All categories

3 years ago

Twice the sum of a number is 9 is equal to three times the difference of the number and 7

2 answers:

5 0

"Twice the sum of a number is 9 is equal to three times the difference of the number and 7" is our problem. Let's translate it into an equation.

Twice 2 times

the sum of a number x +

and 9 9

is equal to =

three times 3 times

the difference of a number x-

and 7 7

We move top down on the right side and make the equation. Then we solve it for x

2x + 9 = 3x - 7 our equation

-x + 9 = -7 subtract 3x on both sides

-x = -16 subtract 16 on both sides

x = 16 divide both sides by -1

Thus the mystery number is 16.

soldi70 [24.7K]3 years ago

3 0

First, write put the information into an equation

2*(x+9) = 3*(x-7)

distribute the 2 and 3
2x + 18 = 3x - 21

Combine like terms (Xs and munbers) (in this case, it's easier to add 15 to both sides and subtract 2x from both sides so both sides end up being positive)
33 = x

x=33

You might be interested in

How to factor 9x^2+5x-12

bekas [8.4K]

Hi Stacey

9x^2+5x-12

Answer : Doesn't factor

I hope that's help and please if you have questions you can ask me !

3 0

3 years ago

Simplify the expression csc(-x)/1+tan^2x)

Charra [1.4K]

Assuming ya meant $\frac{csc(-x)}{1+tan^2(x)}$

to slimplify, we use a variation of the pythagorean identity and a decomposition into the sin and cos

for the pythaogreaon identity
$cos^2(x)+sin^2(x)=1$
divide both sides by $cos^2(x)$
$1+tan^2(x)=sec^2(x)$ since $\frac{sin(x)}{cos(x)}=tan(x)$
subsitute
$\frac{csc(x)}{sec^2(x)}$

recall that $csc(x)=\frac{1}{cos(x)}$
also that cos(x) is an even function and thus cos(-x)=cos(x)
therfore $csc(-x)=\frac{1}{cos(-x)}=\frac{1}{cos(x)}=csc(x)$
so we get

$\frac{csc(x)}{sec^2(x)}$
decompose them into $\frac{1}{cos(x)}$ and $\frac{1}{sin^2(x)}$ to get $\frac{\frac{1}{cos(x)}}{\frac{1}{sin^2(x)}}$
multiply by $\frac{sin^2(x)}{sin^2(x)}$ to get
$\frac{sin^2(x)}{cos(x)}$
we can furthur simlify to get
$(\frac{sin(x)}{cos(x)})(sin(x))=tan(x)sin(x)$
the expression simplifies to tan(x)sin(x)

5 0

3 years ago

Read 2 more answers

What is 8.5 as a mixed number in simplest form

IrinaK [193]

8 5/10
8 1/2

Hope this helped!

4 0

4 years ago

Read 2 more answers

Which expressions are equivalent to -4(3d - 2) - 7?

likoan [24]

-12d+1 is the answer I think. If not then I apologize.....