Write a coordinate proof for each statement.If a line segment joins the midpoints of two sides of a triangle, then its length is equal to one half the length of the third side,
Answers
If a line segment joins the midpoints of two sides of a triangle, then its length is equal to one-half the length of the third side has been proved.
What is a triangle?A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are three sides and three angles in every triangle, some of which may be the same.
The sum of all three angles inside a triangle will be 180° and the area of a triangle is given as (1/2) × base × height.
In the given triangle below;
Line segment BC is intersecting at the midpoint of AD and AE.
Now,
Since ΔABC ≈ ΔADE by similarity property.
So,
AB/AD = BC/DE
AB/(AB + BD) = BC/DE
Since AB = BD = AB lets say,
AB/2AB = BC/DE
BC/DE = 1/2
Hence "If a line segment joins the midpoints of two sides of a triangle, then its length is equal to one-half the length of the third side has been proved".
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Related Questions
Two different tests to write k/4 +16
Answers
Step-by-step explanation:
\begin{gathered}6x - 2y = 6 \\ 6x = 6 + 2y \\ x = \frac{6 + 2y}{6} \end{gathered}
6x−2y=6
6x=6+2y
x=
6
6+2y
Two tents are in the shape of hemispheres, with circular floors. The ratio of their floor areas is 9: 12.25 . If the diameter of the smaller tent is 6 feet, what is the volume of the larger tent? Round to the nearest tenth.
Answers
The volume of the larger tent in the shape of hemispheres, with circular floors, is 89.8 cubic feet.
If the diameter of the smaller tent is 6 feet, then its radius is 3 feet. Solving for the area of its circular floor,
A = πr^2
A = π(3 feet)^2
A = 9π square feet
Using the ratio of the floor areas of the two tents, calculate the area of the circular floor of the larger tent.
9 : 12.25 = 9π square feet : x
where x = area of the circular floor of the larger tent
9x = 12.25(9π)
x = 12.25 π square feet
If the area of the circular floor of the larger tent is 12.25 π square feet, then solving for its radius,
A = πr^2
12.25 π square feet = πr^2
r = 3.5 feet
Hemisphere refers to half of a sphere and its volume is given by the formula V = 2/3πr^3, where r is the radius.
V = 2/3πr^3
V = 2/3 π (3.5 feet)^3
V = 89.79719002 cubic feet
Rounding off to the nearest tenth.
V = 89.8 cubic feet
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Square root of 9 =3=3=3 and 1 half + 1 half
Answers
Write a coordinate proof to prove that Δ A B C is an isosceles triangle if the vertices are A(0,0), B(a, b) , and C(2 a, 0) .
Answers
An isosceles triangle is one with two equal-length sides. ΔABC is an isosceles triangle.
What is the distance between two points ( p,q) and (x,y)?The shortest distance (length of the straight line segment's length connecting both given points) between points ( p,q) and (x,y) is:
D = √[(x-p)² + (y-q)²] units.
Given that the coordinates of the vertices of the triangle are A(0,0), B(a, b), and C(2a, 0). Now, to prove that the given triangle is an isosceles triangle we need to find the length of each side of the triangle.
AB = √[(x₂-x₁)² + (y₂-y₁)²]
= √[(a - 0)² + (b - 0)²]
= √(a² + b²)
BC = √[(x₂-x₁)² + (y₂-y₁)²]
= √[(2a - a)² + (0 - b)²]
= √(a² + b²)
AC = √[(x₂-x₁)² + (y₂-y₁)²]
= √[(2a - 0)² + (0 - 0)²]
= √4a²
= 2a
Since the length AB and BC are the same, while the length of AC is different, therefore, ΔABC is an isosceles triangle.
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The arithmetic mean of two terms in an arithmetic sequence is -6 . One term is -20 . Find the other term.
Answers
The other term is +8.
How to find the other term?A recursive formula is one that defines each term in a sequence by reference to the one before it. The following parameters are defined using the recursive formules:
1. The initial term in the series.
2. The general rule for determining any term from its preceding term.
Formula for the Arithmetic Mean
The ratio of the sum of the items to the total number of items is the arithmetic mean, which is the simplest way to measure central tendency.It is regarded as the most accurate way to measure central tendency. The distribution of the data and the intended use of the data both influence the average that is chosen.
[tex]arithmetic \: mean = \frac{a1 + a2 + a3 + a4 + a5 + .........an}{n} [/tex]
given that
The arithmetic mean of two terms in an arithmetic sequence is -6.One term is -20 .
now, find the other term
[tex]arithmetic \: mean = \frac{a + b}{ 2} [/tex]
[tex] - 6 = \frac{( - 20) + b}{2} [/tex]
[tex]2 \times - 6 = - 20 + b[/tex]
[tex] - 12 + 20 = b[/tex]
[tex]b = 8[/tex]
Hence,the other term is +8.
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3x3 what is the sum to this..?
Answers
Answer:
9
Step-by-step explanation:
3x3=9
Answer:
the sum is 9
Step-by-step explanation:
3×1=3
3×2=6
3×3=9
What sets (types or categories) of numbers do we use as the input to functions that represent sequences?
Answers
Answer:
electrical is a good servant but master
Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.
Answers
To solve problems, construct one-variable equations and inequalities.
How to use them to solve problems?As opposed to an inequality, which links two different values, an equation declares that two expressions are equal.
Create one-variable equations and inequalities, then utilize them to solve issues.
Include simple rational and exponential equations as well as those resulting from linear and quadratic functions.
In order to answer word problems, students should be able to decipher them and create equations and inequalities.
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Write two absolute value functions such that they have a common vertex in Quadrant III and one is the reflection of the other in a horizontal line.
Answers
The functions
y = -|x + 4| - 5y=−∣x+4∣−5
y = |x + 4| - 5y=∣x+4∣−5
Both these functions have got a common vertex in the third Quadrant.
They are the reflections of each other in a horizontal line.
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Jonathan earns $250 plus $40 for every house he paints
Answers
Answer:
250 + 40x
Step-by-step explanation:
x = every house he paints .
im not sure what you want but in case its an equation , here you go .
Answer:
250 + 40x
Step-by-step explanation:
literally what the dude above me said heh
If $9237.05 is put into an account paying %8.82/ a compounding yearly, how much interest will be earned after 16.7 years?
Answers
Answer:
$28,656.82
Step-by-step explanation:
I used the compound interest calculator
A = P(1 + r/100)ⁿ
where A = amount accrued, P = investment amount r = rate% and n = number of years
r = 8.82% = 8.82/100 = 0.082 so 1 + r/100 = 1.0882
[tex]\\A = P(1.0882)^{16.7} = \$37,893.87\\\\\mathrm {Interest} = \$37,893.87 - \$9237.05 = \$28,656.82[/tex]
Answer:
$28,656.82
Step-by-step explanation:
Annual Compound Interest Formula
[tex]\large \text{$ \sf I=P\left(1+r\right)^{t} -P$}[/tex]
where:
I = Total interest earned.P = Principal amount invested.r = Interest rate (in decimal form).t = Time (in years).Given:
P = $9237.05r = 8.82% = 0.0882t = 16.7 yearsSubstitute the given values into the formula and solve for I:
[tex]\implies \sf I=9237.05(1+0.0882)^{16.7}-9237.05[/tex]
[tex]\implies \sf I=9237.05(1.0882)^{16.7}-9237.05[/tex]
[tex]\implies \sf I=9237.05(4.1023777...)-9237.05[/tex]
[tex]\implies \sf I=37893.8685...-9237.05[/tex]
[tex]\implies \sf I=28656.8185...[/tex]
Therefore, the amount of interest that will be earned after 16.7 years is $28,656.82 (nearest cent).
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The table shows the elevation above sea level of the lowest and highest points in the United States.
Location
Death Valley
Mount McKinley/Denali
Elevation Above Sea Level (feet)
-282
20,310
Choose three correct statements.
A. Death Valley is -282 feet below sea level.
B. Death Valley is 1-2821 feet below sea level.
C. Death Valley is 1-2821 feet above sea level.
D. Mount McKinley/Denali is 120, 310| feet below sea level.
E. Mount McKinley/Denall is-120, 3101 feet below sea level.
F. Mount McKinley/Denali is 1-20, 3101 feet above sea level.
Answers
Location Death Valley, Mount McKinley/Denali Elevation Above Sea Level (feet), then the statement B , statement E , statement F are correct.
Death Valley is |-282| feet below sea level. Mount McKinley/Denali is |-20, 310| feet below sea level.Mount McKinley/Denali is |-20, 310| feet above sea level.These three statements are correct.
The table shows the elevation above sea level of the lowest and highest points in the United States.
Location Death Valley
Mount McKinley/Denali
Elevation Above Sea Level (feet)
So, we can write,
Death Valley is |-282| feet below sea level.Mount McKinley/Denali is |-20, 310| feet below sea level.Mount McKinley/Denali is |-20, 310| feet above sea level.You are subtracting the two numbers. Note however, that 282 feet below the sea level = -282
Subtract.
⇒ 20310 - (-282)
Note that two negatives = one positive
⇒ 20310 + 282
⇒ 20592 feet
Therefore, The statement B , statement E , statement F are correct.
Hence,
Death Valley is |-282| feet below sea level. Mount McKinley/Denali is |-20, 310| feet below sea level.Mount McKinley/Denali is |-20, 310| feet above sea level.These three statements are correct.
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Multiply Which equation is the best choice
Answers
Answer:
second option
Step-by-step explanation:
(2 [tex]\frac{4}{5}[/tex] )( - 5 [tex]\frac{2}{3}[/tex] ) ← convert mixed numbers to improper fractions
= [tex]\frac{14}{5}[/tex] × - [tex]\frac{17}{3}[/tex]
= - [tex]\frac{14(17)}{5(3)}[/tex]
= - [tex]\frac{238}{15}[/tex]
= - 15 [tex]\frac{13}{15}[/tex]
how do i subtract inteargers
Answers
Answer:
You remove the difference between the two numbers from each other. E.g., 5-2=3, and 6-4=2.
Step-by-step explanation:
Which set of numbers are imaginary numbers?
Answers
Answer:
the third option contains imaginary numbers
Step-by-step explanation:
Imaginary numbers are the numbers when squared it gives the negative result. In other words, imaginary numbers are defined as the square root of the negative numbers where it does not have a definite value. It is mostly written in the form of real numbers multiplied by the imaginary unit called “i”. so we can express them as follows; √-2 = √-1 × √2 = √2 i.... √-1 = i
√-9 = √-1 × √9 = 3i
y varies directly as x. Describe how the value of y
changes when the value of x is tripled.
Answers
Answer: When x is tripled, y will be tripled.
Step-by-step explanation:
Since y varies directly as x, whatever happens to x will happen to y. This means that if x is tripled, y will also be tripled.
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help I'll mark brainliest
Answers
Answer:
2 + (-7) = -5
Step-by-step explanation:
The arrow pointing down is telling you to add a negative. You cannot add positive numbers and get a negative number as your answer.
Taking away -7 from 2 gives you -5
Simplify.
2 + 8 - 2 [32 + 5 (1 + 2)]}
Answers
Your answer should be - 84.
Explanation:
Starting equation: [tex]2\:+\:8\:-\:2\:\left[32\:+\:5\:\left(1\:+\:2\right)\right][/tex]
-Calculate within parentheses [32 + 5 (1+2)] = 47.
Remaining equation: 2 + 8 - 2 x 47
-Multiply and divide (left to right) 2 x 47 = 94
Remaining equation: 2 + 8 - 94
-Add and subtract (left to right) 2 + 8 - 94 = -84
Your final answer is -84
-----------------------------------------------------------
Hope this helps!
Have a great day and God bless! :)
Determine whether the following statement is always, sometimes, or never true. Explain your reasoning.
Answers
When using the distributive property, if the term outside the parentheses is negative, then the sign of each term inside the parentheses will change: Always TRUE
What do we mean by distributive property?The distributive property of binary numbers in mathematics generalizes the distributive law, which states that equality is always true in elementary algebra. In elementary arithmetic, for example, one has According to one, multiplication distributes over addition.If the term outside the parenthesis is negative when using the distributive property, the sign of each term inside the parentheses will always change.Example can be: -1(27 - 55) = -27 + 55
It is because of the following reason that when we multiply two numbers:
(positive number (+)) × (positive number (+)) = (positive number (+))(positive number (+)) × (negative number (-)) = (negative number (-))(negative number (-)) × (positive number (+)) = (negative number (-))(negative number (-)) × (negative number (-)) = (positive number (+))Therefore, the statement "when using the distributive property, if the term outside the parentheses is negative, then the sign of each term inside the parentheses will change" is Always TRUE.
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The complete question is given below;
Determine whether the following statement is always, sometimes, or never true. Explain your reasoning. When using the distributive property, if the term outside the parentheses is negative, then the sign of each term inside the parentheses will change.
Use the fact that a/b / c/d = a/b ÷ c/d to simplify each rational expression. State any restrictions on the variables.
9m + 6n / m² n² / 12m + 8n/5 m²
Answers
State whether the sentence is true or false. If false, replace the underlined term to make a true sentence.
Determining the arrangement of people around a circular table would require circular permutation.
Answers
True, Determining the arrangement of people around a circular table would require circular permutation.
In statistics, what does a probability mean?
The probability serves as a gauge for how likely an event is to occur. It gauges how likely an event is. P(E) = Number of Favorable Outcomes/Number of Total Outcomes is the formula for probability.Mathematics' study of random events is known as probability, and there are four primary types of probability: axiomatic, classical, empirical, and subjective. Since probability is the same as possibility, you could say that it is the likelihood that a specific event will occur.True, Determining the arrangement of people around a circular table would require circular permutation.
It happens that there are only two ways we can seat three people in a circle, relative to each other's positions.
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Write a relationship for a function whose hx values are 6 less than the cube of x
Answers
The mathematical expression from the algebraic expression is a x^3 - 6.
According to the statement
We have to find that the expression of the statement in the mathematical form.
So, For this purpose, we know that the
An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.
From the given information:
The hx values are 6 less than the cube of x
Then
To convert into the mathematical form:
The cube of the x is in the mathematical form is a x^3
Then
And the 6 less than the cube
And in the mathematical form it becomes the
x^3 - 6.
So, The mathematical expression from the algebraic expression is a x^3 - 6.
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Record your answers on the answer sheet provided by your teacher or on a sheet of paper.
Suppose line l contains points A, B , and C , If A B=7 inches, A C=32 inches, and point B is between points A and C , what is the length of BC? Express your answer in inches.
Answers
Length of BC is 25 inches.
Here,
Line l contains points A, B and C.
A B =7 inches, A C = 32 inches, and point B is between points A and C.
We have to find the length of BC in inches.
What are Collinear points?
If two or more points are lie on a straight line then points are called Collinear points.
Now,
Line l contains points A, B and C.
Point B is between points A and C.
Length of A B = 7 inches and A C = 32 inches
Hence, Length of BC = Length of AC - Length of A B
= 32 - 7 = 25 inches.
Therefore, Length of BC is 25 inches.
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What can you say about and based on the sum of their angles? How are the angles related?
Answers
Answer: Do you have a picture of the problem so it will be more sense?
Step-by-step explanation:
Suppose two boxes of cereal contain the same amount of ounces but cost different amounts. Without computing, how can you determine which Siri will cost more per ounce of cereal? Explain.
Answers
Answer:
The one that costs more.
Step-by-step explanation:
Because you already know that they have the same volume (amount of ounces) and they are different prices, whichever one is more expensive has the higher cost per ounce. {You don't need to solve for a ratio or anything because they have the same number of ounces!!!}
Answer: If the number of ounces are the same, then the box that costs more will also cost more per ounce.
Paul collects comic books. He has 20 books in his collection, and he adds 3 per month. In how many months will he have a total of 44 books in his collection?
F. 5
G. 6
H. 8
J. 15
Answers
In 8 months he will have a total of 44 books in his collection.
The correct answer is an option (H)
In this question,
Paul collects comic books. He has 20 books in his collection, and he adds 3 per month.
We need to find the number of months required to have a total of 44 books in his collection.
Let n be the required number of months.
From given information, we get an equation,
20 + 3n = 44
We solve above equation to find the required number of months.
20 + 3n - 20 = 44 - 20
3n = 24
n = 8
Therefore, in 8 months he will have a total of 44 books in his collection.
The correct answer is an option (H)
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identify the inequalities A, B , and C for which the given ordered pair is a solution.
A. x+y ≤ 2
B. y ≤ (3/2)x-1
C. y>-(1/3)x-2
(-8,-11)
Answers
The inequality y ≤ (3/2)x-1 satisfies the point (-8, -11) option (B) y ≤ (3/2)x-1 is correct.
What is inequality?It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.
It is given that:
The point is (-8, -11)
As we have inequalities shown in the option:
After plotting the inequality in the graph:
From the graph, the point lies in the solution region of the inequality y ≤ (3/2)x-1 which means the point (-8, -11) satisfies the inequality.
Thus, the inequality y ≤ (3/2)x-1 satisfies the point (-8, -11) option (B) y ≤ (3/2)x-1 is correct.
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Solve. Find the area of a pantry shelf that measures 3 yards by 3/7 yard.
Answers
Answer:
The answer is 9/7 yards.
Problem: using the digits -9 to 9 at most one time each, place a digit on each box to create an equation whose solution is a positive whole number. ("_" is what i need to fill in and the "/" are fractions)
_/_(x)+_/_= _
Answers
Considering division signal rules, one possible example of an equation that results in a positive number is:
-9/-3 + 3/1 = 6.
When does a division results in a positive number?A division(fraction) results in a positive numbers if the two terms have the same signal, either both positive or both negative.
Hence, to ensure an expression with a positive result in this problem, the terms in each division got to have the same signal, as the example that follows:
-9/-3 + 3/1 = 6.
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96240 is divisible by 2,3,5,10 true or false
Answers
True
It's true, 96240 is divisible by 2,3,5,10
Hope this helps!
