MATHEMATICS HIGH SCHOOL

How do you prove (3x+2)2 is equivalent to (3x+6)(3x-2)+16i have tried expanding the brackets but I'm still really stuck
thankyou in advance

Answers

Answer 1
Answer: (3x+2)^2=9x^2+12x+4\n\n (3x+6)(3x-2)+16=\n9x^2-6x+18x-12+16=\n9x^2+12x+4

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Answers

We'll use the Pythagorean Theorem to solve this problem.
We know that the Pythagorean Theorem is the following:

a^(2) + b^(2) =c^(2)

where c is the hypotenuse (the side opposite the right angle), and a and b are the legs of the triangle.
To solve, we just have to input what we know. The two legs of the triangle are 60 and 100, so we just have to plug these values in and solve.

60^(2) + 100^(2) = c^(2)

3600 + 10000 = c^(2)

13600= c^(2)

So we know that the distance from one corner of the playing field to the opposite corner is the square root of 13,600 yards.
When we plug this into a calculator, we get

√(13600) ≈ 116.619...

which, when rounded up to the nearest whole number, is 117.
The approximate distance from one corner of the soccer field to the opposite corner is 117 yards.
Hope that helped! =)
The answer is 117 because you do 60 squared plus 100 squared then you find the square root of that product and since it says approximentaly the closest answer would be 117

Hasan deposits $150 in a savings account that earns simple interest at an annual rate of 3%. He makes no other deposits or withdrawals. How much interest does his account earn after five years?

Answers

Answer:

$172.5 hope this helps

Step-by-step explanation:

What is 68,642 rounded to the nearest thousand?

Answers

68,642 rounded to the nearest thousand is 69,000.

It's because 68,642 is closer to 69,000 than to 68,000.

I hope it will help you and give a clue for rounding numbers in the future ;)
The rule of rounding numbers up is if it's 5 or up, round it.  Since your number is 68,642, it would round to 69,000.  Because the 6 in the hundreds place is greater than 5.

Which is the graph of a quadratic equation that has a negative discriminant?

Answers

Answer:

The correct graph is D.

Step-by-step explanation:

Given a quadratic equation :

y=ax^(2)+bx+c

You can find the roots (where the graph intersects the x-axis) applying the following equation :

x1=\frac{-b+\sqrt{b^(2)-4ac}}{2a}

and

x2=\frac{-b-\sqrt{b^(2)-4ac}}{2a}

We define the discriminant as b^(2)-4ac

If b^(2)-4ac>0 then the graph will intersect the x-axis in two points

If b^(2)-4ac=0 then the graph will intersect the x-axis in one point.

Finally, If b^(2)-4ac<0 then the graph won't intersect the x-axis because it will not have real roots.

In this exercise, the graph that doesn't intersect the x-axis is graph D.

Answer:

D

Step-by-step explanation:

A negative discriminant indicates that the quadratic equation has no real roots.

Thus the graph does not touch or intersect the x- axis

The only graph that does not touch or intersect the x- axis is the fourth one

A system of equations can be written to represent coin and pricing problems. True or False.

Answers

The answer to this question is True. Apparently, there are a lot of mathematical problems regarding coin and pricing problems can be written with a system of equations.

What is 2x3x6x4x7x5x0x4x5

Answers


I followed the numbers across, thinking to myself "this won't be
too hard to multiply, because they're all small numbers".  And then
when I got to the zero, I burst out laughing !  It doesn't matter at all
what all the other numbers are.  Once there's a zero in there, the whole
product will be zero, no matter what else gets multiplied along the way.
There could be millions and billions in there.  You wouldn't need to do
any calculating at all.  With zero as a factor, you know right away that
the product is zero.
So your question is 
\sf{2*3*6*4*7*5*} \bf{0} \sf{*4*5=}

We need to use this property:
\sf{a * 0=0}

So then your problem has one number that is a 0. And all these numbers are getting multiplied. That means you could have like a million numbers, but if you multiply it by 0 even once, your final answer will be 0.

So your final answer is 

\boxed{\bf{0}}
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