A gold bar is in shape of a triangular prism,the height is 4,the volume is 216cm³, the lateral area is 288cm and the surface area is 312cm but if the bar is melted and all the molten gold is used to form a solid cube,what is the length of the side of the cube​

Refer to the attachment...

Since the line is parallel to the given equation , slope of required line = slope of the given equation of line

slope = -1/2

Answer:

all real values

Step-by-step explanation:

there is no value for x, where the operations in f(x) would run into an undefined or outright invalid situation. whatever x we can think of, f(x) will calculate a valid y.

Answer:

2*(5x+4) + 2*(3x+2)

= 10x + 8 + 6x + 2

= 16x + 10

The perimeter of the rectangle, in feet, is represented by (16x + 10)

Answer:

(16x + 12) ft

Step-by-step explanation:

Perimeter of the rectangle = 5x + 4 + 3x + 2 + 5x + 4 + 3x + 2

Perimeter of the rectangle = (16x + 12) ft

Answer:

y = 38

Step-by-step explanation:

The sum of the 3 angles in a triangle = 180°

Consider the angles in the large outer triangle, then

x + 46 + 78 = 180

x + 124 = 180 ( subtract 124 from both sides )

x = 56

Consider the 3 angles in the smaller inner triangle, then

y + x + 86 = 180 , that is

y + 56 + 86 = 180

y + 142 = 180 ( subtract 142 from both sides )

y = 38

Answer:

25 feet per second.

Step-by-step explanation:

Let s represent the speed of the water and r represent the radius of the whirlpool.

The speed in a whirlpool varies inversely with the radius. Therefore, we can write that:

[tex]\displaystyle s=\frac{k}{r}[/tex]

Where k is the constant of variation.

We know that the speed is 2.5 feet per second when the radius is 30 feet.

So, s = 2.5 when r = 30. Substitute:

[tex]\displaystyle 2.5=\frac{k}{30}[/tex]

Solve for k:

[tex]k=30(2.5)=75[/tex]

So, our equation is:

[tex]\displaystyle s=\frac{75}{r}[/tex]

Then when the radius is three feet, r = 3. Evaluate for s:

[tex]\displaystyle s=\frac{75}{(3)}=25\text{ feet per second}[/tex]

So, the speed of the water in a whirlpool with a radius of three feet is 25 feet per second.

Answer:

2

Step-by-step explanation:

2(z)+2 = 4

2z = 2 x 2 = 4

To determine which relation is a function, we need to check if each input value (x) corresponds to a unique output value (y). If there is any repetition in the x-values, then it is not a function. in option (0, 0), (1, 1), (2, 2), (3, 3), (4,7) no repetition x-values so c is correct.

Let's analyze each option:

A. (8,-4), (8,4), (6,-3), (6,3), (0, 0)

In this relation, we can see that both 8 and 6 have repeated as x-values. Therefore, option A is not a function.

B. (4, 7), (8,5), (6,4), (5, 3), (4, 2)

Again, we notice that 4 appears twice as an x-value. Hence, option B is not a function.

C. (0, 0), (1, 1), (2, 2), (3, 3), (4,7)

Here, each x-value is unique. No repetition is observed. Therefore, option C represents a function.

D. (0, 0). (1, 0), (1, 1), (2, 1), (1, 2)

In this relation, the x-value of 1 appears three times. Consequently, option D is not a function.

To summarize, option C is the only relation that represents a function since it has distinct x-values corresponding to unique y-values.

Option C is correct answer

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Answer:

1.18 kilometers

Step-by-step explanation:

The middle school is 2.72 kilometers from Marshal house

The school is also 1.54 kilometers away from Ryan house

Therefore the distance of Marshal house from the school can be calculated as follows

= 2.72-1.54

= 1.18 kilometers

Answer:

no

Step-by-step explanation:

A circle will fail the vertical line test, which means a vertical lines intersects two or more points.  If it fails the vertical line test, it is not a function  

Answer:

sf and st

Step-by-step explanation:

Answer:

y=9.25

Step-by-step explanation:

5x+2y=20

5(.3)+2y=20

1.5+2y=20

2y=20-1.5

2y=18.5

y=18.5/2

y=9.25

Answer:

2/18 = 1/9

Step-by-step explanation:

She has a total of 18 menus, so that is our denominator. 2 are for Thai food, so that is our numerator.

2/18 = 1/9

Answer:

Step-by-step explanation:

Number less than 2 is 1.

Probability of 1 out of 6 is:

Probability of heads is:

The probability of both is:

Answer:

m+5=7

Step-by-step explanation:

Answer:

yes

Step-by-step explanation:

To determine if the triangle is right

If the square of the longest side is equal to the sum of the squares on the other 2 sides then it is right.

longest side = 20 and 20² = 400

12² + 16² = 144 + 256 = 400

Thus the triangle is right

We know that,

Volume of sphere = 4/3πr³

41572 = 4/3 × 22/7 × r³

41573 × 21/88 = r³

³√9,920.82 = r

21.48 cm = r

:)

The radius of a sphere with a volume of 41572 cm³ is,

⇒ 21.4 cm

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Now, To find the radius of a sphere with a volume of 41572 cm³, we can use the formula for the volume of a sphere as;

⇒ V = (4/3)πr³

where V is the volume and r is the radius.

Hence, We can rearrange this formula to solve for r:

⇒ r = ∛ (3V/4π)

Substituting the given volume, we have:

r = ∛ (3(41572)/4π)

r ≈ 21.4 cm

Therefore, the radius of the sphere to the nearest tenth of a centimeter is 21.4 cm.

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Answer:

(5,-3)

hope this helps

have a good day :)

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

As you can see, the dot on the line is the starting point and it is open.

An open dot means less than or more than. An closed dot means less than or equal to / more than or equal to.

The line is going right starting from -5, so it is more than 5.

Answer:

n = (1/2)(-1 ± i√2)

Step-by-step explanation:

Among the several ways in which quadratic equations can be solved is the quadratic formula.  Putting to use the coefficients {12, 12, 9}, we obtain the discriminant, b^2 - 4ac:  12^2 - 4(12)(9) = 144 - 432 = -288.  The negative sign of this discriminant tells us that the quadratic has two unequal, complex roots.  These roots are:

      -b ± √(discriminant)

n = ---------------------------------

                 2a

Here we have:

      -12 ± √(-288)           -12 ± i√2√144          -12 ± i12√2

n = ----------------------  =  ------------------------ =  --------------------

            2(12)                             24                           24

or:

n = (1/2)(-1 ± i√2)

Answer:

 [tex]option \ C[/tex]  [tex]3\frac{1}{3}[/tex]

Step-by-step explanation:

[tex]\frac{|2a| - b}{3} \ , \ given \ a = \ 7 \ , \ b \ =\ 4\\\\\frac{|2 \times 7| - 4}{3} = \frac{14 - 4}{3} = \frac{10}{3} = 3\frac{1}{3}[/tex]

Answer:

-11 is the answer

Answer:

f(x) and g(x) are closed under multiplication because when multiplied, the result remains a polynomial.

Step-by-step explanation:

First, to be closed means that once an operation has commenced, the result is a polynomial, just like the two original ones.

When polynomials are multiplied, exponents simply add together, and constants are multiplied. A polynomial is a finite sum of terms in which all variables have whole numbered exponents.

In this scenario, when we multiply polynomials, exponents are solely added together, and one whole number plus another is still a whole number. Similarly, constants multiplied by constants stay as constants, and constants multiplied by variables keeps it in polynomial form. (e.g. 3 * x² makes it 3x², and 3x² is fine in a polynomial).

Therefore, given these facts, f(x) and g(x) are closed under multiplication because when multiplied, the result remains a polynomial.