A box has a base of 12 inches by 12 inches and a height of 30 inches. What is the length of the interior diagonal of the box? Round to the nearest hundredth.

Answer:

[tex] IJ = 2(KL) [/tex]

Step-by-step explanation:

From the information given, the smaller figure was dilated on a scale factor of 2, to produce the bigger figure. In essence, the bigger figure is times 2 of the smaller figure.

Therefore, line IJ would be twice the length of KL.

The relationship that both lines have can be represented as: [tex] IJ = 2(KL) [/tex]

Answer:

5 times

Step-by-step explanation:

Jenna wil most likely pull a yellow marble 1/3 of the time, because the total number of marbles is 6, and there are 2 yellow marbles, 2/6 which is 1/3. 1/3 times 15 is 5. So Jenna will most likely pull a yellow marble 5 times.

Answer:

elimination method

x+2y=4     1

5x-2y=8     2

1+2

6x=12

x=2

plug into x+2y=4

2+2y=4

2y=4-2

2y=2

y=1

(2,1)

so graph 1

Answer:

156.6 square yards

Step-by-step explanation:

To find the surface area of the pyramid, find the area of each surface and add them together.

formula for area of a triangle = 1/2(b·h)

1. There are three triangles with a base of 9 and a height of 9

1/2(9·9) = 40.5

Multiply by the three triangles

40.5 · 3 = 121.5

2. There is one triangle with a base of 9 and a height of 7.8

1/2(9·7.8) = 35.1

3. Add the areas of all surfaces

121.5 + 35.1 = 156.6

Answer:

Step-by-step explanation:

3) G

Step-by-step explanation:

Q(-1,-1) R(3,1) S(2,-4)

x+2 y+3 translation then rotation 180 (x,y) be (-x,-y)

Q -1+2 -1+3 (1,2) (-1,-2)

R 3+2 1+3 (5,4) (-5,-4)

S 2+2 -4+3 (4,-1)

Answer:

See below.

Step-by-step explanation:

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

Cross multiply and distribute.

[tex]u(v-x)=v^2(u-x)\\uv-ux=uv^2-xv^2[/tex]

Move all the u to the left side:

[tex]uv-ux-uv^2=-xv^2[/tex]

Factor out a u:

[tex]u(v-x-v^2)=-xv^2[/tex]

Divide:

[tex]u=\frac{-xv^2}{v-x-v^2}=\frac{xv^2}{x+v^2-v}[/tex]

(I factored out a negative in the second term.)

Answer:

Step-by-step explanation:

The diagonals of the rhombus divide it into 4 congruent right triangles.

So we can use Pythagorean theorem to calculate side of a rhombus.

[tex](\frac e2)^2+(\frac f2)^2=s^2\\\\e=30\,cm\quad\implies\quad\frac e2=15\,cm\\\\f=16\,cm\quad\implies\quad\frac f2=8\,cm\\\\15^2+8^2=s^2\\\\s^2=225+64\\\\s^2=289\\\\s=17[/tex]

Perimeter:

P = 4s = 4•17 = 68 cm

Answer:

3438.

Step-by-step explanation:

6³ ÷ 4 + 2 × 9 (32 × 8 - 17 × 4)

= 6³ ÷ 4 + 2 × 9 (256 - 68)

= 6³ ÷ 4 + 2 × 9 × 188

= 216 ÷ 4 + 2 × 9 × 188

= 54 + 2 × 9 × 188

= 54 + 3384

= 3438

3438 is the answer.

Answer:

Step-by-step explanation:

This problem is on the mensuration of solids.

A sphere is a solid shape.

Given data

radius of sphere = 17 units

The volume of a sphere can be expressed as below

[tex]volume = \frac{4}{3}\pi r^3[/tex]

Substituting our data into the expression we have

[tex]volume = \frac{4}{3}*3.142*17^3[/tex]

[tex]volume = \frac{4}{3}*3.142*4913\\\\volume = \frac{61746.584}{3}= 20582.195[/tex]

The volume of the sphere is given as

20582.195 units

Answer:

(-9,2)

Step-by-step explanation:

The rule for reflecting over the x axis is

(x,y)→(x,−y)

(-9, -2) becomes ( -9, - -2) = (-9,2)

Answer:

(-9,2)

Step-by-step explanation:

It will be -9,2 because when you reflect across x axis you change the y axis not the x axis because if you imagine it it works like that

Answer:

Step-by-step explanation:

Volume = 1/3πr²h

Surface Area = πr(r+√(h²+r²))

V = 1/3π(10)²(34) = 3560 .5 cm³

SA = π(10)(10 + √(34²+10²)) = 1427.5 cm²

Answer:

21

Step-by-step explanation:

4[tex]\frac{1}{5}[/tex] = [tex]\frac{21}{5}[/tex]

5 × [tex]\frac{21}{5}[/tex] = (5×21)/5

[tex]\frac{105}{5}[/tex] = 21

Answer:

x=-1

Step-by-step explanation:

0.5 ( 5 - 7x ) = 8 - ( 4x + 6 )

- Distribute 0.5 by 5 and -7x

2.5 - 3.5x = 8 - ( 4x + 6 )

Second- Distribute the invisible one into 4x and 6

2.5 - 3.5x = 8 - 4x - 6

- Combine like terms: Subtract 6 from 8

2.5-3.5x= - 4x + 2

-Add 4x from both sides of the equation

2.5 + 0.5x = 2

-Subtract 2.5 from both sides of the equation

0.5x = 2- 2.5

0.5x = -0.5

-Then divide each side by 0.5x

0.5x  = -0.5

0.5      0.5

-Cancel the common factor of 0.5

x = - 0.5

      0.5

-Divide -0.5 by 0.5

X = -1

Estimate:

2.3 rounds down to 2

So after multiplying by 2, the area is estimated to be 4 cm squared.

Actual Area:

2.3 x 2 = 4.6

The actual area of the shape is 4.6 cm squared.

Hope this helped!

Answer:

4.6

Step-by-step explanation:

Answer: [tex]y-1=\dfrac32(x+3)[/tex]

Step-by-step explanation:

Slope of a line passes through (a,b) and (c,d) = [tex]\dfrac{d-b}{c-a}[/tex]

In graph(below) given line is passing through (-2,-4) and (2,2) .

Slope of the given line passing through (-2,-4) and (2,2) =[tex]\dfrac{-4-2}{-2-2}=\dfrac{-6}{-4}=\dfrac{3}{2}[/tex]

Since parallel lines have equal slope . That means slope of the required line would be .

Equation of a line passing through (a,b) and has slope m is given by :_

(y-b)=m(x-a)

Then, Equation of a line passing through(-3, 1) and has slope =  is given by

[tex](y-1)=\dfrac32(x-(-3))\\\\\Rightarrow\ y-1=\dfrac32(x+3)[/tex]

Required equation: [tex]y-1=\dfrac32(x+3)[/tex]

Answer:

x = -0.4

x = -(2/5)

Answer:

x = ± √5

Step-by-step explanation:

Please indicate exponentiation by using the symbol " ^ ":

5x^2 + 25x = 0

Divide all three terms by 5.  We get:

x^2 + 5 = 0, or x^2 = -5

Then x = ± √5

Answer:

Amplitude = 2

Step-by-step explanation:

The amplitude of this sine wave is 2 denoted by the coefficient -2 in front of the sin(x).  The negative of the coefficient denotes that the sine wave is the opposite of the standard sine wave.

Cheers.

Answer:

D. zero

Step-by-step explanation:

Since the graphs do not intersect, there are zero solutions.

The number of solutions on the graph is zero

The graph shows a linear equation (the straight line) and a non linear equation (the curve)

From the graph, we can see that the straight line and the curve do not intersect

This means that the graph do not have any solution

Hence, the number of solutions on the graph is zero

Read more about non-linear graphs at:

https://brainly.com/question/16274644

#SPJ5

Answer:

  2n+2 ways to win

Step-by-step explanation:

You generalize by observing patterns in the way you solve the smaller problems.

The number of winning moves is 2n+2: the total of the number of diagonals, columns, and rows.

For an n×n board, there are 2 full-length diagonals, n columns, and n rows, hence 2+n+n = 2n+2 ways to win.

Answer:

25[tex]\sqrt{3}[/tex] +60

Step-by-step explanation: The first thing you need to do is realize that, this figure is a isosceles trapezoid due to the markings on each side.

So now we know both sides are 10.

We also know the the top two angles are congruent to each other and so are the bottom two angles due to the trapezoid being isosceles.

So the top two angles are 120 degrees and bottom two angles are 60 degrees.

It seems like we can't find the sides, let's try drawing two lines from each top angle all the way down to form two right triangles.

Wow, these two triangles are special right triangles in the form of

30 - 60 - 90 degrees.

shorter side = n

longer side = n[tex]\sqrt{3}[/tex]

hypotenuse = 2n

So, 2n = 10

n = 5 for the short side

The bottom base is 4[tex]\sqrt{3}[/tex] + 5 + 5 = 10 + 4[tex]\sqrt{3}[/tex]

The longer side is  5[tex]\sqrt{3}[/tex].

The area of trapezoid = (base1 + base2)/2 * height

= (4[tex]\sqrt{3}[/tex] + 10 + 4[tex]\sqrt{3}[/tex])/2 * 5[tex]\sqrt{3}[/tex] = (10 + 8[tex]\sqrt{3}[/tex])/2 * 5[tex]\sqrt{3}[/tex] = (5+4[tex]\sqrt{3}[/tex])*5[tex]\sqrt{3}[/tex] = 25[tex]\sqrt{3}[/tex] +60

So, 25[tex]\sqrt{3}[/tex] + 60 is our answer.

Answer:

  60 +25√3

Step-by-step explanation:

In the figure of the isosceles trapezoid below, the angles at C and D are supplementary to the given angle, so are 60°. That makes triangle BDE a 30°-60°-90° right triangle, which has side length ratios ...

  DE : BE : BD = 1 : √3 : 2 = 5 : 5√3 : 10

Triangle BDE can be relocated to the other end of the figure to become triangle CAD'. Then the area of concern is that of the rectangle with height 5√3 and length 5+4√3. The area is then ...

  Area = lh = (5√3)(5 +4√3) = 5·5√3 +5·4·3

  Area = 60 +25√3 . . . square units

_____

In the figure, 6.93 = 4√3, and 8.66 = 5√3, 16.93 = 10+4√3.

Answer:

1522km^2

Step-by-step explanation:

To solve this, first convert the percentage to a decimal. That would be .0475.

Now subtract that from 1.0 to get the factor it decreases by. This would be 1-.0475 = .9525

Multiply 2600 x (.9525)^11 = 1522.258 which rounds to 1522 km^2

Answer:

The area will be 1292.98 km² after 11 years.

Step-by-step explanation:

To find what decreases by 4.57% each year in kilometers:

2600 × 4.57/100 = 26 × 4.57

= 118.82 km²

To find the area after 11 years:

118.82 × 11 = 1307.02

2600 - 1307.02 = 1292.98 km²

1292.98 km² is the answer.

Answer:

5 cm

Step-by-step explanation:

The volume (V) of milk in the container is calculated as

V = 8 × 15 × 12 = 480 cm³

After change of position with depth d then

8 × 15 × d = 480

120d = 480 ( divide both sides by 120 )

d = 4 cm

Greetings from Brasil...

a - whole number

FALSE

3/5, for example isnt a whole number

b. natural number

FALSE

0,457888..., for example isnt a natural number

c. integer

FALSE - like a

d. real number

TRUE

The set of real numbers contains the set of rational numbers

ℝ ⊃ ℚ

Answer:

10800

Step-by-step explanation:

1 trimesters cost = 1450 + 350  $

2 year -> 6 trimester

1800$ x 6 = 10800 $

Answer:

reflection across y = x

Step-by-step explanation:

Transformation is the movement of a point from its initial position to a new position. If a shape is transformed, all its point are also transformed. Types of transformation is reflection, rotation, transformation and dilation.

If a point is reflected across the x axis, the x coordinate is the same but the y coordinates is negated. If X(x, y) is reflected across the x axis the new point is X'(x, -y)

If a point is reflected across the y axis, the y coordinate is the same but the x coordinates is negated. If X(x, y) is reflected across the y axis the new point is X'(-x, y)

If a point is reflected across y = x, the x coordinate and y coordinates are interchanged. If X(x, y) is reflected across the y=x axis the new point is X'(y, x)

If a point is reflected across y = -x, the x coordinate and y coordinates are interchanged and both negated. If X(x, y) is reflected across the y=ix axis the new point is X'(-y, -x)

The vertices of △ABC are A(-1, 3), B(2, 4), and C(-5, 6). The vertices of △A′B′C′ are A′(3, −1), B′(4, 2), and C′(6, −5). The reflection of △ABC to form​​ ​△A′B′C′ shows a reflection across x axis since the x and y coordinates are interchanged

Answer:

reflection across y = x

Step-by-step explanation:

Let x = weight and y = height. It is possible to have a certain weight correspond to multiple heights. This means the input x has multiple output y values. Therefore, we cannot have a function here. A function is only possible if for any x input, there is exactly one y output. The x value must be in the domain.

Answer:

18 inches by 36 inches.

Step-by-step explanation:

Since we have given that

The generic version was basedOn the brand name and was 2/3

And given Dimensions of generic version is given by 12inches ×24inches

If we use the first dimensions of 12inches we have

12=2/3 × brand

12×3/2 = brand

=18inches= brand

we use the first dimensions of 24 inches we have

24=2/3 × brand

24×3/2 = brand

=36 inches= brand

brand= 36 inches

Therefore,the dimensions of brand name will be 18 inches by 36 inches.

Answer:

Step-by-step explanation:

Answer:

Hey there!

The answer would be C. 4/15.

4/5(1/3)=4/15

Let me know if this helps :)

Answer:

p= 25/100 = 180/x

Step-by-step explanation:

In order to find the computer's original price, you must use the equation p= 25/100 = 180/x and solve for x.

Answer:

0.75p=p-180

Step-by-step explanation:

0.75p=p-180 is your answer

Answer:

9:45 A.M.

Step-by-step explanation:

First, add the time that took him to hike:

6:30 + 2 hours and 15 minutes = 8:45 A.M.

Next, add the 1 hour that he played volleyball for:

8:45 + 1 hour = 9:45 A.M.

So, he finished playing volleyball at 9:45 A.M.

Answer:

9:45 am

Step-by-step explanation:

He went at 6:30 am to a hike.

It took him 2 hours 15 minutes

=> 6 : 30

+  2    15

=> 8 : 45

He came back from the Hike at 8:45 am

He played volleyball for 1 hour.

=> 8 : 45

+  1

=> 9 : 45

He finished playing volleyball at 9:45 am