Two trains leave the same station at the same time but are headed in opposite directions. One train travels at 80 mph and the other train travels at 65 mph. How much time passes until the trains are 580 miles apart?


__Hours.

Hank added 455.00 more to his bank account. The Total change in Hanks bank account is $455

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

We have been given that Hank, the owner of Hank's Hot Dog Hut, deposited $175 this morning from his late-night sales. In  afternoon, he deposited another $280 from lunch sales.

We need to Just add 175 and 280

175 + 280

455

Therefore, Hank added 455.00 more to his bank account.

Hence The Total change in Hanks bank account is $455

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The complete question is

Hank, the owner of Hank's Hot Dog Hut, deposited $175 this morning from his late-night sales. This afternoon, he deposited another $280 from lunch sales.

What was the total change in Hank's bank account relative to where it started?

Answer:

a= -0.8 and a= 0.8

Step-by-step explanation:

this questions wants u to find a perfect square for numbers if its difficult becuz of the decimals I suggest u move it and bring it back in your final answer

Step-by-step explanation:

180-28=152

152÷2=76

x=76°

Answer:

x=-21/15

Step-by-step explanation:

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

-5x-18=10x+3

15x=-21

x=-21/15

The final image is the same as Translate 5 units down, and then reflect over the y axis.

Transformation is the movement of a point from its initial location to a new location. Types of transformation are translation, reflection, rotation and dilation.

Translation is the movement of a point up, down, left or right.

Transformation is the movement of a point from its initial location to a new location.

The final image is the same as Translate 5 units down, and then reflect over the y axis.

Therefore the coordinates remains same as previous figure.

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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:

  y = {-1/4 for x < -3; +1/4 for x > -3}

  see attached for a graph

Step-by-step explanation:

You want the function y = |x+3|/(4x+12) written as a piecewise function and graphed.

The absolute value function resolves into two pieces, each with its own domain. These let you write the function as a piecewise function.

When (x+3) < 0, the absolute value function negates this value:

  y = -(x+3)/(4(x+3)) = -1/4 . . . . . for x < -3

When (x+3) ≥ 0, the absolute value function does nothing. That means the equation becomes ...

  y = (x +3)/(4(x +3))

When the denominator is zero, the function is undefined. When the denominator is not zero, the function becomes ...

  y = 1/4 . . . . . for x > -3

Then the definition of the piecewise function is ...

  [tex]y=\begin{cases}-\dfrac{1}{4},&x < -3\\\dfrac{1}{4},&x > -3\end{cases}[/tex]

The graph is attached.

Answer:

f(1)= -4

Step-by-step explanation:

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Answer: 10 ways

Step-by-step explanation:

5! / (3! * 2!)=

1*2*3*4*5/(1*2*3*1*2)=

4*5/(1*2)=

20/2=10 ways

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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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

Answer:  l=2w+3

Step-by-step explanation:

Answer:

[tex]\begin{pmatrix}6&-5\\ 0&-2\end{pmatrix}[/tex]

Step-by-step explanation:

[tex]2\begin{pmatrix}2&-3\\ 1&-1\end{pmatrix}=\begin{pmatrix}4&-6\\ 2&-2\end{pmatrix}[/tex]

[tex]\begin{pmatrix}4&-6\\ 2&-2\end{pmatrix}+\begin{pmatrix}2&1\\ -2&0\end{pmatrix}[/tex]=

[tex]\begin{pmatrix}6&-5\\ 0&-2\end{pmatrix}[/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:

64.3738 km/h

Step-by-step explanation:

Answer:

$19

Step-by-step explanation:

56x9=504

523-504=19

The quotient of a number and -5 increased by 7 os at minimum 1 is x ≤ 30.

Sometimes they will ask for a remainder or to find a quotient using the dividend and divisor values. Whatever they ask for, you can quickly discover the right answer if you know how to write it down or how to build the equation based on reading the question.

Here, we assume that the quotient of a number is x, and we first write the formula by deciphering the provided question.

The product of a number's ratio to -5 and 7 is

x/-5 + 7

This is at least one

x/-5 + 7 ≥ 1

Take 7 away from both sides.

x/-5 ≥ -6

Add -5 to both sides. Since this integer is negative, the inequality sign must be changed:

x ≤ 30

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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:

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.

[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]

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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Josh start at 0 on the number line and mark 6 parts that are each 0.20.The product (6 *0.20) represents the total cost which is $1.20 .

A number line is a representation of numbers on a line with the marks  placed at the line at equal intervals. This marks or scale of line can be chosen as per our requirement.

For example if we scale the number line such that  each mark is placed at  an interval of number 1 then number 4 will come at 4th mark as each mark is at 1 unit distance with each other .

Given that josh buys 6 pencils at the bookstore and each pencil is of $0.20

Thus, the total cost of pencils = 6 * 0.20 = 1.20

Now on the given number line the numbers starting from 0 and ending at 2.4 and each one is at 2/10=0.2 intervals

Total marks on the line = ( final - initial number )/(length of each interval)

                                      = ( 2.4-0) /(0.2) =12

To find at how many marks total cost would be placed = total cost / interval length = 1.2 / 0.2 = 6

Therefore, when we start from 0 and at 6 marks at this number line our number value will 1.20 that is our total cost.

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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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The cost of the each stamp is a 4$ and the 9$.

According to the statement

We have to find that the cost of the each stamp.

So, For this purpose, we know that the

The cost function can be used to find the average cost, which is the average amount of money it costs to produce a unit.

From the given information:

Neil needs to mail a USB drive to a friend. He uses 43-cent stamps and 8-cent stamps to pay $2.01 in postage.

Then

48x + 7y = 255

let the value of the two unknowns.

Then

If x = 1, then y = 29.57, which is not a whole number.

If x = 2, then y = 122.71, which is not a whole number.

If x = 3, then y = 15.86, which is not a whole number.

If x = 4, then y = 9, which a a whole number.  This is a solution

And we know that the answer will be in a whole number.

So, The cost of the each stamp is a 4$ and the 9$.

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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]

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 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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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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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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