Solve x+5>−3 and −2x−5≤1 and write the solution in interval notation. If there is no solution, type ∅.

Answer:

x=-21/15

Step-by-step explanation:

3x-18-8x=-2+10x+5

-5x-18=10x+3

15x=-21

x=-21/15

Answer:

1)  A ∪ B =  {0, 1, 2, 3, 4, 5 ,6 ,9}

2)  A ∩ C = {0, 2}

3) A ∪ B ∪ C  = {0, 1, 2, 3, 4, 5, 6 7. 8. 9}

4)  A ∩ B ∩ C = {0}

Step-by-step explanation:

Definitions

Union of two or more sets is the set of elements in all of those sets with duplicates removed. The symbol used is ∪

Intersection of two or more sets is the set of elements common to those sets. Symbol ∩

1) A ∪ B = {0, 1, 2, 3, 4, 5} ∪  {0, 1, 5, 6, 9}  = {0, 1, 2, 3, 4, 5 ,6 ,9}

2) A ∩ C =  {0, 1, 2, 3, 4, 5} ∩  {0, 2, 6, 7, 8} = {0, 2}

3) A ∪ B U C = (AUB) ∪ C

=  {0, 1, 2, 3, 4, 5 ,6 ,9} U  {0, 2, 6, 7, 8} = {0, 1, 2, 3, 4, 5, 6 7. 8. 9}

4)  A ∩ B ∩ C​ =   {0, 1, 2, 3, 4, 5}   ∩   {0, 1, 5, 6, 9} ∩     {0, 2, 6, 7, 8}

= {0}

Answer:

1) A ∪ B = {0, 1, 2, 3, 4, 5, 6, 9}

2) A ∩ C = {0, 2}

3) A ∪ B ∪ C = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}

4) A ∩ B ∩ C​ = {0}

Step-by-step explanation:

Set Notation

[tex]\begin{array}{|c|c|l|} \cline{1-3} \sf Symbol & \sf N\:\!ame & \sf Meaning \\\cline{1-3} \{ \: \} & \sf Set & \sf A\:collection\:of\:elements\\\cline{1-3} \cup & \sf Union & \sf A \cup B=elements\:in\:A\:or\:B\:(or\:both)}\\\cline{1-3} \cap & \sf Intersection & \sf A \cap B=elements\: in \:both\: A \:and \:B} \\\cline{1-3} \sf ' \:or\: ^c & \sf Complement & \sf A'=elements\: not\: in\: A \\\cline{1-3} \sf - & \sf Difference & \sf A-B=elements \:in \:A \:but\: not\: in \:B}\\\cline{1-3} \end{array}[/tex]

Given sets:

Question 1

[tex]\begin{aligned}\sf A \cup B & =\sf \{ 0, 1, 2, 3, 4, 5 \} \cup \{0, 1, 5, 6, 9 \}\\& =\sf \{ 0, 1, 2, 3, 4, 5, 6, 9 \}\end{aligned}[/tex]

Question 2

[tex]\begin{aligned}\sf A \cap C& =\sf \{0, 1, 2, 3, 4, 5 \} \cap \{ 0, 2, 6, 7, 8 \}\\& =\sf \{0, 2 \}\end{aligned}[/tex]

Question 3

[tex]\begin{aligned}\sf A \cup B \cup C& =\sf \{ 0, 1, 2, 3, 4, 5 \} \cup \{0, 1, 5, 6, 9 \} \cup \{0, 2, 6, 7, 8 \}\\& =\sf \{ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 \}\end{aligned}[/tex]

Question 4

[tex]\begin{aligned}\sf A \cap B \cap C& =\sf \left(A \cap B\right) \cap \left(B \cap C\right) \\ & =\sf \left(\{ 0, 1, 2, 3, 4, 5 \} \cap \{0, 1, 5, 6, 9 \}\right) \cap \left(\{0, 1, 5, 6, 9 \} \cap \{0, 2, 6, 7, 8 \} \right)\\& =\sf \{ 0, 1, 5 \} \cap \{0, 6 \}\\ & = \sf \{ 0 \}\end{aligned}[/tex]

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38.7 hours would have passed until the trains are 580 miles apart

The given parameters are

Train 1 = 80 mph

Train 2 = 65 mph

The difference in the speeds of the trains is

d = 80mph - 65mph

Evaluate

d = 15mph

The distance moved is

Distance = 15 * t

At 580 miles apart, we have

15 * t = 580

Divide by 15

t = 38.7 hours

Hence, 38.7 hours would have passed until the trains are 580 miles apart

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Answer:

[tex] \sf \Large x=−5 [/tex]

Step-by-step explanation:

Let's solve your equation step-by-step.

8x+12=2x−18

Step 1: Subtract 2x from both sides.

8x+12−2x=2x−18−2x

6x+12=−18

Step 2: Subtract 12 from both sides.

6x+12−12=−18−12

6x=−30

Step 3: Divide both sides by 6.

6x/6 = −30/6

x=−5

Step-by-step explanation:

8x + 12 = 2x -18

8x - 2x = -18 - 12

6x = -30

6x/6 = -30÷6

x = - 5

Step-by-step explanation:

If rigid transformations can be used to map two shapes onto one another, they are said to be congruent (a sequence of one or more rotations, translations, and reflections). Any series of rigid transformations performed on a triangle results in a congruent triangle.

Let's now analyze rigid transformation.

An isometry, also known as a rigid transformation of the plane, preserves length. Reflections, translations, rotations, and combinations of these three transformations are all considered "rigid transformations".

Example: Congruent shapes include, for instance, the right angle triangle and its preimage.

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The length of diagonal GE is 89 units

What is a quadrilateral?

quadrilateral is a plane mathematical closed figure consist of four side and four edges. There are 7 types of quadrilateral.

Trapezium, Parallelogram, Rectangle, Rhombus, Square, Kite.

It is given that :

length of side EF = 39 units

and, DH = 44.5 units

It is known that :

Diagonals of a Rectangle

A rectangle has 2 congruent diagonals, that is the two diagonals are equal to each other.

The diagonals of a rectangle bisects each other into equal segments.

The diagonals of the rectangular room are:

DF and GE

Thus:

DF = GE

DH = 1/2(DF)

44.5 = 1/2(DF)

DF = 2(44.5)

DF = 89

Therefore :

DF = GE = 89

GE = 89 units

Thus,  The length of diagonal GE is 89 units.

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Answer:

Y = 3/7x-3

Step-by-step explanation:

I don't have an explanation other than the fact I put this into a calculator and this is what it gave me.

Step-by-step explanation:

total number of people are 40

take teach takeaway category and divide it by 40

eg)3÷40 / 11÷40

since there are 360⁰ in a circle, multiply your answer by 360 to get your angle

(3÷40)×360 = a

(11÷40)×360 = b

(9÷40)×360 = c

(2÷40)×360 = d

(15÷40)×360 = e

those are your angles. use a protractor to measure the angles

note : if all your angles add up to 360 the you've done everything correctly

Answer:  l=2w+3

Step-by-step explanation:

Answer:

37%

Step-by-step explanation

Reading the graph we see:

The percent of corn production is used for ethanol is 18%

The percent of corn production is used for exports is 19%

Answer the question:

The percent of corn production used for ethanol OR exports is the sum of the two 18%+19% = 37%

The point that represents an INEFFICIENT point of production is point A.

The correct answer is an option (a)

In this question we have been given a graph of Skateboards vs. Bikes.

We need to find the point that represents an INEFFICIENT point of production.

Inefficient production means the economy can be producing more goods without using any additional resources.

In given production possibility curve, an INEFFICIENT point of production is point A.

Therefore, the point that represents an INEFFICIENT point of production is point A.

The correct answer is an option (a)

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Answer:

Ahmm I guess it is

[tex] \frac{5}{16} \\ [/tex]

Step-by-step explanation:

Cuz I did like

[tex] \frac{20}{64} = \frac{20}{64} \div \frac{2}{2} = \frac{10}{32} = \frac{5}{16} \\ \\ \\ \\ \frac{20}{64} = \frac{20}{64} \div \frac{4}{4} = \frac{5}{16 \\ \\ \\ \\ \\ \\ } [/tex]

so I guess it's correct

Both [tex]f(x)[/tex] and [tex]g(x)[/tex] have real domains.

What is domain?

The domain is all x-values or function inputs, and the range is all y-values or function outputs. When looking at a graph, the domain is all of the graph's values from left to right. The range includes all of the graph's values from bottom to top.

Here, the options

(I) The domain of both [tex]f(x)[/tex] and [tex]g(x)[/tex] are all real numbers,

(II) The axis of symmetry of the graphs of both functions is [tex]x=0[/tex]

are correct.

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Answer:

When you have two negative signs, one turns over, and they integrate together to make a positive. If you have a positive and a negative, there is one dash left over, and the answer is negative.

The percentage of profit would be $1,377 if the dealer would have sold the car for $6,120.

So, we need to obtain 22.5% of $6,120.

Then,

Therefore, the percentage of profit would be $1,377 if the dealer would have sold the car for $6,120.

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Using dilation rules, the dilated triangle is given at the end of the answer. The coordinates of the vertices are as follows:

A'(-6,6), B'(-3,0), C'(3,6).

To dilate a figure by a factor of a, each coordinate of each vertex of the image is multiplied by a, that is, the following rule is applied:

(x,y) -> (ax, ay).

The coordinates of the vertices of ABC are given as follows:

A(-2,2), B(-1,0), C(1,2).

After a dilation with a scale factor of 3, the coordinates of the vertices of A'B'C' will be given as follows:

A'(-6,6), B'(-3,0), C'(3,6).

These coordinates are derived multiplying the coordinates of A, B and C by 3.

The image of the triangle is given at the graph at the end of the answer.

For the image of triangle DEF, each of the coordinates of D, E and F will be multiplied by -1/2 to generate the dilated triangle.

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Answer:

f(1)= -4

Step-by-step explanation:

o_o. .............>|||✓✓✓✓✓

Answer:

x = [tex]\frac{16}{41}[/tex]

y =[tex]\frac{102}{41}[/tex]

Step-by-step explanation:

To use elimination I need either the x terms to be inverses of each other or the y terms to be inverses of each other.  There are a number of ways to do this.  I am going to focus on the y's.  If I multiple the first equation through by 5 and the second equation through by 3.  I will make equivalent equations that will allow the y terms to be eliminated.

14x - 3y = -2

5(14x - 3y) =5(-2)

70x - 15y = -10

4x + 5y = 14

3(4x + 5y) = 3(14)

12x +15y =42

Add together the 2 bold equations above

70x - 15y = -10

12x + 15y = 42

82x          = 32  Divide both sides by 82

x = [tex]\frac{32}{82}[/tex] = [tex]\frac{16}{41}[/tex]

Plug this in either equation to solve for y

y = [tex]\frac{102}{41}[/tex]

The verdict on Adela's idea of retaining the same ratio by adding the same number to both coordinates of the point is that; Adela is incorrect.

It follows from the task content that, Adela claims that you can find an equivalent ratio by adding the same number to both coordinates of the point.

Adela's claim as indicated above is false because, if for instance, 2 is added to both coordinates, then we have; (9, 10).

And, since 9 : 10 is not equivalent to; 7: 8. Adela's claim is incorrect.

On the other hand, to retain the ratio, the coordinates should be multiplied by the same number. For instance by 3; so that we have;

21 : 24 which is equivalent to the ratio, 7 : 8.

The verdict on Adela's idea of retaining the same ratio by adding the same number to both coordinates of the point is that; Adela is incorrect

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Answer:

3 can be made.

Step-by-step explanation:

There are 64 fl. oz. in half gallon. Using 20 oz per recipe, 64 divided by 20 gives you 3.2.

If the income is $54730 and state tax rate is 3.5% then the amount of tax that Erica Matthews needs to pay is $1915.55.

Given that the income is $54730 and state tax rate is 3.5%.

We are required to find the amount of tax that Erica Matthews need to pay.

State Government is basically tax that is levied by state government on the people living in that state.State governments basically use taxpayer dollars to fund road maintenance, law enforcement agencies and other public services.

Income=$54730

Tax rate=3.5%

Tax=54730*3.5/100       (We assumed that full amount is taxable.)

=$1915.55

Hence if the income is $54730 and state tax rate is 3.5% then the amount of tax that Erica Matthews needs to pay is $1915.55.

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Answer:

you did it right!

Step-by-step explanation:

Answer: 47/70

Step-by-step explanation:

Starts with an A ==> 1 possibility out of 14 ==> 1/14

Ends with an even digit from 0-4:

Even digits: 0, 2, 4 ==> 3 possibilities out of 5 ==> 3/5

1/14 + 3/5=

(1/14 + 3/5)*70/70=    ==> get rid of different denominators

(1*70/14 + 3*70/5)/70=

(70/14 + 210/5)/70=

(5+42)/70=47/70

Yes , it is possible to fit a table 9 feet wide through a rectangular doorway 4 feet by 8.

A table with folded legs can pass through a rectangular door at an angle of 45°, forming a triangle to which the Pythagorean theorem can be applied.

Let the two sides of the door be the two sides of triangles a and b, then

        [tex]c^2=4^2+8^2\\c^2=16+64\\c^2=80\\c=8.94[/tex]

Conclusion: Using the Pythagorean theorem, we know that an 8.94 foot table can pass through the door. And we know that 8.94 ≈ 9  

Hence , a 9-feet table can pass through a rectangular door.

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Answer:

64.3738 km/h

Step-by-step explanation:

The area of the polygon is equal to 10.006 square units.

In this case we find a polygon with four vertices, that is, a tetragon, also called quadrilateral. By geometry we know that quadrilaterals can be armed by uniting two triangles and the area of a quadrilateral is equal to the areas of the two triangles. Hence, the polygon NPQR is the result of combining the triangles NPQ and NQR.

First, determine the lengths of the sides of the two triangles:

NP = √[[3 - (- 2)]² + (1 - 1)²]

NP = 5

PQ = √[(3 - 3)² + [1 - (- 1)]²]

PQ = 2

NQ = √[[3 - (- 2)]² + (- 1 - 1)²]

NQ = √29

NR = √[[- 2 - (- 2)]² + [- 1 - (- 1)]²]

NR = 2

QR = √[(- 2 - 3)² + [(- 1) - (- 1)]²]

QR = 5

Second, calculate the areas of the two triangle:

s₁ = 0.5 · (NP + PQ + NQ)

s₁ = 0.5 · (5 + 2 + √29)

s₁ ≈ 6.193

A₁ = √[s₁ · (s₁ - NP) · (s₁ - PQ) · (s₁ - NQ)]

A₁ = √[6.193 · (6.193 - 5) · (6.193 - 2) · (6.193 - √29)]

A₁ ≈ 5.003

s₂ = 0.5 · (NQ + NR + QR)

s₂ = 0.5 · (√29 + 2 + 5)

s₂ ≈ 6.193

A₂ = √[s₂ · (s₂ - NQ) · (s₂ - PQ) · (s₂ - QR)]

A₂ = √[6.193 · (6.193 - √29) · (6.193 - 2) · (6.193 - 5)]

A₂ ≈ 5.003

A = 5.003 + 5.003

A = 10.006

The area of the polygon is equal to 10.006 square units.

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[tex] \large \bf \implies{18 {x}^{ - 1} {y}^{ - 2}}[/tex]

[tex] \bf \longrightarrow(3 {x}^{ - 2}y)(6xy^{ - 3}) \\ \\ \bf \longrightarrow3 \times 6 \times {x}^{ - 2} \times {x}^{1} \times {y}^{1} \times {y}^{ - 3} \\ \\ \bf \longrightarrow18 {x}^{( - 2 + 1)}y^{(1 - 3)} \\ \\ \bf \longrightarrow \boxed{ 18 {x}^{ - 1}y^{ - 2}} \: ans.[/tex]