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
denpristay [2]
3 years ago
15

Parallelogram DEFG, DH = x + 3, HF = 3y, GH = 2x – 5, and HE = 5y + 2. Find the values of x and y.

Mathematics
1 answer:
12345 [234]3 years ago
5 0
Your answer is x = 36, y = 13.

We can find this by first realising that DH = HF, and GH = HE, as they are both diagonals of the parallelogram. This allows us to write the equations:

2x - 5 = 5y + 2
x + 3 = 3y

If we rearrange the equation x + 3 = 3y into x = 3y - 3, we can see that this becomes a pair of simultaneous equations that we can solve with substitution. Then we can substitute 3y - 3 into the first equation and solve for y:

2(3y - 3) - 5 = 5y + 2
6y - 6 - 5 = 5y + 2
6y - 11 = 5y + 2
- 5y
y - 11 = 2
+ 11
y = 13

Now because we know that x = 3y - 3, we can substitute 13 into this equation:

x = 3(13) - 3
x = 39 - 3
x = 36

I hope this helps!
You might be interested in
Daniella is solving 8/9 divided by 4 find her mistake and correct it
AysviL [449]
8/9 * 1/4 = 8/36 division of fractions is equal to the multiplication of the reciprocal
4 0
3 years ago
What is the range, min, and max of the function f(x)=13-20x-x²-3x⁴
Naya [18.7K]

Answer:

  • range: (-∞, 29.4336]
  • min: -∞
  • max: 29.4336

Step-by-step explanation:

I found these using a graphing calculator. (See attached)

The function is a polynomial of 4th degree with a negative leading coefficient. (The coefficient of the 4th-degree term is -3.) Therefore, it opens downward and has a range that extends to -∞. This function only has one global maximum and no local minimum.

_____

The maximum can be found by solving the cubic equation that results from taking the derivative of this function and finding the root of that:

  df/dx = -12x^3 -2x -20 = 0

There are formulas for the solutions of a cubic, but the one negative real root of this cubic can be found easily with a graphing calculator using iteration:

  x ≈ -1.13879908894.

Dividing by -2, the above derivative function can be written as ...

  g(x) = 6x^3 +x +10

The one real zero of it can be found using Newton's Method iteration.

The Newton's Method iterator function is

  h(x) = x - g(x)/g'(x)

where g'(x) is the derivative of g(x), often available as a function on the graphing calculator.

The starting value for the iteration can be the x-value obtained from the graph: -1.139. It only takes about 2 or 3 iterations to find x to the precision of the calculator: x = h(h(x)). This x is the x-coordinate of the maximum, so f(x) is the maximum value: 29.4335546516.

__

The attachments show the function definitions and their use for finding the maximum of f(x) using a TI-84 calculator. Y₁ is the function f(x); Y₂ is its derivative, shown above as g(x). Y₃ is the iterating function, shown above as h(x). The nDeriv( ) function is a calculator function that finds the numerical derivative of its argument.

6 0
3 years ago
Which equation correctly applies the distributive property?
Elodia [21]

Answer:

−3⋅(6.48)=(−3⋅6)+(−3⋅0.4)+(−3⋅0.08)

Step-by-step explanation:

7 0
2 years ago
Read 2 more answers
Given a cylinder with a radius of 6 cm and a height of 12 cm, find the volume of the cylinder. Use 3.14 for \pi
sergey [27]

Answer:

volume = \pi {r}^{2} h \\  = 3.14 \times  {6}^{2}  \times 12 \\  = 1356.48 \:  {cm}^{3}

5 0
3 years ago
The door to the club house has an area of 1,792 square centimeters. If the length of the door is 56 centimeters. How wide is the
babymother [125]

Answer:

The width of the door is 32 cm.

Explanation:

The formula for area is A = l*w

so the equation becomes:

1792 = 56*w

Divide both sides by 56 and you get

w = 32

8 0
3 years ago
Other questions:
  • If f(x) = x2 − 2x + 9 and g(x) = 8 − x, what is (f o g)(−4)?
    5·1 answer
  • Work out the values of a to e please
    11·1 answer
  • !! 100 POINTS SELECTED AND BRAINLIEST!!
    7·2 answers
  • F(x)=-4x^2+10x-8
    11·1 answer
  • What is the distance between -25 and -12 on a number line
    12·2 answers
  • Which expression represents the composition [f o g o h](x) for the functions below? f(x) = –2x^4 g(x) = 4x – 6 h(x) = x – 1
    15·2 answers
  • 45 is 20% of what number?
    14·1 answer
  • Tan(-100°) = _____<br><br> -tan80°<br> tan80°<br> tan(-80°)
    14·2 answers
  • Jamal has saved $2,000 for his
    9·2 answers
  • The square root of pie must be at less ten numbers long
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!