Does anyone know how to rationalise the denominator ???

Does Anyone Know How To Rationalise The Denominator ???

Answers

Answer 1

Answer:

Multiply the entire expression by the radical denominator. This keeps the expression equal and makes the denominator 3, a whole number.

Step-by-step explanation:

The denominator is irrational because it is a radical number, √3.

To rationalize the denominator, multiply the entire expression by √3. The denominator will become a whole number. This works because you multiply top and bottom by the same value.

[tex]\frac{3 + \sqrt{2} }{\sqrt{3}}[/tex]

[tex]= \frac{(\sqrt{3})(3 + \sqrt{2}) }{(\sqrt{3})(\sqrt{3})}[/tex]

[tex]= \frac{(\sqrt{3})(3 + \sqrt{2}) }{3}[/tex]  

√3 X √3 = 3 because:

√3 X √3 = √3²

Squaring a number and also finding its square root are opposites, or reverse operations. They cancel out

You probably need to simplify the rest of the equation too.

[tex]\frac{(\sqrt{3})(3 + \sqrt{2}) }{3}[/tex]

[tex]= \frac{3(\sqrt{3}) + (\sqrt{2})(\sqrt{3})}{3}[/tex]  Distribute over brackets

[tex]= \frac{3(\sqrt{3}) + \sqrt{2*3}}{3}[/tex]   Simplify

[tex]= \frac{3(\sqrt{3}) + \sqrt{6}}{3}[/tex]

Some people use a more simplified version whether they simplify each term in the numerator:

[tex]\frac{3(\sqrt{3}) + \sqrt{6}}{3}[/tex]    (3√3)÷3 = √3

[tex]\sqrt{3} + \frac{\sqrt{6}}{3}[/tex]


Related Questions

What are the coefficients in
W - 8x + 20y + 6z

Answers

Final answer:

The coefficients in the expression W - 8x + 20y + 6z are -8 for x, 20 for y, and 6 for z. W is not considered a variable with a coefficient but would implicitly have a coefficient of 1.

Explanation:

The coefficients in the expression W - 8x + 20y + 6z are the numerical factors that are multiplied by the variables. In this case:

The coefficient for x is -8.The coefficient for y is 20.The coefficient for z is 6.

Coefficients are important as they determine the rate at which the value of the expression changes with respect to changes in the variable values.

Note that W in this expression is not preceded by a coefficient, and if it is supposed to have a coefficient, it is implicitly 1.

However, as the question does not consider W as a variable with a coefficient, we exclude it from the list of coefficients.

How would I graph these equations in a system? : 2r + b = $8.40, and 3r + b = $9.35. If you need specifics, I can tell you the whole story problem. I will mark the best answer as Brainliest.

Answers

Answer:

The value of r is $0.95 and b is $6.5 , The graph of given equation plotted as shown

Step-by-step explanation:

Given as :

The two line equation are

2 r + b = $8.40              .........A    and

3 r + b = $9.35               .........B

Now, Solving equations A and B

i.e (3 r + b) - (2 r + b) = $9.35 - $8.40

Or, (3 r - 2 r) + (b - b) = 0.95

or, r + 0 = 0.95

∴ r = $0.95

Now, put the value og r into eq A

∵ 2 r + b = $8.40  

So, 2× $0.95 + b = $8.40  

Or, $1.9 + b = $8.40  

Or, b = $8.40 - $1.9

∴ b = $6.5

So, The value of r = $0.95 and b = $6.5

Now, for plotting the equation on graph

let put r on x axis

and put b on y-axis

Hence, The value of r is $0.95 and b is $6.5 , The graph of given equation plotted as shown . Answer

Fei yeng"s dog eats 8 ounces of dog food each day.Fri yen bought a 28 pound bag of dog food. How many 8 ounce serving are in a 28 pound of dog food




Answers

One pound equals 16 ounces.
28 times 16=448
448/8” 56

HELPPP In the two squares shown above, m
=0.9. Which of the following is a correct statement about the two squares?
OA. There is not enough information to determine whether the squares are congruent.
OB. The squares are congruent.
OC. The squares are not congruent

Answers

Answer:

OA there is not enough information

Step-by-step explanation:

only the angles are congruent in both squares

Answer:

OA there is not enough information to determine whether the squares are congruent.

Step-by-step explanation:

what is 1/3 + 3/6 =​

Answers

Answer:

5/6

Step-by-step explanation:

1/3+3/6=2/6+3/6=5/6

1/3 plus 3/6 is 5/6 because if you multiply 1/3 by 2/2 you get 2/6 and 2/6 plus 3/6 is 5/6

Please answer if you know the solution. Thx

Answers

Answer:

the first blank is 10

and the second blank is 5

Step-by-step explanation:

While on a ski vacation, a group can rent pairs of skis and snowboards by the week. They get a reduced rate if they rent 7 pairs of skis for every 3 snowboards rented. The reduced ski rate is $45.50 per pair of skis per week, and the reduced snowboard rate is $110 per snowboard per week. The sales tax on each rental is 16%.
The group has $2,500 available to spend on ski and snowboard rentals. What is the greatest number of pairs of skis and snowboards the group can rent if the ratio of pairs of skis to snowboards is 7:3?

Answers

Answer:

The greatest number of pairs of skis and snowboards the group can rent are 21 pairs of skis and 9 pairs of snowboards.

Step-by-step explanation:

Given:

A group can rent pairs of skis and snowboards by the week. They get a reduced rate if they rent 7 pairs of skis for every 3 snowboards rented. The reduced ski rate is $45.50 per pair of skis per week, and the reduced snowboard rate is $110 per snowboard per week.

The sales tax on each rental is 16%.

The group has $2,500 available to spend on ski and snowboard rentals.

If the ratio of pairs of skis to snowboards is 7:3.

Now, to find the greatest number of pairs of skis and snowboards rentals.

So, the rent of 7 pairs of skis = [tex]7\times 45.50=\$318.50.[/tex]

And the rent of 3 pairs of snowboards = [tex]3\times 110=\$330.[/tex]

So, total rental amount of 7 pairs of skis and 3 pairs of snowboards:

[tex]318.50 + 330 = 648.50.[/tex]

Now, to get the rental amount after sales tax:

648.50 + 16% of $648.50.

[tex]=648.50 +\frac{16}{100}\times 648.50.[/tex]

[tex]=648.50+103.76[/tex]

[tex]=\$752.26.[/tex]

The total rental amount after sales tax = $752.26.

As the group has available $2,500.

So, the sets according to the given ratio:

[tex]2500\div 752.26 = 3.32.[/tex]

[tex]=3\ sets.[/tex]

Thus, there are 3 sets of the ratio 7:3.

So, the rental price according to sets are:

The rent of Skis:

[tex]7\times 3 = 21[/tex] 

[tex]21\times 45.50= 955.50[/tex]

The rent of snowboards:

[tex]3\times 3 = 9[/tex]

[tex]9\times 110 = 990[/tex]

So. the total rental amount of skis and snowboards according to sets are:

[tex]955.50 + 990 = 1,945.50[/tex]

Now, the amount of rent after sales tax:

$1945.50 + 16% of $1945.50.

[tex]=1945.50+\frac{16}{100}\times 1945.50[/tex]

[tex]=1945.50+311.28=\$2256.78.[/tex]

Thus, the total cost = $2256.78.

Now, to get the greatest number of pairs of skis to snowboards that can be rent:

[tex]2,500 - 2,256.78 = 243.22[/tex]

The cost of 21 pair of skis and 9 pairs of snowboards is $2256.78 and the group has available only $2500 to spend.

Thus, they can rent only 21 pairs of skis and 9 pairs of snowboards.

Therefore, the greatest number of pairs of skis and snowboards the group can rent are 21 pairs of skis and 9 pairs of snowboards.

what is the approximate area of a sector given O= 56 degrees with a diameter of 12m?​

Answers

Area of sector is 17.584 meters

Solution:

Given that we have to find the approximate area of a sector given O= 56 degrees with a diameter of 12m

Diameter = 12 m

Radius = Diameter / 2 = 6 m

An angle of  56 degrees is the fraction [tex]\frac{56}{360}[/tex] of the whole rotation

A sector of a circle with a sector angle of 56 degrees is therefore also the fraction [tex]\frac{56}{360}[/tex] of the circle

The area of the sector will therefore also be  [tex]\frac{56}{360}[/tex] of the area

[tex]\text{ sector area } = \frac{56}{360} \times \pi r^2\\\\\text{ sector area } = \frac{56}{360} \times 3.14 \times 6^2\\\\\text{ sector area } = 17.584[/tex]

Thus area of sector is 17.584 meters

Solve equation by completing the square round to the nearest hundredth if necessary
X2-4x-=5

Answers

Answer:

x=-1 and x=5

Step-by-step explanation:

we have

[tex]x^{2} -4x=5[/tex]

Solve it by completing the square method

We take the coefficient of x that is -4, divide it by 2 and then square it

so

[tex]-\frac{4}{2}=-2[/tex]

square it

[tex](-2)^2 = 4[/tex]

Adds 4 both sides

[tex]x^{2} -4x+4=5+4[/tex]

Combine like terms right side

[tex]x^{2} -4x+4=9[/tex]

Rewrite as perfect squares

[tex](x-2)^{2}=9[/tex]

take square root both sides

[tex]x-2=\pm3[/tex]

[tex]x=2\pm3[/tex]

therefore

[tex]x=2+3=5[/tex]

[tex]x=2-3=-1[/tex]

Christopher wants to buy a notebook for $2.15, a pack of glue sticks for $5.08, and a pack of pens for $3.08. what is the total cost of three items Christopher wants to buy?
please answer now with a small step by step please!​

Answers

Answer:

The answer to this question would be $10.31

Step-by-step explanation:

To answer this question, you would first need to add the first two numbers which are $2.15 and $5.08 which results in $7.23 and then you would need to add the last number to the amount which then gives you the answer as $10.31.

Answer:$10.31

Step-by-step explanation:

$2.15+ $5.08+ $3.08=$10.31

Put a positive factor back into the square root:

-5*sqrt(0.6)

Answers

Answer:

[tex]-\sqrt{15}[/tex]

Step-by-step explanation:

we know that

To put factor back into the square root, we have to put squared value

we have

[tex]-5\sqrt{0.6}[/tex]

Remember that

[tex]5=\sqrt{5^2}[/tex]

substitute in the expression above

[tex]-5\sqrt{0.6}=-\sqrt{(5^2)(0.6)}=-\sqrt{25*0.6}=-\sqrt{15}[/tex]

store manager wants to
display 45 cans
of soup in an array. Which of
the following
shows 3 ways the cans could
be displayed?
1 X 9,9 X 5,3 X 15
15 X 3,9 X 1,5 X 9
5 X 9,3 X 15,9 x 5
45 X 1,15 X 1,9x1

Answers

Answer:

5x9=45

9×5=45

3×15=45

So the third answer is the correct choice.

Step-by-step explanation:

The best thing you can do with these types of problems is work out each multiplication fact untill you see which ones equal the number you are looking for.

Final answer:

The store manager wants to display 45 cans of soup in an array. The three possible ways to display the cans are 1 X 9, 9 X 5, and 3 X 15.

Explanation:

The store manager wants to display 45 cans of soup in an array. An array is a rectangular arrangement of objects. There are three possible ways the cans could be displayed: 1 X 9, 9 X 5, and 3 X 15.

For example, if the cans are displayed in a 1 X 9 array, there would be 1 row and 9 columns, making a total of 9 cans.

The other two options can be understood in a similar way, with the number before 'X' representing the number of rows and the number after 'X' representing the number of columns.

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Answers to topic 4: Parallel and Perpendicular lines on the coordinate plane

Answers

Answer:

Step-by-step explanation:

y=-2x+4

-5x+10y=5

A:Parallel

B:Perpendicular

C: Neither

Tell whether the lines for each pair of equations are parallel, perpendicular, or neither.

y=(-1/5)x+6

-2x+10y=5

A:Parallel

B:Perpendicular

C:Neither

Understanding parallel and perpendicular lines on the coordinate plane is essential in geometry. Here's how you can determine the relationships between lines in this context.
**Parallel Lines:**
Two lines are parallel if they are always the same distance apart (equidistant) and will never meet. In the coordinate plane, parallel lines can be identified by having the same slope.
To show that two lines are parallel, you must find that they have the same slope. For example, if you have two lines described by the equations:
1. \(y = m_1x + b_1\)
2. \(y = m_2x + b_2\)
If \(m_1 = m_2\), then these two lines are parallel.
**Perpendicular Lines:**
Two lines are perpendicular if they intersect at a right angle (90 degrees). On the coordinate plane, two non-vertical lines are perpendicular if the product of their slopes is -1. This means that the slope of one line is the negative reciprocal of the other.
To show that two lines are perpendicular, you would find that the slopes of the two lines multiplied together equal -1. For instance, if you have two lines defined by:
1. \(y = m_1x + b_1\)
2. \(y = m_2x + b_2\)
These lines are perpendicular if \(m_1 \cdot m_2 = -1\), which means \(m_1 = -\frac{1}{m_2}\) or \(m_2 = -\frac{1}{m_1}\).
**Example 1: Check if lines are parallel**
Suppose you are given two lines with equations:
1. \(y = 2x + 3\)
2. \(y = 2x - 4\)
Both lines have a slope of 2 (since the coefficient of \(x\) in both equations is 2). Since the slopes are equal, these lines are parallel.
**Example 2: Check if lines are perpendicular**
Imagine you are given two lines:
1. \(y = \frac{1}{3}x + 2\)
2. \(y = -3x + 1\)
To determine if they're perpendicular, find the product of the slopes: \(\frac{1}{3} \cdot -3 = -1\). Since the product is -1, these lines are perpendicular.
In summary, for parallel lines, check if the slopes are equal. For perpendicular lines, check if the product of the slopes is -1. Of course, these rules presume you're working with non-vertical lines, since vertical lines have undefined slopes and horizontal lines have a slope of 0. Vertical and horizontal lines are also perpendicular to each other.

how many subsets are there in (a,b,c,d,e,f,h,i)?​

Answers

Answer:

The set has 256 subsets

Step-by-step explanation:

The set is [a,b,c,d,e,f,h,i]

Number of subset can be calculated from the formula

[tex] {2}^{n} [/tex]

where n is the number of element in the set

n=8

This implies that

[tex] {2}^{n} = {2}^{8} =256[/tex]

A movie theater sells 180 adult tickets and 60 children tickets to a movie. As part of a special promotion one ticket will be chosen at random and the winner will receive a prize. What is the probability the winner will be a child.

Answers

Answer:

25%

Step-by-step explanation:

180+60=240

60/240=0.25

0.25*100

25%

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How many 1 4 cup servings are in 3 8 cups of pudding? (in simplest fraction form) A) 1 6 B) 2 3 C) 3 2 D) 3 8

Answers

Answer: is c 3/2

Step-by-step explanation:

The answer is option C) 3/2.

To find out how many 1/4 cup servings are in 3/8 cups of pudding, we can use the formula:

First, let's convert 3 8/10 cups to an improper fraction.

To do this, we multiply the whole number (3) by the denominator (10) and add the numerator (8) to get the numerator of the improper fraction. The denominator remains the same.

(3/8) ÷ (1/4) = (3/8) × (4/1) = 12/8 = 3/2

Therefore, there are 3/2 or 1 1/2 servings of 1/4 cup in 3/8 cups of pudding.

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PLEASE HELP!!!!

Is this relation a function?

A) Yes, for the given x-values, there is one and only one y-value.
B) No, for the given x-values, there is one and only one y-value.
C) Yes, for the given x-values, there is more than one y-value.
D) No, for the given x-values, there is more than one y-value.

Answers

The answer is D. You can't make an equation out of this!

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That answer is D because to can’t make a statement on this

What are the x- and y-coordinates of point P on the
directed line segment from A to B such that Pis the
length of the line segment from A to B?
(2, -1)
(4, -3)
(-1,2)
(3,-2)

Answers

Answer:

answer b

Step-by-step explanation:

The coordinates of p are (3, -2). Option D is correct.

What are coordinates?

A pair of numbers called coordinates are used to locate a point or a form in a two-dimensional plane. The x-coordinate and the y-coordinate are two numbers that define a point's location on a 2D plane.

From the graph, the coordinates of A = (9,-8) and the coordinates of B =(-6, 7) p divides the line segmentin 2/3 thus,

We can use the section formula to find the coordinates of the point P that divides the line segment AB into the ratio 2:3.

The section formula states that if a line segment AB is divided by a point P into two line segments, with lengths in the ratio m:n, then the coordinates of P are:

[tex][Px = (nA_x + mB_x)/(m+n), \\Py = (nA_y + mB_y)/(m+n)][/tex]

In this case, we want to divide the line segment AB into the ratio 2:3, so we have m:n = 2:3. This means that m = 2 and n = 3.

Substituting the given values, we get:

[tex]P_x = (3*9 + 2(-6))/(2+3) = 3\\Py = (3*(-8) + 2*7)/(2+3) = -2[/tex]

Therefore, the coordinates of P are (3, -2).

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If f(x) = x2 + 7, what is the value of f(4)?

Answers

Answer:

18

Step-by-step explanation:

18x9/0-12.6 x 14 x 13.2 = 18

f(x)=x2+7

f(4)=4*2+7

4*2=8

8+7=15

What is said to be 'paid back' by the oxidation of lactic acid after anaerobic respiration?

Answers

Answer:

Carbon dioxide and water.

Answer:

it is carbon dioxide and water

Step-by-step explanation:

Find the value of x in the figure below if RE is parallel to PM.

A. 14.4 units
B. 5 units
C. 7.2 units
D. 9 units

Answers

Answer:

Option C. 7.2 units

Step-by-step explanation:

we know that

triangle PAM is similar to triangle RAE by AA Similarity Theorem

Remember that

If two triangles are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent

so

[tex]\frac{PA}{RA}=\frac{AM}{AE}[/tex]

substitute the given values

[tex]\frac{20+x}{20}=\frac{25+9}{25}[/tex]

solve for x

[tex]\frac{20+x}{20}=\frac{34}{25}[/tex]

[tex]20+x=\frac{34}{25}(20)[/tex]

[tex]x=\frac{34}{25}(20)-20[/tex]

[tex]x=7.2\ units[/tex]

The value of 'x' is 7.2 units and this can be determined by using the properties of the triangle and also by using the arithmetic operations.

Given :

RE is parallel to PMRA = 20AE = 25RP = xME = 9

According to the given data, the side RE is parallel to side PM therefore it can be said that:

[tex]\rm \dfrac{PA}{RA}=\dfrac{MA}{EA}[/tex]

Now, substitute the values of PA, MA, RA, and EA in the above expression.

[tex]\rm \dfrac{x+20}{20}=\dfrac{9+25}{25}[/tex]

Cross multiply in the above equation.

[tex]25 \times (x + 20) = 20\times (34)[/tex]

25x + 500 = 680

Subtract 680 by 500 in the above equation.

25x = 180

DIvide 180 by 25 in the above equation.

x = 7.2

Therefore, the correct option is C).

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any 10th grader solve it
for 50 points​

Answers

Answer:

[tex]\frac{a}{p}\times (q-r)+\frac{b}{q}\times (r-p)+\frac{c}{r}\times (p-q)\neq 0[/tex]  is proved for the sum of pth, qth and rth terms of an arithmetic progression are a, b,and c respectively.

Step-by-step explanation:

Given that the sum of pth, qth and rth terms of an arithmetic progression are a, b and c respectively.

First term of given arithmetic progression is A

and common difference is D

ie., [tex]a_{1}=A[/tex] and common difference=D

The nth term can be written as

[tex]a_{n}=A+(n-1)D[/tex]

pth term of given arithmetic progression is a

[tex]a_{p}=A+(p-1)D=a[/tex]

qth term of given arithmetic progression is b

[tex]a_{q}=A+(q-1)D=b[/tex] and

rth term of given arithmetic progression is c

[tex]a_{r}=A+(r-1)D=c[/tex]

We have to prove that

[tex]\frac{a}{p}\times (q-r)+\frac{b}{q}\times (r-p)+\frac{c}{r}\times (p-q)=0[/tex]

Now to prove LHS=RHS

Now take LHS

[tex]\frac{a}{p}\times (q-r)+\frac{b}{q}\times (r-p)+\frac{c}{r}\times (p-q)[/tex]

[tex]=\frac{A+(p-1)D}{p}\times (q-r)+\frac{A+(q-1)D}{q}\times (r-p)+\frac{A+(r-1)D}{r}\times (p-q)[/tex]

[tex]=\frac{A+pD-D}{p}\times (q-r)+\frac{A+qD-D}{q}\times (r-p)+\frac{A+rD-D}{r}\times (p-q)[/tex]

[tex]=\frac{Aq+pqD-Dq-Ar-prD+rD}{p}+\frac{Ar+rqD-Dr-Ap-pqD+pD}{q}+\frac{Ap+prD-Dp-Aq-qrD+qD}{r}[/tex]

[tex]=\frac{[Aq+pqD-Dq-Ar-prD+rD]\times qr+[Ar+rqD-Dr-Ap-pqD+pD]\times pr+[Ap+prD-Dp-Aq-qrD+qD]\times pq}{pqr}[/tex]

[tex]=\frac{Arq^{2}+pq^{2} rD-Dq^{2} r-Aqr^{2}-pqr^{2} D+qr^{2} D+Apr^{2}+pr^{2} qD-pDr^{2} -Ap^{2}r-p^{2} rqD+p^{2} rD+Ap^{2} q+p^{2} qrD-Dp^{2} q-Aq^{2} p-q^{2} prD+q^{2}pD}{pqr}[/tex]

[tex]=\frac{Arq^{2}-Dq^{2}r-Aqr^{2}+qr^{2}D+Apr^{2}-pDr^{2}-Ap^{2}r+p^{2}rD+Ap^{2}q-Dp^{2}q-Aq^{2}p+q^{2}pD}{pqr}[/tex]

[tex]=\frac{Arq^{2}-Dq^{2}r-Aqr^{2}+qr^{2}D+Apr^{2} -pDr^{2}-Ap^{2}r+p^{2}rD+Ap^{2}q-Dp^{2}q-Aq^{2}p+q^{2}pD}{pqr}[/tex]

[tex]\neq 0[/tex]

ie., [tex]RHS\neq 0[/tex]

Therefore [tex]LHS\neq RHS[/tex]

ie.,[tex]\frac{a}{p}\times (q-r)+\frac{b}{q}\times (r-p)+\frac{c}{r}\times (p-q)\neq 0[/tex]  

Hence proved

A soccer coach spent $162 dollars on 24 pairs of socks for his players. How much did five pairs of socks cost? Verify your answer using mathematical reasoning and language.

Answers

Answer:

$162÷24=$6.75

$6.75-per each

five pairs of socks-$6.75x5=$33.75

Final answer:

To determine the cost of five pairs of socks when the coach spent $162 for 24 pairs, we find the cost per pair ($6.75) and multiply it by 5, resulting in $33.75 for five pairs.

Explanation:

The student's question is, "A soccer coach spent 162 dollars on 24 pairs of socks for his players. How much did five pairs of socks cost?" To solve this, we start by determining the cost per pair of socks. We divide the total cost by the number of pairs to get the price for each pair:

Cost per pair = Total cost / Number of pairs
= $162 / 24 pairs
= $6.75 per pair

Now, to find the cost for five pairs of socks, we multiply the cost per pair by the number of pairs desired:

Cost for five pairs = Cost per pair x 5
= $6.75 x 5
= $33.75

Therefore, five pairs of socks cost $33.75.

A triangle has sides with lengths of 8 inches 10 inches and 11 inches is it a right triangle?

Answers

Answer:

yes it is!

Step-by-step explanation:

if you add 8+10=18

11+10+21

8+11=19

if the numbers do not repeat or add up to one of the numbers you've got as an option it is a right triangle.

Lie is rolling a random number cube. The cube had six sides, and each side is labeled with a different number 1 through 6. What is the probability that he will roll a 5 and then a 3 in two rolls?

Answers

Answer:

[tex]\frac{1}{36}[/tex]

Step-by-step explanation:

We will find the probability of rolling a 5 and then probability of rolling a 3 and then multiply the numbers to get the probability that he will roll a 5 and then a 3 in two rolls.

There are 6 total possibilities (1 through 6).

There are one 5s, so the probability of rolling a 5 would be:

P(roll 5) = 1/6

Also, there is one 3, so rolling a 3 would have the same probability.

P(roll 3) = 1/6

Hence,

Probability of rolling a 5 and then a 3 is:

P(5,3) = 1/6 * 1/6 = 1/36

An ant is on the top of a tree 23 meters tall directly above her home which is 0.3meters below the ground

Answers

Final answer:

Using ants on a stretching ruler to illustrate Hubble's Law shows how objects further away move faster relative to an observer, much like galaxies in the universe, while highlighting the organization and communication in ant colonies.

Explanation:

The scenario described involves ants on various points of a stretchable ruler, illustrating a concept similar to Hubble's Law in cosmology. One ant measures how the distance to the other ants increases as the ruler stretches, showing that ants further away appear to move faster relative to the observing ant. This phenomenon occurs not because the ants are moving of their own volition, but because the ruler itself is stretching, much like space-time expands in the universe.

Furthermore, ants in a colony communicate using pheromones, and their large groups, called colonies, are highly organized with different roles such as workers, soldiers, and a queen. The example of ants traveling on a ruler and cooperating in a colony also demonstrates principles of coordination, communication, and perception from a relative standpoint.

sara can run 49 yards in 7 seconds. At that rate, how many feet can she run in 3 minutes?

Answers

Answer:

3780 feet

Step-by-step explanation:

49/7*60*3(be careful that it is 3 minutes,not seconds)

=1260

Now,we have to convert yards into feet.

1260 yards = 3780 feet

Because feet is three times yard.

Hope this answer helps! ;)

Answer:

Distance ran by Sara in 3 minutes is 3780 feet.

Step-by-step explanation:

We know that,

1 yard = 3 feet

So, 49 yards = 49 × 3 feet = 147 feet

Now, it is given that Sara can run 49 yards in 7 seconds. So, we can say that, Sara can run 147 feet in 7 seconds

So, distance ran by Sara in 7 seconds = 49 yards = 147 feet

Now, distance ran by Sara in 1 second = (147 ÷ 7) feet = 21 feet

Now, 1 min = 60 sec, then 3 min = 3 × 60 sec = 180 sec

So, distance ran by Sara in 3 min or 180 sec = 21 × 180 = 3780 feet

∴ distance ran by Sara in 3 minutes is 3780 feet.

3x^2+12x+12 solve or factor the equation

Answers

Answer:

x = -2 (multiplicity 2).

Step-by-step explanation:

3x^2+12x+12 = 0

3(x^2 + 4x + 4) = 0

3(x + 2)(x + 2) = 0

x = -2 (multiplicity 2).

2 roots - both equal.

Answer:

3(x+2) (x+2)

Step-by-step explanation:

Given 3x²+12x+12

We expand the equation

That is,

3x²+6x+6x+12

We add parentheses to factor out

(3x²+6x)+(6x+12)

3x(x+2)+6(x+2) > Taking out the

common factors.

(3x+6) (x+2)

= 3(x+2) (x+2)

What is the volume of a right circular cylinder with a radius of 4 m and a height of 4 m?

[A] 8π m³

[B] 16π ​m³

[C]​ 64π ​m³

[D] 256π m³

Answers

Answer:

C. 64 pie m^3

Answer: 64[tex]\pi[/tex][tex]m^{3}[/tex]

Step-by-step explanation:

The volume of cylinder is given as

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

r = 4m

h = 4m

Substituting into the formula , we have

V = [tex]\pi[/tex]  x [tex]4^{2}[/tex] x 4

V = [tex]\pi[/tex] x 16 x 4

V = [tex]\pi[/tex] x 64

Therefore : V = 64[tex]\pi[/tex][tex]m^{3}[/tex]

plz help me out asap

Answers

Answer:

Table C represents an exponential function.

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