All categories

3 years ago

Using a table of values, determine the solution to the equation below to the nearest fourth of a unit.

Mathematics

2 answers:

Leto [7]3 years ago

8 0

2x-4=3-x +1
<span>Simplifying 2x + -4 = 3 + -1x + 1
Reorder the terms: -4 + 2x = 3 + -1x + 1
Reorder the terms: -4 + 2x = 3 + 1 + -1x
Combine like terms: 3 + 1 = 4 -4 + 2x = 4 + -1x
Solving -4 + 2x = 4 + -1x
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add 'x' to each side of the equation. -4 + 2x + x = 4 + -1x + x
Combine like terms: 2x + x = 3x -4 + 3x = 4 + -1x + x
Combine like terms: -1x + x = 0 -4 + 3x = 4 + 0 -4 + 3x = 4
Add '4' to each side of the equation. -4 + 4 + 3x = 4 + 4
Combine like terms: -4 + 4 = 0 0 + 3x = 4 + 4 3x = 4 + 4
Combine like terms: 4 + 4 = 8 3x = 8
Divide each side by '3'. x = 2.666666667
Simplifying x = 2.666666667</span>

Viefleur [7K]3 years ago

3 0

Answer:

The solution of the given equation is $x\approx 2.5$ .

Step-by-step explanation:

The given equation is

$2x-4=3^{-x}+1$

Write the equation in system of questions.

$f(x)=2x-4$

$g(x)=3^{-x}+1$

The table of values is

x values f(x) g(x)

0 -4 2

1 -2 1.33

2 0 1.11

3 2 1.037

4 4 1.0123

In initial stage the value of f(x)<g(x) upto x=2. But after x=3, f(x)>g(x). It means the value of x must be lie between 2 and 3.

From the below figure it is clear that the intersection point of both functions is (2.531, 1.062).

$x=2.531$

$x\approx 2.5$

Therefore the solution of the given equation is $x\approx 2.5$ .

You might be interested in

Which equation can be used to determine the distance between the origin and (–2, –4)?

OleMash [197]

Answer:its option a

Step-by-step explanation: the distance formula is y sub 1 minus y sub 2

And x sub 1 minus y sub 2

8 0

3 years ago

Read 2 more answers

Solve x2 + 6x + 7 = 0. (2 points)

Alexandra [31]

Option C: $$x=-3 \pm\sqrt{2}$

Solution:

Given equation is $x^{2}+6 x+7=0$ .

This is a quadratic equation.

Here a = 1, b = 6, c = 7

To solve the given equation by quadratic formula,

$$x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$

Substitute the given values in the quadratic formula, we get

$$x=\frac{-6 \pm \sqrt{6^{2}-4 (1) (7)}}{2 (1)}$

$$x=\frac{-6 \pm \sqrt{36-28}}{2 }$

$$x=\frac{-6 \pm \sqrt{8}}{2 }$

$$x=\frac{-6 \pm2 \sqrt{2}}{2 }$

$$x=\frac{2(-3 \pm\sqrt{2})}{2 }$

2 in the numerator and denominator are cancelled.

$$x=-3 \pm\sqrt{2}$

Option C is the correct answer.

8 0

3 years ago

"A cash drawer contains 29 bills, all twenties and fifties. If the total value of the bills is $820, how many twenties and how m

maks197457 [2]

Answer:

There are 21 twenties and 8 fifties in the drawer.

Step-by-step explanation:

This question can be solved by a system of equations.

I am going to say that:

x is the number of twenties

y is the number of fifties.

A cash drawer contains 29 bills.

This means that x + y = 29.

The total value of the bills is $820.

This means that 20x + 50y = 820.

x + y = 29

20x + 50y = 820

From the first equation, x = 29 - y. So:

20x + 50y = 820

20(29 - y) + 50y = 820

580 - 20y + 50y = 820

30y = 240

y = 8

And

x = 29 - y = 29 - 8 = 21

There are 21 twenties and 8 fifties.

3 0

4 years ago

Read 2 more answers

Because she has limited shelf space, she can't put out all her copies of the CD at once. On Monday morning, she stocked the disp

fenix001 [56]

Now, it look like there is some information missing in the answer. The whole problem should look like this:

Alicia Keys's new album As I Am is climbing the charts, and the manager of Tip Top Tunes expects to sell a lot of copies. Because she has limited shelf space, she can't put out all her copies of the CD at once. On Monday morning, she stocked the display with 40 copies. By the end of the day, some of the copies had been sold. On Tuesday morning, she counted the number of copies left and then added that many more to the shelf. In other words, she doubled the number that was left in the display. At the end of the day, she discovered that she had sold the exact same number of copies as had been sold on Monday. On Wednesday morning, the manager decided to triple the number of copies that had been left in the case after Tuesday. Amazingly, she sold the same number of copies on Wednesday as she had on each of the first two days! But this time, at the end of the day the display case was empty. How many copies of the As I Am CD did she sell each day?

Answer:

She sold 24 copies of the cd each day.

Step-by-step explanation:

In order to solve this problem we must first set our variable up. In this case, since we need to know what the number of sold cd's per day is, that will just be our variable:

x= Number of copies sold.

So we can start setting our equation up. So we take the first part of the problem:

"On Monday morning, she stocked the display with 40 copies. By the end of the day, some of the copies had been sold."

This can be translated as:

40-x

where this expression represents the number of copies left on the shelf by the end of monday.

"On Tuesday morning, she counted the number of copies left and then added that many more to the shelf."

so we represent it like this:

(40-x)+(40-x)

"In other words, she doubled the number that was left in the display."

so the previous expression can be simplified like this:

2(40-x)

"At the end of the day, she discovered that she had sold the exact same number of copies as had been sold on Monday."

so the expression now turns to:

2(40-x)-x this is the number of copies left by the end of tuesday.

"On Wednesday morning, the manager decided to triple the number of copies that had been left in the case after Tuesday."

this translates to:

3[2(40-x)-x]

This is the number of copies on the shelf by the begining of Wednesday.

"Amazingly, she sold the same number of copies on Wednesday as she had on each of the first two days! But this time, at the end of the day the display case was empty."

this piece of information lets us finish writting our equation:

3[2(40-x)-x] -x = 0

since there were no copies left on the shelf, then the equation is equal to zero.

So now we proceed and solve the equation for x:

3[2(40-x)-x] -x = 0

We simplify it from the inside to the outside.

3[80-2x-x]-x=0

3[80-3x]-x = 0

we now distribute the 3 so we get:

240-9x-x=0

we combine like terms so we get:

240-10x=0

we move the 240 to the other side of the equation so we get:

-10x=-240

and divide both sides into -10 so we get:

x=24

so she sold 24 copies each day.

5 0

4 years ago

(brainliest) Mark's work to simplify (-3)(-5)(-2) is shown. Explain his error and show how to find the correct product.

denpristay [2]

Answer:

The error with mark’s work is that a negative times a negative will give a positive. So -3 times -5 is +15 not -15. Then 15 times -2 will get you -30.

3 0

3 years ago

Read 2 more answers