Show that z=1±i satisfies the equation z²-2z+2=0

Answer:

x = -11

Step-by-step explanation:

           JL + LM = JK + KM

x + 2 + 2x + 27 = 9 + 7

x + 2x + 22 + 27 = 9 + 7

Combine like terms,

             3x + 49 = 16

Subtract 49 from both sides,

                      3x = 16 - 49

                     3x  = -33

Divide both sides by 3,

                      x = -33/3

                     x = -11

Since the microwave raises the temperature of water by about 80°F in 5 minutes, the graph that has the slope that represents this rate of increase is option A.

Temperature is seen as a given unit used to stand for hotness as well as the coolness  of a given object or thing, it is said to be mostly  in Fahrenheit as well as Celsius.

Based on temperature, heat energy is one that tends to shift from a hotter  part of a body  to a colder part of the same body.

Note that:

Temperature = 80

Minutes = 5

Y = m

5m  = 80

m = 80/5

m = 16

So y  = 16x

Therefore, the graph that can give you the value above is graph A.

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No the value of functions are not same .

What is function in math?

  - 5 × ( -5)⁻⁹  =  -5 ×  1/-5⁹  ⇒ 1/5⁸  = 1/390625

[ -5 × (-5)]⁻⁹ = [25]⁻⁹  = 1/25⁹ = 1/3814697265625

No the value of functions are not same .

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The name for this new group of tiles will be three x² tiles, eight x tiles and nine unit tiles.

Based on the information, it should be noted that the following can be illustrated:

Number of x² tiles = 2 + 1 = 4

Number of x tiles = 3 + 5 = 8

Number of units tiles = 1 + 8 = 9

In this case, this is appropriately illustrated as three x² tiles, eight x tiles and nine unit tiles.. This will be the new name.

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Answer:

5:2

5x-30 = 2x+30

3x = 60

x = 20

total cars:

5(20)+2(20)

=100+40

=140cars

The equation of the required line is y = - 2x + 11

We need to find the equation of the line parallel to the given line y = -2x + 5 that contains C(4, 3)

Let m be the slope of the required line.

The slope of the line y = -2x + 5 is -2

We know that, the slope of the parallel lines is equal.

So, m = -2

The required line contains point C(4, 3)

Using point-slope form the equation of the line would be,

(y - y1) = m(x - x1)

y - 3 = -2(x - 4)

y - 3 = -2x + 8

y = -2x + 8 + 3

y = -2x + 11

Therefore, the equation of the required line is y = - 2x + 11

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Answer:

Linear Function

Step-by-step explanation:

A linear function has constant slope

That means the ratio of y differences to x differences must be the same throughout the function. In other words the rate of change of the function y value is the same throughout the function

IF we look at the table we see that as x increases by 1, y decreases by 15

For example at x = 0, y = 20 and at x = 1, y = 5

So change in y/change in x = 0  = (5-20)/(1-0) = -15/1 = -15

If we look at another pair of points, say x = 1, y=5 and x = 2, y = -10

we get the rate of change = (-10 - 5)/(2-1) = -15/1 = -15

This is the same for any two x, y pair of values

So it is a linear function

The image of triangle CDE after a rotation of 90º counterclockwise around the origin is graphed at the end of the answer.

When a polygon undergoes a rotation, this rotation is over an angle measure, that defines the coordinate rule for each vertex of the polygon.

For triangle CDE, the vertices are given as follows:

D(-7,-1), C(-7,-7), E(-4,-8).

The rule for a rotation of 90º counterclockwise around the origin, for each vertex (x,y) of the polygon, is given by:

(x,y) -> (-y,x).

Hence, applying the rule above, the vertices of the image of triangle CDE will be given as follows:

D'(1,-7), C'(7,-7), E'(8,-4).

The triangle, with these vertices labeled, is graphed at the end of the answer.

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The mean score in the fifth game that will allow you to advance is 73.

The mean score in the fifth game that will allow you to advance can be gotten this way:

Assign the mean score, the variable, and x.

Compute the scores with remarks as follows:

95 + 91 + 77 + 89 + x  ≥ 85

              5

352 + x ≥ 85

      5

85 × 5 = 425

352 + x ≥ 425

x = 425 - 352

x = 73.

So, the score in the fifth game that will allow you to advance will be 73.

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Step-by-step explanation:

1. find how many are not working

20 - 7 = 13

2. make this into a fraction:

13/20

3. make equivalent to x/100

do this by multiplying by 5

13/20 = 65/100

65/100 is 65% which don't work

Answer:

65%

Step-by-step explanation:

20-7=13, 13/20=0.65, 0.65*100=65 (Which leaves you with your answer)

The number of centers that will be needed to contain the guests is 5.

It should be noted that the question isn't well written but will be answered based on the information given.

From the information, a space center can have at most 7 guests and there are 31 guests. In this case, the number of space centers needed will be calculated by dividing the number of guests by the numbers that are contained in each center.

This will be:

= Number of guests / Number contained by each center

= 31 / 7

= 4 3/7

In this case, since there's a remainder of 3, this implies that we will need an extra space center. Therefore,the total space centre will be:

= 4 + 1

= 5

In this case, the value of 5 that's gotten simply shows the number of space centers that will be needed.

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The common difference of the AP is 4.33 and its first term is 30.

The formula to calculate the nth term of an Arithmetic Sequence is -

a - first term of A.P.

d - Common difference of A.P.

n - position of term

Given is the 1st term of an AP as 30 while the Sum of the its first 7 terms is 56.

We have -

[a] = 30

and -

a + (7 - 1)d = 56

30 + (6)d = 56

6d = 56 - 30

6d = 26

d = 26/6

d = 13/3

d = 4.33

and

the first term of the AP is 30.

Therefore, the common difference of the AP is 4.33 and its first term is 30.

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Answer: 40

Step-by-step explanation:

There are 9 cogs on the outside, and the circumference of a circle is 360 degrees. Dividing 360 by 9 yields 40 degrees.

Answer: a= 3b + 4c -8

Step-by-step explanation:

a= 3b + 4c -8

-2a + 6b = -8c + 16

-6b from the left the isolate a

-2a = -6b - 8c + 16

then divide by -2 to cancel it out

a = 3b + 4c -8

The equation is equivalent to -2a + 6b = -8c + 16 will be a= 3b + 4c -8

A linear equation is an equation that has the variable of the highest power of 1. The standard form of a linear equation is of the form Ax + B = 0.

We are given the linear equation;

a= 3b + 4c -8

-2a + 6b = -8c + 16

-6b from the left the isolate a

-2a = -6b - 8c + 16

Then divide by -2 to cancel it out;

a = 3b + 4c -8

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Part a

[tex](f \circ g)(x)=f(g(x))=\sqrt{x+9}[/tex]

Part b

[tex](g \circ f)(x)=g(f(x))=\sqrt{x}+9[/tex]

Part c

[tex](f \circ g)(7)=\sqrt{7+9}=4[/tex]

Part d

[tex](g \circ f)(7)=\sqrt{7}+9[/tex]

Based on the points given for the line in the table, the equation in slope intercept form is y = -1/2 + 1

To find the equation of a line, you first need to find the slope of the line as:

= Change in y / Change in x

= (0 - 1) / (2 - 0)

= -1 / 2

= - 1/2

Using the slope, find the y-intercept:

y = slope(x) + y-intercept

0 = -1/2(2) + y-intercept

y-intercept = 0 + 1

y-intercept = 1

The equation in slope-intercept form is:

y = -1/2 + 1

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6.85 miles is how deep it is. Under water, sound may travel 4700 feet in a second. The Time takes to travel the sound is 7.69.

Given that,

The deepest area in the ocean is the Marianas Trench in the Pacific Ocean. 6.85 miles is how deep it is. Under water, sound may travel 4700 feet in a second.

We have to calculate the time it takes for sound to travel from the ocean's surface to the Marianas Trench's depths and back, to the nearest tenth of a second.

We know the Distance formula is

Distance =rate×times

Time=Distance/rate

We convert 4700 feet to miles

We get,

4700 feet =0.89 miles

Now,

Time=6.85/0.89

Time=7.69

Therefore, the Time takes to travel the sound is 7.69.

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Answer:

30

Step-by-step explanation:

Answer/Step-by-step explanation:

y = -x - 3

m = slope = (-1/1)

b = y-intercept = -3 or (0, -3)

Point 1: (0, -3)

Point 2: (-1, -2)

Point 3: (1, -4)

I hope this helps!

Answer:

Step-by-step explanation:

  y=-x-3

x | -3 | 0 |

y |  0 | -3|

1) x=-3

y=-(-3)-3

y=3-3

y=0

Thus, (-3,0)

2) x=0

y=-0-3

y=-3

Thus, (0,-3)

Answer:

Step-by-step explanation:

negative

Answer:

D

Step-by-step explanation:

Answer:

[tex]m_1=\frac{Fd^2}{Gm_2}[/tex]

Step-by-step explanation:

[tex]F=G \left(\frac{m_1 m_2}{d^2} \right) \\ \\ \frac{F}{G}=\frac{m_1 m_2}{d^2} \\ \\ \frac{Fd^2}{G}=m_1 m_2 \\ \\ m_1=\frac{Fd^2}{Gm_2}[/tex]

PLUG IN THE VALUE 4 IN THE PLACE OF Y AND SIMPLIFY

[tex] = 6(4) - 78 \\ = 24 - 78 \\ = - 54[/tex]

HOPE THIS HELPS

[tex]e^{-5 \lambda}[/tex] is the probability that we have to wait for more than 5 min for the bus to arrive.

So, [tex]f_X(x)=\lambda e^{-\lambda x}, x \geq 0[/tex] ⇒ [tex]P(x \geq 5)=\int_5^{\infty} f_X(x) d x[/tex]

Now, solving the above function as follows:

[tex]\begin{aligned}&P(x \geq 5)=\int_5^{\infty} f_X(x) d x \\&=\int_5^{\infty} \lambda e^{-\lambda x} d x \\&=\left.\right|_5 ^{\infty} \frac{\lambda e^{-\lambda x}}{-\lambda} \\&=\left.\right|_5 ^{\infty}-e^{-\lambda x} \\&=e^{-5 \lambda}\end{aligned}[/tex]

Therefore, the probability that we have to wait for more than 5 min for the bus to arrive is [tex]e^{-5 \lambda}[/tex].

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The correct question is given below:
Suppose that the buses arrive are scheduled to arrive at a bus stop at noon are always X minutes late, where X is an exponential random variable with probability density function  [tex]f_X(x)=\lambda e^{-\lambda x}, x \geq 0[/tex]. Suppose you arrive at the bus stop precisely at noon. Find the probability that you have to wait for more than 5 min for the bus to arrive

Using linear functions, it is found that:

A linear function, in slope-intercept format, is modeled according to the following rule:

y = mx + b

In which:

In the context of this problem, it is used because the rate of change for each plan is constant, that is, for each device, there is a constant increase in the plan charge.

For the plans in this problem, we have that:

Hence the models for each plan are given as follows, with P representing the number of devices.

The costs will be the same when:

F(P) = M(P)

Hence we solve for P to find the number of plans as follows:

90 + 40P = 120 + 35P

5P = 30

P = 6 devices.

For 3 smartphones, the costs are given as follows:

210 < 225, hence the Family Plan is more affordable.

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Answer: 14 is the number

Step-by-step explanation:

The best choice for the location of the square root of 377 is B. less than 20.

It should be noted that the square root of a number simply means the number that we can multiply but itself which will give the original number.

In this case, it should be noted that the square root of 377 is 19.4. It should be noted that this is close to 20.

Therefore based on the options given the correct option is B.

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Which point is the BEST choice for the location of ✓377?

Less than 15

Less than 20

Less than 14

More than 10

Answer:

B

Step-by-step explanation: