How to add/Subtract fractions With an Example and explain good
Answers
Answer:
The first example is adding fractions. The last is Subtraction.
Step-by-step explanation:
The first step is finding the LCD or Least Common Denominator. In this case, we multiply both denominators by each other 2 x 3 = 6 before we proceed.
Secondly, we multiply the bottom denominator on the right (which is three) and multiply it by numerator and denominator on the left.
\(\frac{1}{2}\) x 3= Multiply the numerator and denominator and you should get this
\(\frac{3}{6}\)
Next multiply \(\frac{1}{3}\) by 2. You should get \(\frac{2}{6}\)
The final step is just to add the numbers on the very top. You should get \(\frac{5}{6}\)
*Also note, pay attention to your question. Some may require decimal form or simplification.
1. \(\frac{1}{2} + \frac{1}{3} = \frac{5}{6}\)
2. \(\frac{3}{6}\) +\(\frac{2}{6}\) = \(\frac{5}{6}\)
3. The answer is \(\frac{5}{6}\)
_________________________________________
The next example is subtraction.
Find the LCD.
Next, start by multiplying \(\frac{3}{5}\) by 3. Penultimately, multiply \(\frac{1}{3}\) by 5. Finally, subtract 9-5 to get 4. The answer should be \(\frac{4}{15}\)
1. \(\frac{3}{5} - \frac{1}{3}\)
2. \(\frac{9}{15}\) - \(\frac{5}{15}\) = \(\frac{4}{15}\)
Related Questions
(5x 10-6)(3x 10-4)(5x 10-6) (3 x 10 - 4) =PLS HELP IT’S DUE TNNNN !
Answers
we can multiply the normal numbers on the one hand and the scientific notation on the other hand
so
\(\begin{gathered} (5\times3)(10^{-6}\times10^{-4}) \\ (15)(10^{-6+(-4)}) \\ =15\times10^{-10}=1.5\times10^{-9} \end{gathered}\)Christie has $200 in her bank account. Every month, she deposits $20 into her account.
The equation of the line that models the amount of money, y, in her account x months from now is y = x .
Answers
Answer:
y = 20x + 200
Step-by-step explanation:
The 200 is the constant. It is only added once, but the monthly deposits are added at 20 every month.
After 1 month:
y = 20x + 200
y = 20(1) + 200
y = 20 + 200
y =220 money deposited.
After 2 months:
y = 20x + 200
y = 20(2) + 200
y = 40 + 200
y =240 money deposited.
After 3 months:
y = 20x + 200
y = 20(3) + 200
y = 60 + 200
y = 260 money deposited
And so on, and so on, and so on...
make x subject
u= cos 0.5x
Answers
By making x the subject of the formula in this equation u = cos(0.5x) gives x = 2cos⁻¹(u).
How to make x the subject of the formula?In Mathematics and Geometry, an equation can be defined as a mathematical expression which shows that two (2) or more thing are equal. This ultimately implies that, an equation is composed of two (2) expressions that are connected by an equal sign.
In this exercise, you are required to make "x" the subject of the formula in the given mathematical equation by using the following steps.
By taking the arc cosine of both sides of the equation, we have the following:
u = cos(0.5x)
cos⁻¹(u) = 0.5x
By multiplying both sides of the mathematical equation by 2, we have the following:
2 × cos⁻¹(u) = 0.5x × 2
x = 2cos⁻¹(u)
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1) How much interest will you pay on a $43,000 car loan with a fixed APR of 4.9% if the loan is
for 5 years?
Answers
With a monthly repayment of $809.49, the total interest on the car loan will be $5,569.67.
How is the total interest computed?We assume that there are monthly repayments and compounding interest on the car loan.
With periodic repayments and compounding interest, the total interest paid on the car loan will be as shown by the car loan calculator.
Car loan = $43,000
Down payment = $0
Fixed Annual Percentage Rate (APR) = 4.9%
Loan term = 5 years
Car Loan Calculator with monthly Repayment:
Payment = $809.49/month
Interest Paid =$5,569.67
Total Paid = $48,569.67
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Question 3
Describe the function between x=-4 and x = -1.
Answers
Answer:
liner increasing
Step-by-step explanation:
In a random sample of 1500 Arts majors who are graduating from the University of Western Cape this summer (2021), we observe that 1380 have already found a job.
What is the proportion of students that have already NOT found a job (rounded off to two decimals)? [3]
Answers
The proportion of Arts majors who have not found a job is 8%, rounded off to two decimal places.
To find the proportion of Arts majors who have not found a job, we first need to calculate the total number of students who have not found a job.
The total number of students who have not found a job would be 1500 - 1380 = 120.
To calculate the proportion of students who have not found a job, we can divide the number of students who have not found a job by the total sample size:
The proportion of students who have not found a job = 120 / 1500 = 0.08 or 8%.
Therefore, the proportion of Arts majors who have not found a job is 8%, rounded off to two decimal places. This suggests that a majority of the graduating Arts majors from the University of Western Cape have found employment before their graduation.
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Add. Write your answer in simplest form.
5 3/4+ 2 11/12
Answers
True or False: If the discriminant is less than zero, then the graph will never cross the x-axis.
False
True
Answers
Answer:
True
Step-by-step explanation:
If the discriminant \(D=b^2-4ac < 0\), then there are two complex roots
If the discriminant \(D=b^2-4ac > 0\), then there are two real roots
If the discriminant \(D=b^2-4ac=0\), then there is only one real root
The figure to the right shows the distance-time graph for a muscle car accelerating from a standstill. Use the information in the figure to answer parts (a) and (b). The table below lists the coordinates of the points.
Answers
The acceleration of the car is 8 m/s^2.
The figure shown in the question is the distance-time graph of a muscle car accelerating from a standstill. The table lists the coordinates of points on the graph.The following observations can be made from the graph and the table: The car is at rest at time t=0 and at distance x=0. It then starts accelerating, and its speed increases uniformly with time. The slope of the distance-time graph is the velocity of the car.
Since the velocity is increasing uniformly, the slope of the graph is a straight line with a positive slope. The area under the graph between two points gives the displacement of the car during that time interval. The displacement can be calculated as the product of the average velocity and the time interval. Using the coordinates in the table, we can calculate the average velocities for each time interval and the displacement during that interval.
(a) The average velocity of the car between t=0 and t=2 is equal to the slope of the graph between the two points (0,0) and (2,32). This can be calculated as the difference in distance divided by the difference in time:Average velocity = (32 - 0) / (2 - 0) = 16 m/sThe displacement during this time interval is given by the area under the graph between the two points:Displacement = (1/2) x 32 x 2 = 32 m
(b) The acceleration of the car is given by the slope of the velocity-time graph. Since the velocity is increasing uniformly with time, the velocity-time graph is also a straight line with a positive slope. The slope of the velocity-time graph is equal to the acceleration. We can calculate the slope of the velocity-time graph between two points using the coordinates in the table. For example, the slope between t=0 and t=2 is given by the difference in velocity divided by the difference in time:Slope = (16 - 0) / (2 - 0) = 8 m/s^2
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Write a numerical expression to represent the phrase "the sum of 25 and the cube of 9." Do not evaluate the expression.
Answers
Answer:
25 + 9^3
Step-by-step explanation:
Solve the equation by first subtracting 2/3 from each side
3x + 2/3 =7 5/6
Answers
The solution to the equation is x = 2 7/18
How to determine the solution to the equationFrom the question, we have the following parameters that can be used in our computation:
3x + 2/3 =7 5/6
Solve the equation by first subtracting 2/3 from each side
So, we have
3x = 7 1/6
Divide both sides of the equation by 3
This gives
x = 2 7/18
Hence, the solution is 2 7/18
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Select the correct answer. Maria donates a fixed amount, a, to a charity each month. If she donates $300 in 12 months, what is the equation for a? A. a + 300 = 12 B. a × 300 = 12 C. a × 12 = 300 D. a + 12 = 300 E. a + 32 = 100
Answers
Answer: C
she donates a for 12 months, the 12 in the a * 12=300. the a is the fixed amount, meaning she will donate a 12 times in a year.
If × is a negative integer less than -1, which of these is the largest? Explain your answer.
Answers
Answer:
B) x ⋅ x
Step-by-step explanation:
Lets substitute -2 for x in the following formulas
A) -2 + -2 = -4
B) -2 ⋅ -2 = 4
C) -2/-2 = 1
Therefore, B is the correct answer
Explanation:
negative times negative makes a positive
If x and y vary directly and y is 12 when x is 2, find y when x is 14.
Answers
As x and y varies directly, the value of y when x = 14 is 84.
What is the value of y when x = 14?Direct variation equation is a linear equation in two variables.
It is expressed as;
x ∝ y
Hence x = ky
Where k is the proportionality constant.
Given that;
x = 2y = 12Proportionality constant k = ?First, we determine the proportionality of constant.
x = ky
k = x/y
k = 2/12
k = 1/6
Now, the value of y when x is 14 will be;
x = ky
14 = (1/6)y
Multiply both sides by 6
14 × 6 = 6 × (1/6)y
14 × 6 = (6/6)y
84 = y
y = 84
Therefore, the value of y is 84.
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How can you use mental math to multiply two numbers?
Answers
Answer: Break the numbers you're multiplying into parts.
Step-by-step explanation:
What I find helps is splitting up the numbers and later adding them back together. An example of this is:
29×14
First I'd do 29×10, and get 290
Then 20×4, followed by 9×4, resulting in 80 and 36 respectively
Finally, 290+80+36= 406
I find the simplest numbers in the problem (2,5,10,20, etc.) and multiply from there. This may not be the best trick, but this is what I find helps. I hope this may help you too, and I wish you the best of luck.
if a polygon is a triangle, then it has exactly three sides. is the converse of the conditional true?
Answers
Answer:
If a polygon is a triangle then it has exactly three sides
A polygon has 3 sides if and only if it is a triangle. Put it all together: Conditional: If a polygon is a triangle, then it has three sides. Converse: If a polygon has three sides, then it is a triangle.
Answer:
yes
Step-by-step explanation:
because the polygon it has tree sides it's called triangle hope it's helpa + b=c make (a) the subject with working
Answers
Step-by-step explanation:
a= c-b pls let me know if it is correct or not
using the line of best fit
Answers
The monthly cell phone bill when shared data equals zero is given as follows:
$26.
How to define a linear function?The slope-intercept representation of a linear function is given by the equation presented as follows:
y = mx + b
The coefficients of the function and their meaning are described as follows:
m is the slope of the function, representing the change in the output variable y when the input variable x is increased by one.b is the y-intercept of the function, which is the initial value of the function, i.e., the numeric value of the function when the input variable x assumes a value of 0. On a graph, it is the value of y when the graph of the function crosses the y-axis.The intercept of the line in this problem is given as follows:
b = 26.
Hence $26 is the monthly cell phone bill when shared data equals zero.
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THIS WAS THE ONE I MEANT TO POST
Find the number of ways four out of nine patients can be chosen to complete a survey
Answers
3/5 = 6/10, so 3 x 6 = 5 x 10 true false
Answers
Answer:
False
Step-by-step explanation:
Should be 3 x 10 = 6 x 5
An art supplies store sells boxes that contain colored pencils and markers. Each box has a colored pencil to marker ratio of 5 to 2. Complete the table for the missing number of colored pencils, markers, or total number of colored pencils and markers in each box for sale.
Answers
Based on the information, we can infer that the tables are completed as follows: 5, 10, 15, 4, 8.
How to complete the table of ratios?To complete the table of the ratios we must take into account the information provided in the fragment. According to the above, in box A for every two markers there are 5 pencils and in box B for every three markers there are 4 pencils. Then the ratios would be the following:
Box A
2 markers, 5 pencils.4 markers, 10 pencils.6 markers, 15 pencils.box B
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whats the same about online school and in-person
for a project pls help thanks :)
Answers
Answer:
You're both learning the same stuff, only in different environments.
Step-by-step explanation:
It doesn't matter about the different environments you are in, you are still learning the same schoolwork that you are required to do.
Answer:
The similarity between online school and in- person is the material learned and how it is taught.
Step-by-step explanation:
wich expression is equivalent to 0.5 * 0.6?
Answers
Answer:
0.3
Step-by-step explanation:
Answer:
0.3
Step-by-step explanation:
I hope this is what you where asking for?
5.Given the sample triangle below and the conditions a=3, c = _51, find:cot(A).
Answers
Depending on the angle we are analyzing on the right triangle, each side of it takes a different name. In this case, we are going to name them depending on the angle A. Then,
a: opposite side (to A)
b: adjacent side
c: hypotenuse
STEP 2: formula for cot(A)We know that the formula for cot(A) is:
\(\cot (A)=\frac{\text{adjacent}}{\text{opposite}}\)Replacing it with a and b:
\(\begin{gathered} \cot (A)=\frac{\text{adjacent}}{\text{opposite}} \\ \downarrow \\ \cot (A)=\frac{b}{a} \end{gathered}\)Since a = 3:
\(\cot (A)=\frac{b}{3}\)STEP 3: finding bWe have an expression for cot(A) but we do not know its exact value yet. First we have to find the value of b to find it out.
We do this using the Pythagorean Theorem. Its formula is given by the equation:
\(c^2=a^2+b^2\)Since
a = 3
and
c = √51
Then,
\(\begin{gathered} c^2=a^2+b^2 \\ \downarrow \\ \sqrt[]{51}^2=3^2+b^2 \\ 51=9+b^2 \end{gathered}\)solving the equation for b:
\(\begin{gathered} 51=9+b^2 \\ \downarrow\text{ taking 9 to the left} \\ 51-9=b^2 \\ 42=b^2 \\ \downarrow square\text{ root of both sides} \\ \sqrt{42}=\sqrt{b^2}=b \\ \sqrt[]{42}=b \end{gathered}\)Then,
b= √42
Therefore, the equation for cot(A) is:
\(\begin{gathered} \cot (A)=\frac{b}{3} \\ \downarrow \\ \cot (A)=\frac{\sqrt[]{42}}{3} \end{gathered}\)Answer: D
Out of 120 customers asked at a restaurant, 38 rounded their bill up to the next whole dollar and donated the difference to the local Children's Hospital. How many consecutive customers must round up the bills so that the percentage of people who donated increases to 50%?
A. 44 customers
B. 40 customers
C. 36 customers
D. 32 customers
Answers
Using proportions, it is found that 44 consecutive customers must round up the bills so that the percentage of people who donated increases to 50%, so option A is correct.
A proportion is the number of desired outcomes divided by the number of total outcomes.
Considering that 38 out of 120 customers rounded their bill up, with x customers added, the proportion will be of 38 + x out of 120 + x.
The desired proportion is 0.5, hence:
\(\frac{38 + x}{120 + x} = 0.5\)
\(38 + x = 60 + 0.5x\)
\(0.5x = 22\)
\(x = \frac{22}{0.5}\)
\(x = 44\)
44 customers, so option A.
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Jackson purchased $5,200 worth of electronic equipment from BetterBuy on their deferred payment plan. The plan
allows the customer to make no down payment and no payment at all for five months. If the entire amount is paid in
full before the five month deferment ends, the finance charge with an APR of 19.8% is applied each month going
back to the first month. How much would it cost Jackson in finance charges if he misses the 5-month deadline?
Answers
Answer:
If Jackson misses the 5-month deadline, it will cost him $429 in finance charges.
Step-by-step explanation:
Since Jackson purchased $ 5,200 worth of electronic equipment from BetterBuy on their deferred payment plan, and the plan allows the customer to make no down payment and no payment at all for five months, while if the entire amount is paid in full before the five month deferment ends, the finance charge with an APR of 19.8% is applied each month going back to the first month, to determine how much would it cost Jackson in finance charges if he misses the 5-month deadline the following calculation should be performed:
5,200 x (1 + (0.198 / 12 x 5)) = X
5,200 x (1 + (0.0165 x 5)) = X
5,200 x (1 + 0.0825) = X
5,200 x 1.0825 = X
5.629 = X
5,629 - 5,200 = 429
Therefore, if Jackson misses the 5-month deadline, it will cost him $429 in finance charges.
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Question 2 (2.02, 2.05): The linear function f(x) represents the average test score in your language arts class, where x is the number of the test taken. The linear function g(x) represents the average test score in your social studies class, where x is the number of the test taken.
Answers
Answer:
A) 80.6, B) 83----------------------
Part AUse the equation f(x) = 0.3x + 80 and find its value at x = 2f(2) = 0.3*2 + 80 = 0.6 + 80 = 80.6Part BUse the table and find the value of g(x) when x = 2g(2) = 83Answer:
A. 80.6
B. 83
Step-by-step explanation:
Part AAverage Test Score (Language Arts class) function:
\(f(x)=0.3x+80\)
To determine the test average after completing test 2, substitute x = 2 into the given function:
\(\begin{aligned} \implies f(2)&=0.3(2)+80\\&=0.6+80\\&=80.6\end{aligned}\)
Part BAverage Test Score (Social Studies class) table:
\(\begin{array}{|c|c|}\cline{1-2} x&g(x)\\\cline{1-2} 1&85\\\cline{1-2} 2&83\\\cline{1-2} 3&81\\\cline{1-2} \end{array}\)
To determine the test average after completing test 2, find the value of the function from the table when x = 2:
\(\implies g(2)=83\)
A baseball diamond is a square whose sides are 90
feet long. Suppose a player running from second base to third base has a speed of 30 feet per second at the instant he is 20 feet from third base. At what rate is the player’s distance from home plate changing at that instant?
Answers
Answer: dy/dt = 37.42 fps
Step-by-step explanation:
First, let's define a few variables.
t = time
x = Distance the player is from third base = 20 feet
dx/dt = Velocity the player is running towards third base = -30 fps (since he is running towards third base, the x value will decrease with time, hence the negative value)
y = Distance between the player and home plate (We will find this value below)
dy/dt = Rate of change between the player's distance from home plate (This is the answer to our problem)
Now, let's use the Pythagorean theorem to relate the x and y terms.
y2 = x2 + 902
Use x = 20 feet to find y in this instant.
y2 = 202 + 902
y = 92.2 feet
Now, let's use implicit differentiation to take the derivative of this expression.
2y*dy/dt = 2x*dx/dt + 902
And let's plug in x, y, and dx/dt to solve for dy/dt.
2(92.2)*dy/dt = 2*20*-30 + 902
dy/dt = 37.42 fps
I need help with this this if answered correctly I’ll give 30 more points
Answers
Answer:
No. Her claim is too large. The actual value is 4 cm.
Because Volume = l³
4³ equals to 64 which means size of the edge is 4cm.
Help me please I need help x^2 - 8x + 16
Answers
The set of factors used to factor the given trinomial are -4 and -4. Therefore, option C is the correct answer.
The given trinomial is x²-8x+16.
Factors of 16 Sum of factors
-1 and -16 -1+(-16)=-17
-2 and -8 -2+(-8)=-10
-4 and -4 -4+(-4)=-8
The set of factors would used to factor the trinomial are -4 and -4.
Therefore, option C is the correct answer.
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