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brilliants [131]

1 year ago

10

Which graph shows the solution of the inequality −|x − 2| + 9 > 6?

1 answer:

mariarad [96]1 year ago

4 0

answer is -1 < x < 5

-|x - 2|+ 9 > 6

Rearrange the terms

-|x - 2| > 6 - 9

-|x - 2| > - 3

then divide both sides of the inequality by the co- efficient of variable

|x - 2| < 3

convert the absolute inequality to standard inequality

-3 <x - 2 < 3

separate compound inequalities into system of inequality

{x - 2}> -3

{x - 2 < 3}

Rearrange variable to the left side of the equation

x > -3 + 2

calculate the sum or difference

x > -1

x -2 < 3

Rearrange variable to the left side of the equation

x < 3 + 2

calculate the sum or difference

x < 5

x > -1 and x < 5

Find intersection

-1 < x < 5

Equations and inequalities are both mathematical sentences formed by relating two expressions to each other. In an equation, the two expressions are deemed equal which is shown by the symbol =. Where as in an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.

learn more about inequality equation here :https://brainly.in/question/15934172

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A florist is arranging flowers in vases. There are 4 red flowers and 5 white flowers in every vase. The florist wants to make on

vichka [17]

There will be 72 flowers in total in the large arrangement.

Step-by-step explanation:

No. of red flowers in vase = 4

No. of white flowers in vase = 5

Ratio of red flowers to white flowers = 4:5

No. of red flowers in large arrangement = 32

No. of white flowers in large arrangement = w

Ratio of red flowers to white flowers = 32:w

Using proportion;

Ratio of red flowers to white flowers :: Ratio of red flowers to white flowers

$4:5::32:w$

Product of extreme = Product of mean

$4*w=32*5\\4w=160$

Dividing both sides by 4

$\frac{4w}{4}=\frac{160}{4}\\w=40$

Total flowers in large arrangement = Red flowers + white flowers

Total flowers in large arrangement = 32 + 40 =72

There will be 72 flowers in total in the large arrangement.

Keywords: ratio, proportion

Learn more about ratios at:

#LearnwithBrainly

5 0

3 years ago

What’s the slope?................

Orlov [11]

M = y2-y1/x2-x1
m = 7- (-2)/ -6-(-7)
m = 9/1

slope = 9

7 0

3 years ago

Evaluate the variable expression when a=-4, b=2, c=-3, and d =4. b-3a/bc^2-d

gtnhenbr [62]

Answer:

Therefore, the variable expression when a=-4, b=2, c=-3, and d =4 is

$\dfrac{b-3a}{bc^{2}-d}=1$

Step-by-step explanation:

Evaluate:

$\dfrac{b-3a}{bc^{2}-d}$

When a=-4, b=2, c=-3, and d =4

Solution:

Substitute, a=-4, b=2, c=-3, and d =4 in above expression we get

$\dfrac{b-3a}{bc^{2}-d}=\dfrac{2-3(-4)}{2(-3)^{2}-4}\\\\=\dfrac{2+12}{18-4}\\\\$

$\dfrac{b-3a}{bc^{2}-d}=\dfrac{14}{14}=1$

Therefore, the variable expression when a=-4, b=2, c=-3, and d =4 is

$\dfrac{b-3a}{bc^{2}-d}=1$

6 0

3 years ago

Brian irons 2/9 of his shirt in 3 3/5 minutes. At this rate, how much of his shirt does he iron each minute?

vodka [1.7K]

The speed for which Brian iron the shirts is given by:

$R = \frac{\frac{2}{9}}{3\frac{3}{5}}$

Rewriting we have:

$R = \frac{\frac{2}{9}}{\frac{18}{5}}$

$R = \frac{10}{162}$

Then, for each minute, we have the amount of ironed shirt is:

$(\frac{10}{162})(1) = \frac{10}{162}$

Answer:

At this rate, Brian plans 10/162 of his shirt.

8 0

3 years ago

Read 2 more answers

A rectangle with an area of 22 - 16.3 + 60 square units could have which possible dimensions?

Burka [1]

Answer:

wasdwasdwasdwasdadadasdasadwawdawwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwsssssssadwasdwa

Step-by-step explanation:

8 0

3 years ago