WILL GIVE BRAINLIEST! Prove that a quadrilateral ABCD with vertices A(–1, –2), B( 2, –5), C(1, –2), and D( –2, 1) is a parallelogram. Find the point of intersection of the diagonals of parallelogram ABCD. Provide your complete solutions and proofs in your paper homework and enter the numeric answers online.
Answers
Answer:
Step-by-step explanation:
To prove a quadrilateral a parallelogram we prove,
1). Length of opposite sides are equal.
2). Slopes of the opposite sides are same.
Length of AB = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
= [tex]\sqrt{(2+1)^2+(-5+2)^2}[/tex]
= [tex]3\sqrt{2}[/tex]
Length of BC = [tex]\sqrt{(2-1)^2+(-5+2)^2}[/tex]
= [tex]\sqrt{10}[/tex]
Length of CD = [tex]\sqrt{(1+2)^2+(-2-1)^2}[/tex]
= [tex]3\sqrt{2}[/tex]
Length of AD = [tex]\sqrt{(-1+2)^2+(-2-1)^2}[/tex]
= [tex]\sqrt{10}[/tex]
Therefore, AB = CD and BC = AD (Opposite sides are equal in length)
Slope of AB = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
= [tex]\frac{-5+2}{2+1}[/tex]
= -1
Slope of BC = [tex]\frac{-5+2}{2-1}[/tex]
= -3
Slope of CD = [tex]\frac{1+2}{-2-1}[/tex]
= -1
Slope of AD = [tex]\frac{-2-1}{-1+2}[/tex]
= -3
Slope of AB = slope of CD and slope of BC = slope AD
Therefore, AB║CD and BC║AD
Hence ABCD is a parallelogram
Related Questions
1. One rule of thumb for estimating crowds is that each person occupies 2.5 square feet. Use this value to
determine the number of people that would fit in a room that is 216 in x 360in.
Answers
Answer:
216 people
Step-by-step explanation:
Given:
2.5 feet² is occupied by 1 person
Dimension of room = 216 in × 360 in
Required:
No. of people that would occupy the room
SOLUTION:
Step 1:
Convert the dimensions of the room from in to ft
Note: 1 foot = 12 inches
216 inches = [tex] \frac{216}{12} = 18 ft [/tex]
360 inches = [tex] \frac{360}{12} = 30 ft [/tex]
Step 2: calculate area of the room.
Area of the room = 30*18 = 540 ft²
Step 3: calculate the no. of people the room will contain.
2.5 ft² will contain one person
Therefore, 540 ft² will contain: [tex] \frac{540}{2.5} = 216 people [/tex]
when you reverse the digits of a certain two-digit number you decrease its value by 45. What is the number if the sum of its digits is 5
Answers
Answer:
The number is 50.
Step-by-step explanation:
We need to understand the problem and convert it into a mathematical equation, or a series of equations. That way, we can solve them with ease.
The first thing we can do is to assign variables to represent the values that we do not know.
Let us assign the first number to be = x and the second number to be = y.
Important!
At this point, we must put their place values into consideration.
Since we are dealing with a two-digit number, we only have tens and units.
We will account for the place values of the variables assigned (x and y) by multiplying them by 10 and 1
x is the tens place value. To occupy this place value, it will become 10x
y is the unit place value. To occupy this place value, it will become 1 X y = y
This means that the original number is of the format x y
To convert this to an equation, it will become 10 (x) + y
Once the number order is reversed we will have 10 (x) + y = 10(y) + x - 45
grouping like terms
10x-x - 10y +y = - 45
9x -9y = - 45
From the second statement, we also have that x + y = 5
hence we have two equations x + y = 5 ---------- equation 1
9x -9y = - 45 ------------ equation 2
solving simultaneously, we have that the two numbers are 0 and 5
The number therefore, is 50
x = 5 and y = 0
If pqr measures 75 what is the measure Of sqr
Answers
Answer:
∠SQR = 53°
Step-by-step explanation:
happy to help
A cookie shop offers 6 varieties of cookies and bakes 5 dozen of each kind every day, from Monday through Friday. How many cookies are baked in four weeks?
Answers
Answer:
7,200 pieces are baked in four weeks
Step-by-step explanation:
Here in this question, we are interested in knowing the number of cookies baked in four weeks.
Okay, here we know that there are 6 varieties with 5 dozen of each kind baked everyday.
A dozen is 12 , this means that 5 dozens will be 5 * 12 = 60
Now, 60 pieces of each variety is baked per day. The total number of cookies baked per day is thus 60 * 6 = 360 pieces
Now, a week is just 5 days here. Since we are not considering weekends. Now, the number of days in 4 weeks will be 4 * 5 = 20 days
Since 360 pieces are baked in a day and we have the baking for 20 days in four week, the number of cookies baked is simply the product of the number of pieces and the number of days.
That will be 20 * 360 = 7200 pieces
65347457467+4609800=?
Answers
Answer:
65,352,067,267
i dont know what else to say.
Hello
Find the missing value in the equation below.
12 + 13 = 34-
Answers
Hope it helps :)
Answer:
Step-by-step explanation:
Yo it's 9 bro hope this helps mane
Q Search
Performance Task
Navigation
Have you ever wondered how sailors navigated the oceans before the Global Positioning
System (GPS)? One method sailors used is called dead reckoning. How does deal
reckoning use mathematics to track locations? Could you use this method today?
1. In nautical navigation, it is common practice to use angle measures in degrees,
distances in nautical miles, and speed in knots (nautical miles per hour). The
relationship between miles per hour and knots is linear. (1 knot = 1.15078 mi/h)
Use this relationship to complete the chart to the nearest tenth of a mile.
knots
mi/h
5 knots
mi/h
10 knots
mi/h
Answers
Answer:
knots mi/h
5 knots 5.7539 mi/h
10 knots 11.5078 mi/h
Step-by-step explanation:
Given
knots mi/h
5 knots _mi/h
10 knots _mi/h
Required
Fill in the gap
From the question, we understand that
[tex]1 knot = 1.15078mi/h[/tex]
Solving (a): 5 knots
Recall:
[tex]1 knot = 1.15078mi/h[/tex]
Multiply both sides by 5
[tex]5 * 1 knot = 1.15078mi/h * 5[/tex]
[tex]5\ knots = 1.15078mi/h * 5[/tex]
[tex]5\ knots = 5.7539\ mi/h[/tex]
Solving (b): 10 knots
Recall:
[tex]1 knot = 1.15078mi/h[/tex]
Multiply both sides by 10
[tex]10 * 1 knot = 1.15078mi/h * 10[/tex]
[tex]10\ knots = 1.15078mi/h * 10[/tex]
[tex]10\ knots = 11.5078mi/h[/tex]
Hence; The complete table is
knots mi/h
5 knots 5.7539 mi/h
10 knots 11.5078 mi/h
What is the value of the expression 3y−zy+5z when y = 6 and z = 2? 1. 1 2. 3 3. 4 4. 16 There is a pic too plz help...fast!!!!
Answers
Answer:
The answer is 1Step-by-step explanation:
[tex] \frac{3y - z}{y + 5z} [/tex]
To find the value of the expression when
y = 6 and when z = 2 , substitute the values into the above formula and solve.
That's
[tex] \frac{3(6) - 2}{6 + 5(2)} \\ = \frac{18 - 2}{6 + 10} \\ \frac{16}{16} [/tex]
We have the final answer as
1Hope this helps you
Answer:
[tex]\Huge \boxed{1}[/tex]
Step-by-step explanation:
[tex]\displaystyle \frac{3y-z}{y+5z}[/tex]
Let y = 6 and z = 2.
[tex]\Rightarrow \displaystyle \frac{3(6)-2}{6+5(2)}[/tex]
Evaluate the expression.
[tex]\Rightarrow \displaystyle \frac{18-2}{6+10}[/tex]
[tex]\Rightarrow \displaystyle \frac{16}{16}[/tex]
[tex]\Rightarrow 1[/tex]
The value of the expression when y = 6 and z = 2 is 1.
Given that Cosecant (t) = negative StartFraction 13 Over 5 EndFraction for Pi less-than t less-than StartFraction 3 pi Over 2 EndFraction use an appropriate identity to find the value of cot(t).
Answers
Answer:
[tex]\bold{cot(t) =\dfrac{12}{5}}[/tex]
Step-by-step explanation:
Given that:
[tex]Cosec (t) = -\frac{13}5[/tex]
for [tex]\pi < t < \frac{3 \pi}2[/tex]
That means, angle [tex]t[/tex] is in the 3rd quadrant.
To find:
Value of cot(t)
Solution:
First of all, let us recall what trigonometric ratios are positive and what trigonometric ratios are negative in 3rd quadrant.
In 3rd quadrant, tangent and cotangent are positive.
All other trigonometric ratios are negative.
Let us have a look at the following identity:
[tex]cosec^2\theta -cot^2\theta =1[/tex]
here, [tex]\theta =t[/tex]
So, [tex]cosec^2t-cot^2t=1[/tex]
[tex]\Rightarrow (-\dfrac{13}{5})^2-cot^2t=1\\\Rightarrow (\dfrac{169}{25})-cot^2t=1\\\Rightarrow \dfrac{169}{25}-1=cot^2t\\\Rightarrow \dfrac{169-25}{25}=cot^2t\\\Rightarrow \dfrac{144}{25}=cot^2t\\\Rightarrow cot(t)=\pm\sqrt{\dfrac{144}{25}}\\\Rightarrow cot(t)=\pm\dfrac{12}{5}[/tex]
But, angle [tex]t[/tex] is in 3rd quadrant, so value of
[tex]\bold{cot(t) =\dfrac{12}{5}}[/tex]
Answer:
12/5
Step-by-step explanation:
Mila spends a winter day recording the temperature once every three hours for science class. At 9 am, the temperature was -1.6°F. Between 9am and noon, the temperature rose 6.6°F. Between noon and 3pm, the temperature increased by 2.8°F. Between 3pm and 6pm, the temperature went down 10.5°F. What was the temperature at 6pm?
Answers
We can conclude the following information:
Every 3 hours the temperature changes.
At 9 AM, the temperature was -1.6°F:
9 AM = -1.6°F =>
Between 9 AM and noon, the temperature rose 6.6°F:
12 PM = -1.6 + 6.6 = 5°F =>
Between noon and 3 PM, the temperature increased by 2.8°F:
3 PM = 5 + 2.8 = 7.8°F =>
Between 3 PM and 6 PM, the temperature went down 10.5°F:
6 PM = 7.8 - 10.5 = -2.7°F
What was the temperature at 6 PM?
-2.7°F
Orville and Wilbur Wright made the first airplane flights in 1903.
Answers
Answer:
True
Step-by-step explanation:
On December 17, 1903, Wilbur and Orville Wright made four brief flights at Kitty Hawk with their first powered aircraft. The Wright brothers had invented the first successful airplane. The Wrights used this stopwatch to time the Kitty Hawk flights.
Answer:
yes
Step-by-step explanation:
Which of the following is equivalent to (2a2-6ab2+4b2)-(-a2+2ab-2b2
Answers
Answer:
Step-by-step explanation:
2a^2 - 6ab^2 + 4b^2 + a^2 - 2ab + 2b^2
3a^2 - 6ab^2 + 6b^2 - 2ab
One of the fractions is a Repeating decimal the other one is terminated which one is which without dividing how can you tell 1/11 9/100
Answers
Answer:
1/11 is a repeating decimal
9/100 is a terminated decimal
Step-by-step explanation:
Properties of the fractional part of 100 can be determined as percentages. Using this, we can see that 9/100 will result in .09 or 9%.
Properties of the fractional part of 11 can be seen to be a non-divisible number resulting in a repeating decimal equivalent. So, 1/11 will result in .090909 ad infinitum.
Note, that odd divisors that are not multiples of 5, typically will result in a repeating decimal.
Cheers.
Using a sheet of graph paper, solve the following system of equations graphically. x+y=0 x-y+2=0
Answers
Answer:
(-1, 1)
Step-by-step explanation:
I used a graphing tool to graph the two lines. When graphed, the lines intercept at point (-1,1). Therefore, it is the solution to the system of equations.
Hope this helps.
The age of Tony and Vihaan are in the ratio of 8:7. Six years later, their ages will be in the ratio 10:9. Find their ages.
Answers
Answer:
24 and 21
Step-by-step explanation:
the ratio of their ages is 8 : 7 = 8x : 7x ( x is a multiplier )
In 6 years
8x + 6 : 7x + 6 = 10 : 9
Express the ratio in fractional form
[tex]\frac{8x+6}{7x+6}[/tex] = [tex]\frac{10}{9}[/tex] ( cross- multiply )
9(8x + 6) = 10(7x + 6) ← distribute parenthesis on both sides
72x + 54 = 70x + 60 ( subtract 70x from both sides )
2x + 54 = 60 ( subtract 54 from both sides )
2x = 6 ( divide both sides by 2 )
x = 3
Thus
Tony = 8x = 8 × 3 = 24
Vihaan = 7x = 7 × 3 = 21
Answer:
Tanay's age = 24yrs
Vihaan's age = 21yrs
Step-by-step explanation:
let the ages of tanay and vihaan be8x,7x
After 6yrs tanay's age=8x+6
vihaan's age=7x+6
a/q=8x+6/7x+6=10/9
=9(8x+6)=10(7x+6)
=72x+54x=70x+60
72x-70x=60-54
2x=6
x=3
tanay's age=8×3=24yrs
vihaan's age=7×3=21yrs
hope this helps you friend
its about geometry i need help its urgent
Answers
Answer:
1) 37
2) 23
3) x = 4
4) 58
Step-by-step explanation:
1) 15 + 22 = 37
2) 54 - 31 = 23
3) 6x + 1 + x + 7 = 36
7x + 8 = 36
7x = 28
x = 4
4) 3x + 10 + 47 = 9x - 39
57 = 6x -39
96 = 6x
16 = x
3(16) + 10 = 58
Answer:
see below
Step-by-step explanation:
22 15
1. L -----------------M------------N LN = 22 + 15 LN = 37
31 ??
2. L -----------------M------------N MN = 54 - 31 MN = 23
|<-----------54 ---------------->|
6X+1 X+7
3. R -----------------S------------T find X
(6x + 1) + (x + 7) = 0
7x = -8
x = - 8/7
47 3X+10
4. D -----------E---------------------F find EF
|<--------- 9X - 39 ------------>|
47 + (3x + 10) = (9x - 39)
3x - 9x = -39 - 10 -47
-6x = -96
x = -96 / -6
x = 16
EF = 3x + 10
EF = 3(16) + 10
EF = 58
Marcus had a rope that was 75 filet long. He cut off part of the rope. After
that, the rope was 56 feet long.
If f = the number of feet Marcus cut off the rope, which mathematical
sentence expresses the information above?
A. 56 - f = 75
B. 75 - f= 56
C. 75+ f = 56
D. f- 75 = 56
Answers
Answer:
The answer is B. 75 - f = 56
Step-by-step explanation:
10 times 0.63 repeating
Answers
Answer:
6.36363
Step-by-step explanation:
Answer:
6.36 repeating
Step-by-step explanation:
10 x 0.63 repeating
When you multiply ten by any number, you move the decimal to the right one place value.
0.6363...
6.3636...
So the answer is 6.36 repeating.
What are the factors of x2 − 64? Prime (x − 4)(x + 16) (x − 8)(x − 8) (x + 8)(x − 8)
Answers
[tex] {x}^{2} - {8}^{2} [/tex]
[tex](x - 8)(x + 8)[/tex]
If f(x)=2x+5, then what is f(3)?
Answers
Answer:
[tex]\Large \boxed{f(3)=11}[/tex]
Step-by-step explanation:
[tex]f(x)=2x+5[/tex]
For f(3), the input for the function f(x) is 3.
Let x (input) = 3.
[tex]f(3)=2(3)+5 \\\\ f(3)=6+5 \\\\ f(3)=11[/tex]
Answer:
11
Step-by-step explanation:
f(x)=2x+5
Let x = 3
f(3) = 2*3+5
= 6+5
= 11
1 2 3 4 5 B 10 Which statement about rational numbers is true? All rational numbers are fractions. Rational numbers never have repeating decimals. Some integers are not rational numbers. O All fractions containing integers are rational numbers.
Answers
Answer:
all fractions containing integers are rational numbers is true I believe.
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
PLEASE HELP ILL MARK U THE BRAINLIEST IT IS URGENT AND ITS GEOMETRY DONT WASTE ANSWERS PLEASE
Answers
Answer:
∠Q = ∠U = 60°
Step-by-step explanation:
Construct the figure QSUT with your own dimensions as long as QR ≅ RU and SR ≅ RT , where R is the common midpoint.
I choose QR = 4 cm and SR = 5 cm
Then measure ∠Q and ∠U to check if they are equal.
I got that ∠Q = ∠U = 60° proving that;
∠Q ≅ ∠U
Jayden walked a total of 12x+5r-8 miles on Monday and Tuesday. If he walked 7x-10r miles on Monday, how
many miles did he walk on Tuesday?
Answers
Answer: Jayden walked 8 miles on Tuesday
Step-by-step explanation:
What is the perimeter of a square with a side length 6x - 5
Answers
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{24x - 20}}}}}[/tex]
Step-by-step explanation:
Given,
Length ( L ) = 6x - 5
Perimeter of a square ( P ) = ?
Finding the perimeter of a square having length of 6x- 5
[tex] \boxed{ \bold{ \boxed{ \sf perimeter \: of \: a \: square \: = 4l}}}[/tex] ( where l is the side of the square )
plug the value of length
⇒[tex] \sf{4(6x - 5)}[/tex]
Distribute 4 through the parentheses
⇒[tex] \sf{4 \times 6x - 4 \times 5}[/tex]
⇒[tex] \sf{24x - 20}[/tex]
Hope I helped!
Best regards!!
solve for x 10+10= -2(4x-10)
Answers
Answer:
x = 0
Step-by-step explanation:
10 + 10 = -2(4x - 10)
20 = -8x + 20
0 = -8x
0/-8 = x
0 = x
Answer: x=0
Step-by-step explanation:
Given
10+10=-2(4x-10)
Combine like term
20=-2(4x-10)
Distributive property (REMEMBER you need to change signs when it is negative outside)
20=-8x+20
Subtract 20 on both sides (subtractive property of equality)
-8x=0
Divide -8 on both sides (division property of equality)
x=0
Hope this helps!! :)
Please let me know if you have any question
You work at a coffee shop and are making a drink using espresso and steamed milk. For a 3-ounce drink, the recipe
calls for 1 ounce of espresso. What fraction of the beverage is steamed milk?
Answers
Answer:
2/3
Step-by-step explanation:
the question says you are making a drink using espresso and steamed milk, it doesn't give you any other ingredients, and its a 3oz. drink so 1oz, of espresso and 2oz. of steamed milk
-4x+-3=17
what is the answer
Answers
Answer:
x = -5
Step-by-step explanation:
-4x + -3 = 17
-4x - 3 = 17
-4x - 3 + 3 = 17 + 3
-4x = 20
-4x/-4 = 20/-4
x = -5
Hope this helps!
Answer:
x=-5
Step-by-step explanation:
-4x+-3=17
First add 3 to both sides.
-4x=20
Then divided by -4
Note: Negatove divided by postive is negative.
20÷(-4) = -5
So.
x=-5
need help due soon thx
Answers
Answer:
Step-by-step explanation:
Let x=0.121212.....
100x=12.121212...
100x-x=12.12121212...-0.121212...
99x=12
x=12/99
so 0.121212... is equal to 12/99
Hope this helps!! :)
Step-by-step explanation:
mark as brainlist
leave a like
values of x in simplest form.
9 – 4|3 + 5x| = 5
Answers
Answer:
x=4/5
Step-by-step explanation:
9 - |12-20x| = 5
=>-|12-20x|= 5-9
=>-|12-20x|=-4
=>12-20x=-4
=>-20x=-4-12
=>-20x=-16
=>x=16/20
=>x=4/5
10 fewer than a number t
Answers
Answer:
t-10
Step-by-step explanation:
fewer than means it comes after
t-10
Answer:
it's t -10
Step-by-step explanation: