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3 years ago

6

Why is it important to consider scale when graphing inequalities?

1 answer:

Olegator [25]3 years ago

6 0

Because to get a straight line you need a scale. Otherwise you will not be able to graph a straight line.

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Simplify and Evaluate

zalisa [80]

$\dfrac{2^{-1} + 5^{-1}}{10^{-1} - 5^{-2}} =$

$= \dfrac{\frac{1}{2} + \frac{1}{5}}{\frac{1}{10} - \frac{1}{5^2}}$

$=\dfrac{\frac{1}{2} + \frac{1}{5}}{\frac{1}{10} - \frac{1}{25}}$

$=\dfrac{\frac{5}{10} + \frac{2}{10}}{\frac{5}{50} - \frac{2}{50}}$

$=\dfrac{\frac{7}{10}}{\frac{3}{50}}$

$= \frac{7}{10} \times \frac{50}{3}$

$= \frac{7}{1} \times \frac{5}{3}$

$= \frac{35}{3}$

4 0

3 years ago

5 of what percent is 3.5

UNO [17]

If you take 3.5 and divide it by 0.05, or times 20, that would make it 70.

7 0

3 years ago

Read 2 more answers

Forty- two people attended s meeting about a zoning ordinance. Six more of the attendees voted in favor of the ordinance than th

kumpel [21]

Let the attendees in opposition be x. This means that the attendees in favour are x+6.
That means x+x+6=42, which is 2x+6=42, so 2x=36 and x=18. Therefore, there are 18 attendees who opposed it.

3 0

3 years ago

Solve x2 + 14x + 17 = –96 for x

jarptica [38.1K]

For this case we have to:

Given the quadratic equation of the form:

$ax ^ 2 + bx + c = 0$

The roots are given by:

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

If we have: $x ^ 2 + 14x + 17 = -96$

We can rewrite it in the following way:

$x ^ 2 + 14x + 17 + 96 = 0\\x ^ 2 + 14x + 113 = 0$

Where:

$a = 1\\b = 14\\c = 113$

Where we have:

$x = \frac {-14 \pm \sqrt {(14) ^ 2-4 (1) (113)}} {2 (1)}$

$x = \frac {-14 \pm \sqrt {(196-452)}} {2}$

$x = \frac {-14 \pm \sqrt {-256}} {2}$

By definition: $\sqrt {-1} = i$

$x = \frac {-14 \pm \sqrt {256} i} {2}$

$x = \frac {-14 \pm16i} {2}$

$x = \frac {-14} {2} \pm \frac {16i} {2}$

$x = -7 \pm8i$

Thus, the roots are given by imaginary numbers:

$x_ {1} = - 7 + 8i\\x_ {2} = - 7-8i$

Answer:

$x_ {1} = - 7 + 8i\\x_ {2} = - 7-8i$

5 0

3 years ago

Read 2 more answers

Given an arithmetic sequence with a3=5 and a5=19, find the 24th term.

krok68 [10]

The 24th term is 152

Step-by-step explanation:

The formula of the nth term of an arithmetic sequence is:

$a_n=a+(n-1)d$ , where

a is the first term
d is the common difference between consecutive terms

The third term means n = 3

∵ $a_3=a+(3-1)d$

∴ $a_3=a+2d$

∵ $a_3$ = 5

- Equate the right hand sides of the third term

∴ a + 2d = 5 ⇒ (1)

The fifth term means n = 5

∵ $a_5=a+(5-1)d$

∴ $a_5=a+4d$

∵ $a_5$ = 19

- Equate the right hand sides of the fifth term

∴ a + 4d = 19 ⇒ (2)

Now we have a system of equations to solve it

Subtract equation (1) from equation (2) to eliminate a

∴ 2d = 14

- Divide both sides by 2

∴ d = 7

- Substitute the value of d in equation (1) to find a

∵ a + 2(7) = 5

∴ a + 14 = 5

- Subtract 14 from both sides

∴ a = -9

The twenty fourth term means n = 24

∵ a = -9 and d = 7

- Substitute the values of a and d in the formula of the nth term

∴ $a_24=-9+(24-1)(7)$

∴ $a_24=-9+(23)(7)$

∴ $a_24=-9+161$

∴ $a_24=152$

The 24th term is 152

Learn more:

You can learn more about the arithmetic sequence in brainly.com/question/7221312

#LearnwithBrainly

5 0

3 years ago