total = 1716
Hence, there are 1716 different combinations
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Answer: 1716 different combinations of the bags
Step-by-step explanation:
Which cross-sectional shapes do you find the most surprising? Explain why.
By critically observing the cross-sections of the three-dimensional object I used, a cone is the cross-sectional shape I find most surprising.
The cross-section of a three-dimensional object?In this exercise, you're required to use an online tool to investigate and determine the cross-sections of three-dimensional objects such as pyramids, cylinders, cones, etc., by passing different planes through them.
By critically observing the cross-sections of the three-dimensional object I used, a cone is the cross-sectional shape I find most surprising because rotating the slice around Y produced a circular curve that transitioned into a parabolic curve.
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The square root of a negative number, such as StartRoot negative 144 EndRoot, is undefined. Explain why the square root of –x, StartRoot negative x EndRoot, is not necessarily undefined and what this means about the domain and range of f(x) = StartRoot negative x EndRoot.
Part A
The reason why the (√(-x)) is not necessarily undefined, is because x is a placeholder, such that x can take on a negative value for which (-x) is a positive number, therefore, √(-x) = √(+ve number) is a defined real number.
Part B
The domain is x ≤ 0
The range is f(x) ≥ 0
What is Real Number?A real number is a value of a continuous quantity that can represent a distance along a line.
Here, The given and required information:
Given that √(-144) = Undefined, why is √(-x) not necessarily undefined
The given function, f(x) = √(-x)
Part A
The square root of a real number with a negative value is an imaginary number
The square root of a real number with a positive value or zero, is a real number
√(144) = ±12
A variable, x, is an input value of a function that is a quantity place holder in the function which is a function argument
The given function is f(x) = √(-x)
Where;
x = An argument of the function
When x ≤ 0, such that x is a negative real number or zero, we have;
x = R⁻ or 0
Therefore;
-x= -R⁻ or 0 = R⁺ or 0
-x = R⁺
From which we get;
f(-x)= √(-x) = √(R⁺) = Defined
f(-x) = √(R⁺) ≥ 0 The range of the function is f(x) ≥ 0
An example, when x = -16, we have;
-x = -(-16) = 16
√(-x) √(16) = 4 (Defined)
Part B;
Thee domain where the function is defined is where x = -R⁻, x ≤ 0
The output of the function f(x) is defined which is the range = f(x) ≥ 0
Thus, the reason why the √(-x) is not necessarily undefined, is because the value of x can represent a negative real number or zero.
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Answer:
If x is a negative number, then negative x is a positive number and the square root can be determined. Therefore, the domain of the function is x ≤ 0. As a result, the range is never negative either, so it is y ≥0.
Step-by-step explanation:
answer on edge
Jerome solved a system of equations and found that it had an infinite number of solutions. Which system could be the system that Jerome solved
One example of a system of equations that has infinite solutions is given by:
x + y = 2.
2x + 2y = 4.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
A system will have infinite solutions when the two equations are multiples, hence one example is given by:
x + y = 2.
2x + 2y = 4.
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What is the simplified value of the expression below?
12.4 x (negative 6.3)
–78.12
–1.97
1.97
78.12
The simplified value of 12.4 x (negative 6.3) is -78.12
How to simplify the expression?The expression is given as:
12.4 x (negative 6.3)
Rewrite properly as:
12.4 x (-6.3)
Evaluate the product using a calculator
-78.12
Hence, the simplified value of 12.4 x (negative 6.3) is -78.12
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Is x + 3 a factor of P(x) = x³ - 5x² + 3x + 9 ? Explain.
Answer:
no
Step-by-step explanation:
using the Factor theorem.
If (x + h) is a factor of f(x) then f(- h) = 0
for factor (x + 3) then evaluate P(- 3)
P(- 3) = (- 3)³ - 5(- 3)² + 3(- 3) + 9 = - 27 - 45 - 9 + 9 = - 72
since f(- 3) ≠ 0 then (x + 3) is not a factor of P(x)
Question 19 of 25
5x
x²-11x
= 1. Solve for x.
4
O A. X = 16
OB. x= 3
O C. x = 6
OD. x = 22
Quadratic equations are equation that has degree of 3. The value of x from the quadratic equation is 3
Factorizing the quadratic equationQuadratic equations are equation that has degree of 3. Given the following equation;
5x²-11x = 1
Equate to zero
5x²-11x - 1 = 0
Find the solution using quadratic solution
[tex]x=\frac{11\pm\sqrt{121-4(5)(-1)}}{2(5)}\\x=\frac{11\pm\sqrt{141} }{10} \\x=\frac{11\pm11.87 }{10} \\x=\frac{22.87}{18}\\ x\approx 3[/tex]
Hence the value of x from the quadratic equation is 3
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What is 95x9 divided by 14?
Answer:
213.75
Step-by-step explanation:
95×9=855
855÷4=213.75
What is the slope of the line that passes through the points (1,3) and (5, -2)?
Answer: A. - 5/4
Step-by-step explanation:
m = y2-y1/x2-x1
m=3+2/1-5
m=5/-4
rhea got a new e-scooter. She wanted to show it to her friend on the way to the library.Her friend ronan's house is due north of her house. Adter showing he new scooter she went to library which is due west from ronaks house.while returning back she drove 17km diagonally to her house find distance between rhea and her friends house. How far is the library from ronaks house.
(Urgent!!)
The distance between rhea and her friend's house could be 8 km and The distance of the library from the rocks house could be 15 km.
What is Pythagoras' Theorem?If ABC is a triangle with AC as the hypotenuse and angle B with 90 degrees then we have:
|AC|^2 = |AB|^2 + |BC|^2
where |AB| = length of line segment AB. (AB and BC are rest of the two sides of that triangle ABC, AC being the hypotenuse).
rhea got a new e-scooter. She wanted to show it to her friend on the way to the library.
Her friend Ronan's house is due north of her house.
After showing him the new scooter she went to the library which is due west from rocks house.
while returning back she drove 17km diagonally to her house.
By Pythagoras' theorem
|AC|^2 = |AB|^2 + |BC|^2
Here we can assume that
AB = The distance between rhea and her friend's house.
BC = The distance of the library from rocks house.
The triplet of the 17 would be (8, 15, 17)
So, we can say that the AB could be 8 km and BC could be 15 km or vice versa.
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Which type of angle is < 3 ?
Answer: C
Step-by-step explanation:
See attached image.
How will the solution of the system y > 2x + Two-thirds and y < 2x + One-third change if the inequality sign on both inequalities is reversed to y < 2x + Two-thirds and y > 2x + One-third?
Answer: There is no solution to the system in its original form. There are no points in common. If the signs are reversed, the system has an intersection with an infinite number of solutions.
Answer:
Step-by-step explanation:344x-5-p-0-9-but=pmc+m2 something like that
A cylindrical cup is 15 centimeters in height. When filled to the very top, it holds 450 cubic centimeters of water. What is the radius of the cup, rounded to the nearest tenth? Explain or show your reasoning.
Answer:
The radius of the cup is 3.1 cm.
Step-by-step explanation:
First, we the volume of a right cylinder is [tex]V = πr^{2} h[/tex].
V = volume of the cylinder[tex]π[/tex] = pir = radius of the cylinderh = height of the cylinderNow, using the information that was given to us, we can plug what we know into the equation: [tex]450=πr^{2}(15)[/tex].
From here, we simply solve for r by isolating it to find the radius. *Remember, what we do to one side we must do to the other.
Divide both sides by 15 to cancel it out on the right: [tex]30=πr^{2}[/tex]Divide both sides by pi to cancel it out on the right: [tex]9.549296586=r^{2}[/tex] (do not round until you have your final answer)Square root both sides to cancel out the exponent on the right: [tex]3.090193616=r[/tex]Round to the nearest tenth to get [tex]r=3.1[/tex]The function h = -16t² + 1000 gives an object's height, h, in feet at t seconds.
When will the object be 128 feet above the ground?
At approximately___
seconds.
8 out of 15
Select the graph that represents the inequality.
2x+3y>6
Answer:
3rd graph
Step-by-step explanation:
Since the inequality has a greater than symbol (>) and not a greater than or equal to symbol ([tex]\geq[/tex]), the graph will have a dotted line, meaning only the third and fourth graphs could be the one.
Since 2x+3y is GREATER THAN 6 and not LESS THAN 6, we know that the shaded part of the graph will be above (or more) than the line. Therefore, the third graph is the graph that represents the inequality.
The attached picture proves it :)
Hope this helps!
x:20=5:x
Calculate the positive value of x
Katherine is landscaping her home with juniper trees and pansies. She wants to arrange 15 pansies around each of 8 trees. Each tree costs $20.75 and a six-pack of pansies costs $2.50. Explain how to write an expression to find Katherine’s final cost.
The mathematical expression that Katherine requires to know the price of the objects that she is going to buy is 8 * ($20.75) + 120 * ($5/12) = $216
How to write an expression for this procedure?To find a mathematical expression for this procedure we must take into account the values that we know.
For example, we know that it requires 15 pansies for each tree. This can be expressed like this:
15 * 8 = 120 pansies.On the other hand, we must calculate the price of each tree and the pansies that are going to be used to surround each one as shown below.
Cost of trees = 8 * $20.75Pansies Cost = 15 * ($5/12)According to the above, the final expression, in which all the necessary data for Katherine is included, is:
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Answer:
Answer From Edge 2023
Step-by-step explanation:
The total cost of the trees must be added to the total cost of the pansies. The tree cost is the cost of one tree times eight. The pansy cost is the cost for 15 pansies multiplied by 8 trees, then divided by the number of pansies in a pack: 20.75(8) + 2.50(15)(8) ÷ 6.
The Algebra Club has decided to rent a convention center for their annual Algebra Gala. The cost for the rental will be split evenly among the attendees, which means that the price per person varies inversely with the number of people attending.
If 25 people attend, the cost will be $30 per person.
How many people would need to attend to get the cost under $20 per person?
A) 28
B) 38
C) 48
D) 58
12. Calculate. a) - (-/-)²2 c) 49
Answer:
write your questions very well
HURRY I NEED HELP QUICK
Gaira was asked to evaluate the algebraic
expression –3.8x + 6 when x = –7.5.
–3.8(–7.5) + 6(–7.5)
28.5 + (–45)
(–16.5)
The value of x the function when x = -7.5 is 34.5
Functions and valuesFunctions are written in terms of variables
Given the expression –3.8x + 6, when the value of x is -7.5, hence;
f(x) = –3.8x + 6
f(-7.5) = -3.8(-7.5) + 6
f(-7.5) = 28.5 + 6
f(-7.5) = 34.5
Hence the value of x the function when x = -7.5 is 34.5
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Given the function f(x)=4x+10 and g(x), which function has a greater slope?
The complete question is
"Given the function f(x) = 4x + 10 and g(x), which function has a greater slope?
x g(x)
2 5
4 7
6 9
f(x) has a greater slope. g(x) has a greater slope. The slopes of f(x) and g(x) are the same. The slope of g(x) is undefined."
The correct option from the given function are A; f(x) has a greater slope.
What is the slope of a line which passes through points ( p,q) and (x,y)?Its slope would be:
[tex]m = \dfrac{y-q}{x-p}[/tex]
The slope of a function in the form of y = mx + C is m,
So the slope in the function
f(x)=4x+10
m = 4
Now when you have a function but you only have a table to evaluate it, to calculate the slope
(p, q) = (4, 7)
(x, y) = (6, 9)
This means that:
[tex]m = \dfrac{y-q}{x-p}\\\\m = \dfrac{9-7}{6-4}\\\\m =1[/tex]
Now that we have both slopes, the slope of g(x) = 1 and the slope of f(x) =4,
Thus, f(x) has a greater slope than g(x).
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QUESTION 8
If cos xº = -
OA. 175⁰
OB. 1500
OC. 1350
OD.
120⁰
-√3
2
and 90°
A
Answer:
B. 150
Step-by-step explanation:
Consider the expressions 7y + 5 − 3 and 7y + 2. Which statement is true?
A map of sweden shows a scale of 5 cm = 16 km. if the distance between knivsta and stockholm is 17.2 cm on the map how many km is it?
Answer:
55.04 km
Step-by-step explanation:
17.2 cm / 5 cm = 3.44
16 km x 3.44 = 55.04 km
You could also solve in this fashion:
[tex]\frac{5}{16}[/tex] = [tex]\frac{17.2}{x}[/tex]
16 x 17.2 = 5x
Multiply 16 x 17.2 = 275.20
Divide the 275.20 by 5 = 55.04
A quadrilateral has rotational symmetry of order 2 and no line of symmetry. What is the name of this quadrilateral?
a. square
b. rectangle
c. parallelogram
d. rhombus
Answer:
c
Step-by-step explanation:
paralallegram can be anything with parrell lines
Answer:
C
Step-by-step explanation:
A quadrilateral has rotational symmetry of order 2 and no line of symmetry.
A parallelogram has no lines of symmetry because it is impossible to draw a line through the center of any parallelogram that divides the figure into two equal halves that are mirror images of each other.
Please help! Problem is below! (25 points max!)
Replace x with -17 and solve:
7(-17) + 2 = -119 + 2 = -117
answer: -117
is negative 108.8 rational?
The number -108.8 is a rational number
How to determine if the number is rational?The number is given as:
negative 108.8
Rewrite properly as:
-108.8
Rational number have terminating decimals, and they can be represented as fractions.
The fraction equivalent of -108.8 is -1088/10
Hence, the number -108.8 is a rational number
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Mike pays $285 in rent every week.
How much will he pay in rent for the entire year?
Answer:
14,820
Step-by-step explanation:
A year has 52 weeks. 285 x 52 = 14820
Answer:
$14820
Step-by-step explanation:
There are 52 weeks in a year. Therefore 285 x 52 = 14820
what is the answer to 54785 plus 43543546546546