Mathematics High School

State the Midpoint formula?

How are the midpoint formula and the Distance formula alike? How are they different?

Give a real-world example that could be addressed using the distance formula.

Give a real-world example that could be addressed using the midpoint formula.

Answers

Answer 1
Let point A (x₁, y₁) and point B (x₂, y₂)

Mid-point formula is given by: [tex][ \frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}] [/tex]

The distance formula is given by: [tex] \sqrt{(x_1-x_2)^2+(y_1-y_2)^2} [/tex]

The two formula are alike because they both need the information of two coordinate points 

They are different because the mid point formula is adding up then divide by two, whereas the distance formula is subtracting then square the answer.

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Real life problem involving distance formula:

Plane A is spotted on a radar with cartesian coordinate (450, 640).
Plane B is spotted on the same radar with cartesian coordinate (350, 540)

Work out the distance between plane A and plane B.
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Real life problem involving mid point formula

Ms. Holland arranges a treasure hunt for a group of scouts. She marks two points, C and D, with cartesian coordinate (-5, 6) and (7, 10) respectively. The clue is that the treasure is buried in the middle point between C and D. Work out the coordinate where the treasure is buried.
 

Related Questions

Find the area of the following shape. A(-5,-8) B(1,-8) C(3,-5) D(1,0) E(-5,-3) F(-3,-6). You must show work to receive credit.

Answers

check the picture below.

now... notice the left-side of the picture. that's the points and shape... ok.. notice the left-side, is really just two rectangles and and four triangles stacked up to each other at the edges.

so.. .just get the area of each rectangle and each triangle, sum them up, and that's the area of the shape.

you can pretty much get the length, width and height of the rectangles and triangles from the grid.

recall area of a triangle = 1/2 bh

Find a formula expressing the radius r of a sphere as a function of its surface area

Answers

The surface area of a sphere :
[tex]A=4 \pi r^2[/tex]

Solving this equation for r:

A/(4* pi) = r^2          apply sqrt to both sides:

r = sqrt [A/(4 pi)]

Then the radius of a sphere as a function of its surface area :
[tex]r= \sqrt{ \frac{A}{4 \pi } } [/tex]

Hope you got the idea

simplify the expression and enter your answer below (19^1/9) ^9

Answers

Multiply 9 by 1/9.

19^1 so in other words, 19.

The simplified expression is 19.

What is expression?

An expression is a sentence with a minimum of two numbers or variables and at least one math operation.

An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division. The terms involved in an expression in math are:

some terms are:

Constant: A constant is a fixed numerical value.Variable: A variable is a symbol that doesn't have a fixed value.Term: A term can be a single constant, a single variable, or a combination of a variable and a constant combined with multiplication or division.Coefficient: A coefficient is a number that is multiplied by a variable in an expression.

given:

(1*9^1/9) ^9

Multiply 9 and 1/9

we get

9*1/9 = 1

and 19* 1= 19

Hence, the simplified expression is 19.

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Write 7x-2-7x+6 in simplest form.

Answers

7x - 7x = 0
-2 + 6 = 4

So, the answer is 4. 

is this answer right

Answers

B IS YOUR ANSWER HOPE IT HELPS
The answer should be B.

Fourteen divided by a number is 14/x, but we're looking for a number divided by 14 which is x/14.
You should use minus rather than less than because less than implies the use of the < symbol.

an ostrich that is 78 inches tall is 15 inches taller than 3 times the height of a kiwi. What is the height of a kiwi in inches

Answers

Turn this into an expression. The height of a kiwi is (k).
78=15+3k
Minus 15.
63=3k
Divide by 3.
21=k
A kiwi is 21 inches tall.
21 inches , because 78 inches minus 15 equals 63 which if divided by 3 equals 21

What number must you add to complete the square? X^2 +12x=40

Answers

You halve the linear coefficient, square it, then add that to both sides.  In this case:

(12/2)^2=6^2=36 so you would add 36 to both sides

x^2+12x+36=76  so that the left side is now a perfect square

(x+6)^2=76

Answer:

36

Step-by-step explanation:

(x+6)^2=76

The bear population increases at a rated of 2% each year. There are 1573 bears this year. What is the growth factor, b?

Answers

that would be 1 + 0.02

Growth factor = 1.02.
Final answer:

To find the growth factor, b, we can use the formula for exponential growth: n = ln(M)/ln(b), where n is the number of years, M is the final population, and b is the growth factor.

Explanation:

To find the growth factor, b, we can use the formula for exponential growth: n = ln(M)/ln(b), where n is the number of years, M is the final population, and b is the growth factor. In this case, the final population is 1573 bears. Let's solve for b: n = ln(1573)/ln(b). To isolate b, we can take the exponential of both sides: b^n = 1573. Now we can solve for b by taking the nth root of 1573. The growth factor, b, is the value that, when raised to the power of the number of years, gives us the final population of bears.

If you are throwing a dart at the circular target pictured below, and it is equally likely to hit any point on the target, what is the probability that the dart will hit the rectangle?
Use 3.14 for ,and round your answer to the nearest tenth of a percent.

Answers

The area of the circle is 100pi in^2, and the area of the rectangle is 48in^2. This means 48/100pi of the circle is the target area, which is 15.3% of the total area, so D is the correct answer.

A car travels 2/5 mile in 1/2 minute. what is the cars speed in miles per hour?

Answers

So a car travels 2/5 mile in 1/2 minute. This means a car travels 4/5 mile in one minute. Then multiply by 60 to find how many miles it travels in 60 minutes, and you can see that you have 240/5, which is equal to 48. Therefore the speed of the car in miles per hour is 48 miles an hour. Hope this helps. Feel free to ask more questions, and ask questions about my explanation.
Final answer:

The speed of the car is 48 miles per hour, based on the given information that the car travels 2/5 miles in 1/2 minute.

Explanation:

To solve this problem, we first need to recognize that the car has traveled 2/5 miles in 1/2 minute. To calculate the speed in miles per hour (mph), we need to find how far the car would go in 1 hour. In other words, how many 1/2 minutes are there in an hour? An hour has 60 minutes, so there are 2*60=120 half-minutes in an hour. If the car travels 2/5 mile in each half minute, then in one hour (or 120 half-minutes), the car would travel 2/5*120=48 miles. Consequently, the car's speed is 48 miles per hour.

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Write an equation that has a hole at x = 4 and a vertical asymptote at x = -3.

Answers

This has to be a rational equation in order to have those characteristics...in other words a fraction. One such equation would look like this:
x^2 - 2x - 8/x^2 - x - 12.  When you factor both the numerator and the denominator you get (x-4)(x+2)/(x-4)(x+3).  Because the (x-4) is in both the top and the bottom of the fraction, you can cancel them out, which makes that (x-4) a removable discontinuity.  The (x+3) exists as a vertical asymptote.

If your front lawn is 24.0 feet wide and 20.0 feet long, and each square foot of lawn accumulates 1050 new snow flakes every minute, how much snow (in kilograms) accumulates on your lawn per hour? assume an average snow flake has a mass of 1.70 mg.

Answers

First find the area of the front lawn:
Area = length * width
Area = 24.0ft * 20.0ft
Area = 480ft^2

Next, find the weight in kilograms of the snow per square foot per hour per ft^2:
[tex]weight\ per\ ft^{2}=\frac{1050\ snowflakes}{minute}\\\\weight\ per\ ft^{2}=\frac{1050\ snowflakes}{minute}*\frac{1.70\ milligrams}{snowflake}*\frac{1\gram}{1000\milligrams}*\frac{1\kilogram}{1000\grams}* \frac{60\minutes}{1\hour}\\\\weight\ per\ ft^{2}=\frac{1050*1.70}{1000*1000*60}*\frac{kg}{hour}=2.975*10^{-5}\ \frac{kg}{hour}\\\\weight=2.975*10^{-5}\ \frac{kg}{hour*ft^{2}}[/tex]

Now multiply the area of the lawn by the weight of the snow per hour per ft^2:
[tex]weight\ of\ snow=lawn\ area*weight\ per\ hour\ per ft^{2}\\\\weight=480\ ft^{2}*2.975*10^{-5}\ \frac{kg}{hour*ft^{2}}\\\\weight=0.01428\ \frac{kg}{hour}[/tex]



Thus your answer is .01428 kg.

Line K is parallel to line L
What angle is congruent to angle 4.

Answers

∠1 and ∠4 are vertical angles (the angles opposite each other when two lines cross).

Vertical angles are congruent, so ∠1 = ∠4

Answer:

Its A, I took the test..

Is it correct to say that a cube with side lengths 6cm have the same volume and surface area?

Answers

Yes it is correct. The surface area requires that you take the area of all the lateral faces, of which there are 6, and add them all together, giving you 216. The volume then requires that you take the length times the width times the height which is also 216. So odd, but yes, they are the same.

Use calculus to find the largest possible area for a rectangular field that can be enclosed with a fence that is 400 meters long.

Answers

the largest rectangular area is actually a square.

 so the side would be 400/4 = 100 feet

 area of a square is S^2

100^2 = 10,000 square feet

Maximum area is 5625m² when the dimensions are 75m × 75m.

To maximize the area of the rectangular field enclosed by a 300-meter-long fence, let's denote the length of one side as x meters and the other side as y meters.

Since the fence length is 300 meters, the perimeter of the rectangle is 2x + 2y = 300, or x + y = 150.

We want to maximize the area, which is given by A = xy.

To find the maximum, we'll use the constraint equation to express one variable in terms of the other, then substitute into the area formula.

1. From the constraint equation, x = 150 - y.

2. Substitute x into the area formula: A = (150 - y)y.

3. Take the derivative of A with respect to y and set it to zero to find the critical points.

4. Solve for y to find the value that maximizes A.

5. Use this value of y to find the corresponding x.

6. Calculate the maximum area using A = xy.

Simplify the expression sin^2x-1/cos(-x)

Answers

Use the Pythagorean identity [tex]sin ^{2} x+cos ^{2} x=1[/tex]
to simplify the numerator.
[tex]sin ^{2} x-1=-cos ^{2} x[/tex]
Now use that fact that
[tex]cos(-x)=cos(x)[/tex] to set up the equivalent fraction:
[tex] \frac{sin ^{2}x-1 }{cos(-x)} = \frac{-cos ^{2}x }{cos(x)} [/tex]
Now reduce between the numerator and denominator to get -cos(x)

When dividing with polynomials, the goal is to determine how many times the dividend divides evenly into the?

Answers

Whether dividing constant terms or polynomials, we always have definitive terms when it comes to division. Suppose we say, 10x divided by 2. The dividend is the 10x and the divisor is the 2. In other words, the dividend is the number to be divided by the divisor, to obtain the answer called the quotient.

When dividing polynomials, your main goal is to be able to divide the dividend evenly into the divisor. For example, we divide x²+2x+1 by x+1. The first thing you're going to focus is, what term will completely divide the first term of the polynomial? That would be x. Why? Because when you multiply x with x+1, the product is x²+x. When you subtract this from the polynomial, the x² will cancel out. All you have to do is subtract x from 2x, yielding x. Then, you carry down the last term of the equation: +1. You do the steps again. The term that will completely divide x+1 by x+1 is 1. When you subtract the two, you will come up with zero. That means there is no remainder. The polynomial is divisible by the divisor. 
                          x + 1
                        ------------------------------------
                  x+1| x²+2x+1
                        - x²+x
                         ----------------------
                                 x +1
                               - x + 
                             ------------
                                    0

Find the three arithmetic means in this sequence. 12 __ __ __ 40

Answers

To answer this question first you have to count the difference between the highest number with the lowest number.
In this case, the difference is: 40-12=28

After that, you need to determine the leaps in the sequence. In this case, there are 4 leaps.  
After that divide the difference with the leaps : 28:4=7
Therefore the sequence will be 12 , 19, 26, 33, 40

A lab found that 670 rats could run through a maze in a mean time of 4.7 seconds. What is the 99% confidence interval for the population mean? Use the formula for margin of error: z•σ/√n. Please explain each step, particularly how to find the population standard deviation.

Answers

Using the formula for margin of error as

MOE = z * σ / √n

would be very difficult since we are not given the value of the standard deviation. Standard deviation value must be given since it is obtained from the experiment.

However, we use another formula for MOE in the form of:

MOE = z sqrt [p (1 – p) / n]

where p is the proportion at 99% confidence interval at z crit value. From the standard distribution tables, this corresponds to a p value of:

z crit = 2.58

p = 0.9951

Therefore the margin of error is:

MOE = 2.58 sqrt [0.9951 (1 – 0.9951) / 670]

MOE = 6.96 x 10^-3 = 0.00696 s

 

We can see that at 99% Confidence interval, the Margin of Error is extremely small (almost 0). For the sake of calculation:

Confidence interval = 4.7 s ± 0.00696 s

Confidence interval = 4.69304, 4.70696

An electrical heating element produces heat depending on the resistance of the element and the current passed through it. The heat produced can be given by the formula h = I2R where h is the heat generated, I is the current, and R is the resistance. If the element has a fixed current of 2 amps passing through it and a variable current of x amps, it is able to produce a heat of 10x3 + 80, depending on the variable resistance for different additional values of current x. Determine the formula for the variable resistance.

Answers

The heat produced by current I is
H = I²R
where
R =  resistance.
According to the formula, heat produced is proportional to the square of the current.

When a current of I = 2 amps is applied, the heat produced is 
H = 10x³ + 80.
This heat includes heat due to a fixed current of 2 amps, and heat due to a variable current of x amps.

Because the heat produced is proportional to the square of the current, write the expressions as
H = (10x)*(x²) + 20*(2²)

The second term on the right is heat due to the fixed current of 2 amps, written as
20*(2²).
Therefore the fixed resistance is R = 20 ohms, and the square of the fixed current is 2².

The first term represents heat due to variable resistance, written as
(10x)*(x²).
Therefore the variable resistance is 10x, and the square of the variable current is x².

Answer:
The variable current is  10x.

Answer:

(10x - 40) + 120 / (x+2)

If a coin is tossed twice what is the probability of getting two heads

Answers

25% because the first FLIP, it was a fifty-fifty chance. FLIP again and the chances are divided by two since you can only get 2 things, either heads or tails.

Find all the points, if any, where the graph of 12x-5y=0 intersects (x+12)^2+(y-5)^2=169.

A. There are no points of intersection.

B. (0,0)

C. (4.5, 10.9)

D. (0,0) and (4.5, 10.9)

Answers

I: 12x-5y=0
II:(x+12)^2+(y-5)^2=169

with I:
12x=5y
x=(5/12)y
-> substitute x in II:
((5/12)y+12)^2+(y-5)^2=169
(25/144)y^2+10y+144+y^2-10y+25=169
(25/144)y^2+y^2+10y-10y+144+25=169
(25/144)y^2+y^2+144+25=169
(25/144)y^2+y^2+169=169
(25/144)y^2+y^2=0
y^2=0
y=0

insert into I:
12x=0
x=0

-> only intersection is at (0,0) = option B

Answer:

(0,0)

Step-by-step explanation:

If you graph [tex]12x-5y=0[/tex] and [tex](x+12)^2+(y-5)^2=169[/tex] along with the points (0,0) and (4.5, 10,9) you with see that the equations intersect at (0,0)

A= (4,5) B= (7,-9) what is AB ?

Answers

If you are needing to find the distance between the two points, you must use a simple formula, cleverly named, the distance formula. Since I can't input special characters into the answer box, I'll explain it the best I can.

( The square root of (  (x - x)^2 + (y - y)^2 )  )

First, we need to find the first x subtracted from the second x, as so:
(4,5) and (7,-9)

4 - 7 = -3

Now, we square the -3.

-3^2 = 
-3 * -3 = 9

Next, we have to find the first y subtracted from the second y.
(4,5) and (7,-9)

5 - (-9) = 14

Now, we square the 14.

14^2 =
14 * 14 = 196

Let's see how the numbers fit in the formula:

sqrt((x - x)^2 + (y - y)^2)

sqrt((4 - 7)^2 + (7 - (-9))^2)

sqrt((-3)^2 + (14)^2)

sqrt( 9 + 196 )

This is where we currently are in the formula, all we have to do now is square root the total of 9 + 196.

sqrt( 9 + 196 )
sqrt( 205 )

The square root of 205 = 14.31782106...

There are a few answers you can consider:

1) sqrt(205)
2) 14.32 units
or
3) 14.31782106

Depending on the answer you desire, use the one that sounds the most correct to you. Although all three are correct, it may not be the answer you require. 

Hope I could help! If my math is incorrect, or I provided answers you were not looking for, please let know! However, if my answer is correct and well explained, please consider marking my answer as Brainliest! :)

Have a good one.
God bless!

a nutrition label indicates that one serving of apple crisp oatmeal has 2.5 grams of fat. how many grams of fat . how many grams of fat how many grams of fat arew there in 3.75 sevings?

Answers

2.5x3.75=9.375 grams of fat!

The sum of two numbers is 70. one number is 8 more than the other. what's the smaller number?

Answers

x=8+y
x+y=70

Rewrite the first equation to x-y=8
Copy the second equation   x+y=70

Add the two equations and you get 2x=78
Therefore, x=39. Since this is the bigger number the smaller number(y) would have to be 31 because you subtract 8 from x which is 39. 39 is your answer. 

Complete the solution of the equation. find the value of y when x equals 11 8x+6y=28

Answers

If x is 11, then we replace x with 11 in the equation.
8(11) + 6y = 28
88 + 6y = 28
We will subtract 88 from both sides to get rid of the constant.
6y = -60
To isolate the variable, we will divide both sides by 6.
y = -10
In this equation, y equals -10.
First, substitute the value of x back into the equation.

8x + 6y = 28 becomes 8(11) + 6y = 28

Now solve for y.

8(11) + 6y = 28
88 + 6y = 28
6y = -60 <-- Subtract 88 from each side
y = -10 <-- Divide both sides by 6

So, y is equal to -10.

Find the quotient of 5+4i/6+8i , and express it in the simplest form

Answers

remember: i² = -1

[tex] \frac{5+4i}{6+8i}= \frac{(5+4i)(6-8i)}{(6+8i)(6-8i)}= \frac{30-40i+24i-32i^2}{36-64i^2}= \frac{30-16i-32(-1)}{36-64(-1)}= \\ \\ = \frac{30-16i+32}{36+64}= \frac{62-16i}{100}=0.62-0.16i[/tex]

Hope this helps

Over the weekend, Statton and Tyler drove to Montana to go hunting. Now they're preparing to go home. Tyler needs gas for his jeep, which gets 22 miles per gallon for gas mileage. When he stops at the gas station, he already has 5 gallons of gas in his tank. he buys more gas for $1.25 per gallon if Tyler spends 22 on gas what is the total distance the boys could travel round if necessary to the nearest tenth

Answers

he bought : 22/1.25 = 17.6 gallons

17.6 +5 = 22.6 gallons total

22 * 22.6 =497.2 miles total he can drive

Answer:

The answer would be 497.2

Step-by-step explanation:

Proof I hope you do well on the test .

A rope 18 feet long is cut into two pieces. one piece is used to form a circle and the other used to form a square. find a function representing the area of both square and circle as a function of the length of one side of the square.

Answers

Please give me a brainliest for this, it was so much work. The answer is

f(x)=x^2 + (4x^2 -18x +81)/pi

570 people die from smoking related diseases everyday ?
A) how many die form related diseases every hour?
B) how many die form related diseases every week?
C) has many die form related diseases every year?

Answers

(570 people/ 1 day)* (1 day/ 24 hours)= 23.75 people/hour.


The rate of people who die from smoking is 23.75 people die per hour.

The rate of people who die from smoking is 3,990 people die per week.

The rate of people who die from smoking is 207,408 people die per year.

Hope this helps and if your feeling generous leave a rate, thanks, and brainliest it would really help me reach expert and I would greatly appreciate ;)

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