Can I get a in depth explanation to simplifying non perfect roots with quotients? Ex: image

Statement Problem: (3)

List the angles of the triangle in order from smallest to largest.

Solution:

First, let's use the Cosine Rule to find the angle B;

Where;

Also, let's use the Cosine Rule to find the angle A;

Lastly, let's use the sum of angles in a triangle theorem to get the third angle, Angle C;

Hence, the angles of the triangle from the smallest to the largest are;

Angle B,

Angle A,

Angle C

The limit as x approaches infinity of 4^x is of infinity, that is:

[tex]\lim_{x \rightarrow \infty} 4^x = \infty[/tex]

The first step in calculating the limit of a function is calculating the numeric value of the function at the value of x which the function approaches.

In this problem, the limit is given as follows:

[tex]\lim_{x \rightarrow \infty} 4^x = 4^{\infty} = \infty[/tex]

There is nothing undetermined, hence the value of limit is of infinity, as we calculated.

If an undetermined value such as 0/0 or infinity/infinity had been reached, then alternatives such as factorization or L'Hospital rule would be searched, but is not necessary in the context of this problem.

Hence, the limit is of infinity.

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Answer:

-4x² - 2x - 2

Step-by-step explanation:

(-4x3 - 22x2 - 12x - 10) ÷ (x + 5)

-5 |  -4    -22    -12     -10

       ↓     20      10      10

  -----------------------------------

      -4     -2       -2       0

          -4x² - 2x - 2

I hope this helps!

Answer:

0.4375

Step-by-step explanation:

Fractions, when the numerator is divided by the denominator, will give the decimal form. Therefore, 7 divided by 16 is 0.4375. It is not a repeating number because the equation doesn't give a repeating number as an answer.

Answer:

0.4375

Step-by-step explanation:

observe

7/16=(((7/2)/2)/2)/2

=((3.5)/2)/2)/2

=(1.75/2)/2

=0.875/2

=0.4375

Solve the equation

First step is to find cos (pi/14), then solve the product)

Solution:

Given the radius of the sphere is 4inches.

The surface area, A, of the sphere is;

But when the radius is doubled;

Hence, when the radius is doubled, the surface area is multiplied by four.

Question:

Solution:

Consider the following system of linear equations:

Equation 1:

Equation 2:

Replacing the above equation into equation 1, we get:

Applying the distributive property, we get:

this is equivalent to:

this is equivalent to:

or

solving for y, we obtain:

Now, replacing this into Equation 2, we obtain:

So that, we can conclude that the correct answer is:

The solution is (-3, 5)

The amount of coffee imported into the country in the year 1997 is approximately 1.344 million pounds.

The amount of coffee imported into the country in the year 2002 is approximately 39.3176 million pounds.

The amount of coffee imported into the country in the year 2007 is approximately 85.8966 million pounds.

A polynomial function can be defined as a mathematical expression which comprises intermediates (variables), constants, and whole number exponents with different numerical value, that are typically combined by using mathematical operations such as:

Next, we would determine the amount of coffee imported into the country by using the given polynomial function as follows:

At 1997, we have the following:

x = 0

P(x) = 0.7166x² + 6.627x + 1.344

P(0) = 0.7166(0)² + 6.627(0) + 1.344

P(0) = 1.344 million pounds.

At 2002, we have the following:

x = 4

P(x) = 0.7166x² + 6.627x + 1.344

P(4) = 0.7166(4)² + 6.627(4) + 1.344

P(4) = 0.7166(16) + 26.508 + 1.344

P(4) = 11.4656 + 26.508 + 1.344

P(4) = 39.3176 million pounds.

At 2002, we have the following:

x = 9

P(x) = 0.7166x² + 6.627x + 1.344

P(9) = 0.7166(9)² + 6.627(9) + 1.344

P(9) = 0.7166(81) + 59.643 + 1.344

P(9) = 58.0446 + 26.508 + 1.344

P(9) = 85.8966 million pounds.

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The volume of water that the cylindrical vase can hold is 10362 cm³.

Volume is a measurement of three-dimensional space that is occupied. It is frequently expressed mathematically using imperial or SI-derived units. Volume and the notion of length are connected.

The circumference of a cylindrical vase is 62.8 centimeters.

The height of the cylindrical vase is 33 centimeters.

Let r be the radius of the cylinder.

The circumference of the cylinder is given as:

C = 2πr

62.8 cm = 2 × 3.14 × r

r = 10 cm

The volume of a cylinder is given as:

V = πr²h where r is the radius and h is the height of the cylinder

Then,

V = 3.14 × ( 10 )² × 33

V = 10362 cm³

Hence, the cylindrical vase can hold 10362 cm³ of water.

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Answer:  Bro above is wrong it's 10,367 cm3    PLATO

Step-by-step explanation: mad maths skills

Answer:

[tex]1\frac{1}{2}[/tex] <2<2 [tex]\frac{6}{11}[/tex]

Step-by-step explanation:

[tex]1\frac{1}{2}[/tex] is less than 2 is less than 2 [tex]\frac{6}{11}[/tex]

[tex]\frac{33}{22} < \frac{44}{22} < \frac{56}{22}[/tex]

1 mile is equivalent to 5280 feet which is equivalent to 5280/440 in = 12 in

Hence, a path of 2miles is equivalent to 24 in on the graph

The connect line is as shown in the image from the School to the Park and it is colored red and 24 in long.

The position of the water fountains are marked in pink on the graph,

The first is 1/3 of the way from the School which is 8 in from the school.

The second is 2/3 of the way from the School which is 16 in from the school.

Let x represent the number of dimes Ed has in its collection.

The total of coins in the collection is 8 more than three times the number of dimes.

The number of coins is 92.

3 times the number of dimes can be symbolized as: 3x

"8 more" is symbolized as +8

So the total number of coins equals:

92=3x+8

From this expression you can determine the number of dimes by solving the equation for x:

x=28 → Ed has 28 dimes in his collection.

(AAS): If two angles and the non-included side of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent

The income of the event is given by the product of the number of tickets and the price of a ticket.

Hence, the income of the event can be represented by

The income of the event represented by -10x² + 180x

The profit is given by

Therefore,

The profit is given by -10x² + 180x - 150

Answer:

∠A ≅ ∠A and ∠ABD ≅ ∠ACB, so ΔABD ≅ ΔACB by the AA (Angle - Angle) Triangle Similarity Theorem.

AB = 10

Explanation:

An angle is congruent to itself, so ∠A ≅ ∠A

On the other hand, taking into account the representation of the angles, we can say that: ∠ABD ≅ ∠ACB

Then, the triangles ABD and ACB are congruent by the AA (Angle-Angle) triangle similarity theorem because we have two congruent angles:

∠A ≅ ∠A

∠ABD ≅ ∠ACB

Now, if two triangles are similar their corresponding sides are proportional.

So, we can formulate the following equation:

Then, replacing AC by (21 + 4), AD by 4, and solving for AB, we get:

Therefore, the answers are:

∠A ≅ ∠A and ∠ABD ≅ ∠ACB, so ΔABD ≅ ΔACB by the AA (Angle - Angle) Triangle Similarity Theorem.

AB = 10

C. Grapes are $0.48 per pound and oranges are $0.77 per pound.

The cost of grapes and oranges are 0.48 and 0.77 respectively.

Cost word problem

Evaluating cost of solution is simple: You determine the time and money you need to develop and implement it. You're looking at the resources needed. Cost of problem, however, equals the price of doing nothing. That is, for what I know, an important economic principle known from cost-benefit analyses.

Given that Peaches cost $4 for a 7-pound bag, grapes cost 15% less per pound than peaches, oranges cost 35% more per pound than peaches.

Cost of 7 pounds of peaches = 4

Therefore cost of 1 pound of peaches = 4/7 = 0.57

Cost of one pound of grapes = 0.57 - 15% of 0.57

                                                 = 0.57 - 0.0855

                                                 = 0.4845

                                                 = 0.48

Cost of one pound of oranges = 0.57 + 35% of 0.57

                                                   = 0.57 + 0.1995

                                                   = 0.7695

                                                   = 0.77

Therefore Grapes are $0.48 per pound and oranges are $0.77 per pound.

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Answer:

The book has 175 pages

Explanation:

Andre says that he has read 1/5 of the book, so the correct diagram should have each rectangle label as a (the number of pages that Andre has read)

because 5 times 1/5 of the book makes the complete book.

On the other side, Elena has read 20 more pages than Andre, so we should have the second rectangle divided and one part should be label as 20 and the sum of a and 20 is equal to 55.

So, the correct diagram is:

Therefore, we can calculate the number of pages that Andre has read as:

a = 55 - 20 = 35

Then, the number of pages of the book is 5 times a, so:

5 x a = 5 x 35 = 175

Therefore, the answer is the book has 175 pages

Solution:

Given:

Signed numbers consist of negative numbers and positive numbers.

Rules of multiplication in signed numbers.

If the signs are the same the result is positive. If the signs are different the result is negative.

This means;

To solve these questions, we expand the brackets by multiplying the signs together using the rule of multiplying signed numbers.

Question 1:

Therefore, the correct answer is OPTION C.

Question 2:

Therefore, the correct answer is OPTION A.

Question 3:

Therefore, the correct answer is OPTION B.

Question 4:

Therefore, the correct answer is OPTION C.

Question 5:

Therefore, the correct answer is OPTION A.

ANSWER

EXPLANATION

In this problem, we have to complete the table by replacing v with each value from 0 to 6 in the table, and compute the corresponding value of s(v) based on the equation,

Find the values for the table,

Answer:

C. y= 15

Step-by-step explanation:

Add 3y +2y = 5y

Add 4+1=5

Subtract 80 -5 =75

Then divide by 5y on both sides to get

y=15

SOLUTION

The graph of

is shown below

Comparing to the options, the answer is option D

Given: If triangle ABC is similar to triangle DEF, the sides of triangle ABC must be congruent to the corresponding sides of triangle DEF.

Required: To determine if the given statement is true or false.

Explanation: If two triangles are similar, then their corresponding sides are in equal proportion. So, if triangle ABC is similar to triangle DEF then

Final Answer: Option B, False is correct.

.

In this case:

Applying the formula, the compound interest can be calculated as follows:

The amount in the account will be $8,878.56.

Answer:

<-13, 8>

Explanation:

Given vectors u and v below:

In order to evaluate v-u, subtract the corresponding elements as follows:

The third option is correct.

Step-by-step explanation/answer:

A number c is no less than -1.5 and less than 5.3.

So -1.5<= c < 5.3

You would label your number line and have a filled in closed circle at -1.5 and an open circle at 5.3 to signify that 5.3 is not a possible value of c.

Answer:

Step-by-step explanation:

$20/hr carpenter pay

$25/hr blacksmith pay

Let c = hours working carpentry

Let b = hours working as blacksmith

c + b = 30   {equation 1}

20c + 25b = 690   {equation 2}

In equation 1 solve for one variable in terms of the other.

c = 30-b

Substitute that into equation 2:

20(30-b) + 25b = 690

600 - 20b + 25b = 690

5b = 90

b = 90/5

b = 18 hours working as a blacksmith

c = 30-b = 30-18 = 12 hours as a carpenter

Answer:

she worked as a carpenter for 12 hours

And a blacksmith for 18 hours

Step-by-step explanation:

B=hours as blacksmith

C=hours as carpenter

20c+25b=690

b+c=30

c=30-b

So we substitute this into the first equation

20(30-b)+25b=690

 600-20b+25b=690

       5b=90

       B= 18

18+c=30

C=12

Given the following phrase:

Let the number = y

The word times means to use the product process

So, the algebraic expression will be as follows:

UPS charges are:

$ 7 for the firsr pound

+ $0.20

FedEx charges are:

$ 5 for the first pound

+ $ 0.30 for each additional pound

Let x to represent the amount of additional pounds

Equation:

7 + 0.20x = 5 + 0.30x

Like terms:

0.20x - 0.30x = 5 - 7

-0.10x = -2

Dividing by -0.10

-0.10x/- 0.10 = -2/-0.10

x = 20

Interpretation

It will take 21 pounds to cost the same: (the first plus 20 additional)