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Given: The line from 0 to 1 is divided in 6 parts and has two points. A and B marked on it.
To find:The fraction for point A and B.
Explanation: The length from 0 to 1 is divided into 6 parts.
Therefore, the length of one part will be 1/6.
The point A is markes at the second division.
Since, 1 division= 1/6
therefore, 2 divisions will be = 2x(1/6)
Therefore, the point A will correspond to the fraction
[tex]\begin{gathered} A=2\times\frac{1}{6} \\ =\frac{2}{6} \\ =\frac{1}{3} \end{gathered}[/tex]Now the next pint B lets count its division.
It is marked at the fifth division.
Therefore, the fraction representing B can be written as:
[tex]\begin{gathered} B=5\times(1\text{ division\rparen} \\ =5\times\frac{1}{6} \\ =\frac{5}{6} \end{gathered}[/tex]Therefore, the point B can be represented as 5/6.
Final answer : Point A = 1/3
and point B = 5/6.
Related Questions
Assume that you have parallel lines. Using the law of detachment and the following conditional, what can you conclude?If you have parallel lines, then the lines are equidistant.
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The Law of Detachment states:
If a conditional is true and its hypothesis is true, then its conclusion is true.
Given the following statement:
"If you have parallel lines, then the lines are equidistant."
Applying the law of detachment, the conclusion will be the lines are equidistant.
Therefore, the answer is CHOICE D.
Answer:
The lines are equidistant.
Step-by-step explanation:
If you have the correct part of the conditional you can assume the conclusion.
what is the area of the circle below? A. 153.94B. 200.36C. 158.63D. 180.25
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As the diameter of the circle is 14 cm
So the radius is half of the circle i.e 7 cm
The area of the circle is:
[tex]undefined[/tex]Please help me with this problem that my son an I are stuck on were not understand what we did wrong. 3.The sequence 6, 18, 54, 162, … shows the number of pushups Kendall did each week, starting with her first week of exercising.(a)What is the recursive rule for the sequence?(b)What is the iterative rule for the sequence?Answer:
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You have the following sequence:
6, 18, 54, 162, ...
You can notice that each element (except the first one) is three times the previous one. Then, for the recursive rule you have:
a) recursive rule:
[tex]a_n=3\cdot a_{n-1}[/tex]Based on the previous result, you can conclude for the iterative rule:
b) iterative rule:
[tex]a_n=6\cdot3^{n-1}[/tex]If you replace n by the index of each element you obtain the given sequence.
4. Noah is solving the inequality 7x + 5 > 2x + 35. First, he solves theequation 7x + 5 = 2x + 35 and gets x = 6. How does the solution to theequation 7x + 5 = 2x + 35 help Noah solve the inequality 7x + 5 > 2x + 35?Explain your reasoning.
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Given the inequality below
[tex]7x+5>2x+35[/tex]Noah first solved the equation by changing the inequality sign to the equality sign as shown below
[tex]\begin{gathered} 7x+5=2x+35 \\ \text{Collect like terms} \\ 7x-2x=35-5 \\ 5x=30 \\ \text{Divide both sides by 5} \\ \frac{5x}{5}=\frac{30}{5} \\ x=6 \end{gathered}[/tex]Noah got x = 6
Solving the given inequality given
[tex]\begin{gathered} 7x+5>2x+35 \\ \text{Collect like terms} \\ 7x-2x>35-5 \\ 5x>30 \\ \text{Divide both sides by 5} \\ \frac{5x}{5}>\frac{30}{5} \\ x>6 \end{gathered}[/tex]The solution to the inequality is x > 6
The solution to the first equation helped Noah in knowing the starting point of the solution to the inequality.
While the inequality sign helped Noah deduce whether the value of x is less than or greater than the solution to the first equation Noah solved
just some basic algebraSolve the following equation:12 = 8a
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12 = 8a
Dividing by 8 at both sides of the equal sign, we get:
[tex]\begin{gathered} \frac{12}{8}=\frac{8a}{8} \\ \frac{3}{2}=a \end{gathered}[/tex]find three consecutive integers such that the second is eight less than twice the third. only an algebraic solution will be accepted.
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first integer n
second integer n+1
third integer n+2
the equation given is
(n+1)=2(n+2)-8
n+1=2n+4-8
we need to clear n
1-4+8=2n-n
n=5
the three numbers are
5, 6,7
To get from her house to school, Amy travels on one street for 2,550 meters. She then turns and travels on another street for 2,774 meters. This route is represented in the figure by the sequence of points K, L, M. According to the angle shown in the figure and the given information, what is the distance, to the nearest meter, from Amy's house to school represented by the line from K to M in the figure?
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Okay, here we have this:
We need to calculate the distance from Amy's house to school represented by the line from K to M in the figure, so we are going to use the cosine law, we obtain the following:
[tex]\begin{gathered} a^2=b^2+c^2-2\cdot b\cdot c\cdot\text{Cos(A)} \\ a^2=2550^2+2774^2-2\cdot2550\cdot2774\cdot\text{Cos(115)} \\ a=\sqrt{-14147400\cos\left(115^{\circ\:}\right)+14197576} \\ a\approx4492 \end{gathered}[/tex]Finally we obtain that the distance, to the nearest meter, from Amy's house to school represented by the line from K to M in the figure is 4492 meters.
The family budget is illustrated in the figure to the right. What is the total take-home pay and what percent is allocated for transportation?The total take home pay is $The percent of the take-home pay allocated for transportation is %
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• Total take-home pay
As we have the quantity for each section, we can add all and get the total as follows:
[tex]390+300+90+70+90+90+170+150+150[/tex]Simplifying:
[tex]=1500[/tex]• Percentage allocated for transportation
To get the percent for transportation, we have to divide the quantity of transportation against the total and multiply it times 100%:
[tex]\frac{150}{1500}\times100\%=10\%[/tex]Answer:
• The total take home pay is $1500
,• The percent of the take-home pay allocated for transportation is 10%
Is the following linear, exponential, or neither? 3,6,9,12,15,18...
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Given:
3,6,9,12,15,18...
We need to find the difference.
The difference between 3 and 6 is 6-3 =3.
The difference between 6 and 9 is 9-6 =3.
The difference between 9 and 12 is 12-9 =3.
The difference between 12 and 15 is 15-12 =3.
The difference between 15 and 18 is 18-15 =3.
Recall that linear have equal differences.
We get an equal difference between each value.
The form of the equation is
[tex]y=3x[/tex]Hence the given is linear.
Let F(x) = f(x ^ 9) and G(x) = (f(x)) ^ 9 You also know that a ^ 8 = 15 , f(a) = 2 , f^ prime (a)=7,f^ prime (a^ 9 )=11
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Answer:
Explanation:
a) F'(a)
From what we have:
[tex]\begin{gathered} F(x)\text{ = f\lparen x}^9) \\ F(a)\text{ = f\lparen a}^9) \\ F^{\prime}^(A)\text{ = f'\lparen a}^9)\text{ = 11} \\ \end{gathered}[/tex]b) G'(a)
[tex][/tex]what is1/3as a decimal
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To find the decimal form of 1/3, we just divide 1 by 3 in the following way:
We can continue but the residue will always be 1, therefore, the decimal form of 1/3 is 0.3333....
please can you help me to do this problem please.
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This situation is represented by an exponential function since it increases double every 4 hours
It has an initial value of 90 pounds of algae:
[tex]\begin{gathered} 12\text{ hours have 3 periods of 4 hours, then} \\ \text{Exponential function is represented:} \\ y=ax^n \\ a=\text{initial value} \\ x=\text{common ratio} \\ n=\text{period} \\ \end{gathered}[/tex]So,
[tex]\begin{gathered} y=90(2)^3 \\ y=90(2)^3 \\ y=720\text{ pounds} \end{gathered}[/tex]2. Israel makes $4.50 an hour as a waiter. Write an expression to represent* 2 points
how much money Israel makes. If you use a variable, make sure to tell me
what it represents!
Your answer
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Answer:
4.5x where x is the number of hours Israel works.
Step-by-step explanation:
Define the variable:
Let x be the number of hours Israel works.Given that Israel makes $4.50 an hour as a waiter, an expression to represent how much money Israel makes is:
[tex]\large\boxed{ 4.5x}[/tex]
What is the answer to 9-5(8-3)x9+26
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Calculating the value of this expression, we have that:
[tex]\begin{gathered} 9-5\mleft(8-3\mright)\cdot9+26 \\ 9-5(5)\cdot9+26 \\ 9-25\cdot9+26 \\ 9-225+26 \\ 9-199 \\ -190 \end{gathered}[/tex]So the value of the expression is -190.
See attached pic for problem. Answer has to include cancelling of units and proper number of significant figures.
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We have:
1 cubic meter = 35.3147 cubic feet
60 seconds = 1 minute
Therefore given 0.618 cubic meters per second:
[tex]0.618\frac{m^3}{s}\times\frac{35.3147ft^3}{1m^3}\times\frac{60s}{1\min }[/tex]Then solve:
[tex]1309.47\frac{ft^3}{\min }[/tex]Answer: 1309.5 cubic feet per minute
In the picture, point C is a point of tangency.815mDA=DE =
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Since the angle at which a tangent of a circle meets a radius of the circle is 90 degrees, the triangle ACD is a right triangle and we can apply the Pythagorean theorem to find the length of side DA, which is the hypothenus, as follows:
[tex]\begin{gathered} \text{hypothenus}^2=opposite^2+adjacent^2 \\ \end{gathered}[/tex][tex]\begin{gathered} DA^2=DC^2_{}+CA^2 \\ \end{gathered}[/tex][tex]\begin{gathered} DA^2=15^2+8^2=225+64=289 \\ DA=\sqrt[]{289}=17 \end{gathered}[/tex]Thus:
[tex]DA=17[/tex]Now, to find the value of DE, we observe that AE is the radius of the circle which we have been given to be 8.
Thus, we have that:
[tex]DE=DA-AE[/tex][tex]DE=17-8=9[/tex]Therefore:
[tex]DE=9[/tex]The value, v, of the hat is less than $9 how do u write the inequality??
Answers
Answer: v<9
Step-by-step explanation:
Jack is working two summer jobs, making $22 per hour tutoring and making $9 perhour landscaping. In a given week, he can work at most 12 total hours and must earna minimum of $180. Also, he must work no more than 8 hours tutoring. If crepresents the number of hours tutoring and y represents the number of hourslandscaping, write and solve a system of inequalities graphically and determine onepossible solution
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The total money Jack is going to make in the given week is a function of the number of hours he is going to dedicate in each of the jobs. if c is the number of hours he will work
I need a better step by step on how to get the answer instead of just “calculate 9 to the power of -5/2 and get 1/243
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The question ask to evaluate the expression:
[tex]9^{-\frac{5}{2}}[/tex]Step 1: Factor the number
[tex]9=3^2[/tex]Therefore, the expression becomes:
[tex]\Rightarrow(3^2)^{-\frac{5}{2}}[/tex]Step 2: Apply the exponent rule given to be
[tex](x^a)^b=x^{a\times b}[/tex]Therefore, we have:
[tex]\Rightarrow(3^2)^{-\frac{5}{2}}=3^{2\times-\frac{5}{2}}=3^{-5}[/tex]Step 3: Apply the exponent rule given to be
[tex]x^{-a}=\frac{1}{x^a}[/tex]Therefore, the expression becomes:
[tex]3^{-5}=\frac{1}{3^5}[/tex]Step 4: Calculate
[tex]3^5=243[/tex]Therefore, we have
[tex]\frac{1}{3^5}=\frac{1}{243}[/tex]ANSWER
[tex]9^{-\frac{5}{2}}=\frac{1}{243}[/tex]Miss Dennison is picking up the books in her classroom for the summer each box holds 9 books she has 24 math books in 27 science books to pack how many boxes will she need
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To determine how many boxes she will need, first step is to calculate how many books Miss Dennison has in total, that is the math books + the science books:
[tex]24+27=51[/tex]She can only pack 9 books per box, to determine how many boxes she needs you have to divide the number of books by the number of books that fit each box:
[tex]\frac{51}{9}=5.67[/tex]This means that she will fill 5 boxes with 9 books and a sixth one will have only 6 books.
She will use a total of 6 boxes.
A ladder leans against a building, making a 46 angle of elevation with the ground.The top of the ladder reaches a point on the building that is 21 feet above theground. To the nearest tenth of a foot, what is the distance, x between the base ofthe building and the base of the ladder? If the answer does not have a tenths placethen include a zero so that it does.
Answers
Given
A ladder leans against a building, making a 46 degree, angle of elevation with the ground.
The top of the ladder reaches a point on the building that is 21 feet above the ground.
To find: The distance, x between the base of the building and the base of the ladder.
Explanation:
It is given that,
The height of the building is 21 feet.
The angle of elevation is 46 degrees.
Therefore,
[tex]\begin{gathered} \tan46=\frac{21}{x} \\ x=\frac{21}{\tan46} \\ x=\frac{21}{1.0355} \\ x=20.27946 \\ x=20.3ft \end{gathered}[/tex]Hence, the value of x is 20.3ft.
Molly’s garden has a unit rate ofStartFraction 3 pink flowers over 2 white flowers EndFractionShe made a table to show how many pink and white flowers she has to plant in various rows.A 2-column table with 4 rows. Column 1 is labeled White (x) with entries 12, 36, B, C. Column 2 is labeled Pink (y) with entries 18, A, 72, 126.What are the missing numbers in the table?A: B: C:
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The table is:
White (x) Pink(y)
12 18
36 A
B 72
C 126
The unit rate is 3/2, so for every y (Pink flowers) and x (White flowers), we get:
[tex]\frac{y}{x}=\frac{3}{2}[/tex]Now, we can use this equation to calculate A. Where y is A and x is 36 white flowers, so, solving for A, we get
[tex]\begin{gathered} \frac{A}{36}=\frac{3}{2} \\ A=\frac{3}{2}\cdot36 \\ A=54 \end{gathered}[/tex]At the same way, we can formulate equations to calculate B and C as:
[tex]\begin{gathered} \frac{72}{B}=\frac{3}{2} \\ 72\cdot\frac{2}{3}=B \\ 48=B \end{gathered}[/tex][tex]\begin{gathered} \frac{126}{C}=\frac{3}{2} \\ 126\cdot\frac{2}{3}=C \\ 84=C \end{gathered}[/tex]Answers: A = 54
B = 48
C = 84
1.8=5.4x-yy=-3.8-6.2xhow to solve this math problem
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We have the following:
[tex]\begin{gathered} 1.8=5.4x-y \\ y=-3.8-6.2x \end{gathered}[/tex]solving:
[tex]\begin{gathered} 1.8=5.4x-(-3.8-6.2x) \\ 1.8=5.4x+3.8+6.2x \\ 6.2x+5.4x=1.8-3.8 \\ 11.6x=-2 \\ x=-\frac{2}{11.6} \\ x=-\frac{2\cdot2.5}{11.6\cdot2.5} \\ x=-\frac{5}{29} \end{gathered}[/tex]now, for y:
[tex]\begin{gathered} y=-3.8-6.2\cdot-\frac{5}{29} \\ y=-3.8\cdot\frac{29}{29}+\frac{31}{29} \\ y=-\frac{110.2}{29}+\frac{31}{29} \\ y=-\frac{79.2\cdot5}{29\cdot5} \\ y=-\frac{396}{145} \end{gathered}[/tex]So, x = -5/29 and y = -396/145
Convert this rational numberto its decimal form and roundto the nearest thousandth.5/7
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0.714
Explanation:
5/7 = 0.7143 (4 decimal place)
To round to the nearest thousandth, we count the numbers after the point and stop at the 3rd number. Then we round the number after it (fourth number) and add to the 3rd number.
If the fourth number is 5 0r more, we round to 1. If less than 5, we round to zero
In this case, the fourth number after the decimal point is 3. Since it is less than 5, we round to zero.
5/7 to the nearest thousandth = 0.714
Simplify and state restrictions. Show the factors before you simplify. a 2a2-a-1 a2–1 Х 4a? +40 2a2+7a+3
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Given:
[tex]\frac{2a^2-a-1}{a^2-1}\times\frac{4a^2+4a}{2a^2+7a+3}[/tex]Factorize the given expression.
[tex]\text{ Use -a=-2a+a.}[/tex][tex]\frac{2a^2-2a+a-1}{a^2-1}\times\frac{4a^2+4a}{2a^2+7a+3}[/tex]Take out the common terms.
[tex]\frac{2a(a-1)+(a-1)}{a^2-1}\times\frac{4a^2+4a}{2a^2+7a+3}[/tex][tex]\frac{(a-1)(2a+1)}{a^2-1}\times\frac{4a^2+4a}{2a^2+7a+3}[/tex][tex]Use\text{ }a^2-1=(a-1)(a+1).[/tex][tex]\frac{(a-1)(2a+1)}{(a-1)(a+1)}\times\frac{4a^2+4a}{2a^2+7a+3}[/tex][tex]\text{Take out the co}mmon\text{ term }4a^2+4a=4a\mleft(a+1\mright).[/tex][tex]\frac{(a-1)(2a+1)}{(a-1)(a+1)}\times\frac{4a(a+1)}{2a^2+7a+3}[/tex][tex]\text{Use 7a=6a+a in }2a^2+7a+3.[/tex][tex]\frac{(a-1)(2a+1)}{(a-1)(a+1)}\times\frac{4a(a+1)}{2a^2+6a+a+3}[/tex]Take out common term.
[tex]\frac{(a-1)(2a+1)}{(a-1)(a+1)}\times\frac{4a(a+1)}{2a(a^{}+3)+(a+3)}[/tex][tex]\frac{(a-1)(2a+1)}{(a-1)(a+1)}\times\frac{4a(a+1)}{(a^{}+3)(2a+1)}[/tex]The restrictions are
[tex]a\ne1,-1,-3\text{ and }\frac{-1}{2}\text{.}[/tex]Simplify the given expression
[tex]\frac{(a-1)(2a+1)}{(a-1)(a+1)}\times\frac{4a(a+1)}{(a^{}+3)(2a+1)}[/tex]Cancel out the common factors.
[tex]\frac{4a}{(a^{}+3)}[/tex]The answer is :
[tex]\frac{2a^2-2a+a-1}{a^2-1}\times\frac{4a^2+4a}{2a^2+7a+3},\text{ }a\ne1,-1,-3\text{ and }\frac{-1}{2}\text{.}[/tex][tex]\frac{4a}{a^{}+3},\text{ }a\ne-3.[/tex]
Castel has homework in four subjects. Heis deciding what order to complete themin.
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I need to know the next 7 terms of the sequences
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Given:
a₁ = 2/5
a₂ = 4/5
Since the first 2 terms are given, let's determine the remaining 3 terms using the given formula:
[tex]\text{ a}_n\text{ = a}_{n-2}\text{ }.\text{ a}_{n-1}[/tex]We get,
For a₃,
[tex]\text{ a}_3\text{ = a}_{3-1}\text{ }.\text{ a}_{3-2}\text{ = a}_1\text{ }.\text{ a}_2[/tex][tex]\text{ a}_3\text{ = \lparen}\frac{2}{5})(\frac{4}{5})\text{ = }\frac{8}{25}[/tex]For a₄,
[tex]\text{ a}_4\text{ = a}_{4-2}\text{ }.\text{ a}_{4-1}\text{ = a}_2\text{ }.\text{ a}_3[/tex][tex]\text{ a}_4\text{ = \lparen}\frac{4}{5})(\frac{8}{25})\text{ = }\frac{20}{125}\text{ = }\frac{4}{25}[/tex]For a₅,
[tex]\text{ a}_5\text{ = a}_{5-2}\text{ }.\text{ a}_{5-1}\text{ = a}_3\text{ }.\text{ a}_4[/tex][tex]\text{ a}_5\text{ = \lparen}\frac{8}{25})(\frac{4}{25})\text{ = }\frac{32}{625}[/tex]Therefore, the first five terms of the sequence are the following:
[tex]\text{ }\frac{2}{5}\text{ , }\frac{4}{5}\text{ , }\frac{8}{25}\text{ , }\frac{4}{25}\text{ , }\frac{32}{625}[/tex]For another two terms.
For a₆,
[tex]\text{ a}_6\text{ = a}_{6-2}\text{ }.\text{ a}_{6-1}\text{ = a}_4\text{ }.\text{ a}_5[/tex][tex]\text{ a}_6\text{ = \lparen}\frac{4}{25})(\frac{32}{625})\text{ = }\frac{128}{15,625}[/tex]For a₇,
[tex]\text{ a}_7\text{ = a}_{7-2}\text{ }.\text{ a}_{7-1}\text{ = a}_5\text{ }.\text{ a}_6[/tex][tex]\text{ a}_7\text{ = \lparen}\frac{32}{625})(\frac{128}{15,625})\text{ = }\frac{4,096}{9,765,625}[/tex]5 times 2 to the power of 2 divided by 2 and x =10
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Answer:
10x or 50
Step-by-step explanation:
5 times 2 to the power of 2 divided by 2 is 50 but idont know why theres a x but um 50 is 10x
what does 17/10x 10/17 equal
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Hello , can you please see attached and give me only the answer.
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ANSWER:
not a solution
STEP-BY-STEP EXPLANATION:
We have the following system of equations:
[tex]\begin{gathered} 2x+5y=-18 \\ 6x-4y=15 \end{gathered}[/tex]We have the point (1, -4), which we can interpret like this:
x = 1
y = -4
We replace these values and if it meets the system of equations, if it is a solution and if not, it is not a solution.
Therefore:
[tex]\begin{gathered} 2\cdot1+5\cdot-4=-18 \\ 2-20=-18 \\ -18=-18 \\ \\ 6\cdot1-4\cdot-4=15 \\ 6+16=15 \\ 22=15 \end{gathered}[/tex]The first equation does, but the second does not, which means that the point (1, -4) is not a solution of the system of equations