Answers
The first hiker went 2 miles east and 1 mile north to point A.
The second hiker went 1 mile west and 3 miles south to point B.
See the figure below.
A
I
1 mile I 1 mile
I---------S------------------I
I 2 miles
I
I
3 miles I
I
I
B
Now we need to see how much east and how much north hiker B is from hiker A.
A
I
1 mile I 1 mile
I---------S------------------I
I 2 miles I
I I
I I
3 miles I I 3 miles
I I
I I
B----------------------------I
3 miles
From point B go 3 miles east, then 3 + 1 = 4 miles north to point B.
The distance between the hikers is the hypotenuse of a triangle with legs of lengths 3 and 4.
3^2 + 4^2 = d^2
9 + 16 = d^2
d^2 = 25
d = 5
The distance between the hikers is 5 miles.
Related Questions
TEXASCHIC! :)
1. Sam is observing the velocity of a car at different times. After three hours, the velocity of the car is 51 km/h. After five hours, the velocity of the car is 59 km/h.
Part A: Write an equation in two variables in the standard form that can be used to describe the velocity of the car at different times. Show your work and define the variables used. (5 points)
Part B: How can you graph the equation obtained in Part A for the first six hours? (5 points)
My answer:
Part A:
y - 51 = 59 - 51 / 5 - 3 (x-3)
y - 51 = 4 (x-3)
y = 4x -12 + 51
y= 4x + 39
where x is the time and y is the velocity of car at any time x.
Part B:
y =4 * 6 + 39 = 24 + 39 = 63 ~km/h
Answers
slope = (59 - 51) / (5 - 3) = 8/2 = 4
y = mx + b
slope(m) = 4
(3,51)...x = 3 and y = 51
sub and find b, the y int
51 = 4(3) + b
51 = 12 + b
51 - 12 = b
39 = b
so ur equation is : y = 4x + 39...but u need it in standard form
y = 4x + 39
-4x + y = 39
4x - y = -39 <==== this is ur equation...x = number of hrs and y = total velocity
====================
ur x axis is the number of hrs
ur y axis is total velocity in km
y = 4x + 39......slope = 4.....y int = (0,39)....x int is (- 9.75,0) or -9 3/4 for graphing purposes)....so start at (-9.75,0)...and since the slope is 4, go up 4 and to the right 1....plot that...then up 4 and to the right 1...plot that...u will cross the y axis at (0,39)....and just connect ur plotted points and u have ur line......or what u can do since it is asking for the first 6 hrs....sub in 1 for x and solve for y....then sub in 2 for x and solve for y...keep doing this up till 6 and u will have ur line up till 6 hrs
The velocity of the car is represented by the equation y = 4x + 39, where 'x' is time and 'y' is the velocity. You can graph this for the first six hours by substituting x=6 to find: y=63 km/h. Thus, the car's velocity after six hours would be 63 km/h.
Explanation:In order to solve this problem, we first find the equation representing the change in the car's velocity. The point (3, 51) represents the condition that after three hours, the car is moving at 51 km/h. Similarly, the point (5, 59) stands for the velocity being 59 km/h after five hours. We derive the slope of the line connecting these two points by subtracting the y-coordinates and dividing by the difference of the x-coordinates, (59-51)/(5-3) = 4.
This slope represents an increase of 4 km/h for every hour that passes. Our equation then becomes y - 51 = 4(x - 3) which simplifies to y = 4x + 39. In this equation, 'x' represents time in hours and 'y' is the car's velocity at any given time 'x'.
For Part B, we graph the equation over the first six hours by inputting x=6 into the equation, giving us y = 4*6 + 39 = 63 km/h. Therefore, after six hours, the car would be moving at a velocity of 63 km/h.
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Change the column heading for the row sum column which represents the total of each type of session, to total number of sessions
Answers
You can change a column heading by clicking it, then right-clicking to select 'Rename Column' and inputting 'Total Number of Sessions'.
Explanation:To change the column heading for the row sum which represents the total of each type of session to 'Total Number of Sessions', you need to follow these steps:
Firstly, click on the column heading which you want to change. This will usually highlight the entire column.Right-click on the highlighted column heading, and select 'Rename Column' from the drop-down menu.In the text box that appears, type 'Total Number of Sessions' and hit 'Enter'.This will effectively rename your column heading to represent the total number of sessions accurately.
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Write a function rule: 7 more than the quotient of a number n and 4 is 9
pls help!!!
Answers
How do I solve this?
Answers
-c^2-4c+21
From here, we’ll factor out a -1 so that we have:
-(c^2+4c-21)
Let’s focus on the quadratic expression inside the parentheses. To find our factors (c + x)(c + y), we’ll need to find two terms x and y that multiply together to make -21 and add together to make 4. It turns out that the numbers -3 and 7 work out perfectly for that purpose (-3 x 7 = -21 and 7 + (-3) = 4), so substituting them in for x and y, we have:
(c + (-3))(c + 7)
(c - 3)(c + 7)
And adding back on the negative from a few steps earlier:
-(c - 3)(c + 7)
What is the standard form of the following equation?
y=−2/5x+4 Use integers for A, B, and C. Enter your answer in the box.
Answers
so
[tex] \frac{-2}{5} x -y=-4 [/tex]
multiply by -1 to make the x coefficient positive
[tex] \frac{2}{5} x+y=4 [/tex]
so we multiply by 5 to make them integers
[tex]2x+5y=20[/tex]
A=2,B=5,C=20
Is - √3 a real number, whole number, natural number, rational number, irrational number, an integer, or imaginary number?
Answers
Write the fraction 20/32 in simplest form.
Answers
The fraction given 20/32 can be written as 5/8 in its simplest form.
How to simplify fractions?The principle of simplifying fraction is to make both the numerator and the denominator smaller numbers but as proportional as the original fraction. This is convenient for mathematical operations and even for understanding proportions.
Now, to simplify fractions we need to divide the nominator and the denominator, the process is shown below:
20/32 divide both numbers by 420/ 4 = 532/ 4 = 8This means the new fraction is 5/8.
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The average rate of change of the function between x = 15 to x = 29 is __________m/s2 and represents the car's acceleration.
Answers
Answer:
sorry guys that other question is absolutely no help at all. The answer is 1.266 m/s squared. I don't know what kind of IDIOT would try and take you to a completely other website.
Step-by-step explanation:
Name 3 decimals between 16.4 and 16.5 draw a number line estmating the placement of all five decimals
Answers
Which statement best explains whether △PQR is congruent to △XYZ?
△PQR is congruent to △XYZ because △PQR can be mapped to △XYZ by a rotation of 180° about the origin.
△PQR is congruent to △XYZ because △PQR can be mapped to △XYZ by a translation 5 units down followed by a reflection across the y-axis.
△PQR is not congruent to △XYZ because there is no sequence of rigid motions that maps △PQR to △XYZ.
△PQR is congruent to △XYZ because △PQR can be mapped to △XYZ by a reflection across the y-axis followed by a reflection across the x-axis.
Answers
Help me please thanks
Answers
I feel really stupid but how do you solve: v+9/3+8
Answers
The answer is v +11.
The answer would be simply
V 11
what are the zeros of the quadratic function f(x)=8x2-16x-15
Answers
Answer: The zeroes of the given polynomial f(x) are
[tex]x=1-\sqrt{\dfrac{23}{8}},~~~x=1+\sqrt{\dfrac{23}{8}}.[/tex]
Step-by-step explanation: We are given to find the zeroes of the quadratic function below:
[tex]f(x)=8x^2-16x-15.[/tex]
To find the zeroes, we must find the roots of the following equation
[tex]f(x)=0\\\\\Rightarrow 8x^2-16x-15=0~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex].
We know that the roots of the quadratic equation of the form [tex]ax^2+bx+c=0,~a\neq 0[/tex] is given by
[tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}.[/tex]
In the given quadratic equation , a = 8, b = -16 and c = - 15.
Therefore, the roots of the equation are
[tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\\\\Rightarrow x=\dfrac{-(-16)\pm\sqrt{(-16)^2-4\times 8\times (-15)}}{2\times 8}\\\\\\\Rightarrow x=\dfrac{16\pm\sqrt{256+480}}{16}\\\\\\\Rightarrow x=\dfrac{16\pm\sqrt{786}}{16}\\\\\\\Rightarrow x=\dfrac{16\pm4\sqrt{46}}{16}\\\\\\\Rightarrow x=\dfrac{4\pm\sqrt{46}}{4}\\\\\\\Rightarrow x=1\pm\sqrt{\dfrac{46}{16}}\\\\\\\Rightarrow x=1\pm\sqrt{\dfrac{23}{8}}\\\\\\\Rightarrow x=1-\sqrt{\dfrac{23}{8}},~~~x=1+\sqrt{\dfrac{23}{8}}.[/tex]
Thus, the zeroes of the given polynomial f(x) are
[tex]x=1-\sqrt{\dfrac{23}{8}},~~~x=1+\sqrt{\dfrac{23}{8}}.[/tex]
Option (C) is correct.
The zeroes of the given polynomial f(x) = 8x^2-16x-15 are x = 1 + [tex]\sqrt{23}[/tex] / 8 and x = 1 -[tex]\sqrt{23}[/tex] / 8 Thus, Option C is correct.
What is a quadratic equation?A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.
We are given to find the zeroes of the quadratic function f(x) = 8x^2 - 16x-15
f(x) = [tex]8x^2-16x-15[/tex] = 0
We know that the roots of the quadratic equation ax² + bx + c = 0 is
x = -b ± [tex]\sqrt{b^2 - 4ac}[/tex] / 2a
In the given quadratic equation , a = 8, b = -16 and c = - 15.
So,
x = -b ± [tex]\sqrt{b^2 - 4ac}[/tex] / 2a
x = -(-16) ± [tex]\sqrt{(-16)^2 - 4(8)(-15)}[/tex] / 2(8)
x = 16 ± [tex]\sqrt{256+ 480}[/tex] / 16
x = 16 ± [tex]\sqrt{786}[/tex] / 16
x = 4 ± [tex]\sqrt{46}[/tex] / 4
x = 1 ± [tex]\sqrt{23}[/tex] / 8
Thus, the zeroes of the given polynomial f(x) are
x = 1 + [tex]\sqrt{23}[/tex] / 8 and x = 1 -[tex]\sqrt{23}[/tex] / 8. Option C is correct.
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∠A and ∠B are vertical angles with m∠A=x and m∠B=4x−30 . What is m∠A ? Enter your answer in the box.
Answers
Answer:
[tex] x = 4x -30[/tex]
We can solve for x subtracting x on both sides:
[tex] x-x= 4x-x-30[/tex]
And then we can add 30 in both sides:
[tex] 30= 3x[/tex]
And dividing both sides by 3 we got:
[tex] x = 10[/tex]
Step-by-step explanation:
For this case we know the measure of two angles:
[tex]m <A = x[/tex]
[tex] m<B = 4x-30[/tex]
And we know that both angles are vertical and by definition vertical angles are the angles opposite each other when two lines cross.
For this case since both angles are vertical we have the property that:
[tex] m<A = m<B [/tex]
And replacing what we got we have:
[tex] x = 4x -30[/tex]
We can solve for x subtracting x on both sides:
[tex] x-x= 4x-x-30[/tex]
And then we can add 30 in both sides:
[tex] 30= 3x[/tex]
And dividing both sides by 3 we got:
[tex] x = 10[/tex]
Sarah has a collection of nickels, dimes, and quarters worth $13.80. she has 10 more dimes than nickels and twice as many quarters as dimes. how many coins of each kind does she have?
Answers
22 dimes = $2.20
44 quarters = $11.00
11.00
2.20
+ .60
———
13.80
annie dome worked from 8:15 am to 11:45 am and from 12:30 pm to 4:15 pm. How many hours did she work? (include steps on how to do this problem)
Answers
How to do this ?? How
Answers
The two bars | | is used to indicate the function absolute value.
Remember this definition:
| x | = - x if x < 0 and x if x > 0
So, | x | > c =>
x > c or x > - c
Therefore:
|ax - b| > c => ax - b > c or ax - b > - c
That is the third option of the answer list.
MATH HELP 20 POINTS!!!
Answers
A) Variable = x ( miles Tim walked )
B) Tim walked X miles, Molly walked 4+x miles ( 4 more than Tim)
Equation: x + x+4 = 10
C) x +x+4 = 10
2x+4 = 10
2x =6
x = 3
D)
Tim walked 3 miles, Molly walked 7 miles
Find the coordinates of the other endpoint of the segment with the given endpoint (6,2) and midpoint (2,0)
Answers
Please help with this equation!!! 30 points!
The following equation is shown.
[tex] x^{2} - \sqrt{2.5} -l + ( -\pi + z ) = A[/tex]
Solve for the variable z.
Answers
z= -x²+l+4.72273148+A
Suppose you work for a large coffee distributor that has a secret coffee blend it sells to local stores. You mix the Mexican Shade Grown blend with the Rift Valley blend, but always in the same proportion. Yesterday, you mixed 80 pounds of the Mexican Shade Grown blend with 24 pounds of the Rift Valley blend. Today, there is 60 pounds of the Mexican Shade Grown coffee left in stock. How many pounds of the Rift Valley coffee should you mix with it to get your secret blend?
Answers
It's 18 pounds of Rift Valley.
To get the secret blend, you should mix 18 pounds of the Rift Valley coffee with the 60 pounds of Mexican Shade Grown coffee.
Explanation:To find out how many pounds of the Rift Valley blend you should mix with the 60 pounds of Mexican Shade Grown coffee, we need to set up a proportion based on the ratio of the two blends. The ratio of the Mexican Shade Grown blend to the Rift Valley blend is 80:24, which can be simplified to 10:3. We can then set up the proportion: 10/3 = 60/x. By cross-multiplying, we get 10x = 180. Dividing both sides by 10, we find that x = 18. Therefore, you should mix 18 pounds of the Rift Valley coffee with the 60 pounds of Mexican Shade Grown coffee to get your secret blend.
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what is the slope of the line given by the equation y=2.3x
Answers
making the slope of this equation 2.3
I believe this is the correct answer. I hope it helps.
The clean up hitter on a baseball tean batted 1/3 of the runs the team scored. The hitter batted in 3 runs. Select the equation that represents the number of n of runs the team scored. Then solve the equation:
a.1/3n=3B.n/3=1/3C.3n=1/3D.3n=9
Answers
a. 1/3 (n)=3
n=9
Evaluate the determinant for the following matrix [144] [522] [155]
Answers
1 4 4
5 2 2
1 5 5
=> Determinant =
1 * (2*5 - 2*5) - 4 * (5*5 - 1*2) + 4 * ( 5*5 - 2*1)
= 1*(10 - 10) - 4*(25 - 2) + 4*(25 -2) = 1*0 + 4* 23 + 4*(25 - 2) = 0 - 4*23 + 4*23 = 0
Answer: 0
What is 2.828427125 to the nearest thousandth?
Answers
Soda is sold in aluminum cans that measure 6 inches in height and 2 inches in diameter. how many cubic inches of soda are contained in a full can?
Answers
v=πr²h (now put in the values to find volume)
v=π(1)²(6)
v=18.85 inches cubed
Therefore, 18.85 inches cubed can be fit into the full can.
Hope I helped :)
A cylinder is a three-dimensional figure that has a radius and a height.
The volume of a cylinder is given as:
Volume = π r²h
The amount of soda in a full can is 18.84 cubic inches.
What is a cylinder?A cylinder is a three-dimensional figure that has a radius and a height.
The volume of a cylinder is given as:
Volume = π r²h
Example:
The volume of a cup with a height of 5 cm and a radius of 2 cm is
Volume = 3.14 x 2 x 2 x 5 = 62.8 cubic cm
We have,
Aluminum cans:
Height = 6 inches
Diameter = 2 inches
Radius = diameter/2 = 2 / 2 = 1 inches
The aluminum can is in the shape of a cylinder.
The volume of the aluminum can:
= πr²h
= 22/7 x 1 x 1 x 6
= 18.84 cubic inches
The amount of soda in a full can is 18.84 cubic inches.
Thus,
The amount of soda in a full can is 18.84 cubic inches.
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REALLY NEED HELP PLEASE!!
The Smith family rented a recreational vehicle for a seven-day vacation. The cost to rent the recreational vehicle was $560 plus $0.50 per mile. How many miles were driven if the total cost was $1350?
Answers
Its 790
$0.50(x) = $1350 - $560
x = $790/$0.50
x = 1,580 miles
If A = James's present age, write an expression for his age seven years from now.
Answers
Answer:
A + 7Step-by-step explanation:
Given,
James's present age be = A
So,
After seven years from now will be +7
Therefore,
James age, seven years after his present age is,
= (A) + (7)
= A + 7
Hence, the required expression is: A + 7 (Ans)
Hello there, I hope you are having a nice day.
We are given that James's present age is A years.
If James's present age is a years, then in 7 years his age will be
A+7
Which means that whatever A is, it will be 7 more in 7 years.
Hence, the expression is A+7 (Answer)
Hope it helps.
~An emotional teen who helps others and listens to her favourite song "How Far I'll Go"
-Grace ;-)
Good luck with your studies.
How does the volume of a cone compare to the volume of a cylinder with the same radius and height?
Answers
cone volume: π * r^2 * h/3
cylinder volume: π * r^2 * h
Now if you compare both of them with information that the radius and height is same, then the cone:cylinder volume ratio would be:
Cone volume/cylinder volume=
π * r^2 * h/3 / π * r^2 * h= 1/3
Cone volume is 1/3 of cylinder volume
Given that ΔJKL ≅ ΔUVW and ΔUVW ≅ ΔABC, complete the following statements. Triangle JKL is congruent to triangle ABCBCACBA. Side LK corresponds to sides UV and ABVU and BCWV and CB. Angle JLK corresponds to angles UVW and ABCUWV and ACBWUV and CAB
Answers
Triangle JKL is congruent to triangle ABC.
Side LK corresponds to sides WV and CB.
Angle JLK corresponds to angles UWV and ACB.
For ΔJKL ≅ ΔUVW and ΔUVW ≅ ΔABC, we conclude congruence JKL ≅ ABC, LK corresponds to UV and AB, and JLK corresponds to UVW and ABC.
The given information implies that triangle JKL is congruent to triangle ABC, and side LK corresponds to sides UV and AB. Angle JLK corresponds to angles UVW and ABC.
Therefore, the statements can be completed as follows:
Triangle JKL is congruent to triangle ABC.
Side LK corresponds to sides UV and AB.
Angle JLK corresponds to angles UVW and ABC.
Therefore, these statements reflect the congruence relationships established through the given information.
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