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3 years ago

Which compound sentence has its solution set shown on the graph below

Mathematics

1 answer:

musickatia [10]3 years ago

8 0

A compound inequality is a sentence with two inequality statements joined either by the word “or” or by the word “and.” “And” indicates that both statements of the compound sentence are true at the same time.

“Or” indicates that, as long as either statement is true, the entire compound sentence is true.

Now as shown in the graph, the solution inequality of the graph is :

x > 3 and x < 5 [please note, circles in the graph indicate exclusion, dots indicate inclusion. in the graph given circles are shown, so it depicts exclusion]

Now let's solve each option to find if it fits in with the above inequality

Option 1 : 2x-4 > 6 or 3x < 9

⇒ x > 5 or x < 3

Option 2 : 2x - 4 < 6 and 3x > 9

⇒ x < 5 and x > 3

Option 3 : 3x + 8 > -7 or -4x < 12

⇒ 3x > -15 or x < -3

⇒ x > -5 or x < -3

Option 4 : 3x + 8 < -7 and -4x > 12

⇒ 3x < -15 and x > -3

⇒ x < -5 and x > -3

So the compound sentence in option 2 : 2x - 4 < 6 and 3x > 9

has its solution set on the graph.

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If 50 grams of a radioactive substance decomposed to 42 grams in 2 years, then, to the nearest gram, the amount left after 5 yea

Inga [223]

Answer:

30 grams

Step-by-step explanation:

50-42=8

8÷2=4

4=1 year

5×4=20

50-20=30

Hope u can understant

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3 years ago

Here are two expressions whose product is a new expression, :

Vera_Pavlovna [14]

Answer:

1. Fill in the box with 1

2. Fill in the box with -2

Step-by-step explanation:

Expression:

$(-2x^3 + [\ ]x)(x^{[\ ]}+1.5) = A$

Solving (1): Fill in the box to make it a polynomial.

To make it a polynomial, we simply fill in the box with a positive integer (say 1)

Fill in the box with 1

$(-2x^3 + [1]x)(x^{[1]}+1.5) = A$

Remove the square brackets

$(-2x^3 + x)(x^1+1.5) = A$

$(-2x^3 + x)(x+1.5) = A$

Open bracket

$-2x^4 - 3x^3 + x^2 + 1.5x = A$

Reorder

$A = -2x^4 - 3x^3 + x^2 + 1.5x$

The above expression is a polynomial.

This will work for any positive integer filled in the box

Solving (2): Fill in the box to make it not a polynomial.

The powers of a polynomial are greater than or equal to 0.

So, when the boxes are filled with a negative integer (say -2), the expression will cease to be a polynomial

Fill in the box with -2

$(-2x^3 + [-2]x)(x^{[-2]}+1.5) = A$

Remove the square brackets

$(-2x^3 - 2x)(x^{-2}+1.5) = A$

Reorder

$A = (-2x^3 - 2x)(x^{-2}+1.5)$

Open brackets

$A = -2x-3x^3-2x^{-1}-3x$

Collect Like Terms

$A = -3x^3-2x-3x-2x^{-1}$

$A = -3x^3-5x-2x^{-1}$

Notice that the least power of x is -1.

Hence, this is not a polynomial.

3 0

3 years ago

Ava and Kelly ran a road race, starting from the same place at the same time. Ava ran at an average speed of 6 miles per hour. K

zalisa [80]

<h2>Hello!</h2>

The answer is:

It will took 0.375 hours for Ava and Kelly to be 3/4 miles apart.

To calculate how long after they start they will be 3/4 miles apart, we need to write two equations.

So, writing the equations, we have:

Calculations for Ava:

We have the following information,

$v_{Ava}=6mph$

Then, writing the equation,

$x_{Ava}=x_{o}+v_{Ava}*t$

$x_{Ava}=x_{o}+v_{6mph}*t$

Calculations for Kelly:

We have the following information,

$v_{Kelly}=8mph$

We need to calculate when Kelly will be 3/4 miles apart of Ava, so, it's position will be the Ava's position plus 3/4 miles.

Then, writing the equation,

$x_{Ava}+0.75miles=x_{o}+v_{Kelly}*t$

$x_{Ava}+0.75miles=x_{o}+v_{8mph}*t$

Now, substituting Ava's speed into the second equation, we have:

$x_{o}+6mph*t+0.75miles=x_{o}+8mph*t$

$6mph*t+0.75miles=+8mph*t$

$8mph*t-6mph*t=0.75miles$

$2mph*t=0.75miles$

$t=\frac{0.75miles}{2mph}=0.375hours$

Hence, we have that it will took 0.375 hours for Ava and Kelly to be 3/4 miles apart.

Have a nice day!

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