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Dovator [93]
3 years ago
15

Use long division to rewrite the following expression (18x^2+5x+5)/(6x^2-4x+1)

Mathematics
1 answer:
Lemur [1.5K]3 years ago
3 0
Answer is 3.
remainder is 17x+2
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Find the domain of f(x) = Square 3 x + 8 ​
vagabundo [1.1K]

The question is a bit ambiguous: you may mean

\sqrt{3x+8}

or

\sqrt{3x}+8

Anyway, in both cases, the domain of a function involving a square root is found by imposing the content of the root to be greateer than or equal to zero. So, in the first case you have

3x+8\geq 0 \iff 3x\geq -8 \iff x\geq -\dfrac{8}{3}

In the second case, you have

3x\geq 0 \iff x\geq 0

6 0
3 years ago
Write y=x^2+16x−7​ in vertex form. Then identify the vertex.
WARRIOR [948]

The vertex form of the function is y = (x + 8)² - 71

The vertex is (-8 , -71)

Step-by-step explanation:

The vertex form of the quadratic equation y = ax² + bx + c is

y = a(x - h)² + k, where

  • (h , k) are the coordinates of the vertex point
  • a, b, c are constant where a is the leading coefficient of the function (coefficient of x²) , b is the coefficient of x and c is the y-intercept
  • h=\frac{-b}{2a}
  • k is the value of y when x = h

∵ y = x² + 16x - 7

∵ y = ax² + bx + c

∴ a = 1 , b = 16 , c  = -7

∵ h=\frac{-b}{2a}

∴ h=\frac{-16}{2(1)}

∴ h = -8

To find k substitute y by k and x by -8 in the equation above

∵ k is the value of y when x = h

∵ h = -8

∴ k = (-8)² + 16(-8) - 7 = -71

∵ The vertex form of the quadratic equation is y = a(x - h)² + k

∵ a = 1 , h = -8 , k = -71

∴ y = (1)(x - (-8))² + (-71)

∴ y = (x + 8)² - 71

∵ (h , k) are the coordinates of the vertex point

∵ h = -8 and k = -71

∴ The vertex is (-8 , -71)

The vertex form of the function is y = (x + 8)² - 71

The vertex is (-8 , -71)

Learn more:

You can learn more about quadratic equation in brainly.com/question/9390381

#LearnwithBrainly

4 0
3 years ago
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I can read a 336-page book in 6 hours. Jayne can read a 144-page book in 3 hours. If I start reading a 5000-page book at noon an
dimulka [17.4K]

Answer:

12:00 am midnight

Step-by-step explanation:

Given;

I can read a 336-page book in 6 hours.

My rate r1 = 336/6 pages per hour = 56 pages per hour

Jayne can read a 144-page book in 3 hours.

Jayne rate r2 = 144/3 = 48 pages per hour

If I start reading a 5000-page book at noon and Jayne starts reading the same book at 10 AM

Taking 10 am as the reference time.

Let x represent the time from 10 am at which they would both be on the same page.

For me;

Since i started by noon; 2 hours after 10 am

Time t1 = x-2

For Jayne;

She started by 10 am

Time t2 = x

For them to be on the same page they must have read the same number of pages;

Number of pages read = rate × time

r1(t1) = r2(t2)

Substituting the values;

56(x-2) = 48(x)

56x - 112 = 48x

x(56-48) = 112

x = 112/(56-48)

x = 14 hours

Since 10 am is the reference, the time would be;

=10 am + x = 10 am + 14 hours

= 24:00

= 12:00 am midnight

8 0
3 years ago
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