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pshichka [43]
2 years ago
11

The table shows three values of x and their corresponding values of f (x) for a linear function f, such that f (r) = 0 and f (0)

= s, where r and s are constants. What is the value of rs?​

Mathematics
1 answer:
Rus_ich [418]2 years ago
7 0

Using a linear function, it is found that the product rs is rs = 81.

<h3>What is a linear function?</h3>

A linear function is modeled by:

y = mx + b

In which:

  • m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.
  • b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.

In this problem, when x changes by 68(from -64 to 68), y changes by -16(from 12 to -4), hence the slope is given by:

m = -16/64 = -0.25.

Hence:

y = -0.25x + b.

When x = 34, y = -4, hence this is used to find b.

-4 = -0.25(34) + b

b = 4.5.

Hence the function is:

y = -0.25x + 4.5.

f(r) = 0, hence:

-0.25x + 4.5 = 0

x = 4.5/0.25

x = 18

r = 18.

f (0) = s, hence s = 4.5.

Then the value of the product is:

rs = 18 x 4.5 = 81.

More can be learned about linear functions at brainly.com/question/24808124

#SPJ1

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Answer:

50

Step-by-step explanation:

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andre [41]

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3 years ago
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The diagonal of a rectangle is 25 in. The width is 15 in. What is the area of the rectangle?
Nana76 [90]

Answer:

375 in² is the answer.

Step-by-step explanation:

Are of rectangle= area of 2 triangle

= 1/2*25*15+1/2*25*15

=187.5+187.5

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7 0
2 years ago
Identify the factors of x2 − 4x − 21. (x − 7)(x 3) (x 7)(x − 3) (x 21)(x − 1) (x − 21)(x 1)
Tanzania [10]

The factors of the quadratic expression x² - 4x - 21 is <u>(x - 7)(x + 3)</u>, making the <u>first option</u> the right choice.

A quadratic expression is of the form ax² + bx + c, which can be factorized using the mid-term factorization method, where b is shown as the sum or difference of two such numbers, whose product is equal to the product of a and c.

In the question, we are asked to factorize the quadratic expression, x² - 4x - 21.

In the given expression, a = 1, b = -4, and c = -21.

Thus, ac = -21.

The numbers having a product 21 are:

1*21 = 21,

3*7 = 21.

Since, 3 - 7 = -4 (That is b), we break b into 3 and -7.

Thus, the expression can now be shown as:

x² - 4x - 21

= x² + (3 - 7)x - 21

= x² + 3x - 7x - 21

= x(x + 3) - 7(x + 3) {By taking common}

= (x - 7)(x + 3) {By taking common}.

Thus, the factors of the quadratic expression x² - 4x - 21 is <u>(x - 7)(x + 3)</u>, making the <u>first option</u> the right choice.

Learn more about factorizing a quadratic expression at

brainly.com/question/52959

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5 0
1 year ago
Need help #14 <br> The center of the circle is (0,-8). The radius is 9.
Shtirlitz [24]
X^2+ (y+8)^2 = 81.....this is C.
X^2 + y^2 + 16y +64=81 so x^2 + y^2 + 16y = 17.....this is D.

So I’d say C and D are correct
3 0
3 years ago
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