Answers
Answer:
[tex]\frac{1}{2}[/tex]
Find the least common factors of both numbers.
[tex]1/3~has~4\\2/12~has~1[/tex]
Multiply the numerator and denominator.
[tex]\frac{1 * 4}{3 * 4} = \frac{4}{12} \\\\\frac{2 * 1}{12 * 1} = \frac{2}{12}[/tex]
Add both numbers together. That does not mean you have to add the denominators. When the denominators are the same, keep them the same.
[tex]\frac{4}{12} +\frac{2}{12} = \frac{6}{12}[/tex]
Simplify.
[tex]\frac{6}{12} -- > \frac{1}{2}[/tex] because they are both halves.
Part I: Determining the common denominator of the terms
Given expression:
[tex]\dfrac{1}{3} + \dfrac{2}{12}[/tex]
To simplify the expression, we need to determine the common denominator of both fractions (1/3 and 2/12). To determine the common denominator of both fractions, we need to determine the LCM of the denominators (12 and 3). Simply write the multiples of (12 and 3) and determine the least common multiple (LCM).
⇒ Multiples of three: 3, 6, 9, 12, 15, 18...⇒ Multiples of twelve: 12, 24, 36, 48, 60...Since the LCM is 12, our common denominator is 12.
Part II: Multiplying both denominators by a number which is equivalent to 12
Now, multiply both denominators by a number such that the denominators are equivalent to 12. Keep in mind that the number you multiply the denominator should also be multiplied to the numerator.
[tex]\implies \dfrac{x}{3x} + \dfrac{2y}{12y} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \huge\text{[}3x = 12; 12y = 12\huge\text{]}[/tex]
[tex]\implies \dfrac{4}{3(4)} + \dfrac{2(1)}{12(1)} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \huge\text{[}x = \dfrac{12}{3} = 4; y = \dfrac{12}{12} = 1 \huge\text{]}[/tex]
[tex]\implies \dfrac{4}{12} + \dfrac{2}{12}[/tex]
Part III: Adding the fractions
Since the denominators are the same, we can now add the fractions;
[tex]\implies \dfrac{6}{12}[/tex]
Part IV: Simplifying the fraction obtained from the above
Since 6 is divisible by 12, we can further simplify the fraction.
[tex]\implies \dfrac{6 \times 1}{6 \times 2}[/tex]
[tex]\implies \boxed{\dfrac{1}{2}}[/tex]
Related Questions
2.5(2x − 5) − (5x + 2) SIMPLE MATH PROBLEM PLS HELP
Answers
2.5 x 5=12.5
2.5 x 5x=12.5x
2.5 x 2=5
Answer:
-14.5
Step-by-step explanation:
[tex]\sf 2.5(2x - 5) - (5x + 2)[/tex]
Remove parentheses from (5x+2):-
[tex]\sf 2.5(2x-5)-5x-2[/tex]
Use the distributive property to multiply 2.5 by 2x−5.
[tex]\sf 5x-12.5-5x-2[/tex]
Combine like terms:-
[tex]\sf (5x-5x)+(-12.5-2)[/tex]
[tex]\sf (5x-5x)=\boxed{0}[/tex]
[tex]\sf -12.5-2=\boxed{-14.5}[/tex]
____________________________A trapezoid has base lengths of 12 centimeters and 13 centimeters. The other sides have lengths of 5 centimeters and 10 centimeters. A rectangle with side lengths of 2 centimeters and 5 centimeters is connected to the side with length 10 centimeters. What is the area of the composite figure? 70 cm2 100 cm2 105 cm2 130 cm2
Answers
Answer:
D. 100 cm^2
Step-by-step explanation:
i did this before so ik im right
Answer: B 100
Step-by-step explanation:
I just took it
please help me with this thank you
Answers
beep bop boop bleep bloop i is bored lol
Please help
pictures are down below
Answers
Traigle ABC is shifted left by 6 units and reflected over the x axis.
Use the fact that the bacteria is doubling every five minutes. What fraction of the bottle was full at 11:20am?
Answers
6 inches = _____ centimeters
Answers
Answer:
15.2 cm
Step-by-step explanation:
Inch to centimeter conversion is multiplying the number of inches by 2.54
6 * 2.54 = 15.24
the 2 is in the tenths place
4 is less than and not equal to 5, therefore the 2 stays the same
6 inches = 15.2 centimeters
hope this helps:)
What is the length of the hypotenuse? If necessary, round to the nearest tenth.
C =
Answers
Answer:
Step-by-step explanation:
Answer:
C^2 = 95 ft is the length of the hypotenuse.
Step-by-step explanation:
To get the hypotenuse, apply the Pythagorean theorem.
The formula is a^2+b^2=c^2, where a and b are the leg lenths and c is the length of the hypotenuse. This is referred to as the Pythagorean theorem.
We know what a and b are, so lets utilize the Pythagorean theorem
.
a^2 + b^2 = c^2 - This is the Pythagorean theorem formula.
76^2 + 57^2 = C^2 - Fill in the equation with a= 76 and b = 57^2.
5776 + 3249 = c^2
9025 = c^2 - C^2 is found by adding A^2 and B^2.
square root of c^2 = square root of 9025 - Take the square root of both sides of the equation.
C = 95 ft - Simplify
C^2 = 95 ft is the length of the hypotenuse. Brainliest? :D
can anyone help me answer this
Answers
so 180 minutes in total
Vada places a box of toys and a box of books together. The box of toys has a length of 5 feet, a width of 3 feet, and a height of 2 feet. The box of books has a length of 6 feet, a width of 4 feet, and a height of 2 feet. What is the combined volume of the boxes?
Answers
Answer:
78 ft cubed
Step-by-step explanation:
First calculate the volume of the toys...
5 x 3 x 2 = 30
Now the book boxes...
6 x 4 x 2 = 48
30 + 48 = 78
The combined volume should be 78 feet cubed! hope this helps!!!
Answer:
78 ft³
Step-by-step explanation:
Volume of a rectangular prism = length × width × height
Toy Box
length = 5 ftwidth = 3 ftheight = 2ft⇒ volume = 5 × 3 × 2 = 30 ft³
Book Box
length = 6 ftwidth = 4 ftheight = 2 ft⇒ volume = 6 × 4 × 2 = 48 ft³
Total combined volume = 30 + 48 = 78 ft³
What are the odds of two threes being rolled by two 6-sided dice?
1/?
Answers
Answer:the odds is 60%
Step-by-step explanation:
because there are 2 dice with 6 sides on each and take the probability of rolling each out of 12 and you have your answer
Question 2 of
Camp Copeland ordered 20 cases of eggs. There are one dozen (12)
eggs in each case. How many eggs were ordered all together?
Answers
Hope it helps
The solution is 240 eggs
The total number of eggs ordered by Camp Copeland is 240 eggs
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Let the number of cases ordered by Camp Copeland be = 20 cases
Let the number of eggs in each case = 12 eggs
So , the equation will be
The number of eggs in 20 cases A = 20 x number of eggs in each case
Substituting the values in the equation , we get
The number of eggs in 20 cases A = 20 x 12
The number of eggs in 20 cases A = 240 eggs
Therefore , the value of A is 240 eggs
Hence , the number of eggs is 240 eggs
To learn more about equations click :
https://brainly.com/question/19297665
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Evaluate the expression when x = -1 and y = 4. Please give your answer in its most reduced form
Answers
Step-by-step explanation:
x = -1, y = 4 We know that, the equation of perpendicular form is x/a + y/b = 1, -1/a + 4/b = 1, -1b + 4a/ab = 1, -1b + 4a = ab, 4a - 1b = ab
pls helpie welpieeee!!
Answers
Answer:
A
Step-by-step explanation:
rate of change of table is 10 equation is 6
solve each problem. round your answer to the nearest hundredth
what is 12% of 36.51
Answers
Answer:
4.38
Step-by-step explanation:
12% of 36.51 can be written as;
[tex](\frac{12}{100} )*(36.51)=x[/tex]
and then you can solve;
=> 0.12 x 36.51 = x
=> 4.38 = x
Hope this helps!
Answer this, please......................
Answers
Answer:
b
Step-by-step explanation:
to sum it up this is the answer: b
Find the equation of the lines a and b
Answers
Answer:
Line A = y = 3x – 2
Line B = y = -4x + 5
Step-by-step explanation:
Find the missing side of the right triangle a=24m and b=7m
Answers
Answer:625
Step-by-step explanation:
a squared plus b squared =c Squared
Julia's family wants to save for her four-year college education. After some research, they
estimate that the total cost for a state school will be about $72,000. They have saved $50,000
so far, and Julia is 14 years old. If her family saves $250 a month for the next 4 years, how much
money will Julia need in financial aid to pay for her education?
Answers
Let the amount of money she needs in addition to pay for her education be ,'x'.
Then,
According to the question,
Amount they have saved + amount they're going to save per month for next 4 years + the financial aid = Total amount they need
$50,000+ $250 x 12 x 4 + x = $72,000$50,000 + $12,000 + x = $72,000$62,000 + x = $72,000x = $72,000-$62,000x = $10,0004 years :-
4(12)48monthsMonthly save:-$ 250
Yearly save:-
250(12)3000$Save for 4years:-
3000(4)=12000$Total amount=50000+12000=62000$
Amount of financial aid:-
72000-6200010000$Which graph represents the piecewise-defined function f(x) = StartLayout enlarged left-brace 1st Row 1st column negative x + 4, 2nd column 0 less-than-or-equal-to x less-than 3 2nd row 1st column 6, 2nd column x greater-than-or-equal-to 3 EndLayout?
On a coordinate plane, a piecewise function has 2 lines. The first line has an open circle at (3, 6), continues horizontally to the left at y equals 6 with an arrow instead of an endpoint. The second line has a closed circle at (3, 0) and continues up to an open circle at (5, 3).
On a coordinate plane, a piecewise function has 2 lines. The first line has a closed circle at (3, 6), continues horizontally to the left at y equals 6 with an arrow instead of an endpoint. The second line has a closed circle at (3, 0) and continues up to a closed circle at (5, 3).
On a coordinate plane, a piecewise function has 2 lines. The first line has an open circle at (0, 4) and continues down to a closed circle at (3, 1). The second line has an open circle at (3, 6), continues horizontally at y = 6 with an arrow instead of an endpoint.
On a coordinate plane, a piecewise function has 2 lines. The first line has a closed circle at (0, 4) and continues down to an open circle at (3, 1). The second line has a closed circle at (3, 6), continues horizontally at y = 6 with an arrow instead of an endpoint.
Answers
Answer:
A FOR EDGE 2022
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
Can anyone help me been stuck for a while
Answers
Answer:
total marbles = 15 + 12 = 27
blue marbles = 12
probability of blue marble = 12/27 simplifies to 4/9
Question:
Can anyone help me been stuck for a while.
Answer:
[tex]\frac{4}{9}[/tex]
Step-by-step explanation:
The bag has 15 white marbles,
and 12 blue marbles.
Add the totals together, and you would get:
27.
turn that into a fraction:
[tex]\frac{12}{27}[/tex]
then simplify:
Find the GCD (or HCF) of numerator and denominator
GCD of 12 and 27 is 3
Divide both the numerator and denominator by the GCD
12 ÷ 3
27 ÷ 3
Reduced fraction:
[tex]\frac{4}{9}[/tex]
Therefore, [tex]\frac{12}{27}[/tex] simplified to lowest terms is:
[tex]\frac{4}{9}[/tex]
Therefore, your answer would be: [tex]\frac{4}{9}[/tex]
Find the value of x iready
Answers
Answer:
As it is straight line so the measure of tatal angle is 180 subtract 180 from. 88 to get the answer
Step-by-step explanation:
The correct answer is 92
PLEASE MARK ME BRAINLIEST IF MY ANSWER IS CORRECT PLEASE
Answer:92
Step-by-step explanation:
what is the area of a circle when the radius is 5ft
Answers
Answer:
78.54 ft²
Step-by-step explanation:
Hello!
The formula for the area of a circle is A = πr², where r is the radius.
Given r is 5, find the area:
A = πr²A = π*5²A = 25πA = 78.5398163397 ≈ 78.54The area is 78.54 ft²
Which is most likely to weigh 2 pounds?
Answers
Answer:
Insert an image.
Step-by-step explanation:
If you may, add a picture so I can see what you mean.
what % could i make 2/5 of a hour? like 10% of a hour. like that.
Answers
well, we can say that 1 hour is 100%, what is 2/5 hr off of it in percentage?
[tex]\begin{array}{ccll} hour&\%\\ \cline{1-2} 1 & 100\\ \frac{2}{5}& x \end{array} \implies \cfrac{1}{~~ \frac{2}{5}~~}=\cfrac{100}{x}\implies \cfrac{5}{2}=\cfrac{100}{x} \\\\\\ 5x=200\implies x=\cfrac{200}{5}\implies x=40[/tex]
You have one type of candy that sells for $7.10/lb and another type of candy that sells for $9.70/lb. You would like to have 10.4 lbs of a candy mixture that sells for $9.40/lb. How much of each candy will you need to obtain the desired mixture
Answers
You will need 5.2 pounds of candy from each candy. The reason is because you have 2 kinds of candy and 10.4 pounds so divide 10.4 by 2 and you get 5.2
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50 points pls help
Alex is mowing a 145.5 square feet law. He used 3/4 gallon of as to mow 3/10 of the law. How many gallons of gas are needed to mow the entire lawn?
Answers
Answer:
2.5 gallons of gasStep-by-step explanation:
Note : we have a proportional relationship between the two variables
_______________________________________
He used 3/4 gallon of gas to mow 3/10 of the lawn
Then
He has to use 1/4 gallon of gas in order to mow 1/10 of the lawn
( we divided both sides by 3)
Then
He has to use 10 × 1/4 gallons of gas to mow 10/10 of the lawn
What that means is :
He has to use 10/4 gallons of gas to mow the entire lawn
In other words :
He has to use 2.5 gallons of gas to mow the entire lawn
________________
Alex is mowing a 145.5 square feet lawn. He used 3/4 gallon of gas to mow 3/10 of the lawn. How many gallons of gas are needed to mow the entire lawn
What is the volume of metal in the hex nut, to the nearest tenth? use 3.14 for π. 21.1 cm3 23.6 cm3 27.6 cm3 31.6 cm3
Answers
The volume of metal in the hex nut to the nearest tenth is 27.6 cm^3.
Calculations and Parameters:Given that:
Diameter of the cylinder: d=1.6 cmApothem of the hexagon: a=2 cmAssuming the thickness of the steel hex nut: t=2 cmVolume of metal in the hex nut: V=?V=Vp-VcVolume of the prism: VpVolume of the cylinder: VcThe central angle in the hexagon: A=360°/n
A=360°/6A=60°tan (A/2)=(L/2) / atan (60°/2)=(L/2) / (2 cm)tan 30° = (L/2) / (2 cm)\sqrt(3)/3=(L/2) / (2 cm)Solving for L/2:
(2 cm) \sqrt(3)/3 = L/22 \sqrt(3)/3 cm = L/2Solving for L:
2 (2 \sqrt(3)/3 cm)=L4 \sqrt(3)/3 cm = LL=4 \sqrt(3)/3 cmAb=n L a / 2Ab=6 (4 \sqrt(3)/3 cm)(2 cm) / 2Ab=24 \sqrt(3)/3 cm^2Ab=8 \sqrt(3) cm^2Vp=Ab hVp=(8 \sqrt(3) cm^2)(2 cm)Vp=16 \sqrt(3) cm^3Vp=16 (1.732) cm^3(1) Vp=27.712 cm^3Cylinder:
Vc=(π d^2/4) hπ=3.14d=1.6 cmHeight of the cylinder: h=t=2 cmVc=[3.14 (1.6 cm)^2 / 4] (2 cm)Vc=[3.14 (2.56 cm^2) / 4] (2 cm)Vc=(2.0096 cm^2) (2 cm)Vc=4.019 cm^3V=Vp-Vc
V=27.712 cm^3 - 4.019 cm^3V=23.693 cm^3V=23.6 cm^3Read more about the volume of a metal here:
https://brainly.com/question/10022398
Answer:
the answer is B 23.6cm^3
Step-by-step explanation: did the test review
Directions: Using trig functions, find the value of each variable. Write your final answer
in the blank. Show your work and round answers to the nearest tenth.
(First problem)
Answers
x = 5.4
[tex]\bold{EXPLANATIONS:}[/tex]
Determine formula of the nth term 2, 6, 12 20 30,42
Answers
Check the forward differences of the sequence.
If [tex]\{a_n\} = \{2,6,12,20,30,42,\ldots\}[/tex], then let [tex]\{b_n\}[/tex] be the sequence of first-order differences of [tex]\{a_n\}[/tex]. That is, for n ≥ 1,
[tex]b_n = a_{n+1} - a_n[/tex]
so that [tex]\{b_n\} = \{4, 6, 8, 10, 12, \ldots\}[/tex].
Let [tex]\{c_n\}[/tex] be the sequence of differences of [tex]\{b_n\}[/tex],
[tex]c_n = b_{n+1} - b_n[/tex]
and we see that this is a constant sequence, [tex]\{c_n\} = \{2, 2, 2, 2, \ldots\}[/tex]. In other words, [tex]\{b_n\}[/tex] is an arithmetic sequence with common difference between terms of 2. That is,
[tex]2 = b_{n+1} - b_n \implies b_{n+1} = b_n + 2[/tex]
and we can solve for [tex]b_n[/tex] in terms of [tex]b_1=4[/tex]:
[tex]b_{n+1} = b_n + 2[/tex]
[tex]b_{n+1} = (b_{n-1}+2) + 2 = b_{n-1} + 2\times2[/tex]
[tex]b_{n+1} = (b_{n-2}+2) + 2\times2 = b_{n-2} + 3\times2[/tex]
and so on down to
[tex]b_{n+1} = b_1 + 2n \implies b_{n+1} = 2n + 4 \implies b_n = 2(n-1)+4 = 2(n + 1)[/tex]
We solve for [tex]a_n[/tex] in the same way.
[tex]2(n+1) = a_{n+1} - a_n \implies a_{n+1} = a_n + 2(n + 1)[/tex]
Then
[tex]a_{n+1} = (a_{n-1} + 2n) + 2(n+1) \\ ~~~~~~~= a_{n-1} + 2 ((n+1) + n)[/tex]
[tex]a_{n+1} = (a_{n-2} + 2(n-1)) + 2((n+1)+n) \\ ~~~~~~~ = a_{n-2} + 2 ((n+1) + n + (n-1))[/tex]
[tex]a_{n+1} = (a_{n-3} + 2(n-2)) + 2((n+1)+n+(n-1)) \\ ~~~~~~~= a_{n-3} + 2 ((n+1) + n + (n-1) + (n-2))[/tex]
and so on down to
[tex]a_{n+1} = a_1 + 2 \displaystyle \sum_{k=2}^{n+1} k = 2 + 2 \times \frac{n(n+3)}2[/tex]
[tex]\implies a_{n+1} = n^2 + 3n + 2 \implies \boxed{a_n = n^2 + n}[/tex]
There is a pair of parallel sides in the following shape. 4 4 6 What is the area of the shape?
Answers
============================================================
Explanation:
It might help to rotate the figure so the parallel sides are horizontal. This is optional.
The parallel bases are [tex]b_1 = 6[/tex] and [tex]b_2 = 4[/tex] in either order.
The height is h = 4 which is always perpendicular to both bases.
Plug these values into the trapezoid area formula.
[tex]A = \frac{h(b_1 + b_2)}{2}\\\\A = \frac{4(6+4)}{2}\\\\A = \frac{4(10)}{2}\\\\A = \frac{40}{2}\\\\A = 20\\\\[/tex]
The area of the trapezoid is 20 square units.
-----------
Another pathway is to break the trapezoid into a rectangle up top and a triangle down below.
The rectangle is 4 by 4 with area 4*4 = 16
The triangle has a base of 6-4 = 2 and height of 4, so its area is base*height/2 = 2*4/2 = 8/2 = 4
Overall the total area is rectangle+triangle = 16+4 = 20 square units.