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3 years ago

sammys mother is 2 years more than 3 times as old as sammy. their combinied age is 42. how old are sammys mother and sammy

Mathematics

1 answer:

kozerog [31]3 years ago

6 0

Sammy's mother is 32 and Sammy is 10.

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Rationalize the denominator of $\frac{\sqrt{32}}{\sqrt{16}-\sqrt{2}}$. The answer can be written as $\frac{A\sqrt{B}+C}{D}$, whe

musickatia [10]

Rationalizing the denominator involves exploiting the well-known difference of squares formula,

$a^2-b^2=(a-b)(a+b)$

We have

$(\sqrt{16}-\sqrt2)(\sqrt{16}+\sqrt2)=(\sqrt{16})^2-(\sqrt2)^2=16-2=14$

so that

$\dfrac{\sqrt{32}}{\sqrt{16}-\sqrt2}=\dfrac{\sqrt{32}(\sqrt{16}+\sqrt2)}{14}$

Rewrite 16 and 32 as powers of 2, then simplify:

$\dfrac{\sqrt{32}}{\sqrt{16}-\sqrt2}=\dfrac{\sqrt{2^5}(\sqrt{2^4}+\sqrt2)}{14}$

$\dfrac{\sqrt{32}}{\sqrt{16}-\sqrt2}=\dfrac{2^2\sqrt2(2^2+\sqrt2)}{14}$

$\dfrac{\sqrt{32}}{\sqrt{16}-\sqrt2}=\dfrac{4\sqrt2(4+\sqrt2)}{14}$

$\dfrac{\sqrt{32}}{\sqrt{16}-\sqrt2}=\dfrac{16\sqrt2+4(\sqrt2)^2}{14}$

$\dfrac{\sqrt{32}}{\sqrt{16}-\sqrt2}=\dfrac{16\sqrt2+8}{14}$

$\dfrac{\sqrt{32}}{\sqrt{16}-\sqrt2}=\dfrac{8\sqrt2+4}7$

So we have A = 8, B = 2, C = 4, and D = 7, and thus A + B + C + D = 21.

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2 years ago

Write the standard form of the line that contains a slope of 2/3 and passes through the point (1, 1). Include your work in your

Aneli [31]

In this item, we are given with the slope, m = 2/3 and intercept of (1,1). The equation of the line that contains these properties is,

y - y₁ = m(x - x₁)

Substituting the known values,

y - 1 = (2/3)(x - 1)

Simplifying,

3y - 3 = 2x - 2

Further simplifying,

 2x - 3y = -1

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3 years ago

Prime number 157, 1057, 263, 3163

Sergio [31]

157, 263, and 3163 are all prime numbers

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2 years ago

During a radio contest, $50 is added to the prize money each time a caller answers the contest question incorrectly. the first c

omeli [17]

Answer:

50x+100=y
y=550

Step-by-step explanation:

Since the first caller can win $100, you add 100 onto the end. After you add 50 for every person who answered incorrectly. X being amount tried/answered incorrectly, and Y being the amount you can win at that given time

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1 year ago

Change 3 radians to degree measures

uysha [10]

π radians =180∘

1 radian = tex] \frac{180°}{ \pi} [/tex]π

3 radians = $\frac{540°}{ \pi}$

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2 years ago

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