At the end of 1994 Walter was half as old as his grandmother. The sum of the years in which they were born is 3838. How old will Walter be at the end of 1999?

Answer:

Both trains are traveling at 90 miles per hour.

Step-by-step explanation:

We are told that the rate is the same for both trains, and we know that the distance traveled by train a plus the distance traveled by train b equals 585 miles.

We will use [tex]Distance=Rate* Time[/tex] formula to solve this problem.

Train A: [tex]D_a=R*2.5[/tex] (Using 2.5 instead of 2 and 1/2)

Train B: [tex]D_b=R*4[/tex]

We can set an equation to solve for rate R of trains as:

[tex]D_a+D_b=585[/tex]

[tex]2.5R+4R=585[/tex]

[tex]6.5 R=585[/tex]

[tex]R=\frac{585}{6.5}[/tex]

[tex]R=90[/tex]

Therefore, rate of both train a and train b is 90 miles per hour.

The total distance between the two stations is

[tex]585 miles[/tex]

Let the distance between the Central Station and station b be x

This implies that the distance between the Central Station and station a is

[tex](585 - x) \: miles[/tex]

[tex]speed=\frac{distance}{time}[/tex]

so, let us write equations in terms of speed for the two trains and solve

 For train a,

[tex]speed=\frac{585 - x}{4 } ....eqn \: 1[/tex]

For train b,

[tex]speed=\frac{x}{2  \frac{1}{2} } .....eqn \: 2[/tex]

We were told that both trains traveled with the same speed

This means that eqn 1 = eqn 2

[tex]\frac{585 - x}{4 }=\frac{x}{2.5} [/tex]

Cross multiplying

[tex]2.5(585 - x)=4(x) [/tex]

Expanding the brackets

[tex]1462.5  - 2.5x =4x[/tex]

Grouping like terms

[tex]1462.5= 4x + 2.5x[/tex]

[tex]6.5x = 1462.5 \\ x = \frac{1462.5}{6.5 } =225 \: miles[/tex]

The speed at which the trains were travelling is

[tex] \frac{225}{2.5}= 90 \: miles /hour[/tex]

Hence the rate of the trains is  

[tex]=90\: miles /hour[/tex]

Answer:

C

Step-by-step explanation:

I would say not enough information. You cannot tell from the givens how A,B and m<2 are related to each other.

Answer C

Answer:

c

Step-by-step explanation:

Answer:

Constant of Proportionality is 50.  

Step-by-step explanation:

Albatross can fly 400 kilometers in 8 hours.

'd' represents the distance and 't' represents the number of hours.

The equation [tex]d=50t[/tex] represents the relationship between the distance and time.

Now, in the equation shown above 50 is the constant of proportionality, and 50 represents the rate of change of distance with time.

The constant of proportionality tells us the rate of change between two variables.

So for every 1 hour of time the distance covered is 50 kilometers.  

11

5 pound = 500 pence

500 pence/ 45 pence= 11.1111111

The zookeepers finish feeding the animals at 8:30 PM

2x+2=20-x

3x=18

x=6

2nd=14

357+421 = 778

Hope this helps :)

The value of x in the isosceles right triangle is 52.5.

The measure of the acute angle in an isosceles right triangle can be determined by setting the expression equal to 90 degrees:

(2x - 15) = 90

Simplifying the equation, we get:

2x = 90 + 15

2x = 105

x = 105/2

x = 52.5

Therefore, the value of x is 52.5.

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Answer:

cost of one sheet of sticker = 2.05

Step-by-step explanation:

given that for every 10 sheets of stickers total c0st increases 20.50

i.e. cost of 10 sheets of stickers = 20.50

When we purchase 1 sheet the price would be reduced.

In other words, direct variation is there for sheets of papers and costs

Hence for 1 sheet of stickers cost would be less than 10 sheets.

So divide by 10

Cost of 1 sheet of sticker = 20.50/10 = 2.05

Final answer:

7 quarters represent 175 percent of a school year since 7 divided by 4, then multiplied by 100 equals 175%. This means 7 quarters is more than the duration of one standard school year.

Explanation:

To calculate what percent of a school year 7 quarters represent, we need to compare 7 quarters to the total number of quarters in a standard school year. Since we know that a school year consists of 4 quarters, we can set up a proportion to determine the percentage.

Step 1: Identify the total number of quarters in a school year, which is 4.

Step 2: Identify the number of quarters we're focusing on, which is 7.

Step 3: Set up a fraction to represent the portion, which is 7 divided by 4 (7/4).

Step 4: Convert this fraction to a percentage by multiplying by 100. So, (7/4) × 100 = 175%.

Therefore, 7 quarters represent 175 percent of a school year, which implies more than one full school year.

106.60 is bigger round up on it and you get 107

$56 a week

earnings = $12 × 28 = $336

saved = [tex]\frac{1}{6}[/tex] x $336 = [tex]\frac{336}{6}[/tex] = $56

the number is - 1

let the number be n then 6 times the number is 6n and added to -4 is

- 4 + 6n = 10n ( equal to 10 times the number )

subtract 6n from both sides

- 4 = 4n ( divide both sides by 4 )

[tex]\frac{-4}{4}[/tex] = n , hence n = - 1

3x + 2y + z = 7   ⇒   z = 7 - 3x - 2y

*****************************************

  5x + 5y + 4z = 3  

= 5x + 5y + 4(7 - 3x - 2y) = 3

= 5x + 5y + 28 - 12x - 8y = 3

= -7x -3y + 28 = 3

= -7x - 3y = -25

*****************************************

  3x + 2y + 3z = 1

= 3x + 2y + 3(7 - 3x - 2y) = 1

= 3x + 2y + 21 - 9x - 6y = 1

= -6x - 4y + 21 = 1

= -6x - 4y = -20

*****************************************

-7x - 3y = -25   ⇒  4(-7x - 3y = -25)   ⇒   -28x - 12y = -100

-6x - 4y = -20   ⇒ -3(-6x - 4y = -20)   ⇒    18x + 12y =  60

                                                                  -10x         =   -40

                                                                       x         =     4

-7x - 3y = -25

-7(4) - 3y = -25

-28  - 3y = -25

        -3y  = 3

           y  = -1

z = 7 - 3x - 2y

  = 7 - 3(4) - 2(-1)

  = 7 - 12 + 2

  = -3

Answer: x = 4, y = -1, z = -3

In 1906 in San Francisco the magnitude of earthquake on richter scale was 8.3.

In the same year the magnitude of earthquake on richter scale in Japan was 4.9.

Now we have to find how many times more was the San Francisco earthquake that the Japan earthquake.

The amount of energy released in an earthquake is very large, so a logarithmic scale avoids the use of large numbers.

The formula used for these calculations is:

[tex]M=log_{10}(\frac{I}{I_{0}})[/tex]

Where M is the magnitude on the richter scale,  I is the intensity of the earthquake being measured and I₀ is the intensity of a reference earthquake.

So because the magnitude is a base 10 log, the Richter number is actually the exponent that 10 is raised to in order to calculate the intensity of the earthquake.

So the difference in magnitudes of the earthquakes can be calculated as follows:

[tex]M=log_{10}(\frac{10^{8.3}}{10^{4.9})}[/tex]

M=3.4

Answer: The San Francisco earthquake was 3.4 times more than Japan earthquake.

Final answer:

The San Francisco earthquake released approximately 2510 times more energy than the earthquake in Japan, calculated using the Richter scale.

Explanation:

To determine how many times stronger the San Francisco earthquake was compared to the earthquake in Japan, we refer to the Richter scale, which is a logarithmic scale. A one-unit increase on this scale represents a ten-fold increase in amplitude of the seismic waves and roughly a thirty-fold increase in energy released. Therefore, to calculate the difference between a magnitude 8.3 earthquake and a magnitude 4.9 earthquake, we subtract the smaller magnitude from the larger one (8.3 - 4.9 = 3.4) and then calculate 10 raised to the power of this difference.

[tex]10^(3.4)[/tex] = 10 x 10 x 10 x 2.51 (approximately), which simplifies to about 2510 times more energy released by the San Francisco earthquake compared to the earthquake in Japan.

If x > 0 and y < 0 then the point (x, y) is located in Quadrant IV.

Look at the picture.

Answer:

II

Step-by-step explanation:

Answer: B

Step-by-step explanation:

[tex]\frac{-7}{9} * \frac{3}{5} = \frac{-7(3)}{9(5)} = \frac{-7(3)}{3 * 3(5)} = \frac{-7}{3(5)} = \frac{-7}{15}[/tex]

Answer:

Option C

Step-by-step explanation:

Given a quadratic equation

x^2+10x+24 =0

We can use either formula or factorization method to solve this equation.

The last term is 24, it is a product of 6 and 4. Sum =6+4 =10

Hence factoring can be done easier

Split the middle term as 6x +4x

x^2+6x+4x+24 =0

x(x+6)+4(x+6)=0

(x+4)(x+6)=0

Either x+4 =0 or x+6 =0

x=-6 or x =-4

Final answer:

To calculate the sale price of the Game Boy with an original price of $50.00 and a discount of 2/5, you multiply the original price by the discount to find the amount reduced ($20), then subtract that from the original price to find the sale price ($30).

Explanation:

The question involves calculating the sale price of an item after a discount. Initially, the original price of the Game Boy is $50.00. The discount is given as 2/5 of the original price. To find the amount of discount, we multiply the original price by 2/5:

Discount = Original Price × Fraction of discount
Discount = $50 × 2/5
Discount = $20

Now, we subtract this discount from the original price to find the sale price:

Sale Price = Original Price - Discount
Sale Price = $50 - $20
Sale Price = $30

Therefore, the sale price of the Game Boy after the discount is $30.

Answer:

I can confirm that the answer is in fact A

Step-by-step explanation:

I took the test and got it right ( edge 2021 )

The linear inequality represented by the graph is y ≤ 1/2x + 2. The correct option is A.

The relation between two expressions that are not equal, employing a sign such as ≠ ‘not equal to, > ‘greater than, or < ‘less than.

A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.

The given inequality y ≤ 1/2x + 2 is represented on the graph attached with the answer below.

In the graph, the linear line cut x-axis at ( -4, 0 ) and y-axis at ( 0, 2 ). And inequality covers the whole space below the line y = 1/2x + 2.

The linear inequality represented by the graph is y ≤ 1/2x + 2. The correct option is A.

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(10m – 6) – (7m – 4)

= 10m - 6 - 7m + 4

= 3m - 2

So

[10m + (–7m)] + [(–6) + 4]

= 3m + (-2)

= 3m - 2 ..............matching answer.

Answer

[10m + (–7m)] + [(–6) + 4]

To add or subtract any algebraic expression,  variables add or subtract with variables and constant term add or subtract with constant terms in the expression.

To solve given expression, we use [10m + (–7m)] + [(–6) + 4] expression.

Given expression is,

                               (10m – 6) – (7m – 4)

Now, variables add or subtract with variables and constant term add or subtract with constant terms in the above expression.

                        10m - 6 - 7m + 4

                      (10m - 7m) + (-6 + 4)

                    [10m + (–7m)] + [(–6) + 4]

So, first option is correct.

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Answer:  Cole and his sister Chloe will take 81 minutes to clean the whole house.

Step-by-step explanation:

Total rooms in the house = 9

Total persons to clean the house = 2 (Cole and his sister Chloe)

Time taken by 1 person to clean one=18 minutes

Time taken by 2 persons to clean one room together=18 divided by 2 = 9 minutes

Time taken by 2 persons to clean 9 rooms (which is the total number of rooms in the house)=9 multiply 9 = 81 minutes

therefore, they will take 81 minutes to clean the whole house.

All you have to do is just add 26.7 with 12.8, with the result being 39.5

Answer:

Average speed = 65 miles per hour

Step-by-step explanation:

Mike drove 100 miles in 2hrs

He stopped to take lunch then;

drove  420 miles in 6hrs

Total distance covered = 100 + 420 miles = 520 miles

Total time taken = 2 + 6 hrs = 8hrs

Average speed = Total distance ÷ total time = 520/8 = 65 miles per hour

C. 46,920 seconds is your answer

Answer:

Step-by-step explanation:

C. 46,920 sec

[tex]f(x)=x^2-6x+9=(x-3)^2[/tex]

This a perfect square so the x-axis is a tangent at x=3

The correct answer is C

See graph

Given function is f(x) = x² -6x +9.

It is a quadratic function whose graph is an upward open parabola.

The zero(s) of the given function would be at x-intercepts of the graph i.e. y = 0.

It means 0 = x² -6x +9

We can solve this quadratic equation using factorization as follows:-

0 = x² -6x +9

0 = x² -3x -3x +9

0 = x(x-3) -3(x-3)

0 = (x-3)(x-3)

Therefore, x = 3 with multiplicity two.

Hence, option C is correct, i.e. The graph of the function touches the x-axis at x = 3.