The 45-45-90 triangle has two congruent sides and one right angle, with each angle measuring 45°. The sides are perpendicular to each other and the length of the hypotenuse is equal to the square root of 2 times the length of a leg.
The 30-60-90 triangle has one right angle and two sides that are proportional. The shortest side is half the length of the hypotenuse and the middle side is equal to the shortest side times the square root of 3. The two acute angles in the triangle measure 30° and 60°, respectively.
In conclusion, both 45-45-90 and 30-60-90 triangles are special right triangles with distinct relationships between their sides and angles.
A triangle is a polygon with three edges and 3 vertices. The terminology for categorizing triangles is more than two thousand years vintage, having been defined on the first actual page of Euclid's elements.
In Euclidean geometry, any three factors, while non-collinear, decide a completely unique triangle and simultaneously, a unique plane (i.e. a -dimensional Euclidean space). In different words, there's best one plane that consists of that triangle, and every triangle is contained in some plane. If the entire geometry is only the Euclidean plane, there is the best one plane and all triangles are contained in it; however, in higher-dimensional Euclidean spaces, this is not real. this text is ready triangles in Euclidean geometry, and in particular, the Euclidean plane, except wherein otherwise stated.
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How do you use the sine rule for a triangle?.
To use the sine rule for a triangle, we will need to know at least two side lengths and the measure of the angle opposite one of those sides.
What is triangle ?
A triangle is a geometric shape that has three straight sides and three angles. Triangles are classified based on the measures of their angles and the lengths of their sides.
What is law of sine ?
The law of sines, is a mathematical relationship that relates the lengths of the sides of a triangle to the sines of its angles. Specifically, the law states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all three sides of the triangle.
It can be written as
[tex]a/sin(A) = b/sin(B) = c/sin(C) = 2R[/tex]
where R is the circumradius of the triangle.
To use the sine law to solve for an unknown side or angle in a triangle, we will need to know at least two side lengths and the measure of the angle opposite one of those sides. Once we have that information, we can use the sine law to find the measure of the unknown angle or the length of the unknown side.
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URGENT!
find the value of x in each supplementary angle pair
Answer:
x = 14°
Step-by-step explanation:
We know that,
→ Straight line is always 180°.
Forming the equation,
→ 156° + (x + 10°) = 180°
Now the value of x will be,
→ 156° + (x + 10°) = 180°
→ x + 166° = 180°
→ x = 180° - 166°
→ [ x = 14° ]
Hence, the value of x is 14°.
The value of x in the given supplementary angle pair is 14°.
Explain the term supplementary angle?Angles that add up to 180 degrees are referred to as supplementary angles. For instance, angle 130° as well as angle 50° are complementary angles since the sum of these two angles is 180°.Two angles are classified as supplementary angles because they combine to generate a linear angle when their sum is 180 degrees. When two angles add up to 90 degrees, however, they are thought to be complimentary angles and together they make a right angle.Then,
156 + (x + 10) = 180
166 + x = 180
x = 180 - 166
x = 14°
Thus, the value of x in the given supplementary angle pair is 14°.
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what is 2/5 of 12,500
Answer: it's 5000 :)
Step-by-step explanation:
Answer: 5000
Step-by-step explanation:
At a Mexican retaurant, you order a taco for $1. 85 and burrito dinner for $7. 35. Sale tax i 7. 5% and you leave a tip of 15%. What i your total bill including tip and tax?
So, your total bill including tip and tax is $11.37
First, calculate the subtotal of the food bill by adding the cost of the taco and burrito dinner:
$1.85 + $7.35 = $9.20
Next, calculate the sales tax by multiplying the subtotal by the tax rate (7.5%):
$9.20 x 0.075 = $0.69
Then add the sales tax to the subtotal to get the total before tip:
$9.20 + $0.69 = $9.89
Then calculate the tip by multiplying the total before tip by the tip rate (15%):
$9.89 x 0.15 = $1.48
Finally, add the tip to the total before tip to get the final total bill including tip and tax:
$9.89 + $1.48 = $11.37
So, your total bill including tip and tax is $11.37
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$1.85 + $7.35 = $9.20
$9.20 x 0.075 = $0.69
$9.20 + $0.69 = $9.89
$9.89 x 0.15 = $1.48
$9.89 + $1.48 = $11.37
So, your total bill including tip and tax is $11.37
What are the advantages of having a graphing calculator?.
The advantages of having a graphing calculator
Increases learning speed.Benefits of solving geometry problems. Advantages of accuracy.Students from high schools or higher classes typically use graphing calculators. Furthermore, if you are a student at any of these levels, you are already familiar with the higher-levelMathematical puzzles become complex just by looking at a few numerical characters, and not all books contain the solutions to all of those puzzles. But you can avoid this situation by using a graphing calculator. One issue we frequently run into when taking a math test is not knowing whether the answer is correct or incorrect. Since a single error can alter the entire answer. The data and graphical lines must exactly match for that to be known.To learn more about graphing calculators here
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(06.01 LC)
The distance formula can be used to prove that a triangle has (5 points)
O congruent sides
O a right angle
O parallel sides
O congruent angles
The distance formula can be used to prove that a triangle has congruent sides.
What is congruent sides?If two sides in geometry are congruent, then they have the same length. Since a square has four sides that are all the same length, it has four congruent sides. We refer to a triangle as being equilateral when its three sides are congruent. We use a slash mark to indicate the congruent sides. An equilateral triangle always has 60° angles. An isosceles triangle is one that possesses two congruent sides.Congruent sides are those in any shape that have sides that have the same length. We can say that two triangles are congruent if, for instance, all three of their sides are the same length and equal to one another. The SSS congruence rule stands for (side-side-side).
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29. Higher Order Thinking If the
numerator and denominator of a fraction
are both odd numbers, can you write
an equivalent fraction with a smaller
numerator and denominator? Give an
example to explain.
Answer:
Yes
Step-by-step explanation:
As long as the odd numbers are not prime numbers, they can still be in a fraction that can be reduced. Not in all cases of course but in some, for instance 9/27 can be reduced to 1/3
What percent of the 8th graders estimated they spend less than an hour a day on social media? Round your answer to the nearest tenth of a percent.
A newly-planted tree needs to be staked with three wires. Each wire is attached to the trunk 3ft. above the ground, and then anchored to the ground 2.5 ft. from the base of the tree. Estimate about how much wire is needed for 6 trees?
33ft wire is needed for 6 trees.
What is addition?Addition is a way of combining things and counting them together as one large group. ... Addition in math is a process of combining two or more numbers.
here, we have,
Each wire is attached to the trunk 3ft. above the ground,
and then anchored to the ground 2.5 ft. from the base of the tree.
So, for each tree total wire = 3+2.5
=5.5 ft.
So, for 6 trees = 5.5*6
=33ft
Hence, 33ft wire is needed for 6 trees.
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Please help me with this Geometry Question
The value of x from the given figure is 12 units.
What are similar triangles?Two triangles are similar if the angles are the same size or the corresponding sides are in the same ratio. Either of these conditions will prove two triangles are similar.
From the given figure,
Consider ΔADC and ΔABC,
∠C=∠C (Reflex property)
AC=AC (Reflex property)
∠BAC=∠CDA=90°
By AA similarity, ΔADC ~ ΔABC
So, AC/BC = DC/AC
x/36 = 4/x
x²=36×4
x²=144
x=12 units
Therefore, the value of x from the given figure is 12 units.
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Please help me understand
The perimeter of the horse corral is 600 feet.
What is Area of Rectangle?The area of Rectangle is length times of width.
The area of any regular polygon is given by the formula: Area = (a x p)/2, where a is the length of the apothem and
p is the perimeter of the polygon.
Given that area of the horse corral is 3000 ft²
Length of the apothem is 10 ft
We need to find the perimeter.
3000=10p/2
6000=10p
Divide both sides by 10
600=perimeter
Hence, the perimeter of the horse corral is 600 feet.
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ΔRST is reflected across the line y = x to form ΔR’S’T’. Find the coordinates of the points R’, S’ and T’.
R(1,-2)
S(2,-8)
T(7,-4)
Answer:
R' ( -2,1)
S' (-8,2)
T' ( -4,7)
Step-by-step explanation:
please help, i dont understand!
10y⁶ is the width of the rectangle and y²+3 is the length of the rectangle.
What is Area of Rectangle?The area of Rectangle is length times of width.
Given that the area of rectangle is 70y⁸+30y⁶
The width of the rectangle is the greatest common factor of 70y⁸ and 30y⁶
70y⁸+30y⁶
10y⁶(y²+3)
10y⁶ is the width of the rectangle.
y²+3 is the length of the rectangle.
Hence, 10y⁶ is the width of the rectangle and y²+3 is the length of the rectangle.
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Two lines that make right angles at their intersection are?
Two lines that make right angles at their intersection are Perpendicular lines.
What is perpendicular in lines?Perpendicular lines are those that cross at a straight angle of 90 degrees.When two lines cross at a straight angle or 90 degree, perpendicular lines are created. Perpendicularity is the name given to this characteristic of lines. In-depth discussions of what a perpendicular is, its characteristics, how it differs from a parallel line, as well as several instances with solutions will all be covered in this article.A perpendicular is a straight line in mathematics that forms a right angle (90 degrees) with another line. In other words, two lines are perpendicular to one another if they connect at a right angle.
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Sara drives 72 miles on 3.2 gallons of gas. She uses this information to calculate how many miles per gallon she can drive. Using this result, how many miles can Sara drive on 12.3 gallons of gas?
Answer:
276.75
Step-by-step explanation:
one gallon lets sara drive 22.5 miles. multiply that by 12.3 and u get 276.75 !
13 Vito is training for a race. He runs 14 miles a day for
16 days. Then he runs 10 miles a day for 3 days. How
many fewer miles does he run the 3 days than the
16 days?
He ran 194 miles fewer he ran in 3 days than the 16 days run.
What is mile?the statute mile, which is 5,280 feet long, is one example of a mile (1.609 km). The mille passus, or "thousand paces," was a unit of measurement used in ancient Rome and equaled 5,000 Roman feet.
The "old London" mile, which was eight furlongs, was first established around the year 1500. The mile at that time was equal to 5,000 feet, with the furlong being 625 feet at that time, using the larger northern (German) foot.
A statute from 1593 that confirmed the use of a shorter foot and made the length of the furlong 660 feet increased the mile by 280 feet during the reign of Queen Elizabeth I, bringing it to 5,280 feet.
The Fewer mile he ran = (16 × 14) - (3 × 10)
= 194 miles
Thus, He ran 194 miles fewer he ran in 3 days than the 16 days run.
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How do you find the equation of the axis of symmetry using factored form?.
To find the equation of the axis of symmetry using factored form, we can use the multiply and conversion method which converts it into vertex form.
It can be multiplied and converted to vertex form.
Example: (x-3)(x+2) f(x)
f(x) = x^2 - x - 6
We can now combine the x terms to finish the square.
f(x) = (x^2 - x +1/4 ) - 6 - 1/4
f(x)= (x - 1/2)^2 -25/4
As a result, the vertex is (1/2, -25/4)
Any quadratic given in factored form can be solved this way.
If the parabola contains the equation y=f(x)=a(xr1)(xr2), the zeroes of f(x), i.e., r1 and r2, can be read off right away. The vertex then has coordinates (h,k), where k=f(h) is the result of inserting x=h through the function f(x), and h=(r1+r2)/2 is the average of the two zeroes.
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k is a non-zero whole number. Given that 15 x 375 x k is a perfect cube, write down the smallest value of k.
Answer:
k = 75
Step-by-step explanation:
Let's write down the prime factors of 15 and 375
15 = 3 x 5
375 = 3 x 5 x 5 x 5
So 15 x 375 = 3 x 5 x 3 x 5 x 5 x 5
= (3 x 3) x (5 x 5 x 5) x 5
This cannot be a perfect cube
However if we multiply this by 3 x 5 x 5 we will get
(3 x 3 x ) x (5 x 5 x 5) x(5 x 5 x 5) which is a perfect cube
Since we are asked to find k such that 15 x 375 x k is a perfect cube
k = 3 x 5 x 5 = 75
ans
k = 75
A circular garden has a circumference of 396cm using π= 22/7. Calculate
a) diameter
b) radius
c) area
The diameter , radius and area of the circle is 126cm, 63cm, 12474cm² respectively.
What is circumference of a circle?The circumference of a circle is the perimeter of the circle. It is the total length of the boundary of the circle.
The circumference of a circle is given as;
C = π d
where d is the diameter of the circle
therefore 396 = 22/7 × d
22d = 396× 7
22d = 2772
divide both sides by 22
d = 2772/22
d = 126 cm
the diameter of a circle is 2 times it's radius
d = 2r
126 = 2r
r = 126/2
r = 63cm
The area of the circle is
A = πr²
A = 22/7× 63× 63
A = 22×9× 63
A= 12474cm²
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consider the function f(x) = -2 (x-3) (x + 1)
The graph for the points (-1, 0), (0, 6), (1, 8), (2, 6) and (3, 0) is plotted below.
What is the function?Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
The given function is f(x)=-2(x-3)(x+1).
Graph the parabola using the direction, vertex, focus, and axis of symmetry.
Direction: Opens Down
Vertex: (1,8)
Focus: (1,63/8)
Axis of Symmetry: x=1
Directrix: y=65/8
Plot the points (-1, 0), (0, 6), (1, 8), (2, 6) and (3, 0).
Therefore, graph for the points (-1, 0), (0, 6), (1, 8), (2, 6) and (3, 0) is plotted below.
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Wally want to determine the height of a tatue that cat a 164-inch hadow by comparing it to hi own height and hadow length. If Wally, who i 69 inche tall, cat a hadow that i 41 inche in length, what i the height of the tatue?
A. 276 inche
B. 300 inche
C. 97 inche
D. 252 inche
The height of the statue is:
A. 276 inches
If Wally, who is 69 inches tall, catch a shadow that is 41 inch in length.
Height of Statue CalculationTo determine the height of the statue, you can use the principle of similar triangles. Similar triangles have the same angles, but not necessarily the same side lengths. You can use the ratio of the height of Wally and the length of his shadow to the height of the statue and the length of its shadow to find the height of the statue.
Height of Wally: 69 inches
Length of Wally's shadow: 41 inches
Height of statue: x
Length of statue's shadow: 164 inches
You can set up the proportion as:
69/41 = x/164
Solving for x, you get:
x = (69 × 164)/41
x = 276 inches
Thus the answer is A. 276 inches.
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find an equation of the plane passing through that is orthogonal to the planes xyz and xyz.
The equation of the plane passing P(1,2,1) and is orthogonal to the two planes: x-y-z-10 = 0, x-2y + z-2=0 is 3x + 2y + z = 8.
We need a point b and a vector v along the line in order to characterize it. We might alternatively begin with the two points a and b and use the formula v = ab.
A point Q and a vector n perpendicular to the plane are required in order to describe a plane. Later on, we'll look at how to get n from various types of information, such as the positions of three points on a plane.
A plane is a flat, endlessly long, two-dimensional surface. A plane is a point with zero dimensions, a line with one dimension, and space with three dimensions in two dimensions. The picture below that is attached shows the answer.
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Question correction:
Find the equation of the plane passing P(1,2,1) and is orthogonal to the two planes: x-y-z-10 = 0, x-2y + z-2=0
On a test that has a normal distribution, a score of 82 falls three standard deviations above the mean, and a score of 64 falls one standard deviation above the mean. Determine the mean of this test.
Answer: mean = 55
Step-by-step explanation:
Distance between 64 and 82 = 18
Each standard deviation is worth 9 units.
So 64 - 9 = 55(mean)
Or use m= x-zq
set of points is shown on the graph.
Scatter plot with a point at negative 3 comma 9, a point at 0 comma 5, a point at 1 comma 8, a point at 6 comma 7, and a point at 8 comma 3.
Which of the following equations is the best model for a line of fit for the data?
y equals 2 thirds times x plus 7
y equals negative 2 thirds times x plus 7
y equals 1 third times x plus 7
y equals negative 1 third times x plus 7
An equation which represents the best model for a line of fit for the data is: y equals negative 2 thirds times x plus 7. The correct option is A.
How to find a line of fit for the data?A scatter plot should be used to determine a linear equation of the line of best fit (trend line) that models the data points described above.
In this scenario, the x-values would be plotted on the scatter plot's x-axis, while the y-values would be plotted on the scatter plot's y-axis.
Right-click on any data point on the scatter plot in Excel, select the format trend line, and then check the box to display an equation for the line of best fit (trend line) on the scatter plot.
From the scatter plot (see attachment) which models the relationship between data points in the table, a linear equation for the line of best fit is given by:
y = -0.33x + 7.
Rewriting the equation as an improper fraction, we have:
y = -2/3(x) + 7
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A tudy how that the more exercie people had a day the more they lept at night which catter plot repreent the relationhip
A tudy how that the more exercie people had a day the more they lept at night which catter plot repreent the relationhip The overall pattern of the scatter plot would show that as the amount of exercise increases, the amount of sleep also increases.
A scatter plot would be used to represent the relationship between the amount of exercise people have per day and the hours of sleep they get at night. The scatter plot would show the number of hours of exercise on the x-axis and the number of hours of sleep on the y-axis. Each point on the scatter plot would represent an individual's exercise and sleep hours. The overall pattern of the scatter plot would show that as the amount of exercise increases, the amount of sleep also increases.
1. A scatter plot is used to represent the relationship between two variables.
2. In this case, the two variables are the amount of exercise people have per day and the hours of sleep they get at night.
3. The x-axis of the scatter plot would represent the amount of exercise, while the y-axis would represent the hours of sleep.
4. Each point on the scatter plot would represent an individual's exercise and sleep hours.
5. The overall pattern of the scatter plot should show that as the amount of exercise increases, the amount of sleep also increases.
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I'm not understanding these questions, can someone help me?
Answer:
see below
Step-by-step explanation:
What number should be added to 2x3 7x2 2x so that the resulting polynomial leaves the remainder 2 when divided by 2x 3?.
4x-2 is added to the given polynomial p(x) to leave the remainder=(-2).
[tex]p(x)=2x^3-7x^2+2x\\g(x)=2x-3\\dviding. p(x) by g(x),\\ we get2x-3)2x^3-7x^2+2x(x^2-2x2x^3-3x^2- +0 -4x^2+2x-4x^2+6x+ -0 -4xq(x)=x^2-2xand, r(x)=-4x\\Now,\\According to division algorithmp\\(x)=g(x)*q(x)+r(x)2x^3-7x^2+2x=(2x-3)(x^2-2x)+(-4x)\\adding 4x-2 on both side,\\ we get\\2x^3-7x^2+2x+4x-2=(2x-3)(x^2-2x)+(-4x)+4x-22x^3-7x^2+6x-2=(2x-3)(x^2-2x)+(-2)[/tex]
4x-2 is added to the given polynomial p(x) to leave the remainder=(-2).
A polynomial is described as an expression that consists of variables, constants, and exponents, which might be mixed with the use of mathematical operations along with addition, subtraction, multiplication, and department (No division operation by a variable).
In arithmetic, a polynomial is an expression that includes indeterminates and coefficients, that entail best the operations of addition, subtraction, multiplication, and fine-integer powers of variables. An instance of a polynomial of an unmarried indeterminate x is x² − 4x + 7.
Polynomials are sums of phrases of the form k⋅xⁿ, in which okay is any wide variety and n is a positive integer. for example, 3x+2x-5 is a polynomial. advent to polynomials.
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Complete Question:
what number must be added to[tex]2x^3-7x^2+2x[/tex] so that the resulting polynomial leaves the remainder -2 when divided by 2x-3
For what value of the variable i the value of the expreion – 3(2x 1) twenty greater than the value of the expreion 8x 5?
The value of the variable for which the value of the expression –3(2x+1) is 20 is greater than the value of the expression 8x+5 is -2.
According to the question, 20 greater than 8x +5 = 8x +5 +20 = 8x +25.
We want this value to be -3(2x +1),
So, solving this equation we get: 8x +25 = -3(2x +1)
=> 8x +25 = -6x -3 (eliminating the parentheses)
Further solving this equation we get,
=> 14x = -28
=> x= -2
Thus, The value of the variable for which the value of the expression –3(2x+1) is 20 is greater than the value of the expression 8x+5 is -2.
Complete question: Find the value of the variable for which the value of the expression –3(2x+1) is 20 greater than the value of the expression 8x+5.
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The value of the variable for which the value of the expression –3(2x+1) is 20 is greater than the value of the expression 8x+5 is -2.
According to the question, 20 greater than 8x +5 = 8x +5 +20 = 8x +25.
We want this value to be -3(2x +1),
8x +25 = -3(2x +1)
8x +25 = -6x -3 (eliminating the parentheses)
14x = -28
x= -2
The support for a window air-conditioning unit forms a triangle and an exterior angle. What is the measure of the exterior angle?.
The measure of the exterior angle in this case is 60+60 = 120 degrees.
What is exterior angle ?
An exterior angle of a polygon is an angle formed between one side of the polygon and a line extended from the endpoint of the opposite side. An exterior angle can be formed by standing outside of the polygon and looking at it.
In a triangle, the measure of an exterior angle is equal to the sum of the measures of the two interior angles opposite to it. In any convex polygon, the sum of the measures of the exterior angles is always 360 degrees.
The support for a window air-conditioning unit forms a triangle. A triangle is a three-sided polygon, and all the interior angles in a triangle add up to 180 degrees. Therefore, the measure of each interior angle of a triangle is (180/3) = 60 degrees.
An exterior angle of a triangle is the angle formed between one side of the triangle and a line extended from the endpoint of the opposite side. In a triangle, the measure of an exterior angle is equal to the sum of the measures of the two interior angles opposite to it.
Therefore, the measure of the exterior angle in this case is 60+60 = 120 degrees.
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Jamal and lin lives 2 miles apart. They each leave their house at the same time and walk towards each other. With jamal walking at 3 mi/h and lin walking at 5 mi/h. How far from jamal house will they meet
Jamal and Lin will meet 3.21 miles from Jamal's house.
What is meet?Meet is a gathering of two or more people for a specific purpose, such as to discuss an issue, make a decision, or socialize. It can take place in person or online, either in a formal or informal setting.
The time it takes for Jamal and Lin to meet is the time it takes for Jamal to travel 2 miles plus the time it takes for Lin to travel 2 miles.
Since Jamal is walking at 3 mi/h, it takes him (2 miles) / (3 mi/h) = 0.67 hours to travel 2 miles.
Since Lin is walking at 5 mi/h, it takes her (2 miles) / (5 mi/h) = 0.4 hours to travel 2 miles.
The total time it takes for Jamal and Lin to meet is 0.67 + 0.4 = 1.07 hours.
Jamal and Lin will meet 1.07 hours after they left their houses.
Since Jamal is walking at 3 mi/h, he will have traveled (1.07 hours) * (3 mi/h) = 3.21 miles when they meet.
Jamal and Lin will meet 3.21 miles from Jamal's house.
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