Kylie needs to pack her baton for a color-guard competition. The baton is 38 inches long. Will it fit in a rectangular box with a base of 13 inches by 35 inches and a height of 13 inches?
What is the diagonal??

HELP ASAP
Quiz is tmmr

Answers

Answer 1

Answer:

The diagonal is 39.54 in

Step-by-step explanation:

First we use the Pythagorean theorem to calculate the length of the diagonal of the base.

If the base measures 13 inches by 35 inches then the diagonal is:

[tex]c = \sqrt{13^2 +35^2}\\\\c= 37.34\ in[/tex]

Now we use the Pythagorean theorem again to find the diagonal of the cube.

If the height of the box is 13 inches and the diagonal of the base is 37.34 inches then the diagonal of the cube will be

[tex]z = \sqrt{37.34^2 +13^2}\\\\z= 39.54\ in[/tex]

The baton will fit in the box if it is placed in the direction of the diagonal of the cube, since:

39.54\ in > 38 inches

Answer 2
Final answer:

Using the 3D Pythagorean theorem, the diagonal of the box is calculated to be approximately 39.53 inches, which means that Kylie's 38-inch baton will fit inside the box diagonally.

Explanation:

Kylie needs to check if her 38-inch long baton will fit diagonally in a box with dimensions of 13 inches by 35 inches by 13 inches. To determine whether the baton will fit, she needs to find the length of the longest diagonal of the box. This is solved by using the 3D Pythagorean theorem, which is an extension of the traditional Pythagorean theorem applied to three dimensions.

To find the length of the diagonal (d), we use the formula:

d = √(l² + w² + h²)

Where l is the length, w is the width, and h is the height of the box. Substituting the given values:

d = √(13² + 35² + 13²)

d = √(169 + 1225 + 169)

d = √1563

d ≈ 39.53 inches

The calculated diagonal length of approximately 39.53 inches indicates that Kylie's baton, which measures 38 inches, will indeed fit inside the box diagonally.


Related Questions

Multiply. Write the result in scientific notation.1.4 • 10^1)(8 • 10^4)

Answers

Answer:

1,12×10^6

Step-by-step explanation:

Which number is an irrational number?


A) √100

B) 1/8

C) - 2.2675

D) ∛16

Answers

For this case we have by definition, that an irrational number is a number that can not be expressed as a fraction \ frac {a} {b}, where a and b are integers and b is different from zero.

A) [tex]\sqrt {100} = 10[/tex], it is rational

B)[tex]\frac {1} {8}[/tex], it is rational

C) [tex]-2.2675[/tex], it is rational

D) [tex]\sqrt [3] {16},[/tex] it is not rational.

Answer:

Option D

The only option that represents an irrational number is D) ∛16.

An irrational number is a number that cannot be expressed as a fraction (ratio) of two integers and has an infinite decimal representation without any repeating pattern.

Let's analyze each option:

A) √100:

The square root of 100 is 10, which is a rational number. It can be expressed as the fraction 10/1.

Therefore, option A) is a rational number.

B) 1/8:

The fraction 1/8 can be expressed as a ratio of two integers. It is equal to 0.125 in decimal form.

Since the decimal representation terminates after a finite number of decimal places, option B) is not an irrational number.

C) - 2.2675:

The number -2.2675 is a decimal number, but it is not an irrational number.

It can be expressed as a rational number by writing it as a fraction. Hence, option C) is not an irrational number.

D) ∛16:

The symbol ∛ represents the cube root. The cube root of 16 is approximately 2.5198.

This number is an irrational number because it cannot be expressed as a fraction of two integers, and its decimal representation continues indefinitely without a repeating pattern.

In summary, the only option that represents an irrational number is D) ∛16.

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2y +6=3y+8
Verify it and explain step by step?

Answers

-6

2y = 3y + 2

-3y

-y = 2 so y = -2

A mirror selling for $98.00, marked up 30% on cost.

M=$

C=$

Answers

Answer:

M = $22.62

C = $75.38

Step-by-step explanation:

Selling Price = $98

Markup = 30%

Selling Price = 100 + 30 = 130%

130% = $98

1% = 98/130

Markup

= 98/130 x 30  

= $22.62

Cost Price

= 98/130 x 100

= $75.38

If your invest $150 at 7% interest compounded annually,in how many years will you have $400?. Give your answer of the nearest tenth of a year?

Answers

Answer:

14.5 years.

Step-by-step explanation:

Given that you invest $150 at 7% interest compounded annually. Now we need to find about in how many years will you have $400. Then round the  answer ot the nearest tenth of a year.

So plug the given values into compound interest formula.

[tex]A=P\left(1+r\right)^t[/tex]

[tex]400=150\left(1+0.07\right)^t[/tex]

[tex]\frac{400}{150}=\left(1+0.07\right)^t[/tex]

[tex]\ln\left(\frac{400}{150}\right)=\ln\left(1+0.07\right)^t[/tex]

[tex]\ln\left(\frac{400}{150}\right)=\ln\left(1.07\right)^t[/tex]

[tex]\ln\left(\frac{400}{150}\right)=t\cdot\ln\left(1.07\right)[/tex]

[tex]\frac{\ln\left(\frac{400}{150}\right)}{\ln\left(1.07\right)}=t[/tex]

[tex]14.4967313882=t[/tex]

Which is approx 14.5 years.

(3a) 3 3aaa 3·3·3a 3a3a3a 3·3·3a 3

Answers

Answer:

3a3a3a

3·3·3a^3

Step-by-step explanation:

(3a)^3 = (3a) (3a) (3a)

          = 3*3*3 * a *a *a

          = 3*3*3 * a^3

           

Answer:

3a3a3a

3·3·3a^3

Step-by-step explanation:

Solve the equation x/4+1=-6

Answers

the answer is x = -28

Please help, What is tan B? a. 8/17 b. 15/8 c. 15/17 d. 8/15​

Answers

tan <B is 16/30 which is 8/15

Answer:

Step-by-step explanation: It’s gotta be b or c.

HELP ME PLEASE URGENT

Answers

Hello!

The answer is:

The third option is the correct option.

[tex](y+4)^{2}=22=y^{2}+8y-6[/tex]

Why?

To find the correct answer, we need to expand the notable product of the given choices, and then, compare it to the given expression.

Also, we must remember how to expand the following notable product:

[tex](a+-b)^{2}=a^{2}+-2*ab+b^{2}[/tex]

We are looking for the following expression:

[tex]y^{2}+8y-6=0[/tex]

So, solving we have:

First option:

[tex](y+4)^{2}=10\\\\y^{2}+2*4y+4^{2} =10\\\\y^{2}+8y+16=10\\\\y^{2}+2*4y+16-10=0\\\\y^{2}+2*4y+6=0[/tex]

Hence, we know that the first option is not the correct option.

Second option:

[tex](y-4)^{2}=10\\\\y^{2}-2*4y+4^{2}=28\\\\y^{2}-8y+16=28\\\\y^{2}-8y+16-28=0\\\\y^{2}-8y-12=0[/tex]

Hence, we know that the second option is not the correct option.

Third option:

[tex](y+4)^{2}=22\\\\y^{2}+2*4y+4^{2} =22\\\\y^{2}+8y+16=22\\\\y^{2}+2*4y+16-22=0\\\\y^{2}+8y-6=0[/tex]

Hence, we know that the third  option is the correct option.

Have a nice day!

Please help ASAP!!!!!​

Answers

Answer: OPTION C

Step-by-step explanation:

Complete the square:

Having the equation in the form [tex]ax^2+bx=c[/tex], you need to add [tex](\frac{b}{2})^2[/tex] to both sides of the equation:

You can identify that "b" in the equation [tex]x^2+6x=5[/tex] is:

[tex]b=6[/tex]

Then:

[tex](\frac{6}{2})^2=3^2[/tex]

Add this to both sides:

[tex]x^2+6x+3^2=5+3^2[/tex]

Rewriting, you get:

[tex](x+3)^2=14[/tex]

Solve for "x":

 [tex]x+3=\±\sqrt{14}\\\\x+3=\±\sqrt{14}\\\\x=\±\sqrt{14}-3[/tex]

Then, the solutions are:

[tex]x=-3+\sqrt{14}\ or\ x=-3-\sqrt{14}[/tex]

45 centimeters is equal to how many inches

Answers

Answer:

Around 17.716 inches

Step-by-step explanation:

Answer:

17.7 inches to the nearest tenth

Step-by-step explanation:

Recall that

1 in=2.54 cm

This implies that;

[tex]1cm=\frac{1}{2.54} in.[/tex]

Or

[tex]1cm=\frac{50}{127} in.[/tex]

This implies that;

[tex]45 cm=45\times\frac{50}{127}in[/tex]

[tex]45 cm=45\times\frac{50}{127}in[/tex]

This simplifies to;

[tex]45 cm=17.7 in[/tex] to the nearest tenth.

Use the graph. HELP NEEDED!!! Answer choices are below.
A. [-3,4]
B. [-2,0]
C. [0,4]
D. [-3,-2]

Answers

ANSWER

A. [-3,4]

EXPLANATION

We want to determine from the graph the interval on which

[tex]f(x) \geqslant 0[/tex]

This refers to the interval on which the the graph lies on or above the x-axis.

This interval is from x=-3 to x= 4

The correct choice is A. [-3,4]

what is the solution to the equation x/2-4=6​

Answers

Answer

x = 20

Explanation

Multiply the entire equation by 2 to get rid of the fraction.

x/2 * 2 = x

-4 * 2 = -8

6 * 2 = 12

Now, we have:

x - 8 = 12

To complete, add 8 to both sides

x = 20

For this case we must find the value of "x" of the following equation:

[tex]\frac {x} {2} -4 = 6[/tex]

So:

We add 4 sides of the equation:

[tex]\frac {x} {2} = 6 + 4\\\frac {x} {2} = 10[/tex]

We multiply by 2 on both sides of the equation:

[tex]x = 20[/tex]

Thus, the value of the variable x is 20

Answer:

[tex]x = 20[/tex]

I need help with my math

Answers

Hello There!

Your answer is In Image Provided.

I have also included steps I made for a question I answered similar to this.

saveu
Quesuun - 14 pollies,
Which is true about the line whose equation is y + 3 = 0?​

Answers

Answer:

expression

A mathematical symbol, or combination of symbols, representing a value, or relation. Example:  

2

+

2

=

4

Step-by-step explanation:

hope this helps

given that (8,-4) is on the graph of f(x), find the corresponding point for the function f(x)+3

Answers

ANSWER

[tex](8, -1)[/tex]

EXPLANATION

If (8,-4) is on the graph of f(x), then

[tex]f(8) = - 4[/tex]

The corresponding point for the function

[tex]f(x) + 3[/tex]

is

[tex](8,f(8)+3)[/tex]

We substitute to obtain:

[tex](8, - 4+3)[/tex]

We now simplify to get;

[tex](8, -1)[/tex]

The corresponding point on f(x)+3 is therefore

[tex](8, -1)[/tex]

A number divisible by 10 if and only if divisible by 5

Answers

Answer:

true

Step-by-step explanation:

numbers divisble by 10 have to be divisible by 5 because the prime factors are 5 and 2

What is the length of segment AB?

A coordinate plane is shown. Point A is located at 0, 12, and point B is located at 5, 0. The two points are connected by a line segment.

Answers

Answer:

length of segment AB is 13

OR

AB = 13

Step-by-step explanation:

Use the Pythagorean Theorem with c being the length of segment AB.

a^2 + b^2 = c^2

5^2 + 12^2 = c^2

169 = c ^2 (square root both sides to get c by itself)

13 = c


At 10:05 a.m., there are 2 microscopic bacteria cells in the bottle. At 10:15 a.m., there are 8 cells in the bottle. At what time will there be 64 cells in the bottle?



Answers

at 10:30 there will be 64 bacteria

Answer:

At 10:20 a.m., there will be 16 cells in the bottle.

At 10:30 a.m. there will be 64 cells in the bottle .

Step-by-step explanation:

PLEASE HELP VERY EASY AND SIMPLE DUE TOMARROW

Answers

Answer:

0.03

Step-by-step explanation:

fraction = part/whole

= 27/900

= 3/100

=0.03

decimal value = 0.03

Which of the following values of x is in the solution set of 2|x + 4| > 14?

Answers

Answer:

-12

Step-by-step explanation:

kumar is saving to buy a bicycle that costs $375.25. so far he has saved $295.25. How much more money does he need

Answers

Answer:

80

Step-by-step explanation:

Kumar needs only $80 to buy bicycle.

What is subtraction?

Subtraction is mathematic operation. Which is used to remove terms or objects in expression.

Given, bicycle costs $375.25.

And so for he has saved $295.25

To find the rest of money, we subtract the total cost to a saved money.

required money = $375.25 - $295.25 = $80

Therefore, he needs only $80 to buy a bicycle.

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For the expression 5x?y3 + xy2 + 8 to be a trinomial with a degree of 5, the missing exponent on the x-term must be
.

Answers

Answer:

2

Step-by-step explanation:

The degree of a polynomial is determined by the largest exponent of the variable within the expression

y³ is of degree 3

xy² is of degree 1 + 2 = 3 ← sum the exponents of the 2 variables

Thus x²y³ is of degree 2 + 3 = 5

For the expression 5x?y³ + xy² + 8 to be a trinomial with a degree of 5, then the missing exponent of the x term must be 2.

Polynomial

Polynomial is an expression that involves only the operations of addition, subtraction, multiplication of variables.

Polynomials are classified based on degree as linear, quadratic, cubic and so on. A trinomial is a polynomial with three terms.

For the expression 5x?y³ + xy² + 8 to be a trinomial with a degree of 5, then the missing exponent of the x term must be 2.

Find out more on Polynomial at: https://brainly.com/question/2833285

Will give brainliest!!!

The length of a rectangle is 2 inches more than the width. If the diagonal is radical 20 inches, find the area of the rectangle.

A) 4 in^2
B) 8 in^2
C) 16 in^2
D) 32 in^2

Answers

Answer:

B.  8 in^2.

Step-by-step explanation:

Let the width be x inches, then the length = x + 2 inches.

So by The Pythagoras theorem:

(√20)^2 =  x^2 + (x + 2)^2

x^2 + x^2 + 4x + 4 = 20

2x^2 + 4x - 16 = 0

x^2 + 2x - 8 = 0

(x + 4)(x - 2) = 0

x = 2, -4    (we ignore the negative so x = 2)

So the area = 2 * (2 + 2)

= 8 in^2.

Answer:

B

Step-by-step explanation:

L = W + 2

[tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex]

(W + 2)2 + W2 = [tex]\sqrt{20} ^{2[/tex]  

2[tex]w^{2}[/tex] + 4W + 4 = 20

2[tex]w^{2}[/tex] + 4W − 16 = 0

W = 2 or W = −4

And,

L = W + 2

L = 2 + 2

L = 4

Therefore,

A = LW = (4)(2) = 8

Find the values of x in this equation: x – 15 x = 2 . A. -7, 3 B. -5, 2 C. -7, 5 D. -2, 5 E. -3, 5

Answers

Answer:

Step-by-step explanation:

The given expression is x- [tex]\frac{15}{x}[/tex] = 2

and we have to solve this for the value of x,

( x- [tex]\frac{15}{x}[/tex]) = (2)

[tex]\frac{x^{2}-15 }{x} =2[/tex]

x² - 15 = 2x

x² - 2x - 15 = 0

x² - 5x + 3x - 15 = 0

x ( x-5 ) + 3(x - 5) = 0

( x+3 )( x-5 ) = 0

( x+3) = 0

x = -3

or ( x- 5 ) = 0

x = 5

Therefore, x = -3 and 5 will be the solution.

Option E is the answer.

Help solve please !

Answers

Answer:

[tex]\log_2(\frac{\frac{x^3}{3}}{x+4})[/tex]

Step-by-step explanation:

The given logarithmic expression;

[tex]3\log_2x-(\log_23-\log_2(x+4))[/tex]

Expand the parenthesis:

[tex]3\log_2x-\log_23+\log_2(x+4)[/tex]

Use the product rule on the last two terms;

[tex]\log_aM+\log_aN=\log_aMN[/tex]

[tex]3\log_2x-\log_23(x+4)[/tex]

[tex]3\log_2x-\log_23(x+4)[/tex]

Apply the power rule:

[tex]\log_2x^3-\log_23(x+4))[/tex]

We now apply the quotient rule of logarithms:

[tex]\log_aM+\log_aN=\log_a(\frac{M}{N})[/tex]

[tex]\log_2x^3-\log_23(x+4)=\log_2(\frac{x^3}{3(x+4)})[/tex]

Or

[tex]\log_2x^3-\log_23(x+4)=\log_2(\frac{\frac{x^3}{3}}{x+4})[/tex]

For the function y=tan theta which angle measure has the same values as 2pi/3

Answers

tan(theta)=tan(pi+theta)

So your answer would be 5pi/3

Answer:

The angle measure [tex]\frac{5\pi}{3}[/tex] has the same value as [tex]\frac{2\pi}{3}[/tex]

Step-by-step explanation:

[tex]tan(\theta)=tan(\pi+\theta)[/tex]

[tex]tan(\theta)=tan(\pi+\theta)[/tex]

so, here [tex]\theta=\frac{2\pi}{3}[/tex]

[tex]tan(\frac{2\pi}{3})=tan(\pi+\frac{2\pi}{3})[/tex]

[tex]tan(\frac{2\pi}{3})=tan(\frac{5\pi}{3})[/tex]

Hence, The angle measure [tex]\frac{5\pi}{3}[/tex] has the same value as [tex]\frac{2\pi}{3}[/tex]

Jarred sells dvds. His inventory shows that he has a total of 3500 dvds. He has 2342 more contemporary titles than classic titles. Let x represent the number of contemporary titles and y represent the number of classic titles. The system of equations models the given information for both types of dvds.

Answers

Answer:

x = classic

x + 2342 = contemporary

3500 = x + (x +2342)

3500= 2x + 2342

and then you would just solve the equation, but it does not ask for a solution

Step-by-step explanation:

x = classic

x + 2342 = contemporary

3500 = x + (x +2342)

3500= 2x + 2342

Answer: Jared has a total of 3500 dvds of two types, contemporarys and classics.

we also know that Jared has 2342 more contemporary dvds than classics.

Now, how we write this as system of equations?

if x is the number of classics, and y the number of contemporarys, then:

1) x + y = 3500

and

2) y - x = 2342

this is the system of equations, but just for fun we can solve it!

in the second equation we can leave y alone in the right side ande get: y = 2342 + x, and then replace it in the first equation.

x + y = 3500

x + (2342 + x) = 3500

2*x = 3500 - 2342 =1158

x = 1158/2 = 579

So Jared has 579 classic titles.

then:

y + x =3500

y + 579 = 3500

y = 3500 - 579 = 2921

And Jared has 2921 contemporary titles.

Rectangle ABCD is graphed on the coordinate plane. The following are the vertices of the rectangle:A(2,0),B(6,0),C(6,7),D(2,7). What is the area of Rectangle ABCD

Answers

28 (unit)^2

find the differences in the x (4) and y (7) coordinates

times them together as you normally find the area of rectangle (L×W)

HELP!! With the question

Answers

Answer:

-x^2+21x+18/ x^3-x^3-16x-20

Step-by-step explanation:

-x^2+21x+18/ (x-5)(x^2+4x+4)

= -x^2+21x+18/ x^3+4x^2+4x-5x^2-20x-20

= -x^2+21x+18/ x^3-x^2-16x-20

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