Solve 2x - 1/2 = 5 1/2
Answers
Answer:
3Step-by-step explanation:
\(5\frac{1}{2}=\frac{11}{2}\\\mathrm{So\:this\:becomes}\\2x-\frac{1}{2}=\frac{11}{2}\\\mathrm{Then,}\\(2x+\frac{-1}{2})+\frac{1}{2}=(\frac{11}{2})+\frac{1}{2}\\2x+\frac{(-1+1)}{2}=(\frac{11}{2})+\frac{1}{2}\\2x+\frac{0}{2}=(\frac{11}{2})+\frac{1}{2}\\\mathrm{Reduce}\\2x+0=(\frac{11}{2})+\frac{1}{2}\\2x=(\frac{11}{2})+\frac{1}{2}\\2x=\frac{(11+1)}{2}\\\mathrm{11+1=12,\:so}\\2x=\frac{12}{2}\\\mathrm{Prime-factorization}\\2x=\frac{(6\times 2)}{(1\times 2)}\)
\(\mathrm{6\times2=12\:and\:1\times2=2\:so\:\frac{12}{2}\:equals\:6,}\\2x=6\\\mathrm{Now,\:divide\:by\:the\:leading\:term,\:2}\\\frac{(2x)}{2}=\frac{6}{2}\\\mathrm{Factorization}\\x=\frac{(3\times 2)}{(1\times 2)}\\\mathrm{3\times2=6\:and\:1\times2=2\:so\:\frac{6}{2}\:equals\:3,}\\x=3\)
Hope this helps.
The solution to the equation 2x - 1/2 = 5 1/2 is x = 3.
Given Equation: 2x - 1/2 = 5 1/2
Step 1: Let's simplify the mixed number 5 1/2 to an improper fraction. 5 1/2 can be written as (11/2).
2x - 1/2 = 11/2
Step 2: To eliminate the fraction, multiply the entire equation by 2 to clear the denominators:
2 (2x - 1/2) = 2 (11/2)
This simplifies to:
4x - 1 = 11
Step 3: Add 1 to both sides of the equation to isolate the variable:
4x - 1 + 1 = 11 + 1
4x = 12
Step 4: Divide both sides of the equation by 4 to solve for x:
(4x)/4 = 12/4
x = 3
Therefore, the solution is x = 3.
Learn more about Equation here:
https://brainly.com/question/29538993
#SPJ6
Related Questions
Find an exponential equation that passes through the points (0, 4) and (2, 9).
Answers
Given:
An exponential equation passes through the points (0,4) and (2,9).
To find:
Exponential equation that passes through the given points.
Solution:
Let the required exponential function is:
\(y=ab^x\) ...(i)
The function passes through the points (0,4) and (2,9). It means the above equation must be true for these points.
\(4=ab^0\)
\(4=a(1)\)
\(4=a\)
And,
\(9=ab^2\)
Substituting \(a=4\), we get
\(9=(4)b^2\)
\(\dfrac{9}{4}=b^2\)
\(\pm \sqrt{\dfrac{9}{4}}=b\)
\(\pm \dfrac{3}{2}=b\)
In an exponential function b>0. So, \(b=\dfrac{3}{2}\).
Putting \(a=4,b=\dfrac{3}{2}\) in (i), we get
\(y=4\left(\dfrac{3}{2}\right)^x\)
Therefore, the required exponential function is \(y=4\left(\dfrac{3}{2}\right)^x\).
will give brainliest to quickest answer
Answers
Answer:
The vertex is option C: (-6, -2)
Step-by-step explanation:
The equation for a parabola is y = a(x – h)² + k where h and k are the y and x coordinates of the vertex, respectively. Thus, the vertex is (-6,2)
Pls mark brainliest.
Find the unit rate:
16 cupcakes in 4 boxes = ? cupcakes per box?
Need answers ASAP!
Answers
Answer:
4 cupcakes
Step-by-step explanation:
4 boxes = 16 cupcakes
Therefore,
1 box = 16/4 = 4 cupcakes
=> 1 box = 4 cupcakes
In the major course requirement in a math department, a student needs to choose one each from algebra, analysis, statistics, and geometry. There are 4 algebra courses, 3 analysis courses, 5 statistics courses, and 2 geometry courses available for major requirement. How many different ways can a student choose major requirement courses from these 4 areas
Answers
There are 120 different ways that a student can choose major requirement courses from these four areas.
In order to solve this problem, we need to use the concept of combinations. A combination is a selection of items from a set, without regard to the order in which they are chosen. The formula for the number of combinations of n objects taken r at a time is:
C(n,r) = n! / (r! * (n-r)!)
where n! means n factorial, which is the product of all positive integers up to n. For example, 5! = 5 * 4 * 3 * 2 * 1 = 120.
To solve this problem, we need to choose one course from each of the four areas: algebra, analysis, statistics, and geometry. The number of choices in each area are:
4 algebra courses
3 analysis courses
5 statistics courses
2 geometry courses
To find the total number of ways to choose one course from each area, we can use the multiplication rule of counting. This states that if there are n1 ways to do the first task, n2 ways to do the second task, and so on up to nk ways to do the kth task, then there are n1 * n2 * ... * nk ways to do all k tasks together.
In this case, there are 4 ways to choose an algebra course, 3 ways to choose an analysis course, 5 ways to choose a statistics course, and 2 ways to choose a geometry course. Therefore, the total number of ways to choose one course from each area is:
4 * 3 * 5 * 2 = 120
Thus, there are 120 different ways that a student can choose major requirement courses from these four areas.
Know more about concept of combinations here:
https://brainly.com/question/31768658
#SPJ11
Obtain numerical solution of the ordinary differential equation y' = 3t−10y²
with the initial condition: y(0)= −2 by Euler method using h=0.5 Perform 3 steps.
Solution of all problems MUST contain general formula and all intermediate results. Perform numerical computations using 4 digits after decimal point.
Answers
The Euler method with a step size of h = 0.5, the approximate numerical solution for the ODE is y(1.5) ≈ -1.1198 x 10^9.
To solve the ODE using the Euler method, we divide the interval into smaller steps and approximate the derivative with a difference quotient. Given that the step size is h = 0.5, we will perform three steps to obtain the numerical solution.
we calculate the initial condition: y(0) = -2.
1. we evaluate the derivative at t = 0 and y = -2:
y' = 3(0) - 10(-2)² = -40
Next, we update the values using the Euler method:
t₁ = 0 + 0.5 = 0.5
y₁ = -2 + (-40) * 0.5 = -22
2. y' = 3(0.5) - 10(-22)² = -14,860
Updating the values:
t₂ = 0.5 + 0.5 = 1
y₂ = -22 + (-14,860) * 0.5 = -7492
3. y' = 3(1) - 10(-7492)² ≈ -2.2395 x 10^9
Updating the values:
t₃ = 1 + 0.5 = 1.5
y₃ = -7492 + (-2.2395 x 10^9) * 0.5 = -1.1198 x 10^9
Therefore, after performing three steps of the Euler method with a step size of h = 0.5, the approximate numerical solution for the ODE is y(1.5) ≈ -1.1198 x 10^9.
Learn more about Euler method here:
https://brainly.com/question/30459924
#SPJ11
If 1/8 of my money is $80. What is 50 % of my money
Answers
Answer:
$320
Step-by-step explanation:
An easy way to solve this problem is to undo the operations, Find the total amount of money, and then find half of the amount. Since (80) is (\(\frac{1}{8}\)) the total amount of money, one has to multiply (80) by (8) to find the total amount of money.
(80) * (8)
= 640
Now one is asked to find (50%) of the money. It is known that (50%) is equivalent to (0.5), therefore multiply (640) by (0.5) to find how much (50%) of the money is.
(640) * (0.5)
= 320
Find the angle between vector bold lower u equals 3 bold lower I plus start root 3 end root bold lower j and vector bold lower v equals negative 2 bold lower I minus 5 bold lower j to the nearest degree. A. 82° B. 38° C. 142° D. 98°
Answers
Answer:
C. 142°
Step-by-step explanation:
You want the angle between vectors u=3i+√3j and v=-2i-5j.
AngleThere are a number of ways the angle between the vectors can be found. For example, the dot-product relation can give you the cosine of the angle:
u•v = |u|·|v|·cos(θ) . . . . . . where θ is the angle of interest
You can find the angles of the vectors individually, and subtract those:
u = |u|∠α
v = |v|∠β
θ = α - β
When the vectors are expressed as complex numbers, the angle between them is the angle of their quotient:
\(\dfrac{\vec{u}}{\vec{v}}=\dfrac{|\vec{u}|\angle\alpha}{|\vec{v}|\angle\beta}=\dfrac{|\vec{u}|}{|\vec{v}|}\angle(\alpha-\beta)=\dfrac{|\vec{u}|}{|\vec{v}|}\angle\theta\)
This method is used in the calculation shown in the first attachment. The angle between u and v is about 142°.
A graphing program can draw the vectors and measure the angle between them. This is shown in the second attachment.
__
Additional comment
The approach using the quotient of the vectors written as complex numbers is simply computed using a calculator with appropriate complex number functions. There doesn't seem to be any 3D equivalent.
The dot-product relation will work with 3D vectors as well as 2D vectors.
<95141404393>
three points t, u, and v on the number line have coordinates t, u, and v, respectively. is point t between points u and v ?
Answers
We can determine coordinates if point t is between points u and v by checking if u < t < v or v < t < u.
To determine if point t is between points u and v, we need to compare their coordinates. If u < v, then point t is between points u and v if and only if u < t < v. On the other hand, if v < u, then point t is between points u and v if and only if v < t < u.
Whether or not point t is between points u and v depends on the relationship between the coordinates of u and v. If u < v, t must fall between them, and if v < u, t must also fall between them.
To know more about coordinates follow the link:
https://brainly.com/question/31306451
#SPJ11
plssssssssssssssssssssssssssss
Answers
Answer:
D) 2275
Step-by-step explanation:
The value of y varies directly with x. If x = 4, then y = 36. Find the value of x when y = 144.
Answers
Answer:
16Step-by-step explanation:
Direct variation formula: y = kx
Given
x = 4, y = 36Finding the coefficient k:
36 = 4kk = 36/4k = 9So the function is
y = 9xSolving for x, when y = 144
144 = 9xx = 144/9x = 16What is the Y-intercept of the line shown above
Answers
Which of the following expressions is correctly written in scientific notation
Answers
Answer:
it is the 3 one
Step-by-step explanation:
For each question below, determine True or False: If a simple random sample is chosen with replacement, each individual has
the same chance of selection on every draw.
Answers
The statement If a simple random sample is chosen with replacement, each individual has the same chance of selection on every draw is True.
If a simple random sample is chosen with replacement, it means that after each selection, the chosen individual is placed back into the population before the next selection is made. In this case, each individual in the population has the same chance of being selected for every draw.
The process of replacing the selected individual ensures that the selection probabilities remain constant throughout the sampling process. As a result, each individual has an equal probability of being chosen on each draw, making the statement true.
To learn more about the simple random sample
https://brainly.com/question/30391235
#SPJ11
Help me with this one
Answers
Answer:
SSS
Step-by-step explanation:
We can see that 2 sides are equal already, and because they share a side, that side is also equal. So, side side side.
Who ever answers I will give brainlyst
- The scatterplot shows the average number of hours each of 13 people spends at work every
week and the average number of hours each of them spends on recreational activities every
week.
Based on the scatterplot, what is the best prediction of the average number of hours a person
spends at work every week if that person spends an average of 10 hours on recreational
activities every week
Answers
Answer:
5h
Step-by-step explanation:
Can u help me out with my newest one???
Answer:
5h
Step-by-step explanation:
Which of the expressions is rational? 25 + 2 7 − 2 64 + 45
Answers
Answer:
All of the expressions
Step-by-step explanation:
A rational number is one that can be written as a ratio, or a number with a terminating decimal.
All of the expressions are whole numbers, so they are all rational.
Javian has a gift card with a $150 balance. He buys several video games that cost $35 each. After the purchases, his gift card balance is $45. Which equation describes how many video games he bought?
a. 45+35x=150
b. 150-45=35x
c. 150=35x=45
d. 150-35x=45
PLEASEEEEEEE HELP!!!!!!!!!!!!!!!
Answers
Answer:
D
Step-by-step explanation:
150-35x=45
X in this equation would be 3
Take 35x3 and you get 105. Plug this in
150-105=45
hope this helps
Felipe has a business where he builds and sells birdhouses. To build 12 birdhouses, he needs \large 5\frac{1}{4} meters of wood. During the holiday season, Felipe was asked to make \large 4\frac{1}{2} times the number of birdhouses he usually makes. How many meters of wood does Felipe need to make that many birdhouses?
Answers
Based on the number of birdhouses that Felipe has to build in the holiday season, the meters of wood that Felipe needs would be 23 ⁵/₈ meters
How many meters of wood are needed?First, find out the number of birdhouses Felipe needs to make:
= Normal number of birdhouses x Increase in holiday season
= 12 x 4¹/₂
= 54 birdhouses
The meters of wood he needs are:
= Number of birdhouses to be made / Number of bird houses he usually makes x Meters of wood needed for birdhouses Felipe usually makes
= 54 / 12 x 5¹/₄
= 23 ⁵/₈ meters
Find out more on solving for quantities needed at https://brainly.com/question/2740942
#SPJ1
~Please help me with this q u e s t i o n~
Answers
Answer:
Point D
Step-by-step explanation:
\( \huge \qquad \sf Answer\)
How to locate a point on a graph (x - y plane) :
The x - coordinate of a point on the graph shows its distance from y - axis and sign refers to its direction that is +ve sign means right side of y - axis and -ve sign means left side of y - axis.
We have been given its x - coordinate as 9, so the required point should be At a distance of 9 units from y - axis and in right side of y - axis.
And similarly, y - coordinate shows distance of point from x - axis, +ve for upward direction and -ve for downward direction.
and we have given the y - coordinate as 0, ao its distance from x - axis is 0. that means the point lies of x - axis.
And by Observing the points clearly we can figure out that the required point is D. that satisfy the condition.
28. Geometry help please
Answers
Step-by-step explanation:
For crossing chords in a circle, the products of the segments are equal
6 * 4 = x * 14 -x
24 = -x^2 + 14x
-x^2 + 14x - 24 = 0 Use quadratic Formula ( or factoring ) to find:
x = 2 or 12 ( drawing is not to scale)
An iterative formula is shown below.
Xn+1 = 3/4xn-1
Work out the values of x2, x3 and x4, starting
with x1 = 2.
Give your answers to 2 d.p.
Answers
The value for the following order of the given iterative formula of xₙ + 1 = 3/4 xₙ₋₁ are:
x₂ = 0.5x₃ = - 0.63x₄ = - 1.47Iterative formula is used to process a repeating procedure to produce a series of results
We have an iterative formula of:
xₙ + 1 = 3/4 xₙ₋₁
We know that:
x₁ = 2
Hence:
x₂ + 1 = 3/4 x₁
x₂ + 1 = 3/4 (2)
x₂ + 1 = 3/2
x₂ = 1/2 = 0.5
x₃ + 1 = 3/4 x₂
x₃ + 1 = 3/4 (1/2)
x₃ + 1 = 3/8
x₃ = -5/8 = - 0.63
x₄ + 1 = 3/4 x₃
x₄ + 1 = 3/4 (-5/8)
x₄ + 1 = -15/32
x₄ = - 47/32 = -1.47
Learn more about Iterative Formula here: brainly.com/question/27751920
#SPJ1
what rule of probability was used to find the probability that none of the six independent field joints failed?
Answers
The rule of probability used to find the probability that none of the six independent field joints failed is the multiplication rule of probability
The rule of probability that was likely used to find the probability that none of the six independent field joints failed is the multiplication rule of probability.
The multiplication rule states that the probability of two or more independent events occurring together is the product of their individual probabilities. In this case, if we assume that the probability of each field joint failing is independent of the others, then the probability of none of the six field joints failing is the product of the probabilities of each joint not failing.
If the probability of each field joint not failing is p, then the probability of none of the six joints failing is given by:
P(none fail) = p × p × p × p × p × p = p^6
So, the multiplication rule of probability was used to calculate the probability of none of the six independent field joints failing by multiplying the individual probabilities of each joint not failing.
Learn more about multiplication rule here
brainly.com/question/30460990
#SPJ4
Complete the steps to solve the equation -13x - 15 = -93.
Answers
Answer:
x = 6
Step-by-step explanation:
-13x - 15 = -93
-13x = -78
x = 6
If you are doing a linear regression, what is the slope of the line predicted by the null hypothesis?
Answers
The null hypothesis is that the linear regression model does not exist. This essentially means that the value of all the coefficients is equal to zero.
What is the null hypothesis?
The null hypothesis is a common statistical theory that contends that there is no statistical relationship or significance between any two sets of observed data and measured phenomena for any given single observed variable.
Here,
We have to find out the slope of the line predicted by the null hypothesis if we are doing a linear regression.
We concluded that the null hypothesis states that the slope is equal to zero, and the alternative hypothesis states that the slope is not equal to zero.
Hence, the null hypothesis is that the linear regression model does not exist. This essentially means that the value of all the coefficients is equal to zero.
To learn more about the null hypothesis from the given link
https://brainly.com/question/13135308
#SPJ4
what equation does this represent?
Answers
4(7-8n)=-2n+8(6-5n) point slope from
Answers
Answer:
n = 2 i beleve
Step-by-step explanation:
i dont know if this is right but i did the math and im in 6th grade so im not really good with that stuff
<3 have a good day <3
Which expression could be used to find the volume of the prism shown below?
A rectangular prism with length of 12, height of 10, and width of 4.
(4 times 12) times 10
(4 + 12) times 10
(10 + 4) times 12
(10 + 12) times 4
Answers
c + 20 - 13 = 100 im doing a test i need help
Answers
Answer:
c is 93
Step-by-step explanation:
work backwards to get c
100 + 13= 113
113-20= 93
so your answer is 93
log 2x + log x = 2
What is the answer
Answers
Answer:
x=5\(\sqrt{2\\\)
Step-by-step explanation:
Answer:
5 sqrt 2
Step-by-step explanation:
Log 2x + log x = 2
log ( 2x * x ) = 2
log (2x^2) = 2
2x^2 = 100
x^2 = 50
x = sqrt (50) = 5 sqrt 2
What is the name of the green segment in the hyperbola below
Answers
The Length of the conjugate axis is equal to 2b. The transverse axis is an essential feature of a hyperbola, as it determines the overall shape of the hyperbola.
In a hyperbola, the name of the green segment is called the transverse axis. The transverse axis is the longest distance between any two points on the hyperbola, and it passes through the center of the hyperbola. It divides the hyperbola into two separate parts called branches.
The transverse axis of a hyperbola lies along the major axis, which is perpendicular to the minor axis. Therefore, it is also sometimes called the major axis.
The other axis of a hyperbola is called the conjugate axis or minor axis. It is perpendicular to the transverse axis and passes through the center of the hyperbola. The length of the conjugate axis is usually shorter than the transverse axis.In the hyperbola above, the green segment is the transverse axis, and it is represented by the letters "2a". Therefore, the length of the transverse axis is equal to 2a.
The blue segment is the conjugate axis, and it is represented by the letters "2b".
Therefore, the length of the conjugate axis is equal to 2b.The transverse axis is an essential feature of a hyperbola, as it determines the overall shape of the hyperbola. In particular, the distance between the two branches of the hyperbola is determined by the length of the transverse axis.
If the transverse axis is longer, then the branches of the hyperbola will be further apart, and the hyperbola will look more stretched out. Conversely, if the transverse axis is shorter, then the branches of the hyperbola will be closer together, and the hyperbola will look more compressed.
For more questions on Length .
https://brainly.com/question/28322552
#SPJ8