Final answer:
The midpoint formula calculates the center point between two points on a coordinate plane, while the distance formula calculates the distance between two points using the Pythagorean theorem.
Explanation:
Understanding the Midpoint and Distance Formulas
The midpoint formula is used to find the exact center point between two defined points on a coordinate plane. To find the midpoint (M) between two points, (X1, Y1) and (X2, Y2), you use the formula:
M = ((X1 + X2) / 2, (Y1 + Y2) / 2)
For example, to find the midpoint between the points (2, 3) and (4, 8), you would calculate:
M = ((2 + 4) / 2, (3 + 8) / 2) = (3, 5.5)
The midpoint between these points is at coordinates (3, 5.5).
The distance formula, on the other hand, is used to determine the distance between two points on a coordinate plane.
The formula is derived from the Pythagorean theorem and is written as:
D = \(√((X2 - X1)^2 + (Y2 - Y1)^2)\)
Using the above points, the distance (D) would be:
D = \(√((4 - 2)^2 + (8 - 3)^2)√ = \(√(4+25) = \(√29\)√
The distance between the two points is the square root of 29.
Practicing these formulas enhances your problem-solving skills and helps in many areas of mathematics, including geometry and algebra.
Prepare 350g of a 2% lidocaine cream using a 1% lidocaine cream a 5% lidocaine cream
What is the area of a triangle that has a base of 15 1/4 in and a height of 18 in?
The area of the triangle is half the product of its base and height. The area of the triangle is 137.25 in².
What is the area of the triangle?The area of the triangle is half the product of its base and height. It is given by the formula,
[tex]\rm \text{Area of triangle} = \dfrac{1}{2} \times base \times height[/tex]
As it is given that the base of the triangle is 15¹/₄ inches, while the height of the triangle is 18 inches. Therefore, the area of the triangle is,
[tex]\rm \text{Area of triangle} = \dfrac{1}{2} \times base \times height[/tex]
[tex]= \dfrac{1}{2} \times 15(1/4)\times 18\\\\\\ = \dfrac{1}{2} \times \dfrac{(15\times 4)+1}{4} \times 18\\\\\\= \dfrac{1}{2} \times \dfrac{61}{4} \times 18\\\\\\=137.25\rm\ in^2[/tex]
Hence, the area of the triangle is 137.25 in².
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how do u estimate 8.36
the initial population was 50 thousand people and the population increased by 12% each year. Determine the function rule for this definition.
Choose the right answer. Two hundred fifty tickets are sold at a church fund raiser. If Sarah buys 15 tickets, the probability that she will win the prize quilt is .
Answer:
Her probability to win the prize quilt is 0.06, or she has a 6% probability of winning it.
Step-by-step explanation:
In statistics, a probability of 100% is represented with a 1. In this case, if Sarah would have bought the 250 tickets, she would have a probability of 1 to win the prize, as
[tex]\frac{250}{250}=1[/tex]
then, if this expression is multiplied by 100, we could say that the precentage of probability would have been 100%...
But Sarah didn't buy the 250 tickets, instead she bought 15, therefore
[tex]\frac{15}{250}=\frac{3}{50}=0.06[/tex]
which means that the probability of her winning the prize quilt is 0.06, or, if multiplied by 100, she has a 6% probability of winning the prize quilt.
Can someone please help me? The measure of the reflex angle in rhombus ABCD is 260°. Find x. Thanks
Trig: Use a half angle formula to find the exact value of the expression?
cos(5pi/12)
The correct answer is [tex]\frac{1}{2}[/tex].
To find the exact value of [tex]\cos(5\pi/12)[/tex] using a half-angle formula, we can follow these steps:
[tex]\cos(2\theta) = 2\cos^2(\theta/2) - 1[/tex]
Substituting [tex]\theta = 5\pi/6[/tex], we get:
[tex]\cos(5\pi/3) = 2\cos^2(5\pi/12) - 1[/tex]
[tex]\cos^2(5\pi/12) = \frac{\cos(5\pi/3) + 1}{2}[/tex]
[tex]\cos(5\pi/3) = \cos(\pi/3 + \pi) = -\cos(\pi/3)[/tex]
[tex]\cos(\pi/3) = \frac{1}{2}[/tex]
[tex]\cos(5\pi/3) = -\frac{1}{2}[/tex]
[tex]\cos^2(5\pi/12) = \frac{-\frac{1}{2} + 1}{2} = \frac{1}{4}[/tex]
[tex]\cos(5\pi/12) = \pm\sqrt{\frac{1}{4}} = \pm\frac{1}{2}[/tex]
Since cosine is an even function, we take the positive value.
[tex]\cos(5\pi/12) = \frac{1}{2}[/tex]
Therefore, the exact value of [tex]\cos(5\pi/12)$ is $\frac{1}{2}[/tex].
Complete question:
Use a half angle formula to find the exact value of the expression?
[tex]\cos(5\pi/12)[/tex]
3x - 12 + 6x + 9?/ Help Please
here goes another question lol oops
You are due a $750 paycheck at the end of the week (Friday), but want to get your hands on the cash on Monday. A payday lender offers to make this deal with you for a fee of 2% of the paycheck. What is the rate you are paying for this service? Assume a 365-day year.
A basketball player made 57 out of 100 attempted free throws. What percent of free throws was made?
For her cell phone plan Heather pays $30 per month plus 0.05 protects she wants to keep her bill under $60 per month with any quality represents the number of texts T Heather can't spend each month while staying within her budget
Convert 15/9 to a decimal. A. 1.64 B. 1.67 C. 1.66 D, 1.69
Jane goes to the fruit market every week. On Monday she buys 10 pears and 11 oranges for $10.05 By Friday she is out of fruit and goes back to the market to purchase 1 pear and one orange for $0.94 How much did Jane spend on 1 orange?
convert 82 into a fraction and decimal
I need help!!! Pleasssse!!!!
The ratio of the length to the width to the height of a rectangular box of cereal is 6:2:7. The sum of the length and the width of the box is 24 centimeters. Find the surface area of the box of cereal
Which expression is equivalent to:
25a + 5b - 13
Answer:
The correct option is 4.
Step-by-step explanation:
The given expression is
[tex]25a+5b-13[/tex]
In option (1), the given expression is
[tex]20a+5a+b-13[/tex]
Combine like terms.
[tex]25a+b-13[/tex]
This expression is not equivalent to the given expression.
In option (2), the given expression is
[tex]20(5a+5b)-13[/tex]
Using distributive property.
[tex]100a+100b-13[/tex]
This expression is not equivalent to the given expression.
In option (3), the given expression is
[tex]30ab-13[/tex]
This expression is not equivalent to the given expression.
In option (4), the given expression is
[tex]5(5a+b)-13[/tex]
Using distributive property.
[tex]25a+5b-13[/tex]
This expression is equivalent to the given expression.
Therefore correct option is 4.
Using an algebraic rule, describe a translation 2 units to the left.
Jackie has a drawer with 20 buttons, each of different color. How many different ways can she choose three buttons for her bookbag?
gloria went to the mall and spent 50 minutes shopping. then she. had lunch for 30 minutes. if gloria arrived at the mall at 11:00 a.m at what time did she finished lunch?
Gloria went to the mall and spent 50 minutes shopping. Then she had lunch for 30 minutes. If Gloria arrived at the mall at 11:00 A.M., at what time did she finish lunch?
15% of the school parking spaces are handicap spaces. The school has 18 handicap spaces. How many parking spaces are there?
Answer:
The answer is "120"
Step-by-step explanation:
I did it myself, and this is the answer i got :) I made sure it was correct but let me know if you have problems!
which of these equations represents functions? check all that apply
Granny has some stickers.if she gives 6 stickers to each of her grandchildren,she will have 5 stickers left.if she gives 7 stickers to each of her grandchildren,she will need 2 more stickers.how many grandchildren does granny have?
Write an equation that represents the data in the table x 5,10,15,20 y 17,22,27,32
A scale drawn on the map shows that 1 inch represents 24 miles. Of two cities are 2.25 inches apart on the map, what is the distance between them in real life?
the width of a rectangle is X and the length is twice he width. if the area of the rectangle is 162, what is X?
To find the value of X in a rectangle with width X and length 2X, we can use the area formula. By solving the equation, we find X = 9, making the width of the rectangle 9 units.
Explanation:To find the value of X, we need to use the given information about the length and width of the rectangle. Let's assume the width of the rectangle is X. Since the length is double the width, it is 2X. The area of the rectangle is given as 162, so we can set up the equation:
Width × Length = Area
X × 2X = 162
Simplifying the equation, we get:
2X^2 = 162
Dividing both sides by 2, we have:
X^2 = 81
Taking the square root of both sides, we find:
X = ±9
Since the width cannot be negative, the value of X is 9. Therefore, the width of the rectangle is 9 units.
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The width of the rectangle is 9 units.
Explanation:To find the width of the rectangle, we can set up the equation for the area. The width of the rectangle is X, and the length is twice the width, meaning the length is 2X. The formula for the area is length times width, so we have X * 2X = 162. Simplifying this equation gives us 2X^2 = 162. Dividing both sides by 2 gives us X^2 = 81. Taking the square root of both sides gives us X = 9. Therefore, the width of the rectangle is 9 units.
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Which of the following is parallel to the line =6x + 1
The ratio of french fries to packets of ketchup in Philip's bag is 8:1. What does this mean? A. There are 7 more french fries than packets of ketchup. B. For every 8 french fries, there is 1 packet of ketchup. C. For every 8 packets of ketchup, there is 1 french fry. D. There are 8 more french fries than packets of ketchup.
ashley measure the shell she collect she records the measurements in the chart
A cake decorator rolls a piece of stiff paper to form a cone. She cuts off the tip of the cone and uses it as a funnel to pour decorative sprinkles into small containers. The cone has a radius of 666 cm and a height of 181818 cm. What is the volume of the cone before the end is cut off? Either enter an exact answer in terms of \piπpi or use 3.143.143, point, 14 for \piπpi.
Answer:
V = 216 pi cm^3.
Step-by-step explanation: