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oee [108]
2 years ago
7

Find all solutions to the equation equation (x - 1)^2 = -4.

Mathematics
1 answer:
tatuchka [14]2 years ago
6 0

Answer:

x = 1±2i

Step-by-step explanation:

(x - 1)^2 = -4.

Take the square root of each side

sqrt( (x - 1)^2) = sqrt(-4)

Sqrt(ab) = sqrt(a)sqrt(b)

We know the sqrt(4) = 2 and the sqrt(-1) = ±i

x-1 = ±2i

Add 1 to each side

x-1+1 = 1±2i

x = 1±2i

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Find the coordinates of the other endpoint of the​ segment, given its midpoint and one endpoint.​ (Hint: Let​ (x,y) be the unkno
gizmo_the_mogwai [7]

Answer:

The other endpoint of the​ segment is (-18,-7).

Step-by-step explanation:

The midpoint of the points (x_1,y_1) and (x_2,y_2) is given by the following formula:

                                          (x_m,y_m)=(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}  )

where (x_m,y_m) = coordinates of the midpoint.

We know that the midpoint is (-15, 2) and an endpoint is (-12, 11). Substituting the information we have gives:

                                         (-15,2)=(\frac{x_1-12}{2}, \frac{y_1+11}{2}  )

To find x_1 we need to solve this equation:

-15=\frac{x_1-12}{2} \\\\\frac{x_1-12}{2}=-15\\\\\frac{2\left(x_1-12\right)}{2}=2\left(-15\right)\\\\x_1-12=-30\\\\x_1-12+12=-30+12\\\\x_1=-18

and to find y_1 we need to solve this equation:

2= \frac{y_1+11}{2}  \\\\\frac{y_1+11}{2}=2\\\\\frac{2\left(y_1+11\right)}{2}=2\cdot \:2\\\\y_1+11=4\\\\y_1=-7

The other endpoint of the​ segment is (x_1,y_1)=(-18,-7).

5 0
3 years ago
Let f(x) = 4x – 5 and g(x) = 3x + 7. find f(x) + g(x) and state its domain.
Tema [17]

We are given the functions:

f(x) = 4 x – 5                       ---> 1

g(x) = 3 x + 7                       ---> 2

 

To find for the value of f(x) + g(x), all we have to do is to add equations 1 and 2:

f(x) + g(x) = 4 x – 5 + 3 x + 7

f(x) + g(x) = 7 x + 2 = y

 

In this case, for any real number value assign to x, we get a real number value of y. This is because the function is linear.

Therefore the domain of the function is all real numbers.

5 0
3 years ago
Write an equation of the line passing through the point (3, -1) and parallel to the line y=2/3x - 5. Show work
alex41 [277]

Answer:

The answer is: y = 2/3x - 3

Step-by-step explanation:

Given point: (3, -1)

Given equation: y = 2/3x - 5, which is in the form y = mx + b where m is the slope and b is the y intercept.

Parallel lines have the same slope. Use the point slope form of the equation with the point (3, -1) and substitute:

y - y1 = m(x - x1)

y - (-1) = 2/3(x - 3)

y + 1 = 2/3x - 6/3

y + 1 = 2/3x - 2

y = 2/3x - 3

Proof:

f(3) = 2/3(3) - 3

= 6/3 - 3

= 2 - 3

= -1, giving the point (3, -1)

Hope this helps! Have an Awesome Day!!  :-)

6 0
2 years ago
Sofia is learning to knit. After her first three stitches, she had to undo the last two. Then she made three more stitches and a
Marizza181 [45]
She’ll have to make 4 more stitches in order to get 6 good ones. Each time she creates 3 she undoes 2 which after 4 more times would leave her with 6 good stitches.
4 0
2 years ago
Brianna babysits on the weekend. She charges $7 per hour. Last weekend she made $63. How many hours did she babysit?
Verizon [17]

Answer:

7h=63 so a because she charges $7 per hour and earned a total of $63

7 0
3 years ago
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