Scientists estimate between 10,000,000 and 50,000,000 monarch
butterflies per hectare spend the winter in Mexico. The monarch butterfly
colony covers an area of 2 hectares. What is the difference between the
greatest and least possible number of butterflies in the monarch colony?

Answer:

x= 4+5i

Step-by-step explanation:

The values of x in the given quadratic equation, x²-8x+41 = 0 are x = 4+5i or x = 4-5i

A quadratic equation is any equation that can be rearranged in standard form as where x represents an unknown value, and a, b, and c represent known numbers, where a ≠ 0.

Given is a quadratic equation, x²-8x+41 = 0, we need to find the values of x,

Since, 41 is a prime number, which can not be factorized so, we will use quadratic formula,

x = [-b ± √(b²-4ac)] / 2a

Here, a = 1, b = -8, c = 41

Therefore,

x = [8 ± √(8²-4(41))] / 2

= [8 ± √(64-164)] / 2

= [8 ± √(-100)] / 2

= [8 ± 10i] / 2

= [4 ± 5i]

Therefore, x = 4+5i or x = 4-5i

Hence, the values of x in the given quadratic equation, x²-8x+41 = 0 are x = 4+5i or x = 4-5i

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Answer:

Third Option

Step-by-step explanation:

Lets use process of elimination to find the answer to this question. It's not the first option because a scribes job was mainly in the government district as writers/record keepers meaning they don't really protect the kingdom from invasion. It's not the second options because Merchants were traders, meaning they don't make up the Pharaohs police force because all they do is sell goods to Egyptians. Then it's not fourth option because farmers, servants, and slaves make up way more then 20% of ancient Egypt. Leaving the third option meaning it's your answer.

Hope this helps.

Answer:

2m + 20

Step-by-step explanation:

Given that:

Cost per meal = m

Tip left = $10

Total cost for each person :

m + 10

Total amount spent by the two :

2(m + 10)

2m + 20

Answer:

The coordinates of P are (12,9)

Step-by-step explanation:

Equations

We are given the endpoints of the segment AB: A(10,8) B(18,12).

It's required to find the coordinates of point P(x,y) along the segment AB such that:

[tex]\displaystyle \frac{AP}{PB}=\frac{1}{3}[/tex]

The ratio of the distances is the same as the ratio of their respective coordinates:

[tex]\displaystyle \frac{x_{AP}}{x_{PB}}=\frac{1}{3}[/tex]

[tex]\displaystyle \frac{y_{AP}}{y_{PB}}=\frac{1}{3}[/tex]

Since

[tex]x_{AP}=x_P-x_A=x-10[/tex]

[tex]x_{PB}=x_B-x_P=18-x[/tex]

Then:

[tex]\displaystyle \frac{x-10}{18-x}=\frac{1}{3}[/tex]

Multiplying by 3 (18-x):

3( x - 10 )= 18 - x

3x - 30 = 18 - x

Adding x and 30:

4x = 48

x = 12

Similarly:

[tex]\displaystyle \frac{y-8}{12-y}=\frac{1}{3}[/tex]

Multiplying by 3 (12-y):

3( y - 8 ) = 12 - y

3y - 24 = 12 - y

Adding y and 24:

4y = 36

y = 9

The coordinates of P are (12,9)

Answer:

14/61 cm per day

Step-by-step explanation:

Use the slope formula  [tex]\frac{y_{2} - y_{1}}{x_{2} - x_{1}}[/tex]

Plug it in [tex]\frac{16-2}{61-0}[/tex]

Simplify [tex]\frac{14}{61}[/tex]

If the graph shows the height of a plant over a 2-month growth period. The rate of change per day will be 14/61.

It is defined as the change in values of a dependent variable with respect to the independent variables. Analyze the points first, then calculate the y-values for each interval. After that, subtract the input and output values. Divide and then simplify the differences to determine the rate of change.

It is given that, the graph shows the height of a plant over a 2-month growth period

The kind of graph must be considered when calculating the rate of change. Finding the ratio between the change in output values and the change in their corresponding input values is how linear graphs with constant rates of change are determined. Look at the following linear graph.

The slope of a linear function represents the pace of change. We have two points to determine the slope,

The rate of change per day is found as,

=y₂-y₁/x₂-x₁

=16-2/61-0

=14/61

Thus, if the graph shows the height of a plant over a 2-month growth period. The rate of change per day will be 14/61.

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Answer:

8 walls

Step-by-step explanation:

While painting the interior of a large house, Gene is going to transfer some paint in a large 5 gallon container to a smaller bucket. Unfortunately he slips and spills 2 gallons of paint all over the floor.

The remaining amount of paint is

= 5 gallons - 2 gallons

= 3 gallons

If each wall in the house takes 9/24 of a gallon to paint, how many walls can he paint with what he has left?

Hence:

9/24 gallon = 1 Wall

3 gallons = x wall

Cross Multiply

9/24 × x = 3 × 1

x= 3 ÷ 9/24

x = 3 × 24/9

x = 8 walls

He can paint 8 walls with what is left.

Answer:

x=37/20

Step-by-step explanation:

4(2x-7)+3(3x-1)=3(2-x)

8x-28+9x-3=6-3x

17x+3x=6+31

20x=37

Answer:

x = [tex]\frac{71}{3}[/tex]

Step-by-step explanation:

1. Simplify/distribute each side.

[tex]4(2)(-7)+3(3)(-1)=3(2-x)[/tex]

[tex]4(2)(-7)+3(3)(-1)=(3)(2)+(3)(-x)[/tex]

[tex]-56+-9=6+-3x[/tex]

2. Flip the equation around.

[tex]-3x+6=-65[/tex]

3. Subtract 6 to balance the equation.

[tex]-3x+6-6=-65-6[/tex]

[tex]-3x=-71[/tex]

4. Divide each side by 3. We know they are in the same fact family.

[tex]\frac{-3x}{-3} = \frac{-71}{3}[/tex]

Answer:

a) She did mistake in Step 2

b) when she take -3y common then the term should be: -3y(x+5) instead she wrote -3y(x-5)

Step-by-step explanation:

We need to find problem in Ms J solution.

Ms J solution:

[tex]Step \ 1: 4x^2 + 20x - 3xy - 15y\\Step \ 2: 4x(x + 5) - 3y(x - 5)\\Step \ 3: (x+5)(4x - 3y)[/tex]

She did mistake in Step 2 when she take -3y common then the term should be: -3y(x+5) instead she wrote -3y(x-5)

Correcting the mistake:

[tex]Step \ 1: 4x^2 + 20x - 3xy - 15y\\Step \ 2: 4x(x + 5)\mathbf{- 3y(x +5)}\\Step \ 3: (x+5)(4x - 3y)[/tex]

Answer:315

Step-by-step explanation:

Answer:

The missing value in the solution to

the equation will be:

Step-by-step explanation:

Given the equation

[tex]y+2\:=-3\left(x\:-\:4\right)[/tex]

As the value of y = -2 is given.

so substituting the value y = -2 in the equation to find the missing value

[tex]\left(-2\right)+2\:=-3\left(x\:-\:4\right)[/tex]

switch the sides

[tex]-3\left(x-4\right)=\left(-2\right)+2[/tex]

[tex]\mathrm{Remove\:parentheses}:\quad \left(-a\right)=-a[/tex]

[tex]-3\left(x-4\right)=-2+2[/tex]

[tex]-3\left(x-4\right)=0[/tex]

[tex]\mathrm{Divide\:both\:sides\:by\:}-3[/tex]

[tex]\frac{-3\left(x-4\right)}{-3}=\frac{0}{-3}[/tex]

[tex]x-4=0[/tex]

[tex]x=4[/tex]

Therefore, the missing value in the solution to

the equation will be:

Answer

the x intercept is (-8,0)

Step-by-step explanation:

Answer:

- 7n ≤ 77

Step-by-step explanation:

- 7n ≤ 77

n ≥ - 11

Answer:

y=28

Step-by-step explanation:

Answer:

there is no slope. y = 4, the line is horizontal

Answer:

No, Each input has one output

Step-by-step explanation:

A circle can't be a function because of its radius and diameter, its not linear so  it might have the same input or output. Therefore, you need a line to have a linear function .!

Pls mark brainiest!

I hope you get this right!

Answer:

-26 × -1 = 26

This is your answer , pls mark me the brainliest!!

Answer:

-1

Step-by-step explanation:

1 x 26 is  like that , -1 x -26 = 26. Hope this helps!

Answer:

134

Step-by-step explanation:

Its 134, i did the math and my old answer had the explanation, but someone deleted it.

Answer:

Yes, its a function

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Not all seventh graders will bring a lunch too school, be in the library, or be in a pre-algebra class, but its reasonable to assume that most will enter the school at the beginning of the day.

Answer:

C.surveying every fifth seventh grader entering the school at the beginning of the school day

Step-by-step explanation:

Answer:

We need the following three rigid motions:

i) Reflection around y-axis, ii) Translation three units in the -y direction, iii) Translation four units in the -x direction.

Step-by-step explanation:

We need to perform three operations on pentagon ABCDE to create pentagon A'B'C'D'E':

i) Reflection around y-axis:

[tex](x',y') = (-x,y)[/tex] (Eq. 1)

ii) Translation three units in the -y direction:

[tex](x'',y'') = (x', y'-3)[/tex] (Eq. 2)

iii) Translation four units in the -x direction:

[tex](x''',y''') = (x''-4, y'')[/tex] (Eq. 3)

We proceed to proof the effectiveness of operations defined above by testing point D:

1) [tex]D(x,y) = (-1, 4)[/tex] Given.

2) [tex](x',y') = (1,4)[/tex] By (Eq. 1)

3) [tex](x'',y'') = (1, 1)[/tex] By (Eq. 2)

4) [tex]D'(x,y) = (-3,1)[/tex] By (Eq. 3)/Result

Answer: 5/4

Step-by-step explanation:

The slope formula is [tex]\frac{y_{2}-y_1 }{x_2-x_1}[/tex]. This is basically the change in y over change in x.

Apply the formula to get: [tex]\frac{5--2}{6-2}[/tex].

Simplify it to get: [tex]\frac{5}{4}[/tex]

Answer:

B

Step-by-step explanation:

Hope this help

Answer: B

B.) 3(3) + 0.75(2) = (3 + 0.75)x

Step-by-step explanation: i hope this helps :)

Answer:

x=74 degrees

Step-by-step explanation:

the sum of angles of triangle=180 degrees

121+y=180 ( the sum of the linear angles is 180 degrees)

y=180-121

y=59 degrees

x+59+47=180

x+106=180

x=180-106

x=74 degrees

Step-by-step explanation:

The sum of two interior angles in a triangle is equal to an exterior angle that's supplementary to the third interior angle

13x - 11 + 4x + 1 = 18x - 15 add like terms

17x - 10 = 18x - 15

- 10 + 15 = 18x - 17x

5 = x

measure of angle A 13x - 11 ➡ 13 × 5 - 11 = 54°

measure of angle B 4x + 1 ➡ 4 × 5 + 1 = 21°

measure of angle C 18x - 15 ➡ 18 × 5 - 15 = 75°

Answer:

C

Step-by-step explanation:

rounding

Answer:

Option (C) is correct.

Step-by-step explanation:

Given that z = 0.3(cos(31°) + i sin(31°)) and 20(cos(18°) + i sin(18°)).

The product of both the complex number is

zw = [0.3(cos(31°) + i sin(31°))] x [20(cos(18°) + i sin(18°))]

=(0.3x20)[cos(31°) x cos(18°) + cos(31°) x i sin(18°) + i sin(31°) x cos(31°)+ i sin(31°) x i sin(18°)]

Here, (0.3x20)=6, is the magnitude of zw, which is stretching of 0.3 by 20.

zw=6[cos(31°) x cos(18°) + i{cos(31°) x sin(18°) + sin(31°) x cos(31°)}+ i² sin(31°)x sin(18°)]

As i²= -1, So

zw=6[cos(31°) x cos(18°) + i{cos(31°) x sin(18°) + sin(31°) x cos(31°)} - sin(31°)x sin(18°)]

=6[{cos(31°) x cos(18°)- sin(31°)x sin(18°)} + i{cos(31°) x sin(18°) + sin(31°) x cos(31°)}]

As cosAcosB - sin A sin B = cos (A+B) and cosAsinB + sin A sos B = sin (A+B), so

zw=6[cos(31°+18°) + i{sin(31°+18°)]

Note that, initially the argument of z is 31° and after rotation of 18° in counterclockwise direction, the argument od zw is 31°+18°= 49°. i.e

zw=6(cos(49°) + isin(49°)).

So, zw can be determined by stretching z by a factor of 20, then rotating by 18° counterclockwise.

Hence, option (C) is correct.

Answer:

C: Stretch z by a factor of 20, then rotate 18° counterclockwise.

Step-by-step explanation:

Took the quiz.

9514 1404 393

Answer:

  5361 feet

Step-by-step explanation:

The tangent of the angle is the ratio of vertical distance to horizontal.

  tan(25°) = (vertical distance)/(horizontal distance)

  horizontal distance = (2500 ft)/tan(25°) ≈ 5361 feet

Answer:

1. +12x and 15

2. 14x

3. 2

Step-by-step explanation:

Step 1: Distribute -3

To distribute -3, you would multiply both -4x and -5 by -3, changing them to 12x and 15

Step 2: Combine 12x and 2x

Then you would combine like terms, meaning that you would add 12x and 2x, creating 14x.

Step 3: Combine 15 and -13

You would finish combining like terms by adding 15 to -13, creating 2