Show how to solve 6/15=2/?

Hey there!!

The ratio radius is given as 3:7

... Let's take the first circle's radius as 3 and the radius of the second's circle as 7.

The formula for the circumference as 2π(radius)

The circumference of the first circle as 2π(3)

... 6π

The circumference of the second circle as 2π(7)

... 14π

Ratio = 6π:14π

... 3:7

Hence, the answer would be option (B)

Hope my answer helps!

Final answer:

The ratio of the circumferences of two circles is the same as the ratio of their radii. In this case, where the ratio of the radii is 3:7, the ratio of their circumferences will also be 3:7.

Explanation:

The ratio of the circumferences of two circles is equal to the ratio of their radii assuming all measurements are in the same units. This relationship is due to the formula for the circumference of a circle, C=2πr, where C is the circumference and r is the radius. Seeing this formula, we can ascertain that if we increase the radius, we increase the circumference by the same factor. Therefore, if the ratio of the radii of two circles is 3:7, the ratio of their circumferences will thereon also be 3:7.

Learn more about Circumference ratio here:

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Answer:

x=

−1

33

y+

3

11

Step-by-step explanation:

Answer:

The values of "p" and "q" are p = -5 and q = -6

Step-by-step explanation:

Let's start by finding the zeroes of the polynomial 2x² - 5x - 3, and then we'll determine the relationship between these zeroes and the zeroes of x² + px + q.

The zeroes of a quadratic polynomial of the form ax² + bx + c can be found using the quadratic formula:

For the polynomial 2x² - 5x - 3, a = 2, b = -5, and c = -3. So, the quadratic formula becomes:

x = [-b ± √(b² - 4ac)] / (2a)

Substitute the values:

x = [-(-5) ± √((-5)² - 4(2)(-3))] / (2(2))

Simplify:

x = (5 ± √(25 + 24)) / 4

x = (5 ± √49) / 4

x = (5 ± 7) / 4

Now, we have two possible values for x:

x₁ = (5 + 7) / 4 = 12/4 = 3

x₂ = (5 - 7) / 4 = -2/4 = -1/2

So, the zeroes of 2x² - 5x - 3 are x₁ = 3 and x₂ = -1/2.

Now, we need to find the relationship between these zeroes and the zeroes of x² + px + q.

If the zeroes of x² + px + q are double in value to the zeroes of 2x² - 5x - 3, it means that for each zero "x" of 2x² - 5x - 3, there will be a corresponding zero "2x" for x² + px + q.

So, for x² + px + q, the zeroes will be 2 times the zeroes of 2x² - 5x - 3:

For x₁ = 3, the corresponding zero for x² + px + q is 2x₁ = 2(3) = 6.

For x₂ = -1/2, the corresponding zero for x² + px + q is 2x₂ = 2(-1/2) = -1.

Now, we have the zeroes of x² + px + q: 6 and -1.

To find "p" and "q," we can use Vieta's formulas. Vieta's formulas state that for a quadratic polynomial of the form ax² + bx + c with zeroes α and β:

α + β = -b/a

α * β = c/a

In our case, for x² + px + q with zeroes 6 and -1:

α + β = 6 - 1 = 5

α * β = 6 * (-1) = -6

Now, let's match these with the coefficients of x² + px + q:

α + β = 5, which corresponds to -p (since there's an "x" term in the middle)

α * β = -6, which corresponds to q (the constant term)

So, we have the following equations:

-p = 5

q = -6

Solve for "p" and "q":

p = -5

q = -6

So, the values of "p" and "q" are p = -5 and q = -6.

If the zeroes of the polynomial x² + px + q are double in value to the zeroes of 2x² - 5x - 3, find the value of p and q

Answer:

 p  and  q  are -5 and -6 respectively.

Step-by-step explanation:

factor

2x²-5x-3=0

(x-3) (2x + 1) = 0

x = 3, -1/2

multiply both by 2 = "double in value to the zeroes"

x = 6, -1

reverse factor them

(x-6)(x+1)

multiply

x2−5x−6

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Answer:

domain is all real numbers except x=4

Step-by-step explanation:

and

We need to find (gof)(x)

Plug in x-4 for f(x)

Now we plug in x-4 for x in g(x)

Domain is the set of all x values for which the function is defined

To find out the x values that is undefined we set the denominator =0 and solve for x

When x=4 the denominator becoems 0 that is undefined

So domain is all real numbers except x=4