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3 years ago

Can anyone help out with these two questions?

Mathematics

1 answer:

nikitadnepr [17]3 years ago

5 0

To find f(3), plug x = 3 in f(x),
∴ f(3) = 3(3)+1 = 9+1 = 10
Therefore, the ordered pair is (3,10)

For second one,
plug x = 10 in f⁻¹(x),

f⁻¹(10) = 10-1/3 = 9/3 = 3

Therefore, the ordered pair is (10,3)

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Chelsey put for $450 into an account with a simple interest rate of 2.5% when she withdrew the money she had earned a total of $

fgiga [73]

Answer:

5.66 years

Step-by-step explanation:

450 x 1.025^(n) = 450 + 67.50

450 x 1.025^(n) = 517.50

1.025^(n) =(517.50 / 450)

1.025^(n) = 1.15

n = ln(1.15) / ln(1.025)

n = 5.66

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3 years ago

Ms. Lynch has 21 coins in nickels and dimes.

bulgar [2K]

Answer:

Step-by-step explanation:So we know x + y = 21 and 5x +10y = 165 We line them up in columns x + y = 21 5x +10y = 165 To eliminate the x variable, I'll multiply every element in the 1st equation by -5. -5x + -5y = -105 5x + 10y = 165 Now we combine (add) the equations, which eliminates x altogether. 5y = 60 ... y = 12 From there, x + 12 = 21 ... x = 21-12 ... x = 9 You should double check. Do 9 nickles and 12 dimes equal $1.65? A very important thing to remember using this method is to do the same thing to each element in the equation that you change! I hope that helps.

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2 years ago

What is the perimeter of the triangle shown on the coordinate plane, to the nearest tenth of a unit?

seraphim [82]

21.6 units

Calculate the length of the 2 inclined sides using the distance formula

d = √(x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = (- 3, 3 ) and (x₂, y₂ ) = (3, 4 )

d = √(3 + 3 )² + (4 - 3)² = √(36 + 1 ) = √37

repeat for (x₁, y₁ ) = (- 3, 3 ) and (x₂, y₂ ) = (3, - 3 )

d = √(3 + 3 )² + (- 3 - 3 )² = √(36 + 36 ) = √72

the vertical side has a length of 7 units

perimeter = √37 + √72 + 7 = 21.6 ( nearest tenth of a unit )

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3 years ago

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1 year ago

The sum of the reciprocals of two consecutive even integers is 7/24. Write an equation that can be used to find the two integers

sergejj [24]

Assume the first even integer is x.
The next even integer will be 2 digits after this digit. So the next even integer will be x+2.

The reciprocals of these two even integers can be written as $\frac{1}{x}$ and $\frac{1}{x+2}$ respectively.

The sum of their reciprocals is 7/24. So we can set up the equation as:

$\frac{1}{x}+ \frac{1}{x+2}= \frac{7}{24}$

Taking LCM on left hand side:

$\frac{x+2+x}{x(x+2)}= \frac{7}{24} \\ \\ 
 \frac{2x+2}{ x^{2} +2x}= \frac{7}{24}$

Cross Multiplying the denominators:

$24(2x+2)=7({ x^{2} +2x}) \\ \\ 
48x+48=7 x^{2} +14x \\ \\ 
7 x^{2} +14x-48x-48=0 \\ \\ 
7 x^{2} -34x-48=0 \\ \\ 

$

Using the quadratic formula to solve the above equation:
$7 x^{2} -34x-48=0 \\ \\ 
x= \frac{34+- \sqrt{1156+1344} }{14} \\ \\ 
x= \frac{34+- \sqrt{2500} }{14} \\ \\ 
x=\frac{34+-50 }{14} \\ \\ 
x=6 \\ x=- \frac{8}{7} 
$

Since, the value of x can only be an integer, we discard the fractional value and keep x=6

So the first even integer is 6 and the next even integer is 8. The sum of reciprocals of 6 and 8 is 7/24

5 0

3 years ago