![Solve The System.x2 + Y2 = 16.y + 4 = X2=(-2.65, [?]) (0,[ ] (2.65, [ ])](https://brainimage.s3.us-east-005.backblazeb2.com/contents/attachments/TtvidbSoGE9CKljb8MM0dK70MI2FQYd0.jpeg)
Answers
Given the system of equations:
[tex]\begin{cases}x^2+y^2=16 \\ y+4=x^2\end{cases}[/tex]As shown in the figure, there are 3 points that are the solutions to the system
For each point given the value of x
So, we will substitute with (x) to find (y)
From the second equation:
[tex]y=x^2-4[/tex]substitute with x = -2.65, 0, 2.65
[tex]\begin{gathered} x=-2.65\rightarrow y=(-2.65)^2-4=3 \\ x=0\rightarrow y=(0)^2-4=-4 \\ x=2.65\rightarrow y=(2.65)^2-4=3 \end{gathered}[/tex]So, the answer will be:
[tex]\begin{gathered} (-2.65,3) \\ (0,-4) \\ (2.65,3) \end{gathered}[/tex]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.
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]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
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]
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.
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
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
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]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]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.
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....
The value, v, of the hat is less than $9 how do u write the inequality??
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Answer: v<9
Step-by-step explanation:
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
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]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]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]
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]what does 17/10x 10/17 equal
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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.
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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.
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.
Convert this rational numberto its decimal form and roundto the nearest thousandth.5/7
Answers
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
In the diagram at the right, the endpoints of the chord are thepoints where the line x = 5 intersects the circle x2 + y2 = 81.What is the length of the chord?
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ANSWER:
The length of the Chord is 15
SOLUTION:
Solve for y when x=5
[tex]\begin{gathered} x^2+y^2=81 \\ y=\sqrt[]{81-x^2} \\ y=\sqrt[]{81-25} \\ y=7.5 \end{gathered}[/tex]Since the value of y is 7.5 we multiply it by 2, to get the length
therefore, the length is 15
22Select the correct answer.Which inequality is graphed on the coordinate plane?
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The line on the graph is a thick line not dashed. This indicates there is an equal to sign attached to the inequality
We only have two options with equal to attached to the inequality
The shading is towards the negative side of y axis (coming down)
So the right option will have a less than and equal to sigh attached:
[tex]\begin{gathered} \text{The correct inequality:} \\ y\text{ }\le\text{ -3x + 2 (option B)} \end{gathered}[/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.
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.
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
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
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]Help me answer the following questions and fill in the blank spaces and make a graph
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EXPLANATION
Since it takes 3 minutes to warm up, and then 6 minutes to make a coffee, we can apply the following relationship:
[tex]M(c)=6+3c[/tex]Where c represents the number of coffees.
Plugging in 12 cups into the equation:
M(c) = 6 + 3*12 = 42
-It will take 42 minutes to make 12 cups of coffee.
In 45 minutes, we can get the amount of cups of coffee obtained by plugging the value into the equation:
[tex]45=6+3\cdot c[/tex]Isolating the value of c:
[tex]\frac{45-6}{3}=c[/tex]Subtracting numbers:
[tex]13=c[/tex]-He can make 13 cups of coffee in 45 minutes.
-The domain of the function is represented by all the Real Numbers.
- The range of the function is represented by all the Real Numbers.
The table is as follows:
Coffee Minutes
0 6
1 3
2 12
3 15
what the difference between these two fractions [tex] \frac{ 5}{1} [/tex]and[tex] \frac{ 5}{5} [/tex]
Answers
Question:
what the difference between these two fractions 5/1 and 5/5
Solution:
5/5 is 1
5/1 is 5
1 is not equal to 5. So the fraction 5/1 is different from 5/5.