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Setler79 [48]
3 years ago
11

Solve for 'p'

Mathematics
1 answer:
Darina [25.2K]3 years ago
6 0
\left(\dfrac{9a^{-4}}{25}\right)^p=\dfrac3{5a^2}
\left(\dfrac9{25a^4}\right)^p=\dfrac3{5a^2}

One way to find p is to notice that the part on the left hand side within the parentheses can be written as a square:

\dfrac9{25a^4}=\dfrac{3^2}{5^2(a^2)^2}=\left(\dfrac3{5a^2}\right)^2

So you could write

\left(\left(\dfrac3{5a^2}\right)^2\right)^p=\left(\dfrac3{5a^2}\right)^{2p}=\dfrac3{5a^2}

Since these two expressions are equal, and the bases are the same, you know the exponents must be equal, with the exponent on the right hand side being 1. So 2p=1, or p=\dfrac12.
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The graph of f(x) = 2x + 4 shifts five units to the right when it is replaced with the graph of f(x) = 2x - k. What is the value
DIA [1.3K]
<h2>Answer</h2>

C.) 1

<h2>Explanation </h2>

Remember the rules for shifting functions:

f(x)+b shifts the function b units upward

f(x)-b shifts the function b units downward

f(x+b) shifts the function b units to the left

f(x-b) shifts the function b units to the right

Since we want tho shift f(x)=2^{x+4} 5 units to the right, we are using the rule: f(x-b) shifts the function b units to the right; in other words, we need to subtract 5 units to the input of the function:

f(x)=2^{x+4-5}

f(x)=2^{x-1}

But notice that there is already a negative sign in f(x)=2^{x-k}, so to get f(x)=2^{x-1}, k must be equal to positive 1.

7 0
2 years ago
Read 2 more answers
A credit union loans a member $6,000 for the purchase of a used car. The loan is made for 15 months at an annual simple interest
lina2011 [118]
You will need the Total Loan Cost Formula which is
(I'm having trouble attaching the graphic - I think the problem is with Brainly).

If nothing else, go to this web page.
It has a calculator and the formula.
http://www.1728.org/loanfrm4.htm

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3 0
3 years ago
Complete the equation of the line through (-9,-9) and (-6,0)
Rudik [331]

For this case we have that by definition, the equation of the line of the slope-intersection form is given by:

y = mx + b

Where:

m: It is the slope of the line

b: It is the cut-off point with the y axis.

According to the data of the statement we have the following points:

(x_ {1}, y_ {1}): (- 9, -9)\\(x_ {2}, y_ {2}): (- 6,0)

We found the slope:

m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}} = \frac {0 - (- 9)} {- 6 - (- 9)} = \frac { 9} {- 6 + 9} = \frac {9} {3} = 3

Thus, the equation is of the form:

y = 3x + b

We substitute one of the points and find b:

0 = 3 (-6) + b\\0 = -18 + b\\b = 18

Finally, the equation is:

y = 3x + 18

Answer:

y = 3x + 18

7 0
3 years ago
An arhitect wants to draw a rectangle with a diagonal of 20 inches. The length of the rectangle is to be 8 inches more than twic
kiruha [24]

The diagonal of a rectangle = sqrt(w^2 + l^2)

w = width

l = length

In this problem,

The diagonal = 20 in

w = x

l = 2x + 8

Let's plug our numbers into the formula above.

20in = sqrt((x)^2 + (2x + 8)^2)

Let's simplify the inside of the sqrt

20 in = sqrt(5x^2 + 32x + 64)

Now, let's square both sides.

400 = 5x^2 + 32x + 64

Subtract 400 from both sides.

0 = 5x^2 + 32x - 336

Factor

0 = (5x - 28)(x + 12)

Set both terms equal to zero and solve.

x + 12 = 0

Subtract 12 from both sides.

x = -12

5x - 28 = 0

Add 28 to both sides.

5x = 28

Divide both sides by 5

x = 28/5

The width cant be a negative number so now we know that the only real solution is 28/5

Let's plug 28/5 into our length equation.

Length = 2(28/5) + 8 = 56/5 + 8 = 96/5

In conclusion,

Length = 96/5 inches

Width = 28/5

4 0
2 years ago
The system when solved is:
Karolina [17]

Answer:

1,-4

its the right answer

3 0
2 years ago
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