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ikadub [295]
3 years ago
7

What is the rate of change for the function f(x)=2x-3

Mathematics
1 answer:
Stolb23 [73]3 years ago
4 0

Answer:

2

Step-by-step explanation:

f(x) = 2x - 3 is a linear function

The rate of change of a linear function is the measure of the slope.

The equation is in slope- intercept form, that is

y = mx + c ( m is the slope and c the y- intercept )

y = 2x - 3 has slope m = 2

Thus rate of change = 2

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On 1st January 2020, Laurie invests P dollars in an account that pays a nominal annual interest rate of 5.5%, compounded quarter
andrezito [222]

Answer:

1) The common ratio =  1.055

2) The year in which the amount of money in Laurie's account will become double is the year 2032

Step-by-step explanation:

1) The given information are;

The date Laurie made the investment = 1st, January, 2020

The annual interest rate of the investment = 5.5%

Type of interest rate = Compound interest

Therefore, we have;

The value, amount, of the investment after a given number of year, given as follows;

Amount in her account = a, a × (1 + i), a × (1 + i)², a × (1 + i)³, a × (1 + i)ⁿ

Which is in the form of the sum of a geometric progression, Sₙ given as follows;

Sₙ = a + a × r + a × r² + a × r³ + ... + a × rⁿ

Where;

n = The number of years

Therefore, the common ratio = 1 + i = r = 1 + 0.055 = 1.055

The common ratio =  1.055

2) When the money doubles, we have;

2·a = a × rⁿ = a × 1.055ⁿ

2·a = a × 1.055ⁿ

2·a/a = 2 = 1.055ⁿ

2 = 1.055ⁿ

Taking log of both sides gives;

㏒2 = ㏒(1.055ⁿ) = n × ㏒(1.055)

㏒2 = n × ㏒(1.055)

n = ㏒2/(㏒(1.055)) ≈ 12.95

The number of years it will take for the amount of money in Laurie's account to double = n = 12.95 years

Therefore, the year in which the amount of money in Laurie's account will become double = 2020 + 12..95 = 2032.95 which is the year 2032

The year in which the amount of money in Laurie's account will become double = year 2032.

3 0
3 years ago
-7-2x=7(x+8) <br><br> What is the answer for this expression
sertanlavr [38]

Answer:

x=-7

Step-by-step explanation:

1. Distribute the 7 into the parenthesis: -7-2x=7x+56

2. Combine like terms by doing the opposite operation to the numbers:  -7=9x+56 (added 2x to 7x)

3. Subtract 56 to each side of the equation: -63=9x

4. To isolate the variable "x," divide each side by 9: x=-7

7 0
3 years ago
A spinner and 6 cards are shown below:
Tems11 [23]

Answer:

1 over 18

Step-by-step explanation:

The spinner has 3 segments and he spun it 1 time.  So, he has a 1 in 3 chance of landing on green.

There are 6 cards so he has a 1 and 6 chance of picking up the yellow card.    

Multiply those and you have 1 over 18

Done!

3 0
2 years ago
Which of the following is NOT true? Question 19 options: (3x2y5)3=27x6y15 (1000x12y20z−3)0=1 52‾‾√3=523 42×43= 165
bixtya [17]

Answer:


Step-by-step explanation:

Lets try to simplify each to check which one is incorrect so it will be NOT true

first one is :

distribute the exponent so :

(3x^2y^5)^3 =3^3x^{2*3}y^{5*3}

27x^6y^{15} CORRECT

Second one is :

(1000x^{12}y^{20}z^{-30})^{0} =1

CORRECT because anything raised to exponent 0 is 1 .

Last one is :

4^2 *4^3 = 4^{2+3}\\=4^{6}\\=(4)^{2*3}\\=16^{3}

so Last is<em> INCORRECT</em>



5 0
3 years ago
I have tried so hard and I cant figure thus out. The. entire problem needs to be finished, this is worth 20 points.
bija089 [108]

Answer:

No the ramp doesn’t meet the law. The slope is 4/50 which is 1/12.5

The slope of the ramp doesn’t meet the law because it’s slope is greater than 1/12. To adjust the ramp so that it meets the law, you could increase the height and/or the horizontal length to increase the slope so it is less than 1/12.


Step-by-step explanation:


5 0
3 years ago
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