Amanda, Bryce, and Corey enter a race in which they have to run, swim, and cycle over a marked course. Their average speeds are given in the table. Corey finishes first with a total time of 1hr 50 min. Amanda comes in second with a time of 2hr 42 min. Bryce finishes last with a time of 3hr 16 min. Find the distance (in mi) for each part of the race.
Answers
The running distance is 4.23 miles, the swimming distance is 1.98 miles and the cycling distance is 35.64 miles.
Each racer travels the same distance and the sum of the distances travelled ([tex]x[/tex]), in miles. By definition of average speed ([tex]v[/tex]), in miles per hour, we get the following system of equations:
Amanda
[tex]t_{A} = \frac{x_{R}}{v_{A, R}}+\frac{x_{S}}{v_{A,S}}+\frac{x_{C}}{v_{A,C}}[/tex] (1)
Where:
[tex]x_{R}[/tex] - Running distance, in miles.[tex]x_{S}[/tex] - Swimming distance, in miles.[tex]x_{C}[/tex] - Cycling distance, in miles. [tex]v_{A,R}[/tex] - Speed of Amanda in the running distance, in miles per hour.[tex]v_{A,S}[/tex] - Speed of Amanda in the swimming distance, in miles per hour.[tex]v_{A,C}[/tex] - Speed of Amanda in the cycling distance, in miles per hour.[tex]t_{A}[/tex] - Total time of Amanda, in hours.Bryce
[tex]t_{B} = \frac{x_{R}}{v_{B, R}}+\frac{x_{S}}{v_{B,S}}+\frac{x_{C}}{v_{B,C}}[/tex] (2)
Where:
[tex]v_{B,R}[/tex] - Speed of Bryce in the running distance, in miles per hour.[tex]v_{B,S}[/tex] - Speed of Bryce in the swimming distance, in miles per hour.[tex]v_{B,C}[/tex] - Speed of Bryce in the cycling distance, in miles per hour.[tex]t_{B}[/tex] - Total time of Bryce, in hours.Corey
[tex]t_{C} = \frac{x_{R}}{v_{C, R}}+\frac{x_{S}}{v_{C,S}}+\frac{x_{C}}{v_{C,C}}[/tex] (3)
Where:
[tex]v_{B,R}[/tex] - Speed of Corey in the running distance, in miles per hour.[tex]v_{B,S}[/tex] - Speed of Corey in the swimming distance, in miles per hour.[tex]v_{B,C}[/tex] - Speed of Corey in the cycling distance, in miles per hour.[tex]t_{B}[/tex] - Total time of Corey, in hours.If we know that [tex]t_{A} = 2.7\,h[/tex], [tex]v_{A,R} = 10\,\frac{mi}{h}[/tex], [tex]v_{A,S} = 4\,\frac{mi}{h}[/tex], [tex]v_{A, C} = 20\,\frac{mi}{h}[/tex], [tex]t_{B} = 3.27\,h[/tex], [tex]v_{B,R} = 7.5\,\frac{mi}{h}[/tex], [tex]v_{B,S} = 6\,\frac{mi}{h}[/tex], [tex]v_{B,C} = 15\,\frac{mi}{h}[/tex], [tex]t_{C} = 1.833\,h[/tex], [tex]v_{C,R} = 15\,\frac{mi}{h}[/tex], [tex]v_{C,S} = 3\,\frac{mi}{h}[/tex] and [tex]v_{C,C} = 40\,\frac{mi}{h}[/tex], then the solution of the linear system of equations is:
[tex]\frac{x_{R}}{10} + \frac{x_{S}}{4} + \frac{x_{C}}{20} = 2.7[/tex] (4)
[tex]\frac{x_{B}}{7.5}+\frac{x_{S}}{6} +\frac{x_{C}}{15} = 3.27[/tex] (5)
[tex]\frac{x_{R}}{15}+\frac{x_{S}}{3} +\frac{x_{C}}{40} = 1.833[/tex] (6)
[tex]x_{R} = 4.23\,mi[/tex], [tex]x_{S} = 1.98\,mi[/tex], [tex]x_{C} = 35.64\,mi[/tex]
The running distance is 4.23 miles, the swimming distance is 1.98 miles and the cycling distance is 35.64 miles.
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At the craft store, Patty bought a bag of yellow and brown marbles. The bag contained 85
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Answer:
51 yellow marbles
Step-by-step explanation:
60% of 85 can be found by multiplying 85 and 0.6 to get 51
Answer:
i got 51 marbles! simple.
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Answer:
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Complete the following proof. Given: (BD) is the perpendicular bisector of (AC) Prove: ∢A≅∢C
Statement Reason
1. (BD) is the perpendicular bisector of (AC) 1. Given
2. Point B is the midpoint of (AC) 2. Definition of perpendicular bisector
3. 3. Definition of midpoint
4. ∢ABD and ∢CBD are right angles 4. Definition of perpendicular bisector
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Answer:
I dont know if this is right but... i tried XD
Step-by-step explanation:
Angle A is congruent to angle C.
What is Triangle?A triangle in geometry is a polygon with three sides and three angles. The sum of the interior angles of a triangle is 180°.
If XYZ is a triangle, it is represented as ΔXYZ
Here, it is given that BD is the perpendicular bisector of AC.
Then by the definition of perpendicular bisector, B is the midpoint of AC.
Consider ΔABD and ΔCBD
ΔABD and ΔCBD are right triangles with ∡ABD = ∡CBD = 90°.
So, ∡ABD ≅ ∡CBD (∵ all right angles are congruent)
Now, by the reflexive property of congruence, every side or angles are congruent to itself.
So BD ≅ BD
Since B is the midpoint of AC, AB = BC.
Hence AB ≅ BC
By SAS theorem, if two sides and an angle of a triangle are congruent to two sides and angles of another triangle, then both triangles are congruent.
Hence ΔABD ≅ ΔCBD
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Hence ∡A ≅ ∡C if BD is perpendicular bisector of AC.
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Ashley has 10 skirts in her closet.
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4 skirts are green
1 skirt is pink
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Answer:
the highest choices are red and green
100 POINTS
Given Point P(3,4), what is the resulting point after the following transformations?
Translate 3 up and 2 left
Rotation 180° around origin
Reflection over y-axis
Answers
Answer:
(1, -7)
Step-by-step explanation:
P(3,4)
3 up ---> y = 4 + 3 = 7
2 left ----> x = 3 - 2 = 1
new point (1, 7)
after 180 rotation around origin
point is (-1, -7)
now reflection over y-axis
(1, -7)
Answer:
[tex](1,-7)[/tex]
Step-by-step explanation:
Refer to the image below
Jenny has three times as many new toys as she has favorite toys.
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answer:
3x = y
step-by-step explanation:
૪・ i am inferring you have to create an equation?
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1. The expression 2p - 15 represents the number of lilies left in the zoo's garden after a storm. If p = 223, how many lilies are left in the garden after the storm? 431 lilies 223 lilies 193 lilies 208 lilies
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446-15=431lilies
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1 is C
2 is D
3 is C
4 is A
5 is D
5 is A
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Answer:
c
Step-by-step explanation:
cody spent 3 hours and 5 minutes looking for his missing cat if he finally found it at 7:35 what time was it when he originally started
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Answer:
4:30
Explanation:
Three hours before 7:35 is 4:35, but you also have to subtract the extra 5 minutes to make it 4:30
The diagram shows a trapezium.
B
D
Diagram NOT accurately drawn
AD = x cm.
BC is the same length as AD.
AB is twice the length of AD.
DC is 4 cm longer than AB.
The perimeter of the trapezium is 38 cm.
Work out the length of AD.
Answers
Perimeter implies the total length of sides of a given figure. Thus the length AD = 4.75 cm.
A plane figure is any type of figure bounded by four straight sides. Examples are square, rectangle, trapezium, rhombus, etc. A trapezium is a type of plane figure which belongs to a family referred to as quadrilaterals.
The perimeter of a given shape is the sum of the length of its boundaries or sides.
Thus the length AD required in the question can be determined by:
AD = x cm
BC = x cm
AB = 2x cm
DC = 4x cm
Perimeter = AD + BC + AB + DC
= x + x + 2x + 4x
Perimeter = 8x
But the perimeter of the trapezium has been given as 38 cm.
Thus,
38 = 8x
x = [tex]\frac{38}{8}[/tex]
= 4.75
Therefore, the length of AD is 4.75 cm.
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1s^2 2s^2 2p^6 3s^2 3p^6 3d^10 4s^2 4p^3
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Answers
Answer: Refer to figure 1 for the diagram needed.
A ' = (-1, 2)
B ' = (-6, 1)
C ' = (-7, 6)
D ' = (-3, 7)
Area = 24 square units
============================================================
Explanation:
Start by drawing an xy axis. Plot the given points A,B,C,D on this grid.
To reflect any given point over the y axis, we apply this rule
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After all of the points have been reflected, you'll get what is shown in figure 1.
------------------
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The area of rectangle FEHG is 6*6 = 36 square units
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Triangle AED = 5*2/2 = 5Triangle AFB = 1*5/2 = 2.5Triangle BCG = 1*5/2 = 2.5Triangle CDH = 1*4/2 = 2Meaning we'll end up with 36-5-2.5-2.5-2 = 24 as the area of quadrilateral ABCD. Because a reflection is a mirror copy, quadrilateral A'B'C'D' will have the same area as ABCD.
PLEASE ANSWER QUICK AND SHOW WORK
Miss Johnson borrow $8,300 to buy a car. She agreed to a
4% interest rate and payments for 5 years.
How much will her interest be?
What is her total debt for buying the car?
Answers
Answer:
Interest: $402.20
Total Debt owed: $9,302.00
Step 1: Multiply the principal (the original amount borrowed) by the interest rate (%):
$8,300 x 4% = 360.00 (interest for one year)
Step 2: Find out how many years she will be paying back the loan and add that number of years to the first payment year ($360). ($360 + 5years = 365 total payments) Then multiply the total number of payments by the interest rate ($365 x .04 = $14.60 interest per payment).
Step 3: Add up all the yearly interests ($14.60 per payment x 12 months = $181.20 yearly interest)
Step 4: Add the yearly interest to the total debt owed.
$9,302 + $181.20 = $9,483.20 total debt
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Step-by-step explanation:
the following things are clear : opposite sides are of equal length, the sum of all angles in a square, rectangle or general parallelogram is 360 degrees, and opposite angles are equal.
so,
y² + 7 = 32
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2×5² = k
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the opposite angle of x is also x.
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The given bar graph shows the number of rooms, bathrooms, fireplaces, and elevators in the building.
Combined, there are 199 rooms, bathrooms, fireplaces, and elevators. The number of rooms exceeds the
number of bathrooms and fireplaces by 68. The difference between the number of fireplaces and elevators is
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the number of rooms, bathrooms, fireplaces, and elevators in the building.
Answers
Using a system of equations, it is found that there are:
132 rooms.38 bathrooms.26 fireplaces.3 elevators.For the system, we have that:
The number of rooms is x.The number of bathrooms is y.The number of fireplaces is z.The number of elevators is w.Combined, there are 199 rooms, hence:
[tex]x + y + z + w = 199[/tex]
The number of rooms exceeds the number of bathrooms and fireplaces by 68, hence:
[tex]x = y + z + 68[/tex]
The difference between the number of fireplaces and elevators is 23, hence:
[tex]z - w = 23[/tex]
If the number of bathrooms is doubled, it exceeds the number of fireplaces and elevators by 47, hence:
[tex]2y = z + w + 47[/tex]
Replacing the third equation into the fourth:
[tex]z = 23 + w[/tex]
[tex]2y = z + w + 47[/tex]
[tex]2y = 23 + w + w + 47[/tex]
[tex]2y = 2w + 70[/tex]
[tex]y = w + 35[/tex]
Then, from the second equation:
[tex]x = y + z + 68[/tex]
[tex]y + z = x - 68[/tex]
We can solve for w, considering that:
[tex]y = w + 35[/tex]
[tex]z = 23 + w[/tex]
[tex]y + z = x - 68[/tex]
[tex]x = y + z + 68[/tex]
[tex]x = w + 35 + w + 23 + 68[/tex]
[tex]x = 2w + 126[/tex]
[tex]x + y + z + w = 199[/tex]
[tex]2w + 126 + w + 35 + 23 + w + w = 199[/tex]
[tex]5w + 184 = 199[/tex]
[tex]5w = 15[/tex]
[tex]w = \frac{15}{5}[/tex]
[tex]w = 3[/tex]
Then, solving for the other variables:
[tex]x = 2w + 126 = 2(3) + 126 = 132[/tex]
[tex]y = w + 35 = 3 + 35 = 38[/tex]
[tex]z = 23 + w = 23 + 3 = 26[/tex]
There are:
132 rooms.38 bathrooms.26 fireplaces.3 elevators.A similar problem is given at https://brainly.com/question/17096268
Determine whether each equation represents a linear or nonlinear function.
Drag each equation into the appropriate box.
Linear Function Nonlinear Function
y = {x-6
y = (x - 5)2
y = 2* +8
y = 3(x + 7)
y = 4x3 - 1
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Answer:
y=1/2x=6 - linear, written as y=mx+b.
y=(x-5)^2 - nonlinear, x has an exponent greater than 1
y=2^x+8 - nonlinear, x is an exponent
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y=4x^3-1 - nonlinear, x has an exponent greater than 1
Step-by-step explanation:
What is the value of x in the equation ?
Answers
Answer:
[tex]x=2[/tex]
Step-by-step explanation:
This is our equation
[tex]2.5\left(6x-4\right)=10+4\left(1.5+0.5x\right)[/tex]
First off we can distribute the 2.5 and the 4
Now our equation is [tex]15x-10=10+6+2x[/tex]
subtract [tex]2x[/tex] from both sides
[tex]13x-10=16[/tex]
add [tex]10[/tex] to both sides
[tex]13x=26[/tex]
Divide both sides by [tex]13[/tex]
[tex]x=2[/tex]
What is the equation of the line that passes through the point (4,7) and has a slope
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Answers
Answer:
See answer below.
Step-by-step explanation:
y - 7 = -1/4(x - 4)
y - 7 = -1/4(x - 4) in point slope form
In slope intercept form: y - 7 = -1/4x + 1
y = -1/4 x + 8
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Step-by-step explanation:
hey.....
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Answers
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Answer:
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Step-by-step explanation:
The area of the surface of a ball is equal to the area of the curved surface of a right circular cylinder. If both the height and diameter of the cylinder are 12cm , find the diameter of the ball
Answers
Answer:
D=12 cm
Step-by-step explanation:
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Which coin does Jeff have the most of in his collection?
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penny
dime
Answers
Answer:
dimes
Step-by-step explanation:
Answer: dimes
Step-by-step explanation:
Can someone tell me which one is the answer? Am I wrong or correct?
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Answer:
I don't believe your wrong mate
can i have help on this q plz
Answers
Answer:
14.8
Step-by-step explanation:
7.4 * 2 = 14.8.
hope this helps
Answer:
54.76[tex]cm^{2}[/tex]
Step-by-step explanation:
The area of a shape is base times height. bh
Since this is a square, all of the sides are the same length. Meaning 7.4*7.4 to make 54.76cm^2.
Two friends, Gabriel and Hudson, had just bought their first cars. Gabriel uses 10 gallons of gas to drive 339 miles in his car. The table below represents the number of miles, yy, that Hudson can drive his car for every xx gallons of gas.
How much farther can Gabriel's car travel on one gallon of gas than Hudson's car?
Answers
Answer- 15.8 Miles
Explanation photo was given above.
HELPPPPPPP ME ASAPPPPPP
Answers
Answer:
D
Step-by-step explanation:
Perpendicular lines intersect to create right angles. That rules out A and B because both have a right angle in them. C has two lines that are parallel. The only one left is D which is neither parralell or perpendicualar.
A toy rocket is launched from the ground, the equation
h= -16t^2+ 80t, models the height of the rocket h in feet at any timet
in seconds.
For which interval of time will the rocket be higher than 64 feet off the
ground?
Answers
Answer:
Step-by-step explanation:
We can graph the function and determine the points where the y value line is greater than 64 feet. We could also solve the equation for h = 64.
Graphing:
A graph is attached. The intersections of the line at height = 64 feet are at (1,64) and (4,64). The first is going up and the second coming down. The period of time the rocket is above 64 feet is from 1 to 4 seconds.
Solving:
h= -16t^2+ 80t
64 = -16t^2+ 80t
-16t^2+ 80t - 64 = 0
Solve using the quadratic formula:
We get two answers: 1 and 4 (seconds)
What is the dividend when the divisor is 8 and the quotient is 96 with a remainder of 3?
dividend:
Explain how you found the dividend.
Answers
Answer:
13
Step-by-step explanation:
13÷8=96r3 आओऋअःनबभसजहलव
The required dividend would be 765 when the divisor is 8 and the quotient is 96 with a remainder of 3.
What is the Quotient?A quotient is defined as the outcome of dividing an integer by any divisor that can be said to be a quotient. The dividend contains the divisor a specific number of times.
Let the required dividend would be x
The divisor is 8 and the quotient is 96 with a remainder of 3 which is given in the question
As per the given question, the solution would be as:
⇒ x ÷ 8 = 96 r3
⇒ x + 3 = 96 × 8
⇒ x + 3 = 768
⇒ x = 768 - 3
⇒ x = 765
Therefore, the required dividend would be 765.
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What are complex integers ?
Answers
Answer:
In mathematics, 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 a symbol, called the imaginary unit, that satisfies the equation i² = −1. Because no real number satisfies this equation, i was called an imaginary number by René Descartes.
Step-by-step explanation:
Complex Integer
(or Gaussian integer), a number of the form a + bi, where a and b are integers. An example is 4 – 7i. Geometrically, complex integers are represented by the points of the complex plane that have integral coordinates.
Complex integers were introduced by K. Gauss in 1831 in his investigation of the theory of biquadratic residues. The advances made in such areas of number theory as the theory of higher-degree residues and Fermat’s theorem through the use of complex integers helped clarify the role of complex numbers in mathematics. The further development of the theory of complex integers led to the creation of the theory of algebraic integers.
The arithmetic of complex integers is similar to that of integers. The sum, difference, and product of complex integers are complex integers; in other words, the complex integers form a ring.
Answer:
An immediate consequence of the definition of arithmetical operations on complex numbers is that the sum, the difference, and the product of two or more complex numbers.
Step-by-step explanation: