Your class tried to construct a tetrahedron using four smaller congruent tetrahedra. However, the result left a gap in the center, as shown in the diagram below. If the volume of each small shaded tetrahedron is 50 in.3, what is the volume of the gap? Explain how you know.

Your Class Tried To Construct A Tetrahedron Using Four Smaller Congruent Tetrahedra. However, The Result

Answers

Answer 1

Answer:

200 in³

Explanation:

The lengths of the sides of the constructed tetrahedron are twice the length of the side of the small tetrahedron of 50 in³. It means that the scale factor for the solid is 2. So, the complete volume of the constructed tetrahedron is equal to

Vn = 2³(50 in³)

Vn = 8(50 in³)

Vn = 400 in³

However, we only use 4 small tetrahedrons, so the volume of these four solids is

4(50 in³) = 200 in³

Then, the volume of the gap is the difference between the volume of the constructed tetrahedron and the volume of the 4 small tetrahedrons

400 in³ - 200 in³ = 200 in³

So, the answer is 200 in³


Related Questions

Please help me with this question my son keeps getting this wrong, please help I have attached the image of the problem from his math paper.

Answers

The terms in the given expression are

[tex]8x^3y^2,4x^2y^3,40xy^3[/tex]

The common factor in all the three time is

[tex]4xy^2[/tex]

Take the common factor outside the brackets and write the remaining inside the brackets.

[tex]4xy^2(2x^2-xy+10y)[/tex]

Simplify.3(x + 4)12 x3 x + 127x3(x+4)

Answers

We need to apply "Distributive Property" in order to get rid of the grouping symbols in the algebraic expression.

Such means to multiply 3 by each of the terms inside the parenthesis. That is:

3 times x and then 3 time 4:

3 times x remains as "3 x" since we don't know the value of "x", and 3 times 4 becomes 12:

3 (x+4) = 3 x + 12

Which seems to be the second option you listed.

Which is closest to X, the distance between the base of the lighthouse and the boat

Answers

we have

then, we use the trigonometric tangent identity:

[tex]\begin{gathered} \tan 25=\frac{22}{x} \\ x=\frac{22}{\tan 25} \\ x=47.2 \end{gathered}[/tex]

answer: x = 47.2

Consider the equation below.
log4(x+3)= log2 (2+x)
Which system of equations can represent the equation?

Answers

Answer:

x=2log(2)−3log(4)log(4)−log(2)

Step-by-step explanation:

I hope this matches one of your answers

The decimal form is -4

Air pressure decreases exponentially with increases in elevation. The air pressure, y, (in atm units) at a given elevation, x, (in meters) can bemodeled using equation y = e where k is the decay constant.At an elevation of 5486 m where the air pressure is 0.5 atm, what is the value of k?O A k=In( 5486)0.5B. k =In(0.5)548654860.5D. k = - In ( 3956

Answers

Take natural log on both side of the equation to simplify it,

[tex]\begin{gathered} \ln y=\ln (e^{-kx}) \\ \ln y=(-kx)\ln e \\ \ln y=-kx \\ k=\frac{-\ln y}{x} \end{gathered}[/tex]

S

Solve for X.
X =?]
5X - 16 x + 10

Answers

-11x + 10 is the answer.
5x-16x+10
calculate the difference
= -11x+10
5x - 16x + 10
-11x + 10

Which sequences are geometric? Select three options.

–2.7, –9, –30, –100, ...
–1, 2.5, –6.25, 15.625, ...
9.1, 9.2, 9.3, 9.4, ...
8, 0.8, 0.08, 0.008, ...
4, –4, –12, –20, ..

Answers

(i) –2.7, –9, –30, –100, ... case of a geometric sequence

(ii) –1, 2.5, –6.25, 15.625, ... case of a geometric sequence

(iii) 9.1, 9.2, 9.3, 9.4, ... not a case of a geometric sequence

(iv) 8, 0.8, 0.08, 0.008, ... case of a geometric sequence

(v) 4, –4, –12, –20, .. not a case of a geometric sequence

What is a geometric sequence?

A geometric sequence is one in which the ratio of two succeeding terms is fixed. The common ratio is what's known as this ratio.

Checking each sequence one by one right now.

(i) –2.7, –9, –30, –100, ...

r=(-9/2.7)=3.33

=(-30/9)=3.33

=(-100/9)=3.33

⇒This is a case of a geometric sequence

(ii) –1, 2.5, –6.25, 15.625, ...

r=(2.5/-1)=2.5

=(-6.25/2.5)=2.5

=(15.625/-6.25)= 2.5

⇒This is a case of a geometric sequence

(iii) 9.1, 9.2, 9.3, 9.4, ...

since the ratio between terms is not the same.

⇒This is not a case of a geometric sequence

(iv) 8, 0.8, 0.08, 0.008, ...

since the ratio between terms is the same.

⇒This is a case of a geometric sequence

(v) 4, –4, –12, –20, ..

since the ratio between terms is not the same.

⇒This is not a case of a geometric sequence

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Answer:

option 1,2,4,5 are correct answers

Step-by-step explanation:

what’s the correct answer answer asap for brain list

Answers

Answer:

B is the correct answer

hope this helped:)

The correct answer is b

Mia Kaminsky sells shoes for Macy’s. Macy’s pays Mia $12 per hour plus a 5% commission on all sales. Assume Mia works 37 hours for the week and has $7,000 in sales. What is Mia’s gross pay

Answers

Mia's gross pay was $794 at the end of the week.

Mia's Gross Pay

To calculate Mia's gross pay, we have to find how much she earned working 37 hours at a rate of $12 per hour.

Total number of hours worked = 37Rate per hour = $12

We can simply multiply both variable to determine how much she earned working for 37 hours.

[tex]37 * 12 = 444[/tex]

Mia earned $444 for that week.

We can add this to her 5% commission which would be 5% of $7000

[tex]5\% of 7000 = 350[/tex]

The sum of Mia's gross pay for the week is

[tex]444 + 350 = 794[/tex]

She earned $794 in gross pay at the end of the week.

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Find the domain of the rational expression: 3x+21
all real numbers except 4
all real numbers except -7
all real numbers except 0
all real numbers except -21

Answers

Answer: The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.

Domain: (−∞,∞)

Range: (−∞,∞)


Hope this helps! :)

Please Help, thank you.

Answers

The interval notation for the change in temperature are-

Increasing temperature; (1, 3) ∪ (6, 8).Decreasing temperature; (0, 1) ∪ (3, 6).What is termed as the interval notation?An interval is represented on a number line using interval notation. In those other words, it is a method of writing real number line subsets. An interval is made up of numbers that fall between two particular given numbers.

For the given function;

Increasing temperature; It is the temperature in which the graph is increasing or we can say that for as the vale of x increases the value of y also increases. Thus, the interval notations are-

Increasing temperature; (1, 3) ∪ (6, 8).

Decreasing temperature: It is the temperature in which the graph is decreasing or we can say that for as the vale of x increases the value of y also decreases. Thus, the interval notations are-

Decreasing temperature; (0, 1) ∪ (3, 6).

Thus, the interval notations for the function are found.

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Which is an algebraic expression for five more than z

Answers

The algebraic expression for 5 more than z is Z + 5.

Given,

5 more than z.

We need to find the algebraic expression.

What are the different algebraic expressions?

We have,

Examples:

- 3 more than M =  M + 3

- 3 less than M =  M - 3

- 3 times M = 3 x M

- 3 times M less than 2 = 3M - 2

- 3 times M more than 2 = 3M + 2

Find the algebraic expression for 5 more than Z.

We have,

5 more than Z = Z + 5

Thus the algebraic expression for 5 more than z is Z + 5.

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PLS HELP WILL MARK BRAINLIEST

Answers

Answer:/Step-by-step explanation:

10. Write the phrase "20 divided by x minus 3 is 12" as a variable expression.

  20

---------- = 12

 x - 3

11. Write the phrase "4 plus the quotient of 9 and y equals 6" as a variable expression.

4 + (9 ÷ y) = 6

I hope this helps!

Simplify the expression below by applying the zero exponent rule. (5-8)^0 = Answer

Answers

Zero Exponent Rule:

[tex]\begin{gathered} a^0=1 \\ a\neq0 \end{gathered}[/tex]

Thus, anything to the power of 0 is "1", except 0.

Let's simplify the expression shown:

[tex]\begin{gathered} (5-8)^0 \\ =(-3)^0 \\ =1 \end{gathered}[/tex]Answer1

what is the means proportional between 4 and 81

Answers

Given

4

18

Procedure

The mean proportional, or geometric mean, of two positive The mean proportional, or geometric mean, of two positive

[tex]\frac{a}{x}=\frac{x}{b}[/tex]

When solving

[tex]\begin{gathered} x=\sqrt[]{a\cdot b} \\ x=\sqrt[]{4\cdot81} \\ x=\sqrt[]{324} \\ x=18 \end{gathered}[/tex]

The answer would be 18

Elon writes an algebraic expression to represent the product of 10 and the difference of 5y and 1. The factors of the expression are______and_____

Answers

The factors of the expression are 2.5 and 11/5.

What is an algebraic expression?

In mathematics, an expression that incorporates variables, constants, and algebraic operations is known as an algebraic expression (addition, subtraction, etc.). Terms comprise expressions. Similar to this, we are describing an algebraic expression when we explain an expression in words that has a variable (an expression with a variable). For instance, the algebraic expression for "3 more than x" can be written. x + 3.

Given Data

Elon writes an algebraic expression to represent the product of 10 and the difference of 5y and 1.

Algebraic expression:

The factors of the expression are:

10 = 5y -1

11 = 5y

y = 11/5

y = 2.5

The factors of the expression are 2.5 and 11/5.

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I am having a hard time understanding explicit formulas with arithmetic sequences. The current sequence I am working with is:2, 8, 14, 20, 26The common difference is 6. I don't know how to come up with the explicit formula when given the sequence.

Answers

Solution

we are given the sequence

[tex]2,8,14,20,26,..[/tex]

The first term = 2

Common difference = 6

The sequence is an arithmetic progression

The nth term is given as

[tex]\begin{gathered} a_n=a+(n-1)d \\ a=2 \\ d=6 \\ a_n=2+(n-1)(6) \\ a_n=2+6n-6 \\ a_n=6n-4 \end{gathered}[/tex]

Therefore, the answer is

[tex]a_{n}=6n-4[/tex]

The graph shows the function f(x).
f(x)
Which equation represents f(x)?
a.f(x) = -√√x
b. f(x) = -√√x-1
c. f(x)=√√/-x-1
d. f(x)=√x

Answers

Answer:

The correct option is 3.

Step-by-step explanation:

The parent cube root function is

From the given graph it is clear that the graph of f(x) is transformed by reflecting the graph of g(x) across y-axis and shifting two units down.

If the parent cube root function is reflected across the y-axis, then x is replaced by -x.

Now, the graph of new function sifts 1 unit down. So, the required function is

The graph shows the function .

From the given graph it is clear that the graph passes through the points (-8,1), (0,-1) and (8,-3).

Check the above function by these points.

At x=-8,

At x=0,

At x=8,

All these points satisfy by the abobe function. It means the above function is correct.

Therefore the correct option is 3.

Find the sum and product of the roots of the equation 4x^2-12=3x

Answers

Given the equation:

[tex]4x^2-12=3x\text{ ----- equation 1}[/tex]

Required: sum and product of the roots of the equation

solution:

For a quadratic equation of the form

[tex]ax^2\text{ + bx + c = 0 ------ equation 2}[/tex]

the sum of the roots is expressed as

[tex]\text{sum of roots = -}\frac{b}{a}[/tex]

the product of the roots is expressed as

[tex]\text{product of roots = }\frac{c}{a}[/tex]

The given quadratic equation can be rewritten in the form as in equation 2 to be

[tex]4x^2-3x-12\text{ = 0 ----- equation 3}[/tex]

In comparison to equation 2,

[tex]\begin{gathered} a\text{ = 4} \\ b\text{ = -3} \\ c\text{ =-12} \end{gathered}[/tex]

Thus,

Sum of roots:

[tex]\begin{gathered} \text{sum of roots = -}\frac{b}{a} \\ =-\frac{-3}{4} \\ =\frac{3}{4} \end{gathered}[/tex]

thus, the sum of the roots is

[tex]\frac{3}{4}[/tex]

Products of roots:

[tex]\begin{gathered} \text{product of roots = }\frac{c}{a} \\ =\frac{-12}{4} \\ =-3 \end{gathered}[/tex]

thus, the product of the roots is

[tex]-3[/tex]

Write the equation of a line that is parallel to the line whose equation is y = 1/3x +6 and passes through the point(-3,5).

Answers

Answer:

y = 1/3 x + 6

Explanation:

The slope of two parallel lines is the same; thereofre the equation of the line we are seeking looks like

[tex]y=\frac{1}{3}x+b[/tex]

where b is a constant hitherto unknown.

Now, we know from point (-3, 5) that when when x = -3, y = 5; therefore,

[tex]5=\frac{1}{3}(-3)+b[/tex]

the above simplifies to

[tex]5=-1+b[/tex][tex]\therefore b=6[/tex]

Hence, the equation of the line is

[tex]y=\frac{1}{3}x+6[/tex]

Simplify −6g(3g + 2).

−18g^2 + 2

−18g^2 − 12g

−18g + 2

−18g − 12g

Answers

Answer:

B. −18g^2 − 12g

Step-by-step explanation:

Hope this helps!
Please tell me if its incorrect

last monday two law students met up at Cafe literature after school to read the pages they were assigned in the legal methods class Alejandro can read one page per minute and he has 28 pages so far Carly who has a reading speed of two pages per minute has read 12 pages so far.Write an equation to describe the pages each student read.Graph the equations.Which are the ratios for each student?

Answers

Let x be the number of minutes they read and y the number of pages they read.

Since Alejandro read one page per minute and he has so far read a total of 28 pages he the total amount of pages he read is:

[tex]y=x+28[/tex]

Now, Carly reads twice as much in the same time but she has read only 12 pages so far, then the amount of pages in her case is:

[tex]y=2x+12[/tex]

The graphf of this equations are:

The rate of change:

Alejandro: 1

Carly: 2

Construct a polynomial function with the stated properties. Reduce all fractions to lowest terms. Third-degree, with zeros of -3,-2, and 1, and a y-intercept of -14.

Answers

Recall that the general form of a third-degree polynomial is:

[tex]g(x)=k(x-a)(x-b)(x-c),[/tex]

where k is a constant, and a, b, and c are the zeros of the polynomial.

Therefore:

[tex]p(x)=k(x+3)(x+2)(x-1).[/tex]

Now, to determine the value of k, we consider the y-intercept:

[tex]p(0)=-14=k(0+3)(0+2)(0-1).[/tex]

Solving for k, we get:

[tex]\begin{gathered} -14=-6k, \\ k=-\frac{14}{-6}, \\ k=\frac{14}{6}, \\ k=\frac{7}{3}. \end{gathered}[/tex]

Finally:

[tex]p(x)=\frac{7}{3}(x+3)(x+2)(x-1).[/tex]Answer: [tex]p(x)=\frac{7}{3}(x+3)(x+2)(x-1).[/tex]

for each problem find the instantaneous rate of change of the function at the given value ...Thank you and God Bless

Answers

Answer:

The instantaneous rate of change of the function at the given value is -2.

[tex]f^{\prime}(0)=-2[/tex]

Explanation:

The instantaneous rate of change of the function at point x=a can be written as;

[tex]f^{\prime}(a)=\frac{df(a)}{dx}[/tex]

For the given function;

[tex]y=2x^2-2x+2[/tex]

Then the derivative of the function is;

[tex]f^{\prime}(x)=y^{\prime}=4x-2[/tex]

substituting x=0, we have;

[tex]\begin{gathered} f^{\prime}(0)=4(0)-2 \\ f^{\prime}(0)=-2 \end{gathered}[/tex]

Therefore, the instantaneous rate of change of the function at the given value is -2.

[tex]f^{\prime}(0)=-2[/tex]

Shavon and Jesiah are having a race. Shavon can run 100 meters in 30 seconds. Jesiah can run 120 meters in 40 seconds. Who is running faster in meters per second, and by how much?

Answers

Shavon is running faster by 0.33 meter.

How to calculate the value?

From the information, Shavon and Jesiah are having a race and Shavon can run 100 meters in 30 seconds. The speed will be:

= Distance / Time

= 100 / 30

= 3.33 meter per second

Jesiah can run 120 meters in 40 seconds. The speed will be:

= Distance / Time

= 120 / 40

= 3 meters per second.

Shavon runs faster. This is illustrated as:

= 3.33 - 3

= 0.33 meter

She's 0.33 meters faster.

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Please help
12​x2+20-3x−5
Factor out the GCF from the entire expression

Answers

I WILL FIRST GROUP THE LIKE TERMS AND SIMPLIFY THEM BEFORE FACTORISING

IT IS VITAL TO SIMPLIFY LIKE TERMS BEFORE FACTORISING.

[tex]12 {x}^{2} - 3x + 20 - 5 \\ = 12 {x}^{2} - 3x + 15[/tex]

THE GCF IN THE EXPRESSION IS 3 MEANING WE WILL DIVIDE EACH AND EVERY TERM IN THE P

EXPRESSION BY 3

[tex] = 3(4 {x}^{2} - x + 5)[/tex]

HOPE THIS HELPS.

True or False. 8 (12 + 3) is equivalent to 120

Answers

Use the order of operations and the distributive property to solve this expression. Work starting from the parenthesis.

8(12 + 3) = 120
8(15) = 120
120 = 120

The equation is true.

Answer:

True because you must do parentheses first so 12+3=15x8=120 so it is equivalent

(3s)/(s^2 - 16) (s-4)/(s^2)

Answers

Answer: =111e3t(33cosh11−−√t+711−−√sinh11−−√t)

Step-by-step explanation:

Find the solution set for y = 4x - 3,
given the replacement set
{(-3, 9), (-2, -11), (0, -2), (2,5)}

Answers

The solution set for y = 4x-3 is {(2,5)} from the replacement set {(-3, 9), (-2, -11), (0, -2), (2,5)}.

The provided function is an equation of line in slope-intercept form of line.

According to which, if a line has slope m and it has the Y-intercept c, then the equation of line will be,

y = mx+c,

One thing to be noted here is, if the line passes through (a,b) then it will satisfy the equation and also, it will be called a solution of the equation.

The equation is y = 4x-3,

The given replacement sets is, {(-3, 9), (-2, -11), (0, -2), (2,5)}.

We will check for each and every element of the set,

1. For (-3,9)

Putting values in,

y = 4x-3

9 = 4(-3)-3

9 ≠ -15

Not a solution.

2. For (-2,11)

Putting values in,

y = 4x-3

11 = 4(-2)-3

11 ≠ -11

Not a solution.

3. For (0,-2)

Putting values in,

y = 4x-3

-2 = 4(0)-3

-2 ≠ -3

Not a solution.

4. For (2,5)

Putting values in,

y = 4x-3

5 = 4(2)-3

5 = 5

It is a solution for the equation y = 4x -3.

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of lines with the following characterizing property. (h) mar + 2) = -1 (b) perpendicular to 3r + 2y = 7 (d) having inclination 60° (f) passing through the origin (h) having slope 6) x-intercept twice y-intercept

Answers

We need to write the equation of the family of the lines with the following characterizing property.

j) x - intercept is twice y - intercept

X- intercept is the value of x when y= 0

Y- intercept is the value of y when x = 0

so, let y- intercept = a

x- intercept = twice y- intercept = 2a

So, the line will pass through the points: ( 2a , 0 ) and ( 0 , a )

The general equation of the line is : y = m * x + b

Where m is the slope and b is y - intercept

[tex]slope=m=\frac{rise}{run}=\frac{y_2-y_1}{x_2-x_1}=\frac{a-0}{0-2a}=\frac{a}{-2a}=-\frac{1}{2}[/tex]

So, the equation of the family will be :

[tex]y=-\frac{1}{2}x+a[/tex]

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