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3 years ago

Name the properties that were used to derive the properties of logarithms.

1 answer:

5 0

The properties that were used to derive the properties of logarithms are:
1. a^x · a^y = a^(x+y) 2. a^x / a^y = a^(x - y) 3. a^0 = 1 4. a^(-x) = 1 / x 5. (a^x)^y = a^(xy)

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Sarah is 3 years older than nine times Mario's age. In 10 years, she will be 1 less than triple his

Natasha2012 [34]

Answer:

3(9m + 13) - (m + 10) = 1

Step-by-step explanation:

Here, we want to write an equation we can use to find the age of Mario.

Let the present age of Mario be M

Age of Sarah is 3 years older than 9

times Mario’s age

Mario’s age is thus;

9m + 3

In ten years, she will be 1 less than triple his age

In 10 years time, sarah age will be 9m +

3 + 10 = 9m + 13

Mario age will be m + 10

Mathematically;

3(9m + 13) - (m + 10) = 1

7 0

2 years ago

A pigpen is to be enclosed using 640 m of fencing along three of its sides, the fourth side being a barn. Determine the dimensio

Basile [38]

Answer:

$W_{max}=480m\\ L_{max}=160m$

Step-by-step explanation:

Since we know we only have 640 feet of fence available, we know that L + W + L = 640, $\implies$ 2L + W = 640. This allows us to represent the width, W, in terms of L: W = 640 – 2L

Remember, the area of a rectangle is equal to the product of its width and length, therefore,

$A_{\rm pigpen}=L(640-2L)\implies 640L-2L^2$

Notice that, quadratic has been vertically reflected, since the coefficient on the squared term is negative, so the graph will open downwards, and the vertex will be a maximum value for the area.

recall,

$x_{max}=-b/2a$
$f(x)_{max}=f(x_{max})$

Since our function is A(L)=640L-2L², we get

a=-2
b=640

plug in the value of a and b into the first formula:

$L_{max}=-(640)/2(-2)\implies 160$

$A(L)_{max}=640(160)-2(160)^2\implies 76800$

hence,the dimensions of the pen that will maximize the area are L=160m and W=76800/160=480m

and we're done!

3 0

2 years ago

Which statements are true about the graph of the function f(x) = x2 – 8x + 5? Select three options.

coldgirl [10]

Answer:

1,4,5

Step-by-step explanation: it ees what it ees

4 0

2 years ago

Ray ML and MN are perpendicular. ray MP ia an angel bisector. find the value of x .

bulgar [2K]

Answer: x = 15

Step-by-step explanation:

First, we will have to acknowledge that Angle M is a complementary angle (that means that it is 90 degrees) meaning that 2x° + 4x° will equal 90 degrees. So, let’s set up this equation.

90 = 2x + 4x

90 = 6x

$\frac{90}{6}$ = $\frac{6x}{6}$