Answers
Answer:
[tex]\frac{\sqrt[3]{20}}{5}[/tex]
Step-by-step explanation:
Let [tex]x = \sqrt[3]{\frac{4}{25}}[/tex], we proceed to show the procedure to determine the simplest form of this number:
1) [tex]\sqrt[3]{\frac{4}{25} }[/tex] Given.
2) [tex]\left(\frac{4}{25}\right)^{1/3}[/tex] Definition of cubic root.
3) [tex][4\cdot (25)^{-1}]^{1/3}[/tex] Definition of division.
4) [tex](4)^{1/3}\cdot [(25)^{-1}]^{1/3}[/tex] [tex]a^{c}\cdot b^{c} = (a\cdot b)^{c}[/tex]
5) [tex]\{(4)^{1/3}\cdot [(25)^{-1}]^{1/3}\} \cdot \{[(25)^{-1}]^{2/3}\cdot [(25)^{-1}]^{-2/3}\}[/tex] Modulative and associative properties/Existence of multiplicative inverse/[tex]a^{b}\cdot a^{c} = a^{b+c}[/tex]
6) [tex]\{(4)^{1/3}\cdot [(25)^{-1}]^{-2/3}\}\cdot \{[(25)^{-1}]^{1/3}\cdot [(25)^{-1}]^{2/3}\}[/tex] Commutative and associative properties
7) [tex]\{(4)^{1/3}\cdot [(25)^{-1}]^{-2/3}\}\cdot (25)^{-1}[/tex] [tex]a^{b}\cdot a^{c} = a^{b+c}[/tex]
8) [tex][(4)^{1/3}\cdot (25)^{2/3}]\cdot (25)^{-1}[/tex] [tex](a^{b})^{c} = a^{b\cdot c}[/tex]
9) [tex][4\cdot (25)^{2}]^{1/3}\cdot (25)^{-1}[/tex] [tex](a^{b})^{c} = a^{b\cdot c}[/tex]/[tex]a^{c}\cdot b^{c} = (a\cdot b)^{c}[/tex]
10) [tex](2500)^{1/3}\cdot (25)^{-1}[/tex] Definition of power and multiplication.
11) [tex][(125)\cdot (20)]^{1/3}\cdot (25)^{-1}[/tex] Definition of multiplication.
12) [tex](125)^{1/3}\cdot [(20)^{1/3}\cdot (25)^{-1}][/tex] [tex]a^{c}\cdot b^{c} = (a\cdot b)^{c}[/tex]/Associative property.
13) [tex]5\cdot [(20)^{1/3}\cdot (25)^{-1}][/tex] Definition of cubic root.
14) [tex]5\cdot [(20)^{1/3}\cdot (5)^{-1}\cdot (5)^{-1}][/tex] Definition of multiplication/[tex]a^{c}\cdot b^{c} = (a\cdot b)^{c}[/tex]
15) [tex][(20)^{1/3}\cdot (5)^{-1}][5\cdot (5)^{-1}][/tex] Commutative and associative properties.
16) [tex](20)^{1/3}\cdot (5)^{-1}[/tex] Existence of multiplicative inverse/Modulative property
17) [tex]\frac{\sqrt[3]{20}}{5}[/tex] Definitions of cubic root and division/Result
Related Questions
I need help with geometry.
Answers
Answer:
x=9
Step-by-step explanation:
AIA's are supplementary 15x+45=180
180-45=130
130/15 = 9
A hotel currently has 280 rooms. The management company
decides to build a new wing that will increase the capacity to 405
rooms. By what percentage will this expand the capacity of the
hotel? (Round to the nearest tenth of a percent.)
a) 30.9%
b) 44.6%
c) 69.1
d) 125.0%
Answers
Answer:
c = 69.1
Step-by-step explanation:
because if you already have 280 rooms and it will increase to 405 rooms essentially all you have to do is 280/405 and that gives you about 69.1%
Use the distributive property to write an equivalent expression for 21x - 14.
Answers
Answer:
7(3x−2)
Step-by-step explanation:
heeeeeeeeeeelp pleaseeeeeeeeeeee
Answers
Answer
<2 = <4 = <6 = <8
All of those are 94 degrees
<1 = <3 = <5 + <7
All of those are 86 degrees
Hope this helps :D
While back-to-school shopping, you find two pairs of jeans that cost $29 each, three shirts that cost $16 each, and a pair of shoes for $21. What is the total cost of these items, if the store is offering a 30% discount?
Answers
Answer:
$88.9
Step-by-step explanation:
First, you have to calculate the total cost of the items by adding up the results of multiplying the price of each item for its quantity:
Total cost=(29*2)+(16*3)+21
Total cost=58+48+21
Total cost=127
Now, you have to calculate 30% of that total and subtract that amount from the total cost:
127*30%=$38.1
127-38.1=$88.9
According to this, the answer is that the total cost of these items is $88.9 if the store is offering a 30% discount.
Haley sells apples from her apple orchard. Last week, she sold 516 apples. Of those apples, 107 or green apples and the rest were red apples. On Monday, Harry's sells 100 apples. Based on last week sales, white how many of the 100 apples she sells on Monday could be expecting to be green.
Answers
Answer: About 21 apples
Step-by-step explanation:
Number of apples sold last week = 516
Number of green apples = 107
Number of red apples = 516 - 107 = 409
Number of apples sold on Monday = 100
Number of apples expected to be green will be:
= 107/516 × 100
= 20.7
= 21 Approximately
Una fábrica de bolígrafos fabrica sus propios productos en tres colores distintos. 25 de su fabricación son bolígrafos azules, 13 son bolígrafos negros y el resto son bolígrafos rojos. a.- ¿Qué fracción de bolígrafos son bolígrafos rojos? b.- Si en total en un día se han fabricado 2250 bolígrafos ¿ Cuántos se han fabricado de cada color?
Answers
Answer:
a) 4/15
b) 900 bolígrafos azules
750 bolígrafos negros
600 bolígrafos rojos
Step-by-step explanation:
Una fábrica de bolígrafos fabrica sus propios productos en tres colores diferentes. 2/5 de su fabricación son bolígrafos azules, 1/3 son bolígrafos negros y el resto son bolígrafos rojos.
a) ¿Qué fracción de bolígrafos son bolígrafos rojos?
Deje que el número total de bolígrafos se represente como 1
La fracción de bolígrafos rojos =
1 - (Fracción de bolígrafos azules + Fracción de bolígrafos negros)
= 1 - (2/5 + 1/3)
El mínimo común denominador es 15
= 1 - (6 + 5/15)
= 1 - 15/11
= 4/15
Por lo tanto, la fracción de bolígrafos rojos = 4/15
b) Si se han fabricado un total de 2250 bolígrafos en un día, ¿cuántos se han fabricado de cada color?
Para bolígrafos azules
2/5 de su fabricación son bolígrafos azules,
= 2/5 × 2250 bolígrafos
= 900 bolígrafos azules
Para bolígrafos negros
1/3 son bolígrafos negros
= 1/3 × 2250 bolígrafos
= 750 bolígrafos negros
Para bolígrafos rojos
4/15 son bolígrafos rojos
= 4/15 × 2250 bolígrafos
= 600 bolígrafos rojos
(2x - 5), (2 +30), and (2x – 5)
Solve for x
Answers
-10(-1/2y+(-7/2)+7y=-25
Answers
Answer:
y = -5
Step-by-step explanation:
-10(-1/2y + (-7/2)) + 7y = -25
Let's first of all expand the bracket to get;
5y + 35 + 7y = -25
12y + 35 = -25
12y = -25 - 35
12y = -60
y = -60/12
y = -5
Al, Bert, and Rob determined that the sum of their ages is 62. Bert is twice as old as Rob, who is 10 years older than Al. How old is each?
Answers
Answer: AI is 8, Rob is 18, and Bert is 36
Step-by-step explanation:
Ok, so the sum of their age is 62. Bert is x2 of Rob. Also someone is 10 years older than AI, lets assume Rob is the guy that is 10 years older. x+y+10+(z times 2)=62. So lets solve it. 62-10=52. 52=x+y+(z times 2). Now if you think about it x and y is the same, because the 10 is already minused. So it's now x*2+z*2=52, if you assume it now, z is x+10. So now it is 52=x*2+(x+10)x2. Now we break out the brackets so its x*2+x*2+20=52. Lets simplify it. x*4+20=52, lets swift the 20 the the other side. x*4=52-20, x*4=32. 32/4=8 so 8 is x. Now we know AI is 8, Rob is 18, and Bert is 36!
awnser photo quick please #8
Answers
Xudjdjsifbdkzjzhdndjd yup
Pls help asp here are some points
Answers
Answer:
(the last one)
Step-by-step explanation:
Hi there!
This looks like a diagnostic. I had to take one last week and it was horrible!
Anyway, the numerator is the product of 5 and the sum of x and y, which can be written as 5(x+y)
The denominator is the product of negative 8 and x, which can be written as -8x.
I hope this helped!
A pool has dimensions of 40m by 20m. We'd like to add a tile path surrounding the pool with a width of 1m all the way around the pool. What's the area of the path?
Answers
A mathematics class consists of 55 boys and 65 girls .what is the ratio of girls to the total numbers of students? *
11:13
13:11
13:24
11:24
Answers
Answer:
I think it's maybe 11:55
Answer:
11:13
Step-by-step explanation:
Just simplify 55:65, by dividing by 5
If you could help I would really appreciate it, but if not that’s fine. Thank you.
Answers
Answer:
c po ang sagot jan parehas tayo
The figure to the right has its Congruent segments marked. AB=__ meters
Answers
9514 1404 393
Answer:
20 meters
Step-by-step explanation:
The single hash mark on AB matches the single hash mark on AC, so AB = AC. AC is marked as 20 meters, so AB is 20 meters.
Find the value of each variable using sine and cosine. Round your answers to the nearest tenth.
Answers
The value of p and q in the right triangle are as follows:
p ≈ 30.6 units
q ≈ 14.9 units
How to find the side of a right triangle?A right triangle is a triangle that has one of its angles as 90 degrees. The sum of angles in a triangle is 180 degrees.
Therefore, the side of a right triangle can be found using trigonometric ratios as follows:
Let's find p and q using the trigonometric ratios.
Hence,
sin 64 = opposite / hypotenuse
opposite side = p
hypotenuse = 34
Therefore,
sin 64 = p / 34
cross multiply
p = 34 sin 64
p = 30.5589975742
p ≈ 30.6 units
Hence,
cos 64 = adjacent / hypotenuse
cos 64 = q / 34
cross multiply
q = 34 cos 64
q = 14.9046189908
q = 14.9 units
Therefore,
p ≈ 30.6 units
q ≈ 14.9 units
learn more on right triangles here: https://brainly.com/question/21633806
#SPJ1
If x=−1and y=−3, then 5(x2−7+y)=
Answers
Answer:
-60
Step-by-step explanation:
(plug in x= -1 and y= -3)
your equation will look like this-
5 ((-1)2-7+(-3))
solve using PEMDAS
i need help with this !!!!
Answers
Explanation: If you try A, B, and C, you’ll find they are all correct, however D seems to be false.
Cathy is making bows from a ribbon that is 11 1/5 yards long. She needs to cut the ribbon into equal pieces that measure 2/5 yard to make each bow. How many bows can Cathy make? Sam solved the problem below but got it incorrect. Explain Sam's error.
Answers
Answer:
28 bows
Step-by-step explanation:
Each bow is an equal piece.
1 bow = 2/5 yard
Total yard of ribbon = 11 1/5 yards
Hence:
2/5 yard = 1 bow
11 1/5 yards = x
2/5x = 11 1/5
x = 11 1/5 ÷ 2/5
x = 56/5 ÷ 2/5
x = 56/5 × 5/2
x = 28 bows
Therefore, Cathy can make 28 bows
Can some one help me with this
Answers
Answer:
C) y = 2x + 3
Step-by-step explanation:
In slope intercept form(y = mx + b), b is the y intercept and m is the slope. The y intercept is y variable when the x variable is 0. In the chart, the y-intercept(b) is 3. Slope is identified by the different in y by the difference in x. In this chart the slope is 2. Now plug in the number into slope intercept form( y = 2x + 3).
9 mugs for $45
What is the rate?
And what is the unit rate?
Answers
Answer: The unit rate is $5 per mug.
Step-by-step explanation:
To find the the unit rate, you will find the amount one mug will cost.
If there are 9 mugs then to get it to one, you will have to divide 9 by 9, and the same way you will have to divide 45 by 9.
45 / 9 = 5
A teacher is taking a group of students on a field trip to a living museum. The
cost of the teacher's ticket is $9. Student tickets cost $4. It costs $57 for
everyone to get into the museum. How many students were on the field trip?
Answers
because it says a teacher which is 9$ subtracted from 57$ which is 48$ divided by 4$ because each student is 4$ which is 12 students
Which numbers are rational? Check all that apply. –19 Negative two-fifths 0 StartFraction 4 Over 7 EndFraction 1.091502… 2.89
Answers
Answer:
everything but 1.091502…
Step-by-step explanation:
Brainliest please
Answer:
A,B,C,D,F
Step-by-step explanation:
A car travels at a speed of 55 kilometers per hour.Find the distance travelled by the car in 12 minutes and 30 seconds.Find the Answers in meters
Answers
Answer:
Step-by-step explanation:
(distance) d = (speed) s * t (time)
= 55km/h * 12.30m/s
= 11.275 km
= 11.275 * 1000
= 11275m
Guys I need someone to solve this problem please it’s for test I’m stuck.
Answers
Answer:
[tex]2x + 18 = 15x + 33 - 8x \\ 2x + 18 = 7x + 33 \\ 2x - 7x = 33 - 18 \\ - 5x = 15 \\ x = - 3[/tex]
Please Help 39 points Math
Answers
Step-by-step explanation:
f(n) = 3(2)^n = 3 * 2^n.
We can see here that 3 is a constant term.
When n = 0, f(0) = 3 * 2^0 = 3.
Hence, on the 1st day 3 leaves fell. (A)
When n = 1, f(1) = 3 * 2^1 = 6.
When n = 2, f(2) = 3 * 2^2 = 12.
Notice that the number of leaves that fell keep doubling.
Therefore the number of leaves that fell on a given day is 2 times the number of leaves that fell on the previous day. (D)
Pls help it due ASAP
Please show workings also
.....
Answers
Answer: A
Step-by-step explanation:
The equation [tex]y=\frac{2}{3}x-1[/tex] is in slope-intercept form([tex]y=mx+b[/tex]). For a line to be parallel to another, it must have the same slope. The slope of the line given is 2/3. Thus, simply plug in 2/3 for the slope to get: [tex]y=\frac{2}{3} x+b[/tex]. Then, because the line passes through -6, 6, plug those values in for x and y, respectively. [tex]6=\frac{2}{3} *-6+b[/tex]
[tex]6=-4+b[/tex]
[tex]10=b[/tex]
Thus, the equation of the line is [tex]y = \frac{2}{3} x+10[/tex], or A
Hope it helps :D
[tex](\frac{1}{4} m^{2} n)^{3} * (-32m^{2}n)[/tex]
PLEASE PROVIDE AN EXPLANATION, I'M UNSURE OF HOW TO FIND THE ANSWER
Answers
Answer:
[tex]\bold{(\frac14m^2n)^3*(-32m^2n)=-\frac12m^8n^4}[/tex]
Step-by-step explanation:
[tex](\frac14m^2n)^3*(-32m^2n)=\\\\=(\frac14)^3*(m^2)^3*n^3*(-32)*m^2*n=\\\\= \frac1{64}*m^{2\cdot3}*n^3*(-32)*m^2*n=\\\\= \frac1{64}*(-32)*m^{6}*m^2*n^3*n=\\\\=-\frac{32}{64}*m^{6+2}*n^{3+1}=\\\\=-\frac12m^8n^4[/tex]
Kate is arranging new furniture in her rectangular sitting room. She has mapped the arrangement on a coordinate pane. A, B, and C represent the sofas, V1 and V2 are decorative vases and AQ represents the aquarium. Find the distance between V2 and the aquarium in Kate's sitting room.
A. 1 units
B. √101
C. √221
D. 11 units
Answers
Answer:
V2 has more room than the Aquarium.
Step-by-step explanation: