1. Find the length (distance) of segments AB, CD, and EF.
AB =
CD =
EF =
2. Find the midpoint of segments AB, CD, and EF.
AB =
CD =
EF =
3. Find the slope of the segments AB, CD, and EF.
AB =
CD =
EF =
Answer:
1) AB=7 CD=3 EF=[tex]3\sqrt{5}[/tex] 2) [tex]M_{AB}=\frac{-1}{2},2[/tex] [tex] \\ M_{EF} =(\frac{5}{2}-3)[/tex] \\ [tex] \\ M_{EF} =(\frac{5}{2}-3)[/tex] 3) AB not inclined CD not inclined EF 6/5
Step-by-step explanation:
1) We can use the Distance Formula to answer the 1st. question.
But in the first case AB I'd rather doing it intuitively because it is a straight line parallel to the x-axis
AB
A(-4,2) and B(3,2)
In this segment, also parallel we can calculate the length as |-4|+|3|=7 since both have the same y coordinate.
Using the Distance formula to check it:
[tex]D=\sqrt{(3--4)^{2}+(2-2)^{2}}\\D=\sqrt{49}\\D=7[/tex]
CD
C(-4,-1) D(-4,-4)
Similar to the first one but this time with different y coordinates.
The length will be calculated by subtracting the absolute values for y:
|-4|-|-1|=4-1 = 3
Using the Distance formula to check it:
[tex]D=\sqrt{(-4--1)^{2}+(-4--4)^{2}}\\D=\sqrt{9}\\D=3[/tex]
EF
E (1,-1) F(4,-5)
In this case there's no straight line.
So right to the Distance Formula:
[tex]D=\sqrt{(-5-1)^{2}+(4-1)^{2}}\\ D=\sqrt{36+9}\\D=\sqrt{45}\\D=3\sqrt{5}[/tex]
2) To find the Midpoints we need to calculate the Mean of these two points.
AB
A(-4,2) and B(3,2)
[tex]M_{AB} =\frac{-4+3}{2},\frac{2+2}{2}\\M_{AB}=\frac{-1}{2},2[/tex]
CD
C(-4,-1) D(-4,-4)
[tex]M_{CD} =\frac{-4-4}{2} ,\frac{-1-4}{2} \\M_{CD} =(0,\frac{-5}{2})[/tex]
EF
E (1,-1) F(4,-5)
[tex]M_{EF} =\frac{4+1}{2} ,\frac{-1-5}{2} \\ M_{EF} =(\frac{5}{2}-3)[/tex]
3) To find the Slope let's calculate the quotient of a difference between y-coordinates over x-coordinates of two given points.
[tex]m_{AB}=\frac{2-2}{3--4}=\frac{0}{7}=0[/tex]
AB is not inclined.
CD
C(-4,-1) D(-4,-4)
[tex]m_{CD}=\frac{-4--1}{-4--4}=\frac{-3}{-4+4}=\frac{-3}{0}[/tex]
Not Defined for all Real Set of Numbers
The line CD is not inclined.
EF
E(1,-1) F(4,-5)
[tex]m_{EF}=\frac{-5-1}{4--1}=\frac{6}{5}[/tex]
The line EF has a slope of 6/5
The cost of an oil change is $21.95. The markup rate is 65%. What is the selling price?
What do you do if you're looking for least common multiple and all your numbers are prime?
What is the measure of ∠SPQ in this rhombus?
m∠SPR = (2x+13)°
m∠QPR = (3x−12)°
Solution:
In a Rhombus The diagonals bisect the angles.
m∠SPR=m∠QPR
Substituting the given values :
2x+13=3x-12
Subtracting 2x both sides:
13=3x-2x-12
13=x-12
Adding 12 both sides:
x=25.
m∠SPR=2x+13=2(25)+13=50+13=63
m∠SPQ=2∠SPR
m∠SPQ=2m∠SPR
m∠SPQ=2x63=126
m∠SPQ= 126 degrees
work out the height of a parallelogram with a base of 10m and an area of 60m2
Tony is now three years older than howard. five years ago the sum of their ages was 59. now, tony is
The Tony age and Howard age be 36 and 33 respectively.
It is required to find the age of tony.
What is age?The amount of time during which someone or something has lived or existed. The length of time that a person has lived or a thing has existed.
Given:
Let Howard age=x
Tony age=x+3
Before 5 year we have,
Howard age=x-5,
Tony age=x+4-5=x-1
Some of there age=59
According to given question we have,
x-5+x-1=59
2x-6=59
2x=65
X=65/2
x=32.5
The age can't be fraction or decimal so we take 33.
Howard age=33
Tony age=33+3=36
Therefore, the Tony age and Howard age be 36 and 33 respectively.
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The function b(n) = 12n represents the number of baseballs b(n) that are needed for n games. how many baseballs are needed for 15 games?
Which ordered pair is a solution to this equation? 2x+3y=16 A.) (11, 1)
B.) (7,2)
C.) (5,2)
D.) (3,2)
5,2 is the answer, this is such easy question my baby brother could do it easy
Which graph represents the solution set for -4(1-×)<-12+2×?
The great pyramid in Egypt was built around 2560 BC over the years it has lost 30 feet of height off its top and is now 451 feet tall. Find the original height of the great pyramid
The price of a set of kitchen cabinets is $1,500 in January. In February, the price is increased by 10%. After not selling, the price is reduced by 5% in March. What is the price in March?
I need help solving 206x12
Which of the following statements about bullying is true? A. Children will independently learn positive behaviors as they mature B. Bullying is not harmful. C. Bullying is just a phase and children will grow out of it. D. Types of bullying include physical, verbal, emotional, and cyberbullying.
Types of bullying include physical, verbal, emotional, and cyberbullying about bullying is true. Correct option is D.
Option D is the correct statement. Bullying can take various forms, and the four main types of bullying are physical (e.g., hitting, pushing), verbal (e.g., name-calling, teasing), emotional (e.g., spreading rumors, excluding someone), and cyberbullying (bullying that takes place online or through digital means). It is essential to recognize and address these different types of bullying to create a safe and supportive environment for children and prevent harm.
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Sonia graphs the equations y = –x2 + 4x and y = x – 4 to solve the equation –x2 + 4x = x – 4. Her graph is shown below. What are the solutions of –x2 + 4x = x – 4? A.–5 and 0
B.–5 and –1
C.–1 and 4
D.0 and 4
Answer
C.–1 and 4
Explanation
Solving the equations y = –x² + 4x and y = x – 4
–x² + 4x = x – 4
x² - 4x + x = 4
x² - 3x = 4
x² - 3x + (3/2)² = 4 + (3/2)²
(x - 3/2)² = 4 + 9/4
= 6.25
x - 3/2 = √6.25 or x - 3/2 = -√6.25
x = 2.5 + 1.5 x = -2.5 + 1.5
= 4 = -1
divide this polynomial:
(x^2-6x-20) divided by (x+2)
* if someone would be able to tell me how to divide this it would be very MUCH appreciated
When the Citizens United decision was handed down, a flood of corporate cash was expected to enter the political system. The ruling did result in more corporate and union spending, but far less than anticipated because__________.?
4.624 to the nearest 10m
The value of the decimal number 4.624 to the nearest 10 places is 4.6
What is rounding off the numbers?When a number is rounded off, its value is maintained but is brought closer to the next number, simplifying the number. For entire numbers as well as decimals at different places of hundreds, tens, tenths, etc., it is done.
A number can be rounded off to its lower value if the number after the decimal is between 0 and 4. The number will be rounded off to its higher value if the number after it is between 5 and 9.
Given decimal number is 4.624. The rounding off is:-
4.624 = 4.6 at 10 places
Therefore, the value of the decimal number 4.624 to the nearest 10 places is 4.6
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How many sides does a polygon have if the sum of interior angles is 11700
To find the value of an expression is called
Which congruence theorem would complete the proof shown?
SSS
SAS
ASA
Answer:
ASA
C is correct
Step-by-step explanation:
We are given table of congruence of triangle.
1. Given: DC || AB and AD|| BC
2. If two lines are parallel then a tranversal line makes eight angles.
∠2=∠3 and ∠1=∠4 ( Alternate interior angle )
3 . If one side is common in two figure then reflexive property use.
CA = CA (Reflexive )
If we take two triangles ΔDAC and ΔCAB are congruent by above property.
ΔDAC ≅ ΔCAB by two angle and one side.
The property of congruence is ASA
4. ΔDAC ≅ ΔCAB by ASA
Hence, The 4th reason is ASA
Tasha earns $400 per week plus a commission of 10% on her weekly sales. Each week she saves of her earnings. In the expression , what does the expression 400 + 0.1s represent in this situation?
the amount Tasha saves each week
the amount Tasha earns each hour
Tasha's weekly commission
Tasha's weekly earnings
Answer:
its D
Step-by-step explanation:
Need help
Kendra is making a large salad for a party. She buys lettuce for $2.25 per pound and tomatoes for $2.65 per pound. She spends at least $8.
Let x represent the number of pounds of lettuce that Kendra buys. Let y represent the number of pounds of tomatoes that Kendra buys.
Which inequality represents this situation?
A. 2.25x+2.65y>8
B. 2.25x+2.65y<8
C. 2.25x+2.65y≤8
D.2.25x+2.65y≥8
Answer: The correct option is
(D) [tex]2.25x+2.65y\geq8.[/tex]
Step-by-step explanation: Given that Kendra is making a large salad for a party. She buys lettuce for $2.25 per pound and tomatoes for $2.65 per pound. She spends at least $8.
x represent the number of pounds of lettuce that Kendra buys and y represent the number of pounds of tomatoes that Kendra buys.
We are to select the inequality that represents the situation.
We have
total amount of money that Kendra spends on lettuce is given by
[tex]a_l=2.5\times x=2.5x[/tex]
and the total amount of money that she spends on tomatoes is
[tex]a_t=2.65\times y=2.65y.[/tex]
Therefore, the inequality can be written as
[tex]a_l+a_t\geq 8\\\\\Rightarrow 2.25x+2.65y\geq8.[/tex]
Thus, option (D) is CORRECT.
ed is using the recipe shown to make fruit salad he wants to use 30 diced stawberries in his vruit sald how many bananas apples and pears should ed use in his fruit sald
Answer:
4
Step-by-step explanation:
The ratio of boys to girls in Mrs. Ronilo's math class is 3 to 2. What percent of the class is boys?
Shirley measures the thickness of a piece of cardboard with a ruler that has centimeter and inch markings. Which of the following is most likely the value that Shirley measures?
3 inches is most likely what she measures because the ruler only has inches and centimeters so inches would be more logical
the number of peaches, p, is three less than half the number of grapes, g. which expression represents the number of peaches in terms of the number of grapes
A.g/2-3
B.2g-3
C.g-3/2
D.3g-2
peaches = 3 less than one half the number of grapes
so from the written problem you can get:
p=1/2g-3
1/2g is the same as g/2
so answer is A. p= g/2-3
The length of a side of an equilateral triangle is 12. find the length of the altitude
Final answer:
To calculate the altitude of an equilateral triangle with side length 12, divide the side by 2 and multiply by [tex]\(\sqrt{3}\)[/tex] giving an altitude of approximately 10.3923 units.
Explanation:
To find the length of the altitude of an equilateral triangle with a side length of 12, you can use the Pythagorean theorem. The altitude of the equilateral triangle creates two 30-60-90 right triangles. The altitude is the longer leg in this case, and the side of the triangle is the hypotenuse. In a 30-60-90 triangle, the longer leg (altitude) is [tex]\(\sqrt{3}\)[/tex]times the shorter leg (half of the side of the triangle).
First, divide the side of 12 into two to get the shorter leg of the right triangle, which is 6. Then, multiply 6 by \(\sqrt{3}\) to find the length of the altitude. This results in:
[tex]\(6 \times \sqrt{3} = 6\sqrt{3} \approx 10.3923\)[/tex]
Therefore, the altitude of the equilateral triangle is approximately 10.3923 units long.
The measure of each interoir angle of a regualr polygon is 144 . how many sides does this polygon have
A patchwork blanket is made up of 10 identical squares.Liam has made 14 squares,Raj has made 12 squares and Gemma has made 15 squares.How many patchwork blankets have they made between them ?
What is the slope of a line that is perpendicular to the line y = 8x + 5?
Answer: [tex]\dfrac{1}{8}[/tex]
Step-by-step explanation:
The given equation of a line : [tex]y = 8x + 5[/tex]
We know that general Slope-intercept form of equation is given by :-
[tex]y=mx+c[/tex], where m is the slope of the line.
When we compare the given equation the general slope intercept form of equation , we get
Slope of line = 8
We know that the product of slopes of two perpendicular line is -1.
Let m be the slope of line that is perpendicular to the line [tex]y = 8x + 5[/tex], then we have
[tex]-8\times m=-1\\\\\Rightarrow\ m=\dfrac{1}{8}[/tex]