What is the median of 1,1,2,3,4,7,8,8

If 5a+4b=25 and 3a-8b=41, solve for a And b

I am Lyosha [343]

Answer:

a = 7

b = − 5 /2

Let's solve your system by substitution.

5a+4b=25 and 3a−8b=41

Rewrite equations:

5a+4b=25;3a−8b=41

Step: Solve5a+4b=25for a:

5a+4b=25

5a+4b+−4b=25+−4b(Add -4b to both sides)

5a=−4b+25

5a = −4b+25

5 a/5 = −4b+25 /5

(Divide both sides by 5)

a= −4 /5 b +5

Step: Substitute

−4 /5 b+5 for a in 3a−8b=41:

3a−8b=41

3( −4 /5 b+5)−8b=41

−52 /5 b+15=41 (Simplify both sides of the equation)

−52 /5 b+15+−15=41+−15 (Add -15 to both sides)

−52 /5 b=26

−52 /5 b /−52 /5 = 26 /−52 /5

(Divide both sides by (-52)/5)

b= −5 /2

Step: Substitute −5 /2 for b in a= −4 /5 b+5:

a= −4 /5 b+5

a= −4 /5 ( −5/ 2 )+5

a=7 (Simplify both sides of the equation)

8 0

3 years ago

A polynomial f(x) has the given zeros of 7-1, and-3

Dmitry_Shevchenko [17]

The polynomial f(x) in expanded form is $f(x) = x^3 - 3x^2 - 25x - 21$

<h3>The polynomial f(x)</h3>

The polynomial zeros are given as:

x = 7, x = -1 and x = -3

Rewrite as:

x - 7 = 0, x + 1 = 0 and x + 3 = 0

Multiply the zeros

f(x) = (x - 7)(x + 1)(x + 3)

Expand

$f(x) = (x - 7)(x^2 + 4x + 3)$

Further, expand

$f(x) = x^3 + 4x^2 - 7x^2 + 3x - 28x - 21$

Evaluate

$f(x) = x^3 - 3x^2 - 25x - 21$

Hence, the polynomial f(x) in expanded form is $f(x) = x^3 - 3x^2 - 25x - 21$

<h3>Rational function g(x)</h3>

We have:

$g(x) = \frac{f(x)}{x^2 - x- 2}$

This gives

$g(x) = \frac{x^3 - 3x^2 - 25x - 21}{x^2 - x- 2}$

Expand the numerator

$g(x) = \frac{x^3 - x^2 - 2x^2 - 2x + 2x - 25x + 4 - 25}{x^2 - x - 2}$

Rewrite as:

$g(x) = \frac{x^3 - x^2 - 2x - 2x^2 + 2x + 4 - 25x - 25}{x^2 - x - 2}$

Factorize

$g(x) = \frac{(x - 2)(x^2 - x- 2) - 25x - 25}{x^2 - x- 2}$

Evaluate the quotient

$g(x) = x - 2 - \frac{25x + 25}{x^2 - x- 2}$

The slant asymptote is the quotient i.e. x - 2

Hence, the slant asymptote of the function g(x) is x - 2

<h3>The discontinuities of g(x)</h3>

In (b), we have:

$g(x) = \frac{x^3 - 3x^2 - 25x - 21}{x^2 - x- 2}$

Set the denominator to 0

$x^2 - x - 2 = 0$

Expand

$x^2 + x - 2x - 2 = 0$

Factorize

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

Factor our x + 1

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

Solve for x

x = 2 or x = -1

2 is greater than -1.

So, the discontinuities and their types are:

Essential discontinuity at x = 2
Removable discontinuity at x = -1

Read more about polynomials at:

brainly.com/question/4142886

#SPJ1

7 0

2 years ago

the difference of twice a number and five is three. find the number. translate the word problem to an equation. which steps desc

marusya05 [52]

Answer:

The number is 4.

The step describe to solve the problem is: add five and then multiply by $\frac{1}{2}$

Step-by-step explanation:

Let the number be x.

As per the given condition as:

The difference of twice a number and five is three.

"Twice a number" means $2x$

"difference of twice a number and five" means $2x -5$

therefore, the translation of the given word problem to an equation is:

$2x-5 =3$

Now, solve the equation : $2x-5 =3$

Addition Property of equality states that you add the same number to both sides of an equation.

Add 5 to both sides of an equation we get;

2x-5+5=3+5

Simplify:

2x = 8

Multiplication property of equality states that you multiply the same number to both sides of an equation.

Multiply by $\frac{1}{2}$ both sides we get;

$2x \times \frac{1}{2} = 8 \times \frac{1}{2}$

Simplify:

x = 4

The steps which describe to solve the problem is: add five and then multiply by $\frac{1}{2}$

Therefore, the number x = 4

8 0

4 years ago

Read 2 more answers

Write the following numbers in increasing order (list the smallest as #1 and the largest as #5)

Talja [164]

Answer:

Square root of 18

4.7

square root of 24

square root of 36

7

Step-by-step explanation:

4 0

3 years ago

Solve 1/x = x - 1<br><br> What is special about the positive solution?

Basile [38]

1 = x^2 - x
x^2-x-1=0
quadratic formula:
$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} = \frac{-1 \pm \sqrt{1^2 - 4(1)(-1)}}{2} = \frac{-1 \pm \sqrt5}{2}$
the positive root is special because it's equal to the golden ratio

7 0

3 years ago