Final answer:
To express 42 + 24 differently, one might use the commutative property (24 + 42), break the numbers into tens and ones (40 + 20 + 2 + 4), or use rounding to aid mental addition (60 + 6). Each method simplifies the problem while reaching the same correct answer.
Explanation:
Another way to express 42 + 24 could be by rearranging the numbers to use commutative property of addition or by changing one or both of the numbers into a sum that makes mental addition easier. For example:
24 + 42 - Which uses the commutative property of addition, meaning that numbers can be added in any order and the result will be the same.
40 + 20 + 2 + 4 - Here we break down both numbers into tens and ones and add them separately.
60 + 6 - By rounding 42 up to the nearest ten (40) and adding 20, you get 60 plus the remaining 2 and 4 to add up to 6.
Each method provides a different way of reorganizing the original problem to potentially simplify the adding process or to suit mental math strategies. Remember, arithmetic has specific rules, but there's flexibility in how we apply them to reach the same correct answer. This shows the beauty and versatility of mathematics.
Final answer:
To express 42 + 24 differently, one can use the commutative property (24 + 42), factor out common numbers (2(21 + 12), or round and adjust (60 + 6), showcasing the variety of methods mathematics provides to reach the same answer.
Explanation:
The question asks for an alternative way to express the sum 42 + 24. One strategy is to use properties of numbers and operations to simplify and find patterns that make it easier to perform calculations in our head. For instance, using commutative property of addition, we can restate 42 + 24 as 24 + 42. Moreover, we can utilize the distributive property by factoring out a common number to make the addition easier, such as expressing it as 2(21 + 12) since both 42 and 24 are divisible by 2, or 6(7 + 4) if you notice that both numbers are divisible by 6. It's also possible to round numbers up, perform the addition, and then adjust back, for example: (40 + 20) + (2 + 4) which simplifies to 60 + 6. Each of these methods provides a different path to the same correct answer, exemplifying that mathematics offers numerous ways to solve a problem, which ultimately reinforces our understanding.
Evan’s family drove to a theme park for vacation. Assume they drove the same speed throughout the trip. The first day, they drove 300 miles in 6 hours. The second day, they drove 250 miles in 5 hours. The third day, they arrived at the park by driving ________ miles in 3 hours. Which number correctly fills in the blank?
300/6 = 50 mph
250/5 =50mph
so they drove 50 miles per hour
so 50 *3 = 150 miles in 3 hours
The equations of two lines are x - 3y = 6 and y = 3x + 2. determine if the lines are parallel, perpendicular or neither.parallelperpendicularneither
Prove that there exists a unique real number solution to the equation x3 + x2 − 1 = 0 between x = 2/3 and x=1
To prove that there exists a unique real number solution to the equation x³ + x² - 1 = 0 between x = 2/3 and x = 1, we can use the Intermediate Value Theorem and the property of the derivative.
Explanation:To prove that there exists a unique real number solution to the equation x³ + x² - 1 = 0 between x = 2/3 and x = 1, we can use the Intermediate Value Theorem.
First, we substitute x = 2/3 into the equation and get a negative value (-1/27). Then, we substitute x = 1 into the equation and get a positive value (1).
Since the function is continuous between x = 2/3 and x = 1, and it changes sign, there must exist a solution somewhere between them.
To show that the solution is unique, we can use the fact that the derivative of the function, 3x² + 2x, is always positive for all real numbers.
This implies that the function is strictly increasing, so it can only intersect the x-axis at one point.
Find the indefinite integral of [tex] \int\limits {\frac{5}{x^\frac{1}{2}+x^\frac{3}{2}} \, dx [/tex]
I have been able to simplify it to [tex] \int\limits {\frac{5\sqrt{x}}{x^3+x}} \, dx [/tex] but that is confusing,
I then did u-subsitution where [tex]u=\sqrt{x}[/tex] to obtain [tex] \int\limits {\frac{5u}{u^6+u^2}} \, dx [/tex] which simplified to [tex] \int\limits {\frac{5}{u^5+u}} \, dx [/tex], a much nicer looking integrand
however, I am still stuck
ples help
show all work or be reported
Answer:
[tex] \displaystyle10 \tan^{-1}( \sqrt {x}^{ } ) + \rm C[/tex]
Step-by-step explanation:
we would like to integrate the following integration:
[tex] \displaystyle \int \frac{5}{ {x}^{ \frac{1}{2} } + {x}^{ \frac{3}{2} } } dx[/tex]
in order to do so we can consider using u-substitution
let our
[tex] \displaystyle u = {x}^{ \frac{1}{2} } \quad \text{and} \quad du = \frac{ {x}^{ - \frac{1}{2} } }{2} [/tex]
to apply substitution we need a little bit arrangement
multiply both Integral and integrand by 2 and ½
[tex]\displaystyle 2\int \frac{1}{2} \cdot\frac{5}{ {x}^{ \frac{1}{2} } + {x}^{ \frac{3}{2} } } dx[/tex]
factor out [tex]x^{\frac{1}{2}}[/tex]:
[tex]\displaystyle 2\int \frac{1}{2 {x}^{ \frac{1}{2} } } \cdot\frac{5}{ (1+ {x}^{ } )} dx[/tex]
recall law of exponent:
[tex]\displaystyle 2\int \frac{ {x}^{ - \frac{1}{2} } }{2 } \cdot\frac{5}{ (1+ {x}^{ } )} dx[/tex]
apply substitution:
[tex]\displaystyle 2\int \frac{5}{ 1+ {x}^{ } } du[/tex]
rewrite x as [tex]\big(x^{\frac{1}{2}}\big)^{2}[/tex]:
[tex]\displaystyle 2\int \frac{5}{ 1+ ( {x ^{ \frac{1}{2} } })^{ 2 } } du[/tex]
substitute:
[tex]\displaystyle 2\int \frac{5}{ 1+ ( u)^{ 2 } } du[/tex]
recall integration rule of inverse trig:
[tex] \displaystyle 2 \times 5 \tan^{-1}(u)[/tex]
simplify multiplication:
[tex] \displaystyle10 \tan^{-1}(u)[/tex]
substitute back:
[tex] \displaystyle10 \tan^{-1}( {x}^{ \frac{1}{2} } )[/tex]
simplify if needed:
[tex] \displaystyle10 \tan^{-1}( \sqrt{x} )[/tex]
finally we of course have to add constant of integration:
[tex] \displaystyle10 \tan^{-1}( \sqrt {x}^{ } ) + \rm C[/tex]
and we are done!
One of the largest pumpkins ever grown weighed about 3/4 ton how many lb did the pumpkin weigh
What metamorphic rock has nonfoliated texture?
Answer:
Marble, quartzite, and soapstone.Step-by-step explanation:
Non-foliated metamorphic rocks are those which don't have a rough texture, like foliated ones, their composition gives them this characteristics: not having layers or banded appearance.
I got it wrong !!! Please help and explain
25 * 2.5 = 62.5 *2 = 125
8x5 = 40
125 +40 = 165 square feet
Triangle abc has been translated to create triangle a'b'c'. angles c and c' are both 32 degrees, angles b and b' are both 72 degrees, and sides bc and b'c' are both 5 units long. which postulate below would prove the two triangles are congruent? sss sas asa hl
ASA
Is the answer i got on my work
Use synthetic division and the Remainder Theorem to find P(a).
P(x) = x3 + 4x2 − 8x − 6; a = −2
−2
0
18
20
Answer:
c: 18
Step-by-step explanation:
harold serves himself 1 1/2 ounces serving of cereal each morning. How many servings does he get from a box of his favorite cereal?
A charity organization had a fundraiser where each ticket was sold for a fixed price. They had to sell a few tickets just to cover necessary production costs of $1200\$1200 $1200 dollar sign, 1200 . After selling 200200 200 200 tickets, they had a net profit of $12,000\$12{,}000 $12,000 dollar sign, 12, comma, 000 . Let P(n)P(n) P(n) P, left parenthesis, n, right parenthesis denote the net profit from the fundraiser PP P P (measured in dollars) as a function of the number of tickets sold nn n n . Write the function's formula
Answer:
[tex]P(n)=66n-1200[/tex]
Step-by-step explanation:
Let x be the revenue collected from selling each ticket.
We have been given that a charity organisation had to sell a few tickets just to cover necessary production costs of $1200. After selling 200 tickets, they had a net profit of $12,000.
Since we know that net profit is the difference between total revenue and total cost.
[tex]\text{Net profit}=\text{Total revenue- Cost}[/tex]
We can represent our given information in an equation to find the revenue collected from each ticket:
[tex]12000=200x-1200[/tex]
Let us solve for x by adding 1200 to both sides of equation.
[tex]12000+1200=200x[/tex]
[tex]13200=200x[/tex]
[tex]x=\frac{13200}{200}[/tex]
[tex]x=66[/tex]
Therefore, the revenue collected from selling each ticket is $66.
Now let us write the net profit, P(n), from fundraiser as the function of number of tickets sold,n.
The revenue from selling n tickets will be 66n.
Production costs = 1200
[tex]P(n)=66n-1200[/tex]
Therefore, our desired function will be: [tex]P(n)=66n-1200[/tex].
A tortoise is walking in the desert. It walks for 3 minutes at a speed of 7.5 meters per minute. For how many meters does it walk?
John wants to buy a watermelon that weighs 5.7 pounds.The watermelon is priced at $1.58 per pound.How much is the total cost of the watermelon
Helppp 3 out of the 5 im gunna post!
look where the line is on the y axis at x =2
answer is y=-3
value is -3
Which characteristic is used to group artworks into periods or styles?
A: Abstract
B: Similar
Color in equations what to color in 1+2+3+4=10 What cubes to color in?
The measure of an angle is 8 greater than 3 times its supplement. Find he measurement of the angle.
What is the measurements of ENV
Branliest offered
A. What is the circumference of the colony?
B. What is the radius of the colony?
Bacteria lives in groups called colonies colonies are usually circular the diameter of a particular bacterial colony is 12 mm their circumference of a circle is equal to Pi 3.14 times its diameter c= πd
When two angles are complementary what is the sum of their measures is 90 degrees. two complementary angles have the measure of 2x-10 degrees and 3x-10 degrees?
Last weekend Jane studied 4 2 3 hours for her history final and 4 1 4 hours for her math exam. How many hours in all did Jane study for the two tests?
Jane studied a total of 5 11/12 hours for her history final and math exam.
Explanation:To find the total number of hours Jane studied for the two tests, we add together the number of hours she studied for each test. Jane studied 4 2/3 hours for her history final and 4 1/4 hours for her math exam.
To add these fractions, we need to have a common denominator. The least common multiple of 3 and 4 is 12. We can convert 2/3 to 8/12 and 1/4 to 3/12.
Now we can add the fractions: 4 8/12 + 4 3/12 = 5 11/12.
Therefore, Jane studied a total of 5 11/12 hours for the two tests.
Final answer:
Jane studied a total of 7 3/4 hours for her history and math exams.
Explanation:
To find out how many hours Jane studied for the two tests, we simply need to add the hours she studied for each test together.
Jane studied 4 2/3 hours for her history final and 4 1/4 hours for her math exam.
We can add these two fractions by finding a common denominator and then adding the numerators.
In this case, the common denominator is 12. So, we have (4 * 4 + 2) / 3 = 18/3 and (4 * 3 + 1) / 4 = 13/4.
Adding these fractions together, we get (18/3) + (13/4) = 54/12 + 39/12 = 93/12. Simplifying this fraction, we get 7 3/4 hours.
Therefore, Jane studied a total of 7 3/4 hours for the two tests.
Which expression is equivalent to sin^2 x-sin x - 2/sin x -2
A. sin x + 1
B. sin x − 1
C. sin2x
D. -sin2x
Ice-Cream Palace has received an order for 3 1⁄2 gallons of ice-cream. The shop packages its ice-cream in 1-quart containers. How many containers will the shop need for this order?
what is the value of x in the equation 6= x/4 - 4
Answer:
c
Step-by-step explanation:
A teacher has 100 pencils in a cup. 16 are more sharp than dull. How many are dull and how many are sharp?
Carlos's gas tank is 19 full. after he buys 6 gallons of gas, it is 13 full. how many gallons can carlos's tank hold
Answer:
25
Step-by-step explanation:
Find the unit rate with the second given unit in the denominator.
72 football cards on 12 pages
A.
B.
C.
D.
Kate has 21 coins (nickels and dimes) in her purse. How many nickels and dimes does she have if she has $1.50? 3 nickels and 18 dimes 5 nickels and 16 dimes 12 nickels and 9 dimes 15 nickels and 6 dimes
The length of a rectangle is twice its width. if the area of the rectangle is 200 yd2 , find its perimeter.
The perimeter of the rectangle is 60 yards
What is the Perimeter of a Rectangle?
The perimeter P of a rectangle is given by the formula, P=2 ( L + W) , where L is the length and W is the width of the rectangle.
Perimeter P = 2 ( Length + Width )
Given data ,
Let the length of the rectangle be = a
Let the width of the rectangle be = b
The length of the rectangle is twice the width
So ,
a = 2b
The area of the rectangle is A = 200 yards²
The area of the rectangle is given by
Area of Rectangle = Length x Width
And , substituting the values for length and width , we get
Area of Rectangle = 2b x b
2b² = 200
Divide by 2 on both sides , we get
b² = 100
Taking square root on both sides , we get
b = 10
a = 2b
a = 20
Therefore , the length of the rectangle is 20 yards and width of the rectangle is 10 yards
Now , the perimeter of the rectangle is P = 2 ( length + width )
Perimeter of the rectangle P = 2 ( 10 + 20 )
= 2 x 30
= 60 yards
Hence , the perimeter of the rectangle is 60 yards
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Which statement is true?