Answer:
x < -3
Step-by-step explanation:
Inequality form: x < -3
Interval Notation: (-[tex]\infty}[/tex],-3)
It’s math please help
Answer:
D because angle U is equal to angle W because it is diverting angle
Find the slope of the line passing through the points [-8, -3] and [-3, 4].
Answer:
[tex]\frac{7}{5}[/tex]
Step-by-step explanation:
Slope of a line = Gradient
[tex]= \frac{y_{2} - y_{1}}{x_{2} -x_{1} }[/tex]
Based on the two points provided in the question:
[tex]x_{1} = -8[/tex]
[tex]y_{1} = -3[/tex]
[tex]x_{2} = -3[/tex]
[tex]y_{2} = 4[/tex]
Slope = [tex]\frac{4 - (-3)}{-3 - (-8)}[/tex]
= [tex]\frac{4 + 3}{-3 + 8}[/tex]
= [tex]\frac{7}{5}[/tex]
Solve the inequalities below. Write the solution set in interval notation and graph the solution.
8x−12>158x-12>15
Solution:
Interval notation for the solution:
Step-by-step explanation:
Inequality Interval Notation Graph
Sajan Rai
Solve the inequalities below. Write the solution set in interval notation and graph the solution.
8x−12>158x-12>15
Solution:
Interval notation for the solution:
(-∞,5/8) U (5/8, ∞)
To graph the solution, we need to find the points that make the inequality true and shade the region that corresponds to these points. On the number line, we can start by finding x values that make the inequality equal to zero:
8x - 12 = 0
x = 12/8 = 3/2
and
15 - 8x = 0
x = 15/8 = 9/4
Next, we need to test values that are less than 3/2 and greater than 9/4 to determine the direction of the inequality. If the inequality is true for values less than 3/2, then we shade the region to the left of 3/2. If the inequality is true for values greater than 9/4, then we shade the region to the right of 9/4. In this case, since the inequality is "greater than," the shading goes to the right of 9/4 and to the left of 3/2.
A crate is 3/4 yard long and 2/4 yard wide. The crate is also 2 feet tall. What is the area of the top of the crate?
(please explain the answer step by step if possible.)
Answer:
The area of the top of the crate can be found by multiplying the length by the width.
First, we need to convert all units to the same unit, either yards or feet. We will convert the length and width to yards:
3/4 yard = 9/12 yards
2/4 yard = 6/12 yards
2. Now we can find the area by multiplying the length by the width:
Area = 9/12 yards * 6/12 yards = (9/12) * (6/12) = 3/4 * 1/2 = 3/8 yards^2
So, the area of the top of the crate is 3/8 yards^2.
An individual's checking account contained $505 on June 1. The individual then made the following transactions. The individual deposited $170, withdrew $226,
← withdrew $39, deposited $120, withdrew $366, and deposited $750. What was the individual's new balance after these transactions?
The individual's new balance after these transactions is $.
graph f(x) = (x+2) (x-4)
Use the parabola tool then choose the vertex followed by one point on the parabola.
Answer:
The vertex of the parabola is at x = 3, and a point on the parabola can be (4, 0). Here is a Brainly link that can provide you with more information about graphing the function f(x) = (x+2) (x-4): https://brainly.com/question/31009433.
The school team has 80 swimmers. The ratio of seventh-grade swimmers to all swimmers is 5 : 16. Write a proportion that gives the number s
of seventh-grade swimmers.
The number of seventh grade winners is 25.
What is a ratio?The quantitative relation between two amounts shows the number of times one value contains or is contained within the other. for example-"the ratio of computers to students is now 2 to 1"
Given here: total swimmers is 80 and the ratio of seventh to all swimmers is 5:16
According to the proportion in the question we get
5/16=s/80
s=5/16 × 80
s=25
The number of seventh grade winners is 25.
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In the state of Indiana, 322000 people lacked basic math skills. If this is 5.6% of the population of Indiana residents aged 5 years and older, estimate the population of Indiana residents aged 5 years and older. Express your answer rounded to the nearest hundredth of a million
The population of Indiana residents aged 5 years and older is around 5.7 million.
What is percentage?Percentage is a way to express a number as a fraction of 100. It is often used to represent ratios and proportions in a more convenient and understandable form, especially in financial and statistical contexts. For example, 50% means 50 per 100, or half of a given quantity. It is denoted using the symbol "%".
Given that,
322000 people lacked basic math skills
5.6% of the population of Indiana residents aged 5 years and older
Let's call the population of Indiana residents aged 5 years and older "x".
The equation to estimate the population is:
322000 = x*5.6/100
322000 = x * 0.056
Dividing both sides by 0.056:
322,000 / 0.056 = x
x = 5750000
So, the population of Indiana residents aged 5 years and older is approximately 5.7 million.
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Let f:[0,2]→R be a twice differentiable function such that f"(x)>0, for all x∈(0,2) If ϕ(x)=f(x)+f(2−x), then ϕis:
A. decreasing on (0,2)
B. decreasing on (0,2) and increasing on (1,2)
C. increasing on (0,2)
D. increasing on (0,1) and decreasing on (1,2)
The answer is C. increasing on (0,2).
What is Strictly convex function?
A real-valued function is said to be convex if the line segment connecting any two points on its graph falls above the graph connecting the two points. A function is convex if and only if its epigraph is a convex set.
Since f"(x) > 0 for all x in (0,2), it follows that f is a strictly convex function on that interval, meaning that its second derivative is positive and its first derivative is increasing.
If f is a strictly convex function on [0,2], then f(2-x) is a strictly concave function on [0,2]. The sum of a strictly convex and a strictly concave function is also a strictly convex function.
Therefore, since f''(x) = f(x) + f(2-x), it follows that f''(x) is a strictly convex function on [0,2], which means that its first derivative is increasing.
Thus, The answer is C. increasing on (0,2).
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Which expression represents "3 times the quantity 1 plus p"?
Answer: 3(1p)
Step-by-step explanation:
Answer: 3+3p or 3p+3
Step-by-step explanation:First write the information given. You will need to multiply the quantity 3 by each of the terms one and p. It should look something like this 3(1+p). Multiply three to both quantities and the answer yields 3+3p or 3p+3.
Here is a frequency distribution table (FDT) for a small data set: data value frequency 14 14 15 11 16 23 17 10 18 13 Find the following measures of central tendency: mean (I (Please show your answer to one decimal place.) median (Please enter an exact answer:) mode (Please enter an exact answer: )
The mean is 14.7, the median is 16, and the mode is 16.
To find the mean, we need to calculate the sum of all the data values and divide it by the total number of observations.
The sum of the data values is:
14 x 14 + 15 x 11 + 16 x 23 + 17 x 10 + 18 x 13 = 196 + 165 + 368 + 170 + 234 = 1043
The number of observations is:
14 + 11 + 23 + 10 + 13 = 71
The mean is calculated as follows,
1043 / 71 = 14.7 (rounded to one decimal place)
The median is the central value in the data collection. To find the median, we need to arrange the data values in ascending order and find the middle value. In this case, we have an odd number of observations, so the median is simply the middle value.
14, 14, 15, 15, 16, 16, 16, 16, 16, 16, 16, 17, 17, 18, 18, 18
The median is 16.
The mode is the value that appears most repeatedly in the data set. In this case, the mode is 16 since it occurs the most (23 times).
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You pick a card at random. Without putting the first card back, you pick a second card at
random.
678
What is the probability of picking an 8 and then picking a number greater than 7?
Write your answer as a decimal.
The value of the probability is 0.167
How to determine the probabilityFrom the question, we have the following parameters that can be used in our computation:
6 7 8
The probability of picking a 8 on the first draw and then picking a number above 7 on the second draw is:
P(6 and then >7) = P(6) x P(>7 | 6)
Given that the cards are not replaced, we have
P(6 and then >7) = 1/3 * 1/2
Evaluate
P(6 and then >7) = 0.167
Hence, the probability is 1/6
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At Cookout, 4 burgers and 3 containers of fries cost $16.40. Your finger rubbed off part of your receipt but you could see that each burger was $3.20. Find the cost of a container of fries. Explain your thinking.
The required container of fries costs $1.20, as er the given condition
What are equation models?The equation model is defined as the model of the given situation in the form of an equation using variables and constants.
Let's call the cost of a container of fries "x".
We know that 4 burgers cost 4 * $3.20 = $12.80.
So the total cost of burgers and fries is $12.80 + 3x = $16.40.
Subtracting the cost of the burgers from both sides:
3x = $16.40 - $12.80 = $3.60
Dividing both sides by 3:
x = $3.60 / 3 = $1.20
So each container of fries costs $1.20.
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5 times of the age of a son is the age of his father. If the sum of their ages is 42 years, determine the age
Answer:
The son is 7 years old.
The father is 35 years old.
Step by step explantation:
Father's age-[tex]5x[/tex]
Son's age-[tex]x[/tex]
[tex]5x+x=42[/tex]
[tex]6x=42[/tex]
[tex]42[/tex]÷[tex]6=7[/tex]
[tex]7[/tex]×[tex]5[/tex][tex]=35[/tex]
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Angle pQR is a right angle. The measure of angle SQR is 25 degrees. The measure of PQS is x degrees. What is the value of x
The value of x is 65°.
What is an angle addition postulate?According to the Angle Addition Postulate, an angle's measure is equal to the sum of the measures of any two adjacent angles. The Angle Addition Postulate can be used to determine the measurement of a missing angle or to determine the angle produced by two or more other angles.
Given:
Angle PQR is a right angle.
The measure of angle SQR is 25 degrees.
The measure of PQS is x degrees.
The angle addition postulates:
∠PQR = ∠SQR + ∠PQS
90° = 25° + x
x = 90° - 25°
x = 65°
Hence, ∠PQS = 65°.
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1. The Corollary to the Polygon Angle-Sum Theorem finds the measure of each interior angle of a regular n-gon.
*Write a formula to find the measure of each interior angle using n=number of sides.
2. The Polygon Exterior Angle-Sum Theorem states that the exterior angles of any polygon add up to 360 degrees.
*Write a formula that can help you find the measure of each individual exterior angle in any polygon. Use n for the number of sides.
3. What is the most precise name for quadrilateral ABCD with vertices A(-2, -1), B(2, 2), C(1, -2), and D(-3, -3)?
1. The formula to find the measure of each interior angle of a regular n-gon is (180 * (n-2))/n degrees.
2. The formula to find the measure of each individual exterior angle in any polygon is 360/n degrees.
3. The most precise name for the quadrilateral ABCD with the given vertices is a parallelogram.
How did we arrive at these assertions?The formula to find the measure of each interior angle of a regular n-gon is given by:
(180 * (n-2))/n degrees
In a regular n-gon, all interior angles are equal.
The sum of the interior angles of a polygon can be found using the formula:
(n-2) * 180 degrees, where n is the number of sides in the polygon.
Dividing the sum of the interior angles by the number of sides (n) gives us the measure of each interior angle:
(180 * (n-2))/n degrees.
2. The formula to find the measure of each individual exterior angle in any polygon is:
360/n degrees.
In any polygon, the sum of the exterior angles is equal to 360 degrees.
3. To find the measure of each individual exterior angle, we divide the sum of the exterior angles (360 degrees) by the number of sides (n) in the polygon:
360/n degrees.
The precise name for the quadrilateral ABCD is a parallelogram because:
It has opposite sides that are parallel to each other.
It has equal opposite sides.
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Please do both questions.
Ps- don’t ind the pics I drew
If the hand moves from the 12 o'clock position to the 5 o'clock position, it has traveled a distance is 9.5 cm.
What is the circumference of the circle?
The Circumference of a circle is basically the perimeter of the circle. It is given as (2×π×r) or (π×d).
The hand on a circular clock moves along the circumference of the circle, and the length of the circumference of a circle is given by the formula:
C = 2 * π * r
where C is the circumference, π is Pi (approximately equal to 3.14), and r is the radius of the circle.
In this case, the radius of the circle is half the length of the hand, or 12cm / 2 = 6cm.
So the circumference of the circle is:
C = 2 * π * 6 = 12 * π
Since the hand moves from the 12 o'clock position to the 5 o'clock position, it has traveled an angle of 5 * (360/12) = 150 degrees.
To find the distance traveled along the circumference, we need to multiply the circumference by the fraction of the circle traveled, which is equal to the angle in radians divided by 2π.
To convert from degrees to radians, we can use the formula:
radians = degrees * (π / 180)
So, the distance traveled by the hand is:
distance = C * (150 * (π / 180)) / (2 * π) = 12 * (150 * (π / 180)) / 2 = 9.5 cm (rounded to the nearest cm)
hence, if the hand moves from the 12 o'clock position to the 5 o'clock position, it has traveled a distance is 9.5 cm.
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in a convergent geometric series the sum to infinity is 18 and the sum of the first four terms is 130÷9 calculate the common ratio
The common ratio is approximately -0.6.
Step by step explanationLet the first term in the geometric series be "a" and the common ratio be "r". Then, the formula for the sum to infinity of a geometric series is:
S = a / (1 - r)
And the formula for the sum of the first n terms of a geometric series is:
Sn = a * (1 - r^n) / (1 - r)
So, using the information given:
18 = a / (1 - r)
And:
130/9 = a * (1 - r^4) / (1 - r)
Solving for "r" using these two equations:
18 = a / (1 - r) ==> a = 18 * (1 - r)
130/9 = a * (1 - r^4) / (1 - r) ==> 130/9 = 18 * (1 - r) * (1 - r^4) / (1 - r) ==> 130/9 = 18 * (1 - r^4)
Dividing both sides by 18:
7/5 = (1 - r^4)
So:
r^4 = 1 - 7/5 = -2/5
Taking the fourth root of both sides:
r = (-2/5)^(1/4)
So, the common ratio is approximately -0.6.
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Really stuck on this problem can someone help
The triangles are not similar because the dimensions of GDM are larger than those of PQR.
What are congruent shapes ?Shapes that are identical to one another are said to be congruent. Both the matching sides and the corresponding angles match. We must examine all of the shapes' angles and sides in order to accomplish this. Two shapes that are similar to one another can be stacked perfectly.
Even though triangles GDM and PQR have the same angle measure, the triangles are not congruent / similar because they are not the same size. Triangle GDM is larger than PQR and so is not congruent to it.
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Charlie buys 3 computer tables for $390. How much did he pay for each table?
Answer:
Step-by-step explanation:
If Charlie buys 3 computer tables for $390, then he paid $390 / 3 = $130 for each table.
Answer: 130 dollars for each table
Step-by-step explanation: Because 3 tables is 390 dollars, we have to divide 390 and 3 to see how much 1 table costs.
390 / 3 = 130
Please answer my question. Find the SA (surface area) of the composite shape. Round to the nearest tenth. Please help.
The total surface area of the composite shape is 488.7 in².
What is a composite shape?
A composite shape is a shape that was produced from two or more fundamental shapes. Composite shapes are also referred to as compound and complex shapes frequently. Every day, composite shapes are around us.
The given composite shape can be divided into multiple shapes, to find the area easily.
For the given question, we can see that the lower portion of the shape is a cuboid and the upper portion is half of the cylinder cut vertically.
We find the areas of the figures separately.
Area of cuboid
Length l = 6 in.
Breadth b = 10 in.
Height h = 8 in.
Area = Area of each faces = 2(lb) + 2(bh) +2(lh)
= 2(6*10) + 2(10*8) + 2(6*8)
= 2*60 +2* 80 + 2* 48
= 376 in²
Area of cylinder
Radius of semicircles r = 5 in.
Height of cylinder h = 6 in.
Area = Area of semicircles + Area of half of the curved surface
= 2 *1/2 * πr² + 1/2 * 2πrh = πr² + πrh = 3.14 * 5² + 3.14 * 5 * 6
= 172.7 in²
The total surface area of the composite shape = Area of cylinder + Area of cuboid - Area of the common surface(rectangle)
= 172.7 + 376 - (l *b) = 548.7 - ( 10*6) = 488.7 in²
Hence the total surface area of the composite shape is 488.7 in².
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How would you discover a mathematical relationship between corresponding terms that occur in two separate number sequences, and what can you say about those terms?
Method to discover the relationship between terms in two number sequences is to find a mathematical function that maps one sequence to the other.
What is a function?A relation is a function if it has only One y-value for each x-value.
One method to discover the relationship between terms in two number sequences is to find a mathematical function that maps one sequence to the other.
To do this, you can start by selecting a set of corresponding terms from each sequence and attempt to express the relationship between them using mathematical operations.
It's important to note that finding a mathematical relationship between two sequences can sometimes be difficult, and in some cases may not be possible.
In such cases, it may be helpful to analyze the sequences using other methods, such as graphical representation or statistical analysis, to gain insight into their behavior.
Hence, method to discover the relationship between terms in two number sequences is to find a mathematical function that maps one sequence to the other.
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Arrange the following measurements from smallest to largest. Show the calculations. A. 1.5 cm B. 2.5 x 10^3 mm C. 3.5 x 10-5 m D. 4.5 km
The measurements arranged from smallest to largest are 0.15 cm, 2.5 mm, 0.000035 m, and 4.5 km.
A. 1.5 cm
B. 2.5 x 10^3 mm
C. 3.5 x 10-5 m
D. 4.5 km
Convert all units to the same unit type.
A. 1.5 cm = 15 mm
B. 2.5 x 10^3 mm
C. 3.5 x 10-5 m = 0.000035 m
D. 4.5 km = 4500 m
Arrange the measurements from smallest to largest.
A. 15 mm
B. 2.5 x 10^3 mm
C. 0.000035 m
D. 4500 m
Convert the measurements back to their original units.
A. 15 mm = 0.15 cm
B. 2.5 x 10^3 mm
C. 0.000035 m = 3.5 x 10-5 m
D. 4500 m = 4.5 km
Rearrange the measurements from smallest to largest.
A. 0.15 cm
B. 2.5 x 10^3 mm
C. 3.5 x 10-5 m
D. 4.5 km
Simplify the units to the same unit type.
A. 0.15 cm
B. 2.5 mm
C. 0.000035 m
D. 4.5 km
Rearrange the measurements from smallest to largest.
A. 0.15 cm
B. 2.5 mm
C. 0.000035 m
D. 4.5 km
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The measurements arranged from smallest to largest are:
C. 3.5 x 10^-5 m
A. 1.5 cm
B. 2.5 x 10^3 mm
D. 4.5 km
To arrange the measurements from smallest to largest, it is necessary to convert all the units to the same type. The units in the measurements A, C, and D are different, so they need to be converted.
Measurement A is 1.5 cm, which can be converted to millimeters by multiplying by 10: 1.5 cm x 10 mm/cm = 15 mm.
Measurement C is 3.5 x 10^-5 m, which can be converted to millimeters by multiplying by 1000: 3.5 x 10^-5 m x 1000 mm/m = 3.5 mm.
Measurement D is 4.5 km, which can be converted to millimeters by multiplying by 10^6: 4.5 km x 10^6 mm/km = 4.5 x 10^6 mm.
Now that all the units are in millimeters, the measurements can be arranged from smallest to largest:
Measurement C (3.5 mm) is smallest, followed by Measurement A (15 mm), Measurement B (2.5 x 10^3 mm), and finally Measurement D (4.5 x 10^6 mm) is largest.
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A rectangular
farm has an area of 1/5 square miles. If
its length is 2/3 miles, what is its width?
Input your answer as a fraction.
Sarah is twice as old as her youngest brother. If the difference between their ages is 15 years. How old is her youngest brother?
Answer:
He would be 15 years old.
Step-by-step explanation:
If the difference is 15, and sarah is double the age, whatever age the youngest brother is, that number if multiplied by 2 or added to 15 needs to be the same answer. You could make a equation by writing those two on either side of the equation and making the unknown sum “x”. This would look like “2x=x+15”. Then to get the final product you would subtract the x on the right side from both side, ending up to be “x=15” in this scenario, that would be the final answer.
Consider the following probability distribution. Complete parts a through e p(x) a. Find u 2.25 (Round to the nearest thousandth as needed.) Find o 3.188 (Round to the nearest thousandth as needed.) b. Find the sampling distribution of the sample mean x for a random sample of n -2 measurements from this distribution. Put the answers in ascending order for x. 0.5 2.5 0.0625 0.25 0.25 0.25 p(x) 0.0625 0.125 (Do not round.) c. Is x an unbiased estimator of H? Yes, x is an unbiased estimator for u
The mean of the probability distribution is 3.188, the sampling distribution is 2.25 and x is an unbiased estimator.
What is the probability distributiona. To find the mean (u) of a probability distribution, we calculate the expected value as follows:
u = ∑x * p(x) = (0.5 * 0.0625) + (2.5 * 0.125) + (0.25 * 0.25) + (0.25 * 0.25) + (0.25 * 0.25) = 2.25
To find the variance (o^2) of the distribution, we calculate it as follows:
o^2 = ∑(x - u)^2 * p(x) = (0.5 - 2.25)^2 * 0.0625 + (2.5 - 2.25)^2 * 0.125 + (0.25 - 2.25)^2 * 0.25 + (0.25 - 2.25)^2 * 0.25 + (0.25 - 2.25)^2 * 0.25 = 0.5625
So, o = √0.5625 = 3.188
b. The sampling distribution of the sample mean x for a random sample of n=2 measurements from this distribution is given by:
x = (x1 + x2) / n = (2.25 + 2.25) / 2 = 2.25
As n approaches infinity, the sample mean x approaches the population mean u, and the distribution of x becomes more and more concentrated around u.
c. Yes, x is an unbiased estimator of u because its expected value is equal to the population mean: E(x) = u.
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Find the zeros and give the multiplicity.
f(x) = x2(5x + 6)9(x − 8)2
Answer:
Zeroes & Multiplicity:
x = 0 : Multiplicity = 2
x = -6/5 : Multiplicity = 9
x = 8 : Multiplicity = 2
Step-by-step explanation:
The equation provided is: [tex]f(x)=x^2(5x+6)^9(x-8)^2[/tex]
Factored Form:We're given the polynomial in factored form, which just means the polynomial is broken down into each of its factors. This is a really convenient form to have a polynomial in as we can easily find the zeroes of the polynomial.
This is due to the Zero Property of Multiplication, which essentially states zero times any number results in zero. So we just have to set each factor equal to zero, and solve, since if one of the factors is zero, then the entire thing becomes zero.
So this gives us the following equations:
[tex]x^2=0\implies x = 0\\\\(5x+6)^9=0\implies x = -\frac{6}{5}\\\\(x-8)^2=0\implies x = 8[/tex]
Now for the multiplicity, we just look at the exponent of the factor we set equal to zero. So x^2 gives us a zero of x = 0, and the exponent is 2, which is also the multiplicity of this zero.
The (5x + 6)^9 gives us a zero of x = -6/5, and the exponent is 9, which is also the multiplicity of the zero. Same thing applies for the zero at x = 8, which has a multiplicity of 2.
What is the percent change from 82 to 67
First find the actual difference:
82 - 67 = 15
Now divide that difference by the starting value (82 in this case):
15 / 82 ≈ 0.182927
Convert that to a percent:
0.182927 = 18.2927%
That's the percent change, a decrease of about 18.2927%
A veterans office recorded one select the correct answer from each drop down menu particular week that they had 50 patients the table shows the record numbers of dogs use the given data to complete the sample proportion and confidence intervals for the situation 
the confidence intervals for the situation is 46%
What is confidence interval?
A confidence interval (CI) for an unknown parameter in frequentist statistics is a range of estimations. The most popular confidence level is 95%, but other levels, such 90% or 99%, are occasionally used for computing confidence intervals. The fraction of related CIs over the long run that actually contain the parameter's true value is what is meant by the confidence level. The degree of confidence, sample size, and sample variability are all factors that might affect the width of the CI. A larger sample would result in a narrower confidence interval if all other factors remained constant. A wider confidence interval would also be required by a higher confidence level and would be produced by a sample with more variability.
the particular week that they had 50 patients the table shows the record numbers of dogs use the given data to complete the sample proportion.
Let's calculate the percentage or proportion of patients that were dogs:
p = (7 + 4 + 5 + 5 + 2)/50 = 23/50 = 0.46
Hence the confidence intervals for the situation is 46%
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A park is in the shape of a rectangle 8 miles long and 6 miles wide. How much shorter is your walk if you walk diagonally across the park than along the two sides of it? Round to the nearest tenth if necessary.
You would need to walk 4 miles less if you walk along the diagonal rather than the two sides.
What is Pythagoras Theorem?A key concept in mathematics is the Pythagorean Theorem, which describes the relationship between the sides of a right-angled triangle. Pythagorean triples are another name for the right triangle's sides. Here, examples are used to explain the theorem's formulation and proof.
The Pythagorean theorem is mostly used to determine a triangle's angle and the length of an ambiguous side. The base, perpendicular, and hypotenuse formulas can all be derived using this theorem.
Given that, park is in the shape of a rectangle 8 miles long and 6 miles wide.
The diagonal of the park is calculated using the Pythagoras theorem.
The Pythagoras theorem is given as:
c² = a² +b²
c² = 8² + 6²
c² = 64 + 36
c² = 100
c = 10
If you walk along the diagonal you need to walk 10 miles.
If you walk along the two sides the distance is:
d = 8 + 6 = 14 miles
Hence, the difference between the distance is:
14 - 10 = 4 miles.
Hence, you would need to walk 4 miles less if you walk along the diagonal rather than the two sides.
Learn more about Pythagoras theorem here:
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