Solve x2 – 10x + 25 = 35 for x.

1 answer:

3 0

$x^2-10x+25=35\\\\x^2-2\cdot5\cdot x + 5^2=35\ \ \ |\text{use:}\ (a-b)^2=a^2-2ab+b^2\\\\(x-5)^2=35\to x-5=\pm\sqrt{35}\ \ \ |+5\\\\\boxed{x=5-\sqrt{35}\ \vee\ x=5+\sqrt{35}}$

$\text{other method}\\\\x^2-10x+25=35\\\\x^2-5x-5x+25=35\\\\x(x-5)-5(x-5)=35\\\\(x-5)(x-5)=35\\\\(x-5)^2=35\\.....$

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The ratio of dimes to quarters in a money bag is 2:14. if the total numbers of coins is 48, how many quarters are there?

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Answer:

There are 42 quarters (and 6 dimes).

Step-by-step explanation:

The given ratio is 2:14. But this does not tell us how many dimes nor how many quarters we have. Instead, it's a ratio. Modify this by multiplying numerator and denominator by n and then find n:

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Then the total number of coins is 2n + 14n =48, implying that:

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A right rectangular prism has a length of 8 centimeters, a width of 3 centimeters, and a height of 5 centimeters. What is the su

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Answer: $158cm^2$

Step-by-step explanation:

You can use the following formula to calculate the surface area of the right rectangular prism:

$SA = 2(wl +lh + hw)$

Where "w" is the width, "l" is the length, and "h" is the height.

Knowing that this rigth rectangular prism has a length of 8 centimeters, a width of 3 centimeters and a height of 5 centimeters, you can substitute these values into the formula.

Then, the surface of the right rectangular prism is:

$SA = 2[(3cm*8cm) + (8cm*5cm) + (5cm*3cm)]\\\\SA=158cm^2$