3 lines are shown. A line with points T, R, W intersects with a line with points S, R, V at point R. Another line extends from point R to point U in between angle V R W. Which pair of angles are vertical angles? AngleWRU and AngleSRT AngleWRS and AngleVRT AngleVRU and AngleTRS AngleVRT and AngleSRT

Answers

Answer 1

Answer:

The vertical angles are ∠ WRS and ∠ VRT ⇒ 2nd answer

Step-by-step explanation:

* Lets explain the meaning of the vertical angles

- Vertical angles are the angles opposite to each other when two lines

  are intersected

- The vertical angle are equal in measures

- Look to attached figure which represents the lines

∵ Line TW intersects line SV at R

∠ WRV and ∠ SRT are vertical angle

∠ WRS and ∠ VRT are vertical angle

∵ RU is between the rays of angle VRW

∴ RU intersects the lines TW and SV at R

∴ No vertical angles between RU and the other two lines because

  it intersects them its endpoint R

* Now lets look to the answer to chose the right one

- ∠ WRU and ∠ SRT are not vertical angles

- ∠ WRS and ∠ VRT are vertical angles

- ∠ VRU and ∠ TRS are not vertical angles

- ∠ VRT and ∠ SRT are not vertical angles

3 Lines Are Shown. A Line With Points T, R, W Intersects With A Line With Points S, R, V At Point R.
Answer 2

The pair of angles that are vertical angles is: ∠WRS and ∠VRT.

What are Vertical Angles?

When two straight lines intersect each other at a point, the opposite angles that are vertical to each other are called vertical angles.

∠WRS and ∠VRT are vertically opposite each other.

Therefore, the pair of angles that are vertical angles is: ∠WRS and ∠VRT.

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Related Questions

40% of what number is 52?
A. 130
B. 200
C. 242
D. 1300

Answers

Answer:

130

Step-by-step explanation:

40 percent of what number is 52?

let this number be x

so, the equation is

40/100 x X= 52

divide 40/100 from both sides

X=52÷40/100

When you divide by a fraction, you multiply by its reciprocal

X=52 x 100/40

X=5200/40

X=130

40 percent of 130 is 52.

The value of the unknown number is 130.

Option A.

What is the value of the unknown number?

Given the parameter:

"40% of what number is 52"

Let's represent the unknown number as "x."

To determine the number for which 40% is equal to 52, we can set up an equation and solve for the unknown number.

Hence:

40% of the number = 52

40% of x = 52

40% × x = 52

Convert the percentage to a decimal.

40% = 40/100 = 0.40

Now, rewrite the equation as:

0.40 × x = 52

0.4x = 52

To solve for the value of "x," divide both sides of the equation by 0.40:

x = 52/0.4

x = 130.

Therefore, 40 percent of 130 is 52.

Option A) 130 is the correct answer.

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Wayne has a recipe in a 3 inches by 5 inches index card that he wants to enlarde to 15 inches long. How wide will the enlargement be?

Answers

Answer:

3 + 15

5 + 15

kalalalalalalalalalalasla

Step-by-step explanation:

What is the supplement of 154°?

Answers

Answer:

Have u tried to look it up

Step-by-step explanation:

The graph represents one side of the roof of a building.
The slope of the line is

Answers

Answer:

The slope of the line is 7/2.

Step-by-step explanation:

If a line passes through two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex], then the slope of the line is

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

From the given figure it is clear that the line passes though two points (0,0) and (4,14).

Using the above formula, the slope of the line is

[tex]m=\frac{14-0}{4-0}[/tex]

[tex]m=\frac{14}{4}[/tex]

[tex]m=\frac{7}{2}[/tex]

Therefore the slope of the line is 7/2.

Answer:

the answer is 7/2

Step-by-step explanation:

What is the value of the expression m^2 + 3m when m=4

Answers

4^2+3(4)=28 hope this helps

Final answer:

The value of the expression m² + 3m when m=4 is found by squaring the m and then multiplying m by 3, which gives a final value of 28.

Explanation:

The value of the expression m² + 3m when m=4 is calculated by substituting the value of m into the expression. First, we take m which is 4, and square it (4²=16), then we multiply m by 3 (3*4=12). Adding these two results together (16+12), we get the final value of the expression.

Step-by-step solution:

m² + 3m

4²+ 3*4

16 + 12

The resulting value is 28.

what is the distributive property of 12 + 20

Answers

Answer:

12 + 20 = 4x3 + 4x5 = 4x(3 + 5)

Step-by-step explanation:

The distributive property states that

a*(b + c) = a*b + a*c

You can use the distributive property in reverse to factor out a common factor from the sum of 2 numbers. If you realize that 12 = 4*3 and 20 = 4*5 then you can write

12 + 20 = 4*3 + 4*5 = 4*(3 + 5)

12(18+2)

that’s the answer yall

What Is simplified form of 2+3 (5-2) to the power of 2

Answers

In order to find the answer you will have to use PEMDAS and simplify making sure not to solve the equation fully.

[tex]2+3(5-2)^2[/tex]

Using PEMDAS:

[tex]2\times2=4[/tex]

[tex]2+3\times(5-4)[/tex]

[tex]5-4=1[/tex]

[tex]2+3\times4[/tex]

[tex]3\times4=12[/tex]

[tex]2+12[/tex]

Therefore your answer is "2+12."

Hope this helps.

Karel wants to buy a points card for his x-box
live account. He can buy a 200 point card
for $10.00 for a 300 point card to $15
W hich card is a better value?

Answers

Answer:

Both cards are the same value.

Step-by-step explanation:

$10 for 200 points = $5 for 100 points

$15 for $300 points = $5 for $100 points

Both cards are the same value.

help me pls. I need help with the question

Answers

Answer:

$173.90

Step-by-step explanation:

The most obvious way to answer this question is to multiply $9.40 by 18.5

This would result in 173.90.

But I realize nobody like to deal with decimals in a multiplication problem, so here's the way I would do it (especially if you don't have a calculator!)

The strategy is to break it down!

Multiply $9.40 x 18 hours to start, since this is easier.

[tex]9.4 x 18 = 169.2[/tex]

So, that's $169.20 for 18 hours of work.

We aren't finished, because Abdel worked for 18.5 hours.

So, what half of $9.40?

[tex]9.4 / 2[/tex]

= 4.7

-or-

$4.70

So, knowing that Abdel makes $4.70 in half an hour, lets just add that onto the $169.20 we got earlier.

169.2 + 4.7 = 173.9

-or-

$173.90 for 18.5 hours of work!

The product of 18 and q

Answers

Answer:

18q

Step-by-step explanation:

18 times q = 18q, thats all

The product of 18 and q is 18q. Multiply 18 and q to get 18q

6.24159 rounded to the hundredths place?

Answers

Answer:

6.24

Step-by-step explanation:

You exclude the 1 5 9 and since the 1 isn't higher than a 5 it remains a 4. Getting you 6.24

6.24159 rounded to the hundredths place is 6.24

Rounding given values to the nearest hundredth is similar to rounding such values to 2 decimal places

Given the value 6.24159, to round this to the nearest hundredth means that;

the values that must be after the decimal point must be 2.

Hence 6.24159 expressed to the nearest hundredth will be 6.24 since the value that supersedes 4 is not up to 5.

Therefore 6.24159 rounded to the hundredths place is 6.24

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What is the answer to this problem work included please

Answers

Answer:

B)  ( x +  3y)²

Step-by-step explanation:

u = x + y    ;  v =  x + 5y

uv = ( x + y ) * ( x + 5y)                

    = x * ( x + 5y) + y * (x + 5y)                    [ x * ( x + 5y) = x*x + x*5y = x² + 5xy]

    = x² + 5xy  + xy  + 5y²

   uv  = x² + 6xy + 5y²----------equ 1

v - u =   x + 5y - ( x+y)

       = x + 5y - x - y

       =  4y

(v-u)² = (4y)² = 16y²

[(v-u)/2]² = 16y² / 2²

              = 16y² / 4 = 4y²

[(v-u)/2]² =  4y²     ----------- equ 2

uv + [(v-u)/2]² = x² + 6xy + 5y² + 4y²      ( from equ 1 and equ 2)

                     = x² + 6xy + 9y²

                     = ( x +  3y)²

Figure ABCD is a parallelogram. Parallelogram A B C D is shown. Angle A is (4 p + 12) degrees and angle C is 36 degrees. What is the value of p? 6 7 8 9

Answers

Answer:

The value of p is 6

Step-by-step explanation:

we know that

In a parallelogram opposite angles are congruent

so

In the parallelogram ABCD

m∠A=m∠C ----> equation A

m∠B=m∠D ----> equation B

we have

m∠A=(4p+12)°

m∠C=36°

substitute the given values in equation A and solve for p

[tex](4p+12)\°=36\°[/tex]

[tex]4p=36-12[/tex]

[tex]4p=24[/tex]

[tex]p=6[/tex]

Answer:

6

Step-by-step explanation:

Simplify this expression 4(1-2b)+7b-10

Answers

4(1-2b)+7b-10

mutiply the bracket by 4

(4)(1)= 4

(4)(-2b)=-8b

4-8b+7b-10 ( combine like terms)

4-10-8b+7b

-6-b or -b-6

Answer: -6-b or -b-6

An expression is defined as a set of numbers, variables, and mathematical operations. The given expression 4(1-2b)+7b-10 when simplified can be written as -(6+b).

What is an Expression?

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.


The given expression 4(1-2b)+7b-10 can be simplified as,

4(1-2b)+7b-10

= 4 - 8b + 7b - 10

= -6 - b

= -(6+b)

Hence, the given expression 4(1-2b)+7b-10 when simplified can be written as -(6+b).

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Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.
Simplify by using fractional exponents.


∛x²

Answers

Answer:

What does X352 4/56=

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im guessing [tex]\sqrt[5]{x}[/tex]

The median for the given set of six ordered values is 28.5
7 12 25 _ 41 50
What is the missing value?

Answers

Final answer:

The missing value in the data set that will preserve the median of 28.5 is 32. This is found by averaging the middle two numbers of the six-number series, solving the equation (25 + missing value)/2 = 28.5.

Explanation:

Calculating the Missing Value in an Ordered Data Set

To determine the missing value in an ordered data set when given the median, you should remember that the median is the middle number in a sorted list of numbers. If the data set has an even number of values, the median is the average of the two middle numbers. For the set 7, 12, 25, _, 41, 50, where the median is given as 28.5, the missing value must be the average of the third and fourth terms since the data set should have six numbers total.

To find the missing value, set up the equation for the median: (25 + missing value)/2 = 28.5. Solve for the missing value:
(25 + missing value) = 28.5 × 2
missing value = (28.5 × 2) - 25
missing value = 57 - 25
missing value = 32

The missing value in the data set to maintain a median of 28.5 is 32.

A doll and a toy t-rex cost $33 together. If the t-rex toy costs $9.50 more than the doll, how much did the doll cost?

Answers

Answer:

The cost of the doll is $11.75

Step-by-step explanation:

Let

x ----> the cost of the doll

y ----> the cost of the toy t-rex

we know that

[tex]x+y=33[/tex] -----> equation A

[tex]y=x+9.50[/tex] ----> equation B

substitute equation B in equation A and solve for x

[tex]x+(x+9.50)=33\\2x+9.50=33\\2x=33-9.50\\2x=23.50\\x=\$11.75[/tex]

therefore

The cost of the doll is $11.75

Answer:

Doll cost = $11.75.

Step-by-step explanation:

Given  :A doll and a toy t-rex cost $33 together. If the t-rex toy costs $9.50 more than the doll.

To find :   how much did the doll cost.

Solution : We have given

A doll and a toy t-rex cost $33 together.

Let the Doll cost = x .

According to question .

t-rex toy costs $9.50 more than the doll.

T-rex cost = $9.50+ x .

Then, A doll and a toy t-rex cost $33 together.

Doll cost + T oy t-rex cost =  $33

Plugging the values

x +  $9.50+ x  =$33 .

2x + $9.50 =$33 .

On subtracting both sides by $9.50

2x =33 - 9.50

2x = 23.5.

On dividing both sides b y 2

x = $11.75

Doll cost  =$11.75

Toy Cost = 9.50 +11.75.

Toy Cost = $21.25

Therefore, Doll cost = $11.75.

can someone walk me through how to do this problem please?​

Answers

Hey!

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

We Know:

m∠AED = 34°

m∠EAD = 112°

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

Solution:

You notice 4 small triangles in both triangles. That shows that both triangles are the same.

The angles are the same for m∠BDC and m∠AED.

The angles are the same for m∠ADB and m∠EAD

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

Angles:

m∠BDC = 34°

m∠ADB = 112°

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

Congruent Angles:

m∠AED ≡ m∠BDC

m∠EAD ≡ m∠ADB

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

Hope This Helped! Good Luck!

The measure of the angle ∠BDC is 34.

The measure of the angle ∠ADB is 112.

We have,

In the diagram,

There are two congruent triangles.

ΔAED and ΔBDC

Now,

The congruent angles are:

∠AED = ∠BDC

∠EAD = ∠DBC

∠ADE = ∠BCD

Now,

∠AED = 34

∠EAD = 112

This means,

∠AED = ∠BDC = 34

∠EAD = ∠DBC = 112

And,

The sum of the three angles inside a triangle is always 180.

So,

∠AED +∠EAD + ∠ADE  = 180

34 + 112 + ∠ADE = 180

∠ADE = 34

Now,

∠ADE = 34

This means,

∠ADE = ∠BCD = 34

Now,

∠ADE + ∠BDC + ∠ADB = 180

34 + 34 + ∠ADB = 180

∠ADB = 180 - 68

∠ADB = 112

Thus,

The measure of the angle ∠BDC is 34.

The measure of the angle ∠ADB is 112.

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NEED ASAP!!
Sixteen of the 24 schools in Ryan’s county are public schools. Ryan used this spinner to predict the probability that the winner of the county spelling bee in each of the next four years will attend a private school. Which set of outcomes from Ryan’s simulation implies that the winner will attend a private school at least three times in that span? Select two options.
A-A-A-A
B-B-A-B
A-B-A-B
A-B-B-B
B-A-B-A

Answers

Hey!

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

Answers:

B-B-A-B

A-B-B-B

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

Explanation:

We assume that the winner is from a private school (B). As we look at the options we can see that there are two options that show B at least 3 times in the span.

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

Hope This Helped! Good Luck!

b and dAnswer:

Step-by-step explanation:

Factor completely 6x2-15x

Answers

Answer:

Step-by-step explanation:

Factor 3x out of 6x2−15x

.

3x(2x−5)

Answer:

Step-by-step explanation:

6x²-15x = 3x(2x- 5)


[tex] \frac{1}{b \frac{2}{7} } [/tex]

Answers

Answer:

[tex]\frac{7}{2b}[/tex]

Step-by-step explanation:

[tex]\frac{1}{b\frac{2}{7}}[/tex]

[tex]\frac{1}{\frac{2b}{7}}[/tex]

[tex]\frac{7}{2b}[/tex]

What is the image of (0, 1) after a reflection over the line y = x?

Answers

Answer:

(1,0) would be the correct answer.

Step-by-step explanation:

any point that is reflected across y=x will change unless it is on the line. if reflected across y=x, the coordinates will become y,x

10. Three fifths of the T-shirts in a T-shirt shop are
blue. Five eighths of those T-shirts are on sale.
One third of the blue T-shirts that are on sale are
size medium. What fraction of the shop's T-shirts
are blue T-shirts that are on sale and are size
medium? Explain.​

Answers

Answer:

1/8

Step-by-step explanation:

Imagine the value of all of the t-shirts are equal to 1.

3/5 of all of them are blue, so 3/5 of 1 --> 3/5 * 1 =3/5

5/8 of the blue tshirts are on sale, so 5/8 of 3/5 --> 5/8 * 3/5 = 3/8

1/3 of those tshirts are medium, so 1/3 of 3/8 --> 1/3 * 3/8 = 1/8

So, 1/8 of all of the tshirts are blue, on sale, and medium

The fraction of the shop's T-shirts that are blue, on sale, and size medium is 1/8.

Determining the fraction of the blue T-shirt

To find the fraction of the shop's T-shirts that are blue, on sale, and size medium,  multiply the fractions representing each condition.

Given:

Three-fifths (3/5) of the T-shirts in the shop are blue.

Five-eighths (5/8) of the blue T-shirts are on sale.

One-third (1/3) of the blue T-shirts on sale are size medium.

To find the fraction of blue T-shirts that are on sale,  multiply the fractions representing each condition:

(3/5) * (5/8) = 15/40 = 3/8

This means that 3/8 of the blue T-shirts are on sale.

To find the fraction of blue T-shirts that are on sale and size medium, multiply this result by the fraction representing the size medium condition:

(3/8) * (1/3) = 3/24 = 1/8

Therefore, the fraction of the shop's T-shirts that are blue, on sale, and size medium is 1/8.

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Harry kept a record of how far he ran
each day last week

Distance (in miles)
Monday 4.5
Tuesday 3.9
Wednesday 4.25
Thursday 3.75
Friday 4.2
On which day did Harry run the
greatest number of miles?​

Answers

Harry ran the most on Monday

2(8q-5) = 4q
What is the answer?

Answers

Answer:

q=5/6

Step-by-step explanation:

16q-10=4q

16q-4q=10

12q=10

q=5/6

solve the equation
5h +2 -h = 22​

Answers

Answer:

h=5

Step-by-step explanation:

5h +2 -h = 22​

4h+2=22

4h=20

h=5

Answer:

h = 5

Step-by-step explanation:

Start by subtracting 2 from both sides or subtraction property of equality

5h - h = 20

Combine like terms

4h = 20

Division property of equality or divide 4 from both sides

Your final answer is h = 5

Hope this helps

- Que

the sum of the digits of a two-digit number is 7 the tens digit is one more than twice the units digits find the number

Answers

Answer: 3+4=7

Step-by-step explanation:

So basically let’s say

A= #1

And So right now we have A+B=7

B= #2

So b=a-1 right? Yeah ok so then what you need to do is find A....

So 7-1=6 and 6÷2 = 3 so

A=3

And Than 3+4=7 so that is your answer

B=4

Final answer:

The two-digit number which meets the criteria that its digits sum to 7 and the tens digit is one more than twice the units digit, is 52.

Explanation:

Let's denote the units digit as 'x' and the tens digit as 'y'. We know that the sum of the digits is 7, which gives us the equation x + y = 7. Secondly, we know the tens digit is one more than twice the units digits, so y = 2x + 1. We can solve these two equations simultaneously.

Substituting y from the second equation in the first gives us x + (2x + 1) = 7. Simplifying this results in 3x + 1 = 7. Upon solving we find x = 2. Substituting x = 2 into the first equation we get y = 7 - 2 = 5. Thus, the number is 52.

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Standard form with given slope
Slope= 2/5, (6,7)

Answers

Answer:

Step-by-step explanation:

1 Simplify brackets.

-3,9=-3,9,-3,-5−3,9=−3,9,−3,−5

2 Since -3,9=-3,9,-3,-5−3,9=−3,9,−3,−5 is false, there is no solution.

No Solution

Done

is 20 a perfect sqaure

Answers

Answer:

No. 16 is and 25 is.

Step-by-step explanation:

Final answer:

The number 20 is not a perfect square because there is no integer that when multiplied by itself equals 20.

Explanation:

The question "is 20 a perfect square" is related to Mathematics and involves understanding what constitutes a perfect square. A perfect square is a number that can be expressed as the product of an integer with itself. In other words, when you multiply an integer by itself, the resulting product is a perfect square. For example, the number 16 is a perfect square because it can be expressed as 4 times 4.

To determine if 20 is a perfect square, we look for an integer that when multiplied by itself equals 20. However, multiplying 4 by 4 gives us 16, and multiplying 5 by 5 gives us 25. Since there is no integer that can be multiplied by itself to give 20, we conclude that 20 is not a perfect square.

In the diagram, line y is parallel to line EF . Lourdes used the diagram to find that m1 = 105°.


What mistake did Lourdes make in finding m1?
A. Lourdes found 180º – (70º + m2).
B. Lourdes found m1 = mE.
C. Lourdes found mD + mF.
D. Lourdes found 180º – (mD + mF

Answers

Answer:

C. Lourdes found m∠D + m∠F.

Step-by-step explanation:

70° + 35° = 105°

This is the Angle Addition Postulate of ∠F and ∠D.

I am joyous to assist you anytime.

The mistake Lourdes did is Lourdes found m ∠ D + m ∠ F. (option C)

What are parallel line?

Parallel lines are those straight lines that are always the same distance apart from each other. Parallel lines never meet, no matter how much they are extended.

Given that, line y is parallel to line EF. Lourdes used the diagram to find that m1 = 105°.

There are many ways to m ∠ 1

A) Since, m ∠ 1, m ∠ 2 and 70° are in straight line, therefore, they are making a linear pair, that mean,

m ∠ 1 + m ∠ 2 + 70° = 180°

Now, m ∠ 2 = 35° (alternate interior angles)

Therefore,

m ∠ 1 + 35° + 70° = 180°

m ∠ 1 = 75°

Therefore, Lourdes's 1st way is correct.

B) If she uses m ∠ 1 = m ∠ E,

That is also correct because, m ∠ 1 and m ∠ E are a pair of alternate interior angles.

C) If she is using m ∠ D + m ∠ F,

She is missing a step in it, after adding m ∠ D and m ∠ F she needs to subtract the sum from 180, because the sum of interior angles of a triangle is 180°, and if she needs to find m ∠ E to find m ∠ 1 then she needs to subtract the sum of m ∠ D and m ∠ F from 180°.

D) As we discussed in option third, in this option Lourdes is subtracting the sum from 180, hence, she is correct here.

Hence, the mistake Lourdes did is Lourdes found m ∠ D + m ∠ F. (option C)

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The chief explained what the situation was.Is this a simple or complex sentence ? Balance the equ. representing the reaction between iron(III)oxide, Fe2O3 and carbon monoxide (CO) to yeild iron (Fe) andcarbondioxide (CO2). Choose all of the angles that are coterminal with -150.-510-210150210570 Click to review the online content. Then answer the question(s) below, using complete sentences. Scroll down to view additional questions.Online Content: Site 1What is a direct democracy? (Site 1) Solve number 20traingle ABC with C=90 slove for the missing partPLEASE HELP!! Round 751.623 to the nearest hundredth Use differentiation rules to find the values of a and b that make the function f(x) = ( x 2 if x 2, ax3 + bx if x > 2 differentiable at x = 2. Keira and Javier are grouping equations based on the number of operations needed to solve them in order to solve them in order to solve the equation -5(2+x)=53 Who said that a government should be chosen by its citizens? -4 1/3 + 5 2/3step by step 1. La habitacin de mi hermana siempre est sucia, pero mi habitacin (ser/estar) ______, _______.2. Estoy contento porque estamos de vacaciones, pero mis padres (ser/estar) _______, ________ porque tienen que trabajar. 3. Tu primo es alto y moreno, pero t (ser/estar) y _______, ________. 4. Mi amigo Fernando dice que las matemticas son difciles, pero yo creo que (ser/estar) ________, ________. Suppose you've just won tickets to go see your favorite band. Unfortunately, the show is the same date as your little sister's birthday party. Assume you can't attend both the concert and the birthday party. This is an example of _______. Given a non-linear system: y=x^3 - 3x^2 - 1 a) Find the linear approximation of the system at the point (1, -3) b) Plot the system and its linear approximation on a same plot using Matlab. Make sure your plot is clear and having labeling Pls help and break down :) Ill give u a thnx and brainlest when another person answers Memory allows one to apply knowledge to a specific task; while memory allows one to store and recall information.. True or False Problem 1 Two positive point charges are released on a frictionless surface. Which of the following best describes their subsequent motion? Select One of the Following: (a) The particles remain stationary. (b) The particles move apart with constant velocity. (c) The particles move apart with a velocity that decreases with time. (d) The particles move apart with a velocity that increases with time. (e) The particles move apart with a velocity that increases for a while and then becomes constant. why does the x axis of a dose-response curve use log units? Review the contributions of Copernicus on the field of science. Using examples, evaluate the scientist and his contribution(s) to European culture. Write 3-4 sentences to justify your choice with examples.99 POINTS tyyyyyyy!!!!!! . Convert BAC4 from hexadecimal to decimal. Show your work. Why is the following situation impossible? Two identical dust particles of mass 1.00 g are floating in empty space, far from any external sources of large gravitational or electric fields, and at rest with respect to each other. Both particles carry electric charges that are identical in magnitude and sign. The gravitational and electric forces between the particles happen to have the same magnitude, so each particle experiences zero net force and the distance between the particles remains constant.