All categories

3 years ago

Solve exponential equations 5x − 2=625

Mathematics

1 answer:

coldgirl [10]3 years ago

6 0

Answer:

Step-by-step explanation:

$5^{x-2}=625\\\\5^{x-2}=5^4\qquad(5^4=5\cdot5\cdot5\cdot5=625)\\\\5^{x-2}=5^4\Rightarrow x-2=4\qquad\text{add 2 to both sides}\\\\x-2+2=4+2\\\\x=6\\\\\text{check:}\\\\5^{6-2}=5^4=625\qquad\bold{CORRECT}$

You might be interested in

Would you rather have pennies to match your weight or quarters to match your height

mezya [45]

Answer:

First you have to divide the number by the weight of one penny (which is 2.5 grams) then take what you get and multiply by the value of one penny (and that is $0.01). After you do that you should end up with $5.376. I looked up some more information on GOOGLE and it said that they rounded this number to $5.38. <u>So your height in quarters is worth way more than your weight in pennies.</u>

<u></u>

4 0

3 years ago

Solve the system of equations <br><br> y=2x+1<br> y=x^2+2x-8

Lemur [1.5K]

Answer:

(3,7) and (-3,-5)

Step-by-step explanation:

To solve the system of equations, graph both functions. The (x,y) point(s) where the functions intersect is the solution(s).

See attached picture.

7 0

4 years ago

Use the subsitution method to solve the system of equations. 2x+3y=12. Y=x-1

Sidana [21]

Answer:

x = 3, and y = 2

Step-by-step explanation:

2x + 3y = 12 -------- (1)

y = x - 1 ---------------(2)

Substitute value of Y in (2) in (1)

2x + 3(x-1) = 12

2x + 3x - 3 = 12

5x - 3 = 12

5x = 12 + 3

5x = 15

x = 15/5

x = 3

Put the value of x in equation 2

y = x-1

y = 3 - 1

y = 2

Therefore, x = 3, and y = 2

Hope u understand

Please mark as barinliest

Thank You

6 0

3 years ago

A worker at a landscape design center uses a machine to fill bags with potting soil. Assume that the quantity put in each bag fo

defon

Answer:

a) The expected value is given by:

$E(X) =\frac{a+b}{2}= \frac{10+12}{2}= 11$

The variance is given by:

$Var(X) = \frac{(b-a)^2}{12}= \frac{(12-10)^2}{12}= 0.3333$

And the standard deviation is just the square root of the variance and we got:

$Sd(x) = \sqrt{0.3333}= 0.5774$

b) $P(X$

And we can use the cumulative distribution function given by:

$F(x) = \frac{x-a}{b-a}, a \leq x \leq b$

And using this function we got:

$P(X$

c) $P(X>10.5)$

And using the complement rule and the cumulative distribution function we got:

$P(X>10.5)= 1-P(X$

Step-by-step explanation:

For this case we define the random variable X=quantity put in each bag , and we know that the distribution for X is given by:

$X \sim Unif (a= 10, b =12)$

Part a

The expected value is given by:

$E(X) =\frac{a+b}{2}= \frac{10+12}{2}= 11$

The variance is given by:

$Var(X) = \frac{(b-a)^2}{12}= \frac{(12-10)^2}{12}= 0.3333$

And the standard deviation is just the square root of the variance and we got:

$Sd(x) = \sqrt{0.3333}= 0.5774$

Part b

For this case we want this probability:

$P(X$

And we can use the cumulative distribution function given by:

$F(x) = \frac{x-a}{b-a}, a \leq x \leq b$

And using this function we got:

$P(X$

Part c

For this case we want this probability:

$P(X>10.5)$

And using the complement rule and the cumulative distribution function we got:

$P(X>10.5)= 1-P(X$

3 0

4 years ago

What is the constant of proportionality in the equation y = 3x?<br> constant of proportionality

mezya [45]

Answer:

Step-by-step explanation:

y = mx + b

in this form, the constant of proportionality is also known as the slope....and it can be found in the m position

y = 3x.....is actually y = 3x + 0....so the slope (constant of proportionality is gonna be 3

8 0

4 years ago

Read 2 more answers