Write down the value of angle x, y and z and give a reason for your answers: Angles

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

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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Answer: 70-20x = 60-15x, where x is the number of pizzas purchased.

Step-by-step explanation:

(TLDR, the solution to the given equation is that the cards will have the same amount of money left on them if both jim and clara buy two pizzas each. feel free read my explanation on how to write equations like this in the future, should you need it.)

so, we know that since jim and clara received $70 and $60 gift cards (respectively), these numbers are called constants, because their original values do not depend on anything (they are given). while these numbers may decrease with the amount of pizzas bought, their original values are fixed.

now, the price for one pizza at jim's pizza restaurant is $20, right? so if you buy 2 pizzas, it'll be $40, 3 pizzas are $60, and so on. but we can actually represent the price of the pizzas as 20x (where x is the number of purchased pizzas, and 20 is the price of one pizza), and this expression works for any number of pizzas you buy. you can also apply this to clara's restaurant, as the total price of the number of pizzas she buys is represented by 15x.

the words charges and left in this problem tells you that you're going to need to subtract from the total amount of money on the gift cards. using the expressions above, the amount of money jim has left on his card can be expressed as 70 (amount of money on the card) MINUS 20x (number of money spent on however many pizzas were bought (x)). likewise, the amount of money left on clara's card after she buys however many pizzas can be represented as 60-15x. you can then set the equations equal to each other and solve for x, which tells you how many pizzas they each need to buy to have the same number of $$ left on their cards.

70-20x = 60-15x

10=5x

2=x. hope this helped :3

Teo can fill 28 glasses in  4 2/3 pitches of juice.

Teo  has 4 2/3 pitches of juice.

First we write the improper fraction (mixed fraction) as a proper fraction.

4 2/3

= [(4 × 3) + 2] / 3

= (12 + 2) / 3

= 14/3

One glass holds 1/6 of a pitcher.

Let m number of glasses hold 14/3 pitches of juice.

By unitary method,

m × (1/6) =  14/3

To find the value of m we need to divide fractions.

m = (14/3) / (1/6)

m = (14/3) × (6/1)

m = 14 × 2

m = 28

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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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Answer:

5/3

Step-by-step explanation:

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

A binomial is a difference of squares if both terms are perfect squares. Remember that we might first need to filter out a common element.

Perfect squares result from squaring an integer. One such example is the number 81, which is a perfect square since it can be derived by squaring 9: 99=81. 144 is a perfect square since it can be generated by squaring the number 12, which results in 12. 169 is a perfect square since it can be squared to produce the number 13. mathematics-specific language Informally: When an integer (a "whole") number, whether positive, negative, or zero, is multiplied by itself, the result is referred to as a square number, a perfect square, or simply "a square". Accordingly, all square numbers are 0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, and so on.

given

A binomial is a difference of squares if both terms are perfect squares. Remember that we might first need to filter out a common element.

If a binomial is found to be a difference of squares, it is factored into two binomials. the first being the first term's square root less the second term's square root.

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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.

yes, 2x + 3 = 5 is a linear equation.

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) component are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables." If a linear equation contains two variables, it is referred to as a linear equation in two variables, and so on.

Non-linear equations are those that do not produce a straight line. It has a changeable slope value and resembles a graphed curve.

Given that,

2x + 3 = 5

or, 2x = 5 - 3

or, 2x = 2

or, x = 2/2

x = 1

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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:

  ∠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.

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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If Swimming Pool On a certain hot summers day, 498 people used the public swimming pool. The number of children is 325 and the number of adult is 173.

Children = x

Adults = y

x + y = 498  Equation .....1

1.50x + 2.50y = 920  Equation ...2

Multiply (1) by 2.50

2.50x + 2.50y = 1,245  Equation  Equation ....3

1.50x + 2.50y = 920  Equation ...2

Subtract (2) from (3)

1x = 325

x = 325/1

x = 325 (Children)

Substitute x = 325 in (1)

x + y = 498

325 + y = 498

y = 498 - 325

y = 173 (Adult)

Therefore 325 children and 173 adults swam at the pool.

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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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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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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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When the points are (4, 2) and (6, 5), the slope is 3/2. The slope of a line determines its direction and degree of steepness.

A line's steepness and direction are determined by the slope of the line. The change in a line's y coordinate relative to its change in x coordinate is referred to as the line's slope. While there has been no net change in the x coordinate, there has been no net change in the y coordinate. hence, the shift in the y coordinate in relation to the shift in the x coordinate. The slope of a line is the rise to run ratio, or the rise divided by the run. It gives information about a line's slope in the coordinate plane. Any two clearly separated points on a line can be used to calculate the slope of any line.

given

slope = [tex]m = \frac{y2 - y1}{x2 - x1}[/tex]

points are ( 4, 2 ) and ( 6, 5)

[tex]\frac{5 - 2}{6 - 4} \\= \frac{3}{2}[/tex]

hence the slope is 3 / 2 .

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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:

1. g=-3

2. a=-2

3. s=19

4. f=-12

5.d=8

6.a=-28

7.w=12

Step-by-step explanation:

1)  take 4-7 to get -3

2)  take 10 divided by -5 to get -2

3) take 10+9 to get 19

4) take 3-15 to get -12

5) take -64 divided by -8 to get 8

6) take -4 times 7 to get -28

7)take 7 plus 5 to get 12

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 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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Answer:

  the median will go up 2.5 points from 76 to 78.5

Step-by-step explanation:

You want to know the effect on the median of adding 85 to the list of scores: 76, 96, 81, 69, 41.

The median is the middle value when the list is sorted into order. The ordered list is ...

  41, 69, 76, 81, 96

The median is 76.

When 85 is added to the list, the sorted list becomes ...

  41, 69, 76, 81, 85, 96

There are two middle scores, so the median is their average:

  (76+81)/2 = 78.5

The median increases 2.5 points from 76 to 78.5 when the score is added.

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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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

The coordinates that can be applied to the equation y > 2 + 9x is the cartesian coordinate system

A system that identifies your precise location on a graph is the Cartesian coordinate system.  

This system can be used to graph a collection of points that will give your equations' solutions, which makes it handy. Each axis will have its own variable in the equations that are employed with this system.

The x-axis, a horizontal axis, and the y-axis, a vertical axis, are the two axes that make up the Cartesian coordinate system.

The variables x and y will be present in equations for lines in this system.

Hence the cartesian coordinate system is applicable for the equation given as y > 2 + 9x

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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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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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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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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.