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Nataliya [291]
3 years ago
5

When "P" Dollars is invested at interest rate "i", compounded annually, for "t" tears, the investment grows to "A" dollars, wher

e A=P(1+i)^t. When Sara enters 11th grade, her grandparents deposit $10,000 in a college savings account. Find the interest rate "i", if the $10,000 grows to $11,193.64 in two years.
Mathematics
1 answer:
ycow [4]3 years ago
4 0
The interest rate is 0.58, or 58 percent.

11,193.64 = 10,000 (1 + i)^2
Divide each side by 10,000.
1.119364 = (1 + i)^2
Take the square root of both sides.
1.058 = 1 + i
Subtract 1
i = 0.58
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FIND THE SUM AND THE DIFFERENCE FOR EACH PAIR OF POLYNOMIALS please show work
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Answer:

12a. Addition = 7y⁵ + 7y³ – 6y – 5

12b. Subtraction = – y⁵ – 3y³ + 8y + 11

13a. Addition = 5x⁴ + x³ – 6x² + 8x + 17

13b. Subtraction = – x⁴ – 9x³ –6x² + 8x + 3

14a. Addition = – 2b⁴ + b³ – 11b² – 1

14b. Subtraction = 4b⁴ + 7b³ – b² + 8b – 1

15a. Addition = m⁵ + m⁴ + m³ + m²

15b. Subtraction = m⁵ – m⁴ – m³ – m² – 10

16a. Addition = 4x⁴ + 12x³ + 18x² + 16x + 4

16b. Subtraction = 4x⁴ – 4x³ + 14x² – 16x + 4

Step-by-step explanation:

12a. Addition

.. 3y⁵ + 2y³ + y + 3

+ (4y⁵ + 5y³– 7y – 8)

————————————

= 7y⁵ + 7y³ – 6y – 5

12b. Subtraction

.. 3y⁵ + 2y³ + y + 3

– (4y⁵ + 5y³– 7y – 8)

¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

= – y⁵ – 3y³ + 8y + 11

13a. Addition

.. 2x⁴ – 4x³ – 6x² + 8x + 10

+ (3x⁴ + 5x³ +...................+ 7)

¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

= 5x⁴ + x³ – 6x² + 8x + 17

13b. Subtraction

.. 2x⁴ – 4x³ – 6x² + 8x + 10

– (3x⁴ + 5x³ +...................+ 7)

¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

= – x⁴ – 9x³ – 6x² + 8x + 3

14a. Addition

...... b⁴ + 4b³ – 6b² + 4b – 1

+ (– 3b⁴ – 3b³ – 5b² – 4b)

¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

= – 2b⁴ + b³ – 11b² – 1

14b. Subtraction

...... b⁴ + 4b³ – 6b² + 4b – 1

– (– 3b⁴ – 3b³ – 5b² – 4b)

¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

= 4b⁴ + 7b³ – b² + 8b – 1

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... m⁵ + m³ – 5

+ (m⁴ + m² + 5)

¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

= m⁵ + m⁴ + m³ + m²

15b. Subtraction

... m⁵ + m³ – 5

– (m⁴ + m² + 5)

¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

= m⁵ – m⁴ – m³ – m² – 10

16a. Addition

.... 4x⁴ + 8x³ + 16x² + 4

+ (4x³ + 2x² + 16x)

¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

= 4x⁴ + 12x³ + 18x² + 16x + 4

16b. Subtraction

.... 4x⁴ + 8x³ + 16x² + 4

– (4x³ + 2x² + 16x)

¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

= 4x⁴ – 4x³ + 14x² – 16x + 4

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When does the value of f(x) = (1/2)x equal the value of g(x) =2x+8 ?
Zanzabum

Answer:

\huge\boxed{f=g(x)\ \text{for}\ x=-\dfrac{16}{3}=-5\dfrac{1}{3}}

Step-by-step explanation:

When does the value of f(x) = (1/2)x equal the value of g(x) =2x+8?

f(x)=g(x)\iff\dfrac{1}{2}x=2x+8\qquad|\text{subtract}\ 2x\ \text{from bpoth sides}\\\\\dfrac{1}{2}x-2x=2x-2x+8\\\\-1\dfrac{1}{2}x=8\qquad|\text{convert the mixed number to the improper fraction}\\\\-\dfrac{2\cdot1+1}{2}x=8\\\\-\dfrac{3}{2}x=8\qquad\text{multiply both sides by}\ -\dfrac{2}{3}\\\\\left(-\dfrac{2\!\!\!\!\diagup}{3\!\!\!\!\diagup}\right)\left(-\dfrac{3\!\!\!\!\diagup}{2\!\!\!\!\diagup}x\right)=\left(-\dfrac{2}{3}\right)\cdot8\\\\x=-\dfrac{2\cdot8}{3}\\\\x=-\dfrac{16}{3}

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