Answer:
Step-by-step explanation:
You need to know what prime factorization is. Basically you split up a number into it's prime factors. Or in other words what prime numbers multiply to get this number. So say you have 36, you can split it into 2*2*3*3. This is the methodology we use.
For the fractions given we want to look at the prime factorization of the denominators. so for 4 = 2*2 and 6 = 2*3. What do we have to do to make them equal. Well, if we multiply 2*2 by 3 and 2*3 by 2 what do we get? 2*2*3 and 2*3*2 which are equal. So there's another way to get common denominators. You also have to multiply the numerators by the same numbers you multiply the denominators by. So in total you do this.
1/4 + 1/6
1/(2*2) + 1/(2*3)
(1*3)/(2*2*3) + (1*2)/(2*3*2)
3/12 + 2/12
5/12
Final answer:
To add fractions with different denominators, find the Least Common Denominator (LCD) rather than multiplying the denominators. For 1/4 and 1/6, the LCD is 12. The resulting addition is 1/4 + 1/6 = 3/12 + 2/12 = 5/12.
Explanation:
Whitney, to add fractions with different denominators more efficiently, we can find a common denominator that is smaller than directly multiplying the two denominators. This is also known as the Least Common Denominator (LCD).
To add 1/4 and 1/6, rather than multiplying the denominators to get 24, we can look for the least common multiple (LCM) of 4 and 6. The LCM of 4 and 6 is 12, because 12 is the smallest number that both 4 and 6 can divide evenly into.
Now we can write each fraction with a denominator of 12:
Multiply the first fraction (1/4) by 3/3 (which is equal to 1) to get 3/12Multiply the second fraction (1/6) by 2/2 (which is equal to 1) to get 2/12Now the fractions have the same denominator:
1/4 + 1/6 = 3/12 + 2/12 = 5/12
By using the LCD, the fractions are now easy to add, and the added result of 5/12 is in simplified form.
42 students arrived at the school dance after it started. in all 78 students attended. write and solve an equation to find how many students arrived at the dance before it started. plz help right when you see it!!!
Answer:
The answer is 36
Step-by-step explanation:
we know 42 students arrived after the dance started and 78 arrived in total. You have to subtract 42 from 78. how I remember this: part+part=whole whole-part=part
I need help with this
#3 is 40 degrees Clockwise.
Sadie has a cousin Nanette in Germany. Both families recently bought new cars and the two girls are comparing how fuel efficient the two cars are. Sadie tells Nanette that her family’s car is getting 42 miles per gallon. Nanette has no idea how that compares to her family’s car because in Germany mileage is measured differently. She tells Sadie that her family’s car uses 6 liters per 100 km. Which car is more fuel efficient? Please explain everything
Sadie’s family’s car is slightly more fuel efficient than Nanette’s family’s car.
Answer:
Sadie's car is more fuel efficient.
Step-by-step explanation:
Consider the provided information.
For comparison both quantity should be same. So convert miles per gallon into kilometers per liter.
Sadie tells her family's car is getting 42 miles per gallon.
To convert miles per gallon into liters per km use the formula:
1 miles per gallon = 0.425144 kilometers per liter
Multiply both the sides by 42.
1×42 miles per gallon = 0.425144×42 kilometers per liter
42 miles per gallon = 17.856 kilometers per liter
That means Sadie's car millage is 17.856 kilometer per liter.
Nanette tells Sadie that her family’s car uses 6 liters per 100 km.
6 Liters = 100 km
Divide both sides by 6.
1 Liters = 16.66..
That means Nanette's car millage is approximately 16.67 kilometer per liter.
Hence, Sadie's car is more fuel efficient.
A single little brown bat can eat up to 1,000 mosquitoes in a single hour.express in scientific notation how many mosquitoes a little brown bat might eat in 10.5
Answer: 1.05 ·10⁴ mosquitoes
Step-by-step explanation:
1,000mosquitoes/hour x 10.5hours =10,500 mosquitoes
Now you have to move decimal point as many space as needed left so that the number is less than ten.
10,500 ↪ 1.0500 because I moved decimal point 4 spaces, its 10⁴
Answer: 1.05 ·10⁴ mosquitoes
[tex]\textit{\textbf{Spymore}}[/tex]
Based on the example above, identify the first operation needed to solve the following equation.
4m/3 = 8
Answer:
See below.
Step-by-step explanation:
I can't see any example but what I would do is first multiply both sides by 3.
4m/3 = 8
4m/3 * 3 = 8 * 3
4m = 24.
The first operation in solving the equation 4m/3 = 8 is multiplying both sides of the equation by 3, which eliminates the fraction and isolates the variable 'm'. After further simplification, the solution to the equation is m = 6.
Explanation:To solve the equation 4m/3 = 8, the first operation we need to perform is to isolate the variable on one side of the equation. We can do this by multiplying both sides of the equation by 3. This cancels out the fraction on the left side, allowing us to solve for 'm'.
In step by step:
Multiply both sides of the equation by 3: (4m/3) * 3 = 8 * 3.This simplifies to 4m = 24.Finally, we divide both sides by 4 to solve for 'm': m = 24/4.m = 6.So, "the solution to the equation is m = 6".
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what is 2.3 round to the nearest tenth
Answer: 2.0 or 2
Step-by-step explanation:
How To Round: 1-4 round down. 5-10 round up.
I hope this helps you!
Answer: 2.0 or just 2
Step-by-step explanation: 3 is lower than 5 so you have to make it a zero
4. Which of the two figures below has the lesser volume?
5. Which of the two figures below has the greater volume?
Answer:
cylinder has greater volume
Using the numbers -4, 10, 8, 2, -3, -5, create two expressions that
equal 6.
The two expressions should be [tex]-4 \div 2 + 8 = 6\ and\ (10 \times -3) \div -5 = 6[/tex].
Given that,
The numbers are -4, 10, 8, 2, -3, -5.We need to develop two expressions that are equivalent to 6.Based on the above information, the calculation is as follows:
[tex]-4 \div 2 + 8 = 6\[/tex]
6 = 6
And,
[tex](10 \times -3) \div -5 = 6[/tex]
6 = 6
Therefore we can conclude that the two expressions should be [tex]-4 \div 2 + 8 = 6\ and\ (10 \times -3) \div -5 = 6[/tex].
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Two expressions using the given numbers that equal 6 are: Expression 1: 10 - 2 - (-3) + (-5) and Expression 2: 10 - 2 + 8 - (-4) - 5. The calculations are done using the order of operations (PEMDAS).
Explanation:The task is to create two mathematical expressions using the numbers -4, 10, 8, 2, -3, and -5, which result in 6. We can accomplish this by utilizing basic arithmetic operations such as addition, subtraction, multiplication, or division. The important thing is making sure all operations adhere to the Order of Operations, also known as PEMDAS (Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction). Here are the two ways you could form expressions:
Expression 1: 10 - 2 - (-3) + (-5). The calculation goes as follow: 10 minus 2 equals 8, then we subtract -3 which is the same as adding 3, so 8 plus 3 equals 11, and finally we subtract 5 to get 6.Expression 2: 10 - 2 + 8 - (-4) - 5. Similarly, you calculate 10 minus 2 equals 8, plus 8 equals 16, add -4 (which is the same as subtracting 4) results in 12, and subtracting 5 gives us 6.Learn more about Mathematical Expressions here:https://brainly.com/question/30350742
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solve for b a + b/c = pq
Answer:
b = c(pq - a)
Step-by-step explanation:
All we need to do is isolate (solve for) the variable b
a + b/c = pq
Subtract a from both sides
b/c = pq - a
Multiply by c on both sides
b = c(pq - a)
Answer:
b = c(pq - a)
Step-by-step explanation:
Find the distance between the points (-5, 0) and (-4,1).
01
O2
02.12
Answer:
[tex]\sqrt{2}[/tex] ≈ 1.414
Step-by-step explanation:
Calculate the distance d using the distance firmula
d = √ (x₂ - x₁ )² + (y₂ - y₁ )²
with (x₁, y₁ ) = (- 5, 0) and (x₂, y₂ ) = (- 4, 1)
d = [tex]\sqrt{(-4+5)^2+(1-0)^2}[/tex]
= [tex]\sqrt{1^2+1^2}[/tex]
= [tex]\sqrt{2}[/tex] ≈ 1.414 ( to 3 dec. places )
Fourteen is 20% of
please help me in need
Answer:
14 / .20 = x
.20 x = 14
x = 14 / .20
x = 70
DOUBLE - CHECK
20 % of 70 = .20 * 70 = 14
Step-by-step explanation:
what does x equal and explain how
Answer:
x = 32Step-by-step explanation:
[tex]\dfrac{x}{8}+2=6\qquad\text{subtract 2 from both sides}\\\\\dfrac{x}{8}+2-2=6-2\\\\\dfrac{x}{8}=4\qquad\text{multiply both sides by 8}\\\\8\!\!\!\!\diagup^1\cdot\dfrac{x}{8\!\!\!\!\diagup_1}=(8)(4)\\\\x=32[/tex]
BRAINLIEST PLUS 100 POINTS
Please show full working out and draw a neat diagram for question five and also note that this is trigonometry
Correct answers only please ;)
Thank you in advance :)
The exact answer is 4√2 + 4
The decimal answer is 9.6568 ( round the answer as needed.)
See the attached picture:
The age of a woman is 4 times the age of her daughter. 5 yrs hence,the age of the woman will be 3 times the age of her daughter. Find the present age of the daughter in yrs.
Answer:
10
Step-by-step explanation:
If W is the present age of the woman and D is the present age of the daughter, then:
W = 4D
W + 5 = 3(D + 5)
Substituting the first equation into the second:
4D + 5 = 3(D + 5)
4D + 5 = 3D + 15
D = 10
The daughter is 10 years old.
Add the following
(This is just a filler so i can post this)
Answer:
9/10
Step-by-step explanation:
You find the lowest common denominator which is 56 and then, you multiply each numerator by the opposite denominator (3 times 7 and 3 times 8) after that you should get 5 45/50 then you simplify it to get 9/10
Plz help me show the work plz
Answer:
all work is shown and pictured
Solve this equation use pemdas 4x(5+8•2)
Answer:84
Step-by-step explanation:
p = perentsis acccording to pemdas you have to multiply then 8x2 =16 +5=21
21 x4 = 84
what is 2 + 2 - 4 + 1500 x 2 - 300 - 2700 equal to?
7. Find the product (3x + 2)(4x2 – 5x + 7).
Answer:
12x³ - 7x² + 11x + 14
Step-by-step explanation:
Each term in the second factor is multiplied by each term in the first factor, that is
3x(4x² - 5x + 7) + 2(4x² - 5x + 7) ← distribute both parenthesis
= 12x³ - 15x² + 21x + 8x² - 10x + 14 ← collect like terms
= 12x³ - 7x² + 11x + 14
The sum of Chris and Mike’s scores on a math quiz is 39. Mike’s score is twice the sum of Chris’ score and 3. Find each student’s quiz score.
Answer: c=11, m=28
Step-by-step explanation:
c= Chris's score
m= Mike's score
c+m=39 we know from the equation that their scores
add up to 39, so this equation is a good starting
point.
c+2(c+3)=39 we also know that Mike's score is twice the sum of Chris's
score and 3 so we can substitute that in for his score.
now we can solve.
c+2c+6=39 distribute
3c+6=39 combine like terms
-6 -6
3c=33 addition property of equality
÷3 ÷3
c=11 multiplication property of equality
Now that we know Chris's score, we simply substitute that number in in our simple equation for earlier to find Mike's score.
11+m=39 substituted in 11 for c
-11 -11
m=28 addition property of equality
There you go! Don't worry, I had a lot of trouble with these types of problems too. That's why I'm so good at them now Hope this helps!
Use A=12bh to find the height of a triangle that has an area of 180 in^2 and a base of 20 in.
Answer:
18 in
Step-by-step explanation:
A=1/2 bh
180 = (20* h)/2
180*2 = 20*h
(180*2)/20 = h
360/20 = h
18 in = h
What is the difference between a day and a line segment
Hello!
I do believe you meant to say:
"What is the difference between a ray and a line segment?"
The difference between a ray and a line segment is:
A ray has one endpoint and continues in one direction. a ray is infinite
A line segment has two endpoints. a line segment is finite
I hope this helps, and have a nice day!
If the outliers are not included in the data set below, what is the mean of the data set?
42, 43, 46, 48, 57, 60, 96, 59, 38, 68, 29 (2 points)
a 47
b 48
c 49
d 52
The mean of the given data set, after removing the outlier, is 49.
Explanation:To determine the mean of a data set, outliers (extremely high or low values) must first be identified and removed. Looking at the given data set: 42, 43, 46, 48, 57, 60, 96, 59, 38, 68, 29; the number 96 is an outlier as it is remarkably higher than the other values.
After removing the outlier, the rest of the data set becomes: 42, 43, 46, 48, 57, 60, 59, 38, 68, 29.
To find the mean (average), sum all these numbers and divide by the count of numbers. The total sum of these numbers is 490, and there are 10 numbers. Therefore, the mean is 49 (490 divided by 10).
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The mean of the data set after removing the outliers is c. 49
How to determine the mean if the outliers are not includedFrom the question, we have the following parameters that can be used in our computation:
The data set
Where, we have
42, 43, 46, 48, 57, 60, 96, 59, 38, 68, 29
The outlier in the data set is 96
If we remove them, we will have the following data set:
42, 43, 46, 48, 57, 60, 59, 38, 68 and 29
The mean of this data set is calculated as follows:
mean = (42 + 43 + 46 + 48 + 57 + 60 + 59 + 38 + 68 + 29) / 10 = 49
Hence, the mean without outliers is 49
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3(d-8)-5=9(d+2)+1 need help
Answer:
d=-8
Step-by-step explanation:
1) Use the Distributive property on the left side of the equation:
3d-24-5=9(d+2)+1
2) Use the Distributive property on the right side of the equation:
3d-24-5=9d+18+1
3) Combine alike terms:
3d-29=9d+19
4) add a 29 to both sides:
3d=9d+48
5) Subtract a 9d from both sides:
-6d=48
6) Divide both sides by -6:
d=-8
Solve the inequality for x 24x > 18(4x – 6) – 30
Answer:
The required solution is: [tex]x<\frac{23}{8}[/tex] or x<2.875 or [tex]\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:\frac{23}{8}\right)\end{bmatrix}[/tex]
Step-by-step explanation:
Consider the provided inequity.
[tex]24x>18(4x-6)-30[/tex]
We need to solve the above inequity of x.
Open the parentheses.
[tex]24x>18\times 4x-18\times 6-30[/tex]
[tex]24x>72x-108-30[/tex]
[tex]24x>72x-138[/tex]
Subtract 72x from both sides.
[tex]24x-72x>72x-138-72x\\-48x>-138[/tex]
Multiply both sides by -1 and reverse the inequality.
[tex]\left(-48x\right)\left(-1\right)<\left(-138\right)\left(-1\right)[/tex]
[tex]48x<138[/tex]
Divide both side by 48.
[tex]x<\frac{23}{8}[/tex]
Hence, the required solution is: [tex]x<\frac{23}{8}[/tex] or x<2.875 or [tex]\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:\frac{23}{8}\right)\end{bmatrix}[/tex]
simplify by distributing and combining like terms
Answer: -9x + 24
Step-by-step explanation:
To do this, we need to multiply each term by -3
So -3(3x -8) turns into
-9x + 24
That’s the answer!
b. You used 13 gallons when you traveled 342 miles. How many miles did you
travel per gallon?
Answer:
26.307 miles per gallon
Step-by-step explanation:
Divide the miles traveled by the number of gallons used.
In this case, divide 342 by 13 to get the answer of 26.307 miles per gallon.
On the surface, it seems easy. Can you think of the integers for x, y, and z so that x³+y³+z³=8? Sure. One answer is x = 1, y = -1, and z = 2. But what about the integers for x, y, and z so that x³+y³+z³=42?
That turned out to be much harder—as in, no one was able to solve for those integers for 65 years until a supercomputer finally came up with the solution to 42. (For the record: x = -80538738812075974, y = 80435758145817515, and z = 12602123297335631. Obviously.)
Answer:
Well ,lets see∉ if you add theose numbers togetherФ it maybe it he answe ris 4=67 *64 ---4 67x54 5xe4t4 6xStep-by-step
Answer:
if i see them it my be 5x6x7=76 6(*)665_+65x673 then add those toether then sub em 56-78-463=738
Step-by-step explanation:
Find the value of x if R is the midpoint of QS QR=5x-7 and QS=96
Answer: The required value of x is 11.
Step-by-step explanation: Given that R is the midpoint of the line segment QS, where
QR=5x-7 and QS=96.
We are to find the value of x.
Since the point R is the midpoint of the segment QS, so we must have
[tex]QR=SR=\dfrac{1}{2}QR\\\\\\\Rightarrow QR=\dfrac{1}{2}QS\\\\\\\Rightarrow 5x-7==\dfrac{1}{2}\times96\\\\\Rightarrow 5x-7=48\\\\\Rightarrow 5x=48+7\\\\\Rightarrow 5x=55\\\\\Righatrrow x=\dfrac{55}{5}\\\\\Rightarrow x=11.[/tex]
Thus, the required value of x is 11.
If R is the midpoint of QS, then x = 11.
We have,
If R is the midpoint of QS, then QR is equal in length to RS.
Therefore:
QR = RS
Given that QR = 5x - 7 and QS = 96, we can set up an equation:
5x - 7 = QS/2
Now, plug in the value of QS:
5x - 7 = 96/2
5x - 7 = 48
Add 7 to both sides:
5x = 48 + 7
5x = 55
Now, divide both sides by 5 to isolate x:
x = 55 / 5
x = 11
So, the correct value of x is 11.
Thus,
If R is the midpoint of QS, then x = 11.
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Factor -4x + 24 - 4x^2
Answer:
- 4(x + 3)(x - 2)
Step-by-step explanation:
Given
- 4x + 24 - 4x² ← rewrite in standard form, that is
- 4x² - 4x + 24 ← factor out - 4 from each term
= - 4(x² + x - 6) ← factorise the quadratic
Consider the factors of the constant term (- 6) which sum to give the coefficient of the x- term (+ 1)
The factors are + 3 and - 2, since
3 × - 2 = - 6 and 3 - 2 = + 1, hence
x² + x - 6 = (x + 3)(x - 2), and
4x² - 4x + 24 = - 4(x + 3)(x - 2)