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3 years ago

Name 3 fractions that are equivalent to: 2/3

2 answers:

4 0

Three fractions equivalent to ⅔ are 4/6 , 8/12, and 16/24
Three fractions equivalent to ¾ are 6/8, 12/16, and 24/32
Three fractions equivalent to 4/5 are 8/10, 16/20 and 32/40

kupik [55]3 years ago

3 0

For 2/3 there are equvialent fractions such as 4/6,6/9,8/12
for 3/4 there is 6/8,9/12,12/16
for 4/5 there is 8/10,12/15,16/20
These can all be figured out by multiplying the numerator and the denomanator by the same number! Each of these fractions can be reduced back to there original fraction! Hope this helps

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You are planning to make an open rectangular box from a 24-in.-by-47-in. piece of cardboard by cutting congruent squares from

miskamm [114]

Answer:

The dimensions are 13.92inches by 36.92inches by 5.04inches

Volume is 2590.18 inches³

Step-by-step explanation:

see attachment for the figure

supposing 'h' is side length of the square and also the height of the box

then, According to the question

Length of the box 'L'= 47 - 2h

Width of the box 'w'= 24 - 2h

Volume of the box 'V'= hLw

Substituting the values of 'L' and 'w' in above equation

V= h(47 - 2h)(24 - 2h)

V=(47h - 2h²)(24 - 2h) => 1128h - 94h²-48h²+4h³

V= 4h³ -142h²+1128h -->eq(1)

Taking derivative on both sides.

V' = 12h² - 284h + 1128

Setting the equation to zero, we will have

0=12h² - 284h + 1128

0= 3h² - 71h + 282

Using Quadratic formula to find h

h= (-b+-√b²-4ac) / 2a

= 71+-√71² - (4 x 3 x 282) / (2 x 3)=> 71+-√5041- 3384 / 6

h =(71+- 40.706)/ 6

EITHER h= 18.6

OR h=5.04

By substituting the value of 'h' in eq(1)

(1)=>V(18.6)= 4(18.6)³ -142(18.6)²+1128(18.6) => -2406.096

(1)=>V(5.04)= 4(5.04)³ -142(5.04)²+1128(5.04) => 2590.18

By ignoring the negative value, we will have h=5.04

Therefore,

L= 47 - 2h => 47 -2(5.04) =>36.92

w= 24 - 2h=> 24- 2(5.04)=> 13.92

The dimensions are 13.92inches x 36.92inches x 5.04inches

Volume is 2590.18 inches³

7 0

3 years ago

What is the volume of a hemisphere with a diameter of 45.7 m, rounded to the nearest tenth of a cubic meter?

worty [1.4K]

24987.2 meters cubed.

Step-by-step explanation:

A Hemisphere is 1/2 of a sphere, so let's find the volume of a sphere and then cut it in half.

The volume of a sphere is V= (4/3)πr3

The diameter is double the size of the radius, so we can find r, the radius, by dividing the diameter,

45.7m, by 2. So r = 22.85 meters

so the volume of the sphere is (4/3)π(22.85 meters)3, which is 49974.35787 meters cubed.

Since we're actually looking for the Hemisphere, we can divide this volume in half to get the volume of the hemisphere as 24987.17894 meters cubed.

And because the answer must be to 1/10th of a cubic meter, that means we only want one decimal point. So we round to 24987.2 meters cubed.

6 0

2 years ago

If a polynomial function f(x) has roots -8, 1, and 6i, what must also be a root of f(x)?

Naddik [55]

Answer:

it must also have the root : - 6i

Step-by-step explanation:

If a polynomial is expressed with real coefficients (which must be the case if it is a function f(x) in the Real coordinate system), then if it has a complex root "a+bi", it must also have for root the conjugate of that complex root.

This is because in order to render a polynomial with Real coefficients, the binomial factor (x - (a+bi)) originated using the complex root would be able to eliminate the imaginary unit, only when multiplied by the binomial factor generated by its conjugate: (x - (a-bi)). This is shown below:

$(x-(a+bi))*(x-(a-bi))=\\(x-a-bi)*(x-a+bi)=\\([x-a]-bi)*([x-a]+bi)=\\(x-a)^2-(bi)^2=\\(x-a)^2-b^2(-1)=\\(x-a)^2+b^2$