A cyclist is stationary when a second cyclist passes travelling at a constant speed of 8 m s−1. The first cyclist then accelerates for 5 s at a constant rate of 2 m s−1 before continuing at constant speed until overtaking the second cyclist. By sketching both graphs, find the equations of the two straight line sections of the graphs and hence find how long it is before the first cyclist overtakes the second.

Answers

Answer 1

Answer:

im not too sure about that sorry!

Step-by-step explanation:

uiwgorihvncjkdnskv

Answer 2

It takes 15 seconds for the first cyclist to overtake the second cyclist.

How can you find how long it took before the first cyclist overtakes the second?

First, identify the two phases of the first cyclist's motion.

Phase 1: The cyclist accelerates from rest to a constant speed of 8 m/s.

Phase 2: The cyclist travels at a constant speed of 8 m/s.

Find the equations of the two straight-line sections of the graph.

The equations of the two straight-line sections of the graph are as follows:

Phase 1:

s = [tex]2t^2[/tex]

Phase 2:

s = 8t

where s is the distance traveled by the cyclist and t is the time

Set the two equations equal to each other to find the time it takes the first cyclist to overtake the second cyclist

The first cyclist overtakes the second cyclist when the first cyclist has traveled a distance of 8 m more than the second cyclist.

Let t be the time it takes the first cyclist to overtake the second cyclist.

The distance traveled by the first cyclist is then 8t, and the distance traveled by the second cyclist is 8(t - 5).

Setting these two expressions equal to each other, we get:

8t = 8(t - 5)

Solving for t, we get:

t = 15

Therefore, it takes 15 seconds for the first cyclist to overtake the second cyclist

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Related Questions

Hi I need help
1) -15+4r=-9
2)5-y/3=-1
3)42=5x-8
That's all, you don't have to show work, but I'd appreciate it:) asap pls

Answers

Equation #1:

-15+4r=-9

We move all terms to the left:

-15+4r-(-9)=0

We add all the numbers together, and all the variables

4r-6=0

We move all terms containing r to the left, all other terms to the right

4r=6

r=6/4

r=1+1/2

Equation #2:

5-y/3=-1

We move all terms to the left:

5-y/3-(-1)=0

We add all the numbers together, and all the variables

-y/3+6=0

We multiply all the terms by the denominator

-y+6*3=0

We add all the numbers together, and all the variables

-1y+18=0

We move all terms containing y to the left, all other terms to the right

-y=-18

y=-18/-1

y=+18

Equation #3:

Simplifying

42 = 5x + -8

Reorder the terms:

42 = -8 + 5x

Solving

42 = -8 + 5x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-5x' to each side of the equation.

42 + -5x = -8 + 5x + -5x

Combine like terms: 5x + -5x = 0

42 + -5x = -8 + 0

42 + -5x = -8

Add '-42' to each side of the equation.

42 + -42 + -5x = -8 + -42

Combine like terms: 42 + -42 = 0

0 + -5x = -8 + -42

-5x = -8 + -42

Combine like terms: -8 + -42 = -50

-5x = -50

Divide each side by '-5'.

x = 10

Simplifying

x = 10

Step-by-step explanation:

hope it's beneficial.

Draw my attention for further explanations.✨✨

What remainder is represented by the synthetic division below?

A vertical line and horizontal line combine to make a L shape. There are two rows of entries within the shape. Row 1 has entries 2, 10, 1, 5. Row 2 has entries blank, negative 10, 0, negative 5. Entry negative 5 is on the outside to the left of the shape, and a third row of entries is outside and below the shape. Row 3 has entries 2, 0, 1, 0.

Answers

The remainder represented by synthetic division is -5.

What is synthetic division?

Synthetic division can be defined as a simplified way of dividing a polynomial with another polynomial equation of degree 1.

Given

A vertical line and a horizontal line combine to make an L shape.

There are two rows of entries within the shape.

Row 1 has entries 2, 10, 1, 5.

Row 2 has entries blank, -10, 0, -5.

Entry -5 is on the outside to the left of the shape. The entry represents the zero of the divisor. This entry to the variable (assume the variable is x) is;

x + 5 = 0

x = -5

Hence, the divisor of the synthetic division is -5.

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Answer:

its a) -5

Step-by-step explanation:

sara scores -4 marks if she got 3 correct answers how many were incorrect

Answers

The number of answers that were incorrect will be 7.

How to depict the information?

From the information given, every correct answer will be +1 while and incorrect answer will be -1. The equation to represent the information will be:

3 - x = -4

where x = incorrect answer

3 - x = -4

-x - 4 - 3

-x = -7

x = 7

In conclusion, the number of answers that were incorrect will be 7.

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Which composition of similarity transformations maps ΔLMN to ΔL'M'N'?

Option A: a dilation with a scale factor less than 1 and then a reflection
Option B: a dilation with a scale factor less than 1 and then a translation
Option C: a dilation with a scale factor greater than 1 and then a reflection
Option D: a dilation with a scale factor greater than 1 and then a translation

Answers

It had to Option D you are very welcome

The diagonals of a rhombus are: A. are the same length and intersect at different angles B. bisect each other at right angles C. bisect each other and intersect at different angles D. are the same length and intersect at a right angle

Answers

Answer:

Step-by-step explanation:

Comment

Either you know the answer to this or you don't. There is no point in eliminating the wrong answers until you get to the right one. It is better to get to the right one immediately.

A rhombus and its diagonals have many interesting properties.  This one is one of those properties. The diagonals are not the same length. The diagonals bisect each other at right angles.

Answer: B

A bag contains 4 red, 7 blue and 5 yellow marbles. Event A is defined as drawing a yellow marble on the first draw and event B is defined as drawing a blue marble on the second draw.
If two marbles are drawn from the bag, one after the other and not replaced, what is P(B|A) expressed in simplest form?

A. 7/16
B. 7/15
C. 14/16
D. 14/15

Answers

Your answer should be C. 14/16 hope this helps!!!

Answer:

The answer is B. 7/15!!!

i just guessed and got it right, but i knew c. wasnt the answer.

Analyze the graph of the cube root function shown
on the right to determine the transformations of
the parent function. Then, determine the values of
a, h, and k in the general equation.
y = a√√x-h+k
h =
k =
DONE✔

Answers

The values of a, h, and k in the general equation is h=1, k=4 and a=2

What is parent function?

The function which can be transformed into different ways is the parent function.

On a coordinate plane, a cubic function approaches the x-axis in quadrant 2, crosses the y-axis at (0, 2), has an inflection point at (1, 4), and the goes through (2, 6).

The given function is

y =a³ √(x -h) + k

Put the coordinate (0,2) in the equation, we get

2 = a³ √(0 -h) + k..................(1)

Plug (1, 4), we have

4 =  a³ √(1 -h) + k..................(2)

Plug (2, 6), we have

6 =  a³ √(2 -h) + k..................(3)

On solving these three equations, we have

h=1

k=4

a=2

Thus, value of h is 1, k is 4 and a is 2.

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Answer:

the rest of the answers are:

C

B

C

A

D F

A C D

A

D

H= 1

K=4

A=2

Step-by-step explanation:

if f(x)=-x+8 and f(-4), then the result is 12

True or False?

Answers

Answer:

[tex] \sf \blue{True✅}[/tex]

Step-by-step explanation:

Given,

[tex]f(x) = - x + 8 \: and \: f( - 4)[/tex]

Solution:

[tex] f( x) = - ( - 4) + 8 \\ \\ = 4 + 8 \\ \\ = 12[/tex]

Hope it help you

Which equation can be used to solve for xxx in the following diagram?




Choose 1 answer:
Choose 1 answer:

(Choice A)
A
2x = 4x2x=4x2, x, equals, 4, x

(Choice B)
B
2x + 4x = 1802x+4x=1802, x, plus, 4, x, equals, 180

(Choice C)
C
2x + 4x = 902x+4x=902, x, plus, 4, x, equals, 90

(Choice D)
D
2x + 4x = 1502x+4x=1502, x, plus, 4, x, equals, 150

Answers

The equation that can be used to determine the value of x is Option B.

What is an Equation ?

An equation is a mathematical statement formed when two algebraic expression are equated by an equal sign.

From the diagram ,

A straight line has an angle of 180 degree.

Therefore from the figure

To determine the value of x

2x + 4x = 180

6x = 180

x =30 degree

Thus the equation that can be used to determine the value of x is Option B.

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What is 2*4*6.5*24.5

Answers

Answer:

1274

it is 1274

Step-by-step explanation:

mark as brainlest for the answer thankyou

What is the y-intercept of the function f(x) = 2.3*?
A. (0,6)
B. (2,0)
C. (0,2)
OD. (0,3)

Answers

The answer is C. (0,2)

I need help answering these questions for geometry :)

1. What happens to the measure of the interior angles as the number of sides of the polygon increases? Explain your answer.
2.What happens to the measure of the exterior angles as the number of sides of the polygon increases? Explain your answer.
4. Explain what happens to the total sum of interior angles as the number of sides in the polygon changes.
5. Explain what happens to the total sum of exterior angles as the number of sides in the polygon changes.

Answers

The answers to the question have been written below

The changes to a polygon

1. If the number of sides of the polygon should increase then the measure of the interior angle would increase by 180.

2. A regular polygon has the sum of its external angles as 360. This is solved as 360/n = 0

Hence the value of the exterior would move towards 0 as its sides increases.

4. As the total sum of the of the polygon changes, it would tend towards infinity.

5. The total sum of the exterior angles as the number of sides changes would tends towards 360 degrees.

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17. What is the value of x in the rhombus
below?
A
C
(x+ 40)
B
3x⁰
D
18

Answers

Answer:

Answer is 12.5 degrees

Answer:

x = 12.5

Step-by-step explanation:

4(x + 40) + 4(3x) = 360

4x + 160 + 12x = 360

16x + 160 = 360

16x = 200

x = 12.5

The sides of a triangle are 5, 12 and 13 inches long. what is the angle between the 2 shortest sides?
a. 30
b. 45
c. 60
d. 90
e. 120

Answers

Answer: 90 degrees

Step-by-step explanation:

The hypotenuse is opposite the right angle, which is created by the two shortest sides.

The price of a coat is $65. In sale, the price is reduced by 15%. What is the price of the coat in sale?

Answers

Answer: $55.25

Step-by-Step Explanation:

Price of the Coat = $65

Step 1 :- Find 15% of $65.

= 15/100 * 65
= 975/100
=> 9.75

15% of $65 = $9.75

Step. 2 :- Subtract $9.75 from $65.

= 65 - 9.75
=> 55.25

Price of the Coat in Sale = $55.25
55.25, 65*15%=55.25…….

What are the more appropriate measures of center and spread for this data
set?
35 40 45
55
90
hi
10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100
select two choices: one for the center and one for the spread.
a. better measure of spread: the standard deviation
select two choices: one for the center and one for the spread

Answers

The more appropriate measure of center is mean.

The more appropriate measure of spread is standard deviation.

What is mean and standard deviation?

Mean is a measure of central tendency that determines the average of a set of numbers. Standard deviation is used to determine the spread of a dataset. It does this by determining the square root of the average of the squared differences of the numbers from the mean of the data set.

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4. Write the function of a linear equation that includes the
points (1,3) and (2,9).

Answers

Answer:

y = 6x - 3

Step-by-step explanation:

the equation of a line in slope- intercept form ( linear function ) is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (1, 3 ) and (x₂, y₂ ) = (2, 9 )

m = [tex]\frac{9-3}{2-1}[/tex] = [tex]\frac{6}{1}[/tex] = 6 , then

y = 6x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (1, 3 ) , then

3 = 6 + c ⇒ c = 3 - 6 = - 3

y = 6x - 3 ← equation of linear function

can someone help with this

Answers

Step-by-step explanation:

-10-2x = 3x+15

5x = -25

x= -5

9x-7=-52
Show all work and justify each step

Answers

Answer:

x = -5

Step-by-step explanation:

9x - 7 = -52

we want to single out x,

add 7 to both sides to be one step closer to getting x alone

9x - 7 + 7 = -52 + 7

9x = -45

divided both sides by 9 to get x alone

9x / 9 = -45 / 9

x = -5

Let me know if you need any clarification!

[tex] 9x - 7 = - 52[/tex]

Firstly rearrange the variable on the left side of the equation...

[tex]9x = - 52 + 7[/tex]

Calculate the sum or differences

[tex]9x = - 45[/tex]

[tex]x = - \frac{45}{9} \\ [/tex]

[tex]x = - 5[/tex]

:)

..

Which value of x would make triangle s u v is-congruent-to triangle t u m by hl? 2 3 4 5

Answers

The question is incomplete. Below you will find the missing content and figure

Which value of x would make triangle ΔSUV is congruent to triangle ΔTUM by HL? Options are 2 3 4 5

The figure is shown below.

The correct option is Option D: the value of x is 5.

Triangles are congruent if the triangles are of the same size and shape. If triangles are congruent the corresponding length of the sides is the same.

Here given that triangle ΔSUV is congruent to triangle ΔTUM.

By the property of the congruent triangle, as triangle ΔSUV and ΔTUM are congruent the corresponding sides are also same.

ΔSUV ≅ΔTUM

⇒ VS≅WT

Given in the question

VS= 2x+9

WT= 4x-1

from above it is clear that

VS=WT

⇒ 2x+9=4x-1

⇒4x-2x=9+1

⇒2x=10

⇒x=10/2

⇒x=5

Therefore the correct option is Option D: the value of x is 5.

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Answer:

It will be 5 on EDG 2022 Your welcome :)

Step-by-step explanation:

David can you 25/6 meters per hour manually, but using a digging machine he can dig 3 times as fast. how many meters would david be able to dig with the machine in an hour?

Answers

Answer:

12.5 meters

Step-by-step explanation:

1 hour manually = 25/6 meters

1 hour using machine = 25/6 × 3 meters

1 hour using machine = 12.5 meters

Hope this helped and have a good day

LK
2(x+2y-x-1⁄2y+3);
When 2(5
4
01x + 2 y +6
Ox+2y+6
07x+8y+6
0176x+4y+3
is simplified, what is the resulting expression?

Answers

2(x+2y-x-1/2y+3)2x+2(2y)-2x-2(1/2y)+2(3)2x-2x+4y-y+63y+6

12. For which of the following quadratic equations are the roots 2 and 57
O A. x²-3x - 10=0
B. x² - 11x 10 = 0
c. x² - 7x + 10 = 0
D. x² + 7x-10=0
O
O
O

Answers

Answer: x²-59x+114=0

explanation:

If the roots are 2 and 57, then:-

sum of roots = 2+57 = 59

and, product of roots = 2×57 = 114

the quadratic equation is given by,

x²-(sum of roots)x+(product of roots)=0

so, x²-59x+114=0 will be the desired quadratic equation.

so, none of the options are correct.

the correct answer is x²-59x+114=0.

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When 3 times a number is subtracted from 45 the result is 5 plus the number. what is the number?

Answers

Answer:

n = 10

Step-by-step explanation:

let the number be n , then

45 - 3n = n + 5 ( subtract n from both sides )

45 - 4n = 5 ( subtract 45 from both sides )

- 4n = - 40 ( divide both sides by - 4 )

n = 10

Answer the following questions
A. 10 -4 ×5=?
B. 3+8×4=?
C. (3+8)×4=?

Answers

Answer:

A=30

B=35

C=44

Step-by-step explanation:

When given
Slope= -6/5
Y-intercept= 2
What is this in Point-Slope form?

Answers

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

Answer:  [tex]\textsf{y - 2 = -6/5(x - 0)}[/tex]

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

Given:  [tex]\textsf{Slope = -6/5, Goes through (0, 2)}[/tex]

Find:  [tex]\textsf{The equation in point-slope form}[/tex]

Solution: We need to take the values that were given to us and plug them into the point-slope form.  It doesn't seem like the problem is asking for anything more than that so we will leave it at that.

Plug in the values

[tex]\textsf{y - y}_1\textsf{ = m(x - x}_1\textsf{)}[/tex][tex]\textsf{y - 2 = -6/5(x - 0)}[/tex]

Since the problem is just asking for the equation in point-slope form the final expression would be y - 2 = -6/5(x - 0).

Answer:

[tex]\sf y - 2 = -\dfrac{6}{5}(x - 0)[/tex]

Step-by-step explanation:

[tex]\sf \large \underline{\textsf{Given:}}\ \textsf{a line with a slope of $-\dfrac{6}{5}$, and a y-intercept of $2$}[/tex]

We're given a y-intercept of 2, but using the slope-intercept form, we can immediately determine that x = 0. Hence, the given point is (0, 2).

Then, we substitute these values into the Point-Slope Form to find the equation.

Here are both forms for future reference:

Slope-Intercept Form: y = mx + b

[ Where: m is the slope, and b is the y-intercept (when x = 0). ]

Point-Slope Form: y - y₁ = m(x - x₁)

[ Where: m is the slope, and (x₁, y₁) is a given point. ]

Substitute the values into the Point-Slope Form:

[tex]\sf\\\implies y - y_1 = m(x - x_1)\\\\\implies y - 2 = -\dfrac{6}{5}(x - 0)[/tex]

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A gym has 65 members. If 35 are men and the
rest are women, what is the ratio of the female
members to the total members of the gym?

Answers

Answer:

Step-by-step explanation:

số nữ là 65- 35= 30

vậy tỷ lệ số tv nữ trên tổng số thành viên của phòng tập là 30/65 = 6/13

The table of values represents a linear function g(x) where c is the number of days that have passed and g(x) is the balance in the bank account

Answers

After 7 days, the balance will be Rs. 628.

(A) The slope of the given function is 40.

(B) In point - slope form it is y - 600 = 40x

   In Slope - intercept form it is y = 40x + 600

   In Standard form it is 40x - y + 600 = 0

(C) g(x) = 4x + 600

(D) After 7 days, the balance will be Rs. 628

Let g(x) = y

(A) We know slope = change in y/change in x

                               = 720-600/3-0

                               = 120/3

                               = 40

Therefore, the slope of the given function is 40.

(B) We know that the equation of a line

in point - slope form is y - y₁ = m(x - x₁)

where ( x₁, y₁ ) is a point on the line

where m is the slope

Therefore, substituting the values, we get,

y - 600 = 40(x - 0)

=> y - 600 = 40x                                    --(i)

What is the  Slope - intercept form?

Slope - intercept form is y  = mx + b

where m is the slope

and b is the y-intercept

To find y intercept, we substitute x = 0 in equation (i)

=> 40*0 - y + 600 = 0

=> -y + 600 = 0

=> y = 600

Therefore, substituting the values, we get,

     y = 40x + 600

in Standard form is ax + by = c

where a, b, and c is constant

Converting the equation found above into the standard form

=> y = 40x + 600

=> 40x - y + 600 = 0

(C) As we had assumed g(x) to be y

=> From equation (i),

 y - 600 = 40x    

can be written as g(x) - 600 = 4x

=> g(x) = 4x + 600                                    --(ii)

(D) We need to find the balance in the bank account after 7 days

=> Balance [g(x)] when x = 7

Therefore, substituting the value of x in equation (ii)

=> g(x) = 4*7 + 600

          = 28 + 600

          = 628

Therefore, after 7 days, the balance will be Rs. 628.

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$9,500 is invested in an account earning 9.1% interest (APR), compounded
quarterly. Write a function showing the value of the account after t years, where t
annual growth rate can be found from a constant in the function. Round all
coefficients in the function to four decimal places. Also, determine the percentage
growth per year (APY), to the nearest hundredth of a percent.

Answers

Answer:

$100.5000

Step-by-step explanation:

becuse $9,500 is fived and it got it

Which expression can be used to convert 22 Australian dollars to US dollars?

Assume 1.2 Australian dollars equals 1 US dollar.

Answers

Answer:

1.2x = 22x = 55/3 ≈ 18.3322 AUD = 18.33 USD

Step-by-step explanation:

1 USD - 1.2 AUD

x USD - 22 AUD

cross multiply

1.2 · x = 1 · 22

1.2x = 22

multiply both sides by 10

12x = 220

divide both sides by 12

x=55/3 ≈ 18.33

USD - United States dollar

AUD - Australian dollar

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What is convection?a type of circular flowa type of heat cella type of heat currenta type of heat transfer Compare Photograph with Iron Maiden." What makes the Def Leppard song more pop oriented (and therefore possessing greater mass appeal)? What is x, the distance between points A and A'? D.15 Part 1. A chemist reacted 15.0 liters of F2 gas with NaCl in the laboratory to form Cl2 and NaF. Use the ideal gas law equation to determine the mass of NaCl that reacted with F2 at 280. K and 1.50 atm.F2 + 2NaCl Cl2 + 2NaFPart 2. Explain how you would determine the mass of sodium chloride that can react with the same volume of fluorine gas at STP.explain please (for 40 pts) a certain value has a standardized score = 1.75. how many standard deviations from the mean does this value fall? is this value greater than or less than the mean? What are the more appropriate measures of center and spread for this data set? 35 40 45 55 90 hi 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 select two choices: one for the center and one for the spread. a. better measure of spread: the standard deviation select two choices: one for the center and one for the spread The price of a coat is $65. In sale, the price is reduced by 15%. What is the price of the coat in sale? The cost of renting a car is $47 /week plus $0.25 /mile traveled during that week. An equation to represent the cost would be y=47+0.25x , where x is the number of miles traveled. What is 2*4*6.5*24.5 A ball is shot from the ground straight up into the air with initial velocity of 40 ft/sec. Assuming that the air resistance can be ignored, how high does it go Answer the following questionsA. 10 -4 5=?B. 3+84=?C. (3+8)4=? In the context of the elements of scientific management, time and motion studies focus on: group of answer choices designing different types of activities to overcome the boredom of overspecialized work. increasing the amount of job responsibility through vertical loading. the inclusion of motivation and hygiene factors that affect job satisfaction. the efficient use of labor to the economic benefit of a corporation. Read the excerpt from julius caesar, act 1, scene 2. cassius. 'tis just; and it is very much lamented, brutus,60 that you have no such mirrors as will turn your hidden worthiness into your eye, that you might see your shadow. i have heard where many of the best respect in rome except immortal caesarspeaking of brutus,65 and groaning underneath this ages yoke, have wished that noble brutus had his eyes. which summary of the passage is the most accurate? cassius says it is a shame brutus does not look in the mirror often enough to see how handsome he is. cassius explains that he laments that brutus does not have "such mirrors as will turn your hidden worthiness into your eye," for if brutus did, "you might see your shadow." cassius says that it is too bad brutus cannot see his hidden greatness. people are tired and grumbling about the government under caesars rule, and while caesar doesnt see that the greatness in brutus, cassius has heard others wishing that brutus could be their leader. cassius tells brutus that he should take caesars job once he becomes confident enough. 9x-7=-52Show all work and justify each step write down some of the major threats posed to the great pyramids by the environment The sum of a number and 3 is less than 10 if x denotes the number what would be the possible values of xx>13x7x In her 1976 Democratic national convention keynote address, which of these inferences about the "common endeavor" Barbra Jordan calls for is best supported by the text?A) It will only work if both parties rally behind one candidate.B) It is the same spirit that led the colonists to victory in the American Revolution.C) It is only possible now because they have arrived in a world where she can be a keynote speaker.D) If the people come together, they can be more powerful than any individual candidate what is 2 plus two.please answer quickly what is the energy of a photon with a frequency of 8.34 x 10^14 hz, in joules? Drag each tile to the correct box. Not all tiles will be used.Consider function f.Place the steps for finding in the correct order.