The segment addition problem was given below which gives the value of x as 20.
Segment addition problem:
Consider three points on a line: A, B, and C. Point B is located between points A and C.
The lengths of the line segments are as follows:
Length of segment AB: 12
Length of segment BC: x
Length of segment AC: 32
Find the value of x.
We have the equation for segment addition: AB + BC = AC
Substitute the given values:
12 + x = 32
Now, solve for x:
x = 32 - 12
x = 20
Therefore, the value of x is indeed 20, and the lengths of the segments satisfy the segment addition property.
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To construct a segment addition problem with a solution of x = 20, use three collinear points A, B, and C and set AB = x and BC = 20 - x, with the entire segment AC being 20 units. Solving the equation x + (20 - x) = 20 confirms that x = 20 is the solution.
Explanation:To write a segment addition problem that solves for x where the solution is x = 20, let’s use three collinear points A, B, and C with point B between A and C. We can then express the lengths of segments AB and BC in terms of x. For instance, if AB is x units long and BC is 20 - x units long, the total length of AC would be 20 units. We can write an equation based on this:
AB + BC = AC
x + (20 - x) = 20
By simplifying, x cancels out on the left-hand side, leaving 20 = 20, which is true for x = 20. Therefore, this is a valid segment addition problem where solving for x yields 20 as the solution.
Here is the step-by-step problem phrased as a question:
Let points A, B, and C be collinear with B between A and C.If AB = x and BC = 20 - x, and AC = 20, find the value of x.A car is a vehicle with four wheels.
Rewrite the statement as a true conditional with a converse that is false.
Write a similar true conditional with a converse that is true
The polynomial 9x2+3x3y2z is what degree?
evaluate the summation of 2n+5 from n=1 to 12
29
36
216
432
How would I solve this?
A ball is thrown from 4 feet off the ground with a vertical velocity of 30 feet per second.
Is the ball at its maximum height after 1 second? In two or more complete sentences, explain how you know whether or not the ball is at its maximum height.
PLZ ASAP, I NEED HELP ASAP
When 8668/25+4141/9-5533/25 is computed and written as a mixed number in simplest form, what is the fractional part of the mixed number, plz give the right answer
Thanks
0.9×10-1 in Standard notation
what operation represents a ratio
What are the limitations of determining a function’s average rate of change by examining the function’s graph?
The limitations of determining a function's average rate of change by examining the function's graph include incomplete information, the need for tangent lines, and limited interval-specific data.
Explanation:When determining a function's average rate of change by examining the function's graph, there are several limitations to consider.
The graph may not provide enough information about the function's behavior between plotted points, leading to an inaccurate estimation of the average rate of change.A curved graph may require the use of tangent lines to calculate the instantaneous rate of change, which may not accurately represent the average rate of change.The graph may not show the function's behavior in different intervals or at certain points, making it difficult to determine the average rate of change for specific intervals or points.These limitations highlight the importance of understanding the limitations of graph analysis and considering alternative methods, such as calculus, to accurately calculate the average rate of change of a function.
the binomial expansion of (x + y^2)^2 is
Answer:
[tex]x^{2}+y^{4}+2xy^{2}[/tex]
Step-by-step explanation:
The given expression is (x + y²)² and we have to simplify it to find the binomial expansion.
(x + y²)² is in the form of (a + b)².
When we expand (a + b)² we get the binomial expression
(a + b)² = a² + b² + 2ab
Now we put the value of a = x and b = y²
(x + y²)² = x² + (y²)² + 2(x)(y²)
= [tex]x^{2}+y^{4}+2xy^{2}[/tex]
Therefore answer is [tex]x^{2}+y^{4}+2xy^{2}[/tex]
Consider the equation
(x^m)^3 = (x^13)^5 times (x^-8)^-5.
The value of m is?
A. 15
B. 28
C. 35
D. 70
It's 35, I figured it out
what is the common difference in the arithmic sequence 30,27,24,21,18
Answer:
-3
Step-by-step explanation:
Its decresing by -3.
A car is purchased for $28,000. After each year, the resale value decreases by
35%. What will the resale value be after 3 years? Use the calculator provided and round your answer to the nearest dollar.
Using the formula for decrement, the resale value of a $28,000 car that depreciates at a 35% rate annually for three years would be roughly $10,012.
Explanation:This question is about calculating the effects of percent decrease over a period of time. Specifically, the student is asked to calculate the value of a $28,000 car, after it undergoes a 35% percent decrease in value each year for three years. This type of problem is typically solved using the formula v = p * ((1 - r)^n), where v is the final value, p is the initial value, r is the rate of decrease, and n is the number of periods. In this case, the initial value (p) is $28,000, the rate of decrease (r) is 35% or 0.35, and the number of periods (n) is 3 years. Substituting these into the formula, we can find that the resale value after 3 years is v = 28000 * ((1 - 0.35)^3) = $10,011.75. Rounding this to the nearest dollar, we get an estimated resale value of $10,012.
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If babe ruth averaged 46 home runs per year, how many home runs did he hit in 12 years
Answer:
He hit 552 home runs in 12 years
Step-by-step explanation:
To solve this problem, we will follow the steps below;
Using proportion;
Let x be the number of home runs he hits in 12 years
46 home runs = 1 year
x = 12
cross -multiply
x × 1 = 46× 12
x = 552 home runs
Therefore, he hit 552 home runs in 12 years
The area of a circle is 28.26 square centimeters. What is its diameter (use 3.14 for Pi)?
What is the square root of 26 in simplest radical form?
Final answer:
The square root of 26 in simplest radical form is just √26, as 26 has no perfect square factor. It can also be expressed as 26 raised to the power of 0.5 based on the concept of fractional powers corresponding to roots.
Explanation:
The square root of 26 in its simplest radical form cannot be simplified further as a perfect square factor because 26 is not a perfect square. However, if we apply the concept of expressing numbers as fractional powers, we can say that any number 'x' squared, written as x², is equivalent to the square root of 'x'. Thus, the square root of 26 can also be written as 26 to the power of 0.5 or 26⁰.⁵.
Expressing the concept mathematically, we can write the square root of any number 'x' as x to the power of 0.5, which is a helpful way to solve for unknown values in various equations. This idea is useful in scenarios where different roots of a number or expressions involving fractional exponents are to be calculated, and it is essential to remember that the square root is just another form of an exponent.
Which of the following lists some of the non-monetary factors that are taken into account when doing cost-benefit analysis
Answer:
A.
product being used by everyone
B.
the aesthetic value of nature
C.
identifying internal costs
D.
categorizing internal and external costs
Step-by-step explanation:
A student scored 98 and 87 on his first two quizzes. Use a compound inequality to find the possible values for a third quiz score that would give him an average between 90 and 95 inclusive
The range of possible scores for the third quiz that would yield an average score between 90 and 95 is 85 to 100, inclusive.
Explanation:The objective is to find the range of possible scores for the third quiz that would give an average score between 90 and 95, inclusive. As per the question, the sum of the student's first two quizzes is 98+87=185. If we denote the third quiz score as 'x', then the equation could be written as (185+x)/3 = average score. Considering the lower and upper limit of the average, we form two inequalities. For the lower limit, it's (185+x)/3 >= 90, which simplifies to x >= 270 - 185, thus x >= 85. For the upper limit, it's (185+x)/3 <= 95, which simplifies to x <= 285 - 185, thus x <= 100. So, the range of scores for the third quiz that would give an average between 90 and 95 inclusive is 85 <= x <= 100.
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If you quadruple the input of a function and the resulting output is one-fourth the original output, what may be true of the function? Check all that apply.
A. The function is inversely proportional.
B. The function is directly proportional.
C. More input results in less output.
D. More input results in more output.
Answer:
More input results in less output.
The function is inversely proportional.
Step-by-step explanation:
those two. other answer is completely wrong
If you quadruple the input of a function and the resulting output is one-fourth the original output, what may be true of the function? The correct options are A. The function is inversely proportional and C. More input results in less output.
In mathematical terms, let's consider the function as f(x), where x is the input, and f(x) is the output.
1. Option A: The function is inversely proportional.
If quadrupling the input (4x) leads to the output being one-fourth of the original output (1/4 f(x)), it implies that f(4x) = 1/4 f(x). Inverse proportionality means that as the input increases, the output decreases, and vice versa. In this case, increasing the input by a factor of 4 (4x) causes the output to reduce to one-fourth of its original value (1/4 f(x)), indicating an inverse relationship.
2. Option C: More input results in less output.
As mentioned earlier, quadrupling the input (4x) and obtaining an output of one-fourth the original (1/4 f(x)) demonstrates that increasing the input leads to a decrease in the output. When x increases, 4x (quadruple of x) will also increase, and as a result, f(4x) will be less than f(x). This aligns with the statement that more input results in less output.
It is important to understand the relationship between the input and output of a function. In this case, the given conditions indicate inverse proportionality and that increasing the input leads to a decrease in the output. Keep in mind that mathematics often deals with relationships between variables, and understanding such relationships can help solve various problems and make predictions about how a system behaves.
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Where can the perpendicular bisectors of the sides of a right triangle intersect?
I. inside the triangle
II. on the triangle
III. outside the triangle
A. I only
B. II only
C. I or II only
D. I, II, or II
please show your work
Evaluate the expression 2(8 - 4)^2 - 10 / 2
Answer:
27
Step-by-step explanation:
2(8 - 4)^2 - 10/2
Using the order PEMDAS, or parenthesis, exponents, multiplication, division, addition, subtraction, we will start with the parenthesis, or 8-4.
2(4)^2 - 10/2
Next is exponents.
2(16) - 10/2
And then multiplication.
32 - 10/2
Then division.
32 - 5
Finally, subtraction.
27
Therefore, the answer is 27.
I just need to know how do I find the domain for this function Y=-4x+2
When the outliers are removed, how does the mean change?
The mean remains the same.
The mean decreases by 2.
The mean increases by 2.
There are no outliers.
What is the sum of 12 and the quantity 8 times a number k is equal to 48? It was on my math homework, it hardly makes any sence to me, please help me, whats the answer?
The question is asking for the solution to the algebraic problem 12 + 8k = 48. By isolating 'k', it is found that the value of 'k' is 4.5.
Explanation:The problem presented here belongs to the branch of algebra. It is showing a relationship between the sum, multiplication, and is presented in a typical algebraic equation format. Let's break it down:
The sum of 12 and a number (which is 8 times k) is equal to 48. This can be written in equation form as:
12 + 8k = 48
To find the value of k, we need to isolate 'k' in the equation. First, subtract 12 from both sides of the equation:
8k = 48 - 12
Then, simplify the right side:
8k = 36
Finally, divide both sides by 8 to solve for k:
k = 36 / 8
So, k = 4.5.
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Suppose that y varies inversely with x, and y=0.2 when x=2. What is an equation for the inverse variation
(05.03)The equation shows the relationship between x and y:
y = −7x + 9
What is the slope of the equation?
−7
−2
7
9
Answer:
Option 1) -7
Step-by-step explanation:
Given : The equation shows the relationship between x and y : [tex]y=-7x+9[/tex]
To find : What is the slope of the equation?
Solution :
The general slope form of the equation is [tex]y=mx+b[/tex]
Where, m is the slope and b is the y-intercept.
Now, We compare the given equation with general form of the equation
[tex]y=-7x+9[/tex]
On comparing, m=-7 and b=9
So, The slope of the given equation is -7.
Therefore, Option 1 is correct.
The area of a rectangular wall of a barn is 300 square feet. its length is 10 feet longer than twice its width. find the length and width of the wall of the barn.
L
* W = 300 sq ft
Length is 10 ft greater than twice the width.
L = 2W + 10
Substituting
(2W+10)*W = 300
2W^2 + 10W = 300
Divide both sides by 2
W^2 + 5W = 150
W^2 + 5W - 150 = 0
Factor
(W +15)(W -10) = 0
Roots are W=-15 and W=10.
A negative width is impossible, so W=10
L = 2W + 10
L = 2(10) + 10
L = 30
length = 30 feet, width = 10 feet
Check: 30*10 = 300
To find the dimensions of the barn wall, we first expressed the given information as an equation using the formula for area. After simplifying and factoring the quadratic equation, we determined the width to be 10 feet and the length to be 30 feet.
Explanation:The question involves finding the length and width of a rectangular wall when given the area and a relationship between the length and width. We know the area of the wall is 300 square feet and that the length is 10 feet longer than twice the width. Let's denote the width as 'w' and the length as 'l'. The relationship between them can be expressed as l = 2w + 10. Using the formula for the area of a rectangle, which is A = l * w, we substitute the given area and the relationship between length and width to create an equation: 300 = (2w + 10) * w.
Solving this quadratic equation:
Expand the right side: 300 = 2w^2 + 10wMove all terms to one side: 2w^2 + 10w - 300 = 0Divide by 2 to simplify: w^2 + 5w - 150 = 0Factor the quadratic: (w + 15)(w - 10) = 0Find the roots: w = -15 or w = 10 (since width can't be negative, w = 10)Substitute w back into the relationship to find l: l = 2(10) + 10 = 30Therefore, the width of the wall is 10 feet, and the length is 30 feet.
The cross section of a square pyramid taken perpendicular to the base that passes through the top vertex produces which two-dimensional shape?
Note: Use all lowercase letters in your answer to receive credit.
Answer:
triangle.
Step-by-step explanation:
given: a square pyramid
to find : shape of cross section made when a plane perpendicular
to base and passes through top vertex.
when a plane cuts the square pyramid perpendicular to base and passes through top vertex we get a cross section made by its two equal slant height and side of the square.
therefore, we get a triangle or more specifically isosceles triangle.
picture is attached.
The amount of candy left in a Halloween bucket is given by the function A(t) = 50(0.8)t where t stands for the number of minutes the candy is available and A(t) stands for the amount of candy left at any given time. How much candy is there after five minutes?
50 pieces
40 pieces
16 pieces
200 pieces
Which combination of compounds will create a buffer solution? a weak acid and a weak base a weak acid and its conjugate base a strong acid and its conjugate base a strong acid and a strong base
Answer:
a weak acid and its conjugate base
Step-by-step explanation:
A Buffer solution is a solution that tends to keep the pH almost constant when small amounts of acids (H +) or bases (OH-) are added, therefore, they are very useful to reduce the impact of drastic changes in (H+) and (OH-) in processes that require a specific pH. They can be prepared by dissolving in water adequate amounts of a weak acid and a salt of its conjugate base, or a weak base and a salt of its conjugate acid.