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
Andreyy89
3 years ago
13

The equation 4x2 – 24x + 4y2 + 72y = 76 is equivalent to

Mathematics
1 answer:
DerKrebs [107]3 years ago
5 0

Answer:

Option 4 is correct.

The equation 4x^2 -24x + 4y^2 + 72y = 76 is equivalent to 4(x-3)^2 + 4(y+9)^2 =436

Step-by-step explanation:'

Given equation: 4x^2 -24x + 4y^2 + 72y = 76

First group the terms with x and those with y;

(4x^2-24x)+(4y^2+72y) = 76

Next, we complete the squares.

We can do this by adding a third term such that the x terms and the y terms are perfect squares.

For this we must either add the same value on the other side of the equation or subtract the same value on the same side so that the equality is maintained.

⇒4(x^2-6x) +4(y+18y) = 76

or

4(x^2 -6x +3^2 -3^2) + 4(y^2 +18y +9^2 -9^2) = 76

4(x^2-6x + 3^2) - 36 + 4(y^2+18y +9^2) - 324 = 76

4(x-3)^2 + 4(y+9)^2 - 360 =76

Add 360 on both sides we get;

4(x-3)^2 + 4(y+9)^2 =360 +76

Simplify:

4(x-3)^2 + 4(y+9)^2 =436

Therefore, the given equation is equivalent to 4(x-3)^2 + 4(y+9)^2 =436

You might be interested in
HURRY ILL PICK BRAINLIEST!!!!!!!
telo118 [61]
<span>30x + 30y = 450 20x + 25y = 345

Here 345 represents the total area (in sq ft) shoveled; x repres. Melinda's rate and y represents Paul's rate.  We need to solve for x and y and then subtract the smaller from the larger.

</span>30x + 30y = 450   Multiply this eqn by 2:      6<span>0x + 60y = 900
</span>20x + 25y = 345   Mult this eqn by -3:          -60x -75y  = -1035
                                                                    ---------------------------
                                                                              -15y  = -135
                                                                                    y = 9

This comes to 9 square feet per minute.
Now, let's find x:    30x + 30y = 450; 30x + 270 = 450; 30x = 180; x = 6

Melinda can shovel 6 sq ft in 1 min, whereas Paul can shovel 9.

The difference is (9 - 6) sq ft / min,     or     3 sq ft / min   (answer)
4 0
2 years ago
Read 2 more answers
75+11(1777-S)=16,671
S_A_V [24]

Answer:

s = 268.27

Step-by-step explanation:

simplify: 75+19547-11s=16671

simplify more: 19622-11s=16671

subtract 19622 on both sides: -11s=-2951

divide both sides by -11: s=268.27

5 0
2 years ago
help quick! if BC is parallel to DE, then all of the following are equivalent to each other except...
Alecsey [184]
Answer is letter c. (CE/AC)
8 0
3 years ago
Read 2 more answers
PLEASE HELP ILL MARK YOU BRAINLIEST!!!!! 75 POINTS Use the function f(x) = 2x2 − 5x + 3 to answer the questions. Part A: Complet
andrew-mc [135]

Answer:

A. (2x-3)(x-1)

B. (1,0) \\(1.5,0)

2x^2-5x+3\\\frac{5(+ or -)\sqrt{(-5)^2-(4)(2)(3)}  }{2(2)} \\\frac{5(+ or -)\sqrt{25-24}  }{4}\\\frac{5(+ or -)\sqrt{1}  }{4}\\ \frac{5(+ or -)1  }{4}\\\frac{5+1}{4} or \frac{5-1}{4} \\ \frac{6}{4} =1.5  and \frac{4}{4} =1

C. Both sides will continue to increase as they go because this is an even degree quadratic equation.

D. You use the two x-intercepts to make sure it is in the correct area and since we know the end behavior all you'd have to assume is that it continues to go up so any negative answers you may accidentally receive would be incorrect.

3 0
3 years ago
What set of reflections would carry triangle abc onto itself?
masha68 [24]
Since all reflections are inverse of itself, carrying any reflection about the same axis twice will carry the preimage back to itself.
7 0
3 years ago
Read 2 more answers
Other questions:
  • Which ordered pair is a solution to the system of equations?
    12·1 answer
  • The ratio of green food coloring 1:2 if we use 6 drops of blue how many drops will we need math
    8·2 answers
  • Write 17/25 as a percent
    5·2 answers
  • Solve equation by taking square root 9r^2-3=-152
    8·1 answer
  • Can y’all tell me the answer of these 4 questions
    15·2 answers
  • What is the slope of (-3,4) and (5,8)
    5·1 answer
  • Identify the outliers of the data set. Then determine if the outlier increases or decreases the value of the mean.
    13·1 answer
  • Help need for test. What is the answer. There is an error in option c. It’s supposed to say line EF not line FF. Will give first
    5·1 answer
  • Can you please help me
    9·2 answers
  • Solve the inequality x+1&lt;3/4 and write the solution in interval notation.
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!