Determine if the triangles can be proved congruent by SSS, SAS, ASA, AAS, or HL.

Answer:

5/3

Step-by-step explanation:

4 4/9 * 3/8 = 40/9 * 3/8 = 120/72 = 10/6 = 5/3

The system X² y² 25 and ay 10 has no real solutions.

To solve this system, we need to solve each equation for y.

For the first equation, X² y² 25, we can divide both sides by X² to get:

y² = 25/X²

Then, take the square root of both sides to get:

y = ± √(25/X²)

For the second equation, ay = 10, we can divide both sides by a to get:

y = 10/a

To find out if the system has real solutions, we need to compare the two equations. Since the two equations are not equal, the system has no real solutions.

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The solution of the inequality is x < 7 and x >= -2.

What is linear inequality?

An inequality is a mathematical statement comparing two values or expressions, usually involving one of the following relational operators: < (less than), > (greater than), <= (less than or equal to), >= (greater than or equal to), or != (not equal to). The solution to inequality is a set of values that make the inequality true.

To solve the inequality -10 < -2x + 4 ≤ 8, we have to solve the inequality twice because of the less than or equal to symbol and greater than or equal to symbol.

First we have to solve -10 < -2x + 4

-2x + 4 > -10

-2x > -14

x < 7

Second, we have to solve -2x + 4 <= 8

-2x + 4 <= 8

-2x <= 4

x >= -2

Hence, the solution of the inequality is x < 7 and x >= -2. This solution is represented by all the values of x that are less than 7 and greater than or equal to -2.

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The value of p for the given logarithmic function  -log(2.1x10^12) is, -8.678  

The logarithmic function is an expression which we can write as, y = logₐx, where a>0 & x>0, It is the inverse of exponential function [tex]x = a^y[/tex].

Formulae for logarithmic function are,

LogAB = LogA + LogB         .................(i)

Logₐaᵇ = b                             ................(ii)

Given expression,

p = -log(2.1x10^12)

p = -log2.1 + log10^12  (by applying formula i )

p = -log2.1 + 12             (by applying formula ii )

p =  -(-3.322) + 12        (log2.1 = -3.322)

p =  -8.678

Hence, the value of p is equal to -8.678

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The area of the hexagonal region exists 2116(√2 + 1) then the value of AB is 046.

All of the inner angles and all of the vertices must be smaller than 180 degrees for a convex hexagon. There are both regular and irregular convex hexagons.

There are no angles inside a convex hexagon. More specifically, no internal angle may exceed 180 degrees. Any internal angle that exceeds 180 degrees is concave.

Let the side length be x

The diagonal BF = √(AB² + AF²) = √(x² + x²) = x√2.

Then the areas of the triangles AFB and CDE in total exists (x²/2) × 2, and the area of the rectangle BCEF equals x × x√2 = x²√2.

Let the equation be

2116(√2 + 1)  = x²√2 + x²

simplifying the above equation, we get

2116(√2 + 1)  = x²(√2 + 1)

2116 = x²

x = 46

Therefore, the value of AB exists 0.46.

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The area of the hexagonal region exists 2116(√2 + 1) then the value of AB is 046.

A convex hexagon requires that all of the inner angles and all of the vertices be smaller than 180 degrees. Convex hexagons come in both regular and irregular varieties.

The interior of a convex hexagon is flat. No internal angle may be greater than 180 degrees, to be more precise. Concavity is defined as an interior angle greater than 180 degrees.

Let the side length be x

The diagonal BF = √(AB² + AF²) = √(x² + x²) = x√2.

Then the areas of the triangles AFB and CDE in total exists (x²/2) × 2, and the area of the rectangle BCEF equals x × x√2 = x²√2.

Let the equation be

2116(√2 + 1)  = x²√2 + x²

simplifying the above equation, we get

2116(√2 + 1)  = x²(√2 + 1)

2116 = x²

By taking root both sides,

x = 46

Therefore, the value of AB exists 0.46.

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Answer:

n = - 1 , n = 3

Step-by-step explanation:

n² - 2n - 3 = 0 ( add 3 to both sides )

n² - 2n = 3

to complete the square

add ( half the coefficient of the x- term)² to bpth sides

n² + 2(- 1)n + 1 = 3 + 1

(n - 1)² = 4 ( take square root of both sides )

n - 1 = ± [tex]\sqrt{4}[/tex] = ± 2 ( add 1 to both sides )

n = 1 ± 2

Then

n = 1 - 2 = - 1

n = 1 + 2 = 3

If it cost them $125 to rent a booth at the farmers market, then their profit will be $2816 - $125 = $2691.

Top Choice Ponce farm wants to set up a booth at a farmers market next weekend, they promise to sell their pistachios at 20% cheaper than the next cheapest farm. They plan to sell 3520 ounces of pistachios at $0.8 per ounce.

The booth rent cost them $125. To calculate the profit, they will subtract the booth cost from the total revenue of pistachios which is $2816. Therefore, their profit will be $2691. They will make this profit after paying for the Farmers Market booth.

If Top Choice Farm's pistachios are 20% cheaper than the next cheapest farm, and the next cheapest farm's pistachios cost $1 per ounce, then Top Choice Farm's pistachios will cost $1 - $1 × 20% = $0.80 per ounce.

If they sell 3520 ounces of pistachios at $0.80 per ounce, then their total revenue from pistachios will be 3520 × 0.8 = $2816

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Answer:

  ∠LOP = 96°

Step-by-step explanation:

Given an inscribed angle of 48°, you want to know the measure of the central angle that subtends the same arc.

The measure of an inscribed angle is half the measure of the arc it subtends.

  ∠LMP = 1/2(arc LP)

  48° = 1/2(arc LP) . . . . . . use the given value

  96° = arc LP . . . . . . . . . multiply by 2

The measure of an arc of a circle is the same as the measure of the central angle it subtends: the arc measure and its central angle measure are identical.

  arc LP = ∠LOP

  96° = ∠LOP

__

Additional comment

That's a long way of saying the central angle is twice the inscribed angle that subtends the same arc. ∠LOP = 2×∠LMP.

Answer:

x= 1/4 - 1/4 x= 1/4 + 1/4

Step-by-step explanation:

Answer:

Type: (+ ve)

Number of solutions: 2

Step-by-step explanation:

We are given an equation (-8x² + 4x - 1 = 0)

Now, change the sign

-8x² + 4x - 1 = 0

8x² - 4x + 1 = 0

Here,

Now, discriminant

D = b² - 4ac

D = (8)² - (4)(8)(1)

D = 64 - 32

D = 32 > 0

Here, 32 is greater than 0 so, it has two solutions.

NP, PM, and MN are all midsegments and bisect each side.

value of x = 5 unit

NP = 12

MP=2x

RQ = 5x-1

SQ=6x

Using Midsegments of a Triangle

A midsegment of a triangle is a segment connecting the midpoints of two sides of a triangle

Triangle Midsegment Theorem

Using Midsegments of a Triangle

Theorem 5-1 Triangle Midsegment Theorem

The segment connecting the midpoints of two sides of a triangle is parallel to the 3rd side and is half as long.

Triangle Midsegment Theorem A segment whose endpoints are the

midpoints of two sides of the triangle

Midsegment

Base

Midsegment = ½ of Base

M = ½ b

NP =1/2(RQ)

12 =1/2(5x-1)

12* 2 = 5x-1

24 =5x-1

24+1 =5x

25 =5x

x=25/5

x = 5 unit

NP, PM, and MN are all midsegments and bisect each side.

value of x = 5 unit

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Answer:

[tex]\boxed{22}.[/tex]

Step-by-step explanation:

Since Elliott drove for a total of 10 hours, and he drove for 120 miles while it was raining and 300 miles after the rain stopped, we know that he drove for a total of 120 + 300 = <<120+300=420>>420 miles.

If he drove for a total of 10 hours and covered a distance of 420 miles, then his average speed was 420 miles / 10 hours = <<420/10=42>>42 mph.

Since Elliott drove 20 mph faster after the rain stopped than he did while it was raining, then we know that his speed while it was raining was 20 mph slower than his average speed of 42 mph. That means his speed while it was raining was 42 mph - 20 mph = <<42-20=22>>22 mph.

1)

a) The equation Y=3/4x+3 can be used to represent the growth of the trees over time.

b) The y-intercept in this equation represents the starting height of the trees, which is 3 feet.

c) In 3 years, the height of the trees will be 5.25 feet according to the equation.

2)

No, the equation 3x - 4y = -12 cannot be used to represent the same information in question #1. This equation is not in slope-intercept form, which is necessary to represent a linear relationship between two variables.

a) The 3 and the 4 in this equation are coefficients of the variables x and y, respectively. They do not represent any specific value or quantity in the context of the problem.

b) It is not possible to determine the height of the tree in 24 years using this equation because it is not in the correct form.

c) To find the x-intercept, we can set y to 0 and solve for x. This gives us x = -3. The x-intercept in this equation represents the number of years at which the height of the tree is 0 feet. This does not have any meaning in the context of the problem.

The number of seeds per square foot is the variable that explains the variation in the yield of the crop in pounds per square foot.

The explanatory variable for this relationship is the number of seeds per square foot. The number of seeds per square foot is the variable that is being manipulated or changed by the farmers in order to observe the effect on the yield of the crop in pounds per square foot.

The farmers observed that the yields were the smallest when the number of seeds per square foot was either very small or very large, this means that there is an optimal number of seeds per square foot that yields the highest crop.

So, the number of seeds per square foot is the variable that explains the variation in the yield of the crop in pounds per square foot.

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Answer:

x - intercept = (15, 0)

y - intercept = (0, 6)

Step-by-step explanation:

x-int. is when y = 0

y-int. is when x=0

Plug in y = 0 and x = 0 to get intercepts.

FOR X-INT.:

12x + 30(0) = 180

12x = 180

x = 15

x-int. is (15, 0)

FOR Y-INT. :

12(0) + 30y = 180

30y = 180

y = 6

y-int. is (0, 6)

The unit price of the portion of the chicken will be $0.50.

To find the portion cost of the chicken, we need to know how much it costs per ounce, and then multiply that by the number of ounces in a serving.

We can begin by calculating the cost per ounce of chicken by dividing the cost per pound by the number of ounces in a pound:

$2 (cost per pound) ÷ 16 (ounces per pound) = $0.125 (cost per ounce)

Now that we know the cost per ounce, we can find the portion cost of the chicken by multiplying it by the number of ounces in a serving:

$0.125 (cost per ounce) × 4 (ounces per serving) = $0.50

So the portion cost of the chicken is $0.50 . So the answer is

C. $0.50.

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The complete question is-

The cost per pound of chicken is $2. Each serving of chicken is about 4 oz. What will be the portion cost of the chicken?

A. $0.75

B. $2

C. $0.50

D. $0.60

E. $1

Answer: length of EF is 18 units.

Step-by-step explanation:

similar triangles (as displayed in the photo) have the same angle measures, but can have different side lengths. however, these side lengths are proportional to each other, meaning that with similar triangles, there will ALWAYS be a number you can multiply the first triangle by to get its similar triangle.

you can find this number by dividing one side length of whichever triangle is bigger with its corresponding side on the other triangle (for example, sides DF and AC correspond, so you'd divide whichever value's bigger by the smaller one. in this case you'd divide 21 by 14.) this gives you 1.5, which tells you that triangle DEF is 1.5 times larger than triangle ABC. so to get EF, just multiply BC (which is 12) by 1.5. this gives you 18. so, EF equals 18. hope this helped :3

With 8 percent increase each year the Sutton family's condo's worth in 8 years will be $216000.

An exponential function is a mathematical function in the form f(x) = ax, where {x} is a variable and {a} is a constant which is called the base.

Given is that Condos in Georgetown go up in value by 10% each year. Sutton family's condo's current worth is $120,000.

We can write the function to calculate the worth after {T} years as follows.

A{T, R} = A{I} {1 + RT}

A{T, R} = {120000} {1 + (10/100) x 8}

A{T, R} = {120000} {1 + 0.1 x 8}

A{T, R} = {120000} {1 + 0.8}

A{T, R} = {120000 x 1.8}

A{T, R} = 216000

Therefore, the Sutton family's condo's worth in 8 years will be $216000.

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Step-by-step explanation:

x^4-9x^2-8x^2+72

x^2(x^2-9)-8(x^2-9)

(x^2-8)(x^2-9)

(x^2-8)(x+3)(x-3)

No, isosceles triangles do not always have to have 90-degree angles.

An isosceles triangle is a triangle with two sides of equal length. While the two sides are equal, they can be of any length. This means that the angles of the isosceles triangle can vary, and the triangle does not always have to have 90-degree angles. In fact, an isosceles triangle can have angles that range from 0 to 180 degrees. The only requirement for an isosceles triangle is that it must have two sides of equal length. As such, an isosceles triangle can have angles that are greater than 90 degrees, angles that are less than 90 degrees, or even angles that are equal to 90 degrees.

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According to the following graph, the for the expression y = 5 is horizontal.

The term graph in math is known as the set of vertices and a binary relation between vertices, adjacency.

Here we have given the expression y = 5.

Now, we have to plot these expression on the graph, then we get the following graph.

Through the given graph, we have identified that the expression makes the horizontal line on the graph.

Here we also know that if the equation of a line is y = 5, then it is a horizontal line.

Here we know that the line is parallel to the x-axis and passes through the point y = 5 at the y-axis.

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The growth in x years for the gym will be represented as [tex]y = 840(1.25)^x[/tex].

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

City Fitness, a popular gym currently has 840 members. Based on its membership statistics since opening a few years ago, City Fitness expects to grow its membership by a factor of 1/4.

The expression can be written as,

[tex]y = 840(1.25)^x[/tex].

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Answer:

y > 14/3

Step-by-step explanation:

-3y<-14

Divided both sides by -3. Because divided by a negative number, the < will switch to the >

y > 14/3

If the sum of 21 and a difference of 6 then the numbers are 27/2 and 15/2.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Let, The two numbers be a and b.

Therefore, (a + b) = 21 and (a - b) = 6.

Adding these two equations, The variable 'b' will cancel out and we'll have

2a = 27.

a = 27/2.

And, 27/2 + b = 21.

b = 21 - 27/2.

b = (42 - 27)/2.

b = 15/2.

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To solve the problem of a system of equations by elimination, we can start with both equations in standard form. Then we can decide which variable will be easier to eliminate.

How can we decide? We want to have the coefficients of any one of the variables be opposites so that we can put the equations together and eliminate that variable.

To solve a simultaneous equation by using the elimination method, you eliminate any one variable first.

Before you can do that, the coefficient of one of the variables in the two equations must be the same.

From the given questions, for the coefficient of one variable in the two equations to be the same, we multiply the first equation by 3.

If we can do this, the coefficient of Y in the two equations will now be 3.

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By Solving this proportion will give you the value of the angle you need to aim your shot.

What is angle of elevation ?

angle elevation can be defined as the angle formed between line of sight and horizontal line.

Draw a diagram of the pool table, labeling the dimensions of the table and the position of the cue ball.

Since the cue ball is 18 inches from the top bumper and 50 inches from the right bumper, you can draw a right triangle with these side lengths.

The dimensions of the pool table can also be used to draw a right triangle, with the horizontal dimension (96 inches) as the base and the vertical dimension (46 inches) as the height.

These two triangles are similar because they are both right triangles and they share a right angle. Therefore, the ratios of their sides are equal.

You can use the ratios of the sides of these triangles to determine the angle at which you should aim your shot. To do this, you can set up a proportion using the corresponding sides of the two triangles. For example, you could use the ratio of the base to the height of the small triangle (18 inches to 50 inches) and set it equal to the ratio of the base to the height of the large triangle (96 inches to 46 inches).

Hence, by  Solving this proportion will give you the value of the angle you need to aim your shot.

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on solving the provided question, we can say that - the graphs which is shown as the straight line graph.

Graphs are visual representations or charts used in mathematics to methodically express data or values. A relationship between two or more objects is frequently represented by a point on a graph. A non-linear data structure called a graph is made up of nodes, or vertices, and edges. Connect the nodes, also known as vertices. This graph comprises a set of vertices V= 1, 2, 3, 5, and a set of edges E= 1, 2, 1, 3, 2, 4, and (2.5), (3.5), (4.5). Statistics graphs (bar charts, pie charts, line charts, etc.) Exponential diagrams. triangle graph, a logarithmic graph

here,

then line which is drawn is straright,

so the graph is straight .

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The amount and numbers are 1. $217.25, 2. $710, 3. $790.25 and 4. 167.

Multiplication of two numbers is defined as the addition of one of the number repeatedly until the times of the other number

1. Cost of a paperback = 25 cents = $0.25

Cost of a hardcover book = $1.25

There were 54 paperbacks and 163 hardcover books sold.

Money library raised = (0.25 × 54) + (1.25 × 163) = $217.25

2. Cost for round trip airfare = $398.60

Cost of room per night = $115.70

Cost of room for two nights = 2 × $115.70 = $231.40

Cab fare from airport to hotel = $40.00

Total fare from airport to hotel and the return = 2 × $40.00 = $80.00

Total cost = $398.60 + $231.40 + $80.00 = $710

3. Total working hour of Paula = 48 hours

Earning for first 35 hours = $14.50/h × 35

                                          = $507.50

Remaining hours = 48 - 35 = 13 hours

Earning for next 13 hours = ($14.50/h × 1.5) × 13

                                          = $282.75

Total earnings =  $507.50 + $282.75 = $790.25

4. Number of cards Will has = 26

Number of cards Liam has = 19

When they combine, total cards = 26 + 19 = 45

When father also shared, total number of cards = 3 × 45 = 135

Number of cards Nestor has = 4 × 8 = 32

Total number of cards = 135 + 32 = 167

Hence all the questions are cleared using multiplication as one of the basic operations.

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Using the information in the table the domain is 4 and the range  [-1,1]

The term "domain" refers to a group of potential input values, and the domain of a graph is made up of all the input values visible on the x-axis. The y-axis displays the range, which is a collection of possible output values.

The domain is typically listed in the left column and the range is typically listed in the right column in a table like the one below. The domain and range of a relation or function, respectively, can be thought of as the input values (x) and the output values (y), respectively.

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The standard form of the polynomial -n²(n² + 5n + 6) is  -n⁴ - 5n³ - 6n².

Polynomials are algebraic expressions that consist of variables and coefficients.

The standard form of a polynomial is expressed by writing the highest degree of terms first then the next degree and so on.

Hence, let's represent the polynomial in standard form as follows:

-n²(n² + 5n + 6)

Open the brackets

-n²(n² + 5n + 6) = -n⁴ - 5n³ - 6n²

Hence,

-n²(n² + 5n + 6) = -n⁴ - 5n³ - 6n²

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