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jeka57 [31]
3 years ago
11

Which of the following is a step in simplifying the expression x multiplied by y to the power of 3 over x to the power of negati

ve 4 multiplied by y to the power of 4, the whole to the power of negative 2.?
Mathematics
1 answer:
Archy [21]3 years ago
7 0

Answer:

Once the rules of exponents are understood, you can begin solving more complicated expressions more easily. Recall that when you take a power to a power, you multiply the exponents, (xa)b= xa·b.


 


What happens when you raise an entire expression inside parentheses to a power? You can use the techniques you already know to simplify this expression.


 


            (2a)4  =  (2a)(2a)(2a)(2a)  =  (2 • 2 • 2 • 2)(a • a • a • a) = (24)(a4) = 16a4


 


Notice that the exponent is applied to each factor of 2a. So, we can eliminate the middle steps.


 


(2a)4  =  (24)(a4), applying the 4 to each factor, 2 and a.


= 16a4


 


The product of two or more numbers raised to a power is equal to the product of each number raised to the same power.



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Jemma is three times as old as Angie. Five years from now the sum of their ages will be 34 years. What are their present ages?
Lapatulllka [165]

Answer: Angie = 6, Jemma = 18

<u>Step-by-step explanation:</u>

Let x represent the current age of Angie

              Current Age           Age 5 years from now

Angie:            x                              x + 5

Jemma:        3x                            3x + 5

5 years from now the sum of their ages is 34

                  (x + 5) + (3x + 5) = 34

                               4x + 10 = 34

                               4x        = 24

                                 x         = 6

Angle's current age is x = 6

Jemma's current age is 3x = 3(6) = 18

5 0
3 years ago
Read 2 more answers
Find the perimeter of the following shape, rounded to the nearest tenth:
OLga [1]

Answer: the perimeter of the shape is 19.1

Step-by-step explanation:

To determine the length of each side of the quadrilateral, we would apply Pythagoras theorem which is expressed as

Hypotenuse² = opposite side² + adjacent side

For line AD,

AD² = 2² + 4² = 4 + 16 = 20

AD = √20 = 4.47

For line AB,

AB² = 1² + 5² = 1 + 25 = 26

AB = √26 = 5.1

For line BC,

BC² = 2² + 4² = 4 + 16 = 20

BC = √20 = 4.47

For line CD,

CD² = 1² + 5² = 1 + 25 = 26

CD = √26 = 5.1

The perimeter of a plane figure is the distance around the figure. Therefore

Perimeter = AB + AB + BC + CD

Perimeter = 4.47 + 5.1 + 4.47 + 5.1 =

19.1

6 0
3 years ago
What is the measure of angle x?
Kitty [74]

The two horizontal lines are parallel.

This makes the 80 degree angle and the angle ox x and 20 degrees are alternate interior angles and are the same.

This means x + 20 needs to equal 80.

X = 80-20 = 60 degrees.

8 0
3 years ago
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Indicate in standard form the equation of the line through the given points, writing the answer in the equation box below.
Aloiza [94]

9514 1404 393

Answer:

  y = 4

Step-by-step explanation:

The given points are on the horizontal line ...

  y = 4

This is the standard-form equation of that line.

7 0
3 years ago
A cooler has a temperature of 32 degrees Fahrenheit. A bottled drink is placed in the cooler with an initial temperature of
FinnZ [79.3K]

Answer:

k \approx 0.44

Step-by-step explanation:

Given function:

f(t) = (ce)^{-kt}+32

As per question statement:

Initial temperature of bottle is 70 ^\circ F.

i.e. when time = 0 minutes, f(t) = 70 ^\circ F

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After t = 3, f(t) = 42^\circ F

42 = 38 \times e^{-k\times 3}+32\\\Rightarrow 42-32 = 38 \times e^{-3k} \\\Rightarrow 10  = 38 \times e^{-3k} \\\Rightarrow e^{3k} = \dfrac{38}{10}\\\Rightarrow e^{3k} = 3.8\\\\\text{Taking } log_e \text{both the sides:}\\\\\Rightarrow log_e {e^3k} = log_e {3.8}\\\Rightarrow 3k \times log_ee=log_e {3.8}   (\because log_pq^r=r \times log_pq)\\\Rightarrow 3k \times 1=log_e {3.8}\\\Rightarrow 3k = 1.34\\\Rightarrow k = \dfrac{1.34}{3}\\\Rightarrow k \approx 0.44

Hence, the value is:

k \approx 0.44

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