The points A, B, C cannot be both collinear and form an equilateral triangle simultaneously. This is proven by applying the Pythagorean theorem and trigonometry laws for triangles, which show that the distances and angles do not match the requirements for an equilateral triangle if the points are collinear (on a straight line).
Explanation:
Given that points A,B,C are collinear and you've stated a variety of scenarios about the positioning of these points. Combining all these restrictions, however, leads to a contradiction. An equilateral triangle's points cannot all be collinear as you've mentioned in your last point. A collinear set of points exists on the same straight line. The points of an equilateral triangle do not fall on the same line. Therefore, it's impossible for points A,B,C to be collinear and also form an equilateral triangle ABC.
Applying the Pythagorean theorem to the positions of these points, we see that the distances on the sides of the triangle will not be equivalent if they are positioned in a straight line. Similarly, with the use of trigonometry laws for triangles, such as the ones for vector equations, the same result is found. The vector equations for collinear points lack the trigonometric components found in equilateral triangles.
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At the end of a party, 3/4 cup of dip is left. Jim divides 4/5 of the leftover dip equally between 2 friends. How much dip does each friend get?
Final answer:
Each friend gets 3/10 cup of dip.
Explanation:
To calculate how much dip each friend gets, we first need to find the amount of dip Jim had after dividing.
Since 3/4 cup of dip was left and Jim divided 4/5 of that dip, we can calculate it as follows:
Amount of dip Jim divided = (3/4) * (4/5) = 3/5 cup
Since there are 2 friends, we divide the amount of dip Jim divided equally:
Amount of dip each friend gets = (3/5) / 2 = 3/10 cup
Therefore, each friend gets 3/10 cup of dip.
If a man runs for a nd hour and a half at 8 miles an hour due South; and he continues south on a bus traveling at 55 miles an hour, for 24 minutes. How far did he travel
he ran 8 * 1.5 = 12 miles
the bus went : 55 * 24/60 = 22 miles
12 +22 = 34 miles total
evaluate m+n for m=5 and n=4
Round 3.4 to the nearest gallons please.
Relationship A has a greater rate than Relationship B. These numbers represent Relationship B. Hours worked: ( 2 ) ( 4 ) ( 5 ) ( 8 ). Amount paid: ( 30.40 ) ( 60.80 ) ( 76 ) (121.60 ). Which equation could represent Relationship A? Hours worked is represented by x and Amount paid is represented by y. Select each correct answer.
( y = 14.9x) ( y = 16.4x ) ( y = 15.2x ) ( y = 15.4x )
Answer:
I took the test and. this is what I got
Step-by-step explanation:
Shelly has a cell phone plant that cost $9.99 per month plus $0.05 per minute. Her total bill for the month is $25.59. Write an equation and solve the equation to find how many minutes she used for the month
Last year a company made a net profit of $20,000 on sales of $1,000,000. This year they made a net profit of $40,000 on sales of $1,000,000. When talking to the shareholders, they claimed that their profit increased by 100%, and asked for a bonus for doing so well. When talking to the union about a possible wage raise, they claimed that their profit only increased by 2%, which hasn't even kept up with inflation. How did they determine these figures? Which one do you think is correct?
A car travels at a constant speed. What is the car's speed between checkpoints, expressed as a unit rate? Use the information given in the picture.
Answer:
The unit rate is 44 miles per hour.
Step-by-step explanation:
The difference between both the checkpoints is given by:
[tex]208-120=88[/tex] miles driven
Time taken to travel 88 miles = [tex]3-1=2[/tex] hours
As the car travels at a constant speed, so we get 88 miles driven in 2 hours.
Hence, per hour distance covered is = [tex]\frac{88}{2}=44[/tex] miles per hour.
A company rents out 15 food booths and 20 game booths at the county fair. The fee for a food booth is $100 plus $5 per day. The fee for a game booth is $50 plus $7 per day. The fair lasts for 'd' days, and all the booths are rented for the entire time. Write and simplify an expression for the amount in dollars the the company is paid.
Find the value of X
how do I find the value of it
To find the value of x, we use the quadratic formula on the equation x² + 0.00088x - 0.000484 = 0, resulting in two possible values for x, with the positive value being the valid solution in real-life contexts. In chemical equilibrium problems, the positive value is used to further calculate important quantities like pH.
Explanation:To find the value of x, we use the quadratic formula. Given the equation x² + 0.00088x - 0.000484 = 0, we can calculate the values for x that satisfy the equation. After applying the quadratic formula, we find two possible values for x, which are x = -0.0024 or x = 0.00139. However, in a real-life context, such as a chemical equilibrium problem, a negative concentration does not make sense. Therefore, we can disregard the negative value and conclude that x actually equals 0.00139.
In problems where x represents a concentration, once we've determined x = 0.0021, we could use this to calculate the concentration of H3O+, which would allow us to find the pH of the solution by plugging this concentration into the pH equation.
When defining what x represents, such as in a statistical context where we might be interested in the number of students who do their homework on time, x would be defined differently. It is essential to understand the context of a problem to accurately determine what x signifies and how to solve for it.
how do phospholipid molecules lead to the compartmentalization of a cell?
Elijah is planning a picnic. He will invite twice as many boys as girls. If he invites 18 people, how many boys and how many girls will get invitations?
The question is about ratios. Based on the condition, Elijah invited twice as many boys as girls which makes up a total of 18 people. We find out that Elijah invited 6 girls and 12 boys.
Explanation:This is a mathematical problem dealing with ratios. From the question, we know that Elijah plans to invite twice as many boys as girls, and the total number of guests will be 18 people.
Assume the number of girls Elijah is inviting is x. Therefore, the boys will be 2x (twice the number of girls).
Now, we form an equation which is the total number of people: x (girls) + 2x (boys) = 18. Solving for x, we get x = 6. So Elijah is inviting 6 girls and 2*6 = 12 boys.
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calculate the rise and run to find the slope of each line
Question 15
Leo bought a bulldozer for $63,103. The value of the bulldozer depreciated at a constant rate per year. The table below shows the value of the bulldozer after the first and second years:
Year
1
2
Value (in dollars)
58,054.76
53,410.38
Which function best represents the value of the bulldozer after t years?
f(t) = 58,054.76(0.92)t
f(t) = 63,103(0.08)t
f(t) = 63,103(0.92)t
f(t) = 58,054.76(0.08)t
Answer:
c f(t) = 63,103(0.92)t
Step-by-step explanation:
Identify the type of transformation given the rule R(x, y) = (–x. –y). a. horizontal translation c. reflection across the x- or y-axis b. vertical translation d. 180° rotation
What is the slope of the line on the graph?
Enter your answer in the box.
Answer:
-2
Step-by-step explanation:
i took the test
The gazelle football team made 5 plays, gaining 4 yards on each play . then they made 4 plays, loosing 10 yards on each play . What was the total change in their positions from where they started ?
Final answer:
The gazelle football team gained 20 yards initially and then lost 40 yards, resulting in a total change in position of -20 yards, ending up 20 yards behind their starting point.
Explanation:
The total change in position for the gazelle football team is determined by the yardage gained and lost during the different plays. Initially, the team gains 4 yards on each of 5 plays, which totals to 4 yards/play × 5 plays = 20 yards gained.
Then, the team loses 10 yards on each of 4 plays, which totals to 10 yards/play × 4 plays = 40 yards lost. To find the overall change in position, we subtract the yardage lost from the yardage gained: 20 yards gained - 40 yards lost = -20 yards.
Therefore, the total change in position from where they started is -20 yards, meaning that they ended up 20 yards behind where they started.
how many solutions does the equation have? 6x+4x-6=24+9x
What is greater than 0.1 and less than 0.2.
Answer:
0.2 > 0.15 > 0.1
Step-by-step explanation:
Equation 13.00 x 0.53
find the error and the correct answer
thx
Answer:
Only 6x6. It equals 36. This is the only thing I found was incorrect. Practice Multiplication!
Step-by-step explanation:
6x5= 30
30+6 = 36
For the proportional relationship y = -5x, what is the ratio of vertical change to horizontal change? Will the graph of the line increase or decrease? A. -51 The graph increases from left to right. B. -50 The graph increases from left to right. C. -51 The graph decreases from left to right. D. -50 The graph decreases from left to right.
how many hours is it to 11:00 to 3:30
Which answer shows this equation in standard form?
7 – 3(x – y) = –5x + 2
A.
–8x + 3y = –5
B.
–2x – 3y = 5
C.
2x + 3y = –5
D.
2x – 3y = –5
Aiden weighs 39 pounds less than his older brother, Jacob. Jacob weighs more than 100 pounds. what could be the weight of the Two brothers?
We can determine that Jacob's weight is any number greater than 100 pounds, and Aiden weighs 39 pounds less than Jacob. Without an exact weight for Jacob, we cannot provide precise weights, only a possible range for both brothers.
To solve the question regarding Aiden and Jacob's weight, we can set up a simple algebraic equation. If Aiden weighs 39 pounds less than Jacob, and Jacob weighs more than 100 pounds, we can use variables to represent their weights.
Let's let J represent Jacob's weight. Therefore, Aiden's weight is J - 39 pounds. We're told that Jacob weighs more than 100 pounds, so J > 100.
For example, if Jacob weighed 110 pounds (which is more than 100 pounds), then Aiden would weigh 110 - 39 = 71 pounds. However, since we don't have an exact weight for Jacob, we cannot determine the exact weights but we can provide a range. Jacob's weight is any number greater than 100 and Aiden's weight is always 39 pounds less than Jacob's weight.
A fraction with fractions in either the numerator or the denominator or both is called a _____.
mixed fraction
complex fraction
compound fraction
parallel fraction
Answer: Parallel fractions
Step-by-step explanation:
The Vega family has 3 year cellphone contract. Javier Vega says that the family gets a total of 3x10(4) minutes of talk time to share during the three years. Is havier correct
Vega says that the family gets a total of 120 minutes of talk time to share during the three years.
What are Arithmetic operations?Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions. The operator that performs the arithmetic operation is called the arithmetic operator.
We have been given that Vegas has a three-year mobile contract. According to Javier Vega, the family receives a total of 3 × 10(4) minutes of talk time to share over the course of three years.
As per the given information, the solution would be as:
⇒ 3 × 10(4)
⇒ 40(3)
⇒ 120
That is how the Vega family has 120 minutes left on their three-year contracts.
Therefore, Vega says that the family gets a total of 120 minutes of talk time to share during the three years.
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are the given lines parallel y=-5 y=3 ? how do you know? ASAP TY
The lines y = -5 and y = 3 are parallel because they are both horizontal lines with a slope of 0. This is the same case with lines Y2 and Y3 from the reference provided; they are parallel because they share the same slope.
Explanation:The lines y = -5 and y = 3 are indeed parallel lines. This is because they are both horizontal lines, which means their slopes are both 0. In mathematics, two lines are parallel if and only if their slopes are equal. In the case of these two lines, since they do not have a variable component (x), they are straight horizontal lines, meaning their slopes are equal and thus, they are parallel.
To illustrate this, contrast it with the given lines in the reference; line Y2 = -173.5+ 4.83x − 2(16.4), and line Y3 = -173.5+ 4.83x + 2(16.4), whereby y = -173.5+ 4.83x is the line of best fit. Y2 and Y3 have the same slope, which shows these lines are also parallel as they share the same inclination and distance apart at all points.
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What is the value of n ?
3 outside angles = 360
n = 360 - 133-142
n = 85
Find the quotient 42j^4 k^2÷(-3j^3 k)
Answer:
[tex]-14jk[/tex]
Step-by-step explanation:
We are asked to find the quotient of our given expression [tex]42j^4k^2\div -3j^3k[/tex]
First of all, we will write our given problem as a fraction.
[tex]\frac{42j^4k^2}{-3j^3k}[/tex]
Using exponent property [tex]\frac{a^m}{a^n}=a^{m-n}[/tex], we will get:
[tex]\frac{42}{-3}(j^{4-3}k^{2-1})[/tex]
[tex]-14j^{1}k^{1}[/tex]
[tex]-14jk[/tex]
Therefore, the quotient of our given problem is [tex]-14jk[/tex].