The rancher should build a square with dimensions of 80 feet by 80 feet to obtain an area of 6400 square feet with 400 feet of fencing.
Explanation:In this Mathematics task, the rancher is looking to build a rectangular area with a fixed amount of fencing. The information provided is:
Length of Fencing = 400 feet Area = 6400 square feet
Let l represent the length and w represent the width of the rectangle. Now, we know that a rectangle's perimeter is given by the formula, 2(l + w), and its area by l*w. Given the Area = 6400 and Length of Fencing = 400, we can set up the following two equations:
lw = 6400 (Area) 2(l + w) = 400 (Perimeter)
Solving these two equations simultaneously, we get l = 80 feet and w = 80 feet. So, the rectangle is actually a square, with equal length and width of 80 feet.
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A quadratic equation is shown below: 10x2 − 3x − 1 = 0 Part A: Describe the solution(s) to the equation by just determining the radicand. Show your work. (5 points) Part B: Solve 16x2 − 2x − 5 = 0 by using an appropriate method. Show the steps of your work, and explain why you chose the method used. (5 points)
A) Consider the equation [tex]10x^2-3x-1=0[/tex]
We have to describe the solutions to this equation.
We will determine the radicand = [tex]b^2-4ac[/tex]
= [tex](-3)^2 - 4(10)(-1) = 9+ 40 = 49[/tex] which is greater than zero,
Therefore, the given equation ha real roots.
B) Consider the equation [tex]16x^2-2x-5=0[/tex]
We will use middle splitting term method to solve this equation.
[tex]16x^2+8x-10x-5 =0[/tex]
[tex]8x(2x+1) -5(2x+1)=0[/tex]
[tex](2x+1)(8x-5)=0[/tex]
So, [tex]2x+1=0[/tex]
[tex]x = \frac{-1}{2}[/tex] and [tex]x = \frac{5}{8}[/tex]
I chose this method, because this is more easier and takes less time.
Polygon ABCD is the result of a translation of polygon EFGH . AB¯¯¯¯¯ is parallel to DC¯¯¯¯¯ in the pre-image. Drag the answers to the boxes to correctly complete the statement about this image. The corresponding segments and in the image are
Answer: The corresponding segments in the in the figure and the image are :
AB and EF,
AD and EH,
CD and HG,
BC and FG,
Step-by-step explanation:
Given: Polygon ABCD is the result of a translation of polygon EFGH .
AB is parallel to DC in the pre-image.
We know that a translation is a rigid transformation which produces congruent images such that the corresponding segments have equal lengths.
So from the given statements the corresponding segments in the figure and the image are :
AB and EF,
AD and EH,
CD and HG,
BC and FG,
A tortoise travels 11 feet in one hour. In each subsequent hour, the tortoise travels one-third the distance it traveled in the previous hour. How far does this tortoise travel in 6 hours?
The distance that a tortoise will cover in 6 hours is:
16.47735 feet.
Step-by-step explanation:It is given that :
A tortoise travels 11 feet in one hour.
In each subsequent hour, the tortoise travels one-third the distance it traveled in the previous hour.
This means that in 2 hours it travels a total of:[tex]11+\dfrac{1}{3}\times 11\ feet[/tex]
which is equal to:
[tex]11\times \dfrac{4}{3}\ feet=\dfrac{44}{3}\ feet[/tex]
in the 3 hours it will travel a total of:[tex]=11+\dfrac{1}{3}\times 11+\dfrac{1}{3^2}\times 11\ feet[/tex]
In 4 hours it will travel a total of:[tex]=11+\dfrac{1}{3}\times 11+\dfrac{1}{3^2}\times 11+\dfrac{1}{3^3}\times 11\ feet[/tex]
In 5 hours it will travel a total of:[tex]=11+\dfrac{1}{3}\times 11+\dfrac{1}{3^2}\times 11+\dfrac{1}{3^3}\times 11+\dfrac{1}{3^4}\times 11\ feet[/tex]
In 6 hours it will travel a total of:[tex]=11+\dfrac{1}{3}\times 11+\dfrac{1}{3^2}\times 11+\dfrac{1}{3^3}\times 11+\dfrac{1}{3^4}\times 11+\dfrac{1}{3^5}\times 11\ feet=16.47735\ feet[/tex]
Hence, the answer is:
16.47735 feet
Sara got 88, 90, 75, 78, 100, 54, 90, 100, 45, and 60 on her English tests. Lee got 77, 67, 99, 79, 100, 65, 79, 89, 58, and 67 on his English tests. What is the mean of Sara's English tests? What is the mean of Lee's English tests? please answer both questions
Find the volume of the triangular prism. Round to the nearest cubic unit.
•288 cm^3
•144 cm^3
•576 cm^3
•71 cm^3
Answer:
114 cm∧3
Step-by-step explanation:
V= area of base x height
1) calculate the area of the base with formula: 1/2 bh
B=1/2 (8) (6)=24 then Multiply to get the area: Bh
2) (24) (6)= 144cm∧3
hope this helps.
the temperature last night was 10 degrees below 0. The next morning by 9 a.m. the temperature had risen 12 degrees. what was the temperature at 9 a.m.?
What is 0.24 ̅ (4 is repeating) expressed as a fraction in simplest form?
Show your work please
Here, we need to find express 0.2444... as a fraction in simplest form.
Let the fraction be expressed as x
Now,
x = 0.2444....
Since, x is recurring in 1 decimal places, we multiply it by 10.
10x = 2.4444....
From left hand-side, x is subtracted and from 0.24444... from right hand side
10x - x = 2.4444.... - 0.24444....
So now,
9x = 2.2
x = [tex] \frac{2.2}{9} [/tex]
x = [tex] \frac{22}{90} [/tex]
x = [tex] \frac{11}{45} [/tex]
Thus, fraction as simplest form = [tex] \frac{11}{45} [/tex]
How many liters equal 1258 cm3
The 1258 cm³ is equal to 1.258 liters.
To convert 1258 cm³ to liters, you can use the fact that 1 liter is equal to 1000 cm³. Therefore, the conversion from cubic centimeters to liters is straightforward.
Identify the given volume: 1258 cm³.
Know the conversion factor: 1 liter = 1000 cm³.
Perform the conversion:
[tex]1258 \ cm^3 \times \left( \frac{1 \ liter}{1000 \ cm^3} \right) = 1.258 \ liters[/tex]
Matt has a rectangular garden that is 10 ft wide and 24 Ft long . He wants to build a fence from one corner to the opposite corner . How many feet of fence does Matt need ???
The length of the fence Matt needs is 26 ft.
Explanation:To find the length of the fence, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the width of the garden is one side of the right triangle, the length of the garden is the other side, and the fence is the hypotenuse.
So, we can calculate the length of the fence as follows:
Length of the fence = √((Width)^2 + (Length)^2)
Substituting the given values, we get:
Length of the fence = √((10 ft)^2 + (24 ft)^2)
Length of the fence = √(100 ft^2 + 576 ft^2)
Length of the fence = √676 ft^2
Length of the fence = 26 ft
Final answer:
To calculate the length of fence needed for Matt's garden, the Pythagorean theorem is used, resulting in needing a fence that is 26 feet long.
Explanation:
Calculating the Fence Length Across a Rectangular Garden
Matt has a rectangular garden with dimensions of 10 feet in width and 24 feet in length. To find the length of the fence that Matt needs to build from one corner of the garden to the opposite corner, we will use the Pythagorean theorem, since the corners of the garden and the fence form a right triangle.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). The formula is c² = a² + b².
For Matt's garden, the length is 'a' = 24 ft and the width is 'b' = 10 ft. Plugging these values into the formula, we get:
c² = 24² + 10²
c² = 576 + 100
c² = 676
We then take the square root of both sides to solve for 'c':
c = √676
c = 26 ft
Therefore, Matt needs 26 feet of fence to reach from one corner of the garden to the opposite corner.
The surface area of a triangular prism is 60 square centimeters. What is the surface area of a similar prism that is smaller by a scale factor of 1 5th
The smaller triangular prism's surface area is calculated by squaring the scale factor of 1/5 (which is 1/25) and then multiplying it by the surface area of the larger prism. The result is 2.4 square centimeters.
The question asks about the surface area of a similar but smaller triangular prism given that the larger prism has a surface area of 60 square centimeters and the scale factor of the smaller prism is 1/5. When the size of an object changes by a scale factor, the surface area changes by the square of that scale factor. For the smaller triangular prism, the surface area will be the square of 1/5, which is 1/25, times the surface area of the larger prism.
To calculate it:
Take the surface area of the larger prism, which is 60 square centimeters.Multiply this area by the square of the scale factor, (1/5)², which is 1/25.The result will give us the surface area of the smaller prism: 60 cm2 * 1/25 = 2.4 cm².Therefore, the surface area of the similar smaller triangular prism by the given scale factor is 2.4 square centimeters.
i need help
Fundraising your school raised 125% of its fundraising goal the school raised $6750.what was the goal
Why was the country of Australia created
Caitlin creates an architectural blueprint of a rectangular dining room. The area of the actual dining room is 900 times as large as the area of the dining room on the blueprint. The length of the dining room on the blueprint is 4 inches. What is the length of the actual dining room?
you plan to leave a 15% tip and your dinner bill is $45(tax included). How much total should you leave
The family room floor in Zacks home has a rectangular area rug that measures 6.5 feet by 9 feet the floor is rectangular and measures 10 feet by 12 feet What area of the floor is not covered by the rug
Final answer:
To find the area of the floor not covered by the rug, calculate the total floor area (120 square feet), subtract the rug's area (58.5 square feet), resulting in 61.5 square feet of uncovered floor.
Explanation:
To find the area of the floor that is not covered by the area rug, we first need to calculate the area of the entire floor and then subtract the area of the rug.
The area of the floor is calculated by multiplying its length and width. So for a floor that measures 10 feet by 12 feet, the area is 10 feet × 12 feet = 120 square feet.
The area rug measures 6.5 feet by 9 feet, which means its area is 6.5 feet × 9 feet = 58.5 square feet.
Now, subtract the area of the rug from the area of the entire floor to find the part of the floor not covered by the rug:
120 square feet - 58.5 square feet = 61.5 square feet.
Therefore, the area of the floor not covered by the rug is 61.5 square feet.
what type of figure is quadrilateral fxyh
Answer: Quadrilateral fxyh is a trapezoid
Step-by-step explanation: Hi, the correct answer is trapezoid.
A trapezoid is a Quadrilateral ( a polygon with four sides) with a pair of opposite sides parallel. These parallel sides are called the bases of the trapezoid, and the other non-parallel sides are known as the "legs" of the trapezoid.
Feel free to ask for more if it´s necessary or if you did not understand something.
In week 3 the two athletes concentrate on biking. Minh's goal is to bike 125 1/2 miles. At the end of the week he found that he actually biked 125 1/6 miles. PJ's Goal was to bike 120 1/4 miles. At the end of the week he found that he actually biked 120 miles. Which athlete was closer to making their goal? Explain
Steven earns extra money babysitting. He charges $31.00 for 4 hours and $54.25 for 7 hours.
Enter an equation to represent the relationship. Let x represent the number of hours Steven babysits and y represent the amount he charges.
The equation is y =
PLEASE HELP WILL GIVE BRANLIEST!!!!!!!!!
According to the table, what is the mode of the average high temperatures for states listed in the chart? A) no mode B) 55° F C) 81° F D) 88° F
please explain how to do this type of math I need help ;-;
Answer:no mode
Step-by-step explanation:
Morgan bought a pair of shoes at a sale of 25%. If the amount she paid was $1000, find the marked price.
The marked price of the shoes that Morgan bought at a 25% discount for $1000 is $1333.33. The calculation was done by dividing the discounted price by (1 minus the discount percentage in decimal form).
The question involves finding the marked price of an item given the discounted price and the discount percentage. Morgan paid $1000 for a pair of shoes after getting a 25% discount. To find the original marked price, we can use the formula:
Discounted Price = Marked Price × (1 - Discount Percentage)
Here, the Discounted Price is $1000, and the Discount Percentage is 25%, which is equivalent to 0.25 in decimal form.
By rearranging the formula to solve for the Marked Price, we get:
Marked Price = Discounted Price ÷ (1 - Discount Percentage)
Now we can calculate:
Marked Price = $1000 ÷ (1 - 0.25) = $1000 ÷ 0.75 = $1333.33
Therefore, the marked price of the shoes was $1333.33.
What is the overlap of Data Set 1 and Data Set 2?
A. High
B. Moderate
C. Low
D. None
enter the missing value into the box to complete the ratio comparing 500 meters to 3 kilometers
The height of a triangle is twice the length of its base. The area of the triangle is 50m^2. Find the height and base to the nearest tenth of a meter
180 miles in 3 hours in fraction form and in word form
60 miles per hour
Or
60/1
PLEASE HELP!!!!!!
Of all students, calculate the relative frequency for males who carpool.
0.204
9
33
0.088
Answer:
It's 0.088.
Step-by-step explanation:
So the males who carpool is 9 right? Well relative frequency is the frequency divided by the total. So we must divide 9 by 102.
9÷102 = 0.088
20 POINT FOR ONE QUESTIONS PLEASE HELP THANK YOU!!! I WILL MARK BRAINLIEST
1. What is the value of z?
Which data set is represented by the modified box plot?
•85, 70, 80, 108, 46, 66, 68, 82, 70, 68
•85, 78, 80, 108, 46, 66, 68, 80, 72, 68
•85, 78, 80, 108, 46, 66, 68, 82, 72, 80
•85, 78, 80, 108, 46, 66, 68, 82, 72, 68
Maria’s math test had 25 questions. She got 84% correct. How many problems did she get wrong
If jeremy gives his horse 12 gallons of water each day. How many one quart pails of water is that
Hey guys I need help with this THANKS!
Answer: c
Step-by-step explanation: hope this helps