The fraction which is halfway between [tex]\frac{1}{2}[/tex] and [tex]\frac{5}{6}[/tex] is equal to [tex]\frac{2}{3}[/tex].
What is a fraction ?
A fraction is used to represent a portion or component of a whole. The numerator and denominator are its two parts.
The two fractions are given which are [tex]\frac{1}{2}[/tex] and [tex]\frac{5}{6}[/tex].
We know that numerator is the top value of the fraction whereas the denominator is the bottom value of the fraction. We need to add the given fractions and then divide it by 2 to find the halfway between the two given functions.
To add the fractions we need to equal denominator firstly. The common denominator of 2 and 6 will be 6 because 6 is a multiple of both 2 and 6.
So ,
Halfway between [tex]\frac{1}{2}[/tex] and [tex]\frac{5}{6}[/tex] is :
= ( [tex]\frac{1}{2}[/tex] + [tex]\frac{5}{6}[/tex] ) / 2
= [tex]\frac{3 + 5}{6}[/tex] / 2
= [tex]\frac{8}{6}[/tex] × [tex]\frac{1}{2}[/tex]
= [tex]\frac{4}{6}[/tex]
or
[tex]\frac{2}{3}[/tex]
Therefore , the fraction which is halfway between [tex]\frac{1}{2}[/tex] and [tex]\frac{5}{6}[/tex] is equal to [tex]\frac{2}{3}[/tex].
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What is the equation of a line that passes through the point (4, 2) and is perpendicular to the line whose equation is y=x/3−1 ?
The ratio of computers to desk is 2 to 3. If there are 15 desk, how many computers are there?
To find the number of computers given the ratio of computers to desks and the number of desks, set up a proportion and solve for the unknown value.
Explanation:In this question, we are given the ratio of computers to desks, which is 2 to 3. We are also given the number of desks, which is 15. To find the number of computers, we can set up a proportion:
2 computers / 3 desks = x computers / 15 desks
By cross-multiplying and solving for x, we find that there are 10 computers.
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How to find slope when there is the y intercept and x-intercept?
Which graph can be used to find the solution(s) to x2 – 1 = x + 1?
Let
[tex]f(x)=x^{2}-1[/tex]
[tex]g(x)=x+1[/tex]
we know that
The function f(x) is a vertical parabola open upward
the vertex is the point [tex](0,-1)[/tex] ------> is a minimum
The function g(x) is a linear equation
The y-intercept is the point [tex](0,1)[/tex] -----> for [tex]x=0[/tex] find the value of g(x)
therefore
the answer in the attached figure
The graph that can be used to find the solution of the given polynomial is given by option C) and this can be determined by using the given data.
Given :
Equation --- [tex]x^2 -1 = x+1[/tex]
The following steps can be used in order to determine the graph that can be used to find the solution of the given polynomial:
Step 1 - Separate LHS and RHS of the given polynomial.
[tex]\rm y = x^2-1[/tex] --- (1)
y = x + 1 --- (2)
Step 2 - Draw the graph of a line (y = x + 1) that passes through the points (-1,0) and (0,1).
Step 3 - Now, draw the graph of the equation (1). The shape of this graph is the upward parabola.
Step 4 - The two graphs intersect each other at (-1,0) and (2,3).
From the above steps, it can be concluded that the correct option is C).
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Please help me asap
It's due tomorrow
Ohhhhhhh! I have a Brainliest
If y varies directly with x in the following table problem, find the constant of variation (k) and write the equation x 6,9,12,15 Y 10,15,20,25
A pizza parlor sold 38mc005-1.jpg pizzas during a dinner hour. If each pizza contained 8 slices, how many slices of pizza were sold?
The options are
38 pizzas times 8 slices each =
38 *8 = 304 slices total
factor the trinomial x^2 - 16x +63
After 6 years, what is the total amount of a compound interest investment of $35,000 at 4% interest, compound quarterly?
Round to the nearest cent.
Assume the ball passes through the points (3,8), (5,20/3), and (6,5) . Use this data to set up a system of three equations and three unknowns (a, b, and c) that will allow you to find the equation of the parabola. Write the system in the space provided.
To solve this question:
First, we need to know the standard equation of a parabola.Then, with the three points given, we can build a system of three equations.Doing this, we get that the system is, with the 3 equations:
[tex]9a^2 + 3b + c = 8[/tex]
[tex]75a + 15b + 3c = 20[/tex]
[tex]36a + 6b + c = 5[/tex]
Equation of a parabola:
A parabola is a second degree polynomial, having an standard equation of:
[tex]y = ax^2 + bx + c, a \neq 0[/tex]
Point (3,8)
This means that when [tex]x = 3, y = 8[/tex]. So
[tex]y = ax^2 + bx + c, a \neq 0[/tex]
[tex]8 = a\times3^2 + 3b + c[/tex]
[tex]9a^2 + 3b + c = 8[/tex]
Thus, [tex]9a^2 + 3b + c = 8[/tex] is the first equation.
(5,20/3)
This means that when [tex]x = 5, y = \frac{20}{3}[/tex]. Thus
[tex]y = ax^2 + bx + c, a \neq 0[/tex]
[tex]\frac{20}{3} = a\times5^2 + 5b + c[/tex]
[tex]25a + 5b + c = \frac{20}{3}[/tex]
[tex]75a + 15b + 3c = 20[/tex]
Thus, [tex]75a + 15b + 3c = 20[/tex] is the second equation.
(6,5)
This means that when [tex]x = 6, y = 5[/tex]. Thus
[tex]y = ax^2 + bx + c, a \neq 0[/tex]
[tex]5 = a\times6^2 + 6b + c[/tex]
[tex]36a + 6b + c = 5[/tex]
Thus, [tex]36a + 6b + c = 5[/tex] is the third equation.
After all, the system of equations is:
[tex]9a^2 + 3b + c = 8[/tex]
[tex]75a + 15b + 3c = 20[/tex]
[tex]36a + 6b + c = 5[/tex]
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Maddie plays 16 Games of tennis. Her went to loss ratio is 10 to 6. She is expected to play 12 more games during the season. How many do you expect her to win
Find the total area of the solid figure with the length, 3 width 5, and height 6
How do you find a literal equation for d=rt,
solve for t.
Answer: [tex]\frac{d}{r} = t[/tex]
Step-by-step explanation: To solve for t in the equation d = rt, all we have to do is get t by itself on the right side of the equation.
Since t is being multiplied by r, we simply divide both sides of the equation by r. On the right, the r's cancel and we are left with r.
On the left side of the equation we have [tex]\frac{d}{r}[/tex].
Therefore, our answer is [tex]\frac{d}{r} = t[/tex].
What is the maximum length possible for her blanket?
Answer: c: 60
Step-by-step explanation:
i did the test
Emma read the statement “the quotient of six and a number, x, is the same as negative two times the difference of x and 4.5.” She translated it as shown below.
Emma should have used division to represent the quotient of six and x, and she should have used parentheses to show that -2 is multiplied by (4.5 - x). Hence the correct options are 1 and 5.
Emma made two errors in translating the statement "the quotient of six and a number, x, is the same as negative two times the difference of x and 4.5." First, instead of representing the quotient of six and x, she incorrectly wrote 6x, which implies multiplication rather than division. The correct representation should be 6/x.
Second, Emma failed to use parentheses to show that -2 is multiplied by the difference of x and 4.5. The correct expression should be -2(x - 4.5) to ensure proper order of operations. These errors impact the accuracy of the translated equation, and correcting them would yield a more faithful representation of the original statement. Hence the correct options are 1 and 5.
Complete question:
Emma read the statement "the quotient of six and a number, x, is the same as negative two times the difference of x and 4.5." She translated it as shown below 6x=-2x-4.5 What errors did Emma make? Select two options
She should have used division to represent the quotient of six and x.
She should not have included an equal sign.
She should have used parentheses to show that -2 is multiplied by (x-4.5).
She should have subtracted the difference (x-4.5) from -2.
She should have used parentheses to show that -2 is multiplied by (4.5-x).
Emma made the following errors in her translation:
E. She should have used parentheses to show that -2 is multiplied by (x-4.5). Emma’s equation, 6x = -2x - 4.5, lacks parentheses around the expression (x-4.5). To correctly represent the difference of x and 4.5 being multiplied by -2, she should have written -2(x-4.5).
D. She should have subtracted the difference (x-4.5) from -2. Emma’s equation does not correctly account for the subtraction of the difference (x-4.5) from -2. The correct equation should be 6x = -2(x-4.5).
The other options are not relevant to Emma’s specific errors in translating the statement.
Emma made the following errors in her translation:
E. She should have used parentheses to show that -2 is multiplied by (x-4.5). Emma’s equation,
6x = -2x - 4.5, lacks parentheses around the expression
(x-4.5). To correctly represent the difference of x and 4.5 being multiplied by -2
, she should have written
-2(x-4.5)
.D. She should have subtracted the difference(x-4.5) from -2
. Emma’s equation does not correctly account for the subtraction of the difference
(x-4.5)
from
-2
The correct equation should be
6x = -2(x-4.5)
Complete question:
Emma read the statement "the quotient of six and a number, x, is the same as negative two times the difference of x and 4.5." She translated it as shown below 6x=-2x-4.5 What errors did Emma make? Select two options
A. She should have used division to represent the quotient of six and x.
B. She should not have included an equal sign.
C. She should have used parentheses to show that -2 is multiplied by (x-4.5).
D. She should have subtracted the difference (x-4.5) from -2.
E. She should have used parentheses to show that -2 is multiplied by (4.5-x).
A train leaves chicago and travels east at 60 mph. another train at the same depot leaves at the same time and travels west at 72 mph. how long before the two trains are 330 miles apart?
The two trains will be 330 miles apart after 2.5 hours.
Explanation:To find how long it takes for the two trains to be 330 miles apart, we can apply the formula for relative velocity:
Relative velocity = sum of their speeds
The first train is moving east at 60 mph, and the second train is moving west at 72 mph. So their relative velocity is 60 mph + 72 mph = 132 mph.
To find the time it takes for the trains to be 330 miles apart, we can use the formula:
Distance = speed × time
330 miles = 132 mph × time
Solving for time, we have:
Time = 330 miles / 132 mph = 2.5 hours
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im pretty sure somone answered this but
Rosemary left a 15% tip for a meal that cost $39.
What was the amount of the tip?
Which ordered pairs lie on the graph of the exponential function f(x)=4(5)2x?
Select each correct answer.
(−1,4/25)
(0,0)
(1,4)
(2,2500)
A college student borrows $3,000 for 3 months to pay for a semester of school. If the interest is $61.88 find the monthly payment
The student must make monthly payments of $1,020.63 to repay the $3,000 loan with $61.88 in interest over 3 months.
The student has borrowed $3,000 for 3 months and the interest incurred on this loan is $61.88. To find the monthly payment, we need to add the total interest to the principal borrowed and then divide it by the number of payments (which is 3 in this case).
The total repayment amount is calculated as $3,000 principal + $61.88 interest = $3,061.88.
Now, we divide the total repayment amount by the number of monthly payments:
Monthly Payment = Total Repayment Amount / Number of Payments
Monthly Payment = $3,061.88 / 3
Monthly Payment = $1,020.63
Therefore, the student will need to make monthly payments of $1,020.63 to repay the $3,000 loan over 3 months.
Match the inequality to the graph of its solution.
a. c + 7 ≤ 3
b. c - 3 > 1
c. c - 7 < 3
case a) [tex]c+7 \leq 3[/tex]
[tex]c+7 \leq 3\\ c\leq3-7\\c\leq -4[/tex]
the solution is the interval-------> (-∞,-4]
the answer case a) in the attached figure
case b) [tex]c-3 > 1[/tex]
[tex]c-3 > 1\\c > 1+3\\c> 4[/tex]
the solution is the interval-------> (4,∞)
the answer case b) in the attached figure
case c) [tex]c-7< 3[/tex]
[tex]c-7< 3\\ c<3+7\\ c< 10[/tex]
the solution is the interval-------> (-∞,10)
the answer case c) in the attached figure
Inequalities are used to represent unequal expressions.
Graph (b) represents [tex]\mathbf{c + 7 \le 3}[/tex]Graph (c) represents [tex]\mathbf{c - 3 > 1}[/tex]Graph (a) represents [tex]\mathbf{c - 7 < 3}[/tex][tex]\mathbf{(a)\ c + 7 \le 3}[/tex]
Subtract 7 from both sides
[tex]\mathbf{c \le -4}[/tex]
The above means that:
The graph points leftThe graph starts at -4, with a closed circleHence, graph (b) represents [tex]\mathbf{c + 7 \le 3}[/tex]
[tex]\mathbf{(b)\ c - 3 > 1}[/tex]
Add 1 to both sides
[tex]\mathbf{c > 4}[/tex]
The above means that:
The graph points rightThe graph starts at 4, with an open circleHence, graph (c) represents [tex]\mathbf{c - 3 > 1}[/tex]
[tex]\mathbf{(c)\ c - 7 < 3}[/tex]
Add 7 to both sides
[tex]\mathbf{c < 10}[/tex]
The above means that:
The graph points leftThe graph starts at 10, with an opened circleHence, graph (a) represents [tex]\mathbf{c - 7 < 3}[/tex]
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A company donates 935 pencils to a shcool the pencil are divided evenly amog 9classroom the rest goes to the library how many pencil were donated to the schooland the library
Answer:
103.8
Step-by-step explanation:
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Which inequality represents this sentence? Ten minus three is greater than one plus two.
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What are the domain and range of the function
the arrows on the end of the line means it continues
both the domain and the range for this graph is negative infinity to infinity
N a contest, a total of $12,000 was divided among the first, second, and third-place winners in the ratio of 3 to 2 to 1, respectively. how much did the first-place winner receive
Which graph represents the inequality y<−1+2x?
How to find the distance between two lines in 3d?
Answer:
Step-by-step explanation:
Astronauts use a tool in space that weigh 5 ounces on Earth. How many grams does the tool weigh? Round your answer to the nearest hundredth.
Answer: 141.75
Step-by-step explanation: Yw future edge users
A game shop sells marbles in clear plastic cylinders. Four marbles fit across the diameter of the cylinder and 10 marbles fit from the base to the top of the cylinder. Each marble has a diameter of 2 cm. What is the area of the plastic that is needed to make one cylinder?
Solve the equation the square root of the quantity x minus 6 plus 2 equals 6 for the variable. Show each step please. Remember the X - 6 is under a square root sign