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
oksian1 [2.3K]
3 years ago
7

Vanessa draws one side of an equilateral triangle ABC on the coordinate plane at points A(-2, 1) and B (4, 1). What are the two

possible coordinates of vertex C? Round to the nearest tenth.
Mathematics
1 answer:
Readme [11.4K]3 years ago
5 0

Answer:

two vertex are: (1 , 6.2) , (1 , - 4.2)

Step-by-step explanation:

A(-2, 1) and B (4, 1)    AB is a parallel segment with  x axis

The 3rd vertex P (x , y) will locate at the mid point of AB

x = (-2) + (4 - (-2)) /2 = 1       P (1 , y)

length AB = 4 - (-2) = 6

AP = AB (equilateral)

BP² = (4 - 1)² + (1 - y)² = 6²

1 - 2y + y² = 36 - 9 = 27

y² - 2y -26 = 0

y = ((-(-2)) ± √(-2)² - 4 x (-26)) / 2 = (2 ± √108) / 2 = 1 ± 5.2

y = 6.2 or y = -4.2

P (1 , 6.2) or P ( 1 , -4.2)

You might be interested in
The formula to find the spring constant, , for a spring with potential energy, , that has been stretched by length, , is shown b
aivan3 [116]

Answer:

the potential energy of the spring

5 0
2 years ago
Read 2 more answers
He length of a rectangle is three times its width. The perimeter of the rectangle is at most 112 cm.
g100num [7]
The equation relating length to width
L = 3W
The inequality stating the boundaries of the perimeter
LW <= 112
When you plug in what L equals in the first equation into the second equation, you get
3W * W <= 112
evaluate
3W^2 <= 112
3W <= 4 \sqrt{7}
W <= \frac{4 \sqrt{7} }{3} cm
8 0
3 years ago
Read 2 more answers
Martin would like to start training to run a marathon. The first week he runs a total of 15 miles. He would like to run 0.3 more
anygoal [31]

Answer: 15.3 miles

Step-by-step explanation:

From the question, we are informed that Martin would like to start training to run a marathon and that first week he runs a total of 15 miles.

We are further told that he would like to run 0.3 more miles each week than the week before. There, the number of miles that Martin will run the second week will be:

= 15 miles + 0.3 miles

= 15.3 miles

3 0
2 years ago
Write an explicit formula for a^n the nth term of the sequence 1,3,9....
frutty [35]

Answer:

  a_n = 3^(n -1)

Step-by-step explanation:

The n-th term of a geometric sequence with first term a1 and common ratio r is given by ...

  a_n = a1·r^(n-1)

Your sequence has first term 1 and ratio r=3, so the sequence is given by ...

  a_n = 3^(n -1)

_____

<em>Comment on sequences and series</em>

The sequences we commonly study are "arithmetic" and "geometric." Each of these has an explicit formula for the n-th term, based on the first term and the common difference or ratio. Similarly, each series (sum of terms of a sequence) also has a formula. That's 4 formulas to keep track of; not difficult. One of them, the formula for the n-th term of a geometric sequence, is shown above.

7 0
3 years ago
Factoring Trinomials
alexandr402 [8]
25 a² + 20 ab +  4 b²

for formula a^x+bx^ky^k+cy ^{2k } find  u,v such that: u.v = a

and u+v = b  then  group according to (ax ^{2k} +ux^ky^k)+(vx^ky^k+cy ^{2k} )

= (25a^2+10ab)+(10ab+4b^2)

factor out 5a from : 25a^2+10ab : 5a(2b+5a)

factor out 2b from : 10ab+4b^2: 2b(2b+5a)

= 5a(2b+5a) + 2b(2b+5a)

factor out : (5a+2b)

= (5a+2b)(5a+2b)

Refine:

(2b+5a)^2

hope this helps!.


3 0
3 years ago
Other questions:
  • A company pays its employees a base salary of $1000 every other week, plus $30 for each sale. How many sales did the employee ha
    7·1 answer
  • brine's kitchen has an area of 81 square feet. the kitchen is 9 times as many square feet as brine's pantry. if the pantry is 3
    7·1 answer
  • An ambulance has a mass of 5.44×105 ounces. Which unit of measurement is most appropriate to measure this mass? milligrams tons
    12·1 answer
  • If the answer is not a whole number, it should be entered as a decimal rounded to the hundredths place.
    11·2 answers
  • Triangle ABC, with angles and lengths as marked, is shown below.
    6·1 answer
  • All three medians intersect at the point of concurrency what’s it called
    7·1 answer
  • This figure consists of two semicircles and a rectangle.
    10·2 answers
  • Consider the function f(x) = x^{2/3} on the interval [-1,8].
    12·1 answer
  • An object’s weight on Earth varies directly to its weight on the Moon. If a man weighs 180 kg on Earth, then he will weigh 30 kg
    12·1 answer
  • One more than nineteen​
    15·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!