Mario claims that a rhombus is sometimes a square, but a square is always a rhombus. Is he correct? Explain your answer.

Answers

Answer 1

Answer: That is correct.This is because a square has all the elements a rhombus has.A rhombus has 4 equal sides,just like a square does.And,a rhombus can't always be a square becase a square also contains 4 equal angles,while a rhombus doesn't.

Answer 2

Answer: yes he is a square and a rhombus are exactly the same shape and figure they both have 4 sides and can sometimes have all equal sides :)

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Main Street and Washington Avenue meet at a right angle. A large park begins at this corner. Joe's school lies at the opposite corner of the park. Usually Joe walks 1.2 miles along Main Street and then 0.9 miles up Washington Avenue to get to school. Today he walked a straight path across the park and returned home along the same path. What is the difference in distance between the two round trips?

Jovita bought 3 1/3 cubic yards of mulch for the garden. She will need 2.5 cubic yards for the flowerbeds. How much mulch is left for Jovita to use for he vegetable garden?(write your answer as a decimal)HURRY IM RUNNING OUT OF TIME

Answers

1/3 = 0.333... (repeating)

-- Jovita bought 3.333 cubic yards.

-- She needs 2.5 cubic yards for the flowers.

-- The rest will be left for the veggies.
If she doesn't spill any, that will be

(3.333) minus (2.5) = 0.833... (repeating) cubic yards.

If 45% of x is 200, what is x?

Answers

' 45% ' means ' 0.45 ' .
' of ' means ' times '.

0.45 times 'x' = 200

Divide each side by 0.45 : x = 200/0.45

x = 444 and 4/9 .

45% of x=200
(45/100)x=200
x=(200*100) / 45=444.4444....≈444.44

Answer: x=444.44

To check
45% of 444.44=0.45 * 444.44≈200

What is 0.08 as a fraction

Answers

Answer is provided in the image attached.

It is 8/100 because there is two numbers and when you have two numbers right of the decimal it will be that number over 100

Write the linear equation 2x + 3y = 12 in slope intercept form .

Answers

idk this one REEE! i’m so sorry i can’t help :(

1. subtract 2x from both sides to get 3y=-2x+12
2. divide 3 from both sides to isolate “y” to get y= -2/3x+ 4

Inverse variation?When a constant force acts upon an object, the acceleration of the object varies inversely with it’s mass. When a certain constant force acts upon an object with mass 4kg, the acceleration of the object is 14m/s^2. If the same force upon another object whose mass is 7kg. What is this objects acceleration?

Answers

Answer:

An Inverse variation states that a relationship between two variables in which the product is always constant.

If one of the variable increases then the other decreases in proportion so that the product is unchanged.

if y is inversely proportional to x, then the equation is of the form

$y = (k)/(x)$ , where k is constant.

As per the given condition, A constant force acts upon an object, the acceleration of the object varies inversely with it's mass.

i.e, $a \propto (1)/(m)$

By definition of inverse variation;

$a = (F)/(m)$ . ......[1] ,where F is the constant force.

It is given that an object has mass(m)= 4kg and the acceleration of an object(a) = 14 $m/s^2$

Substitute these in [1] to find the constant force F;

$14 = (F)/(4)$

$F =14 * 4 = 56 kg m/s^2$

Now, if the same force acts upon the another object whose mass (m) = 7 kg then calculate acceleration.

[1]⇒ $a = (56)/(7) = 8 m/s^2$

therefore, the acceleration of an another object is, $8 m/s^2$

Final answer:

Inverse variation or inverse proportionality represents that one value increases as the other decreases. In the context of physics, it indicates that with a constant force, the acceleration of an object is inversely proportional to its mass. If a 4 kg object has an acceleration of 14 m/s^2, a 7 kg object will have an acceleration of 8 m/s^2.

Explanation:

The concept raised here is related to the law of inverse variation, also known as the inverse proportionality concept found in Physics. This law states that when a constant force acts upon an object, the acceleration of the object is inversely proportional to its mass. Essentially, the more mass an object has, the less it accelerates. We can write this rule as a = F/m, where 'a' is acceleration, 'F' is the applied force, and 'm' is the mass of the object. From the given data, the force 'F' could be calculated from the first scenario where the mass, m = 4 kg and acceleration, a = 14 m/s^2. We have, F = a*m which is 14*4 = 56 N (Newtons). To find the acceleration of the second object with a mass 7 kg and under the same force, we apply the formula a = F/m, leading to a = 56 / 7 = 8 m/s^2. So, the acceleration of the object with 7 kg mass would be 8 m/s^2 under the same force.

Learn more about Inverse Variation here:

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The edge of one cube is 4 m shorter than the edge of a second cube. The volumes of the two cubes differ by 1216 m^3. Find the edge of the smaller cube.

Answers

Volume of cube, V = edge^3
Let edge of cube#1 = (x-4) m, therefore volume of cube#1, v1 = (x-4)^3 m
Let edge of cube#2 = x m, therefore volume of cube#2, v2 = x^3 m
Diff. in volume (in m) = 1216 = v2-v1 = [ x^3 - (x-4)^3 ]
= x^3 - [(x-4)(x-4)(x-4)]
= x^3 - [x^2 - 8x +16(x - 4)]
= x^3 - [ x^3 - 12x^2 + 48x - 64 ]
= 12x^2 - 48x + 64
= 4 (3x^2 - 12x + 16)
Therefore 4 (3^2 - 12x + 16) = 1216
3x^2 - 12x + 16 = 1216/4 = 304
3x^2 - 12x - 288 = 0
3 (x^2 - 4x - 96) = 0
(x^2 - 4x - 96) = 0
(x - 12) (x + 8) =0
(x-12) = 0
Therefore x = 12 m
Edge of cube#2 = x m = 12m
Edge of cube#1 = (x-4) m = 8m

$a- the\ edge\ of\ the\ smaller\ cube\ \ \ \wedge\ \ \ a>0\nV_a-the\ volume\ of\ the\ smaller\ cube\ \ \ \Rightarrow\ \ \ V_a=a^3\n \n(a+4)^3-a^3=1216\ \ \ \wedge\ \ \ (x+y)^3=x^3+3x^2\cdot y+3x\cdot y^2+y^3\n \na^3+3a^2\cdot 4+3a\cdot 4^2+4^3-a^3=1216\n \n12a^2+48a+64-1216=0\ \ \ \Rightarrow\ \ \ 12a^2+48a-1152=0\ /:12\n \na^2-4a-96=0\ \ \ \Rightarrow\ \ \ \Delta=(-4)^2-4\cdot 1\cdot(-96)=16+384=400\n \n √(\Delta) =20\n \na_1= (4-20)/(2\cdot1) =-8<0,\ \ \ a_2= (4+20)/(2\cdot1) =12>0$

$Ans.\ The\ edge\ of\ the\ smaller\ cube=12\ m$

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