Paula has two pieces of wire, one 96 feet long and the other 72 feet long. If she wants to cut them up to produce many pieces of wire that are all of the same length, with no wire left over, what is the greatest length, in feet, that she can make them

Answers

Answer 1

Answer:

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If you pull the information into a mathematical context, you'll notice it is asking for the highest common factor of the 2 numbers

Let's put both of them in prime factorization:

96 = 2^5 x 3

72 = 2^3 x 3^2

Now pick out what is common in these

2^3 x 3 = 24

Thus it would be 24 feet

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Answer 2

Answer: She can make 7 24-foot wires perfectly

Answer:

Hence, we have:

a= 3 and b= 4

Step-by-step explanation:

It is given that:

A complex number, (a + bi), multiplied by (2 + 3i) and added to -i gives the product of (-11 + 5i) and (1 – i).

i.e.

$(a+ib)(2+3i)-i=(-11+5i)(1-i)\n\ni.e.\n\na(2+3i)+ib(2+3i)-i=-11(1-i)+5i(1-i)\n\ni.e.\n\n2a+3ai+2bi+3bi^2-i=-11+11i+5i-5i^2$

Since, we know that :

$i^2=-1$

Hence, we have:

$2a+3ai+2bi-3b-i=-11+11i+5i+5\n\ni.e.\n\n(2a-3b)+i(3a+2b-1)=-11+5+11i+5i\n\ni.e.\n\n(2a-3b)+i(3a+2b-1)=-6+16i$

i.e. we have:

$2a-3b=-6---------(1)$

and

$3a+2b-1=16\n\ni.e.\n\n3a+2b=16+1\n\ni.e.\n\n3a+2b=17------------(2)$

On multiplying equation (1) by 2 and equation (2) by 3 we get:

$13a=39\n\ni.e.\n\na=3$

on putting the value of a into equation (1) we get:

$2* 3-3b=-6\n\ni.e.\n\n6-3b=-6\n\ni.e.\n\n-3b=-6-6\n\ni.e.\n\n-3b=-12\n\ni.e.\n\nb=4$

(a+bi)(2+3i)-i=(-11+5i)(1-i)
2a+3ai+2bi+3bi²-i=-11+11i+5i-5i²
2a+(3a+2b-1)i-3b=-11+16i+5
(2a-3b)+(3a+2b-1)i=-6+16i
Therefore; we have the next system of equations:
2a-3b=-6
3a+2b-1=16

Finally, the system of equations is:
2a-3b=-6
3a+2b=17
We can solve this system of equations by reduction method
2(2a-3b=-6)
3(3a+2b=17)
----------------------
   13a=39 ⇒a=39/13=3

3(2a-3b=-6)
-2(3a+2b=17)
----------------------
   -13b=-52 ⇒ b=52/13=4

Answer: a=3;    b=4

Is rolling an even number on a number cube an outcome or an event

Answers

i is an outcome because whenever you do an expirement the solution is always called an outcome

It will be an event

Evita lives 0.85 mile from her school . write this distance as a fraction in simplest form

Answers

Answer:

$(17)/(20)\text{ miles }$

Step-by-step explanation:

When we write a terminating decimal as a fraction,

Then we follow the below steps,

Step 1 : Write the number with denominator 1,

Step 2 : multiply numerator and denominator by an exponent of 10 ( like 10, 100, 100 etc ) to eliminate the decimal,

Step 3 : simplify the fraction by dividing both numerator and denominator by the HCF of numerator and denominator,

Here, the given number,

0.85

$=(0.85)/(1)$

$=(0.85* 100)/(100)$

$=(85)/(100)$

$=(85/ 5)/(100/ 5)$ ( HCF (85, 100) = 5 )

$=(17)/(20)$

.85 is in the hundredths place so your fraction will be 85/100 then you divide it by 5 and get 17/20 as your answer. Hope this helps

One root of the quadratic equation x^2 − 2x + m = 0 is 9. If the other root is n, what is n−m?

Answers

$9^2-2*9+m=0\n \n 81-18+m=0\n \n m=-63$

$x^(2) -2x-63=0\n \n \Delta=(-2)^2-4.1.(-63)=4+252=256\n \n x=(2 \pm 16)/(2)\n \n x_1=(18)/(2)=9\n \n n=x_2=(-14)/(2)=-7\n \n n-n=-7-(-63)=-7+63=56$

Find the radius of a sphere with a volume of 589 cubic centimeters

Answers

Answer: The radius of a sphere is 5.20 cm.

Step-by-step explanation:

Volume of sphere = $(4)/(3)\pi r^3$ , where r = radius of sphere.

Given : Volume of sphere : 589 cubic centimeters

As per formula , we have

$(4)/(3)\pi r^3=589 \n\n\Rightarrow\ r^3=(589*3)/(4\pi)=(441.75)/(\pi)=(441.75)/(3.14)\n\n\Rightarrow\ r^3=140.684713376\approx140.68\n\n\Rigghtarrow\ r=\sqrt[3]{140.68} \approx5.20$