find the minimum value of x for which the laser beam passes through side b and emerges into the air.

The sizes of the largest circle and sphere that fit in the space at the center of the square and cube are;

17 (a) The radius of the largest circle is r₂ = r₁·(√2 - 1)

(b) The radius of the largest sphere is, r₂ = r₁·(√3 - 1)

The diagonal of a square or a cube is the straight line joining the furthest corners of the square or cube and which passes through their center.

17. (a) The radius of each of the four circles = r₁

The side length of the square = 4·r₁

The radius, r₁, of the largest circle that can fit into the space at the center of the square is therefore found as follows;

The diagonal length of the square = √((4·r₁)² + (4·r₁)²) = 4·r₁·√2

In terms of r₂, we have the following equations for the diagonal of the square;

The length of the diagonal = 2·r₁·√2 + 2·r₁ + 2·r₂ = 4·r₁·√2

2·r₂ = 4·r₁·√2 - 2·r₁·√2 - 2·r₁ = 2·r₁·√2 - 2·r₁

r₂ = r₁·√2 - r₁ = r₁·(√2 - 1)

(b) The length of the diagonal of a cube is √3 × a

Where;

a = The edge length of the cube.

The length of the diagonal of the cube in the question is therefore;

Length of diagonal = 4r₁·√3

In terms of the radius of the sphere, r₂, we have;

Length of diagonal = 2·r₂ + 2·r₁ + 2·r₁·√3

Which gives;

2·r₂ + 2·r₁ + 2·r₁·√3 = 4r₁·√3

2·r₂ = 4r₁·√3 - (2·r₁ + 2·r₁·√3) = 2·r₁·√3 - 2·r₁

2·r₂ = 2·r₁·√3 - 2·r₁

r₂ = r₁·√3 - r₁

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Answer:

Step-by-step explanation:

Statement                     Reason

PR ≅ TR                        Given

<PQR≅<TSR                 Given

<PRQ≅<TRS                Vertical Angles Theorem

PQR=TSR                      SAS  Theorem   (Side-Angle-Side)

Answer:

ig thats the ans

Step-by-step explanation:

5 x x -1 =x3+9

Answer:

5x - 1 = 3x +9

and x = 5

Answer with Step-by-step explanation:

5x - 1 = 3x +9

If u need the solution

5x - 1 = 3x +9

5x-3x = 9+1

2x = 10  ; x = 10/2=5

I hope im right!!

Answer:

D. F(x) = 2(x-3)^2 + 3

Step-by-step explanation:

We are told that the graph of G(x) = x^2, which is a parabola centered at (0, 0)

We are also told that the graph of the function F(x) resembles the graph of the function G(x) but has been shifted and stretched.

The graph of F(x) shown is facing up, so we know that it is multiplied by a positive number. This means we can eliminate A and C because they are both multiplied by -2.

Our two equations left are:

 B. F(x) = 2(x+3)^2 + 3

 D. F(x) = 2(x-3)^2 + 3

Well, we can see that the base of our parabola is (3, 3), so let's plug in the x value, 3, and see which equation gives us a y-value of 3.

y = 2(3+3)^2 + 3 =

2(6)^2 + 3 =

2·36 + 3 =

72 + 3 =

75

That one didn't give us a y value of 3.

y = 2(3-3)^2 + 3 =

2(0)^2 + 3 =

2·0 + 3 =

0 + 3 =

3

This equation gives us an x-value of 3 and a y-value of 3, which is what we wanted, so our answer is:

D. F(x) = 2(x-3)^2 + 3

Hopefully this helps you to understand parabolas better.

Answer:

a. True

Step-by-step explanation:

By ∝= 5% we mean that there are about 5 chances in 100 of incorrectly rejecting a true null hypothesis. To put it in another way , we say that we are 95% confident in making the correct decision.

In the given question the null hypothesis is

H0: u ≤ 1 hour and Ha:  u > 1 hour

So there is a 5% chance that the erroneous conclusion will be made that students spend on average more than 1 hour per assignment.

The given statement is true.

Answer:

100%?

Step-by-step explanation:

Answer:

Step-by-step explanation:

The range of a data set is the difference between the largest number and the smallest number.

Then, for the data set 1:

For the data set 2:

There must exist a vertex u in T such that the distance between u and v is at most (n-1)/2.

To prove the existence of a vertex u in tree T such that the distance between u and v is at most (n-1)/2, we can employ a contradiction argument. Assume that such a vertex u does not exist.

Since the number of vertices in T is odd, there must be at least one path from v to another vertex w such that the distance between v and w is greater than (n-1)/2.

Denote this path as P. Let x be the vertex on path P that is closest to v.

By assumption, the distance from x to v is greater than (n-1)/2. However, the remaining vertices on path P, excluding x, must have distances at least (n+1)/2 from v.

Therefore, the total number of vertices in T would be at least n + (n+1)/2 > n, which is a contradiction.

Hence, there must exist a vertex u in T such that the distance between u and v is at most (n-1)/2.

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The equation to find Shanti's age is y = x - 3 where y is Shanti's age.

Given,

Shanti's sister Uri is Shanti's age plus 3 years.

Uri is 7 years old.

We need to write an equation to find Shanti's age.

We have,

Uri age = Shanti age + 3______(1)

Uri = 7 years old

Putting in (1)

We get,

Uri age = Shanti age + 3

7 = Shanti age + 3

Subtracting 3 on both sides.

7 - 3 = Shanti age + 3 - 3

4 = Shanti age

We see that Shanti's age is 4 years old.

If we have to write an equation then,

Consider Uri's age to be x and Shanti's age to be y.

Now,

Uri age = Shanti age + 3

x = y + 3

Subtracting 3 on both sides

x -3 = y

y = x - 3 is our equation.

Thus the equation to find Shanti's age is y = x - 3.

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Answer:

the answer is 17

wlecome

Step-by-step explanation:

Answer:

the answer would be

Step-by-step explanation:i hope this helped

The area of the triangle is 10 units²

Given the: vertices  of the triangle as J(−2, 1), K(0, 3), and L(3, −4)

The formula of the area of a triangle using the vertices of the triangle is can be given as:

A = 1/2 [x₁(y₂−y₃) + x₂(y₃− y₁)+ x₃(y₁−y₂)] ,

where (x₁, y₁), (x₂, y₂), (x₃, y₃) are the coordinates of the three vertices of the triangle

A = 1/2  [-2(3−(-4)) + 0(-4− 1)+ 3(1−3)]

A = 1/2 [-14 + 0 -6]

A = 1/2 [-20]

A = 10 units²

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Answer:

B

Step-by-step explanation:

\(\dfrac{a^{m}}{a^{n}}=a^{m-n} \ if \ m > n\\\\\\ \dfrac{a^{m}}{a^{n}}=\dfrac{1}{a^{n-m}} \ if \ n > m\\\)

\(\dfrac{16r^{6}z^{3}}{8r^{2}z^{6}}=\dfrac{2r^{6-2}}{z^{6-3}}\\\\ =\dfrac{2r^{4}}{z^{3}}\)

Answer:

x= 7 ;

y+x=18

y=18-x

y=18-7

y=11

Answer:

$80

Step-by-step explanation:

Let the number of hours required to make a mailbox = x

Let the number of hours required to make a toy = y

Each mailbox requires 1 hour of work from Carlo and 4 hours from Anita.

Each toy requires 1 hour of work from Carlo and 1 hour from Anita.

The table below summarizes the information for ease of understanding.

\(\left|\begin{array}{c|c|c|c}&$Mailbox(x)&$Toy(y)&$Maximum Number of Hours\\--&--&--&------------\\$Carlo&1&1&12\\$Anita&4&1&24\end{array}\right|\)

We have the constraints:

\(x+y \leq 12\\4x+y \leq 24\\x \geq 0\\y \geq 0\)

Each mailbox sells for $10 and each toy sells for $5.

Therefore, Revenue, R(x,y)=10x+5y

The given problem is to:

Maximize, R(x,y)=10x+5y

Subject to the constraints

\(x+y \leq 12\\4x+y \leq 24\\x \geq 0\\y \geq 0\)

The graph is plotted and attached below.

From the graph, the feasible region are:

(0,0), (6,0), (4,8) and (0,12)

At (6,0), 10x+5y=10(6)+5(0)=60

At (4,8), 10(4)+5(8)=80

At (0,12), 10(0)+5(12)=60

The maximum revenue occurs when they use 4 hours on mailboxes and 8 hours on toys.

The maximum possible revenue is $80.

The value of a is 5, b is 4, c is 0, d is 3, e is 6 and R is 6 after following the long division method.

According to the question,

We have to divide 430 by 8 by following the long division method.

Note that when we follow long division method then the number by which we are dividing (divisor) is to be multiplied in such a way that the result remains less than the number in the dividend.

Now, we will solve it step by step.

In dividing 43 by 8, we have to multiply 8 by 5. Then, we get 40.

So, we have a = 5, b = 4 and c = 0.

Now, after this we have 30 and the number that we get after multiplication is 24. So, 3 has to be multiplied in 8 to get 24.

So, we have d = 3.

Now, when we will subtract 24 from 30, we will get 6.

So, we have e = 6.

And e is also the remainder, R. So, we have R = 6.

Hence, the values of a, b, c, d, e, and R are 5, 4, 0, 3, 6, and 6 respectively.

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Answer: He should choose the savings account because he can earn more interest and the money in his savings account is more than the money in his checking account.

Step-by-step explanation:

The solution to the system of equations is x = 6 and  y = -5, which is the same as we obtained using the elimination method.

A system of equations is a collection of one or more equations that are considered together. The system can consist of linear or nonlinear equations and may have one or more variables. The solution to a system of equations is the set of values that satisfy all of the equations in the system simultaneously. The given system of equations is:

2x + y = 7 ---(1)

x + y = 1 ---(2)

To solve this system, we can use the method of elimination or substitution.

Method 1: Elimination

In this method, we eliminate one of the variables by adding or subtracting the two equations. To do this, we need to multiply one or both equations by a suitable constant so that the coefficients of one of the variables become equal in magnitude but opposite in sign.

Let's multiply equation (2) by -2, so that the coefficient of y in both equations becomes equal in magnitude but opposite in sign:

-2(x + y) = -2(1) --

Multiplying equation

(2) by -2-2x - 2y = -2

Now we can add the two equations (1) and (-2x - 2y = -2) to eliminate y:

2x + y = 7(-2x - 2y = -2)0x - y = 5

We now have a new equation in which y is isolated.

To solve for y, we can multiply both sides by -1:

-1(-y) = -1(5)y = -5

Now that we know y = -5, we can substitute this value into equation (2) to find x:x + y = 1x + (-5) = 1x = 6

Therefore, the solution to the system of equations is (x,y) = (6,-5).

Method 2: Substitution

In this method, we solve one of the equations for one variable in terms of the other variable and substitute this expression into the other equation to get an equation with only one variable.

From equation (2), we can solve for y in terms of x:y = 1 - x

We can then substitute this expression for y into equation (1):2x + y = 72x + (1 - x) = 7 --Substituting y = 1 - xx + 1 = 7x = 6

Now that we know x = 6, we can substitute this value into equation (2) to find y:x + y = 16 + y = 1 --Substituting x = 6y = -5

Therefore, the solution to the system of equations is (x,y) = (6,-5), which is the same as we obtained using the elimination method.

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Answer:

Try setting up a proportion: \(\frac{5}{15}=\frac{3}{x}\) then cross multiply to solve for x which will try you how many boys are in the class.  Then add the number of boys and girls together.

Step-by-step explanation:

Answer:

4 1/10 when u have a inproper fraction like that every 10 is one whole number

Answer:you need to show the diagram in order for me to

Step-by-step explanation:

The volume of the pyramid is  9333 cubic centimetres

From the question, we have the following parameters that can be used in our computation:

Base dimensions = 40 cm by 20 cm

Height = 35 cm

The volume of the pyramid is calculated as

Volume = Product of Base dimensions and Height/3

substitute the known values in the above equation, so, we have the following representation

Volume = 40 * 20 * 35/3

Evaluate

Volume = 9333

Hence, the volume is 9333

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6 and 60 could be the pair of numbers

The given parameters are:

GCF = 6

LCM = 60

Let the two numbers be x and y

So, we have

x * y = GCF * LCM

This gives

x * y = 6 * 60

By comparison, we have

x = 6 and y = 60

Hence, 6 and 60 could be the pair of numbers

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The amount of cash generated is 78.75 Million.

Price-sales ratio, often known as the P/S ratio or PSR, is a stock valuation indicator. It is computed by dividing the market capitalization of the company by its most recent fiscal year's revenue, or, equivalently, by dividing the share price of the stock by its revenue per share.

The sales ratio will be calculated as below:-

Sales= $450  Million

Fixed Assets= $225  Million

% of capacity utilized. . 65%

Sales at full capacity = actual sales/%of capacity used = 692.31 millions dollars .

Target FA = Full capacity FA/sales = FA/Capacity sales = 32.50%

(225*65% = 146.25, 146.25/450 = 32.50%)

Optimal FA = sales * targeted FA/Sales Ratio = 450*32.50% = 146.25

Cash Generated = Actual FA-optimal FA = 225-146.25 = 78.75 millions dollars

Therefore, the amount of cash generated is 78.75 Million.

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Answer:  13.2

In fraction form, this is 66/5

=============================================================

Explanation:

The five values are in the ratio 1:2:3:4:5 which scales up to 1x:2x:3x:4x:5x for some positive number x.

Add up the pieces of the second ratio and set that sum equal to 198. Then solve for x.

1x+2x+3x+4x+5x = 198

15x = 198

x = 198/15

x = 66/5

x = 13.2 is the smallest number since 1x = 1*13.2 = 13.2 was the smallest value of the ratio 1x:2x:3x:4x:5x.

Answer:

5/13

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

Answer:

x=90°

Step-by-step explanation:

As in the angle, there is a box giving us info that x has to be 90°.

But to be sure that there is no mistake we have to do the following:

So we are looking at the surroundings of angle x (which is on a straight line) we see that it is a right angle and look at the angle on the same line is a right angle too.

The equation right angle=90° helps us see that because there are two right angles on a 180° line (90°+90°+180°).

Therefore the answer is:

x=90°

Answer: 20

Step-by-step explanation:

Multiply 2.4*10-4

Calculate 24-4

the answer is (12x^10000)/5

Answer:

The mean of the sampling distribution of sample means is equal to the population mean, which is 5.3 years.

give thanks for more! your welcome!

Step-by-step explanation:

The rule is in arithmetic progression.

The sequence given is -9, -7, -5, -3, -1

Arithmetic progression is a sequence of numbers such that the difference between the consecutive terms is constant.

Here the common difference(d) of the sequence is

common difference (d) = -7 -(-9) = 2

The formula to find the nth term of the sequence is

\(a_{n}\) = a + (n -1) d

were

a = first term of the sequence

n = number of term

d = common difference

Therefore the rule is in arithmetic sequence.

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