Answers
The answers to the geometry questions are given as follows:
2)
a)
A = 8
b = 10
x = 118°
y = 62°
b)
a = 8
b = 15
y = 50
x = 100°
3)
(a)
∠2 = 25°
3 = 65°
∠4 = 65°
∠5 = 90°
(b)
since SL = 10,
i) LT 10
ii) TM = 10
iii) SM = 10
4)
a) Since m∠118
∠2 = 18°
∠3 = 72°
∠4 = 72°
If FA = 27, then LO = 13.5
5)
a) All the angles in the diagram are equal to ∠45°
b) Line BC = 6√2
c) Line BE = 6
The above are solved using the principles behind the properties of Parallelograms; Rhombus, Rectangle, and Square.
What is the Justification for the above responses?Since the above answers are justified by the qualities or properties of :
Parallelograms; Rhombus, and Rectangle, let's look at them one by one.
2
a)
A = 8 - opposite sides of a parallelogram are equal in length
b = 10 -opposite sides of a parallelogram are equal in length
y = 62° - opposite angles of a parallelogram are of equal measure.
x = 118° - Sum of angles of a parallelogram - 360°. x = (360 - (62*2))/2
= 118°
3)
(a) Here we have a Rhombus.
∠2 = 25° - Opposite angles of a rhombus are equal; Diagonals bisect the angles of a rhombus. Thus ∠1≅∠2
∠3 = 65° - Since diagonals bisect each other at right angles, ∠3 = 180 - (25+90) = 65°
∠4 = 65° - Diagonals bisect the angles of a rhombus. Thus, ∠3≅∠3
∠5 = 90° - [properties of a Rhombus]
(b)
since SL = 10,
i) LT 10 - All sides of a Rhombus are equal
ii) TM = 10 - All sides of a Rhombus are equal
iii) SM = 10 - All sides of a Rhombus are equal
4) Here we have a Rectangle.
a) Since m∠18
∠2 = 18° because The diagonals bisect each other; and both the diagonals have the same length. Thus, m∠2≅∠1 (AAS)
∠3 = 72° - Each interior angle is equal to 90 degrees. Thus, m∠ = 90-18 = ∠72°
∠4 = 72° - because The diagonals bisect each other; and both the diagonals have the same length. Thus, m∠4≅∠3(AAS)
If FA = 27, then LO = 13.5 - The diagonals bisect each other.Thus,
LO = FA/2
LO = 27/2
LO = 13.5
5) Here we have a square.
a) All the angles in the diagram are equal to ∠45°. This is because, the diagonals bisect all interior angles. Since each interior angle is 90°, thus, each of the resulting angle bisected 45°
b) Line BC = 6√2 - This is be
c) Line BE = 6
The length of one-half of the diagonal of a square can be found using the Pythagorean theorem, which relates the lengths of the sides of a right triangle.
Let s be the side length of the square. Then, the length of the diagonal of the square (d) can be found using the equation d = s√2.
In this case, s = 6√2. So, the length of the diagonal (d) is:
d = s√2 = (6√2)√2 = 6(√2)(√2) = 6(2) = 12
Therefore, one-half of the diagonal of the square is:
(1/2)d = (1/2)(12) = 6
So, the length of one-half of the diagonal of the square ABCD is 6.
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Related Questions
each apple tree produces 48,5 kg apples the apples have an average mass of 165g each
calculate the total number of apples produced by the 200 trees
Give your answer correct to the nearest 1000 apples
Answers
5 additional trees give maximum yield and 35 trees per acre will give largest crop of apple.
Let's assume that, we are planting x apple trees extra per acre. So, net 10x apple will be less.
Let say, total number of apples = y
Then, y = (30+x)×(400–10x)
For, optimum number of trees, let's do the differentiation of the above equation with respect to x.
d(y)/d(x) = (400–10x)×1 + (30+x)×(-10)
= 400–10x-300–10x
= 100–20x …………..(1)
For mimima or maxima, the above equation must be equal to 0.
So, 0 = 100–20x
=> x=5
Let's do the second differentiation of equation (1) and substitute the the value of x I.e x=5
[tex]d^2(y)/d(x^2) = -20[/tex]
The above equation is negative for all values of x which indicates that at x=5 we will have the maximum value.
So, the number of trees for maximum apple will be (30+x)
So, 30+5 = 35 trees per acre will give the largest crop of apple.
Hence 5 additional trees give maximum yield and 35 trees per acre will give largest crop of apple.
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two messenger services deliver to a small town. service a has 75% of all the scheduled deliveries, and service b has the remaining 25%. their on-time rates are 80% and 60% respectively. calculate the probability that a package is delivered on time.
Answers
Service a has 75% of all the scheduled deliveries, and service b has the remaining 25%, their on-time rates are 80% and 60% respectively, the probability that a package is delivered on time is 0.75 or 75%.
To calculate the probability that a package is delivered on time, we need to use the law of total probability and the probabilities of on-time delivery for each messenger service.
Let A denote the event that a package is delivered by Service A, and B denote the event that a package is delivered by Service B. Then, we have:
P(on-time delivery) = P(on-time delivery | A) * P(A) + P(on-time delivery | B) * P(B)
where P(on-time delivery | A) is the probability that a package is delivered on time given that it was sent through Service A, and P(A) is the probability that a package is sent through Service A.
Similarly, P(on-time delivery | B) is the probability that a package is delivered on time given that it was sent through Service B, and P(B) is the probability that a package is sent through Service B.
From the information given in the question, we know that P(A) = 0.75, P(B) = 0.25, P(on-time delivery | A) = 0.8, and P(on-time delivery | B) = 0.6. Substituting these values into the above formula, we get:
P(on-time delivery) = 0.8 * 0.75 + 0.6 * 0.25
= 0.6 + 0.15
= 0.75
Intuitively, this result makes sense because Service A, which has a higher on-time rate and delivers 75% of the packages, dominates the total probability of on-time delivery. However, the contribution of Service B cannot be ignored completely and reduces the overall on-time rate slightly.
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b) A plank of wood 3.5 m long is cut into 5 pieces of equal length. How long, in m, is each piece?
Answers
70 cm or 0.7 m
Step-by-step explanation:3.5 x 100 = 350
350 / 5 = 70
Given the point (−,), write the coordinates of a point that is related by a reflection over the -axis. Write your answer with a comma and no spaces. Example 7,2 or -7,-2
Answers
When a point (x, y) is reflected across x-axis then (x, -y) will be the new point and reflected across y-axis then (-x, y) be the point.
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
Graph transformation is the process by which a graph is modified to give a variation of the proceeding graph
Reflection is a process of transformation.
A reflection is a transformation representing a flip of a figure. Figures may be reflected in a point, a line, or a plane.
Let the coordinates of a point be (4, 3).
When the coordinates of a point that is related by a reflection over the x-axis, then the new coordinate will be (4,-3).
(x, y)---->(x, -y)
The reflection of point (x, y) across the y-axis is (-x, y).
(x, y)---->(-x, y)
(4,3) reflection across the y-axis is (-4, 3).
Hence, the reflection of point (x, y) across the y-axis is (-x, y) and reflection of point (x, y) across the x-axis is (x, -y).
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A container of laundry detergent holds 100 fluid ounces. You use 9 fluid ounces each week. The table shows the amount of laundry detergent that remains after a certain number of weeks. Complete the table Number of Weeks Fluid Ounces Remaining in the Container
Answers
The number of fluids remaining after x weeks is given by the following equation:
y = 100 - 9x.
Hence the number of fluids remaining after week x is found replacing x by the week at the above equation.
How to define the linear function?
The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which:
The slope m represents the rate of change.The intercept b represents the value of y when x = 0.For this problem, the parameters are given as follows:
b = 100, which is the capacity of the container.m = -9, as each week, the number of fluid ounces in the container is decreased by 9.Hence the function is given as follows:
y = 100 - 9x.
Missing InformationThe problem is incomplete, hence the function used to obtain the amounts is presented.
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13 25 4 8 17 21 A number is to be written on the blank card. The mode and median of all seven numbers are both the same. Find one possible number that can be written on the blank card.
Answers
Answer:
13 or 17
-------------------
Given numbers:
13, 25, 4, 8, 17, 21Put them in the ascending order:
4, 8, 13, 17, 21, 25Let the possible number to be added be x.
Since x is the median, it should be between 13 and 17:
4, 8, 13, x, 17, 21, 25Also x is the mode. As we see all 6 number are unique, x should be repeat of 13 or 17 in order to be a mode. Therefore the possible number that can be written on the blank card is either 13 or 17.
Solve for r in terms of q, s, and t.
s = -tqr
r=
Answers
Answer:
I didn't understand the question 100% but I think the question is asking you to give an equation from the given one
so the answer will be
-s divided over tq
Consider the information given in Example 3. Describe and correct the error in predicting the number (n) of students in the school who watch zero movies each week.
Answers
Answer:its hard to say
what are parameters? group of answer choices parameters are measured constructs that vary across entities in the sample. parameters summarize data or relationships in the population and are usually estimated from a sample a parameter tells us about how well the mean represents the sample data. all of the options describe parameters.
Answers
The option is: Parameters summarize data or relationships in the population and are usually estimated from a sample.
Parameters are numerical values that describe a population, and they are usually estimated from a sample. Parameters summarize important characteristics of the population, such as the mean, variance, or correlation between variables. These characteristics may vary across different entities in the population, such as individuals, households, or businesses.
In statistical analysis, parameters are important because they allow us to draw inferences about the population from a sample. By estimating parameters from a sample, we can make generalizations about the population and test hypotheses about relationships between variables.
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suppose that the proportions of blood phenotypes in a particular population are as follows: a b ab o 0.42 0.14 0.05 0.39 assuming that the phenotypes of two randomly selected individuals are independent of one another, what is the probability that both phenotypes are o? (enter your answer to four decimal places.)
Answers
The probability that both phenotypes are o is 0.1600
Events classified as independent do not depend on other events for their occurrence. For instance, if we toss a coin in the air and it lands on head, we can toss it again and this time it will land on tail. Both instances include independent occurrences of the two events.
In a probability notation, events and are independent if ( ∣ ) = ( ) . Events and are independent if and only if ( ∩ ) = ( ) × ( ) . If and are dependent events, then ( ∩ ) = ( ∣ ) × ( ) .
the proportions of blood phenotypes in a particular population are as follows: a b ab o 0.42 0.14 0.05 0.39 so for o the value is 0.40 so we put it and slolve .
The samples are independents, so:
P(O1∩O2) = P(O1).P(O2) = 0.40*0.40=0.1600
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**EASY POINTS** There is a circular running path in the park. The diameter of the circle is 350 m. What is the length of one lap around the park?
Answers
Answer:
1099
Step-by-step explanation:
350*pi=1099
Find the sum of 2√5 and 3√7
Answers
Answer:
the sum of 2rude 5 is 4.47-(answer)and the sum of 3 rude 7 is 7.79-(answer).
Hi there, here's your answer:
Given the question [tex]2\sqrt{5} + 3\sqrt{7}[/tex]
Since these two roots have no common factors, we can either leave the expression as it is, or simplify using the values of the roots.
In which case, [tex]\sqrt{5} = 2.236[/tex] and [tex]\sqrt{7} = 2.645[/tex]
On simplifying, we get
[tex]2\sqrt{5}[/tex] = 2 × 2.236 = 4.472
And
[tex]3\sqrt{7}[/tex] = 3 × 2.645 = 7.935
Thus, the sum will be 4.472 + 7.935 = 12.407
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Write the quadratic function in factored form given the parabola has roots of 9 and -6 and passes through the point (-8,-102).
Answers
The quadratic function in factored form given the parabola has roots of 9 and -6 and passes through the point (-8,-102) is f(x) = x²-3x-54
What is a quadratic function?A quadratic function is a polynomial function with one or more variables in which the highest exponent of the variable is two.
Given that, the quadratic function in factored form given the parabola has roots of 9 and -6 and passes through the point (-8,-102).
We know that, the standard form of the quadratic equation is given by,
x²-(α+β)x+αβ=0, where α and β are roots of the equation,
Therefore,
x²-(9-6)x+9(-6) = 0
x²-3x-54 = 0
Hence, the quadratic function in factored form given the parabola has roots of 9 and -6 and passes through the point (-8,-102) is f(x) = x²-3x-54
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State how the triangles are congruent using SSS, SAS, ASA, AAS, or
HL. If they are not congruent, type NOT.
Answers
Answer:
SAS
Step-by-step explanation:
There are two pairs of congruent sides, and the pair of angles between the congruent sides is also congruent.
What is the value of f(x)=23.2x+2.5 at x =-4.2
Answers
Answer:
-94.94
Step-by-step explanation:
f(x)=23.2x+2.5
Let x = -4.2
f(4)=23.2(-4.2)+2.5
=-97.44+2.5
=-94.94
Answer:
Since x = -4.2, just fill it in the equation and solve:
23.2 * -4.2 + 2.5 =
23.2 * -4.2 = -97.44
-97.44 + 2.5 = -94.94
f(x) = -94.94
Step-by-step explanation:
Hope it helps! =D
Hope it ain't wrong either. If so, I'm sorry.
? a retailer entered into an exclusive agreement with a supplier who guaranteed to provide all products at competitive prices. the retailer eventually began to purchase supplies from other vendors who offered better prices. the original supplier filed a lawsuit claiming violation of the agreement. in defense, the retailer had an audit performed on a random sample of 25 invoices. for each audited invoice, all purchases made from other suppliers were examined and compared with those offered by the original supplier. the percent of purchases on each invoice for which an alternative supplier offered a lower price than the original supplier was recorded.26 for example, a data value of 38 means that the price would be lower with a different supplier for 38% of the items on the invoice. a histogram and some computer output for these data are shown below. explain why we should not carry out a one-sample t test in this setting
Answers
A one-sample t-test should not be carried out in this setting because the data is in the form of a frequency distribution and is not continuous, and the distribution is not normal.
In statistics, a one-sample t-test is used to determine whether a sample mean is significantly different from a known population mean. However, in this scenario, the data collected and analyzed is in the form of a frequency distribution, where the percent of purchases for which an alternative supplier offered a lower price was recorded.
A frequency distribution shows the number of times a particular value or range of values occurs in a dataset. In this case, the frequency distribution shows the number of invoices that had a certain percentage of purchases for which an alternative supplier offered a lower price. This type of data is not suitable for a one-sample t-test because a t-test requires continuous data, which is not the case here.
Furthermore, a one-sample t-test assumes that the data is normally distributed. A histogram of the data in this scenario shows that the distribution is not symmetrical and does not resemble a normal distribution. Therefore, carrying out a t-test would not be appropriate.
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Two joggers run 8 miles and then 5 miles west. What is the shortest distance, to the nearest tenth of a mile they must travel to return to their starting position?
Answers
Answer:
A. 9.4 mi
Step-by-step explanation:
Sketch a right triangle with legs of 8 and 5. Shortest distance back to the starting point is the hypotenuse (h) of the triangle:
h² = 8² + 5² = 89
h = √89 = 9.43 mi
question 12
help me asap
Answers
Answer:
ED = 4 cm
Step-by-step explanation:
given 2 secants from an external point to the circle, then the product of one secant's external part and the entire secant is equal to the product of the other secant's external part and that entire secant, that is
CD × CE = CB × CA
8(8 + x) = 6(6 + 10) = 6 × 16 = 96 ( divide both sides by 8 )
8 + x = 12 ( subtract 8 from both sides )
x = ED = 4 cm
A cylindrical measuring jug has a total volume of 500 ml and its radius is 3 cm. There are markings on the jug to show every 100 ml. What is the distance, in cm, between each of these markings?
Answers
Answer:
The volume of a cylinder can be calculated using the formula:
V = πr^2h
Where r is the radius and h is the height. In this case, the volume is 500 ml, or 0.5 liters. To convert liters to cm, we can use the conversion factor 1 liter = 10 cm^3. Therefore, the height of the jug can be calculated as follows:
0.5 liters = 0.5 x 10 cm^3 = 500 cm^3
V = πr^2h
500 = π x (3 cm)^2 x h
h = 500 / (π x (3 cm)^2)
Approximating π as 3.14, we get:
h = 500 / (3.14 x (3 cm)^2)
h = 500 / (3.14 x 9 cm^2)
h = 500 / 28.26 cm^2
h = 17.67 cm
So the height of the cylindrical measuring jug is approximately 17.67 cm. Therefore, the distance between each marking, which represents 100 ml of volume, is 17.67 cm / 5 = 3.534 cm.
Step-by-step explanation:
Answer:
5
Step-by-step explanation:
To determine the distance between each of the markings, we need to determine the height of the jug for each 100 ml increment.
The volume of a cylinder is given by the formula V = πr^2h, where r is the radius and h is the height. We know the volume of the jug is 500 ml, or 0.5 liters, and the radius is 3 cm, so we can solve for the height:
0.5 liters = π * (3 cm)^2 * h
h = 0.5 liters / π * (3 cm)^2
h = 0.5 liters / 9π cm^2
Now that we have the height of the jug per 100 ml, we can divide it by 5 to determine the height between each marking:
Marking height = h / 5
= 0.5 liters / 9π cm^2 / 5
= 0.1 liters / 9π cm^2
So the distance between each of the markings is the height of the jug for each 100 ml increment divided by 5.
find the quadratic equation whose roots are 5 and -9
Answers
The equation of the quadratic equation whose root are 5 and -9 is x² +4x -45
What is quadratic equation?quadratic equation is a second-order polynomial equation in a single variable x ax²+bx+c=0. with a ≠ 0 . Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.
The equation of a quadratic is given as :
x²-(alpha+beta)x + alpha×beta = 0
where alpha and beta are the roots of the quadratic equation.
alpha+beta = 5-9 = -4
alpha × beta = -9× 5 = -45
therefore the equation will be;
x²-(-4)x + ( -45) = 0
x² + 4x -45 = 0
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which of these shapes is a right isosceles triangle?
Answers
A right isosceles triangle is a triangle with a right angle (90 degrees) and two sides that are equal in length. This means that the triangle is also a special case of an isosceles triangle where the two equal sides are adjacent to the right angle.
To identify a right isosceles triangle among a group of shapes, you should look for the shape that has a right angle and two sides of equal length. One way to check for the right angle is to look for a corner that forms a square angle (i.e., 90 degrees), and one way to check for the equal sides is to compare the length of each side.
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The following question may be like this:
What is a right isosceles triangle?
here is a shape. find the total area of the shape
Answers
Answer:
Area A, is x times y
Step-by-step explanation:
To find the area you must multiply the light x width of a rectangle or square
um.... kauser is this u
Calculate the area of a parallelogram which sides are 8cm 13cm and11cm
Answers
Answer:
the answer will be based on which is the base and height, the area of a parallelogram is base×height(bh) so, all you have to do is multiply the base with the height. For example if the base is 7cm, height is 12cm, and the other side is 3cm. The area of the parallelogram from the question will be 84cm²
Solve for x. P S (6x-21)° T Q R
Answers
Answer:
x = 11
Step-by-step explanation:
You want to know the measure of x in a square marked with one portion of the bisected corner angle as being (6x -21)°.
AngleWe presume quadrilateral PQRS is a square, so each of the corner angles is 90°, and each of the diagonals bisects the corner angles. That mean ...
(6x -21)° = 90°/2
6x = 66 . . . . . . . . . . divide by °, add 21
x = 11 . . . . . . . . . . . divide by 6
A rectangular prism measures 7 1/2 cm by 12 cm by 15 1/2 cm. ****If you are stuck, think about how many cubes with 1/2 cm edge lengths fit into 1 cubic centimeter*** Calculate the number of cubes with edge length 1/2 cm that fit in this prism. Cubes What is the volume of the prism in centimeters cubed? centimeters cubed
Answers
Number of cubes with edge length 1/2cm that fit in the prism is 11160 and the volume of the prism is 1395 cubic centimeter
Dimensions of the rectangular prism = [tex]7\frac{1}{2}[/tex] cm × 12 cm × [tex]15\frac{1}{2}[/tex] cm
Convert the mixed fraction to the simple fraction
The dimensions of the rectangular prism = 15/2 cm × 12 cm × 31/2 cm
The volume of the rectangular prism = w × l × h
Where
w is the width
l is the length
h is the height
The volume of the rectangular prim = 15/2 × 12 × 31/2
= 1395 cubic centimeter
The side off the cube = 1/2 cm
Volume of the cube = a^3
= (1/2)^3
= 0.125 cubic centimeter
Number of cubes will fit in rectangular prism = Volume of rectangular prism / Volume of the cube
= 1395 / 0.125
Divide the terms
= 11160 cubes
Therefore, 11160 cubes will fit in the rectangular prism and the volume of the prism is 1395 cubic centimeter
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HELPP ITS THE FINAL PART OF THE TEST!!
Answers
Answer:
Graph C.
The question asks for the graph that consists of:
Non-negative values
Values that are, at most, 80
This means that any graphs where a value goes below 0 or above 80 do not work. C is the only graph that does not go below 0 or above 80.
Find the area of the figure. Use 3.14 for pie
Answers
The area of the figure is 254.8 m²
What is area?Area is the region occupied by an object.
How to find the area of the figure?Since the figure is a rectangle and containing two semi-circles, we find the area of the figure by finding the area of the rectangle and the two semi-circles.
What is the area of the rectangle?The area of the rectangle is given by A = LW where
L = length of rectangle and W = width of rectangleGiven that
L = 16 m and W = 12 mA = LW
= 16 m × 12 m
= 192 m²
What is the area of a semi-circle?The area of a semi-circle with diameter d is A = πd²/4
Now for the first semi-circle, its diameter d' = 8 m.
So, its area A' = πd'²/4
= π(8 m)²/4
= π64 m²/4
= 16π m²
= 16 ×3.14 m²
= 50.24 m²
Also, for the fsecond semi-circle, its diameter d" = 4 m.
So, its area A' = πd'²/4
= π(4 m)²/4
= π16 m²/4
= 4π m²
= 4 × 3.14 m²
= 12.56 m²
So, the area of the figure is A₁ = A + A' + A"
= 192 m² + 50.24 m² + 12.56 m²
= 254.8 m²
So, the area of the figure is 254.8 m²
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6. Ming uses 3/ 4 cup of peanuts and 1/ 4 cup of raisins to make a snack. Which statement correctly compares the fractions?
*
10 points
A. 3/4 = 1/4
B. 1/4 > 3/4
C 3/4 < 1/4
3/4 > 1/4
Answers
Answer:
3/4 > 1/4
Step-by-step explanation:
3/4 is 75%, and 1/4 is 25 percent. 3/4 is greater than 1/4!
Find the radius of the circle circumscribed around an equilateral trapezoid, if the bases of the trapezoid are 9 and 15, and the height is 5.
Answers
So, the length of the diagonal is 5 * √3 = 8.66 meters.
Next, we need to find the midpoint of the two diagonals of the trapezoid, which is the center of the circumscribed circle. The midpoint is found by averaging the length of the two diagonals, which are equal in length:
(9 + 15) / 2 = 12
So, the radius of the circumscribed circle is equal to half the length of the diagonal:
8.66 / 2 = 4.33 meters.
Therefore, the radius of the circle circumscribed around the equilateral trapezoid is 4.33 meters.
A rectangle's length is 12 meters more than 5 times the width. The area is 32 square meters. What is the width?
Answers
Let's call the width of the rectangle "w".
According to the problem, the length of the rectangle is 12 meters more than 5 times the width, so we can write that as:
L = 5w + 12
And the area is given as 32 square meters, so we can write that as:
A = L * w = 32
Now we have two equations:
5w + 12 = L
L * w = 32
We can use the first equation to substitute the value of L in the second equation:
L = 5w + 12
32 = (5w + 12) * w = 5w^2 + 12w
Expanding the right side of the equation, we get:
32 = 5w^2 + 12w
Now we have a quadratic equation that we can solve for w. To do this, we can use the quadratic formula:
w = (-b ± √(b^2 - 4ac)) / 2a
where a = 5, b = 12, and c = -32. Plugging in these values, we get:
w = (-12 ± √(12^2 - 4 * 5 * -32)) / (2 * 5)
w = (-12 ± √(144 + 640)) / 10
w = (-12 ± √(784)) / 10
w = (-12 ± 28) / 10
w = (16 / 10) or ( -40 / 10)
w = 1.6 or -4
Since the width cannot be negative, the width must be 1.6 meters.
