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3 years ago

If 3^2x+1= 3x+5, what is the value of x? 2 3 4 6

Mathematics

1 answer:

REY [17]3 years ago

4 0

Answer:

x = 4

Step-by-step explanation:

Set the exponents equal to each other

$3^{2x+1}=3^{x+5}$

2x + 1 = x + 5

Subtract x from both sides

x + 1 = 5

Subtract one from both sides

x = 4

So, the value of x is equal to 4.

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Which statement describes the inverse of m(x) = x^2 – 17x?

DochEvi [55]

Given:

The function is

$m(x)=x^2-17x$

To find:

The inverse of the given function.

Solution:

We have,

$m(x)=x^2-17x$

Substitute m(x)=y.

$y=x^2-17x$

Interchange x and y.

$x=y^2-17y$

Add square of half of coefficient of y , i.e., $\left(\dfrac{-17}{2}\right)^2$ on both sides,

$x+\left(\dfrac{-17}{2}\right)^2=y^2-17y+\left(\dfrac{-17}{2}\right)^2$

$x+\left(\dfrac{17}{2}\right)^2=y^2-17y+\left(\dfrac{17}{2}\right)^2$

$x+\left(\dfrac{17}{2}\right)^2=\left(y-\dfrac{17}{2}\right)^2$ $[\because (a-b)^2=a^2-2ab+b^2]$

Taking square root on both sides.

$\sqrt{x+\left(\dfrac{17}{2}\right)^2}=y-\dfrac{17}{2}$

Add $\dfrac{17}{2}$ on both sides.

$\sqrt{x+\left(\dfrac{17}{2}\right)^2}+\dfrac{17}{2}=y$

Substitute $y=m^{-1}(x)$ .

$m^{-1}(x)=\sqrt{x+(\dfrac{189}{4}})+\dfrac{17}{2}$

We know that, negative term inside the root is not real number. So,

$x+\left(\dfrac{17}{2}\right)^2\geq 0$

$x\geq -\left(\dfrac{17}{2}\right)^2$

Therefore, the restricted domain is $x\geq -\left(\dfrac{17}{2}\right)^2$ and the inverse function is $m^{-1}(x)=\sqrt{x+(\dfrac{189}{4}})+\dfrac{17}{2}$ .

Hence, option D is correct.

Note: In all the options square of $\dfrac{17}{2}$ is missing in restricted domain.

7 0

3 years ago

What is the area? Please explain steps so I can attempt to understand

yarga [219]

Answer:

$12 \sqrt{2}$

Step-by-step explanation:

you can use hypotenuse formula

45-45-90 isosceles right triangle

so, 45= x

x² + x² = 24²

2x² = 24²

x²= 24.12

x= $\sqrt{288} = 12 \sqrt{2}$

or :

you can use this rule: if you see a 45 45 90 isosceles right triagngle (you can look picture) 45=a cm and 90 = $a\sqrt{2}$

so ;

$a \sqrt{2} = 24$

a= $12 \sqrt{2}$

hope this helps ^-^

3 0

3 years ago