Tricia completed the square of the quadratic function f(x) = x² + 14x + 2 and determined the coordinates of the minimum value are (-7, - 47). Which equation must be Tricia's result?
f(x = (x +7)² + 47
f(x) = (x + 7)² - 47
f(x) = (x - 7)² + 47
f(x) = (x - 7)² - 47

Answers

Answer 1

Answer:

The co-ordinates which give the minimum value for the quadratic function are (-7, -47)

Step-by-step explanation:

i) the quadratic function f(x) = [tex]x^{2}[/tex]  + 14x + 2

                                             = [tex]x^{2}[/tex]  +   14x + 49 - 49 + 2

                                             =  [tex](x + 7)^{2}[/tex]   - 49 + 2

                                            = [tex](x+7)^{2}[/tex]  - 47

ii) The minimum value of the result of the quadratic equation in i) will be achieved when [tex](x + 7)^{2}[/tex] is zero as any square value is always positive and thus the minimum value of a square is always zero.

iii) [tex](x + 7)^{2}[/tex]  is zero when x  = -7 and when x = -7  then y = f(x) = -47

iv) The co-ordinates which give the minimum value for the quadratic function are (-7, -47)


Related Questions

This table shows how the amount of money Sadie makes from selling lemonade is related to the number of cups sold. How much does one cup of lemonade cost?

Answers

Answer:

One cup of lemonade will cost $2.

Step-by-step explanation:

From simple observation and visual inspection we can conclude that one cup of lemonade costs $2.

If 9 cups of lemonade cost $18 then one cup of lemonade will cost $18÷9 = $2

If 2 cups of lemonade cost $4 then one cup of lemonade will cost $4÷2 = $2.

Therefore we can conclude that one cup of lemonade will cost $2.

Find the actual sum of 1 3/4+1 5/8 do the Turman how much David grew into years explain how you know your answer is reasonable

Answers

Answer:

  3 3/8

Step-by-step explanation:

We assume your intended question is ...

  "Find the actual sum of 1 3/4 + 1 5/8 to determine how much David grew in two years. Explain ..." (Proper word choice and punctuation help communication.)

The sum of the two given mixed numbers can be found several ways. One way is to write the fractions using a common denominator:

  1 3/4 + 1 5/8 = 1 6/8 + 1 5/8 = (1 +1) +(6/8 +5/8) = 2 + 11/8 = 3 3/8

David grew 3 3/8 in two years.

__

Both numbers are near and slightly more than 1.5, so their sum will be near and slightly more than 3.

consider the function f(x)=-2x+5 what is f(5) enter your answer in the box

Answers

The value of f(5) is [tex]f(5)=-5[/tex]

Step-by-step explanation:

The function is [tex]f(x)=-2x+5[/tex]

To find [tex]f(5)[/tex] substitute [tex]x=5[/tex] in [tex]f(x)=-2x+5[/tex]

[tex]f(5)=-2(5)+5[/tex]

Multiplying the terms, we get,

[tex]f(5)=-10+5[/tex]

Adding the terms, we get,

[tex]f(5)=-5[/tex]

Thus, the value of [tex]f(5)[/tex] is [tex]f(5)=-5[/tex]

A Carpenter has a wooden stick that is 84 centimeters long. She cuts off 25% from the end of the stick. Then she cuts off the remaining stick into 6 equal pieces. What is the length of each piece

Answers

Answer:

10.5

Step-by-step explanation:

84×0.75=63

63÷6=10.5

Alexa is a songwriter who collects royalties on her songs whenever they are played in a commercial or a movie. Alexa will earn $20 every time one of her songs is played in a commercial and she will earn $110 every time one of her songs is played in a movie. Alexa earned a total of $340 in royalties on 8 commercials and movies. Write a system of equations that could be used to determine the number of commercials and the number of movies on which Alexa's songs were played. Define the variables that you use to write the system

Answers

Answer:

20c +110m = 340; c + m = 8

Step-by-step explanation:

Let c and m represent the number of commercials and movies playing Alexa's songs, respectively.

  20c +110m = 340 . . . . . total royalties earned

  c + m = 8 . . . . . . . . . . . . total number of plays

___

Alexa's songs were played in 6 commercials and 2 movies.

Answer:

she died

Step-by-step explanation:

WILL GIVE BRAINLIEST!! Give an example of a system of two linear equations in two variables with 0, 1, or infinitely many solutions. Explain how you can determine whether this system has 0, 1, or infinitely many solutions without graphing. What does this reveal about the relationship between the lines on the graph?

Write at least 150–300 words please

Answers

Answer:

Step-by-step explanation:

0 solution example

3x+2y=2

3x+2y=4

This is a zero solution example, because you can see that both equations are the same on the left, yet different on the right.

Infinite solution example

3x+2y=2

4y=4-6x

This is an infinite solution example because if you look at both equations, you can see that they are exactly the same.

One solution example

2x+3y=15

x-3y=3

This is an one solution example because if you add the equations you get 3x=18 x=6

plug it in, and you get that x=6, y=1

If a system a infinite solutions, that means that the lines overlap

If a system has no solutions, that means that the lines never touch, or that they are parallel

If a system has one solution, it means that the lines intersect at one point.

Final answer:

A system of two linear equations in two variables can have 0, 1, or infinitely many solutions. The number of solutions can be determined without graphing by comparing the slopes and y-intercepts of the equations. If the slopes are equal and y-intercepts are different, the system has no solution. If the slopes are equal and y-intercepts are equal, the system has infinitely many solutions. If the slopes are not equal, the system has exactly one solution.

Explanation:

One example of a system of two linear equations in two variables with 0, 1, or infinitely many solutions is:

Equation 1: 2x + 3y = 8

Equation 2: 4x + 6y = 16

To determine the number of solutions in this system without graphing, we can use the concept of slopes. If the slopes of the two lines are equal and the y-intercepts are also equal, then the system has infinitely many solutions. If the slopes are equal but the y-intercepts are different, then the system has no solution. If the slopes are not equal, then the system has exactly one solution.

In this example, both equations have the same slope of ½; however, the y-intercepts are different. Therefore, this system has no solution.

This reveals that the two lines in the graph of this system are parallel and will never intersect.

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The perfect squares between 61 and 102

Answers

Answer: 3 perfect squares

Step-by-step explanation: Between the numbers, 61 and 102, there are 3 perfect squares and they are 8 x 8, 9 x 9, and 10 x 10

I have also attached a list of perfect squares and put a yellow rectangle around the perfect squares between 61 and 102.

1. Calculate the sum of the infinite series S. = 16+4+1+....

Answers

Answer:

Step-by-step explanation:

Using the initial value a = 16 and the common ratio r = 1/4, we can use the equation for the sum of an infinite geometric series as |r| < 1:

S = a / (1-r)

  = 16 / (1-(1/4))

  = 16 / (3/4)

  = 64/3

The sum of the series is 64/3.

What is a geometric sequence?

A geometric sequence is one where each phrase is discovered by multiplying the term before it by the same number.

The given series is 16 + 4 + 1 +...

Note that each term of the series is 1/4 of the preceding term, therefore, the series is a geometric series with a common ratio of r = 1/4.

The sum of an infinite geometric series is:

s= a/(1-r)

s= 16/(1-1/4)

s = 64/3

Hence, the sum of the series is 64/3.

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64=[(96 divided by 8) times 5]-42

Answers

Answer:

that statement is not true

Step-by-step explanation:

64=[(96÷8)5}-42

64={(12)5} - 42

64= (60)-42

64=18

but that with subtraction. if you multiply 60 by negative 42 you get -2520 which is still not true

What is the area of a rectangle with length 6 units and width 3 units?

Answers

Answer:

18

Step-by-step explanation:

Answer: 18

Step-by-step explanation: 6 x 3 = 18

What is the slope of the line represented by the equation ? 3x + 4y = 8

Answers

Answer:

-3/4

Step-by-step explanation:

3x + 4y = 8....find the slope

in y = mx + b form, the slope can be found in the m position...so lets put this equation in y = mx + b form

3x + 4y = 8.....subtract 3x from both sides

4y = 8 - 3x.....now divide both sides by 4

y = 2 - 3/4x....rearrange

y = -3/4x + 2

y = mx + b

y = -3/4x + 2

as u can see, the number in the m position (the slope) = -3/4

Final answer:

The slope of the line represented by the equation 3x + 4y = 8 is -3/4.

Explanation:

The slope of a line can be determined from its equation in slope-intercept form, which is of the form y = mx + b. The coefficient of x, m, represents the slope of the line. In the given equation 3x + 4y = 8, we can rearrange it to the slope-intercept form by isolating y: 4y = -3x + 8, y = (-3/4)x + 2. Therefore, the slope of the line represented by this equation is -3/4.

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help me please 10 points

Answers

Answer:

17z + 9 = 4z + 5

13z + 9 = 5 (you have to take the 4x to the opposite of the equal sign to subtract it)

13z = 5 - 9

13z = -4

z = -4/13

Exactly one solution

Giving brainliest please help :c

Answers

Answer:

4 ft

Step-by-step explanation:

missing height = 12 - 8 = 4 ft

Answer:

The missing height = 12 - 8 = 4ft

Step-by-step explanation:

Vega set up a coordinate
system with units of feet to locate the
position of the vegetables she planted
in her garden. She has a tomato plant
at (1, 3) and a pepper plant at (5, 6).
How far apart are the two plants?
Round to the nearest tenth if
necessary.

Answers

The two plants are 5 feet apart.

Step-by-step explanation:

Given,

Point of tomato plant = (1, 3)

Point of pepper plant = (5, 6)

Here,

[tex]x_1=1,\ \ \ \ \ y_1=3\\x_2=5,\ \ \ \ \ y_2=6[/tex]

Distance between two plants = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2[/tex]

[tex]Distance=\sqrt{(5-1)^2+(6-3)^2}\\Distance=\sqrt{(4)^2+(3)^2}\\Distance=\sqrt{16+9}\\Distance=\sqrt{25}\\Distance=5[/tex]

As the unit is feet, therefore,

The two plants are 5 feet apart.

Keywords: addition, points

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-9x-5=-95
Please help!

Answers

-9x - 5 = -95

-9x = -95 + 5

-9x = -90

x = -90/-9

x = 10

Please mark as the Brainliest!

In parallel lines cut by a transversal if m angle RNP =(8x+63) degree and m angle NRS = 5x degree
1. find angle measure of m angle RNP
2. Find angle measure of m angle NRS

Answers

Answer:

Part 1) [tex]m\angle RNP=135^o[/tex]

Part 2) [tex]m\angle NRS=45^o[/tex]

Step-by-step explanation:

The complete question in the attached figure

step 1

Find the value of x

we know that

[tex]m\angle RNP+m\angle NRS=180^o[/tex] ----> by supplementary angles (consecutive interior angles)

substitute the given values

[tex](8x+63)^o+5x^o=180^o[/tex]

Solve for x

[tex]8x+5x=180-63\\13x=117\\x=9[/tex]

step 2

Find the measure of angle RNP

substitute the value of x

[tex]m\angle RNP=(8(9)+63)=135^o[/tex]

step 5

Find the measure of angle NRS

substitute the value of x

[tex]m\angle NRS=5(9)=45^o[/tex]

Write y=1/6x+5 in standard form using integers Please

Answers

The standard form of the line is [tex]6y-x=30[/tex]

Step-by-step explanation:

The equation of the line in this problem, written in the point-slope form, is

[tex]y=\frac{1}{6}x+5[/tex] (1)

We want to rewrite it in the standard form with integers, that means in the form

[tex]ax+by=c[/tex]

where a, b and c are integer numbers.

We start by manipulating eq.(1), by multiplying both terms of the equation by 6:

[tex]6y = \frac{1}{6}x\cdot 6+5\cdot 6\\6y=x+30[/tex]

Now we subtract [tex]-x[/tex] on both sides:

[tex]6y-x = x-x+30[/tex]

So we find

[tex]6y-x=30[/tex]

Which is the standard form of the line.

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passes through (3,-6) and (-1, 2)

Answers

Answer:

Therefore, Equation of line and the slope is

[tex]y=-2x[/tex]

[tex]Slope = -2[/tex]

Step-by-step explanation:

Given:  

Let,  

point A( x₁ , y₁) ≡ ( 3 ,-6)

point B( x₂ , y₂ )≡ (-1 , 2)

To Find:  

Equation of Line AB =? ( Assumption)

Solution:  

Equation of a line passing through a points A( x₁ , y₁) and point B( x₂ , y₂ ) is given by the formula Two -Point Form,  

[tex](y-y_{1})=\dfrac{y_{2}-y_{1} }{x_{2}-x_{1} }\times (x-x_{1})[/tex]  

Now on substituting the slope and point A( x₁ , y₁) ≡ ( 3 , 6) and B( x₂ , y₂ )≡ (-1 , 2) we get  

[tex](y-(-6))=\dfrac{2--6}{-1-3}\times (x-3)\\\\y+6=\dfrac{8}{-4}(x-3)\\\\y+6=-2(x-3)\\y+6=-2x+6\\y=-2x[/tex] .....Required Equation of line

Which is also in the form of

[tex]y=mx[/tex] ....Also called as Equation of line Passing through Origin.

where , m =slope

Therefore, Equation of line and the slope is

[tex]y=-2x[/tex]

[tex]Slope = -2[/tex]

Final answer:

To find the equation of a line passing through two given points, calculate the slope using the slope formula, and then substitute the slope and one of the points into the point-slope form of a line equation. The line passing through the points (3,-6) and (-1,2) is given by the equation y = -2x + 6.

Explanation:

To find the equation of the line that passes through the points (3, -6) and (-1, 2), we use the formula for the slope, denoted as 'm': m = (y2 - y1) / (x2 - x1).

Then, we substitute the given pair of points into this formula to find the slope: m = (2 - -6) / (-1 - 3) = 8 / -4 = -2.

After obtaining the slope, we use the point-slope form of an equation of a line, which is y - y1 = m(x - x1). Substitute one of the given points (3, -6) and the slope -2 in: y - -6 = -2(x - 3).

Simplify this to get the final equation: y = -2x + 6.

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What value of n makes the equation true? -2n + 1.8 =3.2

Answers

Answer:

-0.7

Step-by-step explanation:

-2n+1.8=3.2

-2n=3.2-1.8

-2n=1.4

n=1.4/-2

n=-0.7

a candy company packs lemon drops in the container size shown in the diagram. They need a larger container. Which choice will change the dimensions so that the volume is tripled.

Answers

Answer:

Option B) triple the height

Step-by-step explanation:

The rest of the question is the container has a shape of the cylinder and the options to select the answer.

The options are:

A) triple the radius

B) triple the height

C) triple the diameter

D) triple the circumference

=========================================

the container has a shape of the cylinder

The volume of the cylinder is = π r² h

It is required to choose which option is suitable so change the dimensions so that the volume is tripled.

So, the volume will be V' =  ( 3 π r² h )

Check the options:

A) triple the radius

The new radius = 3r

∴ V = π (3r)² h = 9 π r² h

B) triple the height

The new height = 3h

∴ V = π r² (3h) = 3 π r² h

So, it is no need to check the other options.

The answer is option B

Note: both of option C and D will lead to the same result of option A

Count twenty of fifty equal parts

Answers

Answer:

I think 20/50 is the answer you're looking.

Answer:

20/50

Hope this helps :)

Step-by-step explanation:

The number of visitors to a sporting goods website is 1,940 today. This is 400% of the number of visitors on the first day the site was online. How many visitors did the website have on the first day?

Answers

Answer:

The sporting goods website had 485 visitors on the first day

Step-by-step explanation:

Let's answer the question correctly, this way:

Number of visitors to a sporting goods website today = 1,940 and 400% of the visitors on the first online day

How many visitors did the website have on the first day?

Let's use the Rule of Three Simple, this way:

x = Number of visitors to a sporting goods website on the first online day

Number of visitors     Percentage

1,940                               400%

  x                                    100%

400 * x = 1,940 * 100

x = 194,000/400

x = 1,940/4 = 485

The sporting goods website had 485 visitors on the first day

What is y=-7/5x-3 when y=-10

Answers

Answer:

[tex]x=\frac{1}{5}[/tex]

Step-by-step explanation:

Step 1 :-

given [tex]y= \frac{-7}{5 x} -3[/tex]

substitute given y=-10

[tex]-10+3 = \frac{7}{5 x}[/tex]

[tex]-7 = \frac{-7}{5 x}[/tex]

cancelled (-7) on both sides, we get

[tex]1= \frac{1}{5 x}[/tex]

cross multiplication, we get

[tex]5 x =1[/tex]

[tex]x=\frac{1}{5}[/tex]

Final answer:- [tex]x=\frac{1}{5}[/tex]

verification:-

given [tex]y= \frac{-7}{5 x} -3[/tex]

substitute [tex]x=\frac{1}{5}[/tex]

we get y= -10

Referring to the figure, the circle shown is drawn on grids. Find
A ÷ r and A ÷ r2 (Worth 45 points! Please help!!)

Answers

Answers:

a) [tex]\frac{A}{r}=2.5 \pi=7.85[/tex]

b) [tex]\frac{A}{r^{2}}=\pi=3.14[/tex]

Step-by-step explanation:

Assuming each grid has dimensions of 1x1, the radius of this circle is:

[tex]r=2.5[/tex]

On the other hand, the area of a circle is:

[tex]A=\pi r^{2}[/tex]

With this information we will solve this exercise:

a) [tex]\frac{A}{r}[/tex]

[tex]\frac{\pi r^{2}}{r}=\pi r[/tex]

[tex]\pi r=(3.14)(2.5)=7.85[/tex]

b) [tex]\frac{A}{r^{2}}[/tex]

[tex]\frac{\pi r^{2}}{r^{2}}=\pi=3.14[/tex]

how do you solve the equation -3 1/3 = -1/2g

Answers

[tex]g=\frac{20}{3}[/tex]

Solution:

Given expression is [tex]-3\frac{1}{3}=\frac{-1}{2}g[/tex].

To solve the given expression:

Let us first convert the mixed fraction into improper fraction.

⇒ [tex]-3\frac{1}{3}=\frac{-1}{2}g[/tex]

⇒ [tex]-\frac{(3\times 3 )+1}{3}=\frac{-1}{2}g[/tex]

⇒ [tex]-\frac{10}{3}=\frac{-1}{2}g[/tex]

Do cross multiply on both sides of the equation.

⇒ [tex]-10\times2=(-1\times3)g[/tex]

⇒ [tex]-20 = -3g[/tex]

⇒ [tex]\frac{-20}{-3}=g[/tex]

Both minus in the numerator and denominator are cancelled.

⇒ [tex]\frac{20}{3}=g[/tex]

Hence, [tex]g=\frac{20}{3}[/tex].

x minus 2 equals 5 (x-2=5)

Answers

x=7 that was a easy one

7-81. Aja and Emilie were riding their skateboards. They knew that they could ride 3 miles in 20 minutes.
b. If y represents the distance in miles and x represents the time in minutes, write an equation to
represent the distance traveled for any time.​

Answers

Answer:

[tex]y=\frac{3}{20}x[/tex]

Step-by-step explanation:

We want to write an equation of the form '

[tex]y=mx+b[/tex]

Now [tex]m[/tex] is the slope of the line or 'rise/run', and it is

[tex]m=\frac{ \Delta y }{ \Delta x } =\frac{3miles}{20minutes} =\frac{3}{20}[/tex]

Now for [tex]b.[/tex]

Since at x=0 y= 0 (Aja and Emile haven't traveled any distance)

[tex]0=0+b\\b=0[/tex]

Thus we have the equation

[tex]y=\frac{3}{20}x[/tex]

last week daniel ran 6 miles more than Jasmine . Daniel ran 24 miles. How many miles did Jasmine run ?

Answers

Answer:

18 miles

Step-by-step explanation:

If Daniel ran 24 miles take away the 6 more miles he ran to get 19 miles.

Distance covered by Jasmine is 18 miles when Daniel had ran 6 miles

What is an expression?

Expression in mathematic is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

It is given that Daniel ran 6 miles more than Jasmine last week which means that if Daniel ran 24 miles than jasmine had ran 6 miles less then Danial that is 24 miles subtract 6 miles which comes out be 18 miles :

Distance covered by Jasmine = 24 miles - 6 miles = 18 miles in total

Therefore, Distance covered by Jasmine is 18 miles when Daniel had ran 6 miles.

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Ken drinks 2/7 of a carton of milk each day.How much milk dose he drink in 3 days?

Answers

Answer:

6/7 of a carton

Step-by-step explanation:

3 x 2= 6

6/7

Can someone help me understand what I did wrong? I'm having trouble learning Eliminations.

Answers

Answer:

Step-by-step explanation:

2x + y = 5.....multiply by -3

3x - 2y = 4...multiply by 2

--------------------------

-6x - 3y = -15 (result of multiplying by -3)

6x - 4y = 8 (result of multiplying by 2)

-------------------------add

-7y = - 7 <===== here is one mistake.....its -7, not 7

y = -7/-7

y = 1

now sub 1 in for y in either of ur original equations to find x

not sure why u r multiplying again on ur paper when all u have to do is sub

2x + y = 5

2x + 1 = 5

2x = 5 - 1

2x = 4

x = 4/2

x = 2

solution is : (2,1)

the bad part about elimination is if there is a mistake made in the first part, it carries through to the end. So it is always best to check ur answers.

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Match each system on the left with all words that describe the system on the right. Choices on the right can be used more than once. . In chemistry, one often uses a unit of charge known as the Faraday, F, which has the magnitude of the charge of 1 mole of electrons. How many Coulombs are there in a Faraday The following is the general ledger for ABC Company as of December 31, 20X1. Use this information to answer questions (1) through (4).ABC CompanyGeneral LedgerAs of December 31, 20X1AmountAssetsCash$29,400Accounts receivable8,100Supplies4,900Prepaid rent20,200Equipment (net)63,800LiabilitiesAccounts payable$ 6,300Salaries payable4,000Interest payable1,100Utilities payable3,700Bonds payable38,400Stockholders' equityCommon stock$60,900Retained earnings0Dividends2,100RevenuesSales revenue$54,200Interest revenue1,400ExpensesCost of goods sold$15,100Salaries expense7,100Rent expense4,900Supplies expense1,300Utilities expense4,800Depreciation expense2,500Interest expense2,100Income tax expense3,700What is the amount of gross profit to be reported on ABC Companys 12/31/X1 income statement?$40,500$14,100$39,100$17,800What is the amount of operating income (EBIT) to be reported on ABC Companys 12/31/X1 income statement?$36,100$18,500$14,800$14,100What is the amount of earnings before taxes (EBT) to be reported on ABC Companys 12/31/X1 income statement?$15,000$17,800$12,000$18,500What is the amount of net income to be reported on ABC Companys 12/31/X1 income statement?$17,800$12,000$14,100$18,500 A liter of water was found to contain 10 mg of benzene (C6H6). What is the concentration of benzene in mg/L, ppm, and molarity? A package of aluminum foil is 59.3 yd long, 13 in. wide, and 0.00040 in. thick. If aluminum has a density of 2.70 g/cm3, what is the mass, in grams, of the foil? What is the best meaning of the phrase at the entrance to Auschwitz, Arbeit macht frei?No man is freeWork sets you freeOnly the good are freeEducation makes you free How did bosses and political machines control city governments? A) Shape x8) ShapeC) Shape zD) Shape PesWhich figure appears to be similar to the parallelogram?AB)B The monetary inflation needed to relieve the social and economic hardships of the late nineteenth century eventually came as a result of? Solve this system using the linear combination method. Show your work and explain each step. 2x + y = 8 x y = 4 HELPPPPPPP Julie throws a ball to her friend Sarah. The ball leaves Julie's hand a distance 1.5 meters above the ground with an initial speed of 18 m/s at an angle 42 degrees; with respect to the horizontal. Sarah catches the ball 1.5 meters above the ground.1) What is the horizontal component of the balls velocity when it leaves Julie's hand?2) What is the vertical component of the balls velocity when it leaves Julie's hand?3) What is the maximum height the ball goes above the ground?4) What is the distance between the two girls?5) After catching the ball, Sarah throws it back to Julie. The ball leaves Sarah's hand a distance 1.5 meters above the ground, and is moving with a speed of 14 m/s when it reaches a maximum height of 10 m above the ground.What is the speed of the ball when it leaves Sarah's hand?6) How high above the ground will the ball be when it gets to Julie? (note, the ball may go over Julie's head.) Two parallel plates have equal but opposite charges on their surface. The plates are separated by a finite distance.A fast moving proton enters the space between the two plates through a tiny hole in the left plate A. The electric potential energy of the proton increases as it moves toward plate B.(a) How is the speed of the proton affected as it moves from plate A to plate B?increasesdecreasesstays the same(b) Which plate is at a higher potential?plate Aplate B(c) What can you conclude about the charges on the two plates?Plate A is positive and plate B is negative.Plate A is negative and plate B is positive.(d) What will be the pattern of the equipotential lines in the space between the two plates? (Select all that apply.)Parallel lines more closely packed near plate B.Parallel lines perpendicular to the two plates.Parallel lines parallel to the two plates.Parallel lines more closely packed near plate A.Parallel lines equally spaced. Explain what happened genetically in the insect population over time as the insects were exposed to pyrethroids. Suppose that a company ships packages that are variable in weight, with an average weight of 15 lb and a standard deviation of 10. Assuming that the packages come from a large number of different customers so that it is reasonable to model their weights as independent random variables, find the probability that 100 packages will have a total weight exceeding 1700 lb. Carlo and his family emigrated to the United States from Columbia. Upon arrival, Carlo instructed his family to give up their old ways and start to integrate themselves into mainstream society. This meant learning a new language, dressing in a different way, and eating different foods. Carlo and his family are exemplifying: D is the midpoint of EF.ED = 4x + 6DF = 7x -9Find EF. How important was teamwork on the Lewis and Clark expedition ________ are particularly polarizable. ________ are particularly polarizable. Small polar molecules Large nonpolar molecules Large polar molecules Small nonpolar molecules Large molecules, regardless of their polarity, Three point charges are arranged in a line. Charge q 3 = +5 nC is at the origin. Charge q 2 = -3 nC is located at x- +4.00 cm. Charge q 1 is at x= + 2.00 cm. What is q 1, in magnitude and sign, if the net force on q3 is zero? At the beginning of a basketball game, a referee tosses the ball straight up with a speed of 4.41 m/s. A player cannot touch the ball until after it reaches its maximum height and begins to fall down. What is the minimum time that a player must wait before touching the ball? Steam Workshop Downloader