solve the following simultaneous equations
y=3x-1
x2 +y² = 73

A perpendicular bisector is a bisector to a line segment which makes an angle of 90° with the line segment.

A perpendicular bisector is usually constructed by using a compass and a straightedge. It can also be constructed using a protractor.

Construction of perpendicular bisector using a compass and straightedge.

Thus we get the perpendicular bisector.

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Answer:

y = log4x

Step-by-step explanation:

By excluding (10, 15), a better description can be given for the data set. The correct option is C.

A scatter plot is a particular kind of plot or mathematical diagram that displays values for typically two variables for a collection of data. It uses Cartesian coordinates. A second variable can be shown if the points are coded.

Overall, this data seems to suggest a decreasing trend.  The value (10, 15) is an outlier; if we remove it, the trend appears to be stronger.  Thus if we exclude this value we can give a better description of the data set.

The missing image is attached with the answer below.

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The equation of the line passing through the point ( -2, 7) and the given slope 2 is y = 2x + 11.

As given in the question,

Required line passes through the points :

( x₁ ,y₁ ) = ( -2 , 7 )

And the slope of the line is equal to 2

Standard form of the equation of the line is :

( y - y₁ ) / ( x - x₁ ) = ( y₂ - y₁ ) / ( x₂ - x₁ )

Here slope =  ( y₂ - y₁ ) / ( x₂ - x₁ )

                   = 2

Required equation of the line with given point and the slope is:

( y - 7 ) / ( x -(-2)) = 2

⇒ ( y - 7 ) / ( x + 2 ) = 2

⇒ ( y - 7 ) = 2 ( x + 2 )

⇒ y - 7 = 2x + 4

⇒ y = 2x + 11.

Therefore, the required equation of the line passing through the given point ( -2 , 7 ) and the slope 2 is equal to y = 2x + 11.

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The value of x=2x-10

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Answer:

i think you forgot to write the equations

Their ages are determined using the replacement approach.

The age gap between Joy and her brother is ten years.

It is an equation system in which one is always the highest power of the variable. a figure with only one dimension and no width. It consists of an endless number of parallel points.

Joy and her brother are a combined age of 24, making them.

Three years older than double Joy's age is her brother.

a disparity in ages between Joy and her brother.

Let x be the age of Joy, and y be the age of her brother.

then in accordance with the first requirement.

x + y = 24 .

(1)\s2x + 3 = y .

The resolution of equations 1 and 2. We obtain x = 7 and y = 2x + 3 y = 17, respectively.

The age gap between Joy and her brother is the next point.

y - x = 17 - 7 = 10

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Using the foci and co-vertices, the equation of ellipse is  (x^2/9) + (y^2/9) = 1

An ellipse is defined as the set of all points such that the sum of the distances from the foci to the point is constant. The distance between the foci is 2*c, where c is the distance from the center to either focus.

Given that the foci are at (0, ±3) and the co-vertices are at (±3, 0), we know that the center of the ellipse is at (0, 0) and the distance between the foci is 2c

So the equation of the ellipse with foci at (0, ±3) and co-vertices at (±3, 0) can be written as:

(x²/3²) + (y²/b²) = 1

Where a = 3, b = 9

So, the equation of the ellipse is (x^2/9) + (y^2/9) = 1

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The pair of linear equations 3x + 4y + 5 = 0 and 12x + 16y + 15 = 0. So this pair of equations have no solution.

Given the equation

3x + 4y + 5 = 0

12x + 16y + 15 = 0

Here, a₁ = 3, b₁ = 4, c₁ = 5

         a₂ = 12, b₂ = 16, c₂ = 15

Therefore,

[tex]\begin{aligned} \frac{a_1}{a_2} & = \frac{3}{12} = \frac{1}{4} \\ \frac{b_1}{b_2} & = \frac{4}{16} = \frac{1}{4} \\ \frac{c_1}{c_2} & = \frac{5}{15} = \frac{1}{3} \end{aligned}[/tex]

[tex]\displaystyle \frac{a_1}{a_2} = \frac{b_1}{b_2} \neq \frac{c_1}{c_2}[/tex]

So, the given pair of linear equations are parallel lines and hence will have no solution.

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Perpendicular lines are lines that intersect at a right (90 degrees) angle.

A right angle is one that is 90 degrees in length. It is the most frequently encountered angle in our daily lives. It can be noticed in room corners, box edges, mobile phone screens, and so on.

A square's and a rectangle's sides always make a right angle with each other. It is represented in radians as /2.

The angle formed by two lines that are perpendicular to each other is called a right angle. A right angle is equal to 90° and is in the shape of the letter "L". In the following figure, ray AB and BC form a right angle ABC.

Thus, Perpendicular lines are lines that intersect at a right (90 degrees) angle.

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the properties of quadratic equations in the form x² K are described below.

The equation of the second degree is a quadratic equation. This indicates that it contains a phrase that is squared, at least once. ax² + bx + c = 0, which uses constants or numerical coefficients for the variables a, b, and c, is one of the classic formulae for solving quadratic equations. Unknown variable 'x' is used here. For an equation to have equal roots the value of the discriminant is 0. The discriminant of a quadratic equation ax² + bx + c = 0 is given by the formula.

Properties are:

1. If k > 0. then x² = k has two real solutions or roots : x= (+)ve k.

2. If k = 0, then x' = k has one real solution or root: x = 0

3. If k < 0, then x = k has no real solutions or roots.

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Using the concept of proportions and similar triangle, the value of x is 11

A similar triangle is a triangle that has the same shape as another triangle, but not necessarily the same size. Two triangles are similar if and only if their corresponding angles are equal and the ratios of their corresponding sides are equal.

The Similar Triangles Theorem states that if two triangles have corresponding angles that are congruent, then their corresponding sides are in proportion. In other words, if two triangles have the same shape, the ratio of any pair of corresponding sides is always the same.

In this problem, we can use the concept of proportions to determine the value of x

6 / (48 + 6) = 5 / ( 5 + 3x + 7)

6 / 54 = 5 / 3x + 12

Cross multiply both sides and solve for x

6(3x + 12) = 54 * 5

18x + 72 = 270

18x = 270 - 72

18x = 198

x = 11

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Combining like terms to simplify the expression 10x + x + 8 will be 11x + 8.

An expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. In this case, it is vital to note that they have at least two terms which have to be related by through an operator. Some of the mathematical operations that are illustrated in this case include addition, subtraction, etc.

In this case, combining like terms to simplify the expression 10x + x + 8 will be:

= 10x + x + 8

= 11x + 8

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Complete question

If possible combine like terms to simplify the following expression.

10x + x + 8

The reason behind the name of parent function is the simplest function that still satisfies the definition of a certain type of function.

The term function is known as the special relationship where each input has a single output.

Here we need to define the reason behind the name of parent function.

Basically the term parent function is known as each member of a family of functions is related to its simpler, or most basic, function sharing the same characteristics.

Here the function is also called the parent function and it includes some of the basic characteristics of linear, quadratic, square root, absolute value and reciprocal functions.

As we all know that a family of functions is a set of functions whose equations have a similar form where as the parent function of the family is the equation in the family with the simplest form.

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Answer:

$1020 for 30 books

Step-by-step explanation:

We know

$1020 = 30 books

$34 = 1 book

$1725 = 50 books

$34.50 = 1 books

So, $1020 for 30 books is better

Answer: 1020 for 30 books is a better value

Step-by-step explanation: 1020 divided by 30 is 34 and 1725 divided by 50 is 34.5. When doing these kind of division questions, remember that money always goes on the numerator (top)

Answer:

18 centimeters

Step-by-step explanation:

3 x 3 x 2 x 1 = 18

hope you paas your quiz or test <3

On simplifying the equation (x + 10)² = 256 the dimensions of the original photo is obtained as 6 inches by 6 inches.

What is an equation?

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").

The measure of side of original square photo is x.

The square photo is enlarged by adding 10 inches to it = x + 10

The area of the enlarged square photo is 256 in².

The formula for area of a square is = (side)²

So, the equation to find the side of original photo is -

(x + 10)² = 256

Apply the formula (a + b)² = (a² + 2ab + b²) on the left hand side -

x² + 20x + 100 = 256

x² + 20x + 100 - 256 = 0

x² + 20x - 156 = 0

Factorize the quadratic equation to find the value of x -

x² + 20x - 156 = 0

x² + 26x - 6x - 156 = 0

x(x + 26) - 6(x + 26) = 0

(x + 26) (x - 6)

x = -26, x = 6

Since the side of the square photo cannot be negative, so x = 6 is the correct answer.

The sides of the square are same.

Therefore, the original photo had measurements 6 inches by 6 inches.

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Answer:

B

Step-by-step explanation:

Isosceles has two of the same lengths

Isosceles is also an acute angle, since the angles are less than 90 degrees.

Hope this helped!

The linear equations derived are:

y= 2x-4 ..................................1)

y=5x+3......................................2)

The slope and y-intercept of a linear equation in two variables are two important characteristics of the equation that can be used to graph the equation on a two-dimensional coordinate system.

The slope of a linear equation in the form of y = mx + b is represented by the coefficient of x, which is m. The slope tells us the steepness of the line and the direction it is moving. If m is positive, the line slopes upward to the right, if m is negative, the line slopes downward to the right.

The y-intercept of a linear equation in the form of y = mx + b is represented by the constant term b. The y-intercept is the point where the line crosses the y-axis. It can be found by setting x=0 and solving for y.

On comparing the equations with the general equation of linear equation in two variables we get:

m1=2 and b1=-4

m2=5 and b2=3

Therefore, The linear equations derived are:

y= 2x-4 ..................................1)

y=5x+3......................................2)

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Dalisay hits the Target more than Kendra hits the target.

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

Kendra hits the target 3 times for every 5 misses,

And, Dalisay hits the target 5 times for every 7 misses.

Hence, The rate of hits the target by Kendra is,

⇒ 3/5

⇒ 0.6 times per misses

And, The rate of hits the target by Dalisay is,

⇒ 5/7

⇒ 0.7 times per misses

Hence, Dalisay hits the Target More.

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The formula for quotient of a function is quotient of functions (fg)(x) ( f g ) ( x ) is found by dividing f(x) by g(x) . That is, (fg)(x)=f(x)g(x) ( f g ) ( x ) = f ( x ) g ( x ) .

The Quotient Rule is a technique for figuring out a function's derivative (differentiation) as the ratio of two differentiable functions. It is a formal rule used to issues involving differentiation where one function is split in half by another function.

The quotient is the result of dividing two numbers by each other. As in the case of 8 4 = 2, when the division produced the number 2, the outcome is the quotient. The dividend is 8 and the divisor is 4.

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In graphs, The minutes are shown on the x axis. The water depth is shown on the y axis (inches) Therefore, the depth of the water lowers with increasing minutes. Consequently, there is a change in water depth every minute

Mathematicians use graphs to logically convey facts or values using visual representations or charts. A graph point will typically reflect a relationship between two or more things. Nodes, or vertices, and edges make form a graph, a non-linear data structure. Glue together the nodes, often referred to as vertices. This graph has vertices V=1, 2, 3, 5, and edges E=1, 2, 1, 3, 2, 4, and (2.5), (3.5). (4.5). Statistical charts (bar charts, pie charts, line charts, etc.) graphical representations of exponential growth. a logarithmic graph in the shape of a triangle

The graph shows the depth of water in a bathtub as water drains out.

The graph shows that as the value of x increases, the value of y decreases.

The minutes are shown on the x axis.

The water depth is shown on the y axis (inches)

Therefore, the depth of the water lowers with increasing minutes.

Consequently, there is a change in water depth every minute.

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The additive inverse of the polynomial is [tex]9xy^2 -6x^2y +5x^3[/tex]

Now, According to the question:

Let's know:

What is Additive inverse of the polynomial?

Additive inverse means changing the sign of the number and adding it to the original number to get an answer equal to 0.

Hence, for the given polynomial; [tex](-9xy^2 + 6x^2y -5x^3)[/tex] .

The additive inverse is; -1 ×[tex](-9xy^2 + 6x^2y -5x^3)[/tex]

Therefore;

The additive inverse of the polynomial is [tex]9xy^2 -6x^2y +5x^3[/tex]

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For this repeated subtraction statement, type a division sentence.

24 - y - y - y - y - y = 0 is 24 divided by y or 24÷y

This is a series of subtractions. You keep subtracting y until you get to zero.

Every reduction is a group of y.

Division is essentially just a series of subtractions.

Dividends can be resolved by "subtracting" or crossing off groups of the same size from the total in the visual model until nothing is left. Examples demonstrate how division problems can be resolved by consistently removing the same number (the divisor). In many cases, it is actually simpler to add than to remove. To calculate the dividend, you must first determine how many times to add the number (the divisor).

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Answer:

  3

Step-by-step explanation:

Given that installing 6 apps increases the Eric : Ian app ratio from 3:4 to 5:4, you want to know how many more apps Ian needs to install to have the same number as Eric.

We note that the number of apps representing Ian's apps remains at 4 in both ratios, but increasing Eric's apps by 6 changes his number of ratio units from 3 to 5, a change of 2 ratio units. That is, each ratio unit represents 3 apps.

Eric now has 1 more ratio unit (5) than Ian (4), so Ian needs to increase his number by 1 ratio unit, or 3 apps.

Ian must install 3 apps to have the same number as Eric.

__

Additional comment

To see how many actual apps we're talking about, multiply the ratios by 3. The initial Eric : Ian app ratio was 9 : 12. After Eric installed 6, it became (9+6) : 12 = 15 : 12. So, Ian needs to install 15-12 = 3 apps to have as many as Eric.

Answer:

C) 4 3/4

Step-by-step explanation:

If you're having trouble with fractions, just convert to decimal

53.5 - 48.75 = 4.75 or 4 3/4

[tex](\stackrel{x_1}{6}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{7}~,~\stackrel{y_2}{7}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{7}-\stackrel{y1}{5}}}{\underset{\textit{\large run}} {\underset{x_2}{7}-\underset{x_1}{6}}} \implies \cfrac{ 2 }{ 1 } \implies 2[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{5}=\stackrel{m}{ 2}(x-\stackrel{x_1}{6}) \\\\\\ y-5=2x-12\implies {\Large \begin{array}{llll} y=2x-7 \end{array}}[/tex]

Answer:

Step-by-step explanation:

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