Answer:
On Saturday, when 12 weeks passed
Step-by-step explanation:
Tom gets his hair cut every 3 weeks.
David gets his hair cut every 4 weeks.
Find the least common multiple of numbers 3 and 4:
[tex]3=3\\ \\4=2\cdot 2\\ \\LCM(3,4)=3\cdot 2\cdot 2=12[/tex]
This means that Tom and David will get their hair cut on the same day at 12th week (if the first week when they started has number 0).
You can think in another way:
Tom gets his hair cut every 3 weeks. He got his hair cut after 3 weeks, after 6 weeks, after 9 weeks, after 12 weeks passed.
David gets his hair cut every 4 weeks. He got his hair cut after 4 weeks, after 8 weeks, after 12 weeks passed.
The number of vibrations n n per second of a nylon guitar string varies directly with the square root of the tension T T and inversely with the length L L of the string. If the tension is 256 256 kilograms when the number of vibrations per second is 15 15 and the length is 0.6 0.6 meters, find the tension when the length is 0.3 0.3 meters and the number of vibrations is 12 12 .
The tension when the length is 0.3 meters and the number of vibrations is 12 is 40.96 Kg.
Given, that number of vibrations 'n' per second of a nylon guitar string varies directly with the square root of the tension 'T' and inversely with the length 'L' of the string.
Formulating the relation,
[tex]n \alpha \frac{\sqrt{T} }{L}[/tex]
[tex]n = K\frac{\sqrt{T} }{L}[/tex]
[tex]L \times n = K\sqrt{T}[/tex]
Substitute the values,
T = 256 Kg
n = 15
L = 0.6
[tex]0.6 \times 15 = K \times \sqrt{256}\\K = 9/16\\K = 0.5625\\[/tex]
Now when L = 0.3 and n = 12,
[tex]0.3 \times 12 = 0.5625 \times \sqrt{T}\\\sqrt{T} = 6.4\\ T = 40.96[/tex]
Therefore tension in the string is 40.96Kg .
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Subtract 7a+3a-9 from 5a-6a-4 write your answer in the standard polynomial form
Answer:
-11a +5
Step-by-step explanation:
(5a-6a-4) -(7a+3a-9) = a(5-6-7-3) -4+9 = -11a +5
Three married couples have purchased theater tickets and are seated in a row consisting of just six seats. If they take their seats in a completely random fashion (random order), what is the probability that Jim and Paula (husband and wife) sit in the two seats on the far left?
Answer:
The required probability is : [tex]\frac{1}{15}[/tex]
Step-by-step explanation:
Three married couples have purchased theater tickets and are seated in a row consisting of just six seats.
First we will check the total arrangements that is 6! ways.
6! = [tex]6\times5\times4\times3\times2\times1=720[/tex]
Jim and Paula can sit at far left in 2 ways and the remaining 4 in 4! ways,.
So, probability will be = [tex]2\times\frac{4!}{6!}[/tex]
= [tex]2\times\frac{24}{720}[/tex]
= [tex]\frac{48}{720}[/tex]
= [tex]\frac{1}{15}[/tex]
Krystal and 4 friends were going to the movies. Each ticket cost $12. They bought 2 buckets of popcorn at $4.50 each and then each person bought their own soda at $4.75 each. How much money did they spend in total?
Answer:
Step-by-step explanation:
First you would multiply 12 by four since each person has to have a ticket ($48) next you would multiply 4.50 by two since they bought two buckets of popcorn ($9) then you would multiply 4.75 by four since they each bought their own drink ($15) then you would all three of those totals together to get the final cost of everything ($72)
Hoped that answered your question!
Answer:
$92.75
Step-by-step explanation:
Krystal and 4 friends were going to the movies.
Total person = 5
The cost of each ticket = $12.00
They bought 2 buckets of popcorn at $4.50 each
They all bought soda at $4.75 each.
Total money they spent = (12 × 5) + (4.50 × 2) + (4.75 × 5)
= 60 + 9.00 + 23.75
= $92.75
They spent $92.75 in total.
A researcher would like to evaluate the claim that large doses of Vitamin C can help prevent the common cold. One group of participants is given 500 mg of Vitamin C (500mg per day) and a second group is given a placebo (sugar pill). The researcher records the number of colds each individual experiences during the 3-month winter season. a. Identify the dependent variable for this study.
b. Is the dependent variable discreet or continuous?
c. What scale of measurement (nominal, ordinal, interval, or ratio) is used to measure the dependent variable.
Answer:
a. The dependent variable for this study is the "number of colds each individual experiences during the 3-month winter season" because it depends on the doses of vitamins and placebo.
b. The dependent variable is discrete because the number of colds is like 1,2,3,... so on.
c. The scale of measurement of the dependent variable is Ratio because the number of cold experiences can be 0.
Please please help me out with this!!!!!!!
Answer:
when x= -7
h(-7) = (-7)^2 -5
= (-1)^2*(7)^2-5
= 1*49-5
= 49-5
=44
Therefore , h(-7)=5
Answer:
h(- 7) = 44
Step-by-step explanation:
To evaluate h(- 7) substitute x = - 7 into h(x), that is
h(- 7) = (- 7)² - 5 = 49 - 5 = 44
In the lab, robyn has two solutions that contain alcohol and is mixing them with each other. Soultion A is 6% alcohol and Solution Bis 20% alcohol. She uses 400 milliliters of Solution A. How many milliters of Solution B does she use, if the resulting mixture is a 12% alcohol solution?
Answer:
She needs 300 mililiters of Solution B so that the resulting mixture is a 12% alcohol
Step-by-step explanation:
In this problem you have to take into account that when you are talking about solutions you can't just add the porcentaje because each percentaje represent how many mililiters of the total of the solution are, in this case of alcohol.
So for solving this problem we are first going to establish the variables, because it si solved using a system of equations. In that way we are going to say that:
VT: represents the total volume of the resulting mixture of solution A and solution B at 12% of alcohol
VA: represent the mililiters of solution A, in the problem they say that this value it equals to 400 ml
VB: Represent the mililiters of solution B, that is what we need to find.
From now on, we are just going to use this variables but always keep in mind what does they represent.
VaT: Represent the total volume of alcohol in the resulting mixture solution at 12%
VaA: Represent the volume of alcohol in solution A
VaB: Represent the volume of alcohol in solution B
What comes next? we need to describe the equations from the information we have so that we create a system that can be solve after.
What can we first say about the total volume (VT)? That it is the result of the adition of solution A and B so we can state the following equation:
VT = VA + VB
As we know that VA equals to 400ml we can replace to get:
1) VT = 400ml + VB
But what happens with the other information we have? We now need to take into account the concentration of each solution, so as we can´t add the percentages of alcohol but we can add the volumes of alcohol in each solution we can say that:
2) VaT = VaA + VaB
Now we are going to start to reduce the number of variables changing does that we don't know for those that we do to solve the problem, starting first with the volumes of alcohol.
A porcentaje represents a part of the total volume so to know how much alcohol does each of the solutions has we must do rules of three so that we can leave all the variables in terms of VT, VA and VB:
- VT → 100%
VaT → 12%
VaT = [tex]\frac{12.VT}{100}[/tex] = 0,12.VT
- VA → 100% In this case we know that VA = 400
VaA → 6%
VaA = [tex]\frac{6x400}{100}[/tex]
VaA = [tex]\frac{6x4}{1}[/tex]
VaA=24ml
VaB → 100%
VaB → 20%
VaB = [tex]\frac{20.VB}{100}[/tex] = 0,20.VB
Now we are going to replace this information in the equation number two to get the following expresion:
3) 0,12.VT = 24ml + 0.20VB
At this point we have a system of two equations (remember equation 1) with two variables VT and VB so we are going to do some algebra to clear the variables.
- Replace VT of equation 1 in equation 3
Remeber that VT = 400ml + VB so now we are going to put this information in equation 3) 0,12.VT = 24ml + 0.20VB to get:
4) 0,12 (400ml + VB) = 24ml + 0.20VB
- Use the distributive operation to solve the parentesis
0,12x400ml + 0.12.VB = 24ml + 0.20VB
5) 48ml + 0.12VB = 24ml + 0.20VB
- Organize the information in one side the ones with variables and in the other side just numbers:
0.12VB - 0.20VB = 24ml - 48ml
-0.08 VB = -24ml (do the operations)
As it is a minus in both sides we can divide it and cancel the sign to have:
0,08VB = 24 ml (to clear VB, we must divide in both sides by 0,08)
[tex]\frac{0,08.VB}{0,08} = \frac{24ml}{0.08}[/tex] after doing the division we get:
VB = 300mlwith this you already get the answer of how many mililiters of solution B does she use to get a resulting mixture of 12%.
To verficate we must do the following process:
VT = 300ml + 400ml = 700ml
The total volume of the solution is 700 ml of which 12% equals to:
VaT = 0,12. VT = 0,12(700ml) = 84 ml
VaA = 24ml (Volume of alcohol in solution A, we already calculated)
VaB = 0,20 VB = 0,20(300ml) = 60ml (Volume of alcohol in solution B)
VaT = VaA + VaB (Prove the equation with the values we obtain)
84ml = 24ml + 60ml
84 ml = 84ml
As the equation is the same we have verificated our result.
Robyn needs to use 300 mL of Solution B to achieve a 12% alcohol solution when mixed with 400 mL of Solution A. This was calculated by setting up an equation based on the concentrations and solving for the quantity of Solution B.
To solve this problem, we need to find out how much Solution B (20% alcohol) Robyn needs to add to 400 mL of Solution A (6% alcohol) to get a 12% alcohol solution.
Step-by-Step Solution
First, let's set up the equation assuming she uses x milliliters of Solution B:
Since Solution A is 6% alcohol, in 400 mL of Solution A, there is:
0.06 * 400 = 24 mL of alcoholNext, for Solution B, which is 20% alcohol, the amount of alcohol in x mL of Solution B is:
0.20 * x = 0.2x mL of alcoholWe need the resulting mixture to have a 12% concentration. The total volume of the mixture will be:
400 + x mLThe total amount of alcohol in this mixture will be 12% of the total volume:
0.12 * (400 + x) = 24 + 0.2xSimplify and solve for x:
0.12 * 400 + 0.12 * x = 24 + 0.2x48 + 0.12x = 24 + 0.2x24 = 0.08xx = 300So, Robyn needs to use 300 mL of Solution B.
In the game of billiards called 14.1, players lose points if they receive penalties. Find the difference in the scores of the winner with 50 points and the opponent with –17 points.
Answer:
67 points
Step-by-step explanation:
To find the difference between the winning and losing scores, subtract the losing score from the winning score:
50 -(-17) = 50 +17 = 67
The difference is 67 points.
Which pairs of triangles can be shown to be congruent using rigid motions?
Select Congruent or Not Congruent for each pair of triangles.
Congruent Not Congruent
△ABC and △DEF
△ABC and △JKL
△ABC and △QRS
△JKL and △DEF
△JKL and △QRS
△QRS and △DEF
Did you ever get the answer for this?
Answer:
The order is Congruent, not congruent, not congruent, not congruent,congruent, not congruent
Step-by-step explanation:
-
PLEASE HELP ASAP!!! CORRECT ANSWERS ONLY PLEASE!!! THIS IS THE LAST DAY TO COMPLETE THIS ASSIGNMENT AND I DESPERATELY NEED TO FINISH THIS ASSIGNMENT WITH AN 100%.
Answer:
c. 7,999,999
Step-by-step explanation:
The number of possible phone numbers is the product of the number of possible digits in each position, less the excluded number:
8·10·10 · 10·10·10·10 - 1 = 8,000,000 -1 = 7,999,999
Solve for x.
1+|2+x|=9
x = 4 or x=−8
x = 5 or x=−9
x = 6 or x=−10
x = 7 or x=−11
Answer:
Step-by-step explanation:
1+|2+x|=9
1+|2+x| -1 =9-1
|2+x| = 8
2+x = 8 or 2+x = -8
x=6 or x= -10
Answer:
c
Step-by-step explanation:
i took the k12 test
At Central Online High School, 4510045100 of the students have a dog, 3010030100 have a cat, and 1810018100 have both a dog and a cat. What is the probability that a student who has a dog also has a cat? Enter your answer as a reduced fraction with the / symbol, like this: 3/14
Answer: [tex]\dfrac{2}{5}[/tex]
Step-by-step explanation:
Given : The proportion of students have a dog : [tex]P(D)=\dfrac{45}{100}[/tex]
The proportion of students have a cat : [tex]P(C)=\dfrac{30}{100}[/tex]
The proportion of students have both a dog and a cat : [tex]P(C\cap D)=\dfrac{18}{100}[/tex]
Now, the conditional probability that a student who has a dog also has a cat will be :-
[tex]P(C|D)=\dfrac{P(C\cap D)}{P(D)}\\\\\\\Rightarrow\ P(C|D)=\dfrac{\dfrac{18}{100}}{\dfrac{45}{100}}\\\\\\\Rightarrow\ P(C|D)=\dfrac{18}{45}=\dfrac{2}{5}[/tex]
Hence, the probability that a student who has a dog also has a cat = [tex]\dfrac{2}{5}[/tex]
Answer:
3/5
Step-by-step explanation: I just did the test and got it right. This was after I tried 2/5 and got it wrong.
Barack is solving a problem and his final units need to be in square inches. His current answer is 8 feet squared. What is the equivalent measurement in square inches
Answer:
1152 in²
Step-by-step explanation:
Barack can change the units using a suitable multiplier. It will have a numerator equal to its denominator, and will have units that cancel the square feet and give square inches:
8 ft² × ((12 in)/(1 ft))² = 8×12×12 in² = 1192 in²
_____
12 in = 1 ft . . . so numerator is equal to denominator
The dimensions (width and length) of room1 have been read into two variables : width1 and length1. The dimensions of room2 have been read into two other variables : width2 and length2. Write a single expression whose value is the total area of the two rooms.
To calculate the total area of two rectangular rooms, we multiply the length by the width of each room separately and then add the two results together. The formula used is Total Area = (width1 × length1) + (width2 × length2). This demonstrates a practical application of geometry in everyday situations.
Explanation:The student's question is about calculating the total area of two rectangular rooms given their lengths and widths. To find the area of a rectangle, we multiply its length by its width. Therefore, to find the total area of both rooms, we calculate the area of each room separately and then add the two areas together. The formula for the total area of the two rooms would be:
Total Area = (width1 × length1) + (width2 × length2)
By inserting the specific values for width1, length1, width2, and length2 into this formula, we can calculate the exact total area covered by both rooms.
This approach utilizes basic principles of geometry to combine the areas of the two spaces, providing a clear example of how mathematical concepts are applied in practical situations like room measurements.
A geyser Erupts every fourth day . Another geyser erupts every sixth day. Today both geysers erupted. In how many days will both geysers erupt on the same day again?
In 12 days both geysers erupt on the same day again
What is Least common multiple?The smallest number that is a multiple of each of two or more numbers.
Given:
A geyser Erupts every fourth day.
Another geyser erupts every sixth day.
so, to find how many days will both geysers erupt on the same day again
we have to find the LCM of 4 and 6
So, 4 = 2*2
6= 2*3
LCM (4, 6) =2*2*3 = 12
Hence, 12 days both geysers erupt on the same day again.
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In an editorial, the Poughkeepsie Journal printed this statement: "The median price minus the price exactly in between the highest and lowest minus..."Does this statement correctly describe the median? Why or why not?Choose the correct answer below. A.Yes. It correctly describes the median. B.No. It describes the midrange, not the median. C.No. It describes the mean, not the median. D.No. It describes the mode, not the median.
Answer:
B.No. It describes the midrange, not the median.
Step-by-step explanation:
Further,
The range is the difference between the least and largest value of data. It measures skewness using all data points.
Mean is calculated as the ratio of the sum of all the observations to the total number of observations.
Median is the middle value of the data after arranging them in ascending order.
11 1/2 and 13 3/4 is?
Malik’s recipe for 4 servings of a certain dish requires 3/2 cups of pasta. According to this recipe, what is the number of cups of pasta that Malik will use the next time he prepares this dish?(1) The next time he prepares this dish, Malik will make half as many servings as he did the last time he prepared the dish.(2) Malik used 6 cups of pasta the last time he prepared this dish.What's the best way to determine which statement is sufficient?
Answer:
1)3/4 cups of pasta
2)4
Step-by-step explanation:
1) as malik I use half the cups better divide the initial amount 3/4 by 2
C=[tex]\frac{3}{2} .\frac{1}{2} =3/4[/tex]
2)
As Malik use 6 cups, and each plate needs 3/2 cups, we divide 6 by 3/2
C=[tex]\frac{ \frac{6}{1} }{ \frac{3}{2} }=\frac{6.2}{3} =\frac{12}{3} =4[/tex]
On a coordinate plane, a curved line with minimum values of (negative 2, 0) and (1.05, negative 41), and a maximum value of (negative 0.5, 5), crosses the x-axis at (negative 2, 0), (0, 0), and (1.5, 0), and crosses the y-axis at (0, 0). Which statement is true about the end behavior of the graphed function? As the x-values go to positive infinity, the function’s values go to positive infinity. As the x-values go to zero, the function’s values go to positive infinity. As the x-values go to negative infinity, the function’s values are equal to zero. As the x-values go to negative infinity, the function’s values go to negative infinity.
Answer:
As the x-values go to positive infinity, the function’s values go to positive infinity.
Step-by-step explanation:
With the information given you can plot a rough graph (see attachment)
As the x-values go to positive infinity, the function’s values go to positive infinity. -> True
As the x-values go to zero, the function’s values go to positive infinity. -> False, x = 0 is between a maximum and a minimum
As the x-values go to negative infinity, the function’s values are equal to zero. -> False x-values go to negative infinity, the function's values go to positive infinite
As the x-values go to negative infinity, the function’s values go to negative infinity. False x-values go to negative infinity, the function's values go to positive infinite
Answer: As the x-values go to positive infinity, the function’s values go to positive infinity.
Step-by-step explanation:
just did this
x-3y=6
x=3y+4
solve for x and y
Answer:
1) x = 6, y = -2 + 1/3x
2)
Step-by-step explanation:
1) x-3y=6
-3y=6-x, 6-x/-3y
y = -2 + 1/3x
x - 3(-2+1/3x) = 6
x - 6 + x = 6
2x =12
x = 6
2) x=3y+4
-3y = -x+4
y = -x/-3 +4/-3
y = 1/3x + -4/3
x = 3(1/3x + -4/3)
I am unsure about x on number two...
Use the graphs of f and g to solve Exercises 87, 88, and 89.
87. Find the domain of f + g.
88. Find the domain of [tex]\frac{f}{g}[/tex].
89. Graph f + g.
(You can just explain how to graph it for #89.)
Answers and explanations:
87. The domain of added functions includes the restrictions of both. So the range of the added function in this question is [-4, 3]
88. When finding the domain of a divided function we do the same as adding, but with an extra rule: g can't equal zero. So for this question the domain is (-4, 3)
89. To graph f + g you add the y-values for each x-value. I added a picture to help explain this one!
Answer:
87. [-4, 3]
88. (-4, 3)
89. See Attachment
General Formulas and Concepts:
Algebra I
Reading a Cartesian PlaneCoordinates (x, y)FunctionsFunction NotationDomains - the set of x-values that can be inputted into a function f(x)[Interval Notation] - Brackets are inclusive, (Parenthesis) are exclusiveStep-by-step explanation:
*Notes:
When adding functions, the domain of the new function is defined as the intersections of the domains of f and gWhen dividing functions, the domain of the new function is defined as the intersections of the domains of f and g except for the points where g(x) = 0 (this is because we cannot divide by 0)Step 1: Define
Identify the domains of each function.
Domain of f(x): [-4, 3]
Domain of g(x): [-5, 5]
Step 2: Find 87.
Determine the x-values for each function that overlap/intersect.
f(x) and g(x) have intersect from -4 to 3.
Domain f + g: [-4, 3]
Step 3: Find 88.
Determine the x-values for which g(x) = 0.
The function g(x) equals 0 at x = -4 and x = 3. Therefore, these x-values are excluded in the domain.
Domain of f/g: (-4, 3)
Step 4: Find 89.
To draw a graph of the f + g, we must combine the y-values for each x-value domain in a t-chart and plot by hand.
x | f(x) x | g(x) x | f + g
-4 5 -4 0 -4 5
-3 4 -3 1 -3 5
-2 3 -2 2 -2 5
-1 3 -1 2 -1 5
0 2 0 1 0 3
1 1 1 1 1 2
2 -1 2 1 2 0
3 -3 3 0 3 -3
If 3x-y=123x−y=123, x, minus, y, equals, 12, what is the value of \dfrac{8^x}{2^y} 2 y 8 x start fraction, 8, start superscript, x, end superscript, divided by, 2, start superscript, y, end superscript, end fraction ?
Answer:
[tex]2^{12}=4,096[/tex]
Step-by-step explanation:
You know that [tex]3x-y=12[/tex] and have to find
[tex]\dfrac{8^x}{2^y}[/tex]
Use the main properties of exponents:
1. [tex](a^m)^n=a^{m\cdot n}[/tex]
2. [tex]\dfrac{a^m}{a^n}=a^{m-n}[/tex]
Note that
[tex]8=2^3,[/tex]
then
[tex]7^x=(2^3)^x=2^{3\cdot x}=2^{3x}[/tex]
Now
[tex]\dfrac{8^x}{2^y}=\dfrac{2^{3x}}{2^y}=2^{3x-y}[/tex]
Since [tex]3x-y=12,[/tex] then [tex]2^{3x-y}=2^{12}=4,096[/tex]
Final answer:
The value of the expression [tex]\(\frac{8^x}{2^y}\)[/tex] given the equation 3x - y = 12 is 4096, since 8 can be expressed as 2^3 and the properties of exponents allow us to simplify the expression to 2^12.
Explanation:
The question involves determining the value of a mathematical expression given a specific equation.
Given the equation 3x - y = 12, we want to find the value of [tex]\(\frac{8^x}{2^y}\)[/tex].
This can be done by recognizing that 8 is a power of 2, specifically 8 = 2^3.
Thus, [tex]\(8^x = (2^3)^x = 2^{3x}\)[/tex]. Substituting back into the original expression, we get [tex]\(\frac{2^{3x}}{2^y}\)[/tex].
Using the properties of exponents, when dividing terms with the same base, we subtract the exponents: [tex]\(2^{3x - y}\)[/tex].
Since we know 3x - y = 12, we substitute 12 in place of 3x - y, giving us 2^12.
Therefore, the answer is 2^{12}, or 4096.
Complete column 3 in the table order the masses from greater to least with a rank of 1 for the greater mass.
Answer:
The answer to your question is:
Step-by-step explanation:
1.- 1.09 In the table the order will be
2.- 0.99 1.- 6
3.- 0.919 2.- 10
4.- 0.66 3.- 7
5.- 0.647 4.- 11
6.- 0.394 5.- 5
7.- 0.298 6.- 4
8.- 0.256 7.- 9
9.- 0.23 8.- 8
10.- 0.136 9.- 1
11.- 0.112 10.- 2 11.- 3
Study designed 1: two hundred student were selected at random from those enrolled at large college in California each student in the simple was asked whether he or she ate sweet potatoes more than once in a typical week
The survey design described is a statistical study on college student eating habits, specifically focusing on sweet potato consumption, to obtain quantitative data about behaviour patterns.
Explanation:The student in question is surveying to gather data on a particular behavioural pattern, in this case, the frequency of sweet potato consumption among college students. To achieve results that reflect the larger student body of the college, a random sample of 200 students is selected to answer the survey question. Completing the survey comprises the collection of quantitative data, which can later be analyzed statistically. Surveys are a common method in statistics to investigate various questions and hypotheses. For example, a survey similar to this might be performed to evaluate the number of movies students watch in a week or determine the daily average study time for freshmen students. The effectiveness of the survey method relies on a representative sample accurately reflecting the population of interest.
Show that the points A (-3, 2), B (-6, 4) and C (1, 8) are vertices of a right triangle.
Answer:
See below.
Step-by-step explanation:
For the triangle to be a right triangle there must be a pair adjacent sides which are at right angles to each other - that is whose slope product = -1.
Slope of AB = (4-2)/(-6- -3) = -2/3.
Slope of BC = (8-4)/ (1 - - 6) = 2/7
Slope of AC = (8-2) / (1 - -3) = 6/4 = 3/2.
Now 3/2 * -2/3 = -1 so sides AB and AC are at right angles and the 3 points are the vertices of a right triangle.
To confirm if the points A (-3, 2), B (-6, 4) and C (1, 8) are vertices of a right triangle, we use the Pythagorean theorem. After calculating the distances between each pair of points, we found that the square of the length of the longest side equals the sum of the squares of the lengths of the other two sides, proving that they form a right triangle.
Explanation:To show that the points A (-3, 2), B (-6, 4), and C (1, 8) are vertices of a right triangle, we need to check if the square of the length of the longest side (hypotenuse) is equal to the sum of the squares of the lengths of the other two sides. This is known as the Pythagorean theorem. First, compute the distances between each pair of points using the distance formula:
AB = sqrt[(4-2)^2 + (-6-(-3))^2] = sqrt[2^2 + (-3)^2] = sqrt[4 + 9] = sqrt[13]
BC = sqrt[(8-4)^2 + (1-(-6))^2] = sqrt[4^2 + 7^2] = sqrt[16 + 49] = sqrt[65]
AC = sqrt[(8-2)^2 + (1-(-3))^2] = sqrt[6^2 + 4^2] = sqrt[36 + 16] = sqrt[52]
BC is the longest side, so we need to check if BC^2 = AB^2 + AC^2. Calculating, we find that 65 = 13 + 52, which is true. Therefore, points A, B, and C are vertices of a right triangle.
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Suppose that, in some distant part of the universe, there is a star with four orbiting planets . One planet makes a trip around the star in 6 earth years , the second planet takes 9 earth years, the third takes 15 earth years and the fourth takes 18 earth years . Suppose that at some time the planets are lined up. How many years will it take for them to all line up
Answer: 90 Earth years.
Step-by-step explanation:
Analizing the information provided in the exercise, you need to find the Least Common Multiple (LCM) of the given numbers.
You can follow these steps:
1. You must descompose 6, 9, 15 and 18 into their prime factors:
[tex]6=2*3\\\\9=3*3=3^2\\\\15=3*5\\\\18=2*3*3=2*3^2[/tex]
2. Finally, you need to choose the commons and non commons with their greatest exponents and multiply them. Then you get:
[tex]L.C.M=2*3^2*5=2*9*5\\\\L.C.M=90[/tex]
Therefore, it will take 90 Earth years for them to all line up.
How would I find r?
Answer:
r = 29
Step-by-step explanation:
We assume your diagram is showing ...
CD = CB = rAB = x = 29To find r, use the relationship between the side lengths of the triangle.
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In a 30°-60°-90° triangle, the ratio of shortest to longest sides is 1 : 2. Therefore, we have ...
CD/CA = r/(r+29) = 1/2
2r = r +29 . . . . . . multiply by 2(r+29)
r = 29 . . . . . . . . . .subtract r
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The knowledge of 30°-60°-90° triangle relationships can come from any of several sources. One such source is consideration of what happens when you cut an equilateral triangle along its altitude. (The short side is half the long side of the resulting 30-60-90 triangle.)
Another source is the sine ratio of the 30° angle (trigonometry). Sin(30°) = CD/CA = 1/2.
Need help with Geometric Sequence Please and Explanation
(a⁷ - a⁴) ÷ (a³ + a²)
Answer:
a^4 - a^3 + a^2 - 2a - (2)/(a + 1)
The simplified form of (a⁷ - a⁴) ÷ (a³ + a²) is a³ - a⁴.
The given expression is: (a⁷ - a⁴) ÷ (a³ + a²)
To simplify it:
Factor out common terms: a⁴(a³ - 1) / a²(a + 1)
Cancel out common factors: a⁴(a³ - 1) / a²(a + 1) = a³ - a⁴
Therefore, the simplified form of (a⁷ - a⁴) ÷ (a³ + a²) is a³ - a⁴.
The half-life of radioactive cobalt is 5.27 years. Suppose that a nuclear accident has left the level of cobalt radiation in a certain region at 100 times the level acceptable for human habitation. How long will it be until the region is again habitable?
Answer:
35 years
Step-by-step explanation:
The proportion p that remains after y years is ...
p = (1/2)^(y/5.27)
In order for 1/100 to remain (the level decays from 100 times to 1 times), we have ...
.01 = .5^(y/5.27)
log(0.01) = y/5.27·log(0.5) . . . take logs
y = 5.27·log(0.01)/log(0.5) ≈ 35.01 ≈ 35 . . . . years
Given that the radioactive isotope cobalt-60 has a half-life of 5.27 years, it will take around 36.89 years for it to decay to a level that is safe for human habitation, assuming the initial level is 100 times the safe limit.
Explanation:The subject of this question is the half-life of radioactive substances, specifically cobalt-60. The half-life is the time it takes for half of the radioactive atoms to decay. Cobalt-60 has a half-life of 5.27 years. This implies that 50% of the cobalt-60 will remain after 5.27 years, 25% will remain after 10.54 years (two half-lives), 12.5% will remain after 15.81 years (three half-lives), and so forth.
Understanding this concept, we can calculate when the region will be habitable. Currently, the radiation level is 100 times the acceptable limit. We need to determine how many half-lives it will take for the radiation level to reduce to 1% i.e., 1/100 of its original level. Since each half-life reduces the radiation by half, this is equivalent to finding when the cobalt-60 will be reduced to a fraction of 1/(2^n), where 'n' is the number of half-lives. Using n = 7 gives us 1/128, which is less than 1/100 (it will need to be less to be within safe levels).
So, it will take approximately 7 half-lives for the area to become safe for human habitation again. Since the half-life of cobalt-60 is 5.27 years, it will therefore take about 7 * 5.27 = 36.89 years for the region to become habitable once more.
Learn more about Half-life here:https://brainly.com/question/24710827
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