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3 years ago

10 points HELP ASAP PLEASE AND THANK YOU!!

Mathematics

2 answers:

BARSIC [14]3 years ago

8 0

x=3

multiply 2 to both sides to cancel denominator

subtract 8x from both sides and then divide by 2

iogann1982 [59]3 years ago

6 0

$\dfrac{6+8x}{2}=5x\\\\\dfrac{6}{2}+\dfrac{8x}{2}=5x\\\\3+4x=5x\qquad|\text{subtract 4x from both sides}\\\\3=x\to x=3$

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Yolanda wanted to see if there was a connection between red hair and green eyes. She observed people walking past her on the str

Nutka1998 [239]

Given the frequency table on the relationship between red hair and green eyes.
 Green Eyes Eye Color other than Green Total
Red Hair 18 29 47

Hair Color
other than 114 650 764
Red

Total 132 679 811

The relative frequency table is obtained from a frequency table by dividing each entry of the requency table by the overall total of the frequency table.

The relative frequency table of the frequency table above is given below.
 Green Eyes Other Eye Color Total
Red Hair 18/811 = 0.02 = 2% 29/811 = 0.04 = 4% 47/811 = 0.06 = 6%

Other Hair
Color 114/811 = 0.14 = 14%|650/811 = 0.80 = 80%|764/811 = 0.94 = 94%

Total 132/811 = 0.16 = 16%|679/811 = 0.84 = 84%|811/811 = 1.0 = 100%

Given that x is the relative frequency of people that have other hair color and have green eyes, thus, the value of x is 14%.

Therefore, the value of x in the table = 14%.

8 0

3 years ago

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f x + y is rational, must x and y each be rational? A) Yes; because the sum of rationals is rational. B) No; because the sum of

Rudik [331]

The answer is D) Yes; because x and y must be integers, and integers are rational.

7 0

3 years ago

What is an equation of the line that passes through the point (- 5, - 6) and is parallel to the line 4x - 5y = 35

Elena L [17]

Answer:

4x - 5y = 10

Step-by-step explanation:

Any line parallel to 4x - 5y = 35 will have the same equation EXCEPT that the constant will be different.

Starting with 4x - 5y = 35, replace x with the given x-coordinate -5 and the given y-coordinate -6, and finally the given 35 with the constant C:

4(-5) - 5(-6) = C, or

-20 + 30 = C. Thus, C = 10, and the equation of the new line is

4x - 5y = 10

7 0

3 years ago

Resolve into partial fractions

lisabon 2012 [21]

Answer:

See below

Step-by-step explanation:

$\frac{11 + x}{(2 - x)(x - 3)} = \frac{A}{2 - x} + \frac{B}{x - 3} \\ \\ \therefore \: \frac{11 + x}{(2 - x)(x - 3)} = \frac{A(x - 3) +B(2 - x) }{(2 - x)(x - 3)} \\ \\ \therefore \: 11 + x = Ax - 3A + 2B - Bx \\ \\ \therefore \: 11 + x = - 3A + 2B + Ax - Bx\\ \\ \therefore \: 11 + x = - 3A + 2B + (A - B)x \\ \\ equating \: the \: like \: terms \: on \: both \: sides \\ A - B = 1 \\ \therefore \: A = B + 1.....(1) \\ \\ - 3A + 2B = 11....(2) \\ from \: eq \: (1) \: and \: (2) \\ - 3(B + 1) + + 2B = 11 \\ \\ - 3B - 3 + 2B = 11 \\ \\ - B = 11 + 3 \\ \\ B = - 14 \\ A = - 14 + 1 = - 13 \\ \\ \frac{11 + x}{(2 - x)(x - 3)} = \frac{ - 13}{2 - x} + \frac{ - 14}{x - 3} \\ \\ \frac{11 + x}{(2 - x)(x - 3)} = - \frac{ 13}{2 - x} - \frac{ 14}{x - 3}$

$\frac{12x + 11}{x^2 +x - 6}$

$=\frac{12x + 11}{x^2 +3x-2x - 6}$

$=\frac{12x + 11}{x(x +3) -2(x +3)}$

$\therefore \frac{12x + 11}{x^2 +x - 6}=\frac{12x + 11}{(x +3) (x - 2)}$

$\therefore \frac{12x + 11}{x^2 +x - 6}=\frac{A}{(x +3)}+\frac{B}{(x - 2)}$

$\therefore \frac{12x + 11}{x^2 +x - 6}=\frac{A(x-2)+B(x+3)}{(x-2)(x+3)}$

$\therefore 12x + 11 = A(x-2)+B(x+3)$

$\therefore 12x + 11 = Ax-2A+Bx+3B$

$\therefore 12x + 11 = Ax+Bx-2A+3B$

$\therefore 12x + 11 = (A+B) x-2A+3B$

Equating like terms on both sides:

$A + B = 12\implies A = 12-B... (1)$

$- 2A + 3B = 11... (2)$

Solving equations (1) & (2), we find:

A = 5, B = 7

$\therefore \frac{12x + 11}{x^2 +x - 6}=\frac{5}{(x +3)}+\frac{7}{(x - 2)}$

3 0

3 years ago

What is the range of the function f(x) = 3x2 + 6x – 8?

timama [110]

Answer:

Range is {y | y ≥ –11}

Step-by-step explanation:

This is quadratic equation.

A quadratic equation's range can be found if we find the vertex.

For quadratic equations that have a positive number in front of $x^{2}$ , it is upward opening and thus all the numbers greater than or equal to the minimum value of vertex is the range.

The formula for vertex of a parabola is:

Vertex = $(-\frac{b}{2a}, f(-\frac{b}{2a})$

Where,

$a$ is the coefficient of $x^{2}$
$b$ is the coefficient of $x$

From our equation given, $a=3$ and $b=6$

Now, $x$ coordinate of vertex is $x=-\frac{b}{2a}\\x=-\frac{6}{(2)(3)}\\x=-\frac{6}{6}\\x=-1$

$y$ coordinate of the vertex IS THE MINIMUM VALUE that we want. We get this by plugging in the $x$ value [ $x=-1$ ] into the equation. So we have:

$3(-1)^{2}+6(-1)-8\\=-11$

Hence, the range would be all numbers greater than or equal to $-11$

Third answer choice is the right one.

6 0

2 years ago

Read 2 more answers