You and your friend Rhonda work at the community center. You will be counselors at a summer camp for middle school students. The camp director has asked you and Rhonda to design a zip line for students to ride while at camp. A zip line is a cable stretched between two points at different heights with an attached pulley and harness to carry a rider. Gravity moves the rider down the cable. The camp director is ready to purchase the cable for the zip line. Use the distance between the trees and the change in height you found in question to determine the length of cable needed. Be sure to include: • the required 5% slack in the line, and • 7 extra feet of cable at each end to wrap around each tree. The zip line will be secured to two trees. The camp has a level field with three suitable trees to choose from. All three trees are on level ground. Enter the total length, in feet, of cable needed for the zip line. • Tree 1 is 130 feet from Tree 2. • Tree 2 is 145 feet from Tree 3. Tree 1 is 160 feet from Tree 3. Tree 2
Answers
The total length of cable needed for the zip line, considering the required 5% slack and 7 extra feet of cable at each end, is approximately 302.75 feet.
To determine the total length of cable needed for the zip line, we need to consider the distances between the trees and add the required slack and extra cable for wrapping around the trees.
Given the distances between the trees:
Tree 1 is 130 feet from Tree 2.
Tree 2 is 145 feet from Tree 3.
Tree 1 is 160 feet from Tree 3.
Let's calculate the total length of cable needed step by step:
1. Distance between Tree 1 and Tree 2: 130 feet.
2. Distance between Tree 2 and Tree 3: 145 feet.
3. Total distance from Tree 1 to Tree 3 (via Tree 2): 130 + 145 = 275 feet.
Now, we need to add the required slack in the line. The required 5% slack means we need to increase the total distance by 5%. To calculate this, we can multiply the total distance by 1.05 (1 + 0.05):
Total distance with 5% slack: 275 * 1.05 = 288.75 feet.
Next, we need to add 7 extra feet of cable at each end to wrap around each tree:
Total distance with 5% slack and extra cable for wrapping: 288.75 + 7 + 7 = 302.75 feet.
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The Probable question may be:
You and your friend Rhonda work at the community center. You will be counselors at a summer camp for middle school students. The camp director has asked you and Rhonda to design a zip line for students to ride while at camp. A zip line is a cable stretched between two points at different heights with an attached pulley and harness to carry a rider. Gravity moves the rider down the cable.
The zip line will be secured to two trees. The camp has a level field with three suitable trees to choose from. All three trees are on level ground
Tree 1 is 130 feet from Tree 2.
Tree 2 is 145 feet from Tree 3.
Tree 1 is 160 feet from Tree 3.
The camp director is ready to purchase the cable for the zip line. Use the distance between the trees and the change in height you found in question to determine the length of cable needed.
Be sure to include:
the required 5% slack in the line, and
7 extra feet of cable at each end to wrap around each tree
Enter the total length, in feet, of cable needed for the zip line..
Related Questions
Find the quotient. (3. 683 × 104) (7. 51 × 1012) What is the solution in scientific notation? 4. 9041 × (-9)10 4. 9041 × 10-9 4. 9041 × 109 4. 9041 × 910.
Answers
The value of the expressions (3.683 × 10⁴) and (7.51 × 10¹²) in scientific notation is 4.9041 × 10⁻⁹. Then the correct option is B.
What is division?The division means the separation of something into different parts, sharing of something among different people, places, etc.
The expressions are (3.683 × 10⁴) and (7.51 × 10¹²).
We have to divide (3.683 × 10⁴) from (7.51 × 10¹²).
\(\dfrac{3.683 * 10^4}{7.51*10^{12}}\\\\0.4904*10^{-8}\\\\4.9041*10^{-9}\)
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The distance from Jason’s house to school is 0.5 kilometer. What is this distance in meters?
Answers
Answer:
500
Step-by-step explanation:
Write the greatest and the least numbers formed by the digits 4, 2, 3, 5, 6 and add these numbers.
and those who will give it's correct answer I will make him /her brainlist
Answers
Answer:
Greatest number is 65432
Lowest number is 23456
Step-by-step explanation:
\(65432+23456=88888\)
a management dilemma defines the research question. (True or False)
Answers
Answer:
False
Step-by-step explanation:
the following questions are about a spherical balloon that is being filled with air such that its radius is increasing at a constant rate of 2 cm/sec. how fast is the volume increasing when the radius is 10 cm?
Answers
When the radius is 10 cm, the volume of the balloon is increasing at a rate of 800π cm^3/sec.
When the radius is 10 cm, the balloon is being filled with air at a constant rate of 2 cm/sec. We want to find how fast the volume is increasing.
To solve this, we'll use the formula for the volume of a sphere: V = (4/3) * π * r^3, where V is the volume and r is the radius.
First, we differentiate the volume formula with respect to time (t) to find the rate of change of volume with respect to time.
dV/dt = d/dt [(4/3) * π * r^3]
Next, we substitute the given values into the formula. Since the radius is increasing at a constant rate of 2 cm/sec, we have r = 10 cm and dr/dt = 2 cm/sec.
dV/dt = d/dt [(4/3) * π * 10^3]
Now, we differentiate and substitute the values.
dV/dt = (4/3) * π * 3 * 10^2 * (2)
Simplifying, we get
dV/dt = 800π cm^3/sec
Therefore, when the radius is 10 cm, the volume is increasing at a rate of 800π cm^3/sec.
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Question 1(Multiple Choice Worth 4 points)
(05.07 LC)
A scatter plot is made to model the number of calories in different portions of fish sticks. The data used for the scatter plot are shown in the table:
Number of portions 5 3 8 6 1 4
Number of calories 250 150 400 300 50 200
What does the slope of the model represent?
The number of calories in each portion of fish sticks
The number of fish sticks in each portion
The original number of portions of fish sticks
The price of each portion of fish sticks
Answers
Answer:
The number of calories in each portion of fish sticks.
Step-by-step explanation:
For each portion, the slope goes up showing the number of calories as well. So this is what the slope represents.
Hope it helps!
For a given week, Tammy's Coffee House has available 1584 ounces of A grade coffee and 1536 ounces of B grade coffee. These are blended into 1-pound
packages as follows: an economy blend that contains 3 ounces of A grade coffee and 8 ounces of B grade coffee, and a superior blend that contains 9 ounces of
A grade coffee and 3 ounces of B grade coffee. (The remainder of each blend is made of filler ingredients.) There is a $3 profit on each economy blend package
sold and a $2 profit on each superior blend package sold. Assuming that the coffee house is able to sell as many blends as it makes, how many packages of
each blend should it make to maximize its profit for the week?
Note that the ALEKS graphing calculator can be used to make computations easier.
Economy blend:
Superior blend:
package(s)
package(s)
X
S
Answers
There is a requirement of 176 packets of economy blend and 96 packets of a superior blend to make maximum profit for the week.
Using the given data, calculate the x number of packages of the economy blend as well as the y number of packages of the superior mix.
3x + 11y =1584
6x + 4y = 1440
From the graph of these two equations, three extreme points are deduced: (240,0), (0,144), and (176,96).
The maximum (2x +4y) is the goal function.
Determine the aim function's value at all these extreme points,
The objective function value for (240,0) is 2 × 240 = 480
The objective function value for (0,144) is 4 × 144 = 576
The value of the objective function for (176,96) is 2 × 176 + 4 × 96 = 736
∴ The optimal point is (176,96) where x = 176 and y = 96.
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8y^3-24y^2-32y I am bad at math and need help very badly!
Answers
Answer:
8y(y-4)(y+1)
Step-by-step explanation:
First find the GCF of the three terms, in this case its 8y
8y(y^2-3y-4)
factor y^2-3y-4 by finding two numbers that multiply to -4 and add to -3, in this case, its -4 and 1.
8y(y-4)(y+1)
During the rebuilding after World War II, we were short of tractors. The machine and tractor stations would lend each other equipment as needed. Three machine and tractor stations were neighbors. The first lent the second and third as many tractors as they each already had. A few months later, the second lent the first and third as many as they each had. Still later, the third lent the first and second as many as they each already had. Each station now had 24 tractors.
How many tractors did each station originally have?
Answers
The number of tractors lent by the first, second and third stations results in a system of three simultaneous equations which indicates;
The first originally station had 39 tractors, the second station had 21 tractors and the third station originally had 12 tractors
What are simultaneous equations?Simultaneous equations are a set of two or more equations that have common variables.
Let x represent the number of tractors at the first station, let y represent the number of tractors at the second tractor station, and let z, represent the number of tractors at the third tractor station
According to the details in the question, after the first transaction, we get
Number of tractors at the first station = x - y - z
Number of tractors at the second station = y + y = 2·y
Number of tractors at the third station = z + z = 2·z
After the second transaction, we get;
Number of tractors at the first station = 2·x - 2·y - 2·z
Number of tractors at the second station = 2·y - (x - y - z) - 2·z = 3·y - x - z
Number of tractors at the third station = 2·z + 2·z = 4·z
After the third transaction, we get;
Number of tractors at the first station = 2 × (2·x - 2·y - 2·z) = 4·x - 4·y - 4·z
Number of tractors at the second tractor station = 6·y - 2·x - 2·z
Number of tractors at the third tractor station = 4·z - (2·x - 2·y - 2·z) - (3·y - x - z) = 7·z - x - y
The three equations after the third transaction are therefore;
4·x - 4·y - 4·z = 24...(1)
6·y - 2·x - 2·z = 24...(2)
7·z - x - y = 24...(3)
Multiplying equation (2) by 2 and subtracting equation (1) from the result we get;
12·y - 4·x - 4·z - (4·x - 4·y - 4·z) = 16·y - 8·x = 48 - 24 = 24
16·y - 8·x = 24...(4)
Multiplying equation (3) by 2 and multiplying equation (2) by 7, then adding both results, we get;
14·z - 2·x - 2·y = 48
42·y - 14·x - 14·z = 168
42·y - 14·x - 14·z + (14·z - 2·x - 2·y) = 48 + 168
40·y - 16·x = 216...(5)
Multiplying equation (4) by 2 and then subtracting the result from equation (5), we get;
40·y - 16·x - (32·y - 16·x) = 216 - 48 = 168
8·y = 168
y = 168/8 = 21
The number of tractors initially at the second station, y = 21
16·y - 8·x = 24, therefore, 16 × 21 - 8·x = 24
8·x = 16 × 21 - 24 = 312
x = 312 ÷ 8 = 39
The number of tractors initially at the first station, x = 39
7·z - x - y = 24, therefore, 7·z - 39 - 21 = 24
7·z = 24 + 39 + 21 = 84
z = 84/7 = 12
The number of tractors initially at the third station, z = 12
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(A) Prove that the opposite sides of the rectangle are congruent.
Use Distance Formula: v(x2 - x1)^2 + (y2 - y1)^2
(B) Prove the diagonals of your rectangle are congruent.
(C) Using the slopes for each side, prove there are 4 right angles on the rectangle.
**Please Show All Work**
Answers
A. Using the distance formula, we can state that the opposite sides are congruent because AD = BC = √10 units and AB = CD = √40 units.
B. The diagonals are equal, AC = BD = √50 units.
C. Based on the slopes of each side, there are 4 right angles on the rectangle.
What is the Distance Formula?The distance formula is used to find the distance that exist between tow points that are on a coordinate plane. The formula is: d = \(\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\).
What is the Slope of a Line?
Slope = change in y / change in x.
A. The coordinates of each of the vertices of the rectangle are:
A(1, 2)
B(7, 4)
C(8, 1)
D(2, -1)
Use the distance formula to find AB, CD, BC, and AD.
AB = √[(7−1)² + (4−2)²]
AB = √40
CD = √[(2−8)² + (−1−1)²]
CD = √40
BC = √[(8−7)² + (1−4)²]
BC = √10
AD = √[(2−1)² + (−1−2)²]
AD = √10
Therefore, the opposite sides are congruent because AD = BC = √10 units and AB = CD = √40 units.
B. The diagonals are AC and BD. Find their lengths using the distance formula:
AC = √(8−1)² + (1−2)²]
AC = √50 units
BD = √[(2−7)² + (−1−4)²]
BD = √50 units
Therefore, the diagonals are equal, AC = BD = √50 units.
C. Find the slope of AB, CD, BC, and AD:
Slope of AB = change in y / change in x = rise/run = 2/6 = 1/3
Slope of CD = 2/6 = 1/3
Slope of BC = -3/1 = -3
Slope of AD = -3/1 = -3
-3 is the negative reciprocal to 1/3, this means that, if the two lines that meet at a corner have these two slope, then they will form a right angle because they are perpendicular to each other.
Therefore, there are 4 right angles on the rectangle.
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The divergence test applied to the series 3n 2n +1 tells us that the series the series converges. the series converges the series diverges. further testing is needed.
Answers
The limit of the sequence of terms of a series is zero, this test alone does not prove that the series converges, and further testing is needed to determine convergence or divergence.
The divergence test is a test used to determine if a series converges or diverges. It states that if the limit of the sequence of terms of a series is not zero, then the series diverges.
The series 3n/(2n + 1) can be simplified to
=3/2 - 3/4n + 3/4n+1.
As n approaches infinity, the terms in the series approach 3/4n, which approaches infinity as n approaches infinity.
Therefore, the limit of the sequence of terms of this series is not zero, and so the series diverges. Thus, the answer to the question is the series diverges.
A more general form of the divergence test states that if the limit of the sequence of terms of a series is not zero, then the series diverges. However, if the limit of the sequence of terms of a series is zero, this test alone does not prove that the series converges, and further testing is needed to determine convergence or divergence.
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In simplest form, what is the quotient of 1/6 divided by 2/9?
Answers
step by step: The numbers in 1/6 divided by 2/9 are labeled below:
1 = dividend numerator
6 = dividend denominator
2 = divisor numerator
9 = divisor denominator
To make it a fraction form answer, you multiply the dividend numerator by the divisor denominator to make a new numerator.
Furthermore, you multiply the dividend denominator by the divisor numerator to make a new denominator:
1 x 9
6 x 2
=
9
12
Thus, the answer to 1/6 divided by 2/9 in fraction form is:
9
12
To make the answer to 1/6 divided by 2/9 in decimal form, you simply divide the numerator by the denominator from the fraction answer above:
9/12 = 0.75
The answer is rounded to the nearest four decimal points if necessary.
9/12 can be simplified to 3/4.
Convert rational numbers to their equivalent decimals
Answers
Answer:
In order to change a rational number to a decimal, we just convert the number into the form of a fraction. We then divide the numerator with the denominator and find out the exact value of the division.
!!!Quick!!! Barbara can walk 3200 meters in 24 minutes. How far can she walk in 3 minutes? (In Meters)
Answers
Answer:
400 meters
Step-by-step explanation:
First, divide 3,200 by 24 to find the rate, which is 133.3 (repeated).
Now, multiply 133.3 by 3, which is your answer! 133.3*3=399.9. 399.9 is extremely close to 400, so we can just round it to that.
Hope this helps you out and have a wonderful day (✿◡w◡)
Please help me with this ACT Prep problem.
Answers
Answer:
Option C
Step-by-step explanation:
ΔABC and ΔDEF are similar triangles.
By the property of similar triangles, corresponding sides of the similar triangle are proportional.
\(\frac{AB}{DE}=\frac{BC}{EF}=\frac{AC}{DF}\)
\(\frac{6}{DE}=\frac{6}{3}=\frac{10}{5}\)
\(\frac{6}{DE}=\frac{6}{3}\)
DE = 3
Perimeter of ΔDEF = Sum of measures of the sides of the triangle
= DE + EF + DF
= 3 + 3 + 5
= 11
Therefore, Option C will be the correct option.
HELP IM BEGGING ON MY KNEES FOR SOMEONE WHO KNOWS WHAT TO DO CAUSE IVE GOTTEN IT WRONG AND IM ALLOWED TO RETAKE IT
Answers
Answer:
-3/5
Step-by-step explanation:
from 1st point to second, you go down 3, right 5
Find the volume of a cone with a radius of 6 centimeters and a height of 15 centimeters. Round your answer to the nearest tenth.
Answers
Answer: 565.3 cubic cm
Step-by-step explanation:
V= 1/3Bh
V= 1/3π r^2h
= 1/3 π (6 cm) ^2 (15 cm)
= 1/3 π (36 cm squared) (15 cm)
= 180π cubic cm
about 565.2 cubic cm
π is about 3.14
The value of the volume of a cone with a radius of 6 centimeters and a height of 15 centimeters is,
⇒ 565.2 cubic cm
What is Multiplication?To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
In cone,
Radius = 6 cm
Height = 15 cm
Now, We know that;
Volume of cone is,
V = 1/3π r²h
Substitute all the values we get;
V = 1/3 π (6 cm)² (15 cm)
V = 1/3 π (36) (15)
V = 180π
V = 565.2 cubic cm
Thus, The value of the volume of a cone with a radius of 6 centimeters and a height of 15 centimeters is,
⇒ 565.2 cubic cm
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A tudent olve the following equation and determine that the olution i −2. I the tudent correct? Explain
Answers
a = -2 is the value of linear equation .
What are examples of linear equations?
An equation with only one variable is referred to as a linear equation in one variable. It has the mathematical formula Ax + B = 0, where A and B can be any two real numbers, and x is an unknowable variable with just one possible value. One such linear equation in one variable is 9x + 78 = 18.Step 1 - Write the equation.
3/a + 2 - 6a/a² - 4 = 1/a - 2
Step 2 - rewrite the equation.
3/a + 2 - 6a/a² - 4 = 1/a - 2
Step 3 - Take the LCM.
3(a- 2) - ( a + 2 )/a² - 2² = 6a/a²-4
Step 4 - Further simplify the above expression
3a - 6 - a - 2/a² - 4 = 6a/a² - 4
Step 5 - Cancel out the denominator of both sides and then further simplify.
2a - 8 = 6a
a = -2
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The complete question is -
A student solves the following equation and determines that the solution is −2. Is the student correct? Explain.
3/a + 2 − 6a/a2 − 4 = 1/a − 2
According to the following expression, what is \( z \) if \( x \) is 32 and \( y \) is 25 ? \[ z=(x
Answers
When x = 32 and y = 25, the value of z is calculated as 3200 using the given expression.
According to the following expression, the value of z when x = 32 and y = 25 is:
[z = (x+y)² - (x-y)²]
Substitute the given values of x and y:
\(\[\begin{aligned}z &= (32+25)^2 - (32-25)^2 \\ &= 57^2 - 7^2 \\ &= 3249 - 49 \\ &= \boxed{3200}\end{aligned}\]\)
Therefore, the value of z when x = 32 and y = 25 is \(\(\boxed{3200}\)\).
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Complete Question:
A²,b²,c² are consecutive perfect squares.How many natura numbers are lying between a² and c², if a>0
Answers
Answer:
The quantity of natural numbers between \(a^{2}\) and \(c^{2}\) is \(2\cdot (a + b) + 1\).
Step-by-step explanation:
If \(a^{2}\), \(b^{2}\) and \(c^{2}\) are consecutive perfect squares, then both \(a\), \(b\) and \(c\) are natural numbers and we have the following quantities of natural numbers:
Between \(b^{2}\) and \(c^{2}\):
\(c^{2} = (b+1)^{2}\)
\(c^{2} = b^{2}+2\cdot b + 1\)
\(c^{2}-b^{2} = 2\cdot b + 1\)
And the quantity of natural numbers between \(b^{2}\) and \(c^{2}\) is:
\(c^{2}-b^{2}-1 = 2\cdot b\)
Between \(a^{2}\) and \(b^{2}\):
\(b^{2} = (a + 1)^{2}\)
\(b^{2} = a^{2} +2\cdot a + 1\)
\(b^{2}-a^{2} = 2\cdot a + 1\)
And the quantity of natural numbers between \(a^{2}\) and \(b^{2}\) is:
\(b^{2}-a^{2}-1 = 2\cdot a\)
And the quantity of natural numbers between \(a^{2}\) and \(c^{2}\) is:
\(Diff = 2\cdot a + 2\cdot b + 1\)
Please observe that the component +1 represents the natural number \(b^{2}\)
A feed trial to compare three dietary supplements was conducted using 24 pigs of approximately the same body weight. The 24 pigs came from four litters, with each of the four litters containing six pigs. Within a given litter, the six pigs were randomly assigned to the three dietary supplements, with two receiving each supplement. The pigs were housed in 24 identical pens and fed their assigned diets under identical conditions. This is an example of a block design. What are the blocks in this design?a. The 24 different pigsb. The three different dietary supplementsc. The four different littersd. The 24 identical pensIt is don't D
Answers
The blocks in this design are c. the four different litters. The pigs within each litter were grouped together as a block, and the three dietary supplements were randomly assigned to the two pigs within each block.
This helps control for any variation between litters that could affect the results of the feed trial. The 24 identical pens are not the blocks in this design, but rather the units where the treatments were applied.
A litter is defined as the live birth of several young at once in an animal from the same mother and typically from the same pair of parents, especially three to eight young. The term is most frequently used to refer to the offspring of mammals, although it can also refer to any animal that bears numerous offspring.
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PLEASE HELP ME ANSWER ALL OF THESE QUESTIONS!!!!!!
Answers
Answer:
I think this might help you.
What is 8/9 minus 5/6
Answers
Answer:
1/18
Step-by-step explanation:
Answer the following question\(( - \frac{2}{3} \sqrt{6} )(9 \sqrt{3} \)
Answers
The expression is given as,
\(\frac{-2}{3}\times\sqrt[]{6}\text{ }\times\text{ 9}\sqrt[]{3}\)The given expression is simplified as follows:
\(\begin{gathered} =\frac{-2}{\sqrt{3}\times\sqrt[]{3}}\times\sqrt[]{3\text{ }}\text{ }\times\text{ }\sqrt[]{2}\text{ }\times\text{ 9 }\times\text{ }\sqrt[]{3} \\ =\text{ -2}\sqrt[]{2\text{ }}\text{ }\times\text{ 9} \\ =\text{ -18 }\sqrt[]{2} \end{gathered}\)Thus the result of the given expression is,
\(\text{-18 }\sqrt[]{2}\)What's the area of a regular triangle with a side length of 15? (Explanations step-by-step are appreciated!)
Answers
the area of the equilateral triangle with a side length of 15 is approximately 97.4279 square units.
A regular triangle is also known as an equilateral triangle, which means all of its sides are equal in length. To find the area of an equilateral triangle with a side length of 15, we can use the following formula:
Area = (√(3) / 4) × side²
where "side" is the length of one side of the triangle.
Let's plug in the given value of side length, which is 15, into the formula:
Area = (√(3) / 4) × 15²
Area = (√(3) / 4) × 225
Area = 97.4279 (rounded to 4 decimal places)
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Triangle A'B'C' is the image of triangle ABC after a sequence of rigid motions. Find a sequence of transformations that takes triangle ABC to triangle A'B'C'. Please write the steps separately in a list instead of one continuous paragraph and be detailed in your description of the moves.
Answers
As a result, the transformation sequence from triangle ABC to triangle A'B'C' is: Translation by vector AA' Counterclockwise rotation around A" by the same angle as A'C'A"B"
What precisely is a triangle?A triangle is a closed, the double symmetrical object made up of three line segments called sides that intersect at three points called vertices. Triangles can be identified by about there sides and angles. Based on their sides, triangles could be equilateral (all factions equal), isosceles, or scalene.
Using a vector that connects A and A', we can translate triangle ABC to the left until vertex A coincides with point A'. This repositions all three vertices of triangle ABC, resulting in a congruent triangle A "B"C".
Triangle A"B"C" can be rotated anticlockwise around vertex A" until side A"B" coincides with A'C'. This rotation also relocates vertices B" and C", resulting in a congruent triangle A'"B'"C "'.
Reflection: Triangle A' can be reflected "B'"C"' across the line containing side B'C', which is the perpendicular bisector of A"C", to form triangle A'B'C'. Each point of A'"B'"C is represented by this reflection "'to an equidistant point on A'B'C' from B'C'.
As a result, the transformation sequence from triangle ABC to triangle A'B'C' is:
Translation by vector AA' Counterclockwise rotation around A" by the same angle as A'C'A"B"
A"C" reflection across the perpendicular bisector
To avoid copyright infringement, the images of the triangles in the steps are not included, but the reader can easily visualise them.
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What is the best fit line equation in a scatter plot?
Answers
The required answer is the y = 80
The best fit line equation in a scatter plot represents the relationship between two variables. It is also known as the regression line or the line of best fit. The equation of the best fit line is typically represented as y = mx + b, where y is the dependent variable, x is the independent variable, m is the slope of the line, and b is the y-intercept.
To find the best fit line equation in a scatter plot,
1. Plot the data points on a scatter plot.
2. Visualize the trend or pattern in the data points.
3. Determine whether the relationship between the variables is linear, meaning that the data points roughly form a straight line pattern.
4. Use a statistical method, such as the least squares method, to find the line that minimizes the distance between the data points and the line.
5. Calculate the slope (m) and the y-intercept (b) of the best fit line.
6. Write the equation of the line using the values of m and b.
Using the least squares method, determine that the slope of the best fit line is 2 and the y-intercept is 70.
Therefore, the equation of the best fit line would be:
y = 2x + 70
This equation represents the expected test score (y) based on the number of hours studied (x). For example, if a student studies for 5 hours, estimate their test score by substituting x = 5 into the equation:
y = 2(5) + 70
y = 10 + 70
y = 80
So, according to the best fit line equation, if a student studies for 5 hours, expect their test score to be around 80.
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a) What type of triangle is triangle ABC?
isosceles
b) Give reasons for your answer.
Answers
The type of triangle represented in the image attached to the task content is; Isosceles.
What type of triangle is triangle ABC?By observation; since line AB and DE are parallel lines; it follows from the alternate Angie theorem that; <ABC = <BCE = 80°.
On this note, since angle ACD is 50°, the measure on <ACB is;
180 - 80 - 50 = 50°.
Therefore, since the sum of interior angle measures in a triangle is; 180°.
It follows that; <BAC is; 180 - 80 - 50 = 50°.
Hence, since the base angles; BAC and ACB are equal; it follows that the triangle in discuss is an isosceles triangle.
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Complementary of supplementary? Find the value of x
Answers
Answer: x=6
The two angles shown in each are complementary because they add up to 90°.
10 & 12 would be supplementary to one another because they would add up to 180°.
Step-by-step explanation:
We know that on both 10 & 12 the angles add up to equal 90° so...
10. 8x+7x=90
15x=90
x=6
12. it's the same in pic as 10
The two angles shown in each are complementary because they add up to 90°.
10 & 12 would be supplementary to one another because they would add up to 180°.
What is the value of x?
Enter your answer in the box.
Answers
Answer:
Step-by-step explanation:
3x+ 50= 6x-10
50+10=6x-3x
60=3x
x=20
Answer:
x = 20
Step-by-step explanation:
you can notice that those two are identical, so it's a basic equation
3x + 50 = 6x - 10
and now we can solve it by moving x'es to one side and number to the other (remembering that when you do that you need to change the sign, so if there is "-" then change to "+"):
50 = 6x - 10 - 3x
50 = 3x - 10
50 + 10 = 3x
60 = 3x
20 = x