Final answer:
The expression 3√54−4√24 simplifies to √6 after factoring out the perfect squares under the radicals and combining like terms.
Explanation:
The student's question requires simplifying the expression 3√54−4√24. To simplify a square root, we look for perfect squares that are factors of the number under the root. For √54, we can notice that 54 = 9 * 6, and since √9 is a perfect square, we have 3√54 = 3*√9*√6 = 3*3*√6 = 9√6. Similarly, for √24, it is 24 = 4 * 6, so √24 = √4*√6 = 2*√6, and thus -4√24 = -4*2*√6 = -8√6. Combining these two results, we have 9√6− 8√6, which simplifies to √6. Therefore, the simplified expression is √6.
On any given day, Juan will break even if he earns as much money as he spends. On day 5, he records the expression 16 + (–16). Does Juan break even? Explain.
Final answer:
Juan breaks even on day 5 as the expression 16 + (–16) equals zero, indicating that his earnings match his expenses.
Explanation:
You've asked whether Juan breaks even on day 5 when he records the expression 16 + (–16). In mathematics, breaking even means that income equals expenses, resulting in a net change of zero. The expression Juan recorded represents earning 16 units of money and spending 16 units of money. The negative sign in front of the second number indicates money going out, which is his expense.
To determine if he breaks even, we add the amounts together: 16 + (–16) = 0. Since the sum is zero, Juan does not gain or lose any money, which means he does indeed break even on day 5.
Calculate dy/dx if y = Ln (2x3 + 3x).
Differentiate using the chain rule:
d/du [ln(u)] d/dx[2x^3+3x]
derivative of ln(u) = 1/u
1/u d/dx[2x^3+3x]
1/2x^3+3x d/dx[2x^3+3x]
Differentiate
(6x^2+3) 1/2x^3+3x
Simplify
Dy/dx = 3(2x^2+1) / x(2x^2 +3)
Answer:
[tex]\frac{(6x^2+3)}{(2x^3+3x)}[/tex]
Step-by-step explanation:
[tex]\frac{dy}{dx}[/tex] [tex]ln(x)=[/tex] [tex]\frac{1}{x}[/tex] .
Therefore:
[tex]\frac{dy}{dx}[/tex] [tex]ln(2x^{3}+3x) = \frac{1}{2x^{3}+3x} *6x^2+3[/tex]
[tex]6x^2+3[/tex] is multiplied because of the chain rule.
A supplier sells 2 1/4 pounds of mulch for every 1 1/3 pounds of gravel. The supplier sells 173 pounds of mulch and gravel combined. How many pounds of each item does the supplier sell?
Answer:
[tex]\frac{4,671}{59} pounds[/tex] of mulch and [tex]\frac{5,536}{59}pounds[/tex] of gravel were sold.
Step-by-step explanation:
Mass of mulch sold = x pounds
Mass of gravel sold = y pounds
Total mass of mulch and gravel sold = 173 pounds
x + y = 173 ...[1]
Supplier sells [tex]2\frac{1}{4}[/tex] pounds of mulch for every [tex]1\frac{1}{3}[/tex] pounds of gravel.
That is for [tex]\frac{9}{8}[/tex] pounds of mulch for every [tex]\frac{4}{3}[/tex] pounds of gravel.
Then gravel sold for 1 pound mulch = [tex]\frac{4}{3}\times \frac{8}{9}=\frac{32}{27} pounds[/tex]
Then for x pounds of mulch the gravel sold will be:
[tex]\frac{32}{27} pounds\times x[/tex]
Mass of gravel sold = [tex]y = \frac{32}{27} pounds\times x[/tex]
Putting value of y in [1] :
[tex]x + \frac{32}{27} pounds\times x = 173[/tex]
x =[tex]\frac{4,671}{59} pounds[/tex]
y = [tex]173 pounds -\frac{4,671}{59} pounds=\frac{5,536}{59}pounds[/tex]
[tex]\frac{4,671}{59} pounds[/tex] of mulch and [tex]\frac{5,536}{59}pounds[/tex] of gravel were sold.
What is the area of a parallelogram whose vertices are A(−12, 2) , B(6, 2) , C(−2, −3) , and D(−20, −3) ?
Enter your answer in the box.
To solve this, we simply have to get the length and the width. Based from the graph, we can see that the length is connected by 2 points (-12, 2) and (6, 2) or (-20, -3) and (-2, -3). The height between the two lengths is 5 which can be counted manually.
We use the distance formula to calculate the length from either pair of points.
length^2 = [(-12 – 6)^2 + (2 – 2)^2]
length = 18
Therefore the area is:
Area = length * height
Area = 18 * 5
Area = 90
can someone tell me what the answer for this problem is? (and how you are able to get that answer)
Ricky bought flowers for Susan he spent a total of $14.85 and bought 13 flowers if you knows Lillys cost $1.25 and tulips cost $.90 how many of each flower did he buy Susan
To the nearest square unit what is the area of the regular octagon shown below
Answer: c
Step-by-step explanation: a p e x
The area of the given Octagon is 1,086 units²
What is an Octagon?A polygon of eight angles and eight sides is called an Octagon.
Given is a figure of an Octagon, having radius = 18.1 units and side length = 15 units.
The regular octagon is divided into 8 triangles
Therefore, the area of a regular octagon = the sum of the area of 8 triangles
The area of a triangle = 1/2(base)(height)
Here, base = 15 units and length = 18.1 units
Therefore, the area of a regular octagon = 1/2×15×18.1×8 = 1,086
Hence, The area of the given Octagon is 1,086 units²
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A bowl holds 3/10 cup of oil when it is 2/5 full. Which statement best describes the quotient of 3/10 divided by 2/5?
The maximum amount of oil the bowl can hold is Fraction 3 over 4 cup.
The maximum amount of oil the bowl can hold is Fraction 4 over 3 cups.
The amount of oil that can be still poured in the bowl is Fraction 3 over 4 cup.
The amount of oil that can be still poured in the bowl is Fraction 4 over 3 cups.
Answer:
3/4 cups
Step-by-step explanation:
what is the inverse of the function h(x) = 3x^2 - 1?
Suppose you had d dollars in your checking account. You spent $10 but have at least $50 left. How much money did you have initially? Write, solve, and graph an inequality that represents this situation.
potatoes are selling for $0.48 per pound. how much is 12 lbs. of potatoes?
A $57.60
B $60.06
C $5.76
D $6.06
kelly subscribes to a service called mysongs for downloading music she pays a $7 fee each month to download an unlimited numbers of songs at $0.20 each last month kelly's bill was $23.80
subtract the fee from the total to get the amount actually spent on songs
23.80-7 = 16.80
divide that amount by price per song to get number of songs downloaded
16.80 /0.20 = 84 songs
What additional information could you use to show that ΔSTU ≅ ΔVTU using SAS? Check all that apply.
UV = 14 ft and m∠TUV = 45°
TU = 26 ft
m∠STU = 37° and m∠VTU = 37°
ST = 20 ft, UV = 14 ft, and m∠UST = 98°
m∠UST = 98° and m ∠TUV = 45°
Express the given terminating decimal as a quotient of integers. if possible, reduce to lowest terms. 0.66
The number 0.66 can be written as a terminating decimal as a quotient of integers is 33/50.
What is a fraction?Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
It is given that:
The decimal number is 0.66 which is non-terminating.
As we know, the arithmetic operation can be defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.
We can write the number 0.66 as:
= 66/100
= On simplification:
= 33/50
Thus, the number 0.66 can be written as a terminating decimal as a quotient of integers is 33/50.
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Given the two original statements, can a true conclusion be met? If so, what would it be? If not, why not?
1) If it is June, then it is summer.
2) It is summer.
Conclusion:
From the two original statements above, the answer would be yes, a true conclusion can be met since then It is summer.
What is a possibility?Multiply the total number of possible outcomes by the total number of events. Divide the total number of ways the event can occur by the total number of possible outcomes after determining the probability event and its corresponding consequences.
Given:
1) If it is June, then it is summer.
2) It is summer.
Based on the two original statements, a true conclusion can be made.
Statement 1) says that if it is June, then it is summer. Statement 2) says that it is summer.
Therefore, we can conclude that it is possible that it is June.
However, we cannot conclude for certain that it is June, because there could be other times of the year when it is also summer (depending on the geographic location). For example, in the southern hemisphere, December is summer, not June.
So a possible true conclusion based on these statements is "It is possible that it is June."
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A sequence consists of 16 consecutive even integers written in increasing order. the sum of the first 8 of these even integers is 424. what is the sum of the last 8 of the even integers?
which of the following pairs of functions are inverses of each other?
Answer:
The pair which are inverse of each other are:
Option: C
[tex]f(x)=11x-4\ and\ g(x)=\dfrac{x+4}{11}[/tex]
Step-by-step explanation:
Two functions f(x) and g(x) are said to be inverse of each other if:
fog(x)=gof(x)=x
i.e. the composition of two functions give identity no matter what the order is.
A)
[tex]f(x)=\dfrac{x}{12}+15[/tex] and [tex]g(x)=12x-15[/tex]
Now we calculate fog(x):
[tex]fog(x)=f(g(x))\\\\fog(x)=f(12x-15)\\\\fog(x)=\dfrac{12x-15}{12}+15\\\\fog(x)=x-\dfrac{15}{12}+15\\\\fog(x)=x-\dfrac{55}{4}\neq x[/tex]
Hence, option: A is incorrect.
B)
[tex]f(x)=\dfrac{3}{x}-10\ and\ g(x)=\dfrac{x+10}{2}[/tex]
Now we calculate fog(x):
[tex]fog(x)=f(g(x))\\\\fog(x)=f(\dfrac{x+10}{3})\\\\fog(x)=\dfrac{3}{\dfrac{x+10}{3}}-10\\\\fog(x)=\dfrac{9}{x+10}-10\neq x[/tex]
Hence, option: B is incorrect.
D)
[tex]f(x)=9+\sqrt[3]{x}\ and\ g(x)=9-x^3[/tex]
Now we calculate fog(x):
[tex]fog(x)=f(g(x))\\\\fog(x)=f(9-x^3)[/tex]
[tex]fog(x)=9+\sqrt[3]{9-x^3}\neq x[/tex]
Hence, option: D is incorrect.
C)
[tex]f(x)=11x-4\ and\ g(x)=\dfrac{x+4}{11}[/tex]
Now we calculate fog(x):
[tex]fog(x)=f(g(x))\\\\fog(x)=f(\dfrac{x+4}{11})[/tex]
[tex]fog(x)=11\times (\dfrac{x+4}{11})-4\\\\fog(x)=x+4-4\\\\fog(x)=x[/tex]
Similarly,
[tex]gof(x)=g(f(x))\\\\gof(x)=g(11x-4)\\\\gof(x)=\dfrac{11x-4+4}{11}\\\\gof(x)=\dfrac{11x}{11}\\\\gof(x)=x[/tex]
Hence, option: C is the correct option.
Answer:
D.f(x)=8x³+6 and g(x)=³x-6/8
Step-by-step explanation:
apex
Which of the following number lines represents the solution set of 11 + x ≥ 14?
Answer:
The line that represents the solution set of [tex]11+x\geq 14[/tex] is the second one.
Step-by-step explanation:
If we want to find the line, we need to solve the inequality.
The inequality is [tex]11+x\geq 14[/tex]
If we solve it in terms of x :
[tex]11+x\geq 14[/tex]
[tex]x\geq 14-11[/tex]
[tex]x\geq 3[/tex]
This means that the solution of the inequality [tex]11+x\geq 14[/tex] are all real numbers greater or equal to 3.
The line that represents [tex]x\geq 3[/tex] is the blue line in the second number line.
It is important to notice that [tex]x>3\neq x\geq 3[/tex] because in the second expression the number 3 is included.
In the second line the number ''3'' is included because there is a blue point in the number 3 instead of the first number line where in the number ''3'' the blue point is empty.
A plane has 360 total seats, which are divided into economy class and business class. For every 13 seats in economy class, there are 5 seats in business class.
How many seats are there in each class?
Greg and Josh want to go whitewater rafting in 3 weeks. Josh is able to save the $480 he needs to go on the trip by saving the pay he received for 5 hours of work each week. Greg must save 8 hours worth of pay each week in order to have enough money. How much more money does Josh make than Greg? a. $10 b. $12 c. $14 d. $20
Answer: Option 'b' is correct.
Step-by-step explanation:
Since we have given that
Amount Josh is able to save = $480
Number of hours of work each week = 5
Number of weeks = 3
So, Amount Josh makes is given by
[tex]\dfrac{480}{5\times 3}\\\\=\dfrac{480}{15}\\\\=\$32[/tex]
Similarly,
Number of hours of work each week by Greg = 8
Number of weeks = 3
So, Amount Greg makes is given by
[tex]\dfrac{480}{3\times 8}\\\\=\dfrac{480}{24}\\\\=\$20[/tex]
More amount of money that Josh make than Greg is given by
[tex]32-20\\\\=\$12[/tex]
Hence, Option 'b' is correct.
Hidemi is a waiter. He waits on a table of 4 whose bill comes to $90.27. If Hidemi receives a 15% tip, approximately how much will he receive?
$4.50
$103.50
$13.50
$13.05
Hidemi will receive a tip approximately amount of $13.50 which is the correct answer would be option (C).
Hidemi works as a waiter. He serves a table of four with a bill of $90.27. If Hidemi gets a 15% tip which is given in the equation.
What is the percentage?The percentage is defined as a ratio stated as a fraction of 100.
For example, if Shekharaman received a 57% on his quiz, she received a 67 out of 100. It is written as 57/100 in fractional form and 57:100 in ratio form.
We have to determine the evaluation of 15% of $90.27.
⇒ 15% of 90.27
15% is described as 15/100 in fractional form
⇒ (15/100)(90.27)
15/100 is expressed as 0.15 in decimal form
⇒ (0.15)(90.27)
Apply the multiplication operation, and we get
⇒ 13.540 ≈ 13.50
Therefore, He will receive a tip approximately amount of $13.50.
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A car is traveling at a rate of 120 kilometers per hour. what is the car's rate in miles per hour? how many miles will the car travel in 5 hours? in your computations, assume that 1 mile is equal to 1.6 kilometers.
What is m∠L?
Enter your answer in the box.
°
We are given a triangle JKL.
<J =5x°
<K = 2x°
<L = 3x°.
Note: Sum of angles of a triangle is 180°.
Therefore, <J +<K+<L = 180°.
5x +2x+3x = 180°.
10x = 180
Dividing both sides by 10, we get
10x/10=180/10
x = 18.We need to find the m<L.
m<L =3x° = 3(18) = 54°.
Therefore, m<L = 54°.2(2t+4)=34(24−8t). My math teacher is on crack
What is the value of the expression when n=3?
–2n(5 + n – 8 – 3n)
Answer:
THE THERD OPTOIN YALL TRUST ME PLEASE
Step-by-step explanation:
How do you solve for percent increase and percent decrease?
for increase:
Increase = New Number - Original Number
Then divide the increase by the original number and multiply the answer by 100
For decrease:
Decrease = Original Number - New Number
Then divide the decrease by the original number and multiply the answer by 100
Write an expression for the sum of four consecutive odd integers where 2n +1 represents the smallest odd integer.
Which is the equation of the graphed line written in standard form? y = x x – y = 0 x – y = 0 y = x
Answer:
The equation of the graphed line written in standard form is:x-y=0
Step-by-step explanation:
we know that for graphing lines the equation of a line must be in standard form.
the standard form of a line is given by [tex]ax+by=c[/tex] where a,b,c are some real numbers.
hence, in the given question for graphing our line we must use the equation [tex]x-y=0[/tex] because on comparing it to the general equation of the line [tex]ax+by=c[/tex] we have here a=1, b=-1 and c=0.
therefore the standard form is: [tex]x-y=0[/tex]
Answer:
C. x – y = 0
Step-by-step explanation:
edg. 2020 quiz
Ms. Wilson works at a music store. On Black Friday she sold 6 more than 3 times the number of CDs she sold on Cyber Monday. Ms. Wilson sold a total of 110 CDs on Black Friday and Cyber Monday. How many CDs did she sell on each day?
show the picture
please
535 students of the senior class voted to take a field trip ir 3/4 of the class voted, how many students voted for the trip? Round your answer to the nearest whole number.
Answer:
401 students voted for the trip .
Step-by-step explanation:
As given in the question
535 students of the senior class voted to take a field trip[tex]\frac{3}{4}[/tex] of the class voted .
Thus
[tex]Students\ voted\ for\ the\ trip = \frac{3}{4}\times Total\ students[/tex]
Put value in the above
[tex]Students\ voted\ for\ the\ trip = \frac{3\times 535}{4}[/tex]
[tex]Students\ voted\ for\ the\ trip = \frac{1605}{4}[/tex]
= 401
Therefore 401 students voted for the trip .