All categories

2 years ago

The function f(x) = g(x), where f(x) = 2x – 5 and g(x) = x2 – 6.

Mathematics

1 answer:

den301095 [7]2 years ago

5 0

Answer:

$x=2.4$

Step-by-step explanation:

<u>Solving Equations Using Successive Approximations</u>

We need to find the solution to the equation

$f(x)=g(x)$

where

$f(x)=2x-5$

$g(x)=x^2-6$

The approximation has been already started and reached a state for x=2.5 where

$f(2.5)=0$

$g(2.5)=2.5^2-6=0.25$

The difference between the results is 0.25, we need further steps to reach a good solution (to the nearest tenth)

Let's test for x=2.4

$f(2.4)=-0.2$

$g(2.4)=2.4^2-6=-0.24$

The new difference is -0.2+0.24=0.04

It's accurate enough, thus the solution is

$\boxed{x=2.4}$

You might be interested in

Show the work of 6.2 +3.4

Musya8 [376]

Answer:

9.6

Step-by-step explanation:

When we are adding decimals we try 2 add them like normal integers, but in the end we add the decimal in the same place as it was in the beginning

so 62+34=96 and there's a decimal in the tenths place so its 9.6

8 0

2 years ago

Evaluate the logarithmic expression Log subscript5^25 +log subscript 5^625/logsubscript5^100. The value of the expression, round

Lady bird [3.3K]

Hello !
Here are some rules for logarithms :    log ₐ b = n ⇔ aⁿ = b
                                                             log ₐ aⁿ = n
                                                             log ₐ (b·c) = logₐ b + log ₐ c
                                                             log ₐ bⁿ = n· log ₐ b                                        ____________________________________________________
25=5²
625=5⁴
100 = 5² · 2²
____________________________________________________

(log₅ 25 + log₅ 625) / log₅100 =
(log₅ 5²+ log₅ 5⁴) / log₅ (5² · 2²) =
(log₅ 5²+ log₅ 5⁴) /( log₅ 5² + log₅ 2²) =
(2 + 4)/(2+log₅ 2² ) =
6/ (2+2·log₅2)=
6/2 + 6/ (2·log₅2) =

3+ 3/log₅2
log₅2 = 0.5

So 3+ 3/log₅2 = 3 + 3/0.5 =3 + 6 = 9

Answer : 9

3 0

2 years ago

10. The equation t 0.07c represents the tax, t, based on the cost, c, of an item. Which part of the equation represents the cons

motikmotik

The constant of proportionality stays the same no matter what values the variables take, so in our example independently of the cost of the item (and of the tax value, which is dependent on the cost value).

Here the only value that does not change is the 0.007, the rate! - this is the correct answer.

4 0

2 years ago

can a denominator be negative in literal equation? or should it be converted to positive, and change the numerator signs pls hel

Elis [28]

I don't think it really matters if the denominator is negative in a literal equation. Think about a simpler example with numbers. Does it matter whether a fraction is -1/2 or 1/-2? No, they are both the same. Therefore, I would say that the denominator of a literal equation can be negative.

Good luck with your exams!

4 0

2 years ago

Rounded to the nearest hundredth, what is the positive solution to the quadratic equation 0=2x2+3x-8? Quadratic formula: x =Star

zlopas [31]

Answer:

1.39

Step-by-step explanation:

According to the problem, calculation of the given data are as follows,

Given equation = 0=2x2+3x-8

Here, we use general formula of quadratic equation, then

$x = \frac{-b+-\sqrt{b^{2} - 4ac} }{2a}$

By taking the value by given equation,

a = 2, b = 3, c= -8

by putting the value in equation , we get

x = [- 3 ± √3^2 - 4(2 × -8)] ÷ 2×2

= [- 3 ± √73] ÷ 4

= [- 3 ± 8.544] ÷ 4

So, for positive solution, we get

x = (-3 + 8.544) ÷ 4

x = 1.386 or 1.39

3 0

2 years ago