A straw is placed inside a rectangular box that is 10 inches by 8 inches by 2 inches, as

shown. If the straw fits exactly into the box diagonally from the bottom left corner to

the top right back corner, how long is the straw? Leave your answer in simplest

radical form.

Answers

Answer 1

The length of the straw placed inside a rectangular box with 10 inches by 8 inches by 2 inches is 2√42 inches.

To find the length of the straw, we can use the Pythagorean theorem. The straw acts as the hypotenuse of a right-angled triangle formed by the three dimensions of the box (10 inches, 8 inches, and 2 inches).

Let the length of the straw be represented by 'l'.

According to the Pythagorean theorem:

[tex]l^2 = 10^2 + 8^2 + 2^2[/tex]

[tex]l^2 = 100 + 64 + 4[/tex]

[tex]l^2 = 168[/tex]

Take square root on both sides:

[tex]l = \sqrt{168}[/tex]

[tex]l = \sqrt{4 \times 42}[/tex]

[tex]l = 2 \times \sqrt{42}[/tex]

So, the length of the straw is 2√42 inches in simplest radical form.

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Complete question:

A straw is placed inside a rectangular box that is 10 inches by 8 inches by 2 inches, as shown. If the straw fits exactly into the box diagonally from the bottom left corner to the top right back corner, how long is the straw? Leave your answer in simplest radical form.

Related Questions

[tex] - x - 3 + x = \sqrt{9 - 2x} + x[/tex]

Answers

This is the answer
Thank you

Answer:

x= -8

Step-by-step explanation:

pls just solve its 7th grade not hard :)

Answers

The solving is :

4x = 336
x= 84

Show mathematically why the ratio 15:10 is not equal to 10:15

Answers

Answer:

Hello here is my answer

Step-by-step explanation:

The 2 ratios are 15:10 and 10:15

multiply the numbers of the first ratio with the last number if the second ratio, which means,

15*15=225

10*15=150

we get 225:150

now we multiply the numbers of the second ratio with the last number if the first ratio.which means,

10*10=100

15*10= 150

now compare bot of them

225:150::100:150

we see that 225:150>100:150

hence proven that 15:10 is not equal to 10:15

Whoever answers gets brainliest I need 1-4 ASAP please!!! Thank you

Answers

Step-by-step explanation:

Why is California at higher risk for earthquakes than North Dakota

( Also i know this isnt math but people answer faster when its in math )

Answers

California is at higher risks for earthquakes, because it near the Pacific Ocean

Please please please answer this and show the steps. I’ll give Branliest to whoever replies first

Answers

Answer:

x = -3

y = 4

Step-by-step explanation:

distribute first

7x + 35 = 2y + 6

combine 'like terms'

7x - 2y = -29

do same steps for second equation

4x + 4y = 13 + 3x

x + 4y = 13

System of Equations:

7x - 2y = -29

x + 4y = 13

Multiply the first equation by 2 to eliminate the 'y-term'

14x - 4y = -58 (Now add this to the second equation)

+ x + 4y = 13

15x = -45

x = -3

Substitute -3 for 'x' to find 'y'

-3 + 4y = 13

4y = 16

y = 4

Amber has 36 smarties to share among herself and 3 friends. How many smarties will each of them Receive?

Answers

there are 4 people in total
(including herself)
so 36 smarties should be evenly distributed among 4 people

so answer = 36/4 = 9

Jerry has a bag of counters.
Inside his bag are

2 blue
4 green
5 red and
9 yellow counters
Jerry is going to take a counter at random from his bag.
Write the correct colours to complete these sentences.

The probability that it will be ..................... is 0.2

Answers

Blue is the answer....

The solution is 4 green

The probability of choosing a green counter from the bag is 0.2

What is Probability?

The probability that an event will occur is measured by the ratio of favorable examples to the total number of situations possible

The value of probability lies between 0 and 1

Given data ,

Let the probability of choosing a green counter be = P

Now , the value of P is

Let the total number of blue counters be G = 2

Let the total number of green counters be G = 4

Let the total number of red counters be G = 5

Let the total number of yellow counters be G = 9

So , the total number of counters = number of blue counters + number of green counters + number of red counters + number of yellow counters

Substituting the values in the equation , we get

The total number of counters = 2 + 4 + 5 + 9

The total number of counters = 20

Now , the probability of choosing the green counter P = total number of green counters / total number of counters

Substituting the values in the equation , we get

Probability of choosing the green counter P = 4/20

Probability of choosing the green counter P = 2/10

Probability of choosing the green counter P = 0.2

Therefore , the value of P is 0.2

Hence , the probability of choosing green counter is 0.2

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-7(-2w-2y+4) distributive property to remove the parentheses

Answers

Answer:

14w + 14y - 28

Step-by-step explanation:

-7(-2w - 2y + 4)

Distributive:

14w + 14y - 28

good luck, hope this helps :)

Which is the directrix of a parabola with equation x2 = 8y?
O y = 2
O X=-2
O y=-2
O X=2

Answers

Answer:

Y=-2

Step-by-step explanation:

You would use the vertex form to find the directrix

The directrix is a horizontal line that is y = -2.

Option C is the correct answer.

What is a parabola?

A parabola is an equation of a curve, such that any point on the curve is equidistant from a fixed point called the focus and a fixed line called the directrix of the parabola.

The equation of a parabola:

y = a(x-h)^2 + k

We have,

The directrix of the parabola with equation x^2 = 8y is a horizontal line, and its distance from the vertex is equal to the value of the parameter p.

To find the value of p, we need to rewrite the equation of the parabola in the standard form:

x² = 8y

Dividing both sides by 8, we get:

x²/8 = y

Comparing this equation to the standard form of a parabola with a horizontal axis of symmetry, which is given by (y-k)² = 4p (x-h), we can see that h = 0, k = 0, and p = 2.

Therefore,

The directrix is a horizontal line that is 2 units below the vertex, which is located at (0,0).

i.e

y = -2.

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Item 3
Solve for a.

a+(−4)=−13

a=−17

a=−9

a = 9

a = 17

Answers

Answer:

a = -9

Step-by-step explanation:

a+(-4)=-13

add 4 to each side

a-4+4 = -13+4

a = -9

Answer:

a = - 9

Step-by-step explanation:

a + (-4) = -13

Add 4 to both sides

a + (-4) + 4 = -13 + 4

a + 0 = -9

a = -9

When two numbers have different sign, subtract and the result will have the sign of the bigger number

Please help me please !

Answers

z = 180° - 20°

(Linear pair angles)

z = 160°

y = z

(Measure of arc is equal to the measure of its corresponding central angle)

y = 160°

20, 160, 160 hope it helps

Evaluate this expression for a = 2 and b= 3.

Answers

Answer:

Step-by-step explanation:

replace a with 2 and b with 3 in the expression and solve as follows

(2 + 5)-3 / 3-4 + 2(3+3)/ 2

7 - 3/-1 +12/2

14 + 6 +12/2

32 / 2

What is the slope of the line below? Be sure to scroll down first to see all
answer options.
(-4, 10)
(4,-2)

A)-3
B -2/3
C) 2/3
D) -3/2
E)2
F ) -2

Answers

Answer:

D) [tex]\frac{-3}{2}[/tex]

The slope of the line m = [tex]\frac{-3}{2}[/tex]

Step-by-step explanation:

Step(i):-

Given that the points are (-4,10) and (4,-2)

we have to find that the slope of the line

Step(ii):-

Solution:-

[tex]m = \frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]

[tex]m = \frac{-2-10}{4-(-4) }[/tex]

[tex]m = \frac{-12}{8} = \frac{-3}{2}[/tex]

Final answer:-

The slope of the line m = [tex]\frac{-3}{2}[/tex]

HELP PLEASE WILL GIVE BRAINLIEST IF CORRECT

if p = ( 2 , - 1 ) , find the image of p under the following rotation 270 counterclockwise about the origin

Answers

Answer:

( -1 , -2 )

Step-by-step explanation:

The perimeter of a triangle is 17 inches. One side is 5 inches, and another is 4 inches. What is the length of the third side?

Answers

Answer:

8inches

Step-by-step explanation:

Length of the third side = perimeter - ( side1 + side2 )

= 17 - (5+4)

= 17 - 9

= 8 inches

To eliminate the x terms and solve for y in the fewest steps, by which constants should the equations be multiplied by before adding the equations together? First equation: 6x -5y = 17 Second equation: 7x + 3y = 11 The first equation should be multiplied by 3 and the second equation by -5. The first equation should be multiplied by 3 and the second equation by 5. The first equation should be multiplied by 7 and the second equation by -6. The first equation should be multiplied by 7 and the second equation by 6.

Answers

Answer:

its c

Step-by-step explanation:

i did the test

The first equation should be multiplied by 7 and the second equation by -6. The correct option is C.

What is an expression?

In mathematics, an expression is a group of symbols (variables, constants, and mathematical operations) used to represent a quantity or a relationship between two numbers.

In order to eliminate the x terms and find y in the fewest steps feasible, the equations should be multiplied by constants such that the coefficient of x in one equation is equal to the negative coefficient of x in the other.

The coefficients of x in the first and second equations in this situation are 6 and 7, respectively. To make these coefficients opposite in sign, we can multiply the first equation by 7 and the second equation by -6.

The correct solution is obtained by multiplying the first equation by 7 and the second equation by -6.

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choose five ordered pairs whose first and second coordinates are equal. plot these points and connect them. what kind of figure do you get? in what quadrants does this figure lie in?

Answers

Answer:

The figure is a straight line.

The figure lies in the first and the third quadrants.

Step-by-step explanation:

Take five ordered pairs as [tex](1,1),(2,2),(-1,-1),(-2,-2),(3,3)[/tex]

Here, the first and second coordinates are equal.

Now, plot these points and connect them.

From the graph, it can be observed that the figure is a straight line.

Also, the figure lies in the first and the third quadrants.

PLEASE HELP!!!! IM SO CONFUSED
The hypotenuse of a right triangle measures √69 centimeters and its shorter leg measures 2√5 centimeters. What is the measure of the larger acute angle of the triangle? Round your answer to the nearest tenth of a degree.

Answers

Hey! I believe this is correct :) If you have any questions, feel free to ask!

6. Ashley bought 4 packages of juicek
There are 6 juice boxes in each
She gave 2 juice boxes to each of 3
How many juice boxes does Ashley
pace
have left?
Help me!

Answers

18

Explanation:
4x6=24
2x3=6
24-6=18

Hope this helps!:)

Factor this trinomial.
x2 - 9x+ 20
O A. (x – 4)(x - 5)
O B. (x-2)(x+10)
O C. (x - 2)(x - 10)
O D. (x – 4)(x + 5)

Answers

A is correct, (x-4)(x-5)

The factorization of the given trinomial [tex]x^2 - 9x+ 20[/tex] is (x – 4)(x - 5). The correct option is A.

What is trinomial?

A trinomial is a polynomial that has three terms. To factor a trinomial of the form [tex]ax^2 + bx + c[/tex], you need to find two binomials that multiply together to produce the original trinomial.

To factor the trinomial [tex]x^2 - 9x + 20[/tex], we need to find two numbers that multiply to 20 and add up to -9. These two numbers are -4 and -5. Therefore, we can write:

[tex]x^2 - 9x + 20 = (x - 4)(x - 5)[/tex]

Or, To factor [tex]x^2 - 9x + 20[/tex], you need to find two numbers that multiply to 20 and add up to -9. These numbers are -4 and -5 because -4*(-5) = 20 and -4 + (-5) = -9.

You can factor the trinomial as (x - 4)(x - 5).

Thus, the correct option is A.

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What’s this shape called?

Answers

Answer:

This shape is called triangle

The shape is a concave polygon

Is 5 a solution to the equation 3x + 9 = 18? You must explain your answer.

Answers

Answer:

Step-by-step explanation: No because 3 times 5 is 15 plus 9 will be 24 not 18.

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