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S_A_V [24]
1 year ago
14

PLEASE HELP DUE TODAY ILL GIVE BRAINLIEST 1. An advertising company charges $40 per half-page advertisement and $75 per full-pag

e advertisement. Michael has a budget of $800 to purchase 13 advertisements. (a) Define a variable for each unknown. Write a system of equations to represent the situation. (b) How many half-page advertisements does Michael purchase? Show your work. (c) How many full-page advertisements does Michael purchase? Show your work.
Mathematics
1 answer:
Oksana_A [137]1 year ago
8 0

Answer: inverse of given function = log(x)/log(3)

Step-by-step explanation: how to find the inverse of any function?

in the complete function, replace y with "x" and x with "y"then, solve the obtained equation from step 2 for yand, then the value obtained for "y" is the inverse required i.e. = f^{-1}(x)

now, we solve the problem:

given : - y = 3^x

replacing the value of "y" with "x", we get,

x = 3^y

to solve for "y" we should take the "logarithm" for both sides

log (x) = y log(3)

or y = log(x)/log(3)

or f^(-1) (x) = log(x)/log(3)

( I hope this helped <3 )

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A convex lens has a diameter of 30 mm and a depth of 5 mm at the center. How far from the vertex is the focus?
natima [27]
The formula for determining the distance of the focus from the vertex is as follows,

     f = x² / 4a

where f is focus, x is the radius (half the value of diameter), and a is the depth. Substituting the known values to the given equation,

   f = (30/2 mm)² / (4)(5 mm)

    f = 11.25 mm

<em>ANSWER: 11.25 mm</em>
8 0
1 year ago
Which is the graph of the system x + 3y &gt; –3 and y &lt; One-halfx + 1?
fenix001 [56]

Answer: THE GRAPH IS ATTACHED.

Step-by-step explanation:

We know that the lines are:

x + 3y=-3

y = \frac{1}{2} x + 1

Solving for "y" from the first line, we get:

3y=-x-3\\\\y=-\frac{x}{3}-1

In order to graph them, we can find the x-intercepts and the y-intercepts.

For the line x + 3y=-3 the x-intercepts is:

0=-\frac{x}{3}-1\\\\(1)(-3)=x\\\\x=-3

And the y-intercept is:

y=-\frac{0}{3}-1\\\\y=-1

For the line y=\frac{1}{2} x + 1 the x-intercepts is:

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

And the y-intercept is:

y=\frac{1}{2} (0)+ 1\\\\y=1

 Now we can graph both lines, as you can observe in the image attached (The symbols and > indicates that the lines must be dashed).

By definition, the solution is the intersection region of all the solutions in the system of inequalities.

6 0
1 year ago
Read 2 more answers
Find the semi perimeter of a triangle with sides 9cm 12 cm and 30 cm
alexgriva [62]

Answer:

<h2>25.5 cm</h2>

Step-by-step explanation:

<h3>s =  \frac{a + b + c}{2}</h3>

=  \frac{9 + 12 + 30}{2}cm \\   = \frac{51}{2}cm  \\ 25.5cm

7 0
1 year ago
Felipe planted some seeds for a science project. One of his plants grew 6 2/7 inches in the first week, and then it grew 5 11/14
MatroZZZ [7]

Answer:

<em>The plant grew </em>12\frac{1}{14}<em> inches</em>

Step-by-step explanation:

<u>Operations with Fractions</u>

Felipe planted seeds for a science project. One of the plants grew 6 2/7 inches in the first week and 5 11/14 inches in the second week.

We are required to find the total growth during the two weeks. We have to find the sum of:

6\frac{2}{7}+5\frac{11}{14}

Let's convert both fractions to improper form:

6\frac{2}{7}+5\frac{11}{14}=6+\frac{2}{7}+5+\frac{11}{14}

Adding the integers:

6\frac{2}{7}+5\frac{11}{14}=11+\frac{2}{7}+\frac{11}{14}

Now we find the LCM of 7 and 14 is 14, thus:

6\frac{2}{7}+5\frac{11}{14}=11+\frac{4}{14}+\frac{11}{14}

6\frac{2}{7}+5\frac{11}{14}=11+\frac{15}{14}=11+\frac{14+1}{14}

6\frac{2}{7}+5\frac{11}{14}=11+1+\frac{1}{14}

6\frac{2}{7}+5\frac{11}{14}=12+\frac{1}{14}

Rewriting as a mixed number:

The plant grew 12\frac{1}{14} inches

8 0
1 year ago
Consider the following equations and name the property of equality used to solve for the variable.
Anestetic [448]

Answer:

Subtraction property ; x = 3.25

Division property ; - 6

multiplication property ; - 125

Addition property ; 13

Step-by-step explanation:

A.)

x + 3.75 = 7

Using the subtraction property : subtract 3.75 from both sides

x + 3.75 - 3.75 = 7 - 3.75

x = 3.25

B. )

–3b = 18

According to the division property :

Divide both sides by - 3

-3b / - 3 = 18 / - 3

b = - 6

C.)

m/5 = - 25

Using the multiplication property :

m/5 * 5 = - 25 * 5

m = - 125

D.)

m – 4 = 9

Using the addition property :

Add 4 to both sides :

m - 4 + 4 = 9 + 4

m = 13

8 0
1 year ago
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