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Justin deposited $2,000 into an account 5 years ago. Simple interest was paid on the account. He has just withdrawn $2,876. What

RSB [31]

Answer: 8.76%

Step-by-step explanation:

The formula to find the simple interest is given by :-

$I=Prt$ , where P is the principal amount, r is rate of interest () in decimal and t is the time ( in years). (1)

Given : Justin deposited $2,000 into an account 5 years ago.

i.e. P = $2,000 , t= 5 years

He has just withdrawn $2,876. i.e. Future value = $2,876

Interest (I)=$2,876-$2,000=$876 [Subtract Principal value from Future value]

Substitute all the above values of P , t , and I in the formula (1) , we get

$876 =(2000)r(5)\\\\\Rightarrow\ r=\dfrac{876 }{2000\times5}\\\\\Rightarrow r=\dfrac{876}{10000}=0.0876$

In percent , $r=0.0876\times100=8.76\%$

Hence, the rate of interest = 8.76%

6 0

4 years ago

Correct the errors and fill in the blanks by completing the square.

zmey [24]

Answer:

x = 2 - 5 $\sqrt{3}$ , x = 2 + 5 $\sqrt{3}$

Step-by-step explanation:

x² - 4x = 71

to complete the square

add ( half the coefficient of the x- term )² to both sides

x² + 2(- 2)x + 4 = 71 + 4

(x - 2)² = 75 ( take the square root of both sides )

x - 2 = ± $\sqrt{75}$ = ± 5 $\sqrt{3}$ ( add 2 to both sides )

x = 2 ± 5 $\sqrt{3}$

then

x = 2 - 5 $\sqrt{3}$ , x = 2 + 5 $\sqrt{3}$

8 0

1 year ago

5

NeX [460]

Answer:

(b) the answer

Step-by-step explanation:

8 0

2 years ago

Graph the function y = 4x4 – 8x2 + 4. Which lists all of the turning points of the graph?

Serhud [2]

Answer:

$4(x + 1)^{2}(x - 1)^{2}$

Step-by-step explanation:

STEP 1:

The equation at the end of step 1

$((4 (x^4)) - 2^3x^2) + 4$

STEP 2:

The equation at the end of step 2:

$(2^2x^4 - 2^3x^2) + 4$

STEP 3:

STEP 4: Pulling out like terms

<u>4.1</u> Pull out like factors:

$4x^4 - 8x^2 + 4 = 4(x^4 - 2x^2 + 1)$

Trying to factor by splitting the middle term

<u>4.2</u> Factoring $x^4 - 2x^2 + 1$

The first term is, $x^4$ its coefficient is 1.

The middle term is, $-2x^2$ its coefficient is -2.

The last term, "the constant", is +1.

Step-1: Multiply the coefficient of the first term by the constant 1 • 1 = 1

Step-2: Find two factors of 1 whose sum equals the coefficient of the middle term, which is -2.

-1 + -1 = -2 That's it

Step-3: Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -1 and -1

x4 - 1x2 - 1x2 - 1

Step-4 : Add up the first 2 terms, pulling out like factors :

x2 • (x2-1)

Add up the last 2 terms, pulling out common factors :

1 • (x2-1)

Step-5 : Add up the four terms of step 4 :

(x2-1) • (x2-1)

Which is the desired factorization

Trying to factor as a Difference of Squares:

4.3 Factoring: x2-1

Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)

Proof : (A+B) • (A-B) =

A2 - AB + BA - B2 =

A2 - AB + AB - B2 =

A2 - B2

Note : AB = BA is the commutative property of multiplication.

Note : - AB + AB equals zero and is therefore eliminated from the expression.

Check : 1 is the square of 1

Check : x2 is the square of x1

Factorization is : (x + 1) • (x - 1)

Trying to factor as a Difference of Squares:

4.4 Factoring: x2 - 1

Check : 1 is the square of 1

Check : x2 is the square of x1

Factorization is : (x + 1) • (x - 1)

Multiplying Exponential Expressions:

4.5 Multiply (x + 1) by (x + 1)

The rule says : To multiply exponential expressions which have the same base, add up their exponents.

In our case, the common base is (x+1) and the exponents are :

1 , as (x+1) is the same number as (x+1)1

and 1 , as (x+1) is the same number as (x+1)1

The product is therefore, (x+1)(1+1) = (x+1)2

Multiplying Exponential Expressions:

4.6 Multiply (x-1) by (x-1)

The rule says : To multiply exponential expressions which have the same base, add up their exponents.

In our case, the common base is (x-1) and the exponents are :

1 , as (x-1) is the same number as (x-1)1

and 1 , as (x-1) is the same number as (x-1)1

The product is therefore, (x-1)(1+1) = (x-1)2

Final result :

4 • (x + 1)2 • (x - 1)2

4 0

3 years ago

Read 2 more answers

If the domain of f(x)=-x² is integer values of x such that -3≤x<0, find the range.

slamgirl [31]

The range is the resulting y-values we get after substituting all the possible x-values.

$\text{The domain:}\\\\-3\leq x < 0\to\{-3,\ -2,\ -1\}\\\\\text{The range:}$

Substitute the values of x to the equation of the function:

$f(-3)=-(-3)^2=-9\\\\f(-2)=-(-2)^2=-4\\\\f(-1)=-(-1)^2=-1\\\\\boxed{\{-9,\ -4,\ -1\}}$

8 0

3 years ago