The lengths of two sides of a triangle are shown below:
Side 1: 3x² - 2x - 1
Side 2: 9x + 2x² - 3
The perimeter of the triangle is 5x³+4x2 - x - 3.
Part A: What is the total length of the two sides, 1 and 2, of the triangle? (4 points)
Part B: What is the length of the third side of the triangle? (4 points)
Part C: Do the answers for Part A and Part B show that the polynomials are closed under
addition and subtraction? Justify your answer. (2 points)
(10 points)

The fraction is evaluated to give -114/10

A fraction can be defined as the part of a whole variable, number or element.

There are some number of types of fractions, they include;

From the information, we have that;

12/3+3/4÷(−1/3)−1/2

These are a mixed of proper fractions and improper fractions

Now, expand the bracket, we have

12/3 + 3/4 ÷ -1/3 -1/2

Find the lowest common multiple

48 + 9 /12 ÷ -2 - 3 /6

Add or subtract the values

57/12  ÷ -5/6

Multiply by taking the inverse

57/12 × 6/-5

114/-10

Hence, the value is 114/-10

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Two triangles are congruent if and only if they have the same shape and size.

What is triangle ?

A triangle in which it is having three sides , three angles and the sum of three angles is always 180 degrees.

So, there are several ways to find out if two triangles are congruent, so we will study the triangles above to find the answers:

Case a. (AAS - Angle, Angle, Side)

AAS stands for "angle, angle, side" and means that we have two triangles where we know two angles and the non-included side are equal. So, for the figure above it is true that:

∠B = ∠E

∠A = ∠D

Case b. We don't have any information about this case that allows us to get a conclusion about congruence. Recall that for congruent triangles you need to compare three elements two by two.

Case c. (SSS - Side, Side, Side)

SSS stands for "side, side, side" and means that we have two triangles with all three sides equal. So, for the figure:

Case d.  We only have two equal elements, but it is necessary to have three elements for comparing them doing the comparison two by two. There is not enough information for getting a conclusion.

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Answer:

a(z+e)

Step-by-step explanation:

(a•z) + (a•e) can be rewritten as:

az + ae

as we can see from the newly created expression, a is the common multiple and we need to add a and z up.

So the answer is

a(z+e)

The solutions to both sets of simultaneous equations by graphical method are; No solution

There are three main ways to solve simultaneous linear equations and they are;

1) Elimination method

2) Substitution method

3) Graphical Method

In this question, we are using the graphical method where the solution will be the coordinate of the point of intersection.

1) The 2 simultaneous linear equations are;

y = ¹/₂x + 1

-2x + 4y = 4

The graph of these 2 equations is as attached.

From the first graph attached, we see that both lines overlap each other and as such don't have any point of intersection which tells us there is no solution to the simultaneous linear equations

2) The 2 simultaneous linear equations are;

y = -x - 3

y + x = 2

The graph of these 2 equations is as attached.

From the second graph attached, we see that both lines don't intersect each other and as such don't have any point of intersection which tells us there is no solution to the simultaneous linear equations

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The formula for the slope (also known as the "rise over run" or "gradient") of a line when given the coordinates of two points is:

m = (y2 - y1) / (x2 - x1)

Where (x1, y1) and (x2, y2) are the coordinates of the two points, and m is the slope of the line.

Note that the coordinates must be in a Cartesian coordinate system, and the points must be distinct, otherwise, the denominator (x2 - x1) will be zero and the division by zero is not defined.

For example, if you have two points (2, 4) and (6, 8), you can use the slope formula to find the slope of the line:

m = (8-4) / (6-2) = 4/4 = 1

The slope of the line is 1

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Answer:

12b+3=-2b-4

14b=-7

b=-1/2

Confirm?

-2(-1/2)-4 =-3

12(-1/2)+3=-3

Answer:

-27+17r

Step-by-step explanation:

[tex]3 + 4(r - 6) = 3(2 + 2r) + 7r \\ 3 + 4r - 24 = 6 + 6r + 7r \\ 3 - 6 - 24 + 4r + 6r + 7r \\ - 27 + 17r[/tex]

the formula for a circular diameter is 2r ( 2 times radius)

so 2*1=2

Answer: No, x^2 and 2x are not like terms. Like terms are terms that have the same variable raised to the same exponent. In this case, x^2 and 2x have the same variable, but they are raised to different exponents, so they are not like terms.

Terms can be added or subtracted together, but terms that are not like terms cannot be combined.

For example:

5x^2 and 2x^2 are like terms, so they can be added together (5x^2 + 2x^2 = 7x^2)

5x and 2x are like terms, so they can be added together (5x + 2x = 7x)

On the other hand:

5x^2 and 2x are not like terms, so they cannot be added together.

Step-by-step explanation:

227 18-inch cubes can fit inside the rectangular prism.

You may calculate how many 18-inch cubes can fit within a rectangular prism by dividing the rectangular prism's overall volume by the volume of a single 18-inch cube.

A rectangular prism's volume can be calculated using the formula length x width x height. In this instance, the dimensions are 312 inches long, 212 inches wide, and 3 inches high. As a result, the rectangular prism has a volume of 1,326,720 cubic inches (312 x 212 x 3).

A single 18-inch cube has a volume of 18 x 18 x 18 = 5832 cubic inches.

We divide the volume of the rectangular prism by the volume of a single 18-inch cube to get the number of 18-inch cubes that can fit inside: 1,326,720 / 5832 = 227.

Therefore, the rectangular prism can accommodate 227 18-inch cubes.

Please take note that this is an estimate and that there will not be enough room in the prism to fit 227 cubes exactly.

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The pair in the solution of the equation -2x + 3y = 6 is (0,2).

The set of all values that, when substituted for unknowns, make an equation true is known as the solution.

A specific location on the graph is the solution of a linear equation in two variables, where ax+by = c, meaning that when the x-coordinate is multiplied by a and the y-coordinate is multiplied by b, the sum of these two values equals c. There are essentially an endless number of solutions to a linear equation with two variables.

Now in the question,

To find the pair of solutions of the equation -2x + 3y = 6, we satisfy all the pairs one by one in the given equation

1. Putting the value of (x, y) as (-3,4) in the equation we get-

-2*-3 +3*4 = 6 ⇒ 18 = 6

Therefore LHS ≠ RHS

Hence it is not the solution to the equation.

2. Putting the value of (x, y) as (3,-4) in the equation we get-

-2*3 + 3*-4 = 6 ⇒ -18 = 6

Therefore LHS ≠ RHS

Hence it is not the solution to the equation.

3. Putting the value of (x, y) as (0,2) in the equation we get-

-2*0 + 3*2 = 6 ⇒ 6 = 6

Therefore LHS = RHS

Hence it is the solution to the equation.

4. Putting the value of (x, y) as (3,0) in the equation we get-

-2*3 + 3*0 = 6 ⇒ -6 =6

Therefore LHS ≠ RHS

Hence it is not the solution to the equation.

Thus (0,2) is the solution of the equation.

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a straight line perpendicular to the y-axis, which means that the range is a set of one value  {y|y =4}

What is the domain and range?

Domain and Range.  The range of a function is the set of values that the function assumes. This set is the values that the function shoots out after we plug an x value in.

The domain of x=4 is (−∞,∞) and range is {y|y=4} .

(−∞,∞)

{x|x ∈ R}

y=4

is a straight line perpendicular to the y-axis, which means that the range is a set of one value  {y|y =4}

Set-Builder Notation:{y|y =4}.

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Answer:

8 × 3 = 24

3 × 8 = 24

Step-by-step explanation:

if she should arrange the chairs in 8 rows that will mean she set 3 chairs per row.

if she then changed the arrangement by arranging the chairs in 3 rows that means she set 8 chairs per row.

in the first paragraph that I wrote, here is how I got it.

24÷8 = 3

8 × 3 = 24

in the second paragraph I wrote, here is how I got it.

24 ÷ 3 = 8

3 × 8 = 24

Therefore your answer will be.

8 × 3 = 24

3 × 8 = 24

Answer:

m<y=120

Step-by-step explanation:

m<x=34, m<z=26, = 60.

180-60=120.

angle 3 = 120.

Answer:

D. m<y=120

Step-by-step explanation:

have a good day!

There have been 3 sides and 3 angles in every triangle, some of which might be the same. The hypotenuse, which is the side that faces the right angle, and the legs, which are the other two sides, are given specific names in the case of a right triangle.

A triangle is a three-sided geometry shape with 3 vertices. The internal angle of the triangle, which is 180 degrees, is built. It means that a triangle's internal angles sum to 180 degrees.

It is the polygon with the fewest sides. Or to put it another way, a triangle is a three-sided, two-dimensional shape whose internal angles are 180°.

Triangles are primarily divided into six varieties based on the angles and side length.

The triangles are further divided based on the angles into:

(1) Acute Angle Triangle

(2) Obtuse Angle Triangle

(3) Right Angle Triangle

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So,  the area of the triangle is 12 square inches.

In a two-dimensional plane, the area of a triangle is the region enclosed by it. A triangle, as we all know, is a closed form with three sides and three vertices. Thus, the area of a triangle is the total space filled by the triangle's three sides. The typical formula for calculating the area of a triangle is half of the product of its base and height.

The area of a triangle can be found using the formula: (1/2) * b * h

Given that b = 3 in. and h = 8 in., the area of the triangle would be:

(1/2) * 3 * 8 = (1/2) * 24 = 12 square inches.

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Answer:

c=9.20

Step-by-step explanation:

SOH CAH TOA

Use cos because it deals with the adjacent angle and the hypotenuse, which is all that we have here.

cos (61 degrees) = c/19

plug in cos(61) degrees into your calculator to get .484

.484 = c/19

Multiply both sides by 19 to isolate c by itself.

9.20 = c

The inequality to determine the number of children's table build by Dan on Tuesday is given by x ≤ 5.

As given in the question,

Let us consider 'x' represents the number of children's table build by Dan.

Minimum production times in hour to build the children table is 2 hours.

Children table build by Dan is on Tuesday

Total number of hours Dan works on Tuesday = 10 hours

The required inequality to represent the given condition is :

2x ≤ 10

⇒ x ≤ 10 /2

⇒ x ≤ 5

Therefore, the required inequality to represents the number of children table build by Dan on Tuesday is equal to x ≤ 5 .

Dan builds furniture. The table shows his minimum production times.

Furniture                        Minimum Production Times (hour)

Child’s table                         2

Bench                                   1

Dining table                         4

China cabinet                       7

Dan builds children’s tables on Tuesday. He works 10 hours. Write and solve an inequality to determine how many children’s tables Dan can build that day.

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Answer:

s+7

Step-by-step explanation:

The inequality is x ≤ 5.09, where x is the number of outfits. Rashon can buy at most 5 outfits while staying within his budget.

To determine the number of biking outfits Rashon can buy while staying within his budget, you can set up an inequality using the information provided.

First, calculate the total cost of the reflectors and gloves:

3 reflectors × $10.78 + $32.64 = $38.34 + $32.64 = $71

Then, subtract the cost of the bicycle, reflectors, and gloves from Rashon's budget: $780 - $481.28 - $71 = $227.72

Now, you can use this remaining amount to determine the number of biking outfits Rashon can buy.

Let x be the number of outfits he can buy

You can set up an inequality as follows:

44.95x ≤ $227.72

Dividing both sides by 44.95:

x ≤ 5.09

However, since the number of outfits is an integer, he can only buy 5 outfits at most.

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One of the triangles' base length, b, is 3 cm. Thus, the correct answer is A.

Two congruent triangles and a rectangle were formed from the trapezoid. The two triangles are 12 cm in height. The rectangle is 12 cm in height, 14 cm in width and the base side is 20 cm. It's worth noting that a congruent triangle has the same three sides and three angles.

The triangle's base length may be calculated as follows:

The sides of the triangle may be calculated using the area of the trapezoid:

Where:

Hence:

We know that the height of the triangles is 12 cm and the area of the trapezoid is 204 cm². The area of the rectangle is also given as 14 cm x 12 cm = 168 cm². This information may be used to construct the equation:

Solving for b, we get:

Therefore, the base length of the triangle is 3 cm, and the correct answer is A.

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Answer:

A

Step-by-step explanation:

a

The finance charge on a $6,500 loan with an interest rate of 9.5% compounded monthly over 36 months is $208.21.

The finance charge on a $6,500 loan with an interest rate of 9.5% compounded monthly over 36 months can be calculated using the formula:

Finance Charge = Principal Amount * Interest Rate * Number of Months

Finance Charge = $6,500 * 9.5% * 36

Finance Charge = $208.21

Therefore, the finance charge on a $6,500 loan with an interest rate of 9.5% compounded monthly over 36 months is $208.21.

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If A(0, 3) and B(2,6) be the two points then the equation of the line is y = 1.5x + 3.

A line is a straight, thickness-free, one-dimensional object in geometry that extends indefinitely in both directions.

An object that extends without end in both directions is referred to as a line. Arrowheads are typically used to depict it to demonstrate how it never ends. A line segment is an area within a line that has two end points. Half of a line with one end point makes up a ray. Angle is formed by two rays that have the same terminal point.

Let A(0, 3) this point is the y-intercept of the line B(2,6)

The equation of the line into slope intercept form is equal to y = mx + b

where, m is the slope

b is the y-coordinate of the y-intercept = 3

Find the slope of the line m

The formula to calculate the slope between two points is equal to [tex]$m=\frac{y_ 2-y_ 1}{x _2-x _1}$[/tex]

substitute the values

m = (6 - 3)/(2 - 0)

simplifying the equation, we get

m = 3/2

m = 1.5

The equation of the line is y = 1.5x + 3.

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The base value of a numeral system can be founded by counting the number of unique digits or symbols used in the system.

The base value of a numeral system can be determined by counting the number of unique digits or symbols used in the system. For example, in the base 10 numeral system, which is commonly used in everyday life, the base value is 10 because it uses the digits 0 through 9. In the base 2 numeral system, which is also known as binary, the base value is 2 because it only uses the digits 0 and 1.

Another way to find the base value is to look at the exponent of the highest power of the base in the numeral system. For example, in the number 42 in base 10, the highest power of 10 is 10¹, which is 10. Therefore, the base value is 10. Similarly, in the number 1010 in binary, the highest power of 2 is 2³, which is 8. Therefore, the base value is 2.

It's important to note that when working with different numeral systems, it is essential to know the base value in order to understand the value of the number being represented.

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The value of the given expression, 5 3/5 + 7 1/10 - 2 2/3, is 10 1/3

From the question, we are to simplify the given expression.

The given expression is

5 3/5 + 7 1/10 - 2 2/3

To solve the given expression, we would convert each of the fractions to an improper fraction

Convert the fractions to improper fractions

28/5 + 71/10 - 8/3

Find the LCM of the denominators

LCM of the denominators = 30

Thus,

(168 + 213 - 80) / 30

301/30

10 1/3

Hence, the simplified form of the expression 10 1/3

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The cost of each of the favors is of $5 and the required equation is 8f+265 = 305

An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Given that, A party package costs $265 and covers the entrance fee for guests, a private party room, and an activity guide. Estelle upgraded her package to include a favor for each of her 8 guests, bringing the total to $305.

The addition of 8 favors increase the cost of the party by $40

The equation that can be used to find the number of favors =

8f+265 = 305

Solving for f,

8f = 40

f = 5

Hence, the cost of each of the favors is of $5.

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The average daily cost of Aaron of driving his car to work is $5.1169.

Average cost is calculated by dividing the total cost by the total output quantity.

Miles for a round trip for 1 day = 10.5 miles

Since it is round trip, total miles for 1 day = 10.5 × 2 = 21 miles

Miles for a round trip for 22 days = 21 × 22 = 462 miles

Gallons for 15 miles = 1 gallon

Gallons for 1 mile = 1/15 gallons

Gallons for 462 miles = 30.8 gallons

Cost per gallon = $1.09

Cost for 30.8 gallons = 30.8 × 1.09 = $33.572

Payment for car parking = $79

Total cost per month = $33.572 + $79 = $112.572

Average daily cost = $112.572 / 22 = $5.1169

Hence the average cost per day is $5.1169.

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When 60 of your favorite songs are purchased from a website for $0.97 apiece, the total cost comes to $58.80.

The unit technique is a method of problem-solving where you first calculate the value of a single unit, then multiply that value to get the answer. Simply expressed, a single unit value is extracted from a specified multiple using the unit method. For instance, 40 pens will set you back 400 rupees, or $1.01. The method used to accomplish this might be standardized. a solitary nation. anything has a distinctive component. (Mathematics, Algebra) Its adjoint and reciprocal are equivalent. (Linear Algebra, Mathematical Analysis, Mathematics of Matrix or Operators)

given

This straightforward real-world issue can be resolved by by multiplying the number of tracks by the $0.98 per song price.

60 x 0.98 = $ 58.80

When 60 of your favorite songs are purchased from a website for $0.97 apiece, the total cost comes to $58.80.

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Based on the graphs of the functions f(x) = 2x + 1, and g(x) = 2(x + 3) + 1, a statement which correctly compares the graphs include the following: A. The graph of g is the graph of f translated 3 units left.

In Mathematics, the translation of a geometric figure to the left simply means subtracting a digit from the value on the x-coordinate (x-axis) of the pre-image of a function.

On the other hand, a geometric figure that is translated up simply means adding a digit to the value on the y-coordinate (y-axis) of the pre-image or parent function.

Mathematically, a horizontal translation to the left is modeled by this mathematical expression g(x) = f(x + N) while a vertical translation to the positive y-direction (upward) is modeled by this mathematical expression g(x) = f(x) + N.

Where:

Translating the graph of function f, we have:

g(x) = f(x + N)

g(x) = 2(x + 3) + 1

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