Volume of a figure is measure of the space it occupies. The volume of the larger rectangular prism is given as: Option C: 1620 cm³
If a rectangular prism has dimensions a unit, b unit, and c units, then its volume is given as
[tex]V = a \times b \times c \: \rm unit^3[/tex]
What are similar figures?They are scaled. It means, if two figures are similar, then we can get one figure from another by multiplying some constant value(same for one pair of similar figure) to its dimensions.
For example,
if for given case, one rectangular prism has got dimensions a, b, and c centimetres, then
the second rectangular prism, which is similar, let the scale factor is 'd',t then second prism's dimensions will be a x d units, b x d units, and c x d units.
For first prism(smaller), its one side is given to be 5 cm, let its other two sides be 'b' cm, and 'c' cm, then,
[tex]60 \: \rm cm^3 = 5\times b\times c \\\\b\times c = \dfrac{60}{5} = 12[/tex]
Now, the larger prism has 15 cm corresponding side, thus, scale factor was 3 (since 15 is 3 times 5).
Thus, its dimensions would be 15, 3 x b, 3 x c
Thus, its volume would be
[tex]15 \times 3 \times b \times 3 \times c = 135 \times b\times c = 135 \times 12 = 1620 \: \rm cm^3[/tex]
Thus,
The volume of the larger rectangular prism is given as: Option C: 1620 cm³
Learn more about volume of rectangular prism here:
https://brainly.com/question/21308574
Answer:
I can confirm that the answer is 1620 because I just finished my test
Step-by-step explanation:
[tex] \rm \bold{ If \: f ( x ) = tan \: x , \: Then \: Show \: That \: f (2x) = \frac{2f(x)}{1 -[f(x)] } }[/tex]
⭐Thenku ~
[tex]\qquad \sf \: \huge \bf༆ Answer ༄[/tex]
Here's the solution ~
[tex]\qquad \sf \dashrightarrow \: f(x) = \tan(x) [/tex]
[tex]\qquad \sf \dashrightarrow \: f(2x) = \tan(2x) [/tex]
[tex]\qquad \sf \dashrightarrow \: f(2x) = \dfrac{2 \tan(x) }{1 - { \tan {}^{2} (x) }^{} } [/tex]
replace tan(x) with f(x) in the given equation ~
[tex]\qquad \sf \dashrightarrow \: f(2x) = \dfrac{2 (f(x) )}{1 - { (f {}^{} (x)) {}^{2} }^{} } [/tex]
The expression that was proved is [tex]tan2x=\frac{2[f(x)]}{1-[f(x)^2]}[/tex]
Double angle of functionGiven the trigonometry identity
f(x) = tanx
f(2x) tan2x
From double angle theorem;
[tex]tan2x=\frac{tanx+tanx}{1-tanx(tanx)} \\tan2x=\frac{2tanx}{1-tan^2x}[/tex]
Since f(x) = tan(x), substitute into the result to have:
[tex]tan2x=\frac{2[f(x)]}{1-[f(x)^2]}[/tex] (Proved)
Learn more on double angle here: https://brainly.com/question/14691
Error Analysis A student added the rational
expressions as follows:
5x 7 5x 7(7) 5x + 49
+
+
x
x + 7
Describe and correct the error the student
12
x+7
Х
x+7
x+7
Rational expressions are expressions that can be represented as fractions
The solution to the sum of the rational expressions is [tex]\frac{5x^2 + 7x + 49}{x^2 + 7x}[/tex]
How to determine the errorThe student operation is given as:
[tex]\frac { 5 x } { x + 7 } + \frac { 7} { x } = \frac { 5 x } { x + 7 } + \frac { 7 ( 7 ) } { x + 7 } = \frac{5x + 49}{x + 7}[/tex]
The student's error is that, he multiplied the numerator of 7/x by 7, and he added 7 to the denominator
The correction is as follows:
[tex]\frac { 5 x } { x + 7 } + \frac { 7} { x }[/tex]
Take the LCM
[tex]\frac { 5 x } { x + 7 } + \frac { 7} { x } = \frac{5x^2 + 7(x + 7)}{(x + 7)x}[/tex]
Open the brackets
[tex]\frac { 5 x } { x + 7 } + \frac { 7} { x } = \frac{5x^2 + 7x + 49}{x^2 + 7x}[/tex]
Hence, the solution to the sum of the rational expressions is [tex]\frac{5x^2 + 7x + 49}{x^2 + 7x}[/tex]
Read more about rational expressions at:
https://brainly.com/question/21342
___% of $10 = $2
Please help me I can not figure it out
I need it please
Answer:
20%.Step-by-step explanation:
Sentence should be:
2 is what percent of 10.How we get the %:
To get it, we need to find the fraction of 20% (0.2) (2/10)So, we simply do this:2/10.We then get 20%.2 is 20% of 10.
20% of 10 is 2.
find the inverse
f(x)=(2x-3)^2 -1
A rectangular prism has a length of 8 meters, a width of 6 meters, and a height of 3 meters.
Which equations could be used to determine the volume, V, of the prism?
Select each correct answer.
(A) V = 8 × 6 × 6
(B) V = 8 × 6 × 3
(C) V = 8 × 9
(D) V = 48 × 3
Answer:
(B) V = 8 x 6 x 3
Step-by-step explanation:
The formula to find the volume of a rectangular prism is, V = Length x Width x Height cubic units.
V = 8 x 6 x 3 cm 3.
V = 192 cm 3.
Brainliest?!
hi please figure this out me and my sister are so confused
Answer:
y = - 7
Step-by-step explanation:
Since the solution is always the same for y, y equals that solution and does not depend on x.
Find the surface area of this net.
Answer:
96.Step-by-step explanation:
This might be hard, but here we go.
Given equation:
6 * 4 * 46 * 4²Solve:
6 * 4 * 4= 24 * 4= 96.Solve 2nd equation:
6 * 4²= 6 * 16= 96.Surface area = 96 cm².
Need help, I dont know how to do this
Answer: 126 in
I used a calculator. It matches.
hope this helps =)
I need help on this problem, if you can help me ill really be grateful. If you could also explain it that would be great.
You are trying to solve for the zeros.
Answer:
x=3
Step-by-step explanation:
The square root of 225 is 15
so 15=4x+3
-3 -3
12=4x
If 12=4x then x=3
A.(-2, -1) is a solution to the linear system B.(-2, -1)is not a solution to the linear system
Answer:
A. (-2, -1) is the solution to the linear system
Step-by-step explanation:
Substitute for x and y and see if the equations are true.
-1 = 3(-2) +5 . . . . true
-2 +(-1) = -3 . . . . .true
(-2, -1) is the solution to the linear system.
the sum of a number squared and five
Answer:
(x+5^3 is the answer of this question
A recipe requires 2 eggs 500 grams of flour and two teaspoons of salt how many eggs are needed if you use 2 kg of flour?
en una bolsa hay menos de 30 semillas. podemos hacer grupos de 4 semillas sin que sobre ninguna. si hacemos grupos de 5 semillas tampoco sobra ninguna. ¿Cuántas semillas hay en la bolsa?
write the equation of the line?
Answer: Yellow option
Step-by-step explanation:
The points noted are (0,-2) and (3,-1)
So the slope is (-2--1)/(0-3) = -1/-3 = 1/3
So options blue, green and red are out.
So the only option is yellow
Can someone help me with this pleaseee
Answer:
1=C
2=E
3=D
4=B
5=A
Step-by-step explanation:
Please help me with this question.
======================================================
Explanation:
Focus on the outer ring of numbers only.
The left arm of the angle points at 140. The right arm points at 15. The difference of which is 140-15 = 125
---------------
Alternatively, focus on the inner ring of numbers only.
The left arm points at 40 and the right arm points at 165.
165-40 = 125
We get the same answer as before.
Answer:
Step-by-step explanation:
Hello!
140 -15 =>125°
Please answer this (who ever answers correctly gets brainlest)
Answer:
6
Step-by-step explanation:
[tex] \frac{2}{5} \times 15 = 6[/tex]
[tex]15\div5\times2=6\:or\:15\times\dfrac{2}{5}=6 \\\text{Answer: 6}[/tex]
Simplify the following expressions using the distributive property
-3(z-7)
Answer:
I think that the answer is d=-7
Step-by-step explanation:
-3(z-7)
-3z+21
z=-7
martin works in a furniture store. he earns a base salary of $1,800 per month, plus a 15% commission on the amount of furniture sales he makes during the month. if martin needs to earn at least 3,000 each month to pay his expenses, what is the minimum amount of furniture sales he must make each month?
Answer:
$8000
Step-by-step explanation:
With the provided values you get the equation
1800+.15x=3000
with x being the amount of sales he needs
1. 3000-1800=1200
gives 1200=.15x
2. 1200/.15 = 8000
so x = 8000
Dr.Purple wants to buy candy bars for all his 143 math students. He buys 9 cases plus 8 more individual bars. How many bars are in each case?
There is 15 bars in each case.
Subtract 8 from 143 and you get 135.
Divide 135 by 9 and you get 15 :)
Answer:
143 - 8 = 135
Then 135 ÷ 9 = 15
Answer 15 bars in each case.
Ricky is 5 years older than Ciara. In 6 years the sum of their ages will be 53. How old is Ricky now
Answer:
23 years old
Step-by-step explanation:
Given the following question:
Ricky is 5 years older than Ciara...
6 years their ages will equal 53 years of age.
So, we have to remember that in six years their ages will equal 53 and one is five years older than the other.
[tex]23+6=29[/tex]
[tex]18+6=24[/tex]
[tex]29-5=24[/tex]
[tex]29+24=53[/tex]
[tex]29-6=23[/tex]
[tex]=23[/tex]
Which means Ricky as of right now is "23 years of age" and Ciara as of right now is "18 years of age".
Hope this helps.
what is 29/8 into a improper fraction (Convert mixed number).
Answer:
3 5/8
Step-by-step explanation:
divide 29 by 8,
8 times 3 is 24
29-24, remainder is 5
find the area of a square of the side 8cm
Answer:
64cm squared
All squares side lengths are the same. 8*8=64.Answer:
64cm²
Step-by-step explanation:
8cm x 8cm = (8cm)²
8 x 8 = 64
cm x cm = cm²
=64cm²
Paulo has R$80.00 and Carlos has 2/3of that amount. How many Carlos has? How many do the two have together?
Answer:
53 dollars and 33 cents
Step-by-step explanation:
53.33
We are given –
Paulo has R$ 80.00 and Carlos has 2/3 of that amount.
We are asked to find, how much Carlos owns and how much they have together.
Explanation :-
At first, we just need to multiply 80by 2, and then we will divide the value by 3, so we find that:
[tex]\qquad[/tex][tex] \bf \longrightarrow 80 \times 2 = 160[/tex]
[tex]\qquad[/tex][tex] \bf \longrightarrow \dfrac{160}{3} = 53.3[/tex]
Therefore, we find that Carlos has 53.3 R$.
Now to find out how much they have together. We have to add Paul's amount to Carlos' amount for that.
[tex]\qquad[/tex][tex] \bf \longrightarrow 53.3 +80 =133.3[/tex]
Henceforth, they both have 133.3 R$. together.
I NEED HELP WITH THIS MATH I DONT GET IT!!!!!
Answer:
It's 5
Step-by-step explanation:
-4x+5=-15 (subtract 5)
-4x=-20 (divide by -4)
x=5
Step-by-step explanation:
Work backwards. First, create a function:
f(x) = x
First, instead of adding 5, subtract it:
f(x) = x - 5
Then, divide by -4:
f(x) = (x - 5) ÷ -4
Then plug in -15:
f(-15) = (-15 - 5) ÷ 4
= -20 ÷ -4
= 20 ÷ 4
= 5
does anyone know the answer to ts ?
Answer: C is your answer
Step-by-step explanation:
Find the number that makes the ratio equivalent to 1:7.
Answer:
So 2:14 and 3:21 are two ratios that are equal to 1:7. Students are also asked to determine whether two given ratios are equal, by first writing each ratio as a fraction, then writing each fraction in lowest terms. If the two fractions are the same when written in lowest terms, then the ratios are equal.
Step-by-step explanation:
Above
Please Mark brainliest if this helped i need 3 more!
Answer:
2:14 or 3:21
Step-by-step explanation:
because u multiply
hcf of 18 & 24
Lcm of 18 &24
Answer: GCF = 6, LCM = 72
Step-by-step explanation:
The prime factorization of 18 is 2*3^2 and the prime factorization of 24 is 2^3*3
Therefore, the gcf is 2*3 = 6.
The lcm is 2^3*3^2 = 8*9 = 72
Example 13, can anyone tell me why the bases can be converted into x and y?
Maysoun drove 1116 kilometers in 12 hours. At the same rate, how long would it take her to drive 651 kilometers?
Answer:
7 hours
Step-by-step explanation:
12hrs=1116kms
1hr=1116÷12
1hr=93kms
Xhrs=651kms
Xhrs=(651÷93) ×1
=7×1
=7hrs