The area of a rectangular outdoor stage has been extended on one side. The entire new area in square meters can be written
as 216+ 12x. Factor the expression to find the dimensions of the extended stage.
The factored expression is (blank)
(Factor completely.)

Functions f(x) = x² + 1 and g(x) = x – 4, the value equivalent  to f(g(10)) is, 37

Function is a relation between a set of inputs and a set of outputs which are permissible. In a function, for particular values of x we will get only a single image in y. It is denoted by f(x).

Vertical line test:-

Whenever we want to check whether a given expression is a function or not we can apply a vertical line test, in this test we check for a single image of x , we are getting a single image or more.

If we get more images then it will not be a function.

For example, let us take, y² = 4ax

y = ±√4ax

For single value of x we get two values of y

Hence, it will not be a function.

Given that,

f(x) = x² + 1

g(x) = x – 4

f(g(10)) = ?

f(g(x))  =  (x - 4)² + 1

           =  x² - 8x + 16 +1

           =   x² - 8x + 17

f(g(10)) =  10² - 8×10 + 17

            = 100 - 80 + 17

            = 37

The value of  f(g(10)) is 37

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Answer: No

Step-by-step explanation:

No, the student is not correct because you can still combine the 6x and the 2x, which gets you to 8x + 1 as the most simplified form.

Philip should consider grilling hamburgers and hotdogs as the main options for the picnic.

Based on the survey results, it appears that the most popular food choices among those surveyed are hamburgers and hotdogs. The survey results show that 5 out of 10 people selected hamburger as their preferred food choice, and 2 out of 10 people selected hotdogs.

Chicken hamburger was also mentioned once. It is unclear from the given information what "brought" or "worst" refer to, as they are not specific food items.

In , Philip should put a lot of thought into the menu, the timing, the preparation and the safety aspects of the grilling to make sure that the picnic is a success and that everyone is happy with the food.

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Typically, you could just apply the equations x = r(cos(degrees °)), y = r(sin(degrees °)) to obtain the x, y coordinates on a circle with a known radius and angle.

Three angles in parallel lines facts—alternate angles, co-Interior angles, and matching angles—are used to accomplish this. often referred to as "Z angles." known as "C angles" at times.

The slope-intercept form of a straight line is represented by the equation y = mx + b. In this instance, the points' coordinates are x and y, the gradient is m, and the y-axis' intercept is b.

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there is no solution in the given equation  |3x| + 3 < 2.

In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign ()" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than.

Given an inequality, in the variable of x is |3x| + 3 < 2

Simplifying the given equation

|3x| + 3 < 2

=> |3x| + 3 -3 < 2 - 3

=>  |3x| < -1

Since the Value of the mode cannot be negative thus this is a contradictory statement.

Therefore, the given equation has no solutions.

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Answer: −1/4

I used a calculator so I'm 90% sure this is the awnser.

The height of the building, h, found using ratios between similar figures and within similar figures is as follows;

1. The scale factor, r = 17/6

The height of the building is 99 1/6 meters

2. The within figure ratio is 35/60 = h/170

Heiught of the building is 99 1/6 meters

3. The between figure ratio is 35/h = 60/170

Height of the building is 99 1/6 meters

4. The measure of the angle at the top of the building is 60°

Similar triangles are triangles that have corresponding sides that are proportional, such that the sides of each triangle are a constant multiple of the sides of the other.

The distance from the flagpole = 60 meters

Height of the flagpole = 35 meters

The distance from the building = 170 meters

1. The height of the building found using a scale factor is as follows;

The scale factor, s.f. is the know ratio of the distance from the building to the distance from the flagpole

Therefore; s.f. 170/60 = 17/6

The height of the flagpole is 35 meters

Height of the building = Height of the flagpole × Scale factor

Height of the building = 35 m × 17/6 = 99 1/6

The height of the building found using scale factors is 99 1/6 meters

3. The height of the building found using ratios within the two triangles is found as follows;

The triangles are similar, therefore, their interior angles are congruent, and the trigonometric ratios of the angles are the same.

Within the two triangles, we get;

[tex]\frac{Height \ of \ flagpole}{Distance \ from \ flagpole} = \frac{Height \ of \ building}{Disrtance \ from \ building}[/tex]

35/60 = h/170

h = 170 × (35/60) = 99 1/6

Height of the building = 99 1/6 meters

3. The triangles formed with the flagpole and the triangle formed with the building are similar triangles, therefore;

Between the two triangles, we get

[tex]\frac{Height \ of \ the \ flag[pole}{Height \ of \ the \ building } =\frac{Distance \ from \ the \ flagpole}{Distance \ from \ the \ building}[/tex]

Plugging in the known values, we get;

[tex]\frac{35}{Height \ of \ the \ building} = \frac{60}{170}[/tex]

Height of the building = 35 × 170/60 = 99 1/6

The height of the building is about 99 1/6 meters

4, The triangle formed by the flagpole and the building are similar, therefore, the corresponding angles in the triangles are congruent

The angle at the top of the flagpole corresponds with the angle at the top of the building, therefore;

The angle formed at the top of the flagpole is congruent to the angle formed at the top of the building

The measure of corresponding angles are the same, therefore, the anglle at the top of the building is equal to the angle at the flagpole, which is 60°

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The range of values that we are permitted to enter into our function is known as the domain of a function.

The collection of values that can be plugged into a function's domain are called its parameters. The x values for a function like f are contained in this collection (x). The collection of numbers that the function assumes is known as its range.

The entire range of independent variable values that can exist is referred to as a function's domain.

Let y = f(x) represent a function where x and y are independent variables. The chosen x-value is said to fall within the domain of f if a function f offers a means of effectively producing a single value y while using a value for x to that end.

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35% discount.

To calculate the price after the 35% discount is applied, you would multiply $275.00 by 0.35, which would give you $96.25. Then you would subtract that amount from $275.00, so the final price would be $178.75.

To calculate the price after the 25% and 10% discounts are applied, you would first multiply $275.00 by 0.25, which would give you $68.75. Then you would subtract that amount from $275.00, leaving you with $206.25. Next, you would multiply $206.25 by 0.10, which would give you $20.625. You would then subtract that amount from $206.25, so the final price would be $185.625

In this case, the 35% discount would save the customer $96.25 and the series of discounts would save the customer $89.375. So the better deal is the 35% discount

The angle between Point B and Point A is 0-45° below the horizontal.

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Answer: a. The mode of the data set is the most frequently occurring value. From the results, the most frequent sum is 7, which occurs 6 times. Therefore, the mode of the data set is 7.

b. To find the median, we need to arrange the data set in numerical order. The median is the middle value of the data set. Since the data set has 36 values, and 36 is an even number, the median will be the average of the 18th and 19th values in the ordered data set.

c. The mean of a data set is found by adding all the values and dividing by the number of values. To find the mean of this data set, we add up all the sums (2+3+4+...+12) and divide by 36.

d. The range is the difference between the largest and smallest values in a data set. In this case, the largest sum is 12 and the smallest sum is 2, so the range is 12-2 = 10

Please note that this is a simulation, if you want real results you should collect the data by throwing the dice 36 times and record the scores.

Step-by-step explanation:

A quadratic function is one that has the formula f(x) = ax² + bx + c, where a, b, and c are all integers with a not equal to zero.

To choose the parabola equation that best fits a collection of data, a statistical method known as quadratic regression is performed. To get the equation of the straight line that best fits a collection of data, this sort of regression is an extension of simple linear regression.

Using a collection of data with a parabola-like form, quadratic regression seeks the best-fitting equation. Making a scatter plot is the initial stage in regression.

A quadratic function is one that has the formula f(x) = ax² + bx + c, where a, b, and c are all integers with a not equal to zero. A parabola is the shape that makes up the graph of a quadratic function. If a parabola opens up.

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The value of function f (m + 1) is,

⇒ f (m + 1) = 1 - 3m

A relation between a set of inputs having one output each is called a function.

Given that;

The value of function are,

⇒ f(x) = 4 - 3x

⇒ g(x) = 2x² - 3x + 1

Now, To find the value of f (m + 1), we can substitute the value of x = m + 1 in equation (i), we get;

⇒ f (x) = 4 - 3x

⇒ f (m + 1) = 4 - 3 (m + 1)

⇒ f (m + 1) = 4 - 3m - 3

⇒ f (m + 1) = 1 - 3m

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the given sides WX = XY.

What is congruent of the triangle?

The shapes maintain their equality regardless of how they are turned, flipped, or rotated before being cut out and stacked. We'll see that they'll be placed entirely on top of one another and will superimpose one another. Due to their identical radius and ability to be positioned directly on top of one another, the following circles are considered to be congruent.

Any two figures can be perfectly positioned over one another to demonstrate their congruence. The relationship between two figures that are said to be congruent is described using the word "congruence."

In given ΔXWZ AND XYZ

xz IS common

∠XZW = ∠XZY

ZW=ZY

So, the ΔXWZ and ΔXYZ are congurant.

Hence, the given sides WX = XY.

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According to the lowest percentages available, 1/3 of people surveyed plant gardens.

Explanation:

891/297  = 3.

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On solving the provided question we can say that so SAS, the are congruent triangles

A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.

here,

we have to triangles

with angles as 30,60,90 and 60,60,90 respectively

and 2 sides of 7 cm each.

so SAS, the are congruent triangles

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The solution to the nonlinear system of equations is:

X = ±√(6x)

Y = ±√(6-x)

What is a nonlinear system of equations?

A system of nonlinear equations is a system of two or more equations in two or more variables containing at least one equation that is not linear. Recall that a linear equation can take the form Ax+By+C=0. Any equation that cannot be written in this form is nonlinear.

There are different methods to solve nonlinear systems of equations, but one common way is to use substitution or elimination.

Using substitution:

We can substitute the equation Y^2=6-x into the second equation, to get:

X^2 + (6-x)^2 = 36

Expanding the square and simplifying, we get:

X^2 + 36 - 12x + x^2 = 36

Combining like terms, we get:

X^2 + x^2 - 12x + 36 = 0

Rearranging, we get:

(X^2 + x^2 - 12x) + 36 = 0

Factoring out (X^2 + x^2 - 12x) = 0

Solving for X^2 + x^2 - 12x = 0 using the quadratic formula, we get:

X = ±√(6x)

Substituting this back into the first equation, we get:

Y = ±√(6-x)

So the solution to the nonlinear system of equations is:

X = ±√(6x)

Y = ±√(6-x)

This means that there are four possible solutions, represented by the four points:

(√6, √6)

(-√6, -√6)

(√6, -√6)

(-√6, √6)

Hence, the solution to the nonlinear system of equations is:

X = ±√(6x)

Y = ±√(6-x)

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The measure of the given angles are -

m∠1 = 80°

m∠2 = 10°

Two angles are called complementary when their measures add to 90 degrees.

Given is a complementary angles pair as shown.

We can write -

∠1 + ∠2 = 90

x + (11x - 30) = 90

12x - 30 = 90

12x = 120

x = 10

m∠1 = 11x - 30 = 11 x 10 - 30 = 110 - 30 = 80°.

m∠1 = 80°

m∠2 = x = 10°.

m∠2 = 10°

Therefore, the measure of the given angles are -

m∠1 = 80°

m∠2 = 10°

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Two parallel lines, known as axes—pronounced "ax-eez"—in a coordinate grid are labeled as number lines. Usually referred to as the x-axis, the horizontal axis. Commonly known as the y-axis, the vertical axis.

The Complete Question.

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The count of numbers which would be written from 30 to 36 with both numbers inclusive is infinite.

It follows from the task content that the total count of numbers from 30 to 65 including both numbers is to be determined.

By careful consideration, the numbers which fall between 30 and 65 on the number line are not limited to integers and hence, the count of all numbers between 30 and 65 as required is infinite.

However, if only integers (whole numbers) are to be considered, it follows that the count of all numbers from 30 to 65 including 30 and 65 is; 36.

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Step-by-step explanation:

the solution is their intersection point. it means that at this point they are equal, they share the same "behavior".

so,

one solution at (2, -1)

p+5 is the  algebraic expression for 5 plus a number p

An expression is combination of variables, numbers and operators.

The given sentence is 5 plus a number p

In the given sentence the number p is a variable.

variable is a symbol used to represent a number.

algebraic expression for 5 plus a number p

p+5

Hence, p+5 is the  algebraic expression for 5 plus a number p

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According to triangle proportionality theorem:If a line parallel to one side of a triangle intersects the other two sides of the triangle, then the line divides these two sides proportionally.

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To get system B, the second equation in system A was replaced by the sum of that equation and the first equation multiplied by -3. The solution to system B will be the same as the solution to system A.

What is Linear equation ?

Linear equation can be defined as the equation in which the highest degree is one.

First equation of system A multiplied by -3:

(-3)(x+6y=5)

(-3)(x)+(-3)(6)=(-3)(5)

-3x-18=-15

Sum of the second equation of system A and the first equation multiplied by -3:

(-3x-18)+(3x-7y)=(-15)+(-35)

-3x-18+3x-7y=-15-35

-25y=-50

System B

x+6y=5

-25y=-50

Hence,  To get system B, the second equation in system A was replaced by the sum of that equation and the first equation multiplied by -3. The solution to system B will be the same as the solution to system A.

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The entire expenditures for both children and adults are modelled using graphs and formulae. y = 1.25x + 10 y = 0.75x + 5 a.

The equation C(x)=mx+b represents a linear cost function, where mx stands for the variable cost, b for the fixed cost, and m for the marginal cost.

Admission is $10 for adults, and ride tickets cost $1.25; the line's a y-intercept value is 104.

Admission is $5 for children, and ride tickets cost $0.75 each. When X=0,Y=5, the line b's y-intercept is 54.

When X=20 for a child, y=0.75.20+5=20.

It crosses line 20 and 20.

When X=20 and Y=1.25, 20+10 equals 35 for an adult.

Line an is passed at (20, 35).

A linear model is described by the equation y=mx+b. The y denotes the result, the m denotes the rate of change, the x denotes the input, and the b denotes the constant.

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The required expression for the change in temperature would be final temperature = -39.1 - 72.3.

What is an expression?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

The temperature of water initially is = 72.3°F

The temperature of water after adding ice cubes is = -39.1°

To find the final temperature use the expression -

Final temperature = change in temperature - initial temperature -

Final temperature = -39.1 - 72.3

Rewriting as a sum = -39.1 + (-72.3)

-39.1 + (-72.3)

-39.1 - 72.3

-111.4

Therefore, the change in temperature is = -111.4°F.

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On solving the provided question we cans ay that addition equation that will have a proof drawing with a new ten and a new hundred -  10x +100x + 1000x+ 10000+ 100000x+ ...= 0

An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.

addition equation that will have a proof drawing with a new ten and a new hundred -

10x +100x + 1000x+ 10000+ 100000x+ ...= 0

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An exponential function is one that has the generic formula y = abx, where a 0, b a positive real number, and b 1. Base b is always the same for exponential functions. In a situation where the set of real numbers is the domain, the exponent x is the independent variable.

4x = 40.5 = 2

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