Using the formula for the volume of a cube, it is found that the expression which gives the ratio of the side length of Cube A to the side length of Cube B is:
[tex]r = \frac{3^{\frac{2}{3}}}{5^{\frac{1}{3}}}[/tex]
Which means that option E is correct.
The volume of a cube of side length l is given by:
[tex]V = l^3[/tex]
For Cube A, the volume is of 9 cubic inches, hence:
[tex]l_a^3 = 9[/tex]
[tex]l_a = \sqrt[3]{9}[/tex]
[tex]l_a = 9^{\frac{1}{3}}[/tex]
[tex]l_a = 3^{\frac{2}{3}}[/tex]
For Cube B, the volume is of 5 cubic inches, hence:
[tex]l_b^3 = 5[/tex]
[tex]l_b = \sqrt[3]{5}[/tex]
[tex]l_b = 5^{\frac{1}{3}}[/tex]
Then, the ratio is:
[tex]r = \frac{l_a}{l_b} = \frac{3^{\frac{2}{3}}}{5^{\frac{1}{3}}}[/tex]
To learn more about the volume of a cube, you can take a look at https://brainly.com/question/13030328
Cliek an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the
correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag
the item to the trashcan click the trashcan to clear all your answers
Factor completely, then place the answer in the proper location on the grid
2107.57a+ 30
123456789
===============================================================
Explanation:
I'll use the variable x in place of 'a'
The expression we need to factor is [tex]21x^2-57x+30[/tex] which is in the form [tex]ax^2+bx+c[/tex]
So,
a = 21b = -57c = 30We'll plug those three values into the quadratic formula
[tex]x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-(-57)\pm\sqrt{(-57)^2-4(21)(30)}}{2(21)}\\\\x = \frac{57\pm\sqrt{729}}{42}\\\\x = \frac{57\pm27}{42}\\\\x = \frac{57+27}{42} \ \text{ or } \ x = \frac{57-27}{42}\\\\x = \frac{84}{42} \ \text{ or } \ x = \frac{30}{42}\\\\x = 2 \ \text{ or } \ x = \frac{5}{7}\\\\[/tex]
The two roots of [tex]21x^2-57x+30 =0[/tex] are [tex]x = 2 \text{ and } x = \frac{5}{7}[/tex]
The root x = 2 leads to the factor (x-2) after subtracting 2 from both sides.
The root [tex]x = \frac{5}{7}[/tex] leads to the factor (7x-5) after first multiplying both sides by 7, and then subtract 5 from both sides.
So we have this set of steps:
[tex]x = \frac{5}{7}\\\\7x = 5\\\\7x-5=0\\\\[/tex]
The two factors are (x-2) and (7x-5).
This leads to (x-2)(7x-5)
The last step is to replace x with 'a' so that the variables match up.
We arrive at (a-2)(7a-5)
However, as the next section shows, we have a bit of a problem. Don't worry, it can be easily fixed.
---------------------
Let's expand out that factored expression we found earlier.
[tex](a-2)(7a-5)\\\\b(7a-5)\ \text{ ..... let b = a-2}\\\\7ab - 5b\\\\7a(b) - 5(b)\\\\7a(a-2) - 5(a-2)\ \text{ ..... plug in b = a-2}\\\\7a^2-14a - 5a+10\\\\7a^2-19a+10\\\\[/tex]
That's not good. We should have arrived at the original expression [tex]21a^2-57a+30[/tex]. To fix this discrepancy, we can stick a 3 out front and then notice that:
[tex]3(a-2)(7a-5) = 3(7a^2-19a+10) = 21a^2-57a+30[/tex]
The error has been fixed.
We have the full factorization of 3(a-2)(7a-5)
The order of the factors doesn't matter, so we could have written the answer as 3(7a-5)(a-2). Usually the factor without any variables will be listed first.
Based on the screenshot you posted, if that '7' is locked in place, then the only possible answer is 3(7a-5)(a-2) since you'll have 3 in the first slot, then a ( in the next slot. The other slots are filled out in a similar manner. There are no spaces between any symbol or letter.
8 less than the sum of u and 2
Answer: u < 6
Step-by-step explanation: 2 + u < 8
u < (8-2)
u < 6
Dont know how to calculate it
Answer:
AB = 105
Step-by-step explanation:
Since ∠ A and ∠ B are equal then Δ ABC is isosceles with 2 congruent legs.
AC = BC , substitute values
6x - 7 = 5x + 7 ( subtract 5x from both sides )
x - 7 = 7 ( add 7 to both sides )
x = 14
Then
AB = 7x + 7 = 7(14) + 7 = 98 + 7 = 105
The charge on an ion is
a.
always positive.
b.
always negative.
C.
either positive or negative.
Answer:
C. Either positive or negative
what is the answer in simplest form?
[tex]\\ \sf\longmapsto 2m^2=-200[/tex]
[tex]\\ \sf\longmapsto m^2=-100[/tex]
[tex]\\ \sf\longmapsto m=√-100[/tex]
[tex]\\ \sf\longmapsto m=√100i[/tex]
[tex]\\ \sf\longmapsto m=10i[/tex]
6. If the pattern continues, what would be the ninth number in the pattern?
4 8, 12, 16___
( full question on pic )
Hi! can someone help me please, thank u!
Answer:
20
Step-by-step explanation:
You're counting by 4's. Which are the following 4,8,12,16,20 and so on. Hope this helps :D
YOU guys can write a story or a situation that can be represented by the given equation.
4a + 5 = 12a - 11
Thank you :)
Answer:
If you have a party and your pizza was split up into 16 pieces, 8 people should be able to have 2 pieces.
Step-by-step explanation:
find the length of the rectangular plot of land whose weight is 10 M and perimeter is 44 m
Step-by-step explanation:
Area of this plot =(84×84) m
2
=7056 m
2
length of rectangular plot =144 m.
We know that the area of the square plot is same as the area of the rectangular plot
Let breadth of rectangular plot be x.
then, 144x=7056 [∵ Area of a rectangle =l×b ]
⟹x=
144
7056
=49 m
∴ The width of rectangular plot is 49 m.
NEED HELP PRONTOOO!!!!!!!!!!!!!!!!!!
Answer:
(x + 5)² - 25
Step-by-step explanation:
Given below, if Xy and are congruent, what is the measure of
A. 140°
B. 280°
C. 100°
D. 80°
(it’s A. 140°)
Answer:
holi , cómo estás espero que bien bueno déjame te digo que está facil soy de México pero voy a clases de inglés y ya me la hicieron esa pregunta y es la D hojala te ayude mucho
(1)Pradnya had 5 dozen copies. She gave half of the copies to Anushka and 1/5 times of the copies to Prajwal. How many copies are remaining with her ?
(2) Shrikant bought a watch at Rs. 900. He gave equal number of notes of denomination Rs. 10, Rs. 20, Rs. 50 and Rs. 100. Find the number of notes of Rs. 20 that he gave to the shopkeeper.
(3) Mangalakaku purchased 6016 saplings of lemon. She planted 47 saplings in each row. How many rows will be formed of those saplings?
Explanation:
(i)Total number of copies are at Pradnya = 5 dozen
We know that 1 dozen = 12
⇛5×12 = 60
Given copies to Anushka = half of 60
⇛60/2 = 30 copies
Given copies to Prajwala = 1/5 the copies
⇛ (1/5)×60
⇛60/5
⇛12 copies
Total number of given copies = 30+12 = 42
Remaining copies = 60-42 = 18
Answer: Remaining copies = 18
(ii)Let the number of Rs. 10 notes be X
So given that
all are equal in number
So, Number of Rs 20 notes = Number of Rs. 50 notes = Number of Rs. 100 = X
Total number of notes
= X+X+X+X = 4X
Value of Rs. 10 = 10X
Value of Rs. 20 = 20X
Value of Rs. 50 = 50X
Value of Rs. 100 = 100X
Total amount = Rs. 900
⇛10X +20X +50X+100X = 900
⇛180X = 900
⇛X = 900/180
⇛X = 5
Number of Rs. 10 notes = Number of Rs. 20 notes = Answer: number of Rs. 50 notes = Number of Rs. 100 = 5
(iii) Let the number of rows be X
Number of saplings per each row = 47
Total number of saplings of X rows = 47X
According to the given problem,
Total number of saplings purchased by Mangalakaku = 6016
⇛47X = 6016
⇛X = 6016/47
⇛X = 128
Answer: Total number of rows = 128
PLS HELP ASAP ILL GIVE BRAINLKEST PLS THANKS
Answer: y= (1/4)x
Step-by-step explanation: Best guess given screenshot, matched with desmos.
Find the length of the second base of a trapezoid with one base measuring 18 feet, a height of 5.3 feet, and an area of 125.4 square feet.
Answer:
29.32 feet
Step-by-step explanation:
area of a trapezoid = height/2 * (first base + second base)
125.4 = 5.3 / 2 * (18 + second base)
125.4 = 2.65 * (18 + second base)
We want to solve for the second base. To do this, we can start by isolating the (18+second base) by dividing each side by 2.65
47.32 = 18 + second base
subtract 18 from both sides to solve for the second base
29.32 = second base
the triangle has a right angle at the middle letter.
In AABC, Ĉ = 40°, BC = 4 cm. Find AB.
Can someone help me, please? :((((
Answer:
C 132 square units
Step-by-step explanation:
. Happy Friday
Pleas help me for B and C
Answer:
In no b 7 people has represented □
In no c 2 people referred giraffe than dogs
Answer:
(b)Total 8 complete square in given pictogram represented 64 people.
(c) 6 more people preferred giraffes than dogs.
what is the factor of this 3x - 12
Answer:
3 (x - 4)
Step-by-step explanation:
A t-shirt shop bought a total of 24 t-shirts (t) and hats (h) combined. They bought t-shirts for $12.50 each and hats for $8 each. The store spent a total of $259.50, which system of equations could be used to find the number of hats and t-shirts bought?
Answer:
12.5t + 8h = 259.5
t + h = 24
Step-by-step explanation:
Write one equation to deal with the costs and one equation to deal with the numbers of shirts and hats.
12.5t + 8h = 259.5
t + h = 24
i really need your help on this
Answer:
That is an improper fraction
Step-by-step explanation:
When the numerator (the top) is greater than the denominator (The bottom) then the fraction is improper
Hope this helps!
Answer:
Improper fraction
Step-by-step explanation:
1/2 + (-7) – 2 1/2 - (-2)
what are some expressions that are equivalent to
–
2(5n).
[tex]\huge\textbf{Hey there!}[/tex]
[tex]\large\text{Gu\textbf{id}\textsf{e}}\bf\downarrow[/tex]
[tex]\large\textbf{2 negatives = positive}\\\large\textbf{2 positives = positive}\\\large\textbf{1 negative \& 1 positive = negative}\\\large\textbf{1 positive \& 1 negative = negative}\\\\\large\text{Negatives are BELOW 0}\\\large\text{Positives are ABOVE 0}\\\\\large\textsf{Negatives are on the LEFT side of zero.}\\\large\textsf{Positives are on the RIGHT side of zero.}[/tex]
[tex]\huge\textsf{-2(5n) \boxed{\rightarrow} \bf -10n}\\\\\\\\\huge\boxed{\rightarrow\text{-2n + (-2n) + (-2n) + (-2n) + (-2n)}}\\\huge\boxed{\rightarrow \text{\bf -2n - 2n - 2n - 2n - 2n}}\\\huge\boxed{\rightarrow{\text{-4n - 2n - 2n - 2n}}}\\\huge\boxed{\rightarrow \text{-6n - 2n - 2n}}\\\huge\boxed{\rightarrow \text{\bf -8n - 2n}}\\\huge\boxed{\rightarrow \boxed{\text{ -10n}}}[/tex]
[tex]\huge\text{\bf -5(2n)}\\\huge\boxed{\rightarrow \text{-10n}}[/tex]
[tex]\huge\boxed{\text{\bf Therefore, your answers \underline{\underline{could}} be: }}\\\huge\boxed{\bullet \textsf{ -2n - 2n - 2n - 2n -2n}}\huge\checkmark\\\huge\boxed{\bullet \textsf{ -8n - 2n}}\huge\checkmark\\\huge\boxed{\bullet \textsf{ -5(2n)}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
alex is running in a clockwise direction around a circular track with radius 60 yards. he runs for 20 minutes at a speed of 4 yards per second. find the shortest distance between their starting point and their ending point measured along the track
Answer:
100.9 yards
Step-by-step explanation:
One circuit of the track is a distance of ...
C = 2πr = 2π(60 yd) = 120π yd.
At Alex's running rate, the distance covered in 20 minutes is ...
(4 yd/s)(20 min)(60 s/min) = 4800 yd
The number of circuits will be ...
(4800 yd)/(120π yd/circuit) = 40/π circuits ≈ 12.7324 circuits
The last of Alex's laps is more than half-completed, so the shortest distance to his starting point is 13 -12.7324 = 0.2676 circuits,
That distance is (0.2676 circuits)×(120π yd/circuit) ≈ 100.88 yd
The shortest distance along the track to Alex's starting point is about 100.9 yards.
_____
Additional comment
The exact distance is 120(13π-40) yards. The distance will vary according to your approximation for pi. If you use 3.14, this is about 98.4 yards.
need help with this pls
Answer:
Hence y = (5k -3)/ (1 - k)
.... shown
Prove the following
Step-by-step explanation:
Start by multiplying both sides by cosα:
1 + sinα + (cos²α)/(1+sinα) = 2
sinα + (cos²α)/(1+sinα) = 1
Now multiply both sides by 1+sinα:
sinα + sin²α + cos²α = 1 + sinα
sin²α + cos²α = 1 Q.E.D.
Thats the answer and method i used
Determine if they are congruent. State how they are.
[tex]\huge \bf༆ Answer ༄[/tex]
The Correct choice is ~ D
[tex] \textsf{Not enough information }[/tex]The given triangles are not congruent, because they they just have all their corresponding angles equal to one another, so we need more information ~
PLEASE HELP!!!!
ILL MARK AS BRAINIEST!!!!
ANSWER HOW MUCH U CAN!!!
Answer:
1) C
2) B
3) D
4) A
5) B
Step-by-step explanation:
Hope this helps
MAy I get braineist pls???????????
Answer:
MARK ME AS BRAINLIEST!!!
Step-by-step explanation:
1. A
2. B
3. D
4. A
5. B
HAVE A NICE DAY!!!
:)
Please help question in pic
Answer:
7,3
Step-by-step explanation:
for every 5 it goes right it goes 4 up. 2,1+5,4=7,3
greg drove 300 miles at a constant speed for 5 hours. the speed limit is 70 miles per hour. was his rate grater than the speed limit?
No.
Step-by-step explanation:To find the rate for how many miles Greg drove for 5 hours, we need to divide 300 by 5:
300 / 5 = 60.
60 miles represents the speed for 1 hour.
60<70.
The inequality indicates that his rate (60 miles per hour) is less than the speed limit.
if laura has a school loan of $420,a car loan of $300 and rent of $550,what must she budget just to pay those expenses?
Answer:
1270
Step-by-step explanation:
420+300+550
$420+300=720+550=1270
In science class, the girl to boy ratio is 3 to 7.
If there are 50 students total in the class, how many are boys?
Answer:
There are 35 boys in the class.
Step-by-step explanation:
Girls to Boys ratio = 3:7
Total number of students in class = 50
Let total number of girls be '3x' and total number of boys be '7x'
Total number of girls + Total number of boys = Total number of students
3x + 7x = 50
10x = 50
x = 50/10
x = 5
[tex] \therefore [/tex]
Total number of girls = 3 × 5 = 15
Total number of boys = 7 × 5 = 35