Answers
9514 1404 393
Answer:
IS a parallelogram
Step-by-step explanation:
The slope formula for the slope of the line between points (x1, y1) and (x2, y2) is ...
m = (y2 -y1)/(x2 -x1)
The distance formula for the length of that same line is ...
d = √((x2 -x1)^2 +(y2 -y1)^2)
Here, you're asked to use each of these formulas 4 times, once for each side of the quadrilateral. I find it convenient to let a calculator or spreadsheet do the repetitive calculations. The result is attached.
The attachment shows that opposites sides have the same length and slope, so are parallel. The quadrilateral is a parallelogram. (The two points used in each calculation are the ones on the result line and the line immediately below. That is why point B is copied to the end of the list.)
_____
Additional comments
There are much simpler ways to prove the figure is a parallelogram. My favorite is to add the coordinates of the end points of the diagonals:
B +D = (-2+6, -9-3) = (4, -12)
C +E = (0+4, -5-7) = (4, -12)
These values being the same demonstrates the midpoints of the diagonals are coincident. That will only be the case if the quadrilateral is a parallelogram.
__
If you must use slope and distance formulas, showing either pair of opposite sides is parallel and have the same length is sufficient to guarantee that the other two sides are also parallel and have the same length. That is, the calculations required in this problem only need to be applied to one pair of opposite sides. (Using a spreadsheet, it's not a lot of extra work to do the calculations for both pairs of opposite sides.)
Related Questions
Mr. Green cuts his lawn every 8 days, while Mrs. Grasse cuts her lawn every 10 days. Suppose they both cut their lawns today. What is the least number of days that will pass before both Mr. Green and Mrs. Grasse cut their lawns on the same day again? *
Answers
4. Which of the following graphs represents y = x-2?
HURRRY PLSSSS. I NEED IT ASAP
Answers
Answer:
B
Step-by-step explanation:
when it says -2 that means you go straight down
Answer:
B
Step-by-step explanation:
-2 in the equation is the y intercept and the slope is positive so graph B is the only possible answer
Five less than twice the value of a number is equal to three times the quantity of
four more than one-half the number. What is the
number?
a. Let x be the number. Write and solve an equation to find x. Show your work.
b. Does the solution of your equation solve the original problem? Explain.
Answers
Answer:
a) x = 34
b) yes, it checks out
Step-by-step explanation:
2x - 5 = 3(4 + 1/2x)
multiply both sides by 2 to eliminate fraction
2[2x - 5 = 3(4 + 1/2x)] = 4x - 10 = 24 + 3x
x - 10 = 24
x = 34
check
2(34) - 5 = 3(4 + 34/2)
68 - 5 = 3(4 + 17)
63 = 3(21)
63 = 63
Write an equivalent expression. -2(7+5g)
Answers
Answer:
-2(7) + -2(5g)
Step-by-step explanation:
Using the distributive property we can confirm that:
-2(7) + -2(5g) = -2(7+5g)
Answer:
−14−10g
Step-by-step explanation:
First, solve the product:
-2 ⋅ 7 - 2 ⋅ 5g
Multiply -2 times 7 to -14.
So, the equivalent expression would be:
-14 - 2 ⋅ 5g = -14 - 10g
-14 - 10g
5. Suppose you invested PHP 25,000 at a simple interest at a rate of 2.5%, how much will be your investment after
10 years? a. PHP 43,750.00
C.PHP 45,730.00
b. PHP 31,250.00
d. PHP 47,350
Answers
Answer:
b. PHP 31,250.00
Step-by-step explanation:
Simple interest = principal × rate × time
Principal = PHP 25,000
Rate = 2.5%
Time = 10 years
Simple interest = principal × rate × time
= PHP 25,000 × 2.5% × 10
= 25,000 × 0.025 × 10
= 6,250
Simple interest = PHP 6,250
Investment after 10 years = principal + simple interest
= PHP 25,000 + PHP 6,250
= PHP 31,250
Investment after 10 years = PHP 31,250
What is the area? of this
Answers
Answer:
365 in^2
Step-by-step explanation:
15 - (5+3) = 7 which is the side of the rectangle.
7*20 = 140 is the area of the top rectangle
15*15 = 225 is the area of the bottom square
365 is the total area
Simplify:
(4/2d^2)^3
Answers
it needs to be 20 characters long so
Answer:
Step-by-step explanation:
[tex](\frac{4}{2}d^{2})^{3} =(2d^{2})^{3}\\\\= 2^{3}*(d^{2})^{3}\\\\=8d^{2*3}\\\\= 8d^{6}\\[/tex]
Hint: [tex](a^{m})^{n}=a^{m*n}\\\\[/tex]
what is the solution of 9x+4<7-3n IF X is an element of whole number
Answers
Answer: if you want me to solve for n or x here
Step-by-step explanation: hope this help:)
7) Are the expressions equivalent? *
*
8k + 5k = 13k
Answers
Answer:
Yes it is equivalent
Step-by-step explanation:
Answer:
Yes
Step-by-step explanation:
1. combined your like terms (8+5)k
2. add 8+5
3. Answer 13k (bring your K down)
Hits 2) How many solutions does the inequality have?
A) 0
B) 1
C) 8
D) infinitely many
Answers
9514 1404 393
Answer:
D) infinitely many
Step-by-step explanation:
There are infinitely many points on any portion of the number line. The shading on the graph indicates all numbers less than or equal to 8 are solutions. There are infinitely many such numbers.
Barred owls often lay two eggs, and each resulting chick has an equal probability of being male or female. What is the probability that both chicks are male, given that at least one of them is male?
Answers
Divide.
(8x^3+ 31x^2+ 6x +40) + (2x+8)
Answers
Answer:
divide them by what?
or fivide it with eachother?
15. Considera um losango em que uma diagonal tem 8cm e cuja área é 12cm^2. Qual é o comprimento do lado do losango, arredondado às décimas? Nota: Indica apenas o valor numérico usando algarismos. (Não escrevas unidades de medida na resposta.)
Answers
Answer:
4,3cm
Step-by-step explanation:
Passo 1
Um losango tem 2 diagonais, cujos comprimentos não são iguais
Temos que encontrar o comprimento da segunda diagonal
A fórmula é dada como:
Área de um losango = 1/2 (d1 × d2)
Área do losango = 12 cm²
d1 = Comprimento da primeira diagonal = 8cm
d2 = Comprimento da segunda diagonal = x
12 = 1/2 (8 × x)
12 = 1/2 (8x)
12 = 4x
x = 12/4
x = 3cm
O comprimento da segunda diagonal = 3 cm
Passo 2
A fórmula do comprimento da lateral de um losango é dada como:
s = √d1² + d2² / 2
d1 = 8cm
d2 = 3 cm
s = √8² + 3² / 2
s = √64 + 9/2
s = √73 / 2
s = 8,5440037453 / 2
s = 4,2720018727 cm
Aproximadamente = 4,3 cm
What's the largest fraction in each group? a. 5⁄6 and 29⁄36 b. 5⁄12 and 3⁄8 c. 2⁄5 and 19⁄45 d. 5⁄7, 13⁄14, and 19⁄21
Answers
Solution :
We have to find the largest fraction in each group.
a). [tex]$\frac{5}{6}$[/tex] and [tex]$\frac{29}{36}$[/tex]
[tex]$\frac{5}{6}$[/tex] → when we divide the number 5 with 6, we get 0.833
[tex]$\frac{29}{36}$[/tex] → when we divide 29 by 36, we get the value 0.805
Therefore, in this group, [tex]$\frac{5}{6}$[/tex] is the largest fraction.
b). [tex]$\frac{5}{12}$[/tex] and [tex]$\frac{3}{8}$[/tex]
[tex]$\frac{5}{12}$[/tex] → when we divide the number 5 with 12, we get 0.416
[tex]$\frac{3}{8}$[/tex] → when we divide 3 by 8, we get the value 0.375
Therefore, in this group, [tex]$\frac{5}{12}$[/tex] is the largest fraction.
c). [tex]$\frac{2}{5}$[/tex] and [tex]$\frac{19}{45}$[/tex]
[tex]$\frac{2}{5}$[/tex] → when we divide the number 2 with 5, we get 0.40
[tex]$\frac{19}{45}$[/tex] → when we divide 19 by 45, we get the value 0.42
Therefore, in this group, [tex]$\frac{19}{45}$[/tex] is the largest fraction.
d). [tex]$\frac{5}{7}$[/tex], [tex]$\frac{13}{14}$[/tex] and [tex]$\frac{19}{21}$[/tex]
[tex]$\frac{5}{7}$[/tex] → when we divide the number 5 with 7, we get 0.714
[tex]$\frac{13}{14}$[/tex] → when we divide 13 by 14, we get the value 0.928
[tex]$\frac{19}{21}$[/tex] → when we divide 19 by 21, we get the value 0.904
Therefore, in this group, [tex]$\frac{13}{14}$[/tex] is the largest fraction.
1/2 (12n-3)=14-10n
please help solve the value of n and show work!
Answers
Answer:
n = 31/32
Step-by-step explanation:
Hope I was able to help:))
the amusement park charges $20 to get in plus $1.50 per ride which linear equation represents this relationship y=1.5+20x,y=21.5x,y=1.5x+20,y=20x+1.5
Answers
Step-by-step explanation:
1.50 per ride tones X number of rides plus a 20 entrance fee
y= 1.5x + 20
Roberto is dividing his baseball cards equally between himself, his brother, and his 3 friends. Roberto was left with 9 cards. How many cards did Roberto give away? Write and solve an equation to solve the problem.
PLZZZ HELP MEE ILL GIVE BRAINLIEST AND 50 POINTS!!!
Answers
Answer:
The answer would be 45.
Step-by-step explanation:
5*9=45
Answer:
45
Step-by-step explanation:
First we count how many people he split it between which is 5 and we have to remember the key word here is equal so if he was left with 9 then everybody else did as well. so we multiply 5 times 9 which is 45
Find the value of each variable,
y =
Z=
Answers
y = 119
z = 66
EXPLANATION:
z = 180° - 114° = 66°
y = 360° - (95° + 81° + 66°) = 119°
what is the area of a rectangle if the length is (4x + 2) cm and a width of (5x – 3) cm
Answers
Answer:
20x^2−2x−6
Step-by-step explanation:
(4x+2)(5x+−3)
=(4x)(5x)+(4x)(−3)+(2)(5x)+(2)(−3)
=20x2−12x+10x−6
=20x2−2x−6
Multiply:
4x(5x) = 20x^2
4x(-3) = -12x
2(5x) = 10x
2(-3) = -6
Combine Like Terms:
10x-12x = -2x
Answer:
20x^2 - 2x - 6
Mina tiene \dfrac{4}{5} 5 4 start fraction, 4, divided by, 5, end fraction de la harina necesaria para hacer una hogaza. Se necesita la misma cantidad de harina para hacer 111 hogaza que para hacer 121212 panes. ¿Cuál es el mayor número de panes que Mina puede hacer con la harina que tiene?
Answers
Answer:
El mayor número de panes que Mina puede hacer con la harina que tiene es 9 torrejas de pan.
Step-by-step explanation:
Una hogaza equivale a 12 torrejas de pan, si Mina tiene [tex]\frac{4}{5}[/tex] de la harina necesaria para preparar una hogaza. Entonces, el número total de torrejas es [tex]\frac{4}{5}[/tex] de 12 torrejas de pan. Es decir,
[tex]x = \frac{4}{5}\times 12[/tex]
[tex]x = 9.6[/tex]
Puesto que la cantidad de hogazas en un número entero, se trunca al entero más cercano. En consecuencia, el mayor número de panes que Mina puede hacer con la harina que tiene es 9 torrejas de pan.
The volume of the right prism is 360 cm. What is the surface area of the prism, in square centimeters? Record your answer on the grid. Then fill in the bubbles. 9 cm 15 cm
Answers
Answer:
135 cm
Step-by-step explanation:
need help with all 3 pleaseeee
Answers
A.
D.
Hope this helps!!
A
D
Hope this helps!!
Is Janelle correct? Yes, because the lines are not parallel. Yes, because the lines will intersect. No, because the lines are in the same plane. No, because the lines are perpendicular.
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Answer:
Step-by-step explanation:
No, because the lines are in the same plane.
solve equation by completing the square 5n^2-3n-10=15
Answers
Help please! I don't really understand :/
Answers
WHAT I CAN DO
Read, analyze and solve.
1. Cesar invited 300 kids in the party. Only 15% of the kids did notshow up. How
many kids came to the party?
2. Rosa got 20% of an 80 item test incorrectly. How many items did she get
correctly?
3. There were 50 pupils in Grade Ill. If 28% of the pupils were absent, how many
pupils were present?
4. Out of 50 pupils, only 48 pupils joined the educational fieldtrip. What percent
joined the trip?
5. Among the 50 pupils in a Grade 6 class, 6% are left-handed. How many are left-
handed?
Answers
1.
300 x 0.15 = 45
300 - 45 = 255
255 kids came to the party
//
2.
80 x 0.20 = 16
80 - 16 = 64
She got 64 items correctly
//
3.
50 x 0.28 = 14
50 - 14 = 36
36 pupils were present
//
4.
48 / 50 = 0.96
0.96 x 100 = 96.0%
96% joined the trip
//
5.
50 x 0.06 = 3
3 pupils are left handed
What is the answer to this and how do I do it???
Answers
Answer
C
You just reverse the way you read the question.
the mean of the ages of 5 brothers is 13 years. If the ages of four of the brothers are 12, 16, 14, and 8, how old is the fith brother
Answers
If you want to solve this problem you would need to multiply 13 by 5 and then add 12, 16, 14, and 8 together and subtract it from your product of 13 and 5.
After that just check your answer by seeing if the mean of all the numbers is the same.
0.3 x 103
0 3 x 1025
Write the following as an ordinary number. [
(1 Point
3x10
Answers
0.3 x 1025 = 307.5
3 x 10^5 = 300,000
the two lines below are parallel if the slope of the red line is 5 what is the slope of the green line
Answers
Answer:
5
Step-by-step explanation:
Since the two lines are parallel, they must have the same slope. This means that the slope of green line must be 5 just like the red line. You can also use the slope formula (rise/run) or change in y divided by change in x.