Answers
Given the equation:
\(\frac{2}{3}x-\frac{1}{2}=\frac{1}{3}+\frac{5}{6}x\)Adding 1/2 at both sides of the equal sign and combining similar terms:
\(\begin{gathered} \frac{2}{3}x-\frac{1}{2}+\frac{1}{2}=\frac{1}{3}+\frac{5}{6}x+\frac{1}{2} \\ \frac{2}{3}x+(-\frac{1}{2}+\frac{1}{2})=(\frac{1}{3}+\frac{1}{2})+\frac{5}{6}x \\ \frac{2}{3}x=(\frac{1\cdot2+1\cdot3}{6})+\frac{5}{6}x \\ \frac{2}{3}x=\frac{5}{6}+\frac{5}{6}x \end{gathered}\)Subtracting 5/6x at both sides of the equal sign and combining similar terms:
\(\begin{gathered} \frac{2}{3}x-\frac{5}{6}x=\frac{5}{6}+\frac{5}{6}x-\frac{5}{6}x \\ \frac{2\cdot2-5\cdot1}{6}x=\frac{5}{6}+(\frac{5}{6}x-\frac{5}{6}x) \\ -\frac{1}{6}x=\frac{5}{6} \end{gathered}\)Multiplying by -6 at both sides:
\(\begin{gathered} (-6)\cdot(-\frac{1}{6}x)=(-6)\cdot\frac{5}{6} \\ x=-5 \end{gathered}\)
Related Questions
Work out 132% of 96 m
Give your answer as a decimal in metres (m).
Answers
Answer:
126.72m
Step-by-step explanation: 1.32 x 96 = 126.72, I struggled with that stuff too no shame
Please help me with this I need the help
Answers
Find u. See image below.
Answers
The value of u is 2 in the given right-angled triangle.
The given figure is a right-angled triangle with hypotenuse 'u' and the other two sides as \(\sqrt{2}\) and v.
We have to find the value of 'u' using Pythagoras theorem or trigonometric identities.
What is Pythagoras theorem?It states that the square of the hypotenuse is equal to the sum of the squares of the other two sides.
In a right-angled triangle ABC, if
BC = hypotenuse
AC and AB are the other two sides then,
\(BC^2 = AC^2 + AB^2\).
For this problem, we can find the value of u by using trigonometric identities.
From the figure, we have an angle of 45°.
Consider Cos 45°.
Cos Ф = base / hypotenuse
Cos 45° = \(\sqrt{2}\) / u ...........(1)
From trigonometric identities of cosine.
We have,
Cos 45° = 1 / \(\sqrt{2}\)............(2)
From (1) and (2)
We get,
1 / \(\sqrt{2}\) = \(\sqrt{2}\) / u
u = 2.
Thus the value of u is 2 in the given right-angled triangle.
Learn more about Pythagoras's theorem application here:
https://brainly.com/question/11687813
#SPJ1
Can you answer the question? TKSSS
Answers
Answer:
\(\frac{7}{2}\) π
Step-by-step explanation:
To find the arc length of the partial circle, you have to find a fourth of the circumference
C = \(\frac{1}{4}\) πd - Formula
C = \(\frac{1}{4}\) 14π - Plug in values
C = \(\frac{14}{4}\) π - Simplify/Solve
C = \(\frac{7}{2}\) π
Factorise fully 6x+8
Answers
Answer: To factorize the expression 6x + 8 fully, we can first look for the greatest common factor (GCF) of the two terms. In this case, the GCF is 2.
Step 1: Factor out the GCF:
2(3x + 4)
Now, we have the expression 3x + 4 inside parentheses. This expression cannot be further factorized since there are no common factors other than 1.
Therefore, the fully factorized form of 6x + 8 is:
2(3x + 4)
Step-by-step explanation:)
The factored expression is:
↬ 2(3x + 4)Step-by-step explanation:
To factor the expression, look at its GCF (greatest common factor).
Clearly the GCF of both terms is 2. So what we do next is we divide both terms by 2 :
6x ÷ 2 + 8 ÷ 2The result is :
3x + 4And now the 2 goes outside the parenthesis:
2(3x + 4)Hence, the answer is 2(3x + 4).
Seventy-five 6th- grade students chose to watch a movie on the last day of school. This is 25% of the 6th-grade class. How many total students are in the 6th grade?
Answers
25% = 75/x
To solve for x, we can cross-multiply:
0.25x = 75
Then, we can divide both sides by 0.25:
x = 300
Therefore, there are 300 6th-grade students in total.
answer these questions
Answers
A. True
B.true
C. False
D.true
Question 3: 40, 24
Finde the value of x in the proportion ( 5x+ 1 ):3 =(2x +2): 7(6 x) = (4x) :7
Answers
In the proportion (5x + 1):3 = (2x + 2):7, the value of x is -1/29.
In the proportion (6x):(4x) = 7, there is no value of x that satisfies the proportion.
To find the value of x in the given proportions, let's solve them one by one:
(5x + 1) : 3 = (2x + 2) : 7
To solve this proportion, we can cross-multiply:
7(5x + 1) = 3(2x + 2)
35x + 7 = 6x + 6
Subtracting 6x from both sides and subtracting 7 from both sides:
35x - 6x = 6 - 7
29x = -1
Dividing both sides by 29:
x = -1/29
Therefore, the value of x in the first proportion is -1/29.
(6x) : (4x) = 7
To solve this proportion, we can simplify the left side:
6x / 4x = 7
Dividing both sides by 2x:
3/2 = 7
This equation is not true, as 3/2 is not equal to 7.
Therefore, there is no value of x that satisfies the second proportion.
In summary, the value of x in the proportion (5x + 1) : 3 = (2x + 2) : 7 is -1/29, and there is no value of x that satisfies the proportion (6x) : (4x) = 7.
For similar question on proportion.
https://brainly.com/question/29864115
#SPJ8
Forever Flowers, the nursery that sells the peony plants, has an app that uses
equations to help customers order the correct number of plants. The function rule for
peony plants is P = 1.5n where P represents the number of plants needed for n yards.
a. What type of representation is a function rule?
b. State at least one reason why using this type of representation may be more useful
than other representations
Answers
a. A function rule is a representation of dependent variable, here n, in terms of the independent variable, here P, and is expressed as ƒ(P) = 1.5n.
b. This type of reason is useful because functions in an equation can take input from many variables, but always give the same result, which is unique to that function.
What is a function rule?The connection between the input or domain and the output or range is called a function rule. When there is exactly one value in the range for each domain value, a relation is a function.
f(x), where x is the input value, is how functions are expressed.
All functions have the general form y = f(x)
On any part of the function, a vertical line is drawn. It is a function if and only if it crosses the function at that single point. It is not a function if the line crosses itself more than once.
Learn more about function rule
https://brainly.com/question/6031365
#SPJ9
Use the table below to answer #3
What is the difference between the total amount of bags of box tops collected by 4th grade to 5th grade
Answers
The difference between the total amount of bags of box tops collected by 4th grade to 5th grade is 2 (1/16). Option D
How to find the difference?The given parameters that will help us to get the difference are
The fractions,
We shall be solving the fractions in pars then later we find the difference.
[4 3/12 +5 5/16 +3 3/8} - {3 1/4 +4 1/2 + 3 1/8}
Simplify by find the LCM of each side
[12{12+15+18}/48 ] - {10 (2+4+1)/8
Simplify to get
12 (45/48) - 10[7/8]
subtracting the fractions to have
2 [45 - 42]/48
Making it more simpler to get
2 1/16
Therefore the difference between the two fractions is 2 1/16
Learn more about fractions on https://brainly.com/question/10354322
#SPJ1
Do the segments connecting points A, B, and C form a right triangle? Show work that leads to your answer. Round to the nearest tenths place if necessary.
A= -2,2
B=6,2
C=0,6
Answers
Step-by-step explanation:
we need to calculate the distances between the points as the side lengths of the triangle.
these side lengths must satisfy the Pythagoras principle :
c² = a² + b²
with c being the Hypotenuse (side opposite of the 90° angle) and the longest of the 3 sides, a and b being the legs.
the distance between 2 points is again calculated via Pythagoras, as the coordinate differences (= the legs) with the distance as Hypotenuse create right-angled triangles.
this is then caked the distance formula, but it is all Pythagoras again.
AB² = (xB - xA)² + (yB - yA)² = (6 - -2)² + (2 - 2)² =
= 8² + 0² = 8²
AB = 8
AC² = (0 - -2)² + (6 - 2)² = 2² + 4² = 4 + 16 = 20
AC = sqrt(20)
BC² = (0 - 6)² + (6 - 2)² = (-6)² + 4² = 36 + 16 = 52
BC = sqrt(52)
as sqrt(20) is a little bit more than 4, and sqrt(52) is a little bit more than 7, 8 is the longest side and Hypotenuse.
if this is a right-angled triangle, then
8² = sqrt(20)² + sqrt(52)²
must be true.
but
64 = 20 + 52 = 72
is wrong.
so, the segments do not form a right-angled triangle.
I rlly rlly rlly need help! Complete the following proof. Given: Points R, S, T, Q on circle O Prove: m\overarc RS + m\overarc ST + m\overarc TQ + m\overarc RQ
Answers
Answer:
\(m(\widehat {RS})+m(\widehat{ST})+m(\widehat{TQ}) + m(major\ arc RQ) = 360\ degree\)
Step-by-step explanation:
As we can see in the figure that
The R, S, T ,and Q are the points on the circle O.
Also
The measurement of the circular arc is equivalent to the measurement of the angle at the center of the arc
So by this
\(m(\widehat{RS})=m(\angle ROS)\)
\(m(\widehat{ST})=m(\angle SOT)\)
\(m(\widehat{TQ})=m(\angle TOQ)\)
m(major arc RQ) = m(∠QOR)
So,
\(m(\widehat {RS})+m(\widehat{ST})+m(\widehat{TQ}) + m(major\ arc RQ) = m(\angle ROS)+m(\angle SOT)+m(\angle TOQ)+m(\angle QOR)\)
And as we know that
All angles sum = 360°
Therefore
\(m(\widehat {RS})+m(\widehat{ST})+m(\widehat{TQ}) + m(major\ arc RQ) = 360\ degree\)
Solve (3x+7)=4x for x
Answers
Answer:
x=7
Step-by-step explanation:
(3x+7)=4x
Subtract 3x from each side
(3x+7) -3x=4x-3x
7 = x
25) Find the measure of the side MN.
A) 17.1
B) 18.1
C) 19.1
Answers
The measure of the side MN is 19.1.
What are trigonometric functions?In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.
The different trigonometric identities are expressed as:
cosine, tangent, cotangent, cosecant, secant, and sineFrom the information given, we have that:
The opposite side of the triangle is MNThe adjacent side is 11ftUsing the tangent identity:
\(\text{tan} \ \theta = \dfrac{\text{opposite}}{\text{adjacent}}\)
Substitute the values
\(\text{tan}(60) =\dfrac{\text{MN}}{11}\)
Cross multiply the values, we have:
\(\text{MN} = \sf 1.73(11)\)
\(\text{MN} = 19. 05 \thickapprox\bold{\underline{19.1 \ ft}}\)
Hence, the measure of the side MN is 19.1.
Learn more about trigonometric functions at:
https://brainly.com/question/15768633
Please help!! Will give extra points to the correct answer
Answers
A. The value of 13π/8 to degrees is 146.25°.
B. The two angles in radians that are co-terminal to 13π/8 are 29π/8 and 5π/8.
How to calculate the anglesa) It should be noted that to convert 13π/8 to degrees, we use the formula:
degrees = radians × 180° / π
= (13π/8) × (180° / π)
= 146.25°
b) It should be noted that to find two angles in radians that are co-terminal to 13π/8, we need to add or subtract any multiple of 2π.
Positive angle:
Add 2π to 13π/8:
13π/8 + 2π = (26π + 16π)/16 = 29π/8
Negative angle:
Subtract 2π from 13π/8:
13π/8 - 2π = (26π - 16π)/16 = 5π/8
So the two angles in radians that are co-terminal to 13π/8 are 29π/8 and 5π/8.
Learn more about angles on:
https://brainly.com/question/25716982
#SPJ1
The scores on an examination in psychology are approximately normally distributed with mean 500 and an unknown standard deviation. The following is a
random sample of scores from this examination.
417, 437, 486, 521, 553
Find a 95% confidence interval for the population standard deviation. Then give its lower limit and upper limit.
Carry your intermediate computations to at least three decimal places. Round your answers to at least two decimal places.
Lower limit:
Upper limit:
Answers
Answer:
the 95% confidence interval for the population standard deviation is (46.08, 355.39). The lower limit is 46.08, and the upper limit is 355.39.
Step-by-step explanation:
how do i solve for x
Answers
Answer:
55
Step-by-step explanation:
f(x)= −2x^2 + 8x − 10
{Find } f(-4)
Answers
Answer:
simply you have to substitute (-4) for all the (x) terms-2x²+8x -10-2(-4)²+8×(-4)-10-2(16) - 32 -10-32 -32 - 10-74
How many significant figures are in the number
43.6? 43.6 has [?] significant figures.
Answers
Answer:
43.6 has 3 significant figures.
marci is trying to decide whether to take her daughter to game zone or play place. at game zone she can buy a game card for 10$ and then she will pay 2$ per game. at play place there isn’t a cost for the game card, but the games are 4$ each. how many games would marci have to play for game zone and play place to cost the same amount?
Answers
Answer:
She would play 1 game at game zone and 3 games at play place for them to both cost $12.
What is the meaning of "the notion of finiteness"?
Answers
The notion of finiteness refers to the idea that something has a definite limit or is not infinite. It is a concept that has been applied in various fields of study, such as mathematics, computer science, and philosophy.
In mathematics, finiteness is a fundamental concept used to define various mathematical objects and structures, such as sets, numbers, and sequences. It is also used to define the properties of functions and to study the properties of mathematical systems.
In computer science, the notion of finiteness is crucial for the design and analysis of algorithms and computer programs. Computer scientists use finite state machines, which are mathematical models that describe the behavior of a system that can be in one of a finite number of states.
This concept is essential to the development of computer programs that are efficient, reliable, and secure.
In philosophy, finiteness is a concept that is often used to reflect on the nature of human existence and the limits of human knowledge. It is also used to examine the concept of time and the nature of reality.
In general, the notion of finiteness is a fundamental concept that has many applications in various fields of study.
To learn more about : finiteness
https://brainly.com/question/32403180
#SPJ8
What is the approximate area of a circle with radius 6 cm?
Answers
Answer:
133 m^2
Step-by-step explanation:
to find are of a circle it’s r^2 times pi
6^2 x pi
36 pi
113 m^2
Hopes this helps please mark brainliest
Answer:
Answer C is correct
Step-by-step explanation:
The formula to find the area of a circle is:
A = πr²
Here,
r => radius = 6m
Let us find the area of the circle.
A = πr²
A = 3.14 × 6 × 6
A = 113.04 m²
Approx. = 113m²
2/9 h = 8
h=
Pls tell me what h = !
Answers
Answer:
h=36
.......................
Inputs: People at concession stand Outputs: Cost of their order
this relation a function?
it a constant function?
it a 1-1 function?
Answers
People at the concession stand as input Cost of their order's output.
(1) The relation in question is a function.
(II) This function is not constant. (Each category of concession has a different order cost.)
Not a 1-1 function (iii). (Several persons arrived seeking the same sort of concession. So they all pay the same price for their order.)
A function describes the relationship between patrons' inputs at the concession stand and the cost of their order as an output. A function is a relationship between a set of possible inputs and outputs, where each input is associated to exactly one output.
The quantity of patrons at the concession stand serves as the input in this scenario, while the cost of their order serves as the output.
Learn more about on concession, here:
https://brainly.com/question/32140051
#SPJ1
simplify completely 7 / (x^2+3x-108) - 3 / (4x-36)
Answers
Answer:
-3x+8/4(x-9)(x+12)
Step-by-step explanation:
x
2
+3x−108
7
−
4x−36
3
Factor x
2
+3x−108. Factor 4x−36.
(x−9)(x+12)
7
−
4(x−9)
3
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of (x−9)(x+12) and 4(x−9) is 4(x−9)(x+12). Multiply
(x−9)(x+12)
7
times
4
4
. Multiply
4(x−9)
3
times
x+12
x+12
.
4(x−9)(x+12)
7×4
−
4(x−9)(x+12)
3(x+12)
Since
4(x−9)(x+12)
7×4
and
4(x−9)(x+12)
3(x+12)
have the same denominator, subtract them by subtracting their numerators.
4(x−9)(x+12)
7×4−3(x+12)
Do the multiplications in 7×4−3(x+12).
4(x−9)(x+12)
28−3x−36
Combine like terms in 28−3x−36.
4(x−9)(x+12)
−8−3x
Expand 4(x−9)(x+12).
4x
2
+12x−432
−8−3x
What is the volume of the triangular prism?
please help!! quickly its a test a look at the picture
7th grade math
Answers
The area of the triangle is:
A = (base•height) : 2 = (3•2) : 2 = 3 m2
So the volume is:
V = 3 • 8 = 24 m3
10
Select the correct answer.
This rational inequality can be used to determine the number of seconds, x, that a beginning ice-skater can skate before losing his or her footing.
>13
If Charlene has never ice-skated before, which inequality describes the number of seconds she can expect to skate before losing her footing?
O A. 6>x>6.5
OB. x<6
O c. x<0
O D. 6
OE. x <6
Reset
Next
Answers
The solution of the given inequality is x<6.5. Therefore, option D is the correct answer.
What are inequalities?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
The given inequality is x/x-6 >13.
Multiply x-6 on both the sides of an inequality, we get
x>13(x-6)
x>13x-78
Add 78 on both the sides of an inequality, we get
x+78>13x
Subtract x on both the sides of an inequality, we get
78>12x
12x<78
x<6.5
Therefore, option D is the correct answer.
To learn more about the inequalities visit:
https://brainly.com/question/20383699.
#SPJ1
"Your question is incomplete, probably the complete question/missing part is:"
This rational inequality can be used to determine the number of seconds, , that a beginning ice-skater can skate before losing his or her footing. x/x-6 >13 If Charlene has never ice-skated before, which inequality describes the number of seconds she can expect to skate before losing her footing?
A. 6>x>6.5
B. x<6
C. x<0
D. x<6.5
E. x<6
35,012,129 ____ 35,011,129 greater than less than PLEASE HELP
ANSWER FREE COINS JUST SAY =
Answers
Answer:
35,012,129 > 35,011,129
Answer:
>
Step-by-step explanation:
everything is the same but the 12 and 11
Researchers comparing the effectiveness of two pain medications randomly selected a group of patients who had been complaining of a certain kind of joint pain. They randomly divided these people into two groups, then administered the pain killers. Of the 112 people in the group who received medication A, 84 said this pain reliever was effective. Of the 108 people in the other group, 66 reported that pain reliever B was effective.
(a)Find a 95% confidence interval for the difference in the proportions of people who may find these medications effective. Interpret your interval.
(b) Does this interval contain zero? What does that mean for the hypothesis test of the difference in proportions?
Answers
(a) The 95% confidence interval for the difference in proportions of people who may find these medications effective is 0.029 to 0.231, which suggests that medication A is more effective than medication B in relieving joint pain.
(b) No, the interval does not contain zero, which means that the difference in proportions is statistically significant and supports the hypothesis that medication A is more effective than medication B.
Pls help ASAP
Give the domain and range
Answers
Answer:
D: {-2, 0, 2}
R: {-1, 1, 3