PLEASE HELP! TWO PROBLEMS!!

Vladimir [108]

Answer:

x = -12

Step-by-step explanation:

Set logs up on both sides-

log 16^x = log 64^x+4

The variable goes behind because of the exponent log <em>property</em> (exponents are permitted to go behind the log to multiply)-

x * log 16 = x + 4 * log 64

Divide both logs out-

log 64/log 16 = 1.5

Simplify-

x = x+4(1.5)

1.5x + 6 = x

Remove 1.5-

1 - 1.5 = -.5x

Simplify-

-.5x = 6

Divide both sides-

6/-.5x = -12

Hence, the answer would be -12

4 0

4 years ago

Which of the following is a true statement about the triangles shown on the graph

sveticcg [70]

It's D. Slopes are the same, because if you divide opposite and adjacent side of both triangles, you get the same result. Count the squares, for the smaller triangle it's 2/2=1 and for the bigger one it's 4/4=1.

5 0

3 years ago

Rewrite the equation by completing the square 4x^2-4x+1=0

oee [108]

Answer:

4(x - $\frac{1}{2}$ )² = 0

Step-by-step explanation:

Given

4x² - 4x + 1 = 0

To complete the square the coefficient of the x² term must be 1

Factor out 4 from 4x² - 4x

= 4(x² - x) + 1 = 0

add/subtract ( half the coefficient of the x- term )² to x² - x

4(x² + 2(- $\frac{1}{2}$ )x + $\frac{1}{4}$ - $\frac{1}{4}$ ) + 1 = 0

4(x - $\frac{1}{2}$ )² - 1 + 1 = 0

4(x - $\frac{1}{2}$ )² = 0

8 0

3 years ago

Read 2 more answers

Will someone explain what i did wrong here?

tensa zangetsu [6.8K]

The actual inverse function is:

$f^{-1}(x) = x^2 + 3$

And the domain is [0, ∞).

<h3>Where is the mistake?</h3>

Remember that for a given function f(x) with a domain D and a range R.

For the inverse function, f⁻¹(x) the domain is R and the range is D.

Here, for the given function the domain is x ≥ 3 and the range is [0, ∞).

Then for the inverse function, which is:

$f^{-1}(x) = x^2 + 3$

(to check this, you must have that):

$f^{-1}(f(x)) = x\\\\f(f^{-1}(x)) = x$

The domain will be [0, ∞) and the range x ≥ 3

If you want to learn more about inverse functions:

brainly.com/question/14391067

#SPJ1

7 0

2 years ago

100 Points! What are the classifications of each system?

alexdok [17]

Answer:

Part 1) Is a inconsistent system

Part 2) Is a consistent independent system

Part 3) Is a consistent dependent system

see the attached figure

Step-by-step explanation:

we know that

If a system has at least one solution, it is said to be consistent .

If a consistent system has exactly one solution, it is independent .

If a consistent system has an infinite number of solutions, it is dependent

If a system not have solution, it is said to be inconsistent

Part 1) we have

$x+5y=-2\\x+5y=4$

This system of linear equations has two parallel lines (their slopes are equal) with different y-intercept

so

The lines don't intersect

The system has no solution

therefore

Is a inconsistent system

Part 2) we have

$y=3x+4\\-2x+y=4$

we know that

If two lines have different slopes, then the lines intersect at one point and the system of equations has one solution

In this problem, the lines have different slopes (m=3 and m=2)

so

The lines intersect at one point

The system has one solution

therefore

Is a consistent independent system

Part 3) we have

$3x+y=4$ ----> equation A

$-6x-2y=-8$ ----> equation B

Multiply equation A by -2 both sides

$-2(3x+y)=-2(4)$

$-6x-2y=-8$ ----> equation C

Compare equation B and equation C

Are identical lines

so

The system has infinity solutions

therefore

Is a consistent dependent system

4 0

4 years ago