All Answers 358087 Answers

my choices are quotient, product, sum, or coefficient

Is 2x the product?

2x  is the variable part of the expression....its value depends upon the value of "x"

9 is the constant part

Circumference  = pi * diameter

Circumference  =  pi * 15 m   ≈ 47.12 m

what about with a 15 year loan ?

IGNORE THE FACT THAT IT IS A THING AND BTW I DO KNOW THAT TH LIMIT IS LIKE THAT...

YOU WOULD AFTER INFINTE STEPS GET TO INFINTE SPEED?

Placing those numbers into this calculator, the answer is 1.

It works! and this calculator works!

To make the calculations easy, assume that the square is a 1 x 1 square.

If one side is increased by 13.1%, it is now 1.131.

If the adjacent side is increase by 4.2%, it is now 1.042.

To find the area of this rectangle:  1.131 x 1.04 = 1.178502.

The original square had an area of 1, so this new figure is 17.8502% larger.

He has 8 less quarters than nickles.

q = n - 8

He has 16 coins in total.

q + n = 16

Replace q with n - 8 in the second equation.

(n - 8) + n = 16

n - 8 + n = 16

2n = 16 + 8

n = 24/2 = 12

Replace n with 12 in the first equation.

q = 12 - 8 = 4

He has 4 quarters and 12 nickles.

That is 4($0.25) + 12($0.05) = $1.60  :)

Thank you, that helped alot.

\(\sqrt{9-x^2}\)

Replace x with 3cos θ .

\(=\sqrt{9-(3\cos \theta)^2} \\~\\ =\sqrt{9-9\cos^2 \theta}\)

Factor out a 9.

\(=\sqrt{9(1-\cos^2 \theta)}\)

The Pythagorean identity tells us that 1 - cos²θ = sin²θ

\(=\sqrt{9(\sin^2\theta)} \\~\\ =\sqrt9\cdot\sqrt{\sin^2\theta} =3\sin\theta\)

n = 10 * 3^(1/2) * 27^(3/2) = 10 * 3^(1/2) * 3^(9/2) = 10 * 3^(10/2) = 10 * 3^5

Bye Felicia??? 😂😂

No Guest! Don't leave!

You aright after all..

Please dont be preposterously presumptuous: you really do not know what's in my mind. It's very offensive indeed when you contend vigorously that I believe my answer is better (I totally don't) and when you then decide to tell me to calm down. H's answer is completely fine. I will help out elsewhere where how we did things 55 years ago (i.e. very quickly, in our heads, with the correct answer, cross-checked and assuredly) isn't deprecated. Bye, Felicia.

Calm down ,guest......we appreciate your answer, but there may be several ways to solve the same thing......just because you think that your answer is superior may not make it so.....

Hectictar's answer isn't any more "pedantic" than any other one........

If yall kept it simpler it would be simpler and SAT/GRE would be kaboom

but ok

Let f: first score

Q states that: f+3/2f+86=3 times average=3(82)=246

5/2f=246-86

5f=320

f=64

Let l: last score

l=3/2f=64.(3/2)=96

diff=96-64=32

if yall need to slow it down to really pedantic slowness go widda next answ

Multiply each thing in the first set of parenthesees by each thing in the second set of parenthesees and add the products together.

(2csc x + 2)(2csc x - 2)

 = (2csc x)(2csc x) + (2csc x)(-2) + (2)(2csc x) + (2)(-2)

= 4csc²x - 4csc x + 4 csc x - 4

= 4csc²x - 4

Factor out a 4.

= 4(csc²x - 1)

Rewrite like this.

\(=4(\frac{1}{\sin^2x}-1)=4(\frac{1}{\sin^2x}-\frac{\sin^2x}{\sin^2x})=4(\frac{1-\sin^2x}{\sin^2x})\)

Then, use the Pythagorean identity that says sin² + cos² = 1

\(=4(\frac{cos^2x}{sin^2x})\)

= 4cot²x

Here's how I do this

Forget the " -13" we'll add that in later

Working with the decimal, write  the non-repeating and repeating part,  9535,  and subtract the non- repeating part   =  9535 - 9  =  9526

As a denominator......write the same number of 9s as the number of digits in the repeating part of the decimal- thus, 3 "9s", followed by the same number of 0s as the number of digits in the non-repeating part of the decimal, thus, 1 "0".......thus the denominator  = 9990

So.......the decimal part of the fraction can be represented as  9526 / 9990

Add back the -13 giving the mixed number  of  - (13 + 9526/9990)

Converting this to a fraction, we have  -(139396 / 9990)

Verify this for yourself

Let the train's speed = T

Bus's speed = 11T

11T - T = 50

10T = 50

T = 50 / 10

T = 5 Km/h - train's speed.

5 x 11 = 55 Km/h - Bus's speed.

Let's call the first test score a, second test score b, and third test score c.

(a + b + c) / 3 = 82

c = 3/2 * a = 3a/2

b = 86

Substitute the values we know for b and c into the first equation.

(a + 86 + 3a/2) / 3 = 82

Solve for a.

a + 86 + 3a/2 = 82 * 3

a + 3a/2 = 246 - 86

2a/2 + 3a/2 = 160

5a/2 = 160

a = 160 * 2/5 = 64

Substitute the value we found for a into the second equation to find c.

c = 3(64)/2 = 96

a - c = 64 - 96 = -32

...so her score improved 32 points from her first test to her last test!

Let's see how Muhammed may have arrived at his answer

100   143   162   165  160

    43      19       3     -5             (first difference)

          24     16      8                 (second difference)

                 8       8

We have three non-zero differences, so we will have a 3rd power polynomial =

Ax^3  + Bx^2 + Cx  + D

And  we will have this system of equations

729A   + 81 B   + 9 C   +  D  =   100

512A   +  64B   + 8C    +  D  =   143

343A   +  49B   + 7 C     +  D  =   162

216A   +  36B  +  6C    +    D =    165

Using a matrix solver we have  that :

A = -4/3  ,  B  = 20, C  = -28/13,   D  =  295

So ....our polynomial is

(-4/3)x^2  + 20x^2  - (28/13)x  + 295

And when x  = 5, this evaluates to 160

Did you look under your first post?!

SOH CAH TOA etc

sin x=o/h

cos x=a/h

tan x=o/a

Care to explain what's going on?

f+3/2f+86=3(82)=246

5/2f=160

f=64

l=96

diff=32