1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Airida [17]
3 years ago
6

In parallelogram DEFG, DH = x + 1, HF = 3y, G H = 3 x − 4 , GH = 3x - 4, and HE = 5y + 1. Find the values of x and y. The diagra

m is not drawn to scale.

Mathematics
1 answer:
timofeeve [1]3 years ago
6 0

keeping in mind that in a parallelogram the diagonals bisect each other, namely cut each other into two equal halves.  Check the picture below.

\stackrel{GH}{3x-4}~~ = ~~\stackrel{HE}{5y+1}\implies 3x=5y+5\implies x=\cfrac{5y+5}{3} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{DH}{x+1}~~ = ~~\stackrel{HF}{3y}\implies \stackrel{\textit{substituting "x" in the equation}}{\cfrac{5y+5}{3}+1~~ = ~~3y}

\stackrel{\textit{multiplying both sides by }\stackrel{LCD}{3}}{3\left( \cfrac{5y+5}{3}+1 \right)=3(3y)}\implies 5y+5+3=9y\implies 5+3=4y\implies 8=4y \\\\\\ \cfrac{8}{4}=y\implies \boxed{2=y}~\hfill x=\cfrac{5y+5}{3}\implies x=\cfrac{5(2)+5}{3}\implies \boxed{x=5}

You might be interested in
How many combinations are there of the five letters j, k, l, m, and n using three letters at a time?
nikdorinn [45]
<span>5 n C r 3 = 10 </span><span>がんばってね</span>
7 0
3 years ago
Read 2 more answers
Mario has a rectangular prism completely filled with sand that has a base area of 85 cm² and a height of 15 cm. Mario pours all
just olya [345]

The base area of this second rectangular prism is 51 cm²

The rectangular prism completely filled with sand has a base area of 85cm² and height of 15cm .

<h3></h3><h3> volume of a rectangular prism</h3>
  • volume = Bh

where

B = base area

h = height

Since the first rectangular prism was completely filled with sand and it completely filled the second rectangular prism, it means they both have the same volume.

Therefore,

volume of the first rectangular prism = volume of the second rectangular prism.

  • volume  = Bh
  • volume = 85 × 15
  • volume = 1275 cm³

Therefore, the base area of the second rectangular prism can be calculated as follows:

volume = Bh

1275 = 25B

B = 1275 / 25

B = 51 cm²

learn more on prism here: brainly.com/question/2517494?referrer=searchResults

8 0
3 years ago
A bottom of a 6 foot deep circular pool has an area of 452.4 ft. If the pool is only
inna [77]

Answer:

450.4

Step-by-step explanation:

6 0
3 years ago
Valerie earns 24 dollars per hour.which expression can be used to show how much money she earns in 7 hours
barxatty [35]
It is 168 dollars in 7 hours
5 0
3 years ago
Read 2 more answers
PLEASE HELP ME I GIVE THE BRAINLIEST
Tems11 [23]

Answer:

what grade you in

Step-by-step explanation:

giuhyiufhyeiufheoirgjuoeirgjuer

7 0
3 years ago
Read 2 more answers
Other questions:
  • If the function f(x) has a domain of (g,h) and a range of (j,k), then what is the domain and range of g(x) = m(f(x)] + p?​
    12·1 answer
  • Plz help only 5 questions
    14·1 answer
  • On average, a pair of bike tires can last 18 months if used every day. The length of time bike tires can last is exponentially d
    7·1 answer
  • What is the LCM of 4?
    10·1 answer
  • Cindy goes to dinner with a friend. The total bill is $16.50. Cindy brought $20.00 with her. What is the closest to the maximum
    8·1 answer
  • Rs800 for 3 year at rate of 5 percent p.a
    10·1 answer
  • Help please!!!!!!<br><br> Look at the picture
    15·1 answer
  • Can someone help me solving this differential equation?
    7·1 answer
  • Challenge A cell phone plan costs $19.80 per month for 400 minutes of talk time. It costs an additional $0.06 per minute for eac
    9·1 answer
  • Two gears are connected and rotating at the same time. The smaller gear completes 2 1/2 rotations every time the larger gear com
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!