The line parallel to y=1/4x+1 that passes through the point (6,-2)

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.

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]

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:

Step-by-step explanation:

Neither, they are not congruent.

The base of the triangle = 4(x + 1)

The Area of a triangle is given by the formula:

Substituting these expressions into the formula for the area of a triangle:

b = 4 (x + 1)

The base of the triangle = 4(x + 1)

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

Firstly multiplication operation will be performed and the value on simplification will be -7.

The expression will be solved based on the sequence in order of operations. In the mentioned expression, parenthesis and exponents are not there. Thus, firstly we will multiply the values followed by division. Then we will perform addition and subtraction (PEMDAS).

Performing multiplication first -

Value = 27 ÷ 27 - 8

Performing division at second step -

Value = 1 - 8

We are left with subtraction, so performing it -

Value = -7

Therefore, firstly multiplication will be performed and the value is -7.

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To write a number in scientific notation you must know:

1. A number in scientific notation is written as the product of a number (integer or decimal) and a power of 10

2. A number can be converted to scientific notation by increasing the power of 10 by one for each place the decimal point is shifted to the left.

Then so:

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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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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a)The percentage of bottles expected to have a volume more than 32 oz is 33.60%

b) 85% of 0.3360 is 0.2856

a) The volumes of soda in quart soda bottles can be represented by a Nomal model with a= 32.3 oz

b=8.8 oz

Let S be the volume of randomly selected soda bottles

Y-score: S-a/b

For S=32 oz

Substitute the values of S,a and b into the equation

Y=32-32.3/8.8

Y= - 0.0341

Probability of bottles that have a volume more than 32 oz is

P(S>32)=P(Y>-0.0341)= 0.3360

Percentage of bottles that have volume more than 32 oz will be

0.3360×100%=33.60%

b) 85% of 0.3360 is 0.2856

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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>

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

it is 2 becuase 1 plus 1 is two when you have an apple and a freind gives you an apple you have 2 appelapples

Answer:

1+1=2

Step-by-step explanation:

if you have one of me then you duplicate me or make a dopleganger than you now have 2

have a great day^^

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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All the dimensions of the shape is found as 19 ft.

For the given question, the dimensions of the shape is given as;

The perimeter of the shape = 76 ft.

The formula of the perimeter = sum of length of all sides.

Let 'P' be the perimeter.

P = (4x-5) + (25-x) + (13 + x)  + (3x+1) ing

Simplifying

P = 4x - x + x + 3x - 5 + 25 + 13 + 1

76 = 7x + 34

7x = 76 - 34

7x = 42

x = 6

Thus, the dimensions of the shape is; Put x = 6

Thus, all the dimensions of the shape is found as 19 ft.

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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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Kayleigh have 25 nickels with her.

Given,

The total value of coins Kayleigh have = $5.50

Number of quarters with Kayleigh = 17 quarters

We have to find the number of nickels Kayleigh with her.

Lets see:

1 dollar = 4 quarters

1 dollar = 20 nickels

Here, we have a total of 5.50 dollar

In this, 17 quarters are there.

So,

17 / 4 = 4.25

That is, the value of coins as quarters is $4.25

Now,

5.50 - 4.25 = 1.25

That is,

$1.25 is in the form of nickels.

Number of nickels = 1.25 × 20

Number of nickels = 25

Therefore,

Kayleigh have 25 nickels with her.

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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:

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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Answer:

Step-by-step explanation:

i poopeyd in ma pants

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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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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The zero of the function is 25.6 and it means that the total number of days is 25.6

From the question, the equation of the function is given as

c = 6.4 - 0.25p

The zero of this function is when the function equals 0

This is represented as

c = 0

Substitute c = 0 in c = 6.4 - 0.25p

So, we have

6.4 - 0.25p = 0

The above equation becomes

0.25p = 6.4

Divide both sides by 0.25

p = 25.6

So, the zero is 25.6 and it represents that the total number of days

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Answer:

0≤x≤|R

Step-by-step explanation:

I'm not really sure but I think the domain is all positive real numbers including zero

The probability P(5 ≤ x ≤ 9) is 0.6847

Assume that x has a normal distribution

We have been the mean and standard deviation μ = 6; σ = 2.

To calculate this probability we use the standardized normal distribution and the z-value for 5 and 9.

z = (5 - 6)/2

  = -0.5

and z = (9 - 6)/2

         = 1.5

Then the probability is calculated as:

P(x ≤ 5) = 0.3085

P(x ≤ 9) = 0.9932

P(5 ≤ x ≤ 9) = 0.9932 - 0.3085

P(5 ≤ x ≤ 9) = 0.6847

Therefore, the probability P(5 ≤ x ≤ 9) is 0.6847

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Answers:

[tex](f+g)(\text{x}) = \boldsymbol{2\text{x}^2+2\text{x}-12}[/tex]

Domain = set of all real numbers

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

Work Shown:

[tex](f+g)(\text{x}) = f(\text{x})+g(\text{x})\\\\(f+g)(\text{x}) = (2\text{x}^2+\text{x}-11)+(\text{x}-1)\\\\(f+g)(\text{x}) = 2\text{x}^2+\text{x}-11+\text{x}-1\\\\(f+g)(\text{x}) = 2\text{x}^2+(\text{x}+\text{x})+(-11-1)\\\\(f+g)(\text{x}) = 2\text{x}^2+2\text{x}-12\\\\[/tex]

The domain of each f(x) and g(x) is "set of all real numbers" since we can replace x with any real number to get some output.

By extension, this means the domain of (f+g)(x) is also "set of all real numbers".

It turns out any polynomial will have this domain. We don't have to worry about things like applying square roots to negatives, or dividing by zero. This is why there isn't a restriction on x.

To write "set of all real numbers" in interval notation, we would say [tex](-\infty, \infty)[/tex] to indicate x is anything between negative infinity and positive infinity.

The option that is not equivalent to the given percentage of 40% is; A:0.04.

We are given the percentage as 40%.

Now, this percentage can be rewritten as a proper fraction as;

40% = 40/100

In decimal form, this is expressed as 0.40

Now, the proper fraction 40/100 can be broken down into;

40/100 = 4/10

Further more when we divide both numerator and denominator by 2, we will get the fraction 2/5.

Thus, the only option that is not equivalent to the given percentage is option A which is 0.04.

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The correct options are;

A) 0.04

B) 0.40

C) 2/5

D) 4/10