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
jeka57 [31]
3 years ago
7

In parallelogram DEFG, DH = x + 5, HF = 2y, GH = 4x-3 and HE = 4y + 1. Find the values of x and y. The diagram is not drawn to s

cale.

Mathematics
1 answer:
GalinKa [24]3 years ago
5 0
Rule: The diagonals of any parallelogram bisect each other. In other words, they cut each other in half.

This means DF is cut into two equal pieces: DH and HF.
Similarly, GE is cut into two equal pieces: GH and HE.

DH = HF
x+5 = 2y
x = 2y-5

GH = HE
4x-3 = 4y+1
4(x)-3 = 4y+1
4(2y-5)-3 = 4y+1 ... x has been replaced with 2y-5
8y-20-3 = 4y+1
8y-23 = 4y+1
8y-4y = 1+23
4y = 24
y = 6

If y = 6, then x is
x = 2y-5
x = 2(6)-5
x = 12-5
x = 7

--------------------------------------------

Answers: 
x = 7 and y = 6

You might be interested in
Does anyone know this one! Thanks
Scrat [10]

Answer:

22.4 cm

Step-by-step explanation:

2.8 cm x 8 sides = 22.4 cm

5 0
3 years ago
Read 2 more answers
The Vilas County News earns a profit of $20 per year for each of its 3,000 subscribers. Management projects that the profit per
Mekhanik [1.2K]

Answer:

850

Step-by-step explanation:

Current profit per year = $ 20

Number of subscribers = 3000

For each additional subscriber over 3000, the profit will increase by 1 cent or by $ 0.01. For example, for 3001 (3000 + 1) subscribers, the profit will be $ 20.01 per year. Similarly, for 3002 (3000 + 2) subscribers, the profit will be $20.02 per year and so on.

So, for x additional subscribers over 3000, the profit will increase by 0.01(x). i.e. for (3000 + x) subscribers, the profit will be $(20 + 0.01x)

Since, profit per each subscriber is $(20 + 0.01x), the profit for (3000 + x) subscribers will be:

Total profit = Number of subscribers x Profit per each subscriber

Total profit = (3000 + x)(20 + 0.01x)

We want to calculate how many subscribers will be needed to bring a profit of $109,725. So, we replace Total profit by $109,725. The equation now becomes:

109725=(3000+x)(20+0.01x)\\\\ 109725=60000+30x+20x+0.01x^{2}\\\\ 0.01x^{2}+50x+60000-109725=0\\\\ 0.01x^{2}+50x-49725=0\\

Using quadratic formula, we can solve this equation as:

\\ x=\frac{-50 \pm \sqrt{50^{2}-4(0.01)(-49725)}}{2(0.01)}\\\\ x=\frac{-50 \pm67}{0.02}\\\\ x=\frac{-50-67}{0.02} , x=\frac{-50+67}{0.02}\\\\  x=-5850, x=850

x = -5850 is not a possible solution as this would make the total number of subscribers to be negative. So we reject this value.

Therefore, the answer to this question is 850. 850 more subscribers are needed to being a total profit of $109,725

8 0
3 years ago
What is 5\10 plus +8\100
Tasya [4]

Answer:its 0.58

Step-by-step explanation:

5 0
3 years ago
What is the mean absolute deviation of the data set? 12, 15, 7, 4, 9, 10, 9, 6
bearhunter [10]
Here is an example:
Find the MAD of 2,4,6,8 Step 1 : Find the mean of the data : (2+4+6+8) / 4 = 20/5 = 4 Step 2 : Find the distance between each data and mean. Distance between 2 and 5 is 3 Distance between 4 and 5 is 1 Distance between 6 and 5 is 1 Distance between 8 and 5 is 3
Step 3 : Add all the distances : 3+1+1+3 = 8
Step 4 : Divide it by the number of data : 8 / 4 = 2 2 is the average absolute deviation.
3 0
3 years ago
A restaurant offers the following limited lunch menu:. Main Courses: Beef, Pork Roast, Duck, Quiche. Vegetables: Broccoli, Carro
max2010maxim [7]
The correct answer to this question is "120 ways"

Main Courses consists of Beef, Pork Roast, Duck, Quiche (4), Vegetables consists of Broccoli, Carrots, Potatoes (3), Beverages consists of Coffee, Tea, Milk, Soda and Shakes (5), Desserts consists of Ice Cream, Brownies (2)

The total number of ways can be solved as: 4 * 3 * 5 * 2 = 120
5 0
3 years ago
Other questions:
  • Is it true that a square can have more than one right angle?
    11·1 answer
  • Luis knows that his pool holds 3,050 gallons and that his water pump will pump the water out at a rate of 9 gallons per minute.
    10·1 answer
  • Which equation has slope of 1/2 and y intercept of -5
    12·2 answers
  • The number 10^55 is how many times the number 2 × 10^11 ?
    8·1 answer
  • What's the answer cuz I keep getting the wrong answer
    5·1 answer
  • Answer All Three Questions.
    15·2 answers
  • Answer question in image
    7·1 answer
  • Which of the following is a logical conclusion to the conditional statements
    6·1 answer
  • Math class, last chance to take it!
    11·1 answer
  • Wich time of line are shown in the figure
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!