Mathematics Middle School

find the distance between the points:

(1, 3) and (3, -4)

Please explain and show work

Answers

Answer 1
To calculate distance between two points we use the distance formula sqrt((x2−x1)^2+(y2−y1)^2).  

To start, we find the square of the distance between x1 and x2 and y1 and y2.  The distance between x1 and x2, or 1 and 3, is 2. The distance between y1 and y2, or 3 and -4, is 7.

Now we square 2 and 7 and add them together to get 4 + 49 = 53.

The last thing we do to find the distance is take the square root of 53. 53 is not a perfect square and is also a prime number so our answer in simplest form is still sqrt53.

Related Questions

<ABD has a measure of 36 degrees. a)find the compliment of the angle b)find the supplement of that angle

Answers

a) The complement of an angle is the other angle that can be added to the original to add up to 90 degrees. The complement of <ABD would be 90-36=54

b) The supplement of an angle is whatever number can be added to the original to add up to 180 degrees. The supplement of <ABD would be 180-36=144

What is the value of the expression 3^−4 ?

Answers

Thanks for the question!

When there is a negative exponent, do the problem the same, but make it it’s reciprocal:

3^-4
1/3^4
1/81

Hope this helped!

The required simplified value for the expression [tex]3^{-4}[/tex] is 1 / 81.

Given that,
To determine the simplified value of the expression [tex]3^{-4}[/tex] .

What is simplification?

The process in mathematics to operate and interpret the function or expression to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

What is arithmetic?

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,

Here,
[tex]3^{-4} = 1/3^4[/tex]

3 * 3 * 3 * 3 = 9 * 9 = 81

[tex]3^{-4} = 1 / 81[/tex]

Thus the required simplified value for the expression [tex]3^{-4}[/tex] is 1 / 81.

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An airplane can travel at a speed of 550 mph. Write and solve an equation to find the time it will take to fly from London to Montreal, a distance of approximately 3300 miles

Answers

Final answer:

The time it will take for an airplane to fly from London to Montreal at a speed of 550 mph covering a distance of 3300 miles is approximately 6 hours.

Explanation:

To find the time it will take for an airplane to fly from London to Montreal, we can use the equation for speed, which is:

Speed = Distance \u00f7 Time

Knowing that the plane can travel at a speed of 550 mph and the distance from London to Montreal is 3300 miles, we can rearrange the equation to solve for time:

Time = Distance \u00f7 Speed

Time = 3300 miles \u00f7 550 mph

After calculating, we find that:

Time = 6 hours

Therefore, it will take the airplane approximately 6 hours to fly from London to Montreal at a constant speed of 550 mph, ignoring any other factors such as wind or air traffic delays.

Final answer:

To find the time it will take, we can use the formula Time = Distance/Speed. In this case, it will take approximately 6 hours to fly from London to Montreal.

Explanation:

To find the time it will take to fly from London to Montreal, we can use the formula Time = Distance/Speed. In this case, the distance is approximately 3300 miles and the speed is 550 mph.

Plugging in the values into the formula, we get Time = 3300 miles / 550 mph = 6 hours. So, it will take approximately 6 hours to fly from London to Montreal.

Therefore, the time it will take to fly from London to Montreal is 6 hours.

If 15.9 out of every 100 pregnant women in Georgia deliver their babies by C-section, how many pregnant women out of 25,250 would be expected to deliver by C-section?

Answers

15.9/100 pregnant women = x/25,250 pregnant women. 
15.9 times 25,250 = 401475 divided by 100 = 4014.75 
Answer = 4015 would be expected to deliver by C-section.
P(C-section) = 15.9% or 0.159

Expected number of C-Section out of 25,250:

0.159 x 25,250 = 4,015 Women

I really don't understand this absolute value. please help

Answers

Dang what kinda math they teaching you! that makes no sense! ill try and help though
Let the number = x
then (10-x) = 2(x-1)
10-x=2x-2
3x=12
x = 4

Please help me with my math homework! 20 points!

A culture of 1.08×10^15 bacteria is in petri dish A. A culture of 2.7×10^11 bacteria is in petri dish B.

How many times greater is the number of bacteria in petri dish A than petri dish B?

Enter your answer, in standard notation, in the box.

Answers

To find the number of times the bacteria in petri dish A than petri dish B, let us divide.

So, number of times = [tex]\frac{Number of times bacteria in petri dish A}{Number of times bacteria in petri dish B}[/tex]

[tex]= \frac{1.08(10^{15} )}{2.7(10^{11} )}[/tex]

= 0.4 × [tex]10^{4}[/tex]

= 4000

Hence, the number of bacteria in petri dish A is 4000 times the number of bacteria in petri dish B.

Quinn runs 3 miles 3 times every week. How many miles does Quinn run in 6 weeks

Answers

54 miles. 3 miles 3 times every week. Multiply those two and you get 9 miles total each week, times the week number (6).
He ran 9 miles a week so times the 6 weeks is 54

The table shows the earnings and the number of hours worked if three employees . Complete the table by finding the missing values . Which employee earned the least per hour ? EXPLAIN.

Answers

1. 3.5 hours
2. $9.50/hr
3. 5.4 hours

What is the answer to -1 = 5+x divided by 6

Answers

first, we get the solution on the equation:
-1=5+x
-1-5=5-5+x
x = -6
then, we will divide this answer by 6 as mentioned in the problem as follows:
-6/6 = -1
Hey! Hope that I can help.

To do this, first we can solve the equation.
-1 = 5 + x
-5  -5
-6 = x, then divide -6 by 6 to get your answer.

Answer: x = -1

Study the number 31,342. How many times less is the three in the hundreds place as compared to the three in the 10,000 place?

Answers

It is 100 times smaller

Find the value of y if B is between A and C, AB is 2y, BC is 6y, and AC is 48.

a) 6
b) 4
c) 24
d) 8

Answers

AB + BC = AC
2y + 6y = 48
8y = 48
  y = 6

answer
a) 6

The value of y is 6 and this can be determined by using the arithmetic operations and the given data.

Given :

B is between A and CAB is 2y, BC is 6yAC is 48

The following steps can be used in order to determine the value of y:

Step 1 - The arithmetic operations can be used in order to determine the value of y.

Step 2 - According to the given data, B is between A and C.

Step 3 - The mathematical expression of the above expression is:

AC = BC + AB

Step 4 - Now, substitute the value of the known terms in the above expression.

48 = 6y + 2y

Step 5 - Simplify the above expression.

48 = 8y

y = 6

Therefore, the correct option is a).

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of the 150 people surveyed seven out of 10 said they owned at least one pet how many of the people surveyed owned pets

Answers

15 times 7, which is 105.
15 times seven which is 105

in which square is 25% not shaded

Answers

Square D because 2/8 are not shaded. 2/8=1/4 and 1/4=25%

X to 2nd power equals 9/256

Answers

There are two solutions.. x=16 or x=−16.

A crane cable can support a maximum load of 17,000 kg. If a bucket has a mass of 4,000 kg and gravel has a mass of 1,500 kg for every cubic meter, how many cubic meters of gravel (g) can be safely lifted by the crane? Enter any fractions as reduced improper fractions.

Answers

We can set up a model for this problem

4000 + 1500x = 17,000
1500x + 4000 = 17,000

Now solve for x

1500x + 4000 =  17000
1500x + 4000 - 4000=  17000 - 4000
1500x = 13000
1500x /  1500 = 13000 / 1500
x =  [tex]\frac{26}{3}[/tex]





ax-x=c
solve the equation for x

Answers

Hi, again!

Like last problem, group the x out.

x(a-1) = c

Now divide.

x = c/a-1

Hope this helps!

Change the order and the grouping of the addends so that you can use mental math to find the sum. Then find the sum. 43+39+43+11=

Answers

Final answer:

By applying the commutative property of addition and rearranging the numbers for easier mental calculation, the sum of 43 + 39 + 43 + 11 can be found to be 136.

Explanation:

The question asks to change the order and the grouping of the addends for easier mental calculation, and then to find the sum of 43 + 39 + 43 + 11. By understanding the commutative property of addition, which states that numbers can be added in any order without changing the sum, we can rearrange these numbers for easier addition.

To use mental math effectively, grouping numbers that make round numbers or those that are easier to add can simplify the process. Here, we can group 43 and 43, which are identical, and 39 and 11, which sum up to a round number.

Therefore, by rearranging:

43 + 43 = 86

39 + 11 = 50

Adding these sums together:

86 + 50 = 136

By changing the order and grouping of the addends, we find that the sum is 136.

1. Is it possible for a composite number to have more than one prime factorization? Is it possible for a number to have no prime factors? Why?
2.Give and example of how prime factorization could be used in the real world

Answers

Composite number is defined as a number that can be divided by numbers aside from 1 and by itself.

Prime number are numbers that only has a factors of 1 and itself.

It is very possible for a composite number to have more than one prime factorization. But, it is not possible for a number to not have a prime factor. 

When you factorize a number, you break it down into its most basic factors and these basic factors are all prime numbers.

Prime factorization is basically breaking down numbers to its most basic factors. It can be used in everyday living especially when we deal with numerical transactions like money and values. 


4,444,444 the digit in the hundreds thousands place is 10 times the value of the digit in the ten thousands place?

Answers

If this question is:
"true or false:
the digit in the hundreds thousands place is 10times the value of the digit in the ten thousands place"
then that would be true.
I'm not really sure what you're asking... sorry :|

if you forget to bring the book back to the library, you will pay a fine. is this a negation, conjunction, disjuntion, conditional or biconditional?

Answers

I believe it is a conjunction

The sentence is a conditional statement where the payment of a fine depends on forgetting to return the book. Hence the correct option is Option 4 , conditional

The sentence 'if you forget to bring the book back to the library, you will pay a fine' is a conditional statement. In logic and English grammar, a conditional statement is one where the outcome (the consequent) depends on a certain condition (the antecedent). Here, the antecedent is 'if you forget to bring the book back to the library', and the consequent is 'you will pay a fine'. The structure of this sentence follows the 'if (condition), then (result)' pattern typical of standard conditionals.

For example:

If it rains, the picnic will be canceled.If you study hard, you will pass the exam.

In both examples and the original sentence, the outcome is contingent on the condition being met, which is the hallmark of a conditional statement.

Which is the best estimate for the sum of 31,096 and
58,721?

Answers

89,800 because you round to the nearest hundred and add them

What is 40/3 simplified

Answers

Thanks for the question!

40/3 can't be necessarily simplified, but it can be converted to a mixed number.

It would be 13 1/3

Hope this helps!

So far, 37 miles of a new highway have been completed. This is one mile less than two thirds of the entire length. How long will the new highway be when complete?

Answers

37 = 2/3x - 1
37 + 1 = 2/3x
38 = 2/3x
38 / (2/3) = x
38 * 3/2 = x
114/2 = x
57 = x <=== when complete, the highway will be 57 miles
Final answer:

The total length of the new highway, when complete, will be 57 miles.

Explanation:

The question states that 37 miles of a new highway have been completed and this distance is one mile less than two thirds of the entire length of the highway. To solve this problem, we need to write an equation using the given information and solve for the variable representing the total length of the highway.

Let's denote the total length of the highway as 'x'. According to the problem, two thirds of this length minus one mile equals 37 miles. Forming an equation, we can write (2/3)x - 1 = 37.

To solve for 'x', first add 1 to both sides of the equation to get rid of the '-1' on the left, that gives us (2/3)x = 38. After, to completely isolate 'x', multiply both sides of the equation by the reciprocal of 2/3, which is 3/2. Doing this results in 'x' = 38 * (3/2) = 57 miles.

Therefore, the new highway will be 57 miles long when complete.

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how is 2.25 written as a fraction

Answers

2.25 as a fraction is 2 1/4
'There is not much that can be done to figure out how to write 2.25 as a fraction, except to literally use what the decimal portion of your number, the .25, means. Since there are 2 digits in 25, the very last digit is the "100th" decimal place. So we can just say that .25 is the same as 25/100.' -Google

So 25/100 is your answer.

A water cooler fills 150 glasses in 30 minutes. How many glasses of water can the cooler fill per minute?

Answers

5 per minute
5x30=150

How many shapes are in the world

Answers

There are an infinite number of shapes, because a shape can have any number of sides. This is where we get into our laws of fractals. A fractal is a shape with an infinite perimeter and area, meaning that every level of infinity is another shape, but can be beat by another shape. However, this is all philosophical math and goes way beyond the context of your question.

To keep it short and simple, there are an infinite number of shapes in the world.
There are more than you think ;) There is no limit to shapes, everything comes in shapes and sizes. For example,  A computer has soft edges and it is rectangular. Peole can make up shapes if they want to, But more the merrier!

The teacher separated her class of twenty-eight student into two group. one group has 4 more than twice as many students as the other group. how many students are in each group?

Answers

You can use a system of equations.
x=group 1
y=group 2

x+y=28
2x+4=y

Isolate the variable in equation 1.

y=-x+28

Substitute it into equation 2.
-x+28=2x+4

Solve.
-3x=-24
x=8

Substitute it into one of the equations for y.
-x+28=y
-8+28=y
y=20

There are 8 students in one group and 20 students in the other.

Hope this helps!
x+y=28
x=28-y

x=4+2y
28-y=4+2y
28-4=2y+y
24=3y
24/3=y
y=8
x+y=28
x+(8)=28
x=28-8
x=20
(20)=4+2(8)
20=4+16
20=20
one group=20, other group=8

-4+6(-4x+3) combining like terms & distributive property

Answers

After using distributive property and combining like terms the answer is -2

-4 + 6 (4x+3)

Disribute 6 into both numbers in the parenthesis. So that means...

6 x 4x = 24x

6x3 = 18

Your new expression is:

-4 +24x +18

Combine ALL like terms:

-4 + 18 = 14

New Expression:

14 + 24x

And since you don't have any equal sign, that's as much as you can do to simplify the expression.

(3 – 6y2)(y2 + 2) what is this

Answers

(3 - 6y^2)(y^2 + 2)

3(y^2 + 2) - 6y^2(y^2 + 2) =
3y^2 + 6 - 6y^4 - 12y^2 =
-6y^4 - 9y^2 + 6 <===

Avery and her friends attend a museum. It costs $5 to enter the main exhibit hall, with an added charge of $3 to view each special exhibit. Avery writes an equation that models the total price of visiting the museum as a function of the number of special exhibits they view. What is the slope and y-intercept of Avery’s model?

Answers

I got slope=1/3y - 5/3
And y intercept =5+3x

Hence, slope = 3 and, y-intercept = 5.

What is function?

Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.

Here, given that,

Avery and her friends attend a museum. It costs $5 to enter the main exhibit hall, with an added charge of $3 to view each special exhibit.

Avery writes an equation that models the total price of visiting the museum as a function of the number of special exhibits they view.

Now, let the function be,

f(x)= 3x+5  = the total price of visiting the museum

[where, x= special exhibit & 5=the main exhibit hall]

Let, y = f(x)

So, w get, y=3x+5

Hence, slope = 3

and, y-intercept = 5.

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