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3 years ago

What value of x makes this equation true?

Mathematics

1 answer:

ratelena [41]3 years ago

7 0

Answer:

x = -12

Step-by-step explanation:

-1/4x - 12 = x + 3

-x - 48 = 4x + 12

-x -4x = 12 + 48

-5x = 60

x = -12

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It is exponent laws,can you go step by step plz because I don't get it

Evgen [1.6K]

Remember
(x^m)^n=x^(mn)
and
(x^m)(x^n)=x^(m+n)
and
(x^m)/(x^n)=x^(m-n)

so

(4^2)^3=4^(2*3)=4^6
notice
4^6=(2^2)^6=2^2*6)=2^12

(4/2)^3=2^3

on top we have
(2^12)(2^3)(2^3)=2^(12+3+3)=2^18

on bottom
8^3
conver to base 2
(2^3)^3=2^(3*3)=2^9

now we have
(2^18)/(2^9)=2^(18-9)=2^9

6 0

3 years ago

Find the length of the given segment.<br><br> Find LN

Lapatulllka [165]

Answer:

x+10=1/2*(x+2)

2x+20=x+2

20-2= x-2x

x= -18

now,

LN= X+10

= -18+10

= -8

8 0

2 years ago

Find the inverse of f(x) = -2x+5<br> The inverse is g(x) = <br> Graph the function and its inverse

vovikov84 [41]

Given:

The function is:

$f(x)=-2x+5$

To find:

The inverse of the given function, then draw the graphs of function and its inverse.

Solution:

We have,

$f(x)=-2x+5$

Step 1: Substitute $f(x)=y$ .

$y=-2x+5$

Step 2: Interchange x and y.

$x=-2y+5$

Step 3: Isolate variable y.

$2y=5-x$

$y=\dfrac{5-x}{2}$

Step 4: Substitute $y=f^{-1}(x)$ .

$f^{-1}(x)=\dfrac{5-x}{2}$

Therefore, the inverse of the given function is $f^{-1}(x)=\dfrac{5-x}{2}$ and the graphs of these functions are shown below.

Note: The inverse function is $f^{-1}(x)=g(x)$ .

6 0

2 years ago

Using Newton’s cooling model, what will the temperature of a cup of hot tea be 2 hours after it is poured if its initial tempera

eimsori [14]

Newton's Law of cooling is a differential equation that is simplified by using limits in temperature and time. The simplified equation is:

ln(T-Ts) = ln(T0-Ts) - kt

where
T is the final temperature
T0 is the initial temperature
Ts is the temperature of the surroundings
t is the time
k is a constant

Substituting the values:
ln(T-70) = ln(200-70) - (0.6)(2)
T = 109.16°F

The answer is B.

8 0

3 years ago

I really need help with this one.

lord [1]

So all you really need to do is to substitute the value of x into the equation so like the 1st one will look like this: $f(-3) = 2(-3) + 4 = -2 \\ f(-1) = 2(-1) + 4 = 2 \\ f(0) = 2(0) + 4 = 4 \\ f(2) = 2(2) + 4 = 8 \\ f(4) = 2(4) + 4 = 12$ Those would be the right column for the f(x) values
Now do the same for g(x) $g(-3) = (-3)^2+1 = 10 \\ g(-1) = (-1)^2 + 1 = 2 \\ g(0) = 0^2 + 1 = 1 \\ g(2) = 2^2 + 1 = 5 \\ g(4) = 4^2 + 1 = 17$
You will notice that when x = -1, g(x) = f(x)

6 0

3 years ago