1.) Line segment AB has endpoints A(1,8) and B(7,−4). What are the coordinates of the point located 5/6 of the way from A to B?
O (-4, 11 1/3)
O (3, -2 1/3)
O (6, -2)
O (12, -14)

2.) Line segment AB has endpoints B (-3, 0) and A(5, 4). What are the coordinates of the point located 1/4 of the way from B to A?
O (1, -1)
O (1, 2)
O (3, 3)
O (-1, 1)

3.) Line segment AB has endpoints A(1, 8) and B(7, -4). What are the coordinates of the point located 1/6 of the way from A to B?
O (0, 8 2/3
O (2, 6)
O (8 2/3, -3 1/3)
O (6, -3 1/3)

^Please help, ASAP. These were due yesterday, however I am trying to get this done.
BRAINLIEST AND 5 STARS TO CORRECT RESPONSES ONLY! LOTS OF PTS AVAILABLE TO THOSE WHO PARTICIPATE HOWEVER.

Answers

Answer 1

The coordinates of the 3 respective points from the given parameters are; (6, -2); (-1, 1); (2, 6)

How to find the length of Line Segment?

1) The coordinates of the point located 5/6 of the way from A to B is;

x = ⁵/₆(7 - 1) + 1

x = 6

y = ⁵/₆(-4 - 8) + 8

y = -2

x, y = (6, -2)

2) The coordinates of the point located ¹/₄ of the way from A to B is;

x = -3 + ¹/₄(5 - (-3))

x = -1

y = 0 + ¹/₄(4 - 0)

y = 1

x, y = (-1, 1)

3) The coordinates of the point located ¹/₆ of the way from A to B is;

x = ¹/₆(7 - 1) + 1

x = 2

y = ¹/₆(-4 - 8) + 8

y = 6

x, y = (2, 6)

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Related Questions

The band is raising money for their spring trip. they need to raise at
least $1500. earlier in the year, they made $575 on their annual fruit sale.
now they are selling donuts, where they will earn $5 profit for each box
of donuts they sell. which inequality could be used in order to
determine the number of boxes of donuts, d, they must sell in order to
meet their goal?

Answers

The inequality that can be used  to determine the number of boxes of donuts, d, they must sell in order to meet their goal is $1500 ≥ $575 + $5d.

What is the inequality?

Here are inequality signs and what they denote:

> means greater than< means less than≥ means greater than or equal to ≤ less than or equal to

Total amount that needs to be raised ≥ amount made at the fruit sale + (profit per box x number of boxes)

$1500 ≥ $575 + $5d

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What is the value of the expression below?

2[3(16+)]-8

Answers

Answer:

94

Step-by-step explanation

2 * [3 * (16 + 1)] - 8 =

2 * [3 * 17] - 8 =

2 * 51 - 8

102 - 8 =

94

Find the equation of a line that passes through the points (-4, -2) and (6, 3).

Answers

Answer:

[tex]y=\frac{1}{2} x[/tex]

Step-by-step explanation:

The equation of a line through two points can usually (except when the line is a vertical line) be written in slope intercept form,  [tex]y=mx+b[/tex] , where "m" is the slope of the line, and "b" is the y-intercept of the line.

General outlineFind the slopeFind the y-intercept
Step 1.  Find the slope

To find "m", use the formula for slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m=\dfrac{(3)-(-2)}{(6)-(-4)}[/tex]

[tex]m=\dfrac{3+2}{6+4}[/tex]

[tex]m=\dfrac{5}{10}[/tex]

[tex]m=\dfrac{1}{2}[/tex]

So, the slope is 1/2 and we know that the equation for the line that passes through these two points should look like: [tex]y=\frac{1}{2} x+b[/tex]

Step 2.  Find the y-intercept

To find "b", substitute one of the known points, and solve for "b":

[tex]y=\frac{1}{2} x+b[/tex]

[tex](3)=\frac{1}{2} (6)+b[/tex]

[tex]3=3+b[/tex]

Subtracting 3 from both sides to isolate the "b"...

[tex](3)-3=(3+b)-3[/tex]

[tex]0=b[/tex]

So, the y-intercept is 0.  Substituting into our line equation, [tex]y=\frac{1}{2} x+(0)[/tex] which simplifies to [tex]y=\frac{1}{2} x[/tex]  

PLS I NEED 100% TO GET A GOOD MATH GRADE THIS YEAR

The following box plot shows the number of years during which 24 schools have participated in an interschool swimming meet:

At least how many schools have participated for 1 year or less? (5 points)



6 schools


8 schools


12 schools


14 schools

Answers

1 year or less is at the first quartile mark in the box plot, therefore, the number of schools that participated for a year and less is: A. 6 schools.

What is the First Quartile of a Data Represented in a Box Plot?

The data point at the beginning of the edge of the rectangular box in a box plot is the first quartile mark of the data, which is 1/4 or 25% of the data.

1 year or less is at the first quartile mark in the box plot. That is 1/4 of the total number of schools.

Therefore, schools that participated for a year and less = 1/4(24) = 6 schools.

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I need help please help me and thank you :))​

Answers

Answer:

see explanation

Step-by-step explanation:

∠ CZD = 90° , then

∠ CZF = 90° - ∠ FZD = 90° - 40° = 50°

∠ FZD and ∠ AZG are vertically opposite angles and are congruent , so

∠ AZG = 40°

∠ CZF and ∠ GZE are vertically opposite angles and are congruent , so

∠ GZE = 50°

E

∠ AZB + ∠ BZC = 90° , that is

3x - 2 + 32 = 90

3x + 30 = 90 ( subtract 30 from both sides )

3x = 60 ( divide both sides by 3 )

x = 20

Question 5 and 6 I need answers to

Answers

Answer:

and also mark me the brainliest for the answer

Step-by-step explanation:

What is the range of function g if g(x) =-2f(x-3)

Answers

Answer:

If you entered the function correctly there is not a range  

Step-by-step explanation:

Answer: {y|-♾<y<0}

Step-by-step explanation: i’m taking this summer school class

the lenth of a rectangle is twice the width if the permeter is 20 cm find the width

Answers

L = 2W

perimeter = 2( L + W ) = 20 .

2 ( 2W + W ) = 20

6 W = 20

W = 20/6

= 10/3

L = 20/3

Answer:

10/3

Step-by-step explanation:

Given properties of the rectangle:

The length is twice the width ( So we can say l = 2w ) The perimeter is 20cm

Given this we want to find the width of the perimeter.

Creating a system of equation:

First off we know that perimeter = 2L + 2W

We also know that the perimeter of this rectangle is 20 cm

So we can say that 20 = 2L + 2W

We also know that the length of this rectangle is twice the width or in other words l = 2w

So we have the two equations, 20 = 2l + 2w and l = 2w

Solving the system:

We are going to use the substitution method to solve this system.

The substitution method works when you have two equations, one can be just a plain equation but the other must have one of the variables defined ( by itself on either side of the equal sign )

If you have one of the variables defined, you can plug it in ( substitute ) into the other equation and solve for the other variable.

Plugging in the defined variable into the other equation

Equation : 20 = 2l + 2w

Defined variable : l = 2w

==> plug in l = 2w

20 = 2(2w) + 2w ( now we solve )

==> multiply 2 and 2w

20 = 4w + 2w

==> combine like terms

20 = 6w

==> divide both sides by 6

20/6 = w

==> simplify fraction

10/3  = w

The width = 10/3

Checking our work:

First we must solve for length as well

Solving for length by plugging in width into either equation

l = 2w

==> plug in w = 10/3

l = 2(10/3)

==> multiply 2 and 10/3

l = 20/3

Now to check our we we plug in the length and width into both equations, if both are true then our answer is correct

Equation 1 : 2l + 2w = 20

==> plug in l = 20/3 and w = 10/3

2(20/3) + 2(10/3) = 20

==> simplify multiplication

40/3 + 20/3 = 20

==> add fractions

20 = 20

Equation 2 : l = 2w

==> plug in l = 20/3 and w = 10/3

20/3 = 2(10/3)

==> multiply 2 and 10/3

20/3 = 20/3

Both are correct so our final answer is correct as well! :)

5. you work at a t-shirt printing business. 175 of 3,500 t-shirts shipped are printed improperly. what is the experimental probability that a t-shirt is printed improperly?
a: 6%
b: 1.75%
c: 5%
d: 35%

Answers

Answer:

C: 5%

Step-by-step explanation:

175 out of 3500 = 175/3500

175/3500 = 1/20

1/20 = 0.05

0.05 = 5%

Answer:

C 5%

Step-by-step explanation:

I am smart so trust me

Write the equation of the following line in slope-intercept form. X​

Answers

Answer:

[tex]y=-\frac{1}{2}x+2[/tex]

Step-by-step explanation:

The equation for slope-intercept form is [tex]y=mx+b[/tex].

First, we find b by looking at where the line passes through where [tex]x=0[/tex]. We can see that it is 2, so in our equation for slope-intercept form [tex]b=2[/tex].

Next, we find the slope or m. Find the slope by taking two points and plugging them into this expression [tex]\frac{x_{1}-x_{2}}{y_{1}-y_{2}}[/tex]. To demonstrate, I will choose points (0,2) and (2,1), however, any pair of points will give you the same answer. When we plug in these points, we should get the expression [tex]\frac{0-2}{2-1}[/tex]. By solving this, we get -1/2. Therefore, in our equation for slope-intercept form, [tex]m=-\frac{1}{2}[/tex].

By putting the information we have about m and b together, we get the equation [tex]y=-\frac{1}{2}x+2[/tex].

[tex]\sqrt{25-10\sqrt{3}+3[/tex] Simplify this

Answers

[tex] \sqrt{25 \: - \: 10 \sqrt{3} \: + \: 3} [/tex]

Factor the indicated expression:

[tex] \sqrt{(5 \: - \: \sqrt{3} ) ^{2} } [/tex]

Simplified the index index the root and also the exponent using the number 2.

[tex] \boxed{ \bold{5 \: - \: \sqrt{3} }}[/tex]

MissSpanish

Find the measure of

Answers

Answer:

h=70°

Step-by-step explanation:

h + 110° = 180° {linear pair angles}

h = 180° - 110°

h = 70°

Answer:

h=70

pa brainliest po kuya/ate

Step-by-step explanation:

pa brainliest po

In the statement 10 +(-10) =0, how would you describe the -10?

Answers

Answer:

-10 is the opposite of 10

Step-by-step explanation:

-10 is the opposite of 10 ,because The sum of a number and its opposite equals to zero.

Solve the given inequality and graph the solution on a number line. -X/2 -3/2 = 5/2


No Links:

Answers

X = -8. This is the answer because two negatives multiplied together make a positive integer, and with x equaling -8, the equation would be completed. -8 • -X = 8. 8/2 - 3/2 = 5/2.

Your final answer: X = -8.

Which statements are true about the graph of function f? f(x)=logx

Answers

The true statement about is the graph has a range of {y|-∞ < y < ∞} and decreases as x approaches 0.

What is a logarithm function?

A logarithm function is a type of function that represents the inverse of an exponential function. Mathematically, a logarithmic function is written as [tex]y =log_ax[/tex].

The domain of the given logarithm function f(x) = logx is (x > 0) and its graph wouldn't touch the vertical axis but moves to the right.

Also, the logarithmic function increases as the value of x increases. Thus, this function would decrease when x approaches zero (0).

In conclusion, we can deduce that the range of this function is -∞ < y < ∞.

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Answer:

domain:

c. The graph has a domain of {x|0<x<∞} and approaches 0 as x decreases.

and pretty sure the range is:

b. The graph has a range of {y|-∞<y<∞}and decreases as x approaches 0.

because all real numbers

Step-by-step explanation:

hope this helped

Jane earns an annual salary of £14000 and receives
a pay rise of 1.8%
Lenny earns an annual salary of £11000 and
receives a pay rise of 1.7%
Find which of the employees has the larger pay
increase and by how much.

Answers

The employee that has the larger pay increase is Jane. Her income is larger by £65.

Which employees has the larger pay increase?

Percentage is the fraction out of an amount that is usually expressed as a number out of hundred.

Increase in Jane's salary = £14,000 x 0.018 = £252Increase in Lenny's salary = £11,000 x 0.017 = £187Difference in increase = $252 - £187 = £65

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Needing help with these 2 problems

Answers

Answer:

15) 3.2

17) 13.4

Step-by-step explanation:

To find the missing lengths, you need to use the Pythagorean theorem:

a² + b² = c²

In this form, "c" represents the length of the hypotenuse and "a" and "b" represent the lengths of the other two sides.

You are trying to find one of the side lengths (not the hypotenuse) in 15). To find the other length, you can plug the other values into the equation and simplify to find "b".

15)    a = 4.1     c = 5.2

a² + b² = c²                                    <----- Pythagreom Theorem

(4.1)² + b² = (5.2)²                          <----- Plug values in for "a" and "c"

16.81 + b² = 27.04                         <----- Raise numbers to the power of 2

b² = 10.23                                      <----- Subtract 16.81 from both sides

b = 3.2                                           <----- Take the square root of both sides

You are trying to find the hypotenuse in 17). Since you have been given the lengths of the other sides, you can plug them into the equations and simplify to find "c".

17)   a = 4.4      b = 12.7

a² + b² = c²                                      <----- Pythagreom Theorem

(4.4)² + (12.7)² = c²                           <----- Plug values in for "a" and "b"

19.36 + 161.29 = c²                          <----- Raise numbers to the power of 2

180.65 = c²                                      <----- Add

13.4 = c                                            <----- Take the square root of both sides

Please solve this ASAP!!!

Answers

Hillbilly crazy boy go wild

Can someone help me with this? Thanks!

Answers

Part (a)

There are 3 face cards (jack, queen, king) in any given suit. We have 4 suits. That gives 3*4 = 12 face cards total.

12/52 = 3/13 is the probability of getting a face card on any random selection. This probably does not change for any future selection because we put the current card back. In other words, the deck has not changed. Contrast this with part (b) where the probabilities will change since the card counts decrease each time (since we don't put the card back).

The probability of getting 3 face cards in a row, with replacement, is:

(3/13)*(3/13)*(3/13) = 0.012289 approximately

This converts to the percentage 1.2289% after moving the decimal point two spots to the right. This is the same as multiplying by 100.

Lastly, round that to one decimal place to get 1.2%

Answer:  1.2

The percent sign is already taken care of, so you'll just input the number only.

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

Part (b)

Like mentioned earlier, the probability of a face card is 12/52

I won't reduce that fraction, as you'll see why below.

After that first card is not put back, the 12 decreases to 12-1 = 11 and we have 52-1 = 51 cards left over.

11/51 is the probability of getting another face card, where we have no replacement going on.

Then 10/50 is the probability of getting a third face card. Again, with no replacement.

Therefore,

(12/52)*(11/51)*(10/50) = 0.009955

is the approximate probability of getting 3 face cards in a row with no replacement. Notice the count down 12,11,10 in the numerators. There's also the countdown 52, 51, 50 in the denominators. This nice pattern only happens if we don't reduce the reducible fractions. This is why I didn't reduce.

Anyways 0.009955 converts to 0.9955% which rounds to 1.0% or simply 1%

Answer:   1

Apply the 45º-45º-90º Triangle Theorem to find the length of the hypotenuse of the triangle.

Answers

Answer:

  The sine of the angle = the length of the opposite side. the length of the hypotenuse.

  The cosine of the angle = the length of the adjacent side. the length of the hypotenuse.

  The tangent of the angle = the length of the opposite side. the length of the adjacent side.

Step-by-step explanation:

Answer:

c = a√2

Step-by-step explanation:

Apply the 45º-45º-90º Triangle Theorem to find the length of the hypotenuse of the triangle.

since there is no measure, I will write you the formula:

c (hypotenuse) = a√2

Two airplanes leave Chicago at the same time and fly in opposite directions. If one travels at 450 miles per hour and the other at 550 miles per hour, how long will it take for them to be 4000 miles apart

Answers

450t+550t=4,000

1000t=4000

t=4000/1000

t=4 hours they will be 4,000 apart.

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

20t+12(4.5-t)=70

20t+54-12t=70

8t=70-54

8t=16

t=16/8

t=2 hours at 20 mph.

proof

20*2+12(4.5-2)=70

40+12(2.5)=70

40+30=70

70=70

Which lists the steps in the correct order to find the median of this data set? 24, 16, 23, 30, 18, 29 O 1. Put the numbers in order. 2. Cross off high/low pairs. 3. Add the leftover numbers. 4. Divide the sum by 2. O1. Put the numbers in order. 2. Cross of high/low pairs. 1. Cross off high/low pairs. 2. Add the leftover numbers. 3.Divide the sum by 2. 1. Cross of high/low pairs.​

Answers

Median is the central tendency of the data and always exists in the middle of the data set.

What is the median?

The Median is the middlemost value of the numbers arranged in the ascending orders. Median is the central tendency of the data and always exists in the middle of the data set.

The process of finding the median if the number of data points is even is as follows:

Put the numbers or the data points in the order(increasing or decreasing i.e. ascending or descending order)Next cross of the high/ low pairsAdd the leftover numbersand divide the number( as obtained in the above step by 2)

( if the number of data pints were even then we just need to arrange the numbers and cross the high/low pair and only one data point will be left which acts as the Median of the data set)

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plaese explain this exe i can't understand and tomorrow i have an exman of metahmatice

Answers

Answer:

  B: 610; A: 202,000

  D: 253; C: 2,007,000

Step-by-step explanation:

These are all expressions that can be calculated as is, or that can be simplified a little bit by taking advantage of the distributive property and other properties of addition and multiplication. The idea is to look for numbers that show up more than once, and rearrange the expression so they only show up once.

__

B = (597 -176) +(13 +176)

This is a straight addition problem. The two "176" values have opposite signs, so cancel when they are added. Using the associative and commutative properties of addition, we can rearrange this to ...

   597 +13 +(-176 +176)

  = 597 +13

This can further be rearranged to ...

  = (597 +3) +(13 -3)

  = 600 +10

  = 610

__

A = 2020×173 -2020×73

The factor 2020 can be put outside parentheses using the distributive property:

  = 2020(173 -73)

  = 2020×100

  = 202,000

__

D 17×15 -15 +13

The value 15 is repeated. Terms using it can be combined using the distributive property.

  = 15(17 -1) +13

  = 15(16) +13

  = 240 +13

  = 253

Another way to look at this one is to use the factoring of the difference of squares.

  = (16 +1)(16 -1) +(-15 +13)

  = 16² -1² +(-2)

  = 256 -3

  = 253

__

C 2019×890 -(12000 -2019×110)

Again, we can focus on rearranging so 2019 only needs to show up once.

  = 2019(890 +110) -12000

  = 2019×1000 -12×1000

  = (2019 -12)×1000

  = 2,007,000

A jar contains five blue marbles, six red marbles, and four green marbles. What are the odds you will draw a blue marble from this jar?

Answers

Answer:

Probability=number of specific outcomes/total of all possible outcomes

There are 5 blue marbles and a total of 15 marbles.

So the probability of drawing a blue marble from the jar is:

5/15

1/3

Step-by-step explanation:

Hope this helps

a) Work out the size of angle x. b) Give reasons for your answer. + A E C xº B F 105° G D H​

Answers

Check the picture below.

Please help me with this one.​

Answers

Answer:

V = 16W = 48

Step-by-step explanation:

The triangles are congruent when corresponding sides are congruent.

__

ΔFGH ≅ ΔABC means corresponding sides are ...

  (GH, BC) = (V, 16)

  (HF, CA) = (48, W)

Corresponding sides being congruent means ...

  V = 16

  W = 48

[tex]\huge\fbox\green{question}[/tex]

#Combine the members of the following sets to from new sets.Show the members in diagrams

a)A={Mine,Shine,Hari} and B={Ram,Sita,Dolma}

b)M={3,6,9,12>and N={5,10,15,20}

c)A={Mari,Rahlm,Bishnu}and B={Bishnu, Kishan,Dorge}

d)C={4,8,12,16,20} and F={8,16,24,32}​

Answers

Refer to the attachment

A company provides snack-sized packages of nuts for its office employees.
employees can choose from among five kinds of nuts. which probabilities
correctly complete this probability distribution for 50 packages of nuts, in the
order listed?
nuts
almonds cashews mixed peanuts pecans
12
10
6
14
8
number of
packages
probability
a. probability 0.32 0.24 0.14 0.2 0.1

Answers

The probabilities that correctly complete this probability distribution for 50 packages of nuts will be 0.24, 0.2, 0.12, 0.28, and 0.16.

How to calculate the probability?

From the information given, we have to find the probability for each fruit. This will be:

Almond = 12/50 = 0.24

Cashew = 10/50 = 0.2

Mixed = 6/50 = 0.12

Peanut = 14/50 = 0.28

Pecan = 8/50 = 0.16

Therefore, the probabilities that correctly complete this probability distribution for 50 packages of nuts will be 0.24, 0.2, 0.12, 0.28, and 0.16.

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Solving for interior angle measures, what is the m

Answers

Using the triangle sum theorem, the value of angle ACB in the triangle is: B. 50°.

What is the Triangle Sum Theorem?

According to the triangle sum theorem, the sum of all the angles in a triangle equals 180 degrees.

90 + 7x - 20 + 4x = 180

70 + 11x = 180

11x = 180 - 70

11x = 110

11x/11 = 110/11

x = 10

m∠ACB = 7x - 20

Plug in the value of x

m∠ACB = 7(10) - 20

m∠ACB = 50° (option B).

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A trellis consists of overlapping wooden slats.

1.What is the position of the indicated angles?

2.What should the value of x be in order for the two slats to be parallel?

3. Which theorem or postulate will you use to prove the parallel slats?

4. Find the measure of the indicated angle

Answers

The position of the angles are corresponding angles.

The value of x should be 6 for the slats to be parallel.

The theorem use to prove the parallel slat is the corresponding angle theorem.

The measure of the indicated angles are 42 degrees.

How to know a corresponding angles?

Corresponding angles are the angles that are formed when two parallel lines are intersected by the transversal.

Therefore, the position  of the angles are corresponding angles

Since the angles are corresponding angles, they are congruent.

Therefore,

3x + 24 = 7x

24 = 7x - 3x

24 = 4x

x = 6

The theorem use to prove the postulate is the corresponding  angle theorem.

The measure of the indicated angle can be calculated as follows:

7(6) = 42 degrees.

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Find the slope please HELPPPPP I WILL MARK ITTT IS FOR GEOLOGY!!!!How do flow rate and gass content affect the appearance of lava Simplify the expression: 4+(11-3) ( - 37 + 37 ) - 15 = What is the answerr What is the area of the triangle below?On a coordinate plane, a triangle has a base of 6 units and a height of 9 units.27 square units45 square units54 square units90 square units Billions of dollars are spent on advertisements and marketing about the human body. From fashion and beauty products to weight loss reality shows, technology is the platform to which a person receives these different messages. Advertisers reach their target audience through different forms of technology such as smart phones, tablets, computers, and television. In the end, it can cause a person to think these advertised services and products are needed. - "The Connection between Body Image and Managing Weight" Which statement best summarizes the central idea of the passage? O Consumers spend too much money on health and beauty products in hopes of attaining their ideal body image.O Weight loss is dependent upon the technology a person uses and the advertisements they view.O Creating advertisements for distribution on various media outlets is costly. O A person can develop a negative body image as a result of viewing too many advertisements. a letter is chosen from the nine letters in the word "bumblebee." what is the probability the letter is a b or an e? statistics and probability Fill in the blank with the correct subjunctive form of the verb in parentheses. nosotros ____ (vivir) Which sentence could best be revised to action voice A game has a circular playing area in which you must hit a ball into a circular hole. The area of the playing area is 16ft2. The hole has a diameter of 1 ft. What is the probability of hitting a ball into the circular hole? Express your answer as a percentage rounded to the nearest tenth. Fix the two words that are used incorrectly. So far, the discussions have been amiable, so we're hoping that the teacherswill ascent to the new contract being presented by the district. HELP ASAP PLS!!! Match each expression on the left with an equivalent expression on the right. Some options on the right will be used more than once. A car of mass 500 kg is moving at a speed of 1.2 m/s. A man pushes the car, increasing the speed to 2 m/s. How much work did the man do? A. 1360 J B. 360 J C. 640 J D. 1000 J What is true about AngleQRT? Select two options.Measure of angleQRT = 90Measure of angleQRT = Measure of angleSRTAngleQRT Is-congruent-to AngleSTQMeasure of angleQRT = 2*Measure of angleRTQAngleQRT Is-congruent-to AngleRTQ Microscopes are used to study the structures of rocks. Over time, microscopes have become more and more powerful.As a result of this technological improvement, our structural information of rocks A scientific ___law__ is a statement that explains what always happens under very specific conditions. Description of Activity: Given the following cases below, how will you handle the different situations. Write it down and cite a Psychological theory that will be your guiding principle in dealing with each case.CASE SCENARIO 1 You are one of the school counselors at Batangas National High School. Your caseload includes Sarah, a seventh grader. She was referred to you by her classroom teacher. The teacher has concerns regarding Sarah due to Sarahs recent change in behavior. Historically, Sarah has been a top student and is very outgoing. Sarah is a member of honor society, plays JV basketball, and is a member of the Drama team. Upon her return from summer break, Sarah was noticeably withdrawn and her grades began to drop. She has withdrawn from the Drama team and she seems to have lost interest in basketball. The teacher shared that at a recent parent/teacher conference the parents did not seem concerned about Sarahs behavior changes but rather focused their attention on Sarahs basketball performance. The teacher also informed you that he had tried to connect with Sarah to talk about his concerns but when he tried to do so, Sarah became angry, burst into tears, and stormed out of the room. Sarah has agreed to meet with you upon the encouragement of her parents under the auspice that you will help her with her basketball performance issues. CASE SCENARIO 2Chad is a 9 year old Chinese-Filipino, high school student, who was diagnosed with Cystic Fibrosis when he was 3 months old. While growing up, he has been required to go to the hospital every other month. He now only has to go about once or twice a year. Chad comes into see you at his moms request. His mom, Sylvia, is concerned about the fact that Chad is refusing to take his medication. She has noticed that Chad is starting to cough more and gets exhausted much easier. He stopped taking the medication about two months after Kyle, a friend that Chad had met in the hospital, died. Chad had maintained a friendship with Kyle for about 2 years. Chad respected Kyle because he was one of the few people who didnt consider him a foreigner, a common occurrence despite the fact that his ancestors immigrated to the Phil. in the late 1800s. Kyle had been waiting for a lung transplant, and Chad had observed him rapidly decline in health. Chad refused to discuss Kyles death with his mother. And recently, there were long periods of time when he wouldnt speak to her at all. In a phone conversation with Sylvia, you learned that after Kyles funeral, Sylvia had hoped that Chad could spend the summer with his father (Kevin) and older brother David (15) who live in another state. Kevin owns a small car dealership and David works with him detailing the cars on the lot. The dealership has been successful enough to pay for the numerous surgeries and maintain both middle class households. Kevin and Sylvia divorced when Chad was 6. When Sylvia discussed the idea of Chad coming for the summer, Kevin said he didnt feel it would be a good idea because of animosity between David and Chad. In the initial session, Sylvia explained that David has always felt that I favored Chad because I spent so much time with him. I had to because of his health, but there still is a lot of jealousy. Question 2 of 40How much more will $16,500 earn in interest than $15,000 if both areinvested in savings accounts with APYS of 4.1% for a year?OA. $61.50OB. $156.15OC. $52.05OD. $20.50Please do step by step as to how you got the answer When developing an interval estimate for the difference between two sample means, with sample sizes of n1 and n2, _____. Please help.(check image)