Answer: The ratio of the volumes of two pyramids is 27 : 1331.
Step-by-step explanation: Given that two two pyramids are similar and the ratio between the length of their edges is 3 : 11.
We are to find the ratio of the volumes of two pyramids.
Let a units and b units be the lengths of the edges of the two pyramids.
The, according to the given information, we have
[tex]a:b=3:11.[/tex]
We know that the ratio of the volumes of two similar pyramids is equal to the ratio of the cubes of the lengths of edges of the two pyramids.
Therefore, the ratio of the volumes of two pyramids will be
[tex]V:V'=\dfrac{V}{V'}=\dfrac{a^3}{b^3}=\left(\dfrac{a}{b}\right)^3=\left(\dfrac{3}{11}\right)^3=\dfrac{27}{1331}=27:1331\\\\\\\Rightarrow V:V'=27:1331.[/tex]
Thus, the ratio of the volumes of two pyramids is 27 : 1331.
Please help with this question thank you!
A rectangle is twice as long as it is wide. if its length is increase by 4 cm and its width is decreased by 3 cm, the new rectangle formed has an area of 100 cm2 . find the dimensions of the original rectangle.
PLEASE PLEASE HELP ME QUICK!!!!
Will give brainiest to first answer!
Which of the following inequalities is graphed on the coordinate plane?
A. y > x
B. y is less than or equal to x
C. y is greater than or equal to x
D. y < x
Answer:
u have a solid line...means there is an equal sign in the problem...so that eliminates 2 of them right away...so A and D are incorrectit is shaded below the line....this means it is less then...that eliminates option C leaving u with only one answer choiceso ur answer is : B. y is less then or equal to x
Step-by-step explanation:
P(x) = x2 – 1 and q(x)=5(x-1), which expression is equivalent to (p – q)(x)?
Answer: The required expression is [tex]x^2-5x+4.[/tex]
Step-by-step explanation: We are given that
[tex]p(x)=x^2-1,\\\\q(x)=5(x-1).[/tex]
We are to find the expression that is equivalent to (p-q)(x).
We know that for any two functions f(x) and g(x), we have
[tex](f-g)(x)=f(x)-g(x).[/tex]
Therefore we get
[tex](p-q)(x)\\\\=p(x)-q(x)\\\\=(x^2-1)-(5(x-1))\\\\=x^2-1-5x+5\\\\=x^2-5x+4.[/tex]
Thus, the required expression is [tex]x^2-5x+4.[/tex]
Tony is putting 42 oranges into 4 boxes. Each box holds 12 oranges.
How many more oranges are needed to fill all the boxes?
Will a polynomial times a polynomial always equal a polynomial?
Answer:
yes, it will always be a polynomial but depending on how many terms it has, the answer may change
Step-by-step explanat
You purchase a pair of jeans for $24.99 and a t-shirt for $12.49. Assume sales tax is 7.5%
What is your subtotal? $
What is the tax? $
What is your total? $
What do you do the inequality symbol when you multiply or divide by a negative number?
Point R is located at (3,2) and point S is located at (8,15)
What are to coordinates of the point that partitions The directed line segment RS in a 1:4 ratio?
Answer:
was this right
Step-by-step explanation:
As Mercury revolves around the sun, it travels at a rate of approximately 30 miles per second. Convert this rate to miles per minute. At this rate, how many miles will Mercury travel in 4 minutes?
The number of miles that Mercury travels in 4 minutes will be 7,200 miles.
What is the rate?The rate is the ratio of the amount of something to the unit. For example - If the speed of the car is 20 km/h it means the car travels 20 km in one hour.
Unit modification is the process of converting the measurement of a given amount between various units, often by multiplicative constants that alter the value of the calculated quantity without altering its impacts.
As Mercury revolves around the sun, it travels at a rate of approximately 30 miles per second.
Convert the rate into miles per minute. Then we have
Rate = 30 x 60
Rate = 1,800 miles per minute
At this rate, the number of miles that Mercury travels in 4 minutes will be given as,
D = 1,800 x 4
D = 7,200 miles
The number of miles that Mercury travels in 4 minutes will be 7,200 miles.
More about the rate link is given below.
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Could someone please help me. Thanks!!! 12 points!
Is 0.54 a rational number? Why or why not?
a regular polygon must have ___ sides if each interior angle measure is four times the measure of each exterior angle
The sum of the interior angles of the polygon is 1440° and the number of sides of the polygon is 10 sides
What is the sum of the interior angles of a polygon?The sum of the interior angles of a polygon is given by the formula
Sum of Interior angles of a polygon with n sides is
nθ = 180 ( n - 2 )
where n is the number of sides
θ = angle in degrees
Given data ,
Let the sum of the interior angles of the polygon be S
Now , the number of sides = n
The sum of the exterior angles of a polygon = 360°
And , each interior angle measure is four times the measure of each exterior angle
Substituting the values in the equation , we get
180 ( n - 2 ) = 4 ( 360 )
On simplifying the equation , we get
180n - 360 = 1440
Adding 360 on both sides of the equation , we get
180n = 1800
Divide by 180 on both sides of the equation , we get
n = 10 sides
Hence , the number of sides of the polygon is 10 and it is a decagon
To learn more about sum of the interior angles of a polygon click :
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The length of a rectangle is 6 cm longer than its width. if the perimeter of the rectangle is 36 cm , find its area.
pilar wants to save $100. So far, she has saved $63. Find the length of each side of the square
Any large random sample from a group of people will be representative of the entire group.
a. True
b. False
A palm reader gets paid $80 for each palm she reads, and her goal is to earn $2240 reading palms this month. If she has already read 4 palms this month, how many more palms must she read in order to reach her goal?
A.24
B.28
C.20
D.32
In a sale there is 10% of all prices.a chair costs £63 in the sale.hoow mutch was it before the sale?
PLEASE HELP! What is the first step you will use to solve this equation:
4x +2 = 7x - 13
Question 1 options:
Add 13 to both sides
Subtract 2 from both sides
Add 7x to both sides
Subtract 4x from both sides
What was the one item that was left out of the repeal.?
Given △ABC≅△JKL , m∠B=55° , and m∠L=25° , what is the measure of ∠J ? Enter your answer in the box.
Answer:
m∠J = 100° is the answer.
Step-by-step explanation:
Given : ΔABC ≅ ΔJKL,
m∠B = 55°
m∠L = 25°
To find : ∠J
Since in both the triangles ABC and JKL
m∠A ≅ m∠J
m∠B ≅ m∠K = 55°
m∠C ≅ m∠L = 25°
Since measure of ∠K and ∠L are known then we can calculate the third angle j
m∠J + m∠K + m∠L = 180°
55° + 25° + m∠J = 180°
80° + m∠J = 180°
m∠J = 180 - 80
= 100°
Therefore, m∠J = 100° is the answer.
Find the least common multiple of x 3 - x 2 + x - 1 and x 2 - 1. write the answer in factored form.
a. (x + 1) 2(x - 1)
b. (x + 1)(x - 1)(x 2 + 1)
c. (x 3 - x 2 + x - 1)(x 2 - 1)
d. (x + 1)(x - 1)(x 2 - 1)
The correct answer is d. [tex](x + 1)(x - 1)(x^2 - 1)[/tex].
To find the least common multiple (LCM) of the two polynomials[tex]\(x^3 - x^2 + x - 1\) and \(x^2 - 1\)[/tex], we need to factor each polynomial and then find the LCM of the factors.
First, let's factor [tex]\(x^3 - x^2 + x - 1\)[/tex]:
[tex]\(x^3 - x^2 + x - 1 = x^2(x - 1) + (x - 1) = (x^2 + 1)(x - 1)\)[/tex].
Now, let's factor [tex]\(x^2 - 1\)[/tex]:
[tex]\(x^2 - 1 = (x + 1)(x - 1)\)[/tex].
The LCM of two polynomials is the product of the highest powers of all the factors that appear in either polynomial. Here, we have the factors [tex]\(x - 1\), \(x + 1\), and \(x^2 + 1\)[/tex] from the first polynomial, and the factors [tex]\(x - 1\) and \(x + 1\)[/tex] from the second polynomial.
Since [tex]\(x^2 + 1\)[/tex] is already the highest power of [tex]\(x^2 + 1\) , \(x - 1\) and \(x + 1\)[/tex] are the highest powers of [tex]\(x - 1\) and \(x + 1\)[/tex] respectively, the LCM is simply the product of all these factors:
[tex]\((x + 1)(x - 1)(x^2 + 1)\)[/tex].
However, we notice that [tex]\(x^2 - 1\)[/tex] is actually equal to [tex]\((x + 1)(x - 1)\)[/tex], and since [tex]\(x^2 + 1\)[/tex] is not a factor of [tex]\(x^2 - 1\)[/tex], we do not include it in the LCM. Therefore, the LCM is just [tex]\((x + 1)(x - 1)\)[/tex].
But we must also consider the polynomial [tex]\(x^3 - x^2 + x - 1\)[/tex], which can be rewritten as [tex]\((x^2 + 1)(x - 1)\)[/tex]. Since [tex]\(x^2 + 1\)[/tex] is not a factor of [tex]\(x^2 - 1\)[/tex], it must be included in the LCM to account for the additional factor in the first polynomial.
Thus, the LCM of [tex]\(x^3 - x^2 + x - 1\) and \(x^2 - 1\)[/tex] is [tex]\((x + 1)(x - 1)(x^2 - 1)\)[/tex], which corresponds to option d. This is because we take the highest powers of the common factors [tex]\((x + 1)\) and \((x - 1)\)[/tex], and include the additional factor from the first polynomial, which is [tex]\(x^2 - 1\)[/tex] since [tex]\(x^2 + 1\)[/tex] is not a factor of[tex](x^2 - 1\))[/tex].
Therefore, the final answer is [tex]\(\boxed{(x + 1)(x - 1)(x^2 - 1)}\)[/tex].
Given 7x + 11y = N, what is the highest number N can be to produce an answer of No solution. (X,y) must be positive.
what is 875/1000 simplified
Write a two proof column
Given: 4y=2x-10 ; y=6
Prove: x=17
Samantha bought a shirt for $14.98. She gave the cashier a $20 bill. Which operation(s) finds the amount of change Samantha received?
subtract the cost of the shirt from the amount she gave the cashier
20.00 - 14.98 = 5.02
using subtraction she would get $5.02 back in change
A car is traveling at a constant velocity. After two hours the car has traveled 90 miles. After five hours the car has traveled 225 miles. Assuming a linear equation fits this situation, what are the ordered pairs that you would use to find the linear equation
A car travels 0.75 every minute. Explain how could you use proportional reasoning to find how far the car travels in one hour
Answer:
Sample Response: Identify the unit rate as 0.75 miles per 1 minute. Since there are 60 minutes in an hour, multiply 0.75 time 60 to find how far the car travels in one hour.
Step-by-step explanation:
Is y=4x-1 and 12x=3y+7 parallel, perpendicular, or neither
Answer:
Neither is the answer.
Step-by-step explanation:
If a line y = m₁x + c₁ and y = m₂x + c₂ are perpendicular to each other then m₁ × m₂ = -1
If both the lines are parallel to each other then m₁ = m₂
Now two lines have been given as
y = 4x - 1 ----------(1)
12x = 3y + 7
3y = -12x + 7
y = -4x + [tex]\frac{7}{3}[/tex]------(2)
Now from equation (1) and equation (2),
m₁ = 4 and m₂ = -4
Since m₁ ≠ m₂
Therefore, these lines are not parallel
m₁ × m₂ = 4 × (-4) = -16
Therefore, both the lines are neither parallel nor perpendicular.
H=62.4Ns/33,000 solve for N
please help
Answer:
[tex]N=\frac{33,000H}{62.4s}[/tex]
Step-by-step explanation:
We have been given an equation [tex]H=\frac{62.4Ns}{33,000}[/tex]. We are asked to solve our given equation for N.
Multiply both sides by 33,000:
[tex]H*33,000=\frac{62.4Ns}{33,000}*33,000[/tex]
[tex]33,000H=62.4Ns[/tex]
Switch sides:
[tex]62.4Ns=33,000H[/tex]
Divide both sides by [tex]62.4s[/tex]:
[tex]\frac{62.4Ns}{62.4s}=\frac{33,000H}{62.4s}[/tex]
[tex]N=\frac{33,000H}{62.4s}[/tex]
Therefore, the value of N is [tex]\frac{33,000H}{62.4s}[/tex].