Solve the system of equations using the substitution method.

The expression 3^2*3^3*3^4 is equivalent to?<br> Show all your work please

loris [4]

Cool! So OK I'll take you through it.
You just need to take everything 1 step at a time, as you might already know.

First
3 to the second is 9

Second
The first part included like this 9*(3 to the third) which is 243

Third
The second part is included into the question like 243*(3 to the fourth) which is 243*81

Fourth
243*81 = 19,683

Your Answer
(3^2)*(3^3)*3^4) = 19,693

Hope That Helps and Correct Me If I'm Wrong!

3 0

3 years ago

Read 2 more answers

A garden box has a perimeter of 18½ feet. If the length is 5 feet, what is the area of the garden box?

Travka [436]

Answer:

$area=\frac{85}{4}feet^{2}$

Step-by-step explanation:

1. Approach

Since it is given that the garden box is a rectangle, then the opposite sides are congruent. One can use this to their advantage, by setting up an equation that enables them to solve for the width of the rectangle. After doing so, one will multiply the width by the given length and solve for the area.

2. Solve for the width

It is given that the garden box is a rectangle. As per its definition, opposite sides in a rectangle are congruent. The problem gives the length and the perimeter of the rectangle, therefore, one can set up an equation and solve for the width.

$perimeter=18\frac{1}{2}\\\\length=5$

$2(length+width)=perimeter$

Substitute,

$2(5+width)=18\frac{1}{2}$

Conver the mixed number to an improper fraction. This can be done by multiplying the "number" part of the mixed number by the denominator of the fraction. Then add the result to the numerator.

$2(5+width)=\frac{37}{2}$

Inverse operations,

$2(5+width)=\frac{37}{2}\\/2\\\\5+width=\frac{37}{4}\\-5\\\\width=\frac{17}{4}$

3. Solve for the area

Now that one has solved for the width of the box, one must solve for the area. This can be done by multiplying the length by the width. Since the width is a fraction, one must remember, that when multiplying an integer by a fraction, one will multiply the integer by the numerator (the top of the fraction), and then simplify by reducing the fraction, if possible. Reducing the fraction is when one divides both the numerator and the denominator by the GCF (Greatest Common Factor).

$length=5\\\\width = \frac{17}{4}$

$length*width=area$

Substitute,

$5*\frac{17}{4}\\\\=\frac{85}{4}$

$area=\frac{85}{4}feet^{2}$

4 0

3 years ago

A manufacturer knows that their items have a normally distributed lifespan, with a mean of 12.3 years, and standard deviation of

Zolol [24]

Answer:

probability of lasting longer = 1.7%

Step-by-step explanation:

We are given:

x' = 14 years

μ = 12.3 years

s = 0.8 years

Thus, let's use the formula for the Z-score value which is;

z = (x' - μ)/s

Thus;

z = (14 - 12.3)/0.8

z = 2.125

From the z-distribution table attached, the p-value is ;

P(x' > 2.125) = 1 - 0.983 = 0.017 = 1.7%

Thus,probability of lasting longer = 1.7%

5 0

2 years ago

Round off to the nearest <br> 3,142

Bezzdna [24]

Just put 3.150 lol that what I did

5 0

3 years ago

Draw a model to represent the product 41×16

svlad2 [7]

41×16 is 656 because 1×6 is 6. 6×4 is 24. 1×1 is 1. 1×4 is 4. The numbers left are 246 ( 1×6 + 6×4 ), and 41 ( 1×1 + 1×4 ). All together, the answer is 656. Enjoy! :)

7 0

3 years ago