MATHEMATICS MIDDLE SCHOOL

B(4,5)O (0,0)
What is the general form of the equation for the given circle centered at O(0, 0)?​

Answers

Answer 1
Answer:

Step-by-step answer:

The general form of an equation centered at O(0,0) is given by

x^2+y^2=r^2

where r is the radius, (x,y) is any point on the circumference.

If B(4,5) lies on the circumference, then we can find the radius of the circle by substitution:

4^2+5^2=r^2

=>

r^2 = 16+26 =41

Hence the equation of a circle centred at O(0,0) and B(4,5) on its circumference is

x^2 + y^2 = 41
Answer 2
Answer:

Answer:

Option B for plato is the correct answer

Step-by-step explanation:

B.  x2 + y2 − 41 = 0

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Rectangle R was dilated to form rectangle R prime. Rectangle R has a length of 8 and width of 4. Rectangle R prime has a length of 20 and width of 10. Which is the scale factor of the dilation? Five-fourths StartFraction 2 Over 1 EndFraction Five-halves StartFraction 5 Over 1 EndFraction

Answers

Answer:

5/2

Step-by-step explanation:

20/8= 10/4=5/2

Answer:

5/2

Step-by-step explanation:

I just took the quiz and got it right.

Which fractions are equivalent to 40%?

Answers

All of them except 8/100 because it results 0.08 or 8%.

The rest:

2/5 = 0.4 = 40%

8/20 = 0.4 = 40%

4/10 = 0.4 = 40%

16/40 = 0.4 = 40%
40% = 40/100

8/100 doesn’t equal to 40 because it’s already over 100

2/5 x 20 = 40/100

8/20 x 5 = 40/100

4/10 x 10 = 40/100

16/40 divide by 2 = 1/5 x 20 = 20/100

So your answers are 2/5, 8/20 and 4/10

Can someone tell me how

Answers

the way I get the subsequent term, nevermind the exponents, the exponents part is easy, since one is decreasing and another is increasing, but the coefficient, to get it, what I usually do is.

multiply the current coefficient by the exponent of the first-term, and divide that by the exponent of the second-term + 1.

so if my current expanded term is say 7a³b⁴, to get the next coefficient, what I do is (7*3)/5   <----- notice, current coefficient times 3 divided by 4+1.

anyhow, with that out of the way, lemme proceed in this one.

\bf ~~~~~~~~\textit{binomial theorem expansion} \n\n \qquad \qquad (1+ax)^n\implies \begin{array}{llll} term&coefficient&value\n \cline{1-3}&\n 1&+1&(1)^n(ax)^0\n\n 2&+((1)(n))/(1)\to n&(1)^(n-1)(ax)^1\n\n 3&+(n\cdot (n-1))/(2)&(1)^(n-2)(ax)^2 \end{array}

so, following that to get the next coefficient, we get those equivalents as you see there for the 2nd and 3rd terms.

so then, we know that the expanded 2nd term is 24x therefore

\bf n(1)^(n-1)(ax)1 = 24x\implies n(1)(ax)=24x\implies nax=24x\implies n=\cfrac{24}{a}

we also know that the expanded 3rd term is 240x², therefore we can say that

\bf \cfrac{n(n-1)}{2}~~(1)^(n-2)(ax)^2 = 240x^2\implies \cfrac{n(n-1)}{2}(1)(a^2x^2) = 240x^2 \n\n\n \cfrac{(n^2-n)(a^2x^2)}{2}=240x^2\implies \cfrac{(n^2-n)(a^2)}{2}=\cfrac{240x^2}{x^2}\implies \cfrac{a^2n^2-a^2n}{2}=240 \n\n\n a^2n^2-a^2n=480

but but but, we know what "n" equals to, recall above, so let's do some quick substitution

\bf a^2n^2-a^2n=480\qquad \boxed{n=\cfrac{24}{a}}\qquad a^2\left( \cfrac{24}{a} \right)^2-a^2\left( \cfrac{24}{a} \right)=480 \n\n\n a^2\cdot \cfrac{24^2}{a^2}-24a=480\implies 24^2-24a=480\implies 576-24a=480 \n\n\n -24a=-96\implies a=\cfrac{-96}{-24}\implies \blacktriangleright a = 4\blacktriangleleft \n\n[-0.35em] ~\dotfill\n\n n=\cfrac{24}{a}\implies n=\cfrac{24}{4}\implies \blacktriangleright n=6 \blacktriangleleft

The total weight of 30 bags of flour and 4 bags of sugar is 42.6 kg. If each bag of sugar weighs 0.75 kg, what is the weight of each bag of flour?

Answers

The answer is: Each bag of flour weighs 1,32 kg. 

If we the total weight of the bags is given, and we know both the number of bags of flour and sugar, and we also know the weight of each bag of sugar, then we have to find the unknown, which is X. 30 times X plus 4 times the weight of a bag of sugar would equal 42.6kg. Next step is to put the unknown on one side and the known values on the other side. We have 30 times X equals 42.6 minus 4 times 0.75. 
To find X we need to divide the value with 30, or to sum up 

30X + 4*0.75 = 42.6
30X + 3 = 42.6
X = (42.6 - 3) / 30
X = 1.32 kg

The weight of each bag of flour = 1.32 kg

Further explanation

The division operation is one of the basic arithmetic operations

Common signs used are \large{\boxed{:}}} or \large{\boxed{\slash}}

The division is written by placing the numerator above the denominator with a horizontal line between them or use a slash with the numerator's position and the denominator is parallel

The division is actually an iterative subtraction operation (as many as the number of divisors)

Division is the opposite of multiplying

The general form of division can be stated by:

\large{\boxed{\bold{divident:divisor=quotient+remainder}}

example:

7: 3 = 2 + 1

  • 7 = dividend
  • 3 = divisor
  • 2 = quotient
  • 1 = remainder

Division operation statement:

"7 divided by 3 equals 2 remainder 1"

The form of division can also be expressed in terms of fractions

In the example above, the form of mixed fractions  is

\displaystyle (7)/(3) =2(1)/(3)

Mixed fractions consist of whole number and proper fractions

One variable linear equation is an equation that has a variable and the exponent number is one.  

Can be stated in the form:  

\large{\boxed{\bold{ax=b}}

or  

ax + b = c,

where a, b, and c are constants, x is a variable  

  • The total weight of 30 bags of flour and 4 bags of sugar is 42.6 kg

we translate this sentence into Arithmetic operations :

Let x = bags of flour

y = bags of sugar

\displaystyle 30x+4y=42.6~kg

  • each bag of sugar weighs 0.75 kg

Because there are 4 bags of sugar, the total weight bags of sugar :

\displaystyle = 4*0.75~kg

\boxed{\bold{=3~kg}}

Equation becomes :

\displaystyle 30x+4(0.75~kg)=42.6~kg

\displaystyle 30x+3~kg=42.6~kg

\displaystyle 30x=42.6~kg-3~kg

\displaystyle 30x=39.6~kg

\displaystyle x={(39.6)/(30)

\large{\boxed{\bold{x=1.32~kg}}

Learn more  

the slope-intercept form of the linear equation  

brainly.com/question/1945934  

a graph of a linear equation  

brainly.com/question/1505806  

system of linear equations  

brainly.com/question/11544167  

Keywords : one variable, linear equation , division, bags of flour, sugar, weighs

What is the simplified form of the expression 2 * [(1+14)*7]+6/0.5^3?

Answers

2*(1+ 14)7 + 6/0.5^3
=  2*15*7 + 6/ 0.125
=210 + 6000/125
=  210 + 48 =       258
2 \cdot [(1+14)\cdot7]+6:0.5^3=2\cdot(15\cdot7)+6: ( (1)/(2))^3 =2\cdot105+6: (1)/(8) =\n \n=210+6\cdot 8=210+48=258

Express each number in fraction form before finding the inverse:7,10,1 3/4,

Answers

7=7/1

10=10/1

1+3/4=4/4+3/4=7/4

------------------------

Inverse of 7 is 1/7.

Inverse of 10 is 1/10.

Inverse of 1+3/4 is 1/(1+3/4)=1/(7/4)=(1/1)*(4/7)=4/7.
For the whole numbers all you have to do is put the number over one.

Because if you simplify - for example - 5/1

You'll get 5

For 1 and 3/4 you have to turn it into an improper fraction by multiplying the whole by the denominator

1 x 4

Then add the numerator

1 x 4 = 4 + 3

And since 1 x 4 = 4  + 3 = 7

7 will be your numerator replacing 3

7/4

But you must keep the denominator or the fraction wouldn't make sense

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7 = 7/1

10 = 10/1                                      Hope I helped :)

1 3/4 = 7/4
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The inverse of the numbers/fractions would just be switching the numbers ...

Example :


7/1 = 1/7

10/1 = 1/10

7/4 = 4/7

The example above shows and inverse :)

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Edited answer ...

Edited once more for the convenience of others
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