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3 years ago

Question 1/8

Mathematics

1 answer:

just olya [345]3 years ago

5 0

Answer:

discount = 290 × 1

= 72.50

new price is

290.00

72.50 -

217.50

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Consider a function f(x) such that f(5x) =x-5/5x-1. Find f(x) and hence write down the domain of f(x).

nasty-shy [4]

Answer:

$f(x) = \frac{x - 25}{5x - 5}$

Domain: $x \ne 1$

Step-by-step explanation:

Given

$f(5x) = \frac{x - 5}{5x - 1}$

Required

Determine f(x) and its domain

To determine f(x), we replace 5x with x in f(5x)

So, we have:

$f(5x) = \frac{\frac{5x}{5} - 5}{5x - 1}$

$f(x) = \frac{\frac{x}{5} - 5}{x - 1}$

Take LCM

$f(x) = \frac{\frac{x - 25}{5}}{x - 1}$

$f(x) = \frac{x - 25}{5} * \frac{1}{x-1}$

$f(x) = \frac{x - 25}{5x - 5}$

To get the domain, we set the denominator as

$5x - 5 \ne 0$

$5x \ne 5$

$x \ne 1$

4 0

3 years ago

What is 4/15 / -3.4

seraphim [82]

Answer:

Factor the numerator and denominator and cancel the common facotors which would give you 0.07843137

4 0

3 years ago

Sarah Wiggum would like to make a single investment and have $1.7 million at the time of her retirement in 34 years. She has

vovangra [49]

Answer:

Sarah has to invest $502,958.58 today.

Step-by-step explanation:

This is a simple interest problem.

The simple interest formula is given by:

$E = P*I*t$

In which E is the amount of interest earned, P is the principal(the initial amount of money), I is the interest rate(yearly, as a decimal) and t is the time.

After t years, the total amount of money is:

$T = E + P$

In this question:

$t = 35, I = 0.07, T = 1700000$

She has to invest P today.

$T = E + P$

$1700000 = E + P$

$E = 1700000 - P$

$E = P*I*t$

$1700000 - P = P*0.07*34$

$3.38P = 1700000$

$P = \frac{1700000}{3.38}$

$P = 502958.58$

Sarah has to invest $502,958.58 today.

8 0

3 years ago

The solution to the system is (6,2) Select all the equations that could be the other equation in the system. PLZ HELPPPPPP there

Dovator [93]

9514 1404 393

Answer:

A, C

Step-by-step explanation:

The attached graph shows which lines go through the given point. They are ...

y = 1/2x -1 . . . . 1st selection

y = -1/6x +3 . . . 3rd selection

The equations can be found algebraically by substituting the given point in the equation and seeing if the result is a true statement.

a) 2 = (1/2)(6) -1 = 3 -1 . . . true

b) 2 = -3(6) . . . . false

c) 2 = -1/6(6) +3 = -1 +3 . . . true

d) 2 = 2/3(6) -1 = 4 -1 . . . . false

e) 2 = 4(6) -2 = 24 -2 . . . . false

f) 2 = -3/2(6) +6 = -9 +6 . . . . false

6 0

3 years ago

Help pls with math lotsss of points!!!

sveticcg [70]

Answer:

5x^2+22x-12 x cannot be -5, -4, -2

(x+5)(x+4)(x+2)

Step-by-step explanation:

In order to solve this, your denominator must be the same. Let's start by writing out the two different quadratic formulas:

x^2 + 6x + 8 <-- This should factor out to (x+4)(x+2)

x^2 + 7x + 10 <-- This should factor out to (x+5)(x+2)

Now that you have factored out the two quadratics, plug them into the equation.

5x - 3

(x+4)(x+2) (x+5)(x+2)

Now as we know, -2 cannot be x because it will turn the entire equation undefined. Multiple top and bottom with (x+5) on the right side and (x+4) on the left side.

5x (x+5) - 3(x+4)

(x+5)(x+4)(x+2) (x+5)(x+4)(x+2)

Focus on the top. 5x(x+5) will turn out to be 5x^2+25x. 3(x+4) will turn out to be 3x+12. Combine the two equations because now they are equal to each other and do the subtraction:

5x^2+25x - (3x+12) = 5x^2+22x-12 x cannot be -5, -4, -2

(x+5)(x+4)(x+2) (x+5)(x+4)(x+2)

4 0

2 years ago