2.56 = 2w solve for w

If ABC is a triangle, which when plotted on the cartesian coordinate system, has it's vertices at A(4, 1), B(-3, -2), and C(-1, 3), then the perimeter of triangle ABC will be [√58/(√2 - 1)]

As per the question statement, ABC is a triangle, which when plotted on the cartesian coordinate system, has it's vertices at A(4, 1), B(-3, -2), and C(-1, 3).

We are required to calculate the perimeter of triangle ABC.

To solve this question, first we need to calculate the distances between AB, BC ad AC, which are the three sides of our concerned triangle ABC, and then add them up to obtain our desired answer. And to calculate the lengths of AB, BC ad AC, we will need to use the distance formula which goes as,

"The distance between any two points (x₁, y₁) and (x₂, y₂) can be given by

√[(x₂ - x₁)² + (y₂ - y₁)²]

Considering points A(4, 1) and B(-3, -2), we can say that [(x₁, y₁) = (4, 1)] and [(x₂, y₂) = (-3, -2)]. Therefore, distance AB = √[{(-3) - 4}² + {(-2) - 1}²]

Or, AB = √[{-(3 + 4)}² + {-(2 + 1)}²]

Or, AB = √[(-7)² + (-3)²]

Or, AB = √[(49 + 9)]

Or, AB = √58

Similarly considering points A(4, 1) and C(-1, 3), we can say that

[(x₁, y₁) = (4, 1)] and [(x₂, y₂) = (-1, 3)].

Therefore, distance AB = √[{(-1) - 4}² + (3 - 1)²]

Or, AC = √[{-(1 + 4)}² + (3 - 1)}²]

Or, AC = √[(-5)² + (2)²]

Or, AC = √[(25 + 4)]

Or, AC = √29

Finally considering points B(-3, -2) and C(-1, 3), we can say that

[(x₁, y₁) = (-3, -2)] and [(x₂, y₂) = (-1, 3)].

Therefore, distance BC = √[{(-1) - (-3)}² + {3 - (-2)}²]

Or, BC = √[{-(1) + 3}² + (3 + 2)²]

Or, BC = √[(3 - 1)² + (5)²]

Or, BC = √[(4 + 25)]

Or, BC = √29

Therefore, the perimeter of Triangle ABC  = (AB + BC + AC)

Or, perimeter of Triangle ABC  = (√58 + √29 + √29)

Or, perimeter of Triangle ABC  = [√(29 * 2) + √29 + √29]

Or, perimeter of Triangle ABC  = [(√29*√2) + √29 + √29]

Or, perimeter of Triangle ABC  = √29(√2 + 1 + 1)

Or, perimeter of Triangle ABC  = √29(√2 + 2)

Or, perimeter of Triangle ABC  = (√29*√2)(1 + √2)

Or, perimeter of Triangle ABC  = (√58)(1 + √2)

Or, perimeter of Triangle ABC  = [tex]\frac{\sqrt{58} (1+\sqrt{2})(1-\sqrt{2}) }{(1-\sqrt{2})} =\frac{\sqrt{58} [(1)^{2}-(\sqrt{2})^2 }{(1-\sqrt{2})}}[/tex]

Or, perimeter of Triangle ABC  = [tex]\frac{\sqrt{58} [(1-2) }{(1-\sqrt{2})}}=\frac{-\sqrt{58}}{(1-\sqrt{2})}}=\frac{\sqrt{58}}{(\sqrt{2}-1)}}[/tex]

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Daniel's mother should leave the house at 1:10 P.M. to arrive at the playground at the same time as Daniel.

According to the question,

We have the following information:

Speed of Daniel = 4 miles per hour

So, it means that Daniel covers 4 miles in 1 hour.

1 hour = 4 miles or 4 miles = 1 hour

1 mile = 1/4 hour

1/4 hour means (60/4) minutes or in other words 15 minutes.

Now, Daniel will cover 1 mile in 15 minutes.

So, the time taken by Daniel to cover 2 miles = 15*2 minutes

Time taken by Daniel to cover 2 miles = 30 minutes

So, Daniel will reach the playground at 1:30 P.M.

Now, speed of Daniel's mother = 6 miles per hour

So, we have:

6 miles = 1 hour

6 miles = 60 minutes

1 mile = 60/6 min

1 mile = 10 min

So, to cover 2 miles, Daniel's mother will take (2*10) minutes or 20 minutes.

Now, Daniel will reach the playground at 1:30 P.M.

So, Daniel's mother should start from her house at 1:10 P.M.

Hence, Daniel's mother should start at 1:10 P.M.

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Answer:

Gabriel spent $12 in just Donuts. If fritters are $2 a piece, he could buy 2 fritters at max. Perhaps he bought an extra donut to equal $17.

Step-by-step explanation:

Answer:

7 donuts and 5 fritters

Step-by-step explanation:

If he gets paid $20 per hour to work at the grocery store and $2 per hour to work at nursery,

Part a

He will earn $449 if he works 13 hours at the grocery store and 9 hours at the nursery

Part b

He will earn 20g + 21n, if he works g hours at the grocery store and n hours at the nursery

The payment at the grocery store per hour = $20

The payment at the nursery per hour = $21

Part a

Number of hours he works at the grocery store = 13 hours

Number of hours he works at nursery = 9 hours

Total pay = 13×20 + 9×21

= 260 + 189

= $449

Part b

Number of hours he works at the grocery store = g hours

Number of hours he works at nursery = n hours

Total pay = 20g + 21n

Hence, If he gets paid $20 per hour to work at the grocery store and $2 per hour to work at nursery,

Part a

He will earn $449 if he works 13 hours at the grocery store and 9 hours at the nursery

Part b

He will earn 20g + 21n, if he works g hours at the grocery store and n hours at the nursery

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Solution given to both questions below, they reveal the given answers.

The steps are self-explanatory, let me know if anything is unclear.

Answer:

[tex]\textsf{24.} \quad \dfrac{1}{(x-2)(x-3)}[/tex]

[tex]\textsf{25.} \quad x=1, \quad x=-1[/tex]

Step-by-step explanation:

Given expression:

[tex]\dfrac{2}{(x-2)(x-3)}+\dfrac{2}{(x-1)(3-x)}+\dfrac{1}{(1-x)(2-x)}[/tex]

When adding rationals with different denominators, make the denominators the same by finding the least common denominator.

Create a common denominator by:

[tex]\textsf{Multiplying the first fraction by $\dfrac{x-1}{x-1}$}.[/tex]

[tex]\textsf{Multiplying the second fraction by $\dfrac{-(x-2)}{-(x-2)}$}.[/tex]

[tex]\textsf{Multiplying the third fraction by $\dfrac{x-3}{x-3}$}.[/tex]

[tex]\implies \dfrac{2}{(x-2)(x-3)} \cdot \dfrac{x-1}{x-1}+\dfrac{2}{(x-1)(3-x)}\cdot \dfrac{-(x-2)}{-(x-2)}+\dfrac{1}{(1-x)(2-x)}\cdot \dfrac{x-3}{x-3}[/tex]

[tex]\implies \dfrac{2(x-1)}{(x-1)(x-2)(x-3)}+\dfrac{-2(x-2)}{-(x-1)(x-2)(3-x)}+\dfrac{x-3}{(1-x)(2-x)(x-3)}[/tex]

[tex]\implies \dfrac{2(x-1)}{(x-1)(x-2)(x-3)}+\dfrac{-2(x-2)}{(x-1)(x-2)(-3-(-x))}+\dfrac{x-3}{(-(-1+x))(-(-2+x))(x-3)}[/tex]

[tex]\implies \dfrac{2(x-1)}{(x-1)(x-2)(x-3)}+\dfrac{-2(x-2)}{(x-1)(x-2)(x-3)}+\dfrac{x-3}{(x-1)(x-2)(x-3)}[/tex]

[tex]\textsf{Apply the fraction rule} \quad \dfrac{a}{d}+\dfrac{b}{d}+\dfrac{c}{d}=\dfrac{a+b+c}{d}:[/tex]

[tex]\implies \dfrac{2(x-1)-2(x-2)+(x-3)}{(x-1)(x-2)(x-3)}[/tex]

Expand the numerator:

[tex]\implies \dfrac{2x-2-2x+4+x-3}{(x-1)(x-2)(x-3)}[/tex]

[tex]\implies \dfrac{x-1}{(x-1)(x-2)(x-3)}[/tex]

Cancel the common factor (x - 1):

[tex]\implies \dfrac{1}{(x-2)(x-3)}[/tex]

Given equation:

[tex](4x-1)(x+2)=2+7x[/tex]

Expand the left side:

[tex]\implies 4x^2+7x-2=2+7x[/tex]

Subtract 7x from both sides:

[tex]\implies 4x^2+7x-2-7x=2+7x-7x[/tex]

[tex]\implies 4x^2-2=2[/tex]

Add 2 to both sides:

[tex]\implies 4x^2-2+2=2+2[/tex]

[tex]\implies 4x^2=4[/tex]

Divide both sides by 4:

[tex]\implies \dfrac{4x^2}{4}=\dfrac{4}{4}[/tex]

[tex]\implies x^2=1[/tex]

Square root both sides:

[tex]\implies \sqrt{x^2}=\sqrt{1}[/tex]

[tex]\implies x= \pm 1[/tex]

Therefore, the solutions are:

[tex]x=1, \quad x=-1[/tex]

Answer:

1. b = 2A/h

2. h = 2A/b

Step-by-step explanation:

All you have to do is isolate the variable.

1.

Isolate b:

A = 1/2 x b x h

Multiply each side by 2

2A = b x h

Isolate b by dividing both sides by h

b = 2A/h

2.

Isolate h:

A = 1/2 x b x h

Multiply each side by 2

2A = b x h

Isolate h by dividing both sides by b

h = 2A/b

Answer: (0,4) and (-1,-1)

Step-by-step explanation:

1) Plug in all of each equation

1a) (0,4)

3(0)-(4)<10

0-4< 10

-4< 10

2(0)+6(4)>=-8

0+24 >= -8

24>= -8

Works!

1b) (2,-1)

3(2)-4(-1)<10

6+4<10

10<10

Nope.

1c) (2,-2)

3(2)-4(-2)<10

6+8<10

14<10

Nope.

1d) (8,2)

3(8) -4(2) < 10

24 - 8 < 10

16<10

Nope.

1f) (-1,-1)

3(-1)-4(-1) < 10

-3 +4 < 10

1 < 10

2(-1)+6(-1)>=-8

-2+-6 >= -8

-8 >= -8

Works.

Answer:

Step-by-step explanation:

Neither, they are not congruent.

a) Total purchase price for the bicycle is $19,145

b) The difference between the hire purchase price and the cost price for the bicycle is $2,825.50

c) The percentage of difference between the hire purchase price and the cost price for the bicycle is 17%

Percentage:

Percentage means a fraction or a ratio in which the value of whole is always 100.

Given,

A bicycle has cash price $16,319.50. It can be bought on hire purchase with a deposit of $6,900 and ten monthly installments of $1,224.50 each.

Here we need to following:

a) Purchase price for the bicycle

b) Difference between the hire purchase price and the cost price for the bicycle

c) Percentage of the cash price.

The total purchase price is calculated by adding the deposit and the ten month installment.

So, the total purchase price is,

=> 6900 + (10 x 1224.50)

=> 6900 + 12245

=> 19145.

Therefore, the total purchase price is $19145.

Now, the difference between the hire purchase price and the cost price for the bicycle is calculated as,

=> 19145 - 16319.50

=> 2825.50

So, the difference between the hire purchase price and the cost price for the bicycle is $2,825.50

Now, we have to calculate the percentage by using the following expression,

x% of 16,319.50 = 2825.50

x% = 2825.50/16319.50

x% = 0.1731

x = 17.31.

Therefore, there is 17% difference in the hire purchase price and the cost price for the bicycle.

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Answer:

see explanation

Step-by-step explanation:

there are 15 students , 9 of which are boys, then

number of girls = 15 - 9 = 6

ratio of boys : girls = 9 : 6 = 3 : 2 ← in simplest form

The product of 4 1/10 and -3 5/12 is -14 1/120

Fractions are simply described as a subset of a whole or the part of a whole.

They are several types of fractions, some of which includes;

Some examples of mixed fractions; 3 1/4, 5 1/2, 6 1/4

Some examples of simple fractions; 1/2, 1/4, 1/6

Some examples of proper fractions; 3/4, 4/5, 6/7

Some examples of improper fractions; 3/2, 4/3, 6/5

Given the mixed fractions;

4 1/10  ×  -3 5/12

convert to improper fractions

41/10 × - 41/12

Multiply through

- 1681/120

Find the ratio

- 14 1/ 120

Hence, the value is - 14 1/ 120

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the conclusion is that angle AOZ  and XOB is approximately equal

We are given that WOA and AOZ are equal, and since the AB intersects the line WY and XZ, were from the vertical angles theorem, This hypothesis says that when two straight lines meet, they frame two sets of linear sets with congruent angles, then angle WOZ and XOY equal and XOW and YOZ are too, now since the Ab intersects those angle on pint A and by the transitive property If any angles or segments are congruent to the same angle, at that point they are consistent to each other, according to which it was clear that both the angle BOY and XOB are approximately equal, there  vertical angle which are angles WOA and AOZ are equal  to them, So it can be concluded that the angle AOZ and XOB are equal too.

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Answer:

b

Step-by-step explanation:

for edmuntum

The equation x + |y| = y + |x| that contains the absolute values of x and y, is satisfied when the values of x and y are given by the iniquities;

The absolute value or modulus of a real number gives its non negative value irrespective of the sign (positive or negative) of the number.

The given equation is presented as follows;

x + |y| = y + |x|

The possible values of x and y are;

-10 ≤ x ≤ 10 and -10 ≤ y ≤ 10

Collecting the absolute values of the equation on one side gives;

|y| - |x| = y - x, which gives;

+y - +x = y - x

The equation is therefore satisfied when both x and y are larger than zero.

Therefore, x + |y| = y + |x|, gives;

0 ≤ x ≤ 10, and 0 ≤ y ≤ 10

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Examples of permutation matrices are the identity matrices with a permutation in rows. Permutation matrices are invertible and the inverse is a permutation matrix as well.

A permutation matrix is a square matrix which contains exactly one 1 in each row and all other entries 0.

So a permutation matrix can be obtained by rearranging the rows or columns of an identity matrix. Identity matrix is also a permutation matrix with entry 1 exactly once in each row and all other entries 0.

Example of a permutation matrix:

[tex]\left[\begin{array}{ccc}1&0&0\\0&0&1\\0&1&0\end{array}\right][/tex]

A permutation matrix is invertible because an identity matrix is invertible [since det(I) = 1] and a permutation matrix is just got by exchanging rows or columns which does not change its determinant. So the determinant of a permutation matrix ≠ 0 and hence invertible.

The inverse of a permutation matrix is its transpose itself. The transpose is again a permutation matrix.

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Answer: The answer is 15

Step-by-step explanation: 25*  3/5 is 15 so 15 out of 25 is what percent of the class has brown eyes

The coordinates of A are (-5, -5).

How to determine the midpoint of a given segment?
The center point of a straight line can be located using the midpoint formula. We can use this midpoint formula to determine the coordinates of the supplied line's midpoint in order to discover its location on a graph. Assuming that the line's endpoints are (x₁, y₁) and (x₂, y₂), the midpoint (a, b) is determined using the following formula:
(a , b) ≡ (((x₁ + x₂)/2), ((y₁ + y₂)/2))

Given, the line segment under consideration is AB as endpoints.
And, the co-ordinate of B is = (6, 1)
Also, the midpoint of segment AB i.e. M is = (0.5, -2)
Let the co-ordinate of A be = (x, y)
Using the available literature and formula, we get
(0.5, -2) ≡ (((x + 6)/2), ((y + 1)/2))
Equating both parts in the given equation,
0.5*2 = x + 6 ⇒ 1 = x + 6 ⇒ x = -5
and, (-2)*2 = y + 1 ⇒ -4 = y + 1 ⇒ y = -5
Therefore, the co-ordinates of A are (-5, -5).

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Answer:

Step-by-step explanation:

i poopeyd in ma pants

The first five terms of the given function is:

f(1) = 2.3

f(2) = 5.6

f(3) = 8.9

f(4) = 12.2

f(5) = 15.5

Functions: The core concept of mathematics calculus is functions. The unique varieties of relations are the functions. In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation. Typically, these functions are identified by letters like f, g, and h.

The given function is f(n) = 3.3n-1 for n>= 1

The first 5 terms of this function are as follows:

f(1) = 3.3(1)-1

= 3.3-1 = 2.3

f(2) = 3.3(2)-1

= 6.6-1 = 5.6

f(3) = 3.3(3)-1

= 9.9-1

=8.9

f(4) = 3.3(4)-1

= 13.2-1

=12.2

f(5) = 3.3(5)-1

= 16.5-1

= 15.5

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Part of a full number and a means of dividing a number into equal pieces are represented by fractions.The denominator is the total number of parts in the whole, while the numerator is the number of equal portions being counted.

Solve the problem ?

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Answer:

Step-by-step explanation:

You want to find the number of bags of popcorn (x) and candies (y) Taylor bought for $81, given that popcorn costs $9 and candies cost $4.50, and she bought 6 more candies than popcorns.

The equations relating x and y are ...

The attached graph shows the solution of thees equations is ...

  (x, y) = (4, 10)

Taylor bought 4 bags of popcorn and 10 candies.

<95141404393>

Toads are in the pond is 27.

The quantitative relation between two amounts showing the number of times one value contains or is contained within the other.

"the ratio of men's jobs to women's is 8 to 1".

Given that,

The ratio of toads to frogs was 3: 10.

Let the number of toads = 3x

number of frogs = 10x

9 more frogs then entered the pond and the ratio of toads to frogs became 3:11.

[tex]\frac{3x}{10x+9} =[/tex] [tex]\frac{3}{11}[/tex]

[tex]\frac{x}{10x+9} = \frac{1}{11}[/tex]

11x = 10x+9

x = 9

number of toads = 3x = 3×9 = 27

Hence, Toads are in the pond is 27.

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The break-even points for her graph are given approximately as follows:

C. 15 and 47.

The expenses and the revenue are defined as follows:

The break-even points are the points in which the expenses and the revenue are equal.

In the context of this problem, the functions are given as follows:

The break-even point is given by the intersection of the two curves, which happen around x = 15 and x = 47, hence option C is the correct option.

The problem is given by the image at the end of the answer.

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Answer:

Almost!

Step-by-step explanation:

Problems 1-9 and 11 are correct, but not problem 10 or 12

For problem 10, 12/6 does equal 6/1, so it would just be the whole number of 6 as your final answer as it doesn't need to be simplified further.

For problem 12, -4/6 can be simplified further to -2/3 by dividing by 2.

Answer: Very close!

Step-by-step explanation:

Problems 7, 8, 9, and 11 are correct but not 10 or 11, because they are not in simplest form.

2/1 can be simplified to 2, and -4/6 can be simplified to -2/3.

Answer:

-18/35

Step-by-step explanation:

6m/m-3    + m/m+1

Simplify

Identify the common factor

{6m/m-3 + m/m+1

(m+1) . (6-3) /(m+1)  +  (m-3)/ (m+1)

Add fractions with the same denominator together.

terms to put constants on the left and reorder them

Solution

7m^{2}+3m   /  m^2-2m-3

The answered are 7  3  2 3

What does the algebraic expression M mean?

The slope of a line is represented by the letter "m" in algebra. A line's slope defines both its direction and steepness.

The order in which you perform operations in arithmetic and algebra is governed by a number of laws. The Commutative, Associative, and Distributive Laws are the three that receive the most attention. People have discovered over time that adding or multiplying doesn't depend on the order of the numbers

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Answer:

See below

Step-by-step explanation:

the two angles add to a total of 360 °

5x - 40    + `150 = 360

x = 50°

It should be noted that the conversion of the measurement of 290 inches will be 0.7366 decameter.

How to illustrate the information?

It should be noted that from the information,.it about equivalents dimensional analysis, to convert the given measurement to the unit indicated.

In this case, we want to convert 290 in. to dam.

It should be noted that we have to divide rye length value by 393.7

Therefore, it should be noted that 290 inches will be:

= 290 / 393.7

= 0.7366 decameter.

Therefore, it should be noted that the conversion of the measurement of 290 inches will be 0.7366 decameter.

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