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
jonny [76]
2 years ago
12

Michael graphs the equations y= -1/2+4 and y = x + 1 to solve the equation -1/2x+4= x+1. His graph is shown below. What are the

solution(s) of -1/2x+4= x+1?
A. –1 and 8
B. 1 and 4
C. 2
D. 3
Mathematics
1 answer:
arlik [135]2 years ago
5 0

Answer:

C.        x= 2

Step-by-step explanation:

You might be interested in
Can someone help me do part two please? It’s very important send a picture or something. I don’t even care if you tell me the st
Nataly_w [17]
<h3>Explanation:</h3>

1. "Create your own circle on a complex plane."

The equation of a circle in the complex plane can be written a number of ways. For center c (a complex number) and radius r (a positive real number), one formula is ...

  |z-c| = r

If we let c = 2+i and r = 5, the equation becomes ...

  |z -(2+i)| = 5

For z = x + yi and |z| = √(x² +y²), this equation is equivalent to the Cartesian coordinate equation ...

  (x -2)² +(y -1)² = 5²

__

2. "Choose two end points of a diameter to prove the diameter and radius of the circle."

We don't know what "prove the diameter and radius" means. We can show that the chosen end points z₁ and z₂ are 10 units apart, and their midpoint is the center of the circle c.

For the end points of a diameter, we choose ...

  • z₁ = 5 +5i
  • z₂ = -1 -3i

The distance between these is ...

  |z₂ -z₁| = |(-1-5) +(-3-5)i| = |-6 -8i|

  = √((-6)² +(-8)²) = √100

  |z₂ -z₁| = 10 . . . . . . the diameter of a circle of radius 5

The midpoint of these two point should be the center of the circle.

  (z₁ +z₂)/2 = ((5 -1) +(5 -3)i)/2 = (4 +2i)/2 = 2 +i

  (z₁ +z₂)/2 = c . . . . . the center of the circle is the midpoint of the diameter

__₁₂₃₄

3. "Show how to determine the center of the circle."

As with any circle, the center is the <em>midpoint of any diameter</em> (demonstrated in question 2). It is also the point of intersection of the perpendicular bisectors of any chords, and it is equidistant from any points on the circle.

Any of these relations can be used to find the circle center, depending on the information you start with.

As an example. we can choose another point we know to be on the circle:

  z₄ = 6-2i

Using this point and the z₁ and z₂ above, we can write three equations in the "unknown" circle center (a +bi):

  • |z₁ - (a+bi)| = r
  • |z₂ - (a+bi)| = r
  • |z₄ - (a+bi)| = r

Using the formula for the square of the magnitude of a complex number, this becomes ...

  (5-a)² +(5-b)² = r² = 25 -10a +a² +25 -10b +b²

  (-1-a)² +(-3-b)² = r² = 1 +2a +a² +9 +6b +b²

  (6-a)² +(-2-b)² = r² = 36 -12a +a² +4 +4b +b²

Subtracting the first two equations from the third gives two linear equations in a and b:

  11 -2a -21 +14b = 0

  35 -14a -5 -2b = 0

Rearranging these to standard form, we get

  a -7b = -5

  7a +b = 15

Solving these by your favorite method gives ...

  a +bi = 2 +i = c . . . . the center of the circle

__

4. "Choose two points, one on the circle and the other not on the circle. Show, mathematically, how to determine whether or not the point is on the circle."

The points we choose are ...

  • z₃ = 3 -2i
  • z₄ = 6 -2i

We can show whether or not these are on the circle by seeing if they satisfy the equation of the circle.

  |z -c| = 5

For z₃: |(3 -2i) -(2 +i)| = √((3-2)² +(-2-i)²) = √(1+9) = √10 ≠ 5 . . . NOT on circle

For z₄: |(6 -2i) -(2 +i)| = √((6 -2)² +(2 -i)²) = √(16 +9) = √25 = 5 . . . IS on circle

4 0
3 years ago
Help shaded parts need answers
Andrej [43]

Answer:

? i cant understand this!!!!!!!

Step-by-step explanation:

4 0
3 years ago
Complete the point-slope equation of the line through (-1,6)(−1,6)left parenthesis, minus, 1, comma, 6, right parenthesis and (1
velikii [3]

Answer:

y-6 = -\frac{1}{2} (x+1)

Step-by-step explanation:

For this case we have two points given (-1,6) and (1,5)

And we want to complete the point slope equation of the line:

y-6 = m(x-x_o)

We need to find the slope and we can use the following formula:

m = \frac{y_2 -y_1}{x_2 -x_1}

And replacing the info we got:

m= \frac{5-6}{1-(-1)}=-\frac{1}{2}

And then the equation would be given by:

y-6 = -\frac{1}{2} (x- (-1))

And our final answer would be:

y-6 = -\frac{1}{2} (x+1)

3 0
3 years ago
Calculate the interest rate when the principal is $300 and interest earned is $40 after 3
stich3 [128]

Answer:

4.4%

Step-by-step explanation:

solution:

principal (p) = $300

time(t) = 3 years

interest (I ) =$40

rate (r) = ?

we know that,

I = (PTR)/100*

OR, 40 = (300 *3 * R)/100

or, 40 = (900R)/100

or, 40 = 9R

or, 40/9 = R

or, R = 4.4%

Rate(r) =4.4%

3 0
3 years ago
Jessie enjoys running everyday for excercise. On Monday, he ran 3.30 miles. On Tuesday, he ran 3.09 miles and on Wednesday he ra
White raven [17]
He ran the farthest on Monday.
3 0
3 years ago
Other questions:
  • What is the height of a rectangular prism that has a volume of 280 cubic meters,a length of 8 meters, and a width of 7 meters? S
    7·1 answer
  • The graph below shows a line segment XY: graph of line segment XY with endpoints at negative 1 comma 3 and 1 comma negative 1 Wh
    15·2 answers
  • Anna shipped a small package from
    12·1 answer
  • Give the degree of the polynomial <br> -3w+x^6y^5-2+5y^4w^3x^2
    8·1 answer
  • At the neighborhood Fourth of July party, Mrs. O’Conner plans to serve banana pudding. She plans to make two batches for every 9
    8·1 answer
  • 2) Find xif y =18<br> Y = 6x - 24
    14·2 answers
  • ( 10.2 -1)+(5.2 48 -8)
    7·1 answer
  • There are 28 girls and 22 boys on the swim team. What percentage of the team is made up of girls?
    5·2 answers
  • Help with question 1 will give brainlest
    5·1 answer
  • I NEED HELP what is the slope intercept form of y+6=4/5(x+3)
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!