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2 years ago

If y varies directly as x, and y is 6 when x is 72, what is the value of y when x is 8?

Mathematics

2 answers:

IRINA_888 [86]2 years ago

6 0

Answer:

For the case when x = 8, we have that y = 2/3.

Step-by-step explanation:

The idea that y varies directly as x, can be written in an equation as:

y = k*x, where k is an unknown constant (until now).

We know that y=6 when x=72, then, substituting these values in the above formula gives us the value of k:

6 = k*72, then: k = 6/72 = 1/12.

Now, we can rewrite our initial expression with the known value of k as:

y = (1/12)*x

For the case when x = 8, we have that:

y = (1/12)*8 = 8/12 = 2/3.

Len [333]2 years ago

4 0

Assumption: y=kx then sustitude y=6,x=72 into y=kx
then 12y=x

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What is the area of Shaded part?

svetlana [45]

Answer:

1π

Step-by-step explanation:

suppose the radius of semicircle P is r,

then the radius of semicircle Q = (r+d)/2 ... d≤r

radius of semicircle R = (r-d)/2

area P = 1/2 (r)²π

area Q = 1/2 ((r+d)/2)² π = 1/8 (r² + 2rd + d²)π

area R = 1/2 ((r-d)/2)² π = 1/8 (r² - 2rd + d²)π

shaded area = P-Q-R = 1/2 r²π - 1/4 (r² + d²)π

= ((r² - d²)/4) * π

because there is no constant r value in the question and d value changes with the r change, when the vertical segment length equal the semicircle P radius (r), r=2 and d = 0

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8 0

2 years ago

How many ways can eight letters be arranged into groups of five where order matters and the first two letters are already chosen

fenix001 [56]

Answer:

120

Step-by-step explanation:

Since we're dealing with a problem where the order matters and the first two letters are already chosen we need to subtract the number of letters and the number of available slots per group.

We use the permutation formula to find the answer, but before that let's check values.

n = 8

k = 5

Now since there are two letters already chosen we have to deduct two from both the value of n and k.

n = 6

k = 3

Now we can use the permutation formula:

$_{n}P_{k}=\dfrac{n!}{(n-k)!}$

$_{6}P_{3}=\dfrac{6!}{6-3)!}$

$_{6}P_{3}=\dfrac{6!}{3!}$

$_{6}P_{3}=\dfrac{6*5*4*3*2*1}{3*2*1}$

The 3*2*1 cancels out and leaves us with:

$_{6}P_{3}=6*5*4$

$_{6}P_{3}=120$

So there are 120 possible ways to arrange eight letters into groups of five where order matters and the first two letters are already chosen.

6 0

3 years ago

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konstantin123 [22]

Answer:

The value of x = 9

Step-by-step explanation:

Angle Bisector Theorem

An angle bisector of a triangle would cut the opposite side into two segments that are proportional to the other two sides of the triangle.

Thus,

$\frac{x}{15}=\:\frac{12}{20}$

Cross Multiply the expression

$\:20\times x=12\times 15$

Divide both sides by 20

$\frac{20x }{20}=\frac{180}{20}$

$x=9$

Therefore, the value of x = 9

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2 years ago

The partial factorization of x2 – x – 12 is modeled with algebra tiles. Which unit tiles are needed to complete the factorizatio

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Answer: Answer is C

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Step-by-step explanation:

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3 years ago

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sattari [20]

Work out the top subtraction first:

3/9 - 8/12

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= 1/3

and the bottom part:-

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3 years ago