Are the triangles congruent, if so by what theorem/postulate

Write the equation of the line with the given slope and y-intercept

goldenfox [79]

Answer:

A) y = x - 3/4

Step-by-step explanation:

The equation of the line with slope m and intercept b is

y = mx + b

Here were have slope = m = 1.

y-intercept = b = -3/4

Equation:

y = mx + b

y = 1x + (-3/4)

y = x - 3/4

Answer: A) y = x - 3/4

4 0

2 years ago

answer to #10 and #13. can’t figure out how to use interval notation to write domain and range for graphs.

Lyrx [107]

Interval notation is used to write a set of real numbers from one value to another value.
On the left, you start with left parenthesis or left bracket.
Then you follow by two numbers separated by a comma.
You then finish with a right parenthesis or right bracket.
To include a number, use a square bracket.
To exclude a number use parenthesis.
To write the set of numbers, you need to list the smallest number in the set followed by the largest number in the set. An interval is always stated with two numbers, from the smallest in the set to the largest in the set. The numbers are always separated by a comma.

Examples:

1) All numbers from 6 to 10, including 6 and 10.
Algebra: 6 <= x <= 10
Interval: [6, 10]
Notice brackets since both 6 and 10 are included in this interval.

2) All number from 5 to 20, including 5 but not including 20.
Algebra 5 <= x < 20
Interval: [5, 20)
Bracket with 5 means include 5. Parenthesis with 20 means 20 is not included.

3) All numbers greater than or equal to 7.
Algebra: x >= 7
Interval: [7, ∞)
The 7 has a bracket because it is included. Infinity always has parenthesis.
With the infinity symbol, always use parenthesis, not square bracket.

4) All numbers less than -5.
Algebra: x < - 5
Interval: (-∞, 5)

Now for your problems.

10.
This is a line. Both the domain and range all all real numbers.
That means the interval is from negative infinity to positive infinity.
(-∞, ∞)
Both the domain and range are that same interval, all real numbers, from negative infinity to positive infinity.

13.
The domain is all real numbers as you can see the x-coordinates extend left forever and right forever. The domain is the same interval as the domain and range of problem 10.

The range is zero and all positive numbers.
You can think of it a all values of y such that y is greater than or equal to zero. Notice that zero is included in the interval.

[0, ∞)

Since zero is included, we use a left bracket, not left parenthesis.
With infinity, we alyways use parentheses, not brackets.

8 0

3 years ago

Which statements are true regarding elements of the given sets? Check all that apply. Paris ∈ F. The Statue of Liberty ∈ A. The

jek_recluse [69]

Answer:

Paris F, Abraham Lincoln belongs to none of these sets, and The Eiffel Tower is in more than one of these sets

Step-by-step explanation:

8 0

3 years ago

Answer this math question

jenyasd209 [6]

Which one do you want to he answered?

7 0

3 years ago

Suppose that receiving stations X, Y, and Z are located on a coordinate plane at the points (4,5), (-6,-6), and (-14,2

Lilit [14]

Answer:

(-2, -3)

Step-by-step explanation:

A careful graph shows the point (-2, -3) is at the intersection of the circles whose radii are the given distances from the receiving stations.

_____

The simultaneous equations for the circles can be solved algebraically.

The epicenter is 10 units from X, so lies on the circle ...

(x -4)^2 +(y -5)^2 = 10^2

x^2 -8x +16 +y^2 -10y +25 = 100

x^2 +y^2 -8x -10y = 59

__

The epicenter is 5 units from Y, so lies on the circle ...

(x +6)^2 +(y +6)^2 = 5^2

x^2 +12x +36 +y^2 +12y +36 = 25

x^2 +y^2 +12x +12y = -47

__

The epicenter is 13 units from Z, so lies on the circle ...

(x +14)^2 +(y -2)^2 = 13^2

x^2 +28x +196 +y^2 -4y +4 = 169

x^2 +y^2 +28x -4y = -31

__

Subtracting the second equation from each of the other two, we get ...

(x^2 +y^2 -8x -10y) -(x^2 +y^2 +12x +12y) = (59) -(-47)

-20x -22y = 106 . . . . eq1 -eq2

(x^2 +y^2 +28x -4y) -(x^2 +y^2 +12x +12y) = (-31) -(-47)

16x -16y = 16 . . . . . . . .eq3 -eq2

These simultaneous linear equations can be solved a variety of ways. We might use substitution:

x = y+1 . . . . . from eq3 -eq2 divided by 16

10(y +1) +11y = -53 . . . . . from eq1 -eq2 divided by -2

21y = -63 . . . . . . . . . . . . simplify, subtract 10

y = -3

x = y+1 = -2

The epicenter is located at (x, y) = (-2, -3).

8 0

3 years ago