The tip of a solid metal cone was placed into a cube that has 10 inch edges, as shown.
If the water in the cube rose from 6 inches to 8 inches when the cone was placed in the cube, what is the
radius of the base of the submerged portion of the cone?

Luke's square mosaic increased in area by 3.25 square meters after he added a border, turning the side length from 3 meters to 3.5 meters.

Luke originally made a square mosaic with side lengths of three meters. The area of this original square is calculated by squaring the side length: 3 meters × 3 meters = 9 square meters. When Luke added a border to his mosaic, the side length became 3.5 meters. Calculating the new area, we square the new side length: 3.5 meters × 3.5 meters = 12.25 square meters.

The increase in the area of the mosaic is the difference between the new area and the original area, which is 12.25 square meters - 9 square meters = 3.25 square meters. Therefore, the area of Luke's mosaic has increased by 3.25 square meters after adding the border.

Answer:

A. π

Step-by-step explanation:

this is a graph of  a cosine function and and the interval during which it completes one cycle starting from the origin, according to the graph is  π

Answer:

Step-by-step explanation:

We know: If a quadrilateral is inscribed in a circle, then the sum of measures of opposite angles is equal to 180°.

Therefore we have the equations:

[tex](1)\qquad2x+(2x+4)=180\\\\(2)\qquad y+(3y+8)=180[/tex]

Solve:

[tex](1)\\2x+2x+4=180\qquad\text{subtract 4 from both sides}\\\\4x=176\qquad\text{divide both sides by 4}\\\\x=44\\\\(2)\\y+3y+8=180\qquad\text{subtract 8 from both sides}\\\\4y=172\qquad\text{divide both sides by 4}\\\\y=43[/tex]

Answer:

A. x=44 y=43

Step-by-step explanation:

i just did the test yrdlf

Answer:

Step-by-step explanation:

Whether you use b or x for the variable does not matter.

5 - 7 is a money problem

If you have 5 dollars and spend 7 where are you? You should think you have a debt of 2. So the answer from your point is - 2

5b - 7b = - 2b

5x - 7x = - 2x

Answer:

-1/3

Step-by-step explanation:

To find the slope you have to find the rise over run. Start at the first point then  go down 3 and over to the right 1. Your slope is -1/3.

Answer:

A

Step-by-step explanation:

Calculate the slope m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (1, 4) and (x₂, y₂ ) = (2, 1) ← 2 points on the line

m = [tex]\frac{1-4}{2-1}[/tex] = [tex]\frac{-3}{1}[/tex] = - 3 → A

Answer:

A

Step-by-step explanation:

A cube has 6 sides

Only one side of the cube has 2 on it

The probability of getting 2 would be 1/6

Only one side of the cube has 6 on it

The probability of getting 6 would be 1/6

For both events to happen together

1/6 x 1/6 = 1/36

To find the probability of rolling a 2 on the first die and a 6 on the second, multiply the independent probabilities of each event (1/6 for each die) to get 1/36, making the correct answer A) 1/36.

The question asks for the probability of rolling two number cubes and getting a 2 on the first number cube and a 6 on the second number cube. When rolling two dice, the outcome of one die does not affect the other, so the probabilities of each outcome are independent. Since a die has six faces, the probability of rolling any specific number on a single die is 1/6.

Therefore, the probability of rolling a 2 on the first die is 1/6 and the probability of rolling a 6 on the second die is also 1/6. To find the combined probability of both events happening together, you multiply the probabilities of each event by each other, which is (1/6) × (1/6) = 1/36. So, the correct answer is A) 1/36.

Answer:

2/6

Step-by-step explanation:

There are 6 sides, and two are green. That makes it 2/6

Answer:

2/6

Step-by-step explanation:

Answer:

AC = 5

Step-by-step explanation:

AC is the diagonal of the rectangle ABCD and splits the rectangle into 2 right triangles.

Using right triangle ABC with hypotenuse AC

Applying Pythagoras' theorem gives

AC² = AB² + BC² ← substitute given values

AC² = 4² + 3² = 16 + 9 = 25

Take the square root of both sides

AC = [tex]\sqrt{25}[/tex] = 5

Well that’s it for today I just wanna was a really good day I wanna

To find the actual speed and direction of the canoe, we can add the velocity of the canoe relative to the water to the velocity of the current. Using vector addition, the approximate resultant velocity of the canoe is 2.19 miles per hour at an angle of 51.3° relative to the shore.

To find the approximate actual speed and direction of the canoe, we can use vector addition. The canoe's velocity relative to the water is 2 miles per hour in the direction of 55°. The velocity of the current is 1 mile per hour due east. We can add these two vectors to find the resultant vector, which represents the total velocity of the canoe relative to the shore.

Using the formula for vector addition, we can find the magnitude and direction of the resultant velocity. The magnitude can be found using the Pythagorean theorem: Vtotal = √(Vcanoe)2 + (Vcurrent)2. The direction can be found using the tangent function: θ = tan-1(y/x), where y is the vertical component of the resultant vector and x is the horizontal component.

In this case, the resultant velocity of the canoe will be approximately 2.19 miles per hour (rounded to two decimal places) and the canoe will move in a direction of 51.3° (rounded to one decimal place) relative to the shore.

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ANSWER

[tex]a_{14} = 5[/tex]

EXPLANATION

The given matrix is a 4 by 4 matrix.

We want to find

[tex]a_{14}[/tex]

This is the entry in Row 1 Column 4.

We trace row 1 Column 4 and identify the entry in their intersection.

This entry is 5

[tex]a_{14} = 5[/tex]

Answer:

450pi

Step-by-step explanation:

The volume of this figure is just the sum of the volumes of two cones. They both have radius of 5 and one has a height of 7 and the other has a height of 11.

The easiest way (for me) to calculate the volume is to find the average of the heights (9) and multiply the volume of a cone with the same radius as the other two and the other height by two.

The volume for a cone is just (pi*r^2*h)/3, so the 'average' cone's volume is 25pi * 9/3 or 75pi.

Double this to get 150pi.

Alternatively, you could calculate the volumes of the two cones using separate heights, but here you will end up with non-whole numbers (times pi) for both cones if you use that method.

Answer:

471.24 in³

Step-by-step explanation:

Volume of the left cone

= 1/3 π (5)²(7)

= 175π/3 in³

Volume of the right cone

= 1/3 π(5)²(11)

= 275π/3 in³

Total volume

= 175π/3 + 275π/3  

= 150π

= 471.24 in³

Answer:

1.

Step-by-step explanation:

( 1 - sin^2 O ) / cos^2 O

Now 1 - sin^2 O = cos^2 O

So the function becomes cos^2 O / cos^2 O

= 1.

Answer:

the costs of the career is low

Step-by-step explanation:

Answer:

120°

Step-by-step explanation:

Answer:

He drove 244 miles

Step-by-step explanation:

First multiply 4/7*427/1 and you get 1,708/7

Then convert 1,708/7 to 244/1

And so your answer is 244

Ben drove 244 miles before he stopped for lunch.

In mathematics, a fraction is used to denote a portion or component of the whole. It stands for the proportionate pieces of the whole.

As per the given data:

Ben has already driven 4/7 of the way to his friend's house before he stopped to eat lunch.

The total distance from Ben's house to his friend's house is 427 miles.

We have to find the Ben has already driven before he stopped to eat lunch.

Distance Ben's driven = 4/7 of the total distance

Distance Ben's driven = 4/7 × 427

Distance Ben's driven = 4 × 61 = 244 miles

Ben's already drove 244 miles before he stopped for lunch.

Hence, Ben drove 244 miles before he stopped for lunch.

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Here is the process I did:

2(6x+4)-6+2x=3(4x+3)+1

Step 1: Distribute the 2 to the numbers in the parentheses (6x +4) on the left side of the equation

6x(2)+4(2)-6+2x=3(4x+3)+1

12x+8-6+2x=3(4x+3)+1

Step 2: On the left side of the equation combine like terms

x's go with x's (12x and 2x):

(12x + 2x)+8-6=3(4x+3)+1

14x+8-6=3(4x+3)+1

normal numbers go with normal numbers ( 8 and -6):

14x+(8+(-6))=3(4x+3)+1

14x+2=3(4x+3)+1

Step 3: Distribute the 3 to the numbers in the parentheses (4x+3) on the right side of the equation

14x+2=4x(3) +3(3) + 1

14x+2=12x + 9 + 1

Step 4: On the right side of the equation combine like terms

normal numbers go with normal numbers ( 9 and 1):

14x+2=12x + (9 + 1)

14x+2=12x + 10

Step 5: Bring 2 from the left side to the right by subtracting it to both sides

14x+(2-2)=12x + (10-2)

14x = 12x + 8

Step 6: Bring 12x from the right side to the left by subtracting it to both sides

(14x - 12x) = (12x - 12x) + 8

2x = 8

Step 7: Isolate x by dividing 2 to both sides

[tex]\frac{2x}{2}  =\frac{8}{2}[/tex]

x = 4

Hope this helped!

Given equation is  one degree equation in x

Also it has only one variable 'x' hence it requires only one equation to solve for x  and the equation is given.

hence solution for x can be given as

2(6x+4)-6+2x =3(4x+3)+1

12x + 8 - 6 +2x = 12x + 9 + 1

12x +2 +2x =12x + 10

14x +2 = 12x +10

14x-12x = 10-2

2x = 8

x = 8/2= 4

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The answer is 67.6

You have to find the angle that has cos=8/21=0.381.

Answer:

67.6 degrees

Step-by-step explanation:

You need to use cosine to solve this.

so, cosine is adjacent leg over hypotenuse. which is 8/21. and it is 0.381.

and when you do cos^-1 (0.381), then it is 67.6.

Answer:

a general proposition not self-evident but proved by a chain of reasoning; a truth established by means of accepted truths.

Step-by-step explanation:

Answer:a general proposition not self-evident but proved by a chain of reasoning; a truth established by means of accepted truth

Step-by-step explanation:

the distance is 13 length units

Final answer:

Using the Pythagorean Theorem, we calculate the distance between the points (5, -2) and (-7, 3) to be 13 units.

Explanation:

To find the distance between two points on a coordinate plane, we use the Pythagorean Theorem. Given points (5, -2) and (-7, 3), we calculate the difference in the x-coordinates and y-coordinates separately and then square each result.

d² = (5 - (-7))² + (-2 - 3)²

= (5 + 7)² + (-5)²

= 12² + (-5)²

= 144 + 25

= 169

Now, taking the square root of both sides to calculate the distance:

d = √(169)

= 13

Therefore, the linear distance between the two points, often denoted as 'PQ', is 13 units.

Answer:

x= 3/4

Step-by-step explanation:

x^3 = 27/64

x= (3 is the exponent of the squared root √ (27/64)

x=3/4

The measure of the major arc is found by calculating the circumference of the entire circle 2πr and then using the proportion that the angle of the major arc represents out of 360 degrees.

The measure of the major arc in a circle depends on the angle subtended by the arc at the center of the circle. If we define the angle Θ (theta) in degrees, that subtend the arc, the length of the major arc can be found by using the circumference of the entire circle, which is 2πr (where r is the radius), and the proportion of the circle that the major arc represents. Since the entire circle is 360 degrees, if the major arc corresponds to an angle Α, which is the complement of Θ (since Α + Θ = 360 degrees for the minor and major arcs together), the major arc length will be 2πr (Α/360). To summarize, if you're given the central angle of the minor arc or can otherwise determine the central angle for the major arc, you can use this proportion to calculate the arc length.

Answer:

72 mm^3

Step-by-step explanation:

To find the volume of the combined object, we can find the volume of each cube and add it together

Volume of the 4 mm cube

V = s^3

V = 4^3 = 64 mm^3

Volume of the 2 mm cube

V = s^3

V = 2^3 = 8 mm^3

Add the volumes together

64+8 = 72 mm^3

Answer:

72 mm^3

Step-by-step explanation:

To find the volume of this irregular figure, first find each of the cubes.

Part I. Finding the bottom cube

Since the volume of a cube is s^3 where s is the side, we can plug 4 in and we get 64 mm^3.

Part II. Finding the top cube

Using the formula for volume of a cube, we get the volume of the upper cube to be 8 mm^3.

Part II. The total volume of the irregular figure

To find the total volume we simply add the two volumes together. In doing so, we get 64+8 = 72 mm^3 as our volume.

Answer:

30

Step-by-step explanation:

If P is the number of peach trees and T is the total number of trees, then:

P = 2/5 T

P + 18 = T

If we substitute the first equation into the second:

2/5 T + 18 = T

18 = 3/5 T

T = 30

The gardener has 30 trees.

Answer:

14 years old

Step-by-step explanation:

Assume Ray's sister's age is x.  

Ray's age is (x/2)+3, i.e (x+6)/2  

If Ray is 10yrs old,then  

(X+6)/2 = 10,  

x+6 = 20  

x = 14  

Therefore,Ray's siSter's /e is 14years

Answer:

It's 0.90.

Step-by-step explanation:

Answer:

the answer is B

Step-by-step explanation:

I believe the answer will be (9,9)

Vehicle A travels 750 feet and Vehicle B travels 600 feet in 15 seconds. Adding these distances together, we find they are 1350 feet apart after 15 seconds.

The subject of your question falls under the realm of Mathematics, specifically in the area of vector addition or relative velocity. Let's imagine the two vehicles are moving away from each other in a straight line at an angle. We mainly need to consider the relative velocity of vehicle B to vehicle A.

After 15 seconds, vehicle A will have traveled (50 feet/second * 15 seconds) = 750 feet. Similarly, vehicle B will have traveled (40 feet/second * 15 seconds) = 600 feet. In this situation, the total distance separating vehicle A and vehicle B is the sum of their individual distances traveled, which equals 750 feet + 600 feet = 1350 feet.

Therefore, the two vehicles are 1350 feet apart after 15 seconds.

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Answer:

a = 0

b = 2

Step-by-step explanation:

Synthetic division gives rise to two equations:

b -2a = 2

b +2a = 2

The solution to these equations is (a, b) = (0, 2).

___

The remainder from the division is the lower-right sum shown in the attached tables. For the factor x+2, the remainder from dividing your cubic by x+2 is (4b-8a-8). Setting this to zero and putting it into standard form gives the first equation shown above.

The remainder from division by (x-2) is (4b+8a-4). Setting this to 4 and putting the result into standard form gives the second equation above.

___

Pen skips and chocolate smudges make the first attachment less "professional" than it might otherwise be. Please forgive. The graph in the second attachment verifies this result.

Answer:

A

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 5x + 2 ← is in slope- intercept form

with slope m = 5

• Parallel lines have equal slopes, hence

y = 5x + c ← is the partial equation of the parallel line

To find c substitute (- 6, - 1) into the partial equation

- 1 = - 30 + c ⇒ c = - 1 + 30 = 29

y = 5x + 29 → A

y = –4x + 33

y-33 = –4x

y-33/4 = x

X=y-33/4.

Answer: The answer to your question is (8.25, 0)

Step-by-step explanation:

To simplify the expression (6.15x+0.24y)">">1.5 + 5.9x - 1.6y, divide the terms in the parenthesis by 1.5 and then combine like terms to yield the simplified expression 10.0x - 1.44y.

To simplify the expression (6.15x+0.24y)">">1.5 + 5.9x - 1.6y, first, divide the terms within the parenthesis by 1.5. This action distributes the division across each term:

This simplifies to:

Now, combine like terms with those outside the parenthesis:

Therefore, the simplified expression is:

10.0x - 1.44y