Y=6x-2 function rule

x = 10% solution

y = 15% solution

let's start at the beginning, without the equation just yet, so let's start off by making a table for the substances and let's use the decimal format for the percentages to get the actual amounts.

[tex]\begin{array}{lcccl} &\stackrel{mL}{quantity}&\stackrel{\textit{\% of mL that is}}{\textit{alcohol only}}&\stackrel{\textit{mL of}}{\textit{alcohol only}}\\ \cline{2-4}&\\ \textit{10\% sol'n}&x&0.10&0.10x\\ \textit{15\% sol'n}&y&0.15&0.15y\\ \cline{2-4}&\\ mixture&50&12&6 \end{array}~\hfill \begin{cases} x + y = 50\\\\ 0.10x+0.15y=6 \end{cases} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{using the 1st equation}}{x+y=50\implies y=50-x}\hspace{5em}\stackrel{\textit{substituting on the 2nd equation}}{0.10x+0.15(\underset{y}{50-x})=6} \\\\\\ 0.10x+7.5-0.15x=6\implies -0.05x+7.5=6\implies -0.05x=-1.5 \\\\\\ x=\cfrac{-1.5}{-0.05}\implies \boxed{x=30}\hspace{15em}\stackrel{50~~ - ~~30}{\boxed{y=20}}[/tex]

Slope-intercept form is −8x+9. One of the formulas used to get a line's equation is the slope-intercept formula.

Slope-intercept is a specific form of linear equations. The equation of the line is written in the slope-intercept form, which is: y = mx + b, where m represents the slope and b represents the y-intercept. In our equation, y = − 3 x + 5 , we see that the slope of the line is − 3 .

A method of formulating a line's equation that makes it simple to identify the slope and y-intercept is known as the slope-intercept form. The y-intercept, or point where the line crosses the y-axis, is where the slope, or steepness, of the line is located.

-8x + y = -9

move y to right side

-8x = -9-y

Divide both sides by -8

-8x/-8x = -(9/-8) - (y/-8)

Simplify

-8x/-8x = -(9/-8) - (y/-8)

Simplify -8x/-8x : x

Simplify  -(9/-8) - (y/-8) : -9 - y / 8

x = -(-9 - y / 8)

y = mx + b.

y = −8x+9

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The total number of red roses sold by the florist is 455.

A Fraction represents the parts of a whole or collection of objects. The first and most common form of representing a fraction is [tex]\frac{a}{b}[/tex].

Here, a is the numerator, and b is the denominator.

Number of Roses sold by The florist = 715

Fraction for the number of red roses sold = [tex]\frac{7}{11}[/tex] (7 out of 11 roses)

We have to find the number of red roses sold by the florist.

Now,

The number of red roses sold by the florist will be

[tex]\frac{7}{11} \ of\ 715[/tex]

[tex]=\frac{7}{11}*715[/tex]

[tex]=\frac{7*715}{11}[/tex]

[tex]=\frac{5005}{11}[/tex]

[tex]=455[/tex]

Hence, the total number of red roses sold by the florist is 455.

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A line representing the "rise" and the "run" of the line is shown in the image attached below. Also, a slope of this line in simplest form is equal to 1.27.

Mathematically, the slope (pitch) of a geometric figure or line can be calculated by using this formula:

Slope (pitch) = V/H

Where:

V represents the rising vertical distance (rise) of an object.

H represents the horizontal distance (run) an object runs through.

From the graph of this line, we would choose the following data points for the rise and run:

Rise (x, y) = (2.5, 2)

Run (x, y) = (8, 9)

Substituting the selected data points into the formula, we have;

Slope (pitch) = (9 - 2)/(8 - 2.5)

Slope (pitch) = 7/5.5

Slope (pitch) = 1.27

At point (2.5, 2), the equation of this line is given by:

y - y₁ = m(x - x₁)

Where:

y - 2 = 1.27(x - 2.5)

y - 2 = 1.27x - 3.175

y = 1.27x - 3.175 + 2

y = 1.27x - 1.175

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The value of the function at x = -1, 0, 1, 2, and 3 will be -4, 3, 2, -1, and 0, respectively.

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

From the graph of f(x), then the value of the function at x = -1, 0, 1, 2, and 3 will be given as,

x             f(x)                        Feedback

-1             -4               Point is in the fourth quadrant

0              3                      Point is in the y-axis

1               2               Point is in the first quadrant

2             -1               Point is in the second quadrant

3              0                      Point is in the x-axis

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The scale factor from JKL to MNO is 1/2, and the scale factor from MNO to JKL is 2.

The ratio among comparable dimensions of an object and a model with that object is known as an exponent in algebra. The replica will be larger if the scale factor is a whole number. The duplicate will be lowered if the step size is a fraction.

It is given that:

The scale factor from JKL to MNO:

The scale factor = JK/MN = 4/8 = 1/2

The scale factor from MNO to JKL:

The scale factor = MN/JK = 8/4 = 2

JL = 11/2 = 5.5 cm

LK = 5 cm

ON = 5x2 = 10 cm

Angle JLK  = Angle MON

Thus, the scale factor from JKL to MNO is 1/2, and the scale factor from MNO to JKL is 2.

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Answer:

[tex]x < \frac{17}{5}[/tex]

Step-by-step explanation:

Take a look at the attachment...

Hope this helps! :)

The values for which the given equation satisfies are provided in main body.

What is linear equation?

An equation that has the highest degree of one is understood as a equation. this suggests that no variable in an exceedingly equation has an acquaintance over one. The graph of a equation continually forms a line.

Main body:

According to the question:

y-1= 1/5 (x+5)

To solve this , we need to let one value for x and find its value for y.

Let x= 0

y-1= 1/5 (0+5)

y-1= 1/5 (5)

y =2

for x = 0 , y =2

Let x = 5

y-1= 1/5 (5+5)

y-1= 1/5 (10)

y = 3

for x = 5 , y = 3

Hence the graph is straight line.

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Answer: Sir in what way would you like me to explain this

Step-by-step explanation:

Answer:

30 every 5 days

Step-by-step explanation:

Answer: -18

Step-by-step explanation:

((-3)2)3

((-3) x 2) x 3

Apply rule (-a) = - a

(-3) = -3

-3 x 2 x 3

-6 x 3

= -18

Answer:

This statement is False.

Step-by-step explanation:

It is not impossible, but on MOST occasions, you will get a decimal number.

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The system of equations are x = 12.071 , y = 10.929

Let x and y are adult and children’s respectively

From the question, we have

Bill and Jose’s discount cinema sold adult tickets for $5.70 each and children’s tickets for $4.30 each.

5.70x + 4.30y = 115.80.............(i)

x+y = 23 ............(ii)

Solving, we get

x = 12.071

y = 10.929

Subtraction:

Subtraction serves as a representation for the act of removing items from a collection. The negative symbol stands for subtraction. For example, if four of the nine oranges that are stacked together (as in the above illustration) are then transported to a basket, the stack will now contain five oranges rather than nine. Therefore, the difference between 9 and 4 is 5, which equals 9 minus 4. In addition to applying it to natural numbers, subtraction can also be used with other kinds of numbers. The letter "-" represents subtraction. Minuend, subtrahend, and difference are the three numerical components that make up the subtraction operation.

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Answer:

Step-by-step explanation:

2 times 7 equals  14 8 times 4 equals 32 32 plus 14 equals 46

Ed’s profit on “Good Luck” cards in 2017 is $450.

Given that, Ed's profit on “Good Luck” cards in 2018 was £360. This was a decrease of 20% on his profit in 2017.

The profit or gain is equal to the selling price minus the cost price. Loss is equal to the cost price minus the selling price.

Let x be the profit on "Goodluck" card in 2017.

Now, x - 20% of x=360

⇒ x - 20/100 × x = 360

⇒ x - 0.2x = 360

⇒ 0.8x = 360

⇒ x = 360/0.8

⇒ x = 450

Therefore, Ed’s profit on “Good Luck” cards in 2017 is $450.

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"Your question is incomplete, probably the complete question/missing part is:"

Ed's profit on “Good Luck” cards in 2018 was £360.This was a decrease of 20% on his profit in 2017.Work out Ed's profit on “Good Luck” cards in 2017.

a) The probabilities are given as follows:

i) Exactly 2 green: 0.0479 = 4.79%.

ii) At most 3 blue: 0.2174 = 21.74%.

iii) Between 8 and 12 red: 0.6926 = 69.26%.

b) The binomial distribution is not used as there is not a fixed number of trials, and also the trials are not independent, as there is no replacement.

The mass probability formula, giving the probability of x successes, is of:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are given by:

The parameter n is dependent of the sample size of 25, hence:

n = 25.

For item i, the probability is of P(X = 2) with p = 88/400 = 0.22, hence, using the binomial distribution, it is of:

0.0479 = 4.79%.

For item ii, the probability is of P(X <= 3) with p = 60/400 = 0.15, hence, using the binomial distribution, it is of:

0.2174 = 21.74%.

For item iii, the probability is of P(8 <= X <= 12), with p = 160/400 = 0.4, hence the probability is of:

0.6926 = 69.26%.

For problem b, the binomial distribution cannot be used, as:

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Answer:

9q+7

Step-by-step explanation:

1. Add 6q+3q, which is 9q

2. Then add 2+5, which is 7

3. Then combine those answers and you get a final answer of 9q+7

Answer:

9q+7

Step-by-step explanation:

1. Group all like terms: 6q+3q  and 2+5

2. Add the like terms together. 6q+3q= 9q.         2+5=7

3. Rewrite the equation 9q+7

ANSWER : 9q+7

Answer:

Step-by-step explanation:

Vector:

AB = { 2 - 5;  7 - 3;  -1  - (-1) } = { -3; 4; 0 }

Vector modulus:

| AB | =  √ ( (-3)² + 4² + 0² ) = √ (9 + 16 + 0 ) = √ 25 = 5

Unit vector:

U = -(3/5)·i + (4/5)·j + 0/5·k

U = -(3/5)·i + (4/5)·j

The image of (-8, 7) after dilation by a scale factor of 1/3 centered at the origin is : (-8/3, 7/3)

Given point P (-8, 7)

The point is dilated by a scale factor of 1/3 centered at the origin is equivalent to multiplying the point by 1/3 for both the co-ordinates.

Therefore, the new point is given by :

P' = (-8×(1/3), (7)×(1/3))

P' = (-8/3, 7/3)

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The given expression √3x²+√4x is defined for x > 0

By property |f(x)| < c

⇒ f(x) < 0   and  - f(x) < 0

⇒√3x²+√4x < 0 and -(√3x²+√4x) < 0

⇒ x < -√4/3   and  x < -√4/3

Therefore x should be greater than 0.

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Answer:

Step-by-step explanation:

Assuming that a linear function can be in all different directions, but remain straight. It might be B. Because the answer shows (0,-1) and the other solutions don't have a y-intercept with a 0 x-intercept...?

The two relationships between the two triangles QRS and TUV is that they are similar triangles.

Option b is correct.

What is a similar triangle?

If two triangles have an equal number of corresponding sides and an equal number of corresponding angles, then they are comparable.

Similar figures are described as items with the same shape but varying sizes, such as two or more figures. The polygon with three sides is a triangle. The prerequisites for a triangle's resemblance are that the corresponding angles on both triangles must be identical, and the corresponding sides must be proportional to one another.

In the given question, we have:

The two triangles: QRS and TUV;

and we have the measure of the angles;

∠Q = 76°

∠R = 26°

∠S = 76°

∠T = 76°

∠U = 26°

∠V = 76°

and the sides measure:

RQ = 4cm;

RS  = 2cm;

SR = 4cm;

UT = 12cm;

TV = 6cm;

UV = 12cm;

So, when we find the proportion of the corresponding sides, we get:

The ratio of sides is as [tex]\frac{1}{2}[/tex];

and all the corresponding angles are equal;

So, we can say that the two triangles are similar;

Hence, The two triangles are similar;

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The length of the curve is 2.0036.

The equation of the curve is y = e^(x). The interval is 0 ≤ x ≤ 1. A curve is a smoothly drawn figure or line in a plane that has a bend or twist in it. A curve is defined as a continuous and smooth flowing line with no sudden twists. A curve is an abstract concept in mathematics that describes the path of a continuously moving point. The arc length of a curve y = f(x) in the increasing interval from a to b is given below.

[tex]L = \int\limits^a_b {\sqrt[]{ 1 + (\frac{dy}{dx})^{2}} \, dx[/tex]

dy/dx = d(e^x)/dx = e^x

(dy/dx)² = e^(2x)

The length of the given curve is calculated below.

[tex]L = \int\limits^1_0 {\sqrt[]{ 1 + e^{2x}}, dx[/tex]

L = [√(1+e^2x) + (1/2)ln(√(1+e^2x) - 1) - (1/2)ln(1 + √(1+e^2x))] from limits 0 to 1.

L = [√(1+e²) + (1/2)ln(√(1+e²) - 1) - (1/2)ln(1 + √(1+e²))] - [√(1+1) + (1/2)ln(√(1+1) - 1) - (1/2)ln(1 + √(1+1))]

L = [√(1+e²) + (1/2)ln(√(1+e²) - 1) - (1/2)ln(1 + √(1+e²))] - [√2 + (1/2)ln(√2 - 1) - (1/2)ln(1 + √2)]

L ≈ 2.0036

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Answer:

20 sections per friend

Step-by-step explanation:

First find the total number of sections

5 * 12 = 60 sections

Divide by 3 friends

60/3 = 20

20 sections per friend

The elements of (OUR)', (O∩R)', and O∩R will be {23, 29}, {22, 23, 24, 26, 28, 29, 30}, and {null}, respectively.

Sets are groups of clearly specified components. The number of items in a finite set is denoted by a curly bracket.

O and R are the subsets of a Universal set, U, such that

U = {22,23,24,25,26,27,28,29,30}

O = {prime numbers} = {23, 29}

R = {even numbers} = {22, 24, 26, 28, 30}

The elements of (OUR)' will be given as,

(OUR)' = {23, 29}

The elements of (O∩R)' will be given as,

(O∩R)' = {22, 23, 24, 26, 28, 29, 30}

The elements of O∩R will be given as,

O∩R = 0

The elements of (OUR)', (O∩R)', and O∩R will be {23, 29}, {22, 23, 24, 26, 28, 29, 30}, and {null}, respectively.

The Venn diagram is given below.

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