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
DedPeter [7]
2 years ago
12

One vertex of an equilateral triangle is at the origin and the other vertex is at (3,4)

Mathematics
2 answers:
Keith_Richards [23]2 years ago
4 0

Answer:

(5 , 0)

Step-by-step explanation:

Illusion [34]2 years ago
3 0

Answer:

5 units

Step-by-step explanation:

Points:

  • (0, 0) and (3, 4)

The distance:

  • d= √(4-0)²+(3-0)² = √16+9= √25 = 5

Sides of the triangle are 5

You might be interested in
Find the distance from point A(−9,−3) to the line y = x−6. Round your answer to the nearest tenth.
Vladimir79 [104]

The distance from point A(−9,−3) to the line y = x−6 is 8.5 units

<u>What is slope ?</u>

A line's steepness is determined by its slope. In mathematics, slope is determined by "rise over run" (change in y divided by change in x).

step 1

Find the slope of the perpendicular line to the given line

y=x-6 ---> given line

The slope is m=1

Remember that

If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)

m1*m2 = -1

we have

m1=1

substitute

(1)*m2 = -1

so

m2 = -1

step 2

Find the equation of the perpendicular line to the given line

The equation in point slope form is

y-y1=m(x-x1)

we have

m=-1

(x1,y1)=(−9,−3)

substitute

y+3=-1(x+9)--> equation in point slope form

y+3= -x-9

y= -x-12---> equation in slope intercept form

step 3

Find the intersection point between the given line and the perpendicular line to the given line

we have the system of equations

y = x−6.

y= -x-12

Solve the system by graphing

The intersection point is (-3,-9)

see the attached figure

step 4

we know that

The distance between the point A and the point (-3,-9) is the same that the distance between point A and the line y=x-6

the formula to calculate the distance between two points is equal to

d=√[(y2-y1)² + (x2-x1)²]

substitute the values

d=√[(-9+3)² + (-3+9)²]

d= √72 units

simplify

d= 6√2 = 8.5 units

To learn more about the slope from the given link

brainly.com/question/16949303

#SPJ1

8 0
11 months ago
Please help this was due yesterday!
CaHeK987 [17]

Answer:

a) <

b) <

c) >

d) <

e) >

Step-by-step explanation:

5 0
3 years ago
Carlos drove to the train station and back. The trip there took five hours and the trip back took four hours. What was Carlos' a
katrin2010 [14]

Answer: 54.4 mph

Step-by-step explanation:

First find the distance to the train station. If it took Carlos 4 hours to come back driving at 68 mph, the distance is:

= Speed * time

= 68 * 4

= 272 miles

This means that Carlos drove for 5 hours to cover 272 miles the first time. His average speed was therefore:

= Distance / time

= 272/5

= 54.4 mph

3 0
2 years ago
The heights of women aged 20 to 29 are approximately normal with mean 64 inches and standard deviation 2.7 inches. Men the same
ohaa [14]

Answer:

z=(x-mu)/o

Step-by-step explanation:

X - Heights of women aged 20 to 29: X is N(64, 2.7)

Y - Heights of men aged 20 to 29: X is N(69.3, 2.8)

a) X=6'=72"

b) Y = 72"

c) 72' women can be taken as very tall but men moderately taller than average

d) Y<5'5" =65"

e) X>73"

Z>

Almost 0% can be taken

f) IQR =Q3-Q1

3 0
2 years ago
Use the augmented matrix to determine if the linear system is consistent. Is the linear system represented by the augmented matr
Crazy boy [7]

Answer:

The correct option is (A).

Step-by-step explanation:

If the reduced row echelon form of the coefficient matrix of a linear system of equations in four different variables has a pivot, i.e. 1, in each column, then the reduced row echelon form of the coefficient matrix is say A is an identity matrix, here I₄, since there are 4 variables.

\left[\begin{array}{cccc}1&0&0&0\\0&1&0&0\\0&0&1&0\\0&0&0&1\end{array}\right]

Then the corresponding augmented matrix [ A|B] , where the matrix is the representation of the linear system is AX = B, must be:

\left[\begin{array}{ccccc}1&0&0&0&a\\0&1&0&0&b\\0&0&1&0&c\\0&0&0&1&d\end{array}\right]

Now the given linear system is consistent as the right most column of the augmented matrix is a linear combination of the columns of A as the reduced row echelon form of A has a pivot in each column.

Thus, the correct option is (A).

8 0
3 years ago
Other questions:
  • Below is the graph of y = g(x)
    12·1 answer
  • -9x+6=-x+4<br> What is x??
    8·2 answers
  • Find the slope of the line containing points (1,3) (-3,-8)
    11·2 answers
  • What is 20% of 80. ​
    15·1 answer
  • Fill in the blank.<br> 65+26 is the same as 61 +
    15·2 answers
  • Please help I gotta find the unknown #
    6·1 answer
  • A variety pack of chocolates contains chocolate candies with different fillings. one eighth of the candy has coconut filling, 5/
    9·1 answer
  • What is the slope of this line that contains these points: (-4, -6) and (2,6)?​
    14·1 answer
  • Is 3.734795.... a rational or irrational number? and why
    15·1 answer
  • Linear Regression - Christmas Trees
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!