Al drives from Boston to Washington D.C. and then returns. On his trip to Washington, he travels 60 miles per hour. On his return trip, he travels 50 miles per hour. His trip to Boston takes an hour and a half longer than his trip to Washington. How far apart are Washington and Boston? Make a equation

Answers

Answer 1
Equation: 1.5T +50=60
T is the Time in hours
Washington and Boston are 6.667 hours away.
Answer 2

The distance apart from Washington and Boston is 450 miles.

What is speed?

Speed is the ratio of distance and time.

It shows how fast an object is moving at a given time.

We have,

Trip from Boston to Washington:

Speed (2) = 60 miles per hour

Trip from Washington to Boston:

Speed (1) = 50 miles per hour

Speed = Distance / Time

Time = Distance / Speed

Distance is the same for both trips.

Time taken for the trip from Washington to Boston = t(1)

Time taken for the trip from Boston to Washington = t(2)

His trip to Boston takes an hour and a half longer than his trip to Washington.

This can be written as,

t(1) - t(2) = 1.5 hours

Distance ( 1/50 - 1/60) = 1.5

Distance (  (6 - 5)/300 ) = 1.5

Distance (1 / 300) = 1.5

Distance = 1.5 x 300

Distance = 450 miles

Thus,

The distance apart from Washington and Boston is 450 miles.

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Related Questions

For the following geometric sequence, find the recursive formula.
{-80, 20, -5, ...}

Answers

Divides by -4 throughout
common ratio/r=-1/4
ar^(n-1), where a is the first term
substitute all the numbers in it
-80(-1/4)^(n-1)

Answer:

[tex]a_n =-\frac{1}{4} \cdot a_{n-1}[/tex]

Step-by-step explanation:

{-80, 20, -5, ...}

General recusive formula for geometric sequence is

[tex]a_n = r \cdot a_{n-1}[/tex]

Where 'r' is the common ratio

To find common ratio 'r' we divide second term by first term

[tex]r=\frac{20}{-80} =-\frac{1}{4}[/tex]

Replace 'r' with -1/4

First term is -80

Recursive formula becomes

[tex]a_n =-\frac{1}{4} \cdot a_{n-1}[/tex]

Jordan makes 100 3-point shots per basketball practice. She makes 44 of these shots. What decimal represents the number of the shots she made?

Answers

100/44=0.44

0.44 is the answer
100/44=0.44

this is because she took 100 shots and made 44 of them in. the three doesn't matter because they never asked for the amount of points.

Rational Exponent
Explain why the square root of a number is defined to be equal to that number to the 1/2 power.

Answers

The concept of radicals and radical exponents is tricky at first, but makes sense when we look into the logic behind it. 

When we write a radical in exponential form, like writing √x as x^(1/2), we are simply putting the power of the radical in the denominator (bottom number) of the exponent, and the numerator is the power we raise the exponent to, or the power that would be inside the radical. 
In our example, √x is really ²√(x¹), or the square root of x to the first power. For this reason, we write it as x^(1/2).

Let's say we wanted to write the cubed root of x squared, in exponential form. 
In radical form, it would look like this:
³√(x²) . This means we square x, and then take the cubed root.
In exponential form, remember that we take the power of the radical (3), and make that the denominator of the exponent, and keep the numerator as the power that x is raised to (2). 
Therefore, it would be x^(2/3), or x to the 2 thirds power. 

Just like when multiplying by a fraction, you multiply by the numerator and divide by the denominator, in exponential form, you raise your base number to the power of the numerator, and take the root of the denominator. 

Answer:

Sample Response:

Squaring and square root are inverses, so one should "undo" the other. That is, squaring the square root of a number results in the number. Using the power of a power rule, you multiply the exponents. Since a number to the first power is itself, the product of the exponents must equal 1. This means that the power of the square root must be the reciprocal of 2, or one half.

Step-by-step explanation:


Find the y-intercept of the line whose equation is 2x - 3y = -6.

Answers

to find y intercept, make x = 0 then solve equation:

2x-3y=-6

2(0) - 3y=-6

-3y =-6

y = -6 / -3

y=2

 so y intercept is (0,2)

the answer to your problem is (2x-3y=12) good luck ;)

What is f(-4) if f(x)=|7x-3|

Answers

Substitute the given into the function

f(-4) = |7(-4) - 3|
now solve
f(-4) = |-28 - 3|
f(-4) = | -31| 
the absolute value of |-31| is 31
so, 
f(-4) = 31

Hope this helps :)
f(-4) means subsitute -4 for every x you see in the function

f(-4)=|(7(-4)-3|
f(-4)=|-28-3|
f(-4)=|-31|

|-31| means absolute value of -31 which just takes the distance the number is from 0 (or makes it positive if it is negative and leaves it alone if it is positive)

|-31|=31
f(-4)=31

Randy is twice as old as his sister jane. together the sum of their ages is 15. how old is randy?

Answers

Final answer:

Randy is 10 years old.

Explanation:

The question is about solving a simple algebraic equation involving ages.

We are told Randy is twice as old as his sister Jane, and the sum of their ages is 15 years.

If we let Jane's age be represented by 'j', then Randy's age would be '2j' as he is twice as old as Jane.

The equation to represent the sum of their ages is:

j + 2j = 15

To find Jane's age, we combine the like terms:

3j = 15

Now, we divide both sides of the equation by 3 to isolate 'j':

j = 15 / 3

j = 5

Therefore, Jane is 5 years old. To find Randy's age, we multiply Jane's age by 2:

Randy's age = 2 * Jane's age

Randy's age = 2 * 5

Randy's age = 10

So, Randy is 10 years old.

The following triangle FOX is transformed using a rotation: Triangle FOX is shown. F is at negative 1, 1, O is at negative 2, 3, X is at negative 3, 0. Which could be coordinates of F'O'X' after the rotation? (4 points)

Answers

I think it is 1,1,O but I don’t think you should believe me because I don’t know this very well

The answer is F=(1,1), O=(3,2), X=(0,3)

What is the slope is the x the top ordered pairs or the bottom !??? HELLPPP

Answers

These will always be (x,y) so the top is x=-2 and y=-2. Slope is the difference in y/x or (x-x)/(y-y) make sure you stay in order, first set () minus second set ().
[tex]\bf \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({{ -2}}\quad ,&{{ -2}})\quad % (c,d) &({{ 1}}\quad ,&{{ 1}}) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{1-(-2)}{1-(-2)}\implies \cfrac{1+2}{1+2} \\\\\\ \cfrac{3}{3}\implies 1[/tex]

Un número entero de tres dígitos es igual a 25 veces la suma de sus dígitos. Si los tres dígitos se invierten, el número que resulta excede al número dado por 198.
El dígito de las decenas en uno menos que la suma de los dígitos de las centenas y de las unidades. Encuentra el número.

Answers

La repuesta es 375,porque 3+7+5 es 15,y 15x25 es 375. Tambien el digito de las decenas es uno menos que la suma de los digitos de las centenas y de las unidades.

The sum of 6 consecutive odd numbers is 204. What is the fourth number in this sequence?

Answers

204 /6 = 34

29 +31 +33 + 35 +37 +39 = 207

4th number = 35

The fourth number is 35

Graph each equation by using the x- and y-intercepts

Answers

You have the correct graph. Plug in y = 0 and solve for x to get x = -3. Do the same for x = 0 and solve to get y = -3. 

x intercept = -3 which is the point (-3,0)
y intercept = -3 which is the point (0,-3)

Nice job on getting the correct graph with the correct points.

What number is 30% of 150?.

Answers

Here is your answer:

30% of 50=45

Your answer is 45 because...

150/x=100/30
(150/x)*x=(100/30)*x
150=3.33333333333*x
(3.33333333333) to get x
150/3.33333333333=x
45=x
x=45

Your answer is...
x=45

The expression below represents the number of bacteria in a petri dish after t hours.

Interpret the meaning of the expression.

A. The initial number of bacteria is 57, and the growth rate is 3.1% per hour.
B. The initial number of bacteria is 57, and the growth rate is 31% per hour.
C. The initial number of bacteria is 131, and the growth rate is 5.7% per hour.
D. The initial number of bacteria is 131, and the growth rate is 57% per hour.

Answers

Solving this problem requires the supplement of the actual expression. However I believe you forgot to include it with the question.

However I believe that the expression is in the form of:

y = A e^(-k t)

where,

y is the number of bacteria after time t

A is a constant and represents the initial number of bacteria

k is the growth rate in decimal form

t is time

 

So whatever is located in A is the initial number of bacteria, while k times 100% is the growth rate.

Answer:

A

Step-by-step explanation:

which of these ordered pairs is a solution to the inequality 4x+y>-6

Answers

The ordered pair is (1, -1) a solution to the inequality 4x+y>-6. which is the correct answer would be option (C).

What is inequality?

Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.

We must determine if the inequality holds for a certain set of ordered pairs in order to determine which ordered pairs constitute the answer to the inequality.

We have been given inequality is:

⇒ 4x + y > -6

Option (A) (1, -12)

⇒ 4x + y > -6

Substitute x = 1 and y = -12 in the inequality, we get

⇒ 4(1) + (-12) > -6

⇒ -8  > -6

This is false.

Option (B) (0, -9)

⇒ 4x + y > -6

Substitute x = 0 and y = -9 in the inequality, we get

⇒ 4(0) + (-9) > -6

⇒ -9  > -6

This is false.

Option (C) (1, -1)

⇒ 4x + y > -6

Substitute x = 1 and y = -12 in the inequality, we get

⇒ 4(1) + (-1) > -6

⇒ 3  > -6

This is true.

Hence, the correct answer would be an option (C).

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The sides of a triangle are in the ratio 5:12:13. Describe the length of the shortest side is the perimeter is not more than 120 inches

Answers

5,12,13 is a triple, i.e. integer values of a right triangle.  It's Perimeter is 30.
Then <= 120 yields 4 times this triple, yielding another triple of 20,48,52

Julie yard is rectangular.One side of the yard is 100 feet wide. The total area of the yard is 3,000 square feet. What is the length of the other side of the yard?

Answers

Area= length x width
Divide area by width to find missing side
3000➗100= 30
The other side is 3O feet .

The number 1.258201... can be classified as which of the following? Select all that apply. Real, rational, irrational, whole, integer ,natural
Its a multiple choice question

Answers

It is real and irrational.

The decimal does not terminate and the decimal pattern does not repeat, so the number can not be rationalized.

The number can be classified as both real and irrational

The given number:

= 1.258201

A real number is any  number that can represent a distance along a line

A rational number is a real number that can be expressed in form a ratio, it usually have terminating decimals.

An irrational number is any real number that cannot be expressed in form of ratio, it doesn't have terminating or repeating decimals.

A whole number does not contain fractions, it is usually positive integers.

Integers are whole numbers that includes negative and positive numbers.

The given number is a real number but it doesn't contain terminating or repeating decimals. Hence it is irrational number.

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Karl runs a car wash. On the Monday, he recorded a loss of $80 and recorded it as -$80. On Tuesday he earned a profit of $120. What is Karl's balance at the end of Tuesday?

Answers

Karl's balance at the end of Tuesday is a net profit of $40, after combining his loss of $80 from Monday with his profit of $120 from Tuesday.

To find Karl's balance at the end of Tuesday, we need to combine his loss from Monday with his profit from Tuesday. Karl recorded a loss of -$80 on Monday. On Tuesday, he made a profit of $120. Add the two amounts together to find Karl's total balance after these two days.

Monday: -$80
Tuesday: +$120

Combining them, -$80 (loss) + $120 (profit) equals to a net profit of $40.

Therefore, Karl's balance at the end of Tuesday is $40.

a ride at an amusement park rises 8 feet every horizontal change of 2 feet. how could you determine the slope of the ride?

Answers

The slope would be 4/1 or in simplest form: 4 because the slope is y/x and when you simplify 8/2, its 4/1.

The function f(x) = x2 – 4x + 4 is shifted 3 units to the right to create g(x).

A. g(x) = (x – 3)2 – 4(x – 3) + 4
B. g(x) = (x2 – 4x + 4) – 3
C. g(x) = (x2 – 4x + 4) + 3
D. g(x) = (x + 3)2 – 4(x + 3) + 4

Answers

Answer:

answer is A for APEX..

Step-by-step explanation:

The function f(x) = [tex]x^{2} -4x+4[/tex] is shifted 3 units to the right to create

g(x) = [tex](x-3)^{2}-4(x-3)+4[/tex] .

What is shifting of a function?

A shift is a rigid translation in that it does not change the shape or size of the graph of the function. All that a shift will do is change the location of the graph. A vertical shift adds/subtracts a constant to/from every y-coordinate while leaving the x-coordinate unchanged.

Given

f(x) = [tex]x^{2} -4x+4[/tex]

The function f(x) = x2 – 4x + 4 is shifted 3 units to the right to create g(x).

If the function is shifted to the left it is going to plus(+).

If the function is shifted to the right it is going to minus(-).

So, x = x - 3

g(x) = [tex](x-3)^{2}-4(x-3)+4[/tex]

The function f(x) = [tex]x^{2} -4x+4[/tex] is shifted 3 units to the right to create

g(x) = [tex](x-3)^{2}-4(x-3)+4[/tex] .

Option A is correct.

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I only just started learning Algebra, and my teacher just threw all these worksheets at us without explaining much. Can someone please explain the concept of Algebra? Staring with this question, please:

Answers

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

Answer:

x = -8

Step-by-step explanation:

Hello!

Algebra is based on the concept of unknown values called variables, the value of each variable must remain the same in each problem.

Here are steps to solve your problem!

1. Pull out like terms:

-x - 8  =   -1 • (x + 8)

2. Solve  -x-8 = 0

Add 8 to both sides of the equation:

-x = 8

Multiply both sides of the equation by (-1)

x = -8

Therefore, x = -8

Hope this Helps!

Solve the following system of equations.

x − 2y = 5
−3x + 2y = 7

A. x = 3, y = −1
B. x = 11, y = 11/2
C. x = 3, y = 1
D. x = −6, y = -11/2

Answers

Hey Kayla!

Let me help you out real quick.

x - 2y = 5
-3x + 2y = 7

We need to solve x - 2y =5 for x
x - 2y = 5
x = 5 + 2y
Now substitute 2y + 5 for x in -3x + 2y = 7
-3x + 2y = 7
-3(2y + 5) + 2y = 7
-6y - 15 + 2y = 7
-4y - 15 = 7
-4y = 7 + 15
-4y = 22
y = 22/-4
y = -11/2

Now we need to substitute -11/2 for y in x= 2y + 5
x = 2y + 5
x = 2(-11/2) + 5
x = -22/2 + 5
x = -6

Thus,

The answer is x = -6 and y = -11/2

The correct answer is option D

Good luck with your studies :)

You got it! 

We start with triangle ABC and see that angle ZAB is an exterior angle created by the extension of side AC. Angles ZAB and CAB are a linear pair by definition. We know that m∠ZAB + m∠CAB = 180° by the . We also know m∠CAB + m∠ACB + m∠CBA = 180° because . Using substitution, we have m∠ZAB + m∠CAB = m∠CAB + m∠ACB + m∠CBA. Therefore, we conclude m∠ZAB = m∠ACB + m∠CBA using the .

Answers

Final answer:

To prove that m∠ZAB = m∠ACB + m∠CBA, we start with triangle ABC and use the fact that angles in a triangle add up to 180°. Angle ZAB and CAB are a linear pair, so they add up to 180°. By substitution, we can conclude that m∠ZAB = m∠ACB + m∠CBA.

Explanation:

To prove that m∠ZAB = m∠ACB + m∠CBA, we start with triangle ABC. Angle ZAB is an exterior angle created by the extension of side AC. Angle ZAB and CAB are a linear pair, which means they add up to 180°. We also know that angle CAB + angle ACB + angle CBA = 180° because the angles in a triangle add up to 180°. Using substitution, we have m∠ZAB + m∠CAB = m∠CAB + m∠ACB + m∠CBA. Therefore, we can conclude that m∠ZAB = m∠ACB + m∠CBA using the fact that the angles in a triangle add up to 180°.

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If you shift the linear parent function, f(x) = x, down 6 units, what is the equation of the new function?

A. g(x) = x + 6
B. g(x) = x
C. g(x) = 6x
D. g(x) = x – 6

Answers

Answer:

Option D is correct

[tex]g(x) = x-6[/tex]

Step-by-step explanation:

Vertically down :

If y =f(x) is a parent function, then the new function g(x) b units  vertically down is, g(x) = f(x) -b.

As per the statement:

Given the parent function:

[tex]f(x) = x[/tex]

To shift linear parent function vertically down 6 units.

By definition we have;

g(x) = f(x) -6

⇒[tex]g(x) = x-6[/tex]

Therefore, the equation of new function g(x) is, [tex]g(x) = x-6[/tex]

Please help!!!

System of Equations Applications


Bill and Cody are selling cookie dough for a school fundraiser. Customers can buy packages of white chocolate chip cookie dough and packages of double chocolate chip cookie dough. Bill sold 9 packages of white chocolate chip cookie dough and 2 packages of double chocolate cookie dough for a total of $200. Cody sold 2 packages of white chocolate chip cookie dough and 13 packages of double chocolate chip cookie dough for a total of $283. find the cost each of one package of white chocolate chip cookie dough and one package of double chocolate chip cookie dough.

Answers

We will use w for white choco cookies and b for choco cookies.
Bill sold 9 for w and 2 for b for a total of 200. So 9w + 2b = 200
Cody sold 2 for w and 13 for b for a total of 283. So 2w + 13b = 283

Lets solve by elimination.

[tex]\begin{bmatrix}9w+2b=200\\ 2w+13b=283\end{bmatrix}[/tex]

[tex]\mathrm{Multiply\:}9w+2b=200\mathrm{\:by\:}2:\quad 18w+4b=400[/tex]
[tex]\mathrm{Multiply\:}2w+13b=283\mathrm{\:by\:}9:\quad 18w+117b=2547[/tex]

[tex]\begin{bmatrix}18w+4b=400\\ 18w+117b=2547\end{bmatrix}[/tex]

18w + 117b = 2547
-
18w + 4b = 400
/
113b = 2147

[tex]\begin{bmatrix}18w+4b=400\\ 113b=2147\end{bmatrix}[/tex]

[tex]113b=2147 \ \textgreater \ \mathrm{Divide\:both\:sides\:by\:}113 \ \textgreater \ \frac{113b}{113}=\frac{2147}{113} \ \textgreater \ b=19[/tex]

[tex]\mathrm{For\:}18w+4b=400\mathrm{\:plug\:in\:}\ \:b=19[/tex]

[tex]18w+4\cdot \:19=400 \ \textgreater \ \mathrm{Multiply\:the\:numbers:}\:4\cdot \:19=76 [/tex]

[tex]18w+76=400 \ \textgreater \ \mathrm{Subtract\:}76\mathrm{\:from\:both\:sides} [/tex]

[tex]18w+76-76=400-76 \ \textgreater \ 18w=324 \ \textgreater \ \mathrm{Divide\:both\:sides\:by\:}18[/tex]

[tex]\frac{18w}{18}=\frac{324}{18} \ \textgreater \ w=18[/tex]

Therefore the cost of the white chocolate chip cookies is $18 and the double choco is $19
Bill: 9w+2d=$200
Cody:. 2w+13d= $283

2(9w+2d=$200)
-9(2w+13d=$283)

18w+4d=$400
-18w-117d=-$2547

-113d= -2147

d= $19

9w+2(19)=200

9w+38=200

9w= 162

w= $18

double chocolate chip cookie dough:$19
white chocolate chip cookie dough: $18

Amy has 1/2 hour to do 5 chores. She plans to spend the same fraction of an hour on each chore. She wants to use the number line to help her determine what fraction of an hour she can spend on each chore.

Answers

The number line needed is

<-----------(5/2)----------->

Note: 5/2 is determined by multiplying (1/2)(5).

50 POINTS! + BRAINLIEST! PLEASE HELP

Answers

slope = rise over run = y/x

A (-1,3) slope = 3/-1 = -3

B (1,2) slope = 2/1 = 2

C (-3,-1) slope = -1/-3 = 1/3

2 lines need to be negative reciprocals in order to be a right triangle

negative reciprocal of -3 is 1/3

 so this is a right triangle

Answer: yes it is

Step-by-step explanation: put into a graph and it will become clear

|3x-2|+2y if x=-4,y=7,and z=-9

Answers

The answer would be 26 because you would replace all the variables making the equation be |3*-4-2|+2*7. Then you would solve the absolute value making it 12+2*7. Next solve the multiplication making the equation 12+14 making your answer 26.

A triangle has sides of lengths 6, 2, 7. Is it right triangle?

Answers

By the pythagoreans' theorem,

All right-angle triangle with the opposite squared + adjacent squared = hypotenuse squared.

6² + 2² ≠ 7²
Therefore the triangle is not a right angle triangle

Answer is B.

Zack is purchasing a bag of apples. The cost of apples is proportional to the weight of the apples in pounds as shown on the graph. Which statements are true about the cost of the apples?

Which statements are true about the cost of the apples?

Select each correct answer

1 lb of apples will cost Zack $2.50.

10 lb of apples will cost Zack t $4.

4 lb of apples will cost Zack $10.

2.5 lb of apples will cost Zack $1.

Answers

Answer:

1 lb of apples will cost Zack $2.504 lb of apples will cost Zack $10

Step-by-step explanation:

The graph axesand common sense tell you that each ordered pair represents ...

  (weight, cost)

So the ordered pairs (1, 2.50) and (4, 10) mean ...

  1 lb of apples will cost Zack $2.50

  4 lb of apples will cost Zack $10

A and C should be the correct answers if I'm not mistaken

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