help asap!!!!!
Select the correct answer from each drop-down menu.
Consider polygon JKLMNO on the coordinate grid.
first: 12.5, 25, 17,07
second: 20, 30, 50
third: 47, 37, 61, 68.5
Answers
Answer:
12.5
30
68.5
Step-by-step explanation:
Related Questions
if y= 2x-3 were chnged to y=2x+5 how would the graph of the new function compare with the original
Answers
I think that is what you asked
The new function moved up by 8 units from the original.
The only difference in the functions is the y-intercept. The slope remained the same ([tex]2[/tex]), but the y-intercept went up by 8, meaning the function moved up 8 units.
See the attached image for a graph of both functions. The new function is the solid blue line.
If the side lengths of a polygon are: 4x, 6x, 12, and 18 what is the value of x if the perimeter is 118?
Answers
The value of x for given polynomial is 8.8.
What is Polygon?The definition of a polygon is given as a closed two-dimensional figure with three or more straight lines.
Here, the length of sides of given Polygon are:
4x, 6x, 12, 18
Perimeter of polygon = 118 units.
We know that,
Perimeter of polygon = Sum of all sides
118 = 4x + 6x + 12 + 18
118 = 10x + 30
118 - 30 = 10x
10x = 88
x = 88/10
x = 8.8
Thus, the value of x for given polygon is 8.8.
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Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options. x < 5 –6x – 5 < 10 – x –6x + 15 < 10 – 5x A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right. A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.
Answers
The correct representation of the inequality –3(2x – 5) < 5(2 – x) is -6x + 15 < 10 - 5x. It an open circle is at 5 and a bold line starts at 5 and is pointing to the right.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Given the inequality:
–3(2x – 5) < 5(2 – x)
= -6x + 15 < 10 - 5x
= -x < -5
= x > 5
The correct representation of the inequality –3(2x – 5) < 5(2 – x) is -6x + 15 < 10 - 5x. It an open circle is at 5 and a bold line starts at 5 and is pointing to the right.
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Answer: The correct representation of the inequality –3(2x – 5) < 5(2 – x) is -6x + 15 < 10 - 5x. It an open circle is at 5 and a bold line starts at 5 and is pointing to the right. What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.Given the inequality:–3(2x – 5) < 5(2 – x)= -6x + 15 < 10 - 5x= -x < -5= x > 5The correct representation of the inequality –3(2x – 5) < 5(2 – x) is -6x + 15 < 10 - 5x. It an open circle is at 5 and a bold line starts at 5 and is pointing to the right.
Step-by-step explanation:
2. State the domain and range of the relation shown. Is the relation a function?
Y=3x+1
Answers
Answer:
Domain: [tex](-\infty, \infty)[/tex]Range: [tex](-\infty, \infty)[/tex]The relation is a function.Step-by-step explanation:
The domain and range of all linear functions is the set of real numbers.
What is the equation of the line that passes through the point (3, -1) and is perpendicular to the equation y = -3x + 2? A. y=-3x+8
B. y = -3x
C. y=(1/3)x
D. Y =(1/3)x-2
Answers
Answer:
A) y = –3x+8
Step-by-step explanation:
first off, a negative equation means the graph is downward sloping from left to right –> \. So with this in mind you can immediately eliminate C and D because they are upward sloping graphs. B also doesn't work because it doesn't go through (3,–1). This leaves A as the right answer
the constant number is the number on the y-axis. So, for –3x+2, +2 is the y-coordinate on the y-axis. the slope is -3x meaning down 3, right 1. –3x+8 is the only answer that is perpendicular.
A membership committee of three is formed from four eligible members. let the eligible members be represented by a, b, c, and d. the possible outcomes include s = {abc, abd, acd, bcd}. which statements about the situation are true? select three options.
Answers
The correct statements are:
There are four ways to choose the committee.
There are three ways to form the committee if person D must be on it.
If persons B and C must be on the committee, there are two ways to form the committee.
It is given that:
A membership committee of three is formed from four eligible members.
1)
There are four ways to choose the committee.
This statement is true.
since we have to choose 3 members out of the 4 members so we can use the method of combination.
2)
There are three ways to form the committee if person D must be on it.
This statement is also true.
since D has to be in the committee, this means we have to choose 2 more people out of the three people to form the committee.
3)
If seven members are eligible next year, then there will be fewer combinations.
This statement is wrong.
Since we have to choose 3 members out of 7 members so the number of possible combinations will be:
i.e. there are 35 combinations possible.
4)
If persons B and C must be on the committee, there are two ways to form the committee.
if B and C have to be in the committee then we have to choose just one person out of the two people left.
Hence, the statement is true.
5)
If persons A and C must be on the committee, then there is only one way to form the committee.
If A and C have to be in the committee then as in last option we have to choose any one of the two person left.
so possible number of ways are 2.
Hence, the statement is false.
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Please help me solve this.
Answers
Answer:
I think that is a FORMULA.it can't be solved if we don't know the values of atleast one of the x and y.
Hope this helps.
Good luck ✅.
Which set of data does not have a mode?
(A) 1, 2, 5, 6, 8
(B) 1, 3, 5, 5, 6
(D) 1, 1, 1, 2, 2
(C) 1, 5, 5, 5, 5
Answers
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Question reads....}[/tex]
[tex]\textbf{Which set of data does not have a mode?}[/tex]
[tex]\huge\textbf{The choices that you have provided:}[/tex]
[tex]\textbf{(A) 1, 2, 5, 6, 8}[/tex]
[tex]\textbf{(B) 1, 3, 5, 5, 6}[/tex]
[tex]\textbf{(C) 1, 5, 5, 5, 5}[/tex]
[tex]\textbf{(D) 1, 1, 1, 2, 2}[/tex]
[tex]\huge\textbf{Okay, so let's get the understanding}\\\\\huge\textbf{of the word mode is:}[/tex]
[tex]\large\textbf{The best way to understand what \boxed{\bf mode} it is known as}\\\\\large\textbf{the number you see MORE THAN once. }[/tex]
[tex]\huge\textbf{Now that we got that information out of}\\\\\huge\textbf{the way, we can answer your question by}\\\\\huge\textbf{doing process of elimination.}[/tex]
[tex]\huge\textsf{Option A.}[/tex]
[tex]\textbf{1, 2, 5, 6, 8}[/tex]
[tex]\large\textbf{None of the numbers r.e.p.e.a.t so this cann be your}\\\\\large\textbf{answer.}[/tex]
[tex]\huge\textsf{Option B.}[/tex]
[tex]\textbf{ 1, 3, 5, 5, 6}[/tex]
[tex]\large\textbf{1}\rightarrow\large\textbf{ is r.e.p.e.a.t.e.d once}\\\large\textbf{3}\rightarrow\large\textbf{ is r.e.p.e.a.t.e.d once}\\\large\textbf{5}\rightarrow\large\textbf{is r.e.p.e.a.t.e.d twice}\\\large\textbf{6}\rightarrow\large\textbf{is r.e.p.e.a.t.e.d once}[/tex]
[tex]\large\textbf{Just because majority of your numbers r.e.p.e.a.t.e.d}\\\\\large\textbf{once that doesn't mean it does have a mode rarely.}\\\\\\\\\\\large\textbf{So, Option B. isn't your answer because it has a mode.}[/tex]
[tex]\huge\textsf{Option C.}[/tex]
[tex]\textbf{ 1, 5, 5, 5, 5}[/tex]
[tex]\large\textbf{1}\rightarrow\large\textbf{is r.e.p.e.a.t.e.d once}\\\large\textbf{5}\rightarrow\large\textbf{is r.e.p.e.a.t.e.d four times}[/tex]
[tex]\large\textbf{Option C. isn't your answer because it has a mode.}[/tex]
[tex]\huge\textsf{Option D. }[/tex]
[tex]\textbf{1, 1, 1, 2, 2}[/tex]
[tex]\large\textbf{1}\rightarrow\large\textbf{is r.e.p.e.a.t.e.d three times}\\\large\textbf{2}\rightarrow\large\textbf{is r.e.p.e.a.t.e.d twice}[/tex]
[tex]\large\textbf{Just because we have like two modes, it still doesn't mean}\\\large\textbf{you don't have a mode. It 's kind of cool that you have more}\\\large\textbf{than once mode.}[/tex]
[tex]\large\textbf{Option D. isn't your answer because it has a mode though}\\\large\textbf{because it has like 2 sets of modes.}[/tex]
[tex]\huge\textsf{Therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\textsf{Option\ A. 1, 2, 5, 6, 8}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Urgent! I really need help
Answers
Answer:
58.0°
Step-by-step explanation:
The mnemonic SOH CAH TOA is intended to remind you of the relationships between sides of a right triangle and trig functions of the acute angles.
ApplicationHere, the hypotenuse of the triangle is given (17 cm), as is the side adjacent to angle x (9 cm). This suggests using the relation ...
Cos = Adjacent/Hypotenuse
cos(x) = (9 cm)/(17 cm) = 9/17
The angle for this cosine value is found using the inverse trig function.
x = arccos(9/17)
x ≈ 58.034°
Rounded to the nearest tenth, the angle is ...
x = 58.0°
__
Additional comment
Of course, the angle y is the complement of this:
y = 32.0°
Which set of systems of equations represents the solution to the graph?
an upward opening parabola decreasing from negative 3 comma 4 to a minimum at negative one comma zero and then increasing to 1 comma 4 and a downward opening parabola increasing from negative 2 comma negative 3 to a maximum at 0 comma 1 and then decreasing through the point 2 comma negative 3
Answers
The correct graph for the given sets of equation is given attached below.
Equation no 2 gives the perfect solution to the graph.
A parabola, is cross section cut out of the cone and represented by an equation [tex]Y=4ax^2[/tex]
Clearly, by property of the parabola, the curve of parabola should symmetric to its axis. From this property set of Equation (2) i.e. downward opening parabola increasing from negative 2 comma negative 3 to a maximum at 0 comma 1 and then decreasing through the point 2 comma negative 3 Holds the property of the parabola
Thus, the required solution for the sets of equation (2) is given in the attachment.
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Which of the following are solutions to the equation below?
Check all that apply.
9x² - 6x + 1 = 7
☐ A. x = -√7 +1
3
B. X=
=
C. x=
☐ D. x=
= 2√2
2√2
3
☐ E. X=
-√7
3
☐ F. x =
<=
X= √²+1
3
+1
+1
Answers
Step-by-step explanation:
therefore A is the correct answer
The table represents an exponential function
X123
1648366
4
y
9
What is the multiplicative rate of change of the
function?
of
0 0 00
ON W/NW/
02
Answers
The multiplicative rate is 9 if the table that shows an exponential function option fourth is correct.
What is an exponential function?It is defined as the function that rapidly increases and the value of the exponential function is always positive. It denotes with exponent y = a^x
where a is a constant and a>1
We have a table that shows an exponential function.
As we know the exponential function:
y = a(b)ˣ
Plug x = 1, y = 6
6 = ab ...1
Plug x = 2, y = 4
4 = ab² ...2
Divide equations 1 and 2
ab²/ab = 4/6
b = 2/3
Plug the value of b in the 1 equation.
a(2/3) = 6
a = 9
y = 9(2/3)×
The multiplicative rate = 9
Thus, the multiplicative rate is 9 if the table that shows an exponential function option fourth is correct.
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look at image...........
Answers
Answer:
Step-by-step explanation:
2x + 3y = 6
y = x/3 - 3
Since the second equation is already solved for y, we can easily use the substitution method.
Substitute y in the first equation with x/3 - 3
2x + 3(x/3 - 3) = 6
2x + x - 9 = 6
3x = 15
x = 5
Now use the second equation, and x = 5, to solve for y.
y = x/3 - 3
y = 5/3 - 3 = 5/3 - 9/3
y = -4/3
Answer: (5, -4/3)
Answer:
your answer would be B
Step-by-step explanation:
Please answer with everything needed i appreciate everyones help:)
Answers
Answer:
Hey there....
Step-by-step explanation:5
This is ur answer....
Expression : -x + 5Working :-
x = Unknown number
x + 5 = Sum of the number and Five
x + 5 - 2x = Previous sum decreased by the the twice of the unknown number.
-x + 5 = combine the terms
•••••••••••••••••••••••••••••••••••••••••••••••••••••••••
Hope it helps!
Brainliest pls!
Have a good day!^^
Step-by-step explanation:
x is the number.
(x + 5) - 2x : the sum of the number and 5 decreased by twice the number.
or simplified without the brackets
x + 5 - 2x = 5 - x
it is not clear if you need the general expression showing both conditions (the first up there), or the then simplified result
5 - x
Find the inverse of the function
y = log₂ (x-3)
Answers
replace h(x) with y:
y=2^(x-3)=(2^x)*(2^-3)=(2^x)/(2^3)=(2^x)/8
y=2^x/8
solve for x:
8y=2^x
log2(8y)=x
Answer:
[tex]f^{-1}(x)=2^x+3[/tex]
Step-by-step explanation:
Given:
[tex]y=\log_2(x-3)[/tex]
To find the inverse of the given function, make x the subject.
[tex]\textsf{Apply log law}: \quad \log_ab=c \iff a^c=b[/tex]
[tex]\implies 2^y=x-3[/tex]
Add 3 to both sides:
[tex]\implies x=2^y+3[/tex]
Swap x for [tex]f^{-1}(x)[/tex] and y for x:
[tex]\implies f^{-1}(x)=2^x+3[/tex]
Find an equation for the line that passes through the points (6,1) and (-4,3)
Answers
Answer: $$y=-2/3x+2$$
Explanation: Given that we have the slope and a point on the graph we can use the point slope formula to find the equation of the line.
How do the areas of the parallelograms compare? the area of parallelogram abcd is 4 square units greater than the area of parallelogram efgh. the area of parallelogram abcd is 2 square units greater than the area of parallelogram efgh. the area of parallelogram abcd is equal to the area of parallelogram efgh. the area of parallelogram abcd is 2 square units less than the area of parallelogram efgh.
Answers
option third "The area of parallelogram ABCD is equal to the area of parallelogram EFGH" is correct.
What is parallelogram?In two-dimensional geometry, it is a plane shape having four sides, in which two pairs of sides are parallel to each other and equal in length. The sum of all angles in a parallelogram is 360°.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
The area of the parallelogram is:
A = b×h
Here b is the base length and h is the height
In ABCD parallelogram:
A = (3)×(3)
A = 9 square units
EFGH parallelogram:
a = (3)×(3)
A = 9 square units
The area of parallelogram ABCD is equal to the area of parallelogram EFGH.
Thus, option third "The area of parallelogram ABCD is equal to the area of parallelogram EFGH" is correct.
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what is the slope of this line?
y-9=1/5(x-2)
Answers
Answer: D) 1/5
Step-by-step explanation:
Format for point-slope form: y-y₁=m(x-x₁)
x1, y1 is a point on the line
m is the slope
So in this equation, m = 1/5
so, the slope is 1/5
hope this helps!
Find the value of x.
Answers
The value of 'x' is 25.00
How to determine the value of xThe given figure is a triangle
To find the value of 'x', first find the value of the other side
Using
Hypotenuse square = opposite square + adjacent square
16^2 = 10^2 + y^2
256 = 100 + y^2
Make y subject of formula
y = √ 256- 100
y = √ 156
y= 12. 49
To find 'x'
28^2 = x^2 + 12.59^2
784 = x^2 + 158. 51
x^2 = 784 - 158. 51
x^2 = 625. 49
x =√ 625. 49
x = 25.00
Thus, the value of 'x' is 25.00
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Solve the following proportion by cross multiplying:
( x - 3 ) / 4 = ( 2x + 2 ) / 6
Answers
Answer:
- 13
Step-by-step explanation:
Solving
[tex] \frac{(x - 3)}{4} = \frac{(2x + 2)}{6} \\ \\ cross \: multiplying \\ 6 \times (x - 3) = 4 \times (2x + 2) \\ 6x - 18 = 8x + 8 \\ 6x - 8x = 8 + 18 \\ - 2x = 26 \\ dividing \: bothsides \: by \: - 2 \\ \frac{ - 2x}{ - 2} = \frac{26}{ - 2} \\ x = - 13[/tex]
[tex] \implies \: \sf{ \dfrac{x \: - \: 3}{4} \: = \: \dfrac{2x \: + \: 2}{6} } \\ \\ \implies \: \sf{6( x \: - \: 3) \: = \:4(2x \: + \: 2)} \: \\ \\ \implies \: \sf{6 \times ( x \: - \: 3) \: = \: (2x \: + \: 2)}\\ \\ \implies \: \sf{6x \: - \: 18 \: = \:8x \: + \: 8}\\ \\ \implies \sf{6x \: - \: 8x \: = \:18\: + \: 8}\\ \\ \implies \sf{ - 2x \: = \:18\: + \: 8}\\ \\ \implies \sf{ - 2x \: = \: 26}\\ \\ \implies \sf{ - x \: = \: \dfrac{26}{2} }\\ \\ \implies \sf{ - x \: = \: \cancel{\dfrac{26}{2} }}\\ \\ \implies \sf{ - x \: = \: 13}\\ \\ \implies \red{\bf{ x \: = \: - 13}}[/tex]
Helen got a 7% reduction in the price of a pair jeans that are normally $32. What is the approximate percent in the price?
Answers
A percentage is a way to describe a part of a whole. The approximate percent decrease in the price is 21.87%, thus, the correct option is B.
What are Percentages?A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.
To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.
Given the reduction in the price is $7, while the original cost is $32. Therefore, the approximate percent decrease in the price is,
Percentage decrease = 7/32 × 100%
= 21.87%
Hence, the approximate percent decrease in the price is 21.87%, thus, the correct option is B.
The correct question is:
Helen got a $7 reduction in the price of a pair of jeans that are normally $32. What is the approximate percent decrease in the price?
The percent decrease is approximately 15%.
The percent decrease is approximately 21%.
The percent decrease is approximately 43%.
The percent decrease is approximately 78%
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HELP ASAP
Given: ABCD is a parallelogram.
Prove: A is congruent to FCE.
Answers
Answer:
Step-by-step explanation:
C is equal to A. Because angle FCE is on the other side with C, it has to be equal to A
ABCD is a parallelogram (Given)
As opposite angles of a parallelogram are equal
<A=<BCD--(1)Also
<BCD=<FCE(Opposite angle)-(2)From (1) and (2)
<A is congruent to <FCE
The point P(x, y) is on the terminal ray of angle Theta. If Theta is between Pi radians and StartFraction 3 pi Over 2 EndFraction radians and = Negative five-halves, what are the coordinates of P(x, y)?
P(Negative StartRoot 21 EndRoot, –2)
P (StartRoot 21 EndRoot, –2)
P(–2, StartRoot 21 EndRoot)
P(–2, Negative StartRoot 21 EndRoot)
Answers
The coordinates of P(x, y) is: A. P(Negative StartRoot 21 EndRoot, –2)
Coordinates of P(x, y)Given:
Radians=3π/2
theta=-5/2
Hence:
Hypotenuse = - 5
Altitude = 2
Using Pythagorean theorem
Hypotenuse² = Altitude² + Base²
-5²= 2² + Base²
25 ² - 4 ² = Base²
Base = √21
Thus P(x,y) :
= P(-√21 : -2)
Therefore the correct option is A.
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Please assist me on this question please
Answers
Answer:
12 units
Step-by-step explanation:
x is to 16 as 9 is to x
x/16 = 9/x cross multiply
x^2 = 144
x =12
Mass (kg)
45
61
57
78
68
Length (cm)
112
138
133
180
175
Which of the options is the most appropiate to suow data in the table?
Pictogram
Pie chart
Bar chart
Line Graph
Scatter Graph
Answers
Answer:
Line or scatter graph.
Step-by-step explanation:
I prefer line, although some of the points deviate a bit. But the line shows a definite relationship between mass and length.
See attached graph.
Select the correct answer from each drop-down menu.
The slope of the line in the graph is [ ]. The y-intercept is [ ]. The equation of the line is y= [ ], and x is [ ]
BOX 1:
A. 2
B. 3
C. -2
D. -3
BOX 2:
A. -3
B. 3
C. 4
D. -4
BOX 3:
A. 2
B. 3
C. -2
D. -3
BOX 4:
A. -3
B. +3
C. +4
D. -4
Answers
For the linear function in the graph, we have that:
The slope is of 3.The y-intercept is of -4.The equation of the line is: y = 3x - 4.What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.The line goes through point (0,-4), hence:
The y-intercept is of -4.
The function also goes through point (2,2), hence the slope is:
m = (2 - (-4))/(2 - 0) = 6/2 = 3.
Then, the equation of the line is:
y = 3x - 4.
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una fracion reducicion a su minima expresion en igual a 1/8 . si la suma de sus terminos es 72. hallar la diferencia entre ellos
Answers
La diferencia entre el denominador y el númerador de la fracción es:
64 - 8 = 56.
¿Como encontrar la fracción?
Tendremos una fracción de la forma:
[tex]\frac{a}{b}[/tex]
Tal que:
[tex]\frac{a}{b} = \frac{1}{8}[/tex]
[tex]a + b = 72[/tex]
Eso es un sistema de ecuaciones
Primero, podemos reescribir la primer ecuación como:
[tex]8a = b[/tex]
Ahora podemos reemplazar "b" en la segunda ecuación por "8a", así obtenemos:
[tex]a + 8a = 72\\\\9a = 72\\\\a = 72/9 = 8[/tex]
Ahora podemos obtener el valor de b:
[tex]b = 8a = 8*8 = 64[/tex]
La diferencia entre a y b es:
[tex]b - a = 64 - 8 = 56[/tex]
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What is the radius of a hemisphere with a volume of 4635 ft 3 , 4635 ft 3 , to the nearest tenth of a foot?
Answers
Step-by-step explanation:
Hemisphere Formulas in terms of radius r:
V = (2/3)πr.
Hereof, What is the radius of a hemisphere? As latter is 4πr2 , curved surface area of a hemisphere of radius r is 2πr2 . and hence total surface area of hemisphere is 2πr2+πr2=3πr2 . Hence, radius of hemisphere is 4 cm.
Triangle Z W X is shown. Angle Z W X is a right angle. An altitude is drawn from point W to point Y on side Z X to form a right angle. The length of W X is b, the length of X Y is a, the length of Y Z is 5, and the length of W Y is 6.
What is the approximate value of b, rounded to the nearest tenth?
7.2 units
7.8 units
8.6 units
9.4 units
Answers
The approximate value of b in the triangle is D. 9.4 units.
How to calculate the value?From the information, it should be noted that WZY and XWY are similar triangle.
The corresponding ratio will be:
XW/WZ = XY/WY = WY/ZY
The calculation of WZ using Pythagoras will be 7.81.
This will be substituted into the ratio.
b/7.81 = 6/5
5b = 46.86
b = 9.4 units.
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Duane rode his bike at 14 miles per hour for 3 hours, then put the bike down and began walking at miles 2 per hour. Elizabeth started jogging at 5 miles per hour along the same path at the same time that Duane started biking. When she reached the bike, she began riding it at 10 miles per hour. How many hours will it have been since they started when Elizabeth catches up to Duane
Answers
Elizabeth will take 9 hours and 45 minutes to catch up with Duane using the given speed-distance-time values.
The speed-distance-time relations are:
Speed = Distance/Time, Distance = Speed*Time, and Time = Distance/Speed.
The distance traveled by Duane on the bike at 14 miles per hour for 3 hours = 14*3 miles = 42 miles.
The time that Elizabeth takes to cover 42 miles jogging at 5 miles per hour = 42/5 hours = 8.4 hours.
The distance traveled by Duane in the extra time which Elizabeth took to reach his bike (8.4 - 3 = 5.4 hours) walking at 2 miles per hour = 2*5.4 = 10.8 miles.
Now, the distance between Elizabeth and Duane is 10.8 miles, before Elizabeth starts riding the bike.
Keeping the distance constant, we calculate the relative speed to calculate the time to cover this distance.
Relative speed = Elizabeth's speed - Duane's speed {As Elizabeth is moving towards Duane, that is, covering the distance but Duane is moving away from Elizabeth, that is, increasing the distance}.
or, Relative speed = 10 - 2 = 8 miles per hour.
Time taken to cover the distance = 10.8/8 = 1.35 hours.
Therefore, the total time taken by Elizabeth to catch up with Duane = 8.4 + 1.35 hours = 9.75 hours or 9 hours and 45 minutes.
Learn more about the speed-distance-time relations at
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