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3 years ago

Use a table to find two consecutive integers between which the solution lies.

Mathematics

1 answer:

jolli1 [7]3 years ago

4 0

Answer:

-5 and -4

Step-by-step explanation:

It is far easier just to solve the equation than to determine appropriate integer bounds on the solution.

In the attachment, we show a couple of initial trials at solutions. The nearness of y=5 to being correct suggests that the next higher integer may be helpful, too. It is.

We find -4 and -5 to bracket the solution.

_____

The actual solution is (3.4 -1.3)/-0.5 = -4.2.

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Factorise 9w² - 100

ohaa [14]

Answer:

$9\, w^{2} - 100 = (3\, w - 10) \, (3\, w + 10)$ .

Step-by-step explanation:

Fact:

$\begin{aligned} & (a - b)\, (a + b)\\ =\; & a^{2} + a\, b - a\, b - b^{2} \\ =\; & a^{2} - b^{2} \end{aligned}$ .

In other words, $(a^{2} - b^{2})$ , the difference of two squares in the form $a^{2}$ and $b^{2}$ , could be factorized into $(a - b)\, (a + b)$ .

In this question, the expression $(9\, w^{2} - 100)$ is the difference between two terms: $9\, w^{2}$ and $100$ .

$9\, w^{2}$ is the square of $3\, w$ . That is: $(3\, w)^{2} = 9\, w^{2}$ .
On the other hand, $10^{2} = 100$ .

Hence:

$9\, w^{2} - 100 = (3\, w)^{2} - (10)^{2}$ .

Apply the fact that $a^{2} - b^{2} = (a - b) \, (a + b)$ to factorize this expression. (In this case, $a = 3\, w$ whereas $b = 10$ .)

$\begin{aligned}& 9\, w^{2} - 100 \\ =\; & (3\, w)^{2} - (10)^{2} \\ = \; & (3\, w - 10)\, (3\, w + 10)\end{aligned}$ .

8 0

2 years ago

Solve the system of equations given . -2x+5y=-3

algol13

For this case we have the following system of equations:

$-2x + 5y = -3\\y-15 = 3x$

We multiply the second equation by -5:

$-5y + 75 = -15x$

Now we add the equations:

$-2x-5y + 5y + 75 = -3-15x\\-2x + 75 = -3-15x\\-2x + 15x = -75-3\\13x = -78\\x = \frac {-78} {13}\\x = -6$

We find the value of the variable "y":

$y = 3x + 15\\y = 3 (-6) +15\\y = -18 + 15\\y = -3$

THE solution is: (-6, -3)

Answer:

(-6, -3)

3 0

3 years ago

You can upgrade lighting at your factory to LED bulbs that cost $6.95 each and last an average of 5 years. It costs S3 in labor

marshall27 [118]

Answer:

11.95 dollars

Step-by-step explanation:

Cost of one LED bulb = 6.95 dollars

Cost of changing one bulb = 3 dollars

Life of each bulb = 5 years.

In 10 years, only one time after 5 years the bulbs would have been changed

Hence cost of 100 lamps = 695 and

cost of changing once = 500

Total cost = 1195 dollars for 11 years

Divide this by 10 years to get average cost per year

Cost of 100 lamps per year = 1195/100 = 11.95 dollars

8 0

3 years ago

Solve log x - 2 = 3 A. 1 B. 100,000 C. 10,000 D. 10

ahrayia [7]

Answer: $100,000$

Step-by-step explanation:

Given :

$logx - 2 = 3$

add 2 to both sides

$log x = 5$

Therefore :

$x = 10^{5}$

$x = 100,000$

4 0

2 years ago

Question 3 of 5 How many solutions does 6 + = -5 - Lo have? 31 10 ? O A. One solution O B. Infinitely many solutions O C. Two so

GrogVix [38]

Answer:

En la Imagen adjunta

Step-by-step explanation:

Toca Para Abrir Imagen

Espero haberte ayudado si es así dame Corona

5 0

2 years ago

Read 2 more answers