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WITCHER [35]
3 years ago
6

If y varies directly as x and inversely as z and y = 4 when x = 2 and z = 7, find y when x =

Mathematics
1 answer:
S_A_V [24]3 years ago
4 0

Answer:

y = 28

Step-by-step explanation:

Given that y varies directly as x and inversely as z then the equation relating them is

y = \frac{kx}{z} ← k is the constant of variation

To find k use the condition y = 4 when x = 2 and z = 7, then

4 = \frac{2k}{7} ( multiply both sides by 7 )

28 = 2k ( divide both sides by 2 )

14 = k

y = \frac{14x}{z} ← equation of variation

When x = 6 and z = 3 , then

y = \frac{14(6)}{3} = 14 × 2 = 28

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What is the oblique asymptote of the function f(x) = the quantity x squared minus 5x plus 6 over the quantity x minus 4?
Paraphin [41]

Answer:

x - 1

Step-by-step explanation:

We know that, a slant or oblique asymptote of a rational function is the asymptote that helps in determining the direction of the function.

It occurs when the polynomial in the numerator is a higher degree than the polynomial in the denominator.

Now, we divide the numerator by denominator using long division method and the first two terms in the quotient ( forming a linear function ) is the equation of the oblique asymptote.

We are given the rational function, f(x) = \frac{x^{2}-5x+6}{x-4}.

After dividing we get that, the quotient is x - 1.

Hence, the equation of the oblique asymptote is x-1.

4 0
3 years ago
Help again idk how to do this
creativ13 [48]

Answer:

it's,

( {5}^{3} ) ^{ - 4}  \\

Step-by-step explanation:

( {5}^{3} ) ^{ - 4}  \\  =  {5}^{ - 12}

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3 years ago
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Is x=5 the solution to the following equation? Show your work with the substitution property
guapka [62]

Answer:

yes

Step-by-step explanation:

2x-4=6

Let x = 5

2*5 - 4 = 6

10 -4 =6

6 = 6

Since this is true, x=5 is a solution to the equation

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3 years ago
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True or false: every point in quadrant III is mapped to a point in quadrant IV
strojnjashka [21]

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3 years ago
What is the solution to 3(–3x + 9) = −18?
Rus_ich [418]

Answer:

x = 5 (If solved algebraically)

No Solution (If the parentheses are absolute value lines)

Step-by-step explanation:

Result when solving this way: 3|-3x + 9| = -18

1) Divide both sides by 3
|-3x + 9| = -18/3

2) Simplify 18/3 to 6

|-3x + 9| = -6

3)  Break down the problem into these 2 equations.

-3x + 9 = -6

- (-3x + 9) = -6

4) Solve the 1st equation: -3x + 9 = -6

- Subtract 1 from both sides.

-3x = -6 - 9

-Simplify -6 - 9 to -15.

-3x = -15

-Divide both sides by -3.

x = -15/-3

- Two negatives make a positive.

x = 15/3

- Simplify 15/3 to 5.

x = 5

6)  Solve the 2nd equation:  - (-3x+ 9) = -6

1 - Remove parentheses

3x - 9 = -6

2 - Add 9 to both sides

3x = -6 + 9

3 - Simplify -6 + 9 to 3.

3x = 3

- Divide both sides by 3.

x = 1

6) Collect all solutions.

x = 1,5

7) Check solution.

When x = 1, the original equation 3|-3x + 9| = -18 does not hold true.

We will drop x = 1 from the solution set.

8) Check solution.

When x = 5, the original equation 3|-3x + 9| = -18  does not hold true.

We will drop x = 5 from the solution set.

9) Therefore,

No solution exists.

Result when solving algebraically:

Simplifying

3(-3x + 9) = -18

Reorder the terms:

3(9 + -3x) = -18

(9 * 3 + -3x * 3) = -18

(27 + -9x) = -18

Solving

27 + -9x = -18

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-27' to each side of the equation.

27 + -27 + -9x = -18 + -27

Combine like terms: 27 + -27 = 0

0 + -9x = -18 + -27

-9x = -18 + -27

Combine like terms: -18 + -27 = -45

-9x = -45

Divide each side by '-9'.

x = 5

Simplifying

x = 5

5 0
2 years ago
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