Find the equation of the line that goes through ( 0, 2 ) and ( 3, 4 ).

Answer:

x = 16±2√94 over 3

Step-by-step explanation:

Move terms to the left side.

0 = -6x² + 64x + 80

- ( -6x²+64+80) = 0

Distribute

- ( - 6x²+64x+80) = 0

6x² - 64x - 80 = 0

Common factor

6x² - 64x - 80 = 0

2 (3x²-32x--40) = 0

Divide both sides by the same factor

2 (3x²-32x--40) = 0

3x² - 32x - 40 = 0

Use the quadratic formula (Not explainin this, I forgot this one.)

Simplify

1.Evaluate the exponet

2.Mulitply the numbers

3.Add the numbers

4.Evaluate the sqaure root

5.Mulitply the numbers(Do this 2 more times.)

x = 32±4√94 over 6

Separate the equations

to solve for the unknown varible, separate into two eqautions: one with a plus and another with a minus.

Solve

Rearrange and isolate the varible to find each solution.

Answer:

The two answers would be 0 and ln (7)

Step-by-step explanation:

Hope it helps:)

An undecidable problem is one that should have a "yes" or "no" answer but has no algorithm that can correctly answer on all inputs.

According to the theories of computational complexity and computability, an undecidable problem is one for which it has been demonstrated that it is impossible to create an algorithm that always yields the right yes-or-no response. As an illustration, it can be shown that there is no algorithm that can accurately predict whether arbitrary programmes will eventually halt when run.

Any question that is simply yes or no on an infinite list of inputs is a decision problem. It is customary to define the decision problem as the set of inputs for which the problem returns yes because of this. Natural numbers as well as values of other kinds, such as strings in a formal language, can be used as these inputs.

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Answer:

{x,y}={6,-2}

Step-by-step explanation:

System of Linear Equations entered :

[1]    3x + 5y = 8

  [2]    2x - 5y = 22

Solve by Substitution :

// Solve equation [2] for the variable  x

 [2]    2x = 5y + 22

 [2]    x = 5y/2 + 11

// Plug this in for variable  x  in equation [1]

  [1]    3•(5y/2+11) + 5y = 8

  [1]    25y/2 = -25

  [1]    25y = -50

// Solve equation [1] for the variable  y

  [1]    25y = - 50

[1]    y = - 2

// By now we know this much :

   x = 5y/2+11

   y = -2

// Use the  y  value to solve for  x

 x = (5/2)(-2)+11 = 6

Graphic Representation of the Equations :

The answer should be: {x,y}={6,-2}

The greatest poible value of b is (72-14)/(14-(-2))×(x+2)+14.

Possible value is the potential for something to have a particular outcome, result, or consequence. It is the amount of beneficial or desirable result that can be achieved, given the available resources. Possible value is often determined by assessing various factors such as cost, risk, and time. It is an important concept in economics, finance, and business, as it helps to identify the most beneficial course of action.

The greatest possible value of b is found by solving the equation of the line through A and B, which is y = (72-14)/(14-(-2))×(x+2)+14.

Setting the y-value to 0 and solving for x gives x = -14, which means b = 14. Therefore, the greatest possible value of b is 14.

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On [0,∞] the function grows, whereas on [-∞, 0], it shrinks. f has absolute minimum value is 0, and it also has the same relative minimum value (0,0).

On the graph, you are able to see a "open circle" at it when x< 0. (0, 0).

There consequently no absolute maximum value of f due to the graph's infinitely high y values.

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Answer:

Step-by-step explanation:

We know that : Percentage means 'divided by 100'

therefore, 1/2 percent = 1 / 2 ÷ 100 = 0.5 ÷100 = 5÷1000= 0.005

1

To find an unknown number we can use properties of equality.

Algebraic Method

Another word to describe an unknown number is "variable". For the equation, I will call this variable x. Any variable can be used, but x is the most common.

We can write an equation to describe the situation. The statement says that the product of 15 and x is 15. This means that 15 * x = 15. Now we can use algebra to solve this equation.

To find x, divide both sides by 15.

Identity Property of Multiplication

Additionally, if you know all the properties of equality, you can answer this question without doing any math. One of the properties of equality is the identity property of multiplication. The identity property states:

This means that any number multiplied by 1 is itself. So, since the factor and product are equal, the other factor must be 1. If you plug 15 in for a, you can see how this property applies to this situation.

After solving the equation: the nearest cent, the interest earned is $467.

Interest is a mathematical concept used to describe the cost or gain associated with the use of money over a period of time. It is usually expressed as a percentage rate of the principal (the amount borrowed or invested). Interest can be earned or paid, depending on the situation.

Using the formula B=p(1+r)t, John's final balance after 1 year is B = 4069(1+0.12)1 = $4,536.28.
The interest earned in 1 year is the difference between the final balance and the starting amount, which is $4,536.28 - $4,069 = $467.28. To the nearest cent, the interest earned is $467.

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Answer:

Step-by-step explanation:

the first equation we konw x=-2y-1,

then -2y-1=y+5

so, y = -2, x=3

Answer:

y = -2

x = 3

Step-by-step explanation:

y + 5 + 2y = -1 (substitute)

3y + 5 = -1        (Simplify)

3y = -6            (Get rid of 5)

y = -2                 (Divide)

x = -2 + 5         (plug in y)

x = 3                 (simplify)

hope this helps :)

Answer:

x=-3

y=10

Step-by-step explanation:

The function form of the given function would be  [tex]f(x)=log_b(x)[/tex].

What is a function?

In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.

The given function is f(x) = logbx.

So the function form would be the function of x is equal to the logarithmic of x having base b.

so this can be written as

       [tex]f(x)=log_b(x)[/tex]

Hence, the function form of the given function would be  [tex]f(x)=log_b(x)[/tex].

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The function form of the given function would be  [tex]f(x)=log_b(x)[/tex].

What is a function?

In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.

The given function is f(x) = logbx.

So the function form would be the function of x is equal to the logarithmic of x having base b.

so this can be written as

[tex]f(x)=log_b(x)[/tex]

Hence, the function form of the given function would be  [tex]f(x)=log_b(x)[/tex].

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36 square units make up the larger circle's surface area.

We can use the fact that the smaller circle is tangent to the larger circle and passes through its center to find the area of the larger circle. Since the radius of the smaller circle is tangent to the larger circle, the radius of the larger circle is double the radius of the smaller circle.

Let's call the radius of the smaller circle "r" and the radius of the larger circle "R". We know that R = 2r.

We know that the area of a circle is given by the formula A = πr^2.

We know that the area of the smaller circle is 9 square units, we can use this formula to find the radius:

A = πr^2 => r^2 = 9/π => r = sqrt(9/π)

Now we can use the formula of the area of a circle with R-value to get the area of the larger circle:

A = πR^2 => A = π(2r)^2 => A = 4πr^2 => A = 4π(9/π) => A = 36

So the area of the larger circle is 36 square units

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Answer: It is a straight line

Step-by-step explanation:

By using properties for angles we can find and solve some linear equations, there we can see that x = 30°.

Remember that the sum of the interior angles of a triangle must give 180°, and we also know that the angle defined by a line is 180°.

Let's define N as the angle located at vertex N of the right triangle in the left side, we then can write:

2x + 90° + N = 180°

And we also can write the linear equation:

105° + 45° + N = 180°

Solving this one, we can find the value of N.

N = 180° - 45° - 105°  =30°

N = 30°

Replacing that in the equation with x we will get:

2x + 90° + 30°  =180°

2x = 180° - 90° - 30°

2x = 60°

x = 60°/2 = 30°

The value of x is 30°.

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[tex]2(q+p)=1+5q\implies 2q+2p=1+5q\implies 2q+2p-5q=1 \\\\\\ 2q-5q=1-2p\implies q(2-5)=1-2p\implies -3q=-2p+1 \\\\\\ q=\cfrac{-2p + 1}{-3}\implies q=\cfrac{2}{3}p-\cfrac{1}{3}[/tex]

Answer:

Step-by-step explanation: 2(q+p)=1+5q

2q+2p=1+5q

2q-5q=1-2p

-3q=1-2p/:(-3)

q=-1/3+2/3 p

The constant of proportionality is 2

From the question, we have the following parameters that can be used in our computation:

1 scoop of ice cream = 1/2 cup of milk

5 scoops of ice cream = 2.5 cups of milk

The constant of proportionality (k) is then calculated as

k = Scoop of ice cream/Cup of milk

So, we have

k = 5/2.5

Evaluate

k = 2

In (a), we have:

k = 2

A proportional relationship is represented as

s = km

Where

s = scoop of ice cream

m = cup of milk

So, we have

s = 2m

In (b), we have

s = 2m

To graph the relationship, we start by generating a table of values and then plot the points

Recall that

s = 2m

So, we have

18 = 2m

Divide by 2

m = 9

Hence, the number of cups is 9

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Answer:

y = 1

Step-by-step explanation:

locate x = - 4 on the x- axis, go vertically up to meet the graph at (- 4, 1 ), so

when input x = - 4 the output is y = 1

The product of the two polynomials is (8x³)(4x⁷) = 32x¹⁰.

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Answer:

  24

Step-by-step explanation:

You want to know the number such that the triple of the number added to its half part is equal to the difference between four times the number and 12.

The given relation can be expressed in math symbols as ...

  3n +n/2 = 4n -12

Adding 12 -n/2, we get ...

  12 = n/2

  24 = n . . . . . multiply by 2

The number is 24.

To identify the solutions in solving linear inequalities in two variables, you can first graph the equation on a coordinate plane. Then, you can use the boundary line to identify which regions of the plane satisfy the inequality.

Any points in the shaded regions will be solutions to the inequality. Additionally, you can use the boundary line to identify the points that are not solutions by finding the points that lie on the boundary line.

Example:

x + 2y ≥ 4

The graph of this inequality is a line with a slope of -2/1 and a y-intercept of 4/2. The line will be shaded on the side of the line containing the greater values, which in this case is the side containing the origin.

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Answer: To divide two rational expressions, you need to first find the least common denominator (LCD) of the two expressions. The LCD is the least common multiple of the two denominators.

In this case, the rational expressions are x/(3x-1) and (x-2)/(2x). The LCD of these two expressions is (3x-1)(2x), which can be factored as 6x(x-1).

To divide the two rational expressions, you need to express each expression as a fraction with the LCD as the denominator.

The first expression, x/(3x-1), can be rewritten as (x * (2x))/(3x-1 * (2x)) = (2x^2)/(6x^2-2x).

The second expression, (x-2)/(2x), can be rewritten as ((x-2) * (3x-1))/(2x * (3x-1)) = (3x^2-3x+2)/(6x^2-2x).

To divide these two expressions, you can divide the numerators and the denominators separately:

(2x^2)/(6x^2-2x) ÷ (3x^2-3x+2)/(6x^2-2x)

= (2x^2) ÷ (3x^2-3x+2)

= (2/3)x^2 ÷ (x^2-x+2/3)

Therefore, the quotient of the rational expressions x/(3x-1) and (x-2)/(2x) is (2/3)

Step-by-step explanation:

We found that translations have the following three properties: line segments are taken to line segments of the same length;

angles are taken to angles of the same measure; and. lines are taken to lines and parallel lines are taken to parallel lines.

Properties of Translations

- Distance Where the lengths of the segments stay the same.

-Angle Measures These remain the same.

-Parallelism Where the parallel lines will stay parallel.

-Collinearity The points will stay on the same line.

-Orientation The order of the letters will stay the same.

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Answer: $52.57 for each basic yearbook and $153.5 for each deluxe yearbook

Step-by-step explanation:

First, do Mr. Boyer's class to find out how much each deluxe yearbook is:

2,763 ÷ 18 = $153.5

Then do, Mrs. Wu's class: First, multiply 153.5 by the 6 deluxe yearbooks ordered;

153.5 x 6 = 921

After, subtract 921 from 2,025:

2,025 - 921 = 1104

The remaining $1104 is the total cost of the 21 basic yearbooks ordered. Divide the total cost by the number of yearbooks ordered to find the unit price:

1104 ÷ 21 = 52.5714285714

Round to the nearest hundredth: $52.57

Please give brainliest

The angles and their relationships are -

a) ∠x = 135° (corresponding angles), ∠y = 135° (vertical angles)

b) ∠y = 45° (liner pair angles), ∠x (not enough information provided)

c) ∠x = 135° (corresponding angles), ∠y = 45° (liner pair angles)

d) ∠x = 45° (liner pair angles), ∠y (not enough information provided)

What is angle pair relationship?

In Geometry, there are five fundamental angle pair relationships:

Complementary Angles

Supplementary Angles

Adjacent Angles

Linear Pair

Vertical Angles

a) In the first diagram -

∠x = ∠a as they are both corresponding angles to each other.

So, ∠x = 135°.

Similarly, ∠y = ∠x as they both are vertically opposite angles to each other.

So, ∠y = 135°.

b) In the second diagram -

∠y + ∠a =180° as they are both form a linear pair of angles.

So, ∠y = 180° - ∠a

∠y = 180° - 135°

∠y = 45°.

Now, ∠x cannot be deduced and no proper information is given in the image.

c) In the third diagram -

∠x = ∠a as they are both corresponding angles to each other.

So, ∠x = 135°.

Now, ∠y + ∠x =180° as they are both form a linear pair of angles.

So, ∠y = 180° - ∠x

∠y = 180° - 135°

∠y = 45°.

d) In the fourth diagram -

∠x + ∠a =180° as they are both form a linear pair of angles.

So, ∠x = 180° - ∠a

∠x = 180° - 135°

∠x = 45°.

Now, ∠x cannot be deduced and no proper information is given in the image.

Therefore, all the angles are and their relationships are found.

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Answer:

A

Explanation:

A line graph is a unique type of graph which is used in statistical application which represents the change in a quantity with respect to another quantity.

The price of different flavors of chocolates varies which can be represented, these variation is plotted in a two-dimensional XY plane.

If the relation include two measures can be presented by using a straight line in a graph called as linear graphs or a linear graph.

There are different types of the line graph, Simple Line Graph refers to Only one line is plotted on the graph, Multiple Line Graph where More than one line plotted on the same set of axes.

Compound Line Graph refers to the information can be divided into two or more types of data and this line graph is called a compound line graph which can be drawn to show the component.

As a professional artist and judging from the current sales ratio and commission rates, one would earn more if one apprenticed for Sara.

As evident in the task content; the current ratio of Sara's sales to Ravi's sale is 100 : 2.

Since Sara's pieces of art sell for $25, the total earnings is; 25 × 100 = $2500.

Hence, since the commission rate is 60%, it follows that the commission earned on sales of Sara's pieces is; 60% of 2500 = 0.6 × 2500 = $1500.

Also, since Ravi's pieces each cost $2000, it follows that for 2 pieces, the total earnings is; 2 × $2000 = $4,000.

Hence, since the commission rate for Ravi's pieces is 25%, the commission earned is therefore; 25% of 4000 = 0.25 × 4000 = $1000.

On this note, one would earn more if one apprenticed for Sara.

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The equation is x + 0.3 = 9.124 and the value of x is 8.824.

The following is a linear equation in one variable. It can be expressed in the form of ax+b=0. Here a and b are integers and x is a variable that has only one solution. In these type of equations only one variable is present.

We can write an equation to find the score without the penalty by using the information provided. Let x be the score without the penalty. We know that the final score (with the penalty) is 9.124 and that the penalty is 0.3 points. Therefore, we can set up the equation:

x + 0.3 = 9.124

To find the score without the penalty, we need to subtract 0.3 from both sides of the equation:

x = 9.124 - 0.3

x = 8.824

So, the score without the penalty is 8.824

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Answer:

when pi = 3.14, A = 63.535

when pi = pi, A = 63.61725

Step-by-step explanation:

Area of a circle = pi × radius (4.5) squared (^2)