Answer:
To find the sum of a + b where a and b are rational number.
1. when a and b are natural numbers
just add them . for example a =3, b=8
then ,a + b = 11
2. When a and b are whole numbers,
simply add them . for example a= 0, b=8
a+ b = 0 + 8= 8
3. When a and b are integers
for example, a =-1 b=8,
a+ b= -1+ 8 =7,
a=-2, b= -8
a+ b= -2-8=-10
a= -6 , b=2
a+ b= -6 + 2= -4
a= 8, b= -2
a+ b= 8 +(-2) =6
I have written this because Rational number = [Integers{Whole number(Natural number)}]
now when a= Any fraction=[tex]\frac{p}{q}[/tex] and b = Any fraction=[tex]\frac{u}{v}[/tex]
now ,
[tex]\frac{p}{q} + \frac{u}{v}[/tex]
Find L.C.M of q and v
= if q and v are Co-prime , just multiply them to find their L.C.M.
For example 14,9. LCM=14×9=126
Otherwise, Find factors of q and v . Then take out common factors first and then multiply the remaining with with common factors.For example
q=12 and v=18
12 =2×2×3
18=2×3×3
common factor =2,3
non common=2,3
L.C.M= 2×2×3×3=36
Suppose LCM of q and v = r
then ,[tex]\frac{p}{q} + \frac{u}{v}[/tex]
=[tex]\frac{{\frac{r}{q}}\times p+{\frac{r}{v}\times u}}{r}\\[/tex]
= [tex]{{\frac{r}{q}}\times p+{\frac{r}{v}\times u}} = k[/tex]
then ,
a + b=[tex]\frac{k}{r}[/tex]
What is the slope of this line?
The slope of this line is -3/4
In order to find this, we look for two points on the line and then use the slope formula. Two points that are on the line are (0, 2) and (4, -1). Plug these into the following formula.
m (slope) = (y2 - y1)/(x2 - x1)
m = (-1 - 2)/(4 - 0)
m = -3/4
Ben exercises every 12 days and isabel every 8 days Ben and isabel both exercised today. how many days will it be until they exercise together again?
96 days
12 x 8 = 96
to check I did:
8 x 1 = 8
8 x 2 =16
etc.
I did the same thing with 12,
To find out how many days it will be until Ben and Isabel exercise together again, we need to determine the least common multiple (LCM) of their exercise intervals. The LCM of 12 and 8 is 24.
Explanation:To find out how many days it will be until Ben and Isabel exercise together again, we need to determine the least common multiple (LCM) of their exercise intervals. Ben exercises every 12 days, while Isabel exercises every 8 days.
To find the LCM of 12 and 8, we can list the multiples of each number and find the smallest number that appears in both lists. The multiples of 12 are 12, 24, 36, 48, 60, 72, and so on. The multiples of 8 are 8, 16, 24, 32, 40, 48, 56, 64, and so on. The smallest number that appears in both lists is 24.
Therefore, Ben and Isabel will exercise together again in 24 days.
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the density of aluminum is 2.70g/cm3 what is the volume of a 612 g piece of aluminum
We can see here that the volume of the 612 g piece of aluminum is approximately 226.67 cm³.
What is density?Density is a physical property of matter that measures how much mass is contained in a given volume of a substance. In other words, it quantifies how closely packed the particles (atoms, molecules, or ions) are within a material. Density is typically expressed in units such as grams per cubic centimeter (g/cm³) in the metric system or pounds per cubic inch (lb/in³) in the imperial system.
To find the volume of a 612 g piece of aluminum, you can use the formula for density:
Density = Mass/Volume
You have the density (2.70 g/cm³) and the mass (612 g), and you want to find the volume. Rearrange the formula to solve for volume:
Volume = Mass/Density
Inputting the values:
Volume = 612g/2.70g/cm³
Calculate the volume:
Volume = 612/2.70
Volume ≈ 226.67cm³
So, the volume of the 612 g piece of aluminum is approximately 226.67 cm³.
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50 PTS
A cyclist travels at distance of 400 meters in 120 seconds towards school, calculate his speed. (Show your work) Calculate his velocity if the direction is North East (NE)
The cyclist in practice question 2, comes to a stop position within 15 seconds. Calculate his acceleration. (Show your work) Is this an example of positive or negative acceleration?
1. Speed = 3.33333 Meters per second, 400/120=3.33333, average speed = total distance/elapsed time
2. Velocity = 3.33333 Meters, 400/120, V = distance / time
3. Acceleration = -0.222222[tex]m/s^2[/tex], acceleration = (velocity2 - velocity1) / time
acceleration = net_force / mass
Answer:
2 A. 400÷120=3.33
2 B. d/t=v
400/120=3.33 N E
3.
3.3m/s/15s=0.22m/s^2
downhill= negative slope=negative acceleration(slowing down)
Can anyone help me? I’m stuck
Angle A and Angle BCA are corresponding angles and equal.
Angle x and Angle BCA are VERTICAL angles and equal.
Therefore Angle A = Angle BCA = Angle x = 62 degrees.
Calculate your pay if you work h hours in one week and are Paid $10 per hour
To find your pay for a week, multiply the total hours worked (h) by the hourly wage ($10). For example, working 40 hours would yield a total pay of $400. A $2 per hour raise increases your hourly wage to $12 and represents a 20% pay increase.
Explanation:To calculate your pay if you work h hours in one week at a rate of $10 per hour, you simply multiply the number of hours worked by the hourly wage. This can be expressed in the following formula:
Total pay = Hourly wage imes Number of hours worked
So, if you work h hours, your total pay will be:
Total pay = $10/hour imes h hours
This means that if you work 40 hours in a week, for example, your total pay would be:
Total pay = $10/hour imes 40 hours = $400
If your boss is impressed with your work and gives you a $2 per hour raise, your new hourly wage would be $12 per hour. The percentage change in pay in this case is 20%, calculated by dividing the raise amount by the original wage ($2/$10 = 0.20 or 20%).
HELP ME PLEASE!! A minor league baseball team plays 109 games in a season. If the team won 13 more than three times as many games they lost, how many wins and loses did the team have?
Let losses = X
They won 13 more than 3 times as many so wins = 3X +13
Now you have wins + loses = total games:
X +3X + 13= 109
Combine like terms:
4x + 13 = 109
Subtract 13 from each side:
4x = 96
Divide each side by 4:
x = 96 / 4
X = 24
Wins = 3X +13
3(24) +13 = 72+13 = 85
Wins = 85 games
Losses = 24 games
Please help me find 2,4,6,8, and 10
It appears as though you're to figure out the quotient some way (as by using a calculator), then verify that the product of quotient and divisor gives the dividend.
2. 96 ÷ 6 = 16
... (6×10) + (6×6) = 96
... 6 × 16 = 96
4. 84 ÷ 6 = 14
... (6×10) + (6×4) = 84
... 6 × 14 = 84
6. 104 ÷ 4 = 26
... (4×20) + (4×6) = 104
... 4 × 26 = 104
8. 102 ÷ 6 = 17
... (6×10) + (6×7) = 102
... 6 × 17 = 102
10. 64 ÷ 4 = 16 . . . . Ken will make 16 gift bags, each containing 4 pens.
jessie is 45, his age is 5 years more than 4 times sals age how old is sal?
Sal is 10 years old. If you want to check you can do 10*4+5 and get 45
Find the product.
(6 a + b ) 2
Answer:
12a+2b
Step-by-step explanation:
what is the translation for y=x square+ 6
Answer:
y=x^2+6
you need to add in the exponent
What is the slope of this line?
23
−23
13
−13
the answer is -1 hope this helps
The slope of this line is -1
solve the system of equations by graphing: -1/3x + y=-1, y=4+1/3x
[tex]-\frac{1}{3}x[/tex] + y = -1 ⇒ y = [tex]\frac{1}{3}x[/tex] - 1
To graph this line, plot a point at the y-intercept (0, -1), than plot the next point using the rise over run from the slope [tex](\frac{1}{3})[/tex] by counting up 1 and to the right 3 of the y-intercept. This gives you a second point of (3. 0). Draw a line through those two coordinates.
Answer: Plot (0, -1) and (3, 0) and draw a line through them.
***************************************************************************************
y = 4 + [tex]\frac{1}{3}x[/tex] ⇒ y = [tex]\frac{1}{3}x[/tex] + 4
Same as above. Plot the y-intercept (0, 4) and then use rise over run from the slope to plot (3, 5).
Answer: Plot (0, 4) and (3, 5) and draw a line through them.
***********************************************************************************
You should end up with two PARALLEL lines. Since the lines never intersect, there are no solutions to this system of equations.
Answer: No Solution
Solve 2/3-4x+7/2=-9x+5/6
A.x=-3/2
B.x=-2/3
C.x=2/3
D.x=3/2
Twice the difference of a number and 2 is equal to three times the sum of the number and 9. Find the number
2(x - 2) = 3(x + 9)
Distributive property.
2x - 4 = 3x + 27
Subtract 2x from both sides.
-4 = x + 27
Subtract 27 from both sides.
-31 = x
Subtract. 86,700,000 − 3.45 × 10^7 5.22 5.22×10^6 5.22×10^7 5.22×10^8
86,700,000 − 3.45 × 10^7
= 8.67 × 10^7 − 3.45 × 10^7
= (8.67 - 3.45) × 10^7
= 5.22 × 10^7
Hope it helps
By Subtracting the given expression 86,700,000 − 3.45 × [tex]10^7[/tex] we get Option b) 5.22 × [tex]10^7[/tex].
To subtract 3.45 × [tex]10^7[/tex] from 86,700,000, we need to perform a mathematical operation involving exponents.
To perform the subtraction, we start by rewriting the numbers in scientific notation form, where a number is expressed as a product of a coefficient and a power of 10.
Given expression: 86,700,000 - 3.45 × [tex]10^7[/tex]
Step 1: Rewrite 86,700,000 in scientific notation:
86,700,000 = 8.67 × [tex]10^7[/tex]
Now, the expression becomes: 8.67 × [tex]10^7[/tex] - 3.45 × [tex]10^7[/tex]
Step 2: Subtract the coefficients:
8.67 - 3.45 = 5.22
Step 3: Keep the common base (10) and subtract the exponents:
[tex]10^7[/tex] (common base) - [tex]10^7[/tex] = [tex]10^7[/tex]
Combining the coefficient and the exponent, we get the final result:
5.22 × [tex]10^7[/tex] (option b)
When we subtract numbers in scientific notation, we first need to make sure both numbers have the same exponent. In this case, we converted 86,700,000 to scientific notation as 8.67 × [tex]10^7[/tex]. Then, we subtracted the coefficients, which gave us 5.22. The exponent remains the same, which is [tex]10^7[/tex]. So, the final answer is 5.22 × [tex]10^7[/tex].
The correct option is b) 5.22 × [tex]10^7[/tex].
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Complete Question
Choose the correct answer form the given options:
Subtract. 86,700,000 − 3.45 × [tex]10^7[/tex]
a) 5.22 5.22×[tex]10^6[/tex]
b) 5.22×[tex]10^7[/tex]
c) 5.22×[tex]10^8[/tex]
Question 42 Unsaved
Find the least common multiple of x3 - x2 + x - 1 and x2 - 1. Write the answer in factored form.
Question 42 options:
(x3 - x2 + x - 1)(x2 - 1)
(x + 1)(x - 1)(x2 + 1)
(x + 1)(x - 1)(x2 - 1)
(x + 1)2(x - 1)
[tex]x^3-x^2+x-1=x^2(x-1)+1(x-1)=\boxed{(x-1)}(x^2+1)\\\\x^2-1=x^2-1^2=\boxed{(x-1)}(x+1)\\\\LCM=\boxed{(x-1)}(x^2+1)(x+1)[/tex]
[tex]Answer:\ (x+1)(x-1)(x^2+1)[/tex]
Marissa bought 12.8 pounds of potatoes at $1.35 a pound. How much did Marissa spend on the potatoes?
17.28 dollars is the answer
12.8 * 1.35 =17.28
Therefore Marissa spent $17.28 on potatoes.
a snail crawl 4 m in 1 hour how many centimeters will the snail crawl in 2 hours
Solve 18n-7p-15n=5p for n
The solution to the given equation 18n - 7p - 15n = 5p for n is n = 4p. Thus, the option D is correct.
The equation is given as follows:
18n - 7p - 15n = 5p
Combine like terms by subtracting 15n from 18n:
(18n - 15n) - 7p = 5p
3n - 7p = 5p
Move the term containing n to the other side of the equation by adding 7p to both sides:
3n - 7p + 7p = 5p + 7p
3n = 12p
Solve for n by dividing both sides of the equation by 3:
(3n)/3 = (12p)/3
n = 4p
Therefore, the solution to the equation 18n - 7p - 15n = 5p for n is n = 4p.
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Describe a real life multiplication situation for which a estimate makes sense
Estimation is useful in calculating the total cost of items in a grocery store basket.
Explanation:An example of a real-life multiplication situation where estimation makes sense is calculating the total cost of items in a grocery store basket. Let's say you have a basket with 3 apples that cost $1.50 each and 2 yogurts that cost $2.75 each. To estimate the total cost, you can round the prices to the nearest dollar and multiply: 3 x $2 + 2 x $3 = $6 + $6 = $12. This estimation gives you a rough idea of the total cost without needing to calculate exact values.
Audra was drawing a perpendicular bisector of segment AB with a compass. She started with line segment AB. Then, she placed her compass point on A and open the compass more than halfway to B. Which of the following is Audra’s next step?
A perpendicular bisector must go through the midpoint of a line, in this case AB. Since Audra opened her compass to more than half way she needs to close it partially until she is on the midpoint.
Answer:
Given that Audra was drawing a perpendicular bisector of segment AB with a compass. She started with line segment AB. Then, she placed her compass point on A and opened the compass more halfway to B.
Her next step will be "Using the width of the compass from the previous step, draw two arcs to the left and right of both A and B".
Step-by-step explanation:
Answer number one please
30 bass and 5 perch, so then you will bet minimal costs
What is the direct variation equation for the table of ordered pairs?
X Y
20 24
30 36
40 48
The equation for the direct variation is y = 1.2x
In order to find this, we start with the base for any direct variation equation.
y = kx.
Now we use the ordered pairs to find the value of k to model the equation.
y = kx
24 = k(20)
1.2 = k
Now that we know this, we can model the equation as y = 1.2x and test for the other values --- each of which work in the newly written equation.
Answer:
its actually 0.8x
Step-by-step explanation:
im saying this for future people
Given the midpoint (1.5,1.5) and the endpoint (5,7) where is the other endpoint located
The formula of a midpoint:
[tex]M_{AB}\left(\dfrac{x_A+x_B}{2},\ \dfrac{y_A+y_B}{2}\right)[/tex]
We have:
[tex]M(1.5,\ 1.5)\to x_M=1.5,\ y_M=1.5\\A(5,\ 7)\to x_A=5,\ y_A=7[/tex]
Substitute
[tex]\dfrac{5+x_B}{2}=1.5\qquad|\cdot2\\\\5+x_B=3\qquad|-5\\\\x_B=-2\\\\\dfrac{7+y_B}{2}=1.5\qquad|\cdot2\\\\7+y_B=3\qquad|-7\\\\y_B=-4[/tex]
Answer: (-2, -4)Kara invested 1250 in production pf a friends music cd her friend paid her back at 6% annual interest after 36 months how much money does kara get back
Ask google for help on that.
use the fact that there are 2pi radians in each circle to find another angle, smaller than 2pi, that is equivalent to 17pi/6. Show steps please
we are given angle as
[tex]\theta=\frac{17\pi}{6}[/tex]
we can write it as
[tex]\theta=\frac{12\pi+5\pi}{6}[/tex]
now, we can break it
[tex]\theta=\frac{12\pi}{6}+\frac{5\pi}{6}[/tex]
On simplifying
[tex]\theta=2\pi +\frac{5\pi}{6}[/tex]
we know all angles repeats itself after 2pi
so,
[tex]2\pi + \theta= \theta[/tex]
so, we get
[tex]\theta=\frac{5\pi}{6}[/tex]...............Answer
Final answer:
To find an angle equivalent to 17pi/6 radians and smaller than 2pi, subtract multiples of 2pi. In this case, subtracting one full circle (2pi) from 17pi/6 yields an equivalent angle of 5pi/6 radians.
Explanation:
To find an angle equivalent to 17pi/6 radians that is smaller than 2pi radians, we can subtract multiples of 2pi until we get an angle that lies between 0 and 2pi. This is because angles that differ by full circles (multiples of 2pi) are equivalent in the circular system.
First, calculate how many full circles 17pi/6 radians contain:
17pi/6 ÷ 2pi = 17/12 ≈ 1.4167
Since 1.4167 is more than 1 but less than 2, we know that 17pi/6 radians contain one full circle plus some additional angle. To find this angle, subtract the full circle from 17pi/6.
17pi/6 - 2pi = 17pi/6 - 12pi/6 = 5pi/6
Thus, 5pi/6 radians is equivalent to 17pi/6 radians but is less than 2pi and thus satisfies the conditions of the problem.
The price of one share or acme company declined $5 per day for 4 days un a row. How much did the price of one share change in total after the 4 days?
5 X 4 = $ 20 $ Your answer is 20.
can someone help me with this one math problem ? picture is below
How do you write 0.253 in two other forms?
Expanded form
0.200 + 0.050 + 0.003
Standard (word) form
zero and two hundred fifty three
hope that helps :)
253/1000 and 253% is the answer to your question :)