Using the numbers provided below, write two powers that have the same value.

11. Solve 5(2x – 3) = x – 15 + 9x for x.

zepelin [54]

Answer:

$\boxed{\bold{True \ For \ All \ x}}$

Explanation:

[ Step One ] Group Like Terms

$\bold{5\left(2x-3\right)=x+9x-15}$

[ Step Two ] Combine Similar Elements: $\bold{x+9x=10x}$

$\bold{5\left(2x-3\right)=10x-15}$

[ Step Three ] Expand $\bold{5\left(2x-3\right): \ 10x-15}$

$\bold{10x-15=10x-15}$

[ Step Four ] Add 15 To Both Sides

$\bold{10x-15+15=10x-15+15}$

[ Step Five ] Simplify

$\bold{10x=10x}$

[ Step Six ] Subtract 10x From Both Sides

$\bold{10x-10x=10x-10x}$

[ Step Seven ] Simplify

$\bold{0=0}$

[ $\boxed{\bold{Final \ Answer}}$ ]

➤ $\bold{Both \ Sides \ Are \ Equal, \ True \ For \ All \ x}$

$\boxed{\bold{Mordancy}}$

4 0

3 years ago

If the function m not-equals 0 has an inverse function, which statement must be true? B not-equals 0

Kipish [7]

Answer:

Option a: m ≠ 0

Step-by-step explanation:

After a small online search, I've found that the complete question is:

If the function f(x) = m*x + b has an inverse function, which statement must be true?

a) m ≠ 0

b) m = 0

c) b ≠ 0

d) b = 0

Ok, if g(x) is an inverse of the function f(x), then:

g( f(x)) = x

f( g(x)) = x

Let's assume that f(x) = m*x + b has an inverse, and this inverse function is g(x).

Because f(x) is linear, g(x) is also linear, then:

g(x) = n*x + c

Let's find the values of A and B.

We know that:

f( g(x)) = x = m*(n*x + c) + b

then

x = m*n*x + m*c + b

Then we must have:

m*n = 1

(m*c + b) = 0

From the first equation m*n = 1

We get:

n = 1/m

The slope of the inverse function is one over the slope of the original function.

Because m is on the denominator, m can not be equal to zero (because a division by zero is not defined)

Then the correct option is the option a, m ≠ 0.

6 0

3 years ago

Read 2 more answers

The variables x=9 and y=15 vary directly. Write an equation that relates the variables

erik [133]

Answer:

x = 0.6y.

Step-by-step explanation:

x = ky is direct variation where k is some constant;

Now we find k:-

Substituting for x and y:

9 = k*15

k = 9/15 = 0.6

So the equation is

x = 0.6y.

7 0

2 years ago

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Evaluate 3x+4(y+3) when x is 5 less than the quotient of y and 3, and y=18.

romanna [79]

It is given that x is 5 less than the quotient of y and 3.

And given value of y is 18 .

So quotient of y and 3 is

$\frac{18}{3} = 6$

And 5 less than 6 =1

So we have y=18 and x=1

Given expression is

$3x+4(y+3)$

At x=1 and y=18, we will get

$3(1)+4(18+3) =3 + 4(21)$

$= 3+84=87$

4 0

3 years ago

Running from the top of a flagpole to a hook in the ground there is a rope that is 13 meters long. If the hook is 5 meters from

bagirrra123 [75]

Answer:

12 meters

Step-by-step explanation:

Looking at the problem we can see that it typifies a right angled triangle. The rope running from the top of the flagpole to the hook on the ground is the hypotenuse of the triangle. Let us call this hypotenuse c. Let the distance between the hook and the foot of the flagpole be b. Let the height of the flagpole be a.

From Pythagoras theorem;

c^2 = a^2 + b^2

a^2= c^2 - b^2

a= √c^2-b^2

From the question

c= 13 metres

b= 5 metres

a= the unknown

a= √c^2-b^2

a= √(13)^2 - (5)^2

a= √169 - 25

a= √144

a= 12 meters

6 0

3 years ago

Read 2 more answers