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Fittoniya [83]
3 years ago
15

You invest $5000 into an account earning 4% interest compounded quarterly. Write an

Mathematics
1 answer:
lidiya [134]3 years ago
8 0

Answer:

A (in $USD) = 5,000(1 + .04/4)^4(8)

A = 5000(1 + 0.01)^32

A = 5000(1.01)^32

A = 5000(1.37494068)

A ≈ 6874.7034

<u>A = $6875 or $6875.7 (depending on rounding requirement)</u>

Step-by-step explanation:

Compound Interest Formula

A = P(1+ r/n)^n(t)

  • A is the amount in the account after t years
  • P is the principal (original amount invested)
  • r is the annual rate, expressed as a decimal
  • n the number of times the interest is calculated a year*
  • t is the number of years

*If the interest is compounded monthly n = 12, if quarterly n = 4, if daily n = 365.

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6x-24<br> 2x+12 <br> Solve for X
Makovka662 [10]

Answer:

x = 9

Step-by-step explanation:

Simplifying

6x + -24 = 2x + 12

Reorder the terms:

-24 + 6x = 2x + 12

Reorder the terms:

-24 + 6x = 12 + 2x

Solving

-24 + 6x = 12 + 2x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-2x' to each side of the equation.

-24 + 6x + -2x = 12 + 2x + -2x

Combine like terms: 6x + -2x = 4x

-24 + 4x = 12 + 2x + -2x

Combine like terms: 2x + -2x = 0

-24 + 4x = 12 + 0

-24 + 4x = 12

Add '24' to each side of the equation.

-24 + 24 + 4x = 12 + 24

Combine like terms: -24 + 24 = 0

0 + 4x = 12 + 24

4x = 12 + 24

Combine like terms: 12 + 24 = 36

4x = 36

Divide each side by '4'.

x = 9

Simplifying

x = 9

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1 year ago
(6t4, 3) (-2tn 3)<br> Simplify
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Help me please Only no.2 no.3 no.8 no.6 no.9 and no.10
Reil [10]

Answer:

2) x³ (x² + 1) (x + 1)

3) (x - 6) (x + 6)

6)  (x + 3) (x - 4)

8) (5x + 3) (x - 2)

Step-by-step explanation:

I'm providing the solutions for numbers 2, 3, 6, and 8, in order to give you the opportunity to apply and practice the techniques demonstrated here for numbers 9 and 10.

<h3>2) x⁶ + x⁵ + x⁴ + x³ = 0 </h3>

Factor out the highest possible common term, applying the product rule of exponents, a^{m} a^{n} = a^{m+n}

x³ (x³ + x² + x¹ + 1) = 0

Next, apply the special factoring technique into the exponential expressions inside the parenthesis), the factor by grouping:

The factors for the given polynomial are: x³ (x² + 1) (x + 1)

<h3> 3) x² - 36 = 0 </h3>

Use the <u>difference of two squares factoring</u>, where it states: u² - v² = (u - v) (u + v)

Since 36 is a perfect square of 6², then we can establish the following factors using the difference of squares:

Factors:  (x - 6) (x + 6).

<h3>6) x² - x - 12 = 0 </h3>

For this quadratic trinomial, find factors that will produce a product of <em>a</em> × <em>c</em> (1 × -12) and sum of b (-1):

The possible factors of -12 that also results to a sum of -1 are:  

3 × -4 = -1

 Hence, the possible factors of x² - x - 12 = 0 could be (x + 3) (x - 4). Verify whether this is correct by performing the FOIL method:

(x + 3) (x - 4) = x² - 4x + 3x - 12 = x² - x - 12

Therefore, the factors of x² - x - 12 = 0 are: (x + 3) (x - 4).

<h3>8) 5x² - 7x - 6 = 0 </h3>

where a = 5, b = -7, and c = -6

Given this quadratic trinomial, we can use the factoring by grouping, where it states: find the values of u and v such that the product of uv is the same as the product of <em>ac</em>:  u × v = a × c, and that the sum of (<em>u</em> + <em>v </em>) is the same as <em>b</em>.  

In other words, we must find the factors of u × v that have a product of a × c and a sum of b:

<em>u × v </em>= <em>a × c</em> = 5 × (-6) = -30  

u + v = b = -7

The possible factors of -30 are:

-3 × 10 = -30

3 × -10 = -30

Out of these factors, the factors 3 × -10 = -30 will have the same sum as the value of b = -7:

3 + (-10) = -7

Hence, u = 3, v = -10.

Now, we can group the trinomial as follows:

(<em>ax</em>² + <em>ux </em>) + (<em>vx </em>+ <em>c </em>)

(5x² + 3x) + (-10x - 6)

For the last step, factor out the common terms from both groups:

(5x² + 3x) + (-10x - 6)  

x (5x + 3) - 2(5x + 3)

Combine common terms together: (5x + 3) and (x - 2)

Therefore, the factors of the given quadratic trinomial are: (5x + 3) (x - 2).

5 0
3 years ago
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