Someone please help with this? Thank you!​

Someone Please Help With This? Thank You!

Answers

Answer 1

Table values are -3, -1, 3, 5, 13

Define the term function?

A function is a mathematical object that maps each element from one set to a unique element in another set. Functions are represented using symbols and can be described using graphs, tables, or equations.

Given function is,

[tex]f(x)=2x +3[/tex]

Solve for x = -3,   f(-3) = 2×(-3) + 3 = -6 + 3 = -3

f(-3) = -3

Solve for x = -2,   f(-2) = 2×(-2) + 3 = -4 + 3 = -1

f(-2) = -1

Solve for x = 0,   f(0) = 2×(0) + 3 = 0 + 3 = +3

f(0) = 3

Solve for x = 1,   f(1) = 2×(1) + 3 = 2 + 3 = 5

f(1) = 5

Solve for x = 5,   f(5) = 2×(5) + 3 = 10 + 3 = 13

f(5) = 13

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Someone Please Help With This? Thank You!

Related Questions

Question
Find the value of y
for the given value of x
.

y=x+5;x=3

Answers

Answer: y is equal to 8

Step-by-step explanation:

by substituting the x for its vale of three we can add the two values to get 8 or y=8

One little cat can eat a bag of treats in 15 minutes while another cat can eat the same bag of treats in 10 minutes. What part of the bag can they eat together in the given time? 1 minute. 2 minute, and 3 min

Answers

the two cats can eat 1/6 of the bag in one minute, 1/3 of the bag in two minutes, and 1/2 of the bag in three minutes.

Answer:

1 minute = 1/6

2 minutes = 1/3

3 minutes =1/2

Step-by-step explanation:

one can eat a bag in 15 minutes so in 1 minute this cat can eat 1/15 of a bag

the other cat can eat a bag in 10 minutes so in 1 minute the cat can eat 1/10 of the bag

to find how much they can eat in 1 minute, add 1/10 and 1/15 which gives you 1/6. to find 2 and 3 minutes just multiply by 1/6 by 2 or 3

write down the name of shape W

Answers

A hexagon with two lines

hope helped you please make me brainalist and keep smiling dude

I hope you are form India

Suppose that the insurance companies did do a survey. They randomly surveyed 400 drivers and found that 320 claimed they always buckle up. We are interested in the population proportion of drivers who claim they always buckle up.a.i. x = __________ii. n = __________iii. p′ = __________b. Define the random variables X and P′, in words.c. Which distribution should you use for this problem? Explain your choice.d. Construct a 95% confidence interval for the population proportion who claim they always buckle up.i. State the confidence interval.ii. Sketch the graph.iii. Calculate the error bound.e. If this survey were done by telephone, list three difficulties the companies might have in obtaining random results.

Answers

We are interested in the population proportion of drivers who claim they always buckle upa.i. x = 320 ii. n = 400 iii. p′ = 0.8

b. The random variable X represents the number of drivers out of the sample of 400 who claim they always buckle up, while P′ represents the sample proportion of drivers who claim they always buckle up.

c. The distribution to use for this problem is the normal distribution because the sample size is large enough (n=400) and the population proportion is not known.

d. i. The 95% confidence interval for the population proportion who claim they always buckle up is (0.7709, 0.8291).

ii. The graph is a normal distribution curve with mean p′ = 0.8 and standard deviation σ = sqrt[p′(1-p′)/n].

iii. The error bound is 0.0291.

e. Three difficulties the insurance companies might have in obtaining random results from a telephone survey are:

Selection bias: The survey might not be truly random if the telephone numbers selected are not representative of the population of interest.

Nonresponse bias: People may choose not to participate in the survey or may not be reached, which could bias the results.

Social desirability bias: Respondents may give socially desirable answers rather than their true opinions, which could also bias the results.

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Factor completely.
7b^2-63

Thank you :DDD

Answers

Since both terms are perfect squares, factor using the difference of squares formula, [tex]a^2-b^2=(a+b)(a-b)[/tex] where [tex]a=b[/tex] and [tex]b=3[/tex]

Answer:[tex]7(b+3)(b-3)[/tex]

the number of minutes needed to complete a job, m, varies inversely with the number of workers, w. three workers can complete a job in 30 minutes. how many minutes would it take 6 workers to complete the job?

Answers

The number of minutes needed to complete a job, m, varies inversely with the number of workers, w.

Three workers can complete a job in 30 minutes.

To find, out how many minutes would it take 6 workers to complete the job.

The formula used for inverse variation is, m1w1 = m2w2

Where, m1 = 30,

w1 = 3,

m2 = ?

and w2 = 6

Substitute the given values in the above formula, 30 × 3 = m2 × 6

Simplify the above expression,90 = 6m2

Divide both sides by 6,90 / 6 = m2m2 = 15

Hence, it will take 15 minutes for 6 workers to complete the job.

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HELP

Given the information in the diagram of circle P below, find:

Answers

Based on the information in the diagram of circle P, the magnitude of the missing angle are as follows;

m∠BPC = 80 degrees.

m∠ADC = 205 degrees.

What is the central angle property?

In Mathematics and Geometry, the central angle property states that an inscribed angle is equal to one-half the measure of a central angle that is subtended by the same arc.

Based on the information provided about circle P, the central angle of circle P is represented by m∠BPC and the measure of arc BC is equals to 80 degrees. Therefore, the magnitude of angle BPC is given by:

m∠BPC = 80 degrees.

Since m∠A is an inscribed angle, its magnitude can be calculated as follows;

m∠A = 1/2(m∠BPC)

m∠A = 1/2(80)

m∠A = 40 degrees.

For the magnitude of m∠ADC, we have:

m∠ADC = 360 - (80 + 75)

m∠ADC = 360 - 155

m∠ADC = 205 degrees.

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Let n be a positive integer. If a == (3^{2n}+4)^-1 mod(9), what is the remainder when a is divided by 9?

Answers

Let n be a positive integer. We can use the properties of modular arithmetic to calculate this remainder. Let's start with a = (32n + 4)-1 mod 9. We can rewrite this as a = 9 - (32n + 4)-1 because 9 = 0 mod 9.

We can use Fermat's Little Theorem to calculate (32n + 4)-1. This theorem states that (32n + 4)-1 mod 9 = (32n + 4)8 mod 9.

Using the identity (a + b)n mod m = ((a mod m) + (b mod m))n mod m, we can simplify the equation to (32n mod 9 + 4 mod 9)8 mod 9.

32n mod 9 = 0, so (32n mod 9 + 4 mod 9)8 mod 9 = 48 mod 9 = 1.


Finally, a = 9 - 1 = 8 mod 9, so the remainder when a is divided by 9 is 8.

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Write the HCF of x
3y
4z
2 and x
2y
3z
5, where x, y, z are
distinct prime numbers

Answers

the HCF of x, 2y, 3y, 4z, x², 3z, and 5, where x, y, z are

distinct prime numbers is 1.

To find the highest common factor (HCF) of the given numbers, we need to find the common factors of each pair of numbers and then find the highest common factor of all the resulting common factors.

First, let's find the prime factors of the given numbers:

x = a prime number (distinct from y and z)

2y = 2 × y

3y = 3 × y

4z = 2² × z

3z = 3 × z

x² = a prime number squared (distinct from y and z)

5 = a prime number

Next, we can pair up the numbers and find their common factors:

Common factors of x and 2y: 1, 2, y

Common factors of 3y and 4z: 1, 2, 3, y, z, 6

Common factors of x² and 3z: 1, 3, x, z, xz

Common factors of 5 and 2: 1

Finally, we find the highest common factor of all the resulting common factors:

The highest common factor of x, 2y, 3y, 4z, x², 3z, and 5 is 1, since it is the only factor that is common to all the pairs.

Therefore, the HCF of x, 2y, 3y, 4z, x², 3z, and 5 is 1.

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Which choice is an exponential function?
Of(x)=x²+6
Of(x)=5(3)*
Of(x) = 3x + 7
Of(x) = |2x+ 41

Answers

Answer:1st one

Step-by-step explanation:

What is an equation for the quadratic function represented by the table shown?

Answers

y=-x^2+4x-1..hope this helps

It is well documented that a typical washing machine can last anywhere between 5 to 20 years. Let the life of a washing machine be represented by a lognormal variable, Y = eX where X is normally distributed. In addition, let the mean and standard deviation of the life of a washing machine be 14 years and 2 years, respectively. [You may find it useful to reference the z table.] a. Compute the mean and the standard deviation of X. (Round your intermediate calculations to at least 4 decimal places and final answers to 4 decimal places.) b. What proportion of the washing machines will last for more than 15 years? (Round your intermediate calculations to at least 4 decimal places, "z" value to 2 decimal places, and final answer to 4 decimal places.) c. What proportion of the washing machines will last for less than 10 years? (Round your intermediate calculations to at least 4 decimal places, "z" value to 2 decimal places, and final answer to 4 decimal places.) d. Compute the 90th percentile of the life of the washing machines. (Round your intermediate calculations to at least 4 decimal places, "z" value to 3 decimal places, and final answer to the nearest whole number.)

Answers

a. The mean of X is 1.7549 and the standard deviation is 0.3536.

b. To calculate the proportion of washing machines that will last for more than 15 years, we need to use the standard normal distribution table. The z-score for 15 years is (15-14)/0.3536 = 2.822. Using the table, we find that the proportion of washing machines that will last for more than 15 years is 0.9968.

c. To calculate the proportion of washing machines that will last for less than 10 years, we need to use the standard normal distribution table. The z-score for 10 years is (10-14)/0.3536 = -2.822. Using the table, we find that the proportion of washing machines that will last for less than 10 years is 0.0032.

d. To calculate the 90th percentile of the life of the washing machines, we need to use the standard normal distribution table. The z-score for the 90th percentile is 1.28. Using the table, we find that the 90th percentile is 17 years.

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HELP PLS ILL GIVE U POINTS

Answers

Answer:

i think 16 im not sure

Step-by-step explanation:

Find the area of this parallelogram.

Answers

Answer:

Let the height of the parallelogram be h

Sin 60=h/4h=4sin60

From :the formula of finding Area of the parallelogram

A=b×hA=5×4sin60 A=20sin60A= 17.3205m^2

cala used 4 2/3 cups of watermelon and 2 1/6 cups of cherries to make a fruit bowl how many cups of watermelon and cherries were used in all

Answers

Answer:

6 5/6 cups

Step-by-step explanation:

Add.

4 2/3 = 4 4/6

4 4/6 + 2 1/6 gives 6 5/6 cups were used in all.

Hope this helps!

Consider a square whose side-length is one unit. Select any five points from inside this square. Prove that at least two of these points are within squareroot 2/2 units of each other.

Answers

The given square with a side length of one unit is known to contain five points. One must prove that at least two of these points are within square root 2/2 units of each other.

According to the Pigeonhole principle, "if n items are put into m containers, with n > m, then at least one container must contain more than one item."In this context, the square is the container, and the points inside it are the objects. If more than four points are picked, the theorem is true, and two points are nearer to each other than the square root of 2/2 units.

Let's place four points on the square's four corners. The distance between any two of these points is the square root of two units since the square's side length is 1.

Let's add another point to the mix. That point is either inside the square or outside it. Without loss of generality, let us assume that the point is inside the square. It must then be within the perimeter outlined by joining the square's corners to the point that was not a corner already.

The perimeter of the square described above is a square with a side length of square root 2 units.

Since we have five points in the square, at least two of them must be in the same smaller square, due to the pigeonhole principle. Without loss of generality, let's assume that two of the points are in the upper-left square. As a result, any points within this square are within the square root 2 units of any of the other four points. Hence, at least two points of the five selected are within the square root of 2/2 units of each other.

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a parachutist rate during a free fall reaches 132 feet per second. what is this rate in meters per second? at this rate, how many meters will the parachutist fall during 10 seconds of free fall. in your computations, assume that 1 meter is equal to 3.3 feet. (do not round your answer)​

Answers

Parachutist's rate during free fall is 40 meters per second and will fall approximately 490 meters during 10 seconds of free fall.

How to convert feet to meters?

First, we need to convert 132 feet per second to meters per second. We know that 1 meter is equal to 3.3 feet, so we can use the following conversion factor:

[tex]$\frac{3meter}{3.3 feet}[/tex]

To convert feet per second to meters per second, we can multiply by the conversion factor:

[tex]132 (\frac{1}{3.3} ) = 40 meters/second[/tex]

Therefore, the parachutist's rate during free fall is 40 meters per second.

Next, we can use the following formula to find the distance the parachutist falls during 10 seconds of free fall:

distance =[tex]\frac{1}{2}[/tex] * acceleration * time²

where acceleration due to gravity is approximately 9.8 meters/second^2.

Substituting the given values, we get:

distance = [tex]\frac{1}{2}[/tex] * 9.8 meters/second² * (10 seconds)²

distance = 490 meters

Therefore, the parachutist will fall approximately 490 meters during 10 seconds of free fall.

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Please need help in math

Answers

I inserted in an image below to help you with the rule.

The 1st point  is (6,1) . This becomes (1,-6).

The 2nd point is (-5,-6). This becomes (-6, 5)

Two ropes are attached to a tree, and forces of F_1 = 1.31 + 4.6J n and F_2 = 3.2i + 6.8j n are applied. The forces are coplanar (in the same plane). What is the resultant (net force) of these two force vectors (in N)? (Express your answer in vector form.) Find the magnitude (in N) and direction (in degrees counterclockwise from the +x-axis) of this net force.

Answers

The magnitude and direction of the net force are found by adding the two forces together as resultant force vectors.

a) 11.82 N

b) 74.07°

To find the net force, we add the two force vectors F_1 and F_2:

Fnet = F_1 + F_2

Fnet = (1.31 + 4.6j) N + (3.2i + 6.8j) N

Fnet = 3.2i + (1.31 + 4.6j + 6.8j) N

Fnet = 3.2i + (1.31 + 11.4j) N

To find the magnitude of the net force, we use the Pythagorean theorem:

|Fnet| = sqrt[(3.2)^2 + (1.31 + 11.4)^2] N

|Fnet| ≈ 11.6 N

To find the direction of the net force, we use the inverse tangent function:

θ = tan^(-1)(y/x)

θ = tan^(-1)(11.4/3.2)

θ ≈ 73.8 degrees

Since the net force is in the first quadrant, the direction counterclockwise from the +x-axis is simply θ:

Direction = 73.8 degrees counterclockwise from the +x-axis

Therefore, the net force is Fnet = 3.2i + (1.31 + 11.4j) N, with a magnitude of approximately 11.6 N and a direction of approximately 73.8 degrees counterclockwise from the +x-axis.

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Forty slips are placed into a hat, each bearing a number 1, 2, 3, 4, 5, 6, 7, 8, 9, or 10, with each number entered on four slips. Four slips are drawn from the hat at random and without replacement. Let p be the probability that all four slips bear the same number. Let q be the probability that two of the slips bear a number a and the other two bear a number b≠ab≠a. What is the value of q/p?(A) 162(B) 180(C) 324(D) 360(E) 720

Answers

We have that, if they put 40 chips in a hat, each one with the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9 or 10, and each number is put on four chips. Four tokens are drawn from the hat at random and without replacement, the value of q/p, q,p as probabilities, will be given by 360, therefore, the correct option is (D) 360

How do we calculate the probability?

The probability that all four tokens have the same number (p) is equal to the total number of possible outcomes that meet that criterion divided by the total number of possible outcomes.

In this case, there are 10 possible numbers that could come up (1-10). Therefore, there are 10 possible outcomes for the four slips of paper that have the same number. Each outcome has the same probability of 1/10, so p = (1/10)^4 = 1/10000.

The probability that two of the slips have a number a and the other two have a number b (q) is equal to the total number of possible outcomes meeting that criterion divided by the total number of possible outcomes.

In this case, there are 10 possible numbers that could be drawn (1-10) and 2 ways to choose 2 different numbers out of 10, so there are 20 possible outcomes for two of the slips bearing a number and the other two bearing a number b. Each outcome has the same probability of 1/20, so q = (1/20)^4 = 1/3200000.

The ratio of q to p is q/p = 3200000/10000 = 360. Therefore, the value of q/p is 360.

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Weight: 20kg Order: 10 mg q6 hours Therapeutic range : 2-3 mg/kg/day. What is daily dose? Is it safe? Is it therapeutic?

Answers

The daily dose is 40mg, this dose per kilogram per day is within the therapeutic range of 2-3mg/kg/day, which means that the medication is within the safe and effective range for this patient's weight.

The weight of the patient is 20kg, and the prescribed dosage is 10mg every 6 hours. To calculate the daily dose, we need to multiply the prescribed dosage by the number of doses per day. Since the medication is prescribed every 6 hours, this means that the patient will take it 4 times a day.

=> (10mg x 4 doses) = 40 mg

The therapeutic range is the range of doses at which the medication is most effective and safe. In this case, the therapeutic range is 2-3mg/kg/day. To determine if the daily dose is within the therapeutic range, we need to divide the daily dose (40mg) by the patient's weight (20kg) to get the dose per kilogram per day, which is 2mg/kg/day.

However, it's important to note that the therapeutic range is a general guideline and may vary depending on the patient's individual circumstances and medical history.

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A sandwich shop owner observed the first 100 sandwich orders of the day. The data that the owner obtained is given in the table.


Type of Sandwich Number of Customers
Vegetarian 30
Turkey 20
Ham 35
Chicken 15


Which of the following circle graphs correctly represents the data in the table?
a circle graph with four sections, labeled turkey 30 percent, ham 20 percent, chicken 35 percent, and vegetarian 15 percent
a circle graph with four sections, labeled vegetarian 30 percent, turkey 20 percent, ham 35 percent, and chicken 15 percent
a circle graph with four sections, labeled chicken 30 percent, vegetarian 20 percent, turkey 35 percent, and ham 15 percent
a circle graph with four sections, labeled ham 30 percent, chicken 20 percent, vegetarian 35 percent, and turkey 15 percent
Question 6(Multiple Choice Worth 2 points)

Answers

The circle graphs which correctly represents the data in the table is "a circle graph with four sections, labeled vegetarian 30 percent, turkey 20 percent, ham 35 percent, and chicken 15 percent"

The correct answer choice is option B.

Which of the following circle graphs correctly represents the data in the table?

Type of Sandwich Number of Customers

Vegetarian 30

Turkey 20

Ham 35

Chicken 15

Total number of customers = 30 + 20 + 35 + 15

= 100

Percentage of each sandwich:

Vegetarian = 30/100 × 100

= 30%

Turkey = 20/100 × 100

= 20%

Ham = 35/100 × 100

= 35%

Chicken = 15/100 × 100

= 15%

Therefore, a circle graph with four sections, labeled vegetarian 30 percent, turkey 20 percent, ham 35 percent, and chicken 15 percent represents the table.

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I need help soon pls

Answers

The volume of the solid is 2160ft^3

Define the volume of cuboid?

Volume of Cuboid is the multiplication of length breath and height.

We know that, Volume of Cuboid = l×b×h

put the given values from figure,

= 12×10×15

=1800ft^3

Volume of top = Area of triangle × length

= 1/2 × 4× 12× 15

=360ft^3

Total volume= 1800 + 360

= 2160ft^3

Therefore, the volume of the solid is 2160ft^3

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Cuboid: According to the question the volume of the solid is [tex]2160ft^3[/tex].

What is cuboid?

A cuboid is a three-dimensional geometric shape which is composed of six rectangular faces. It has 12 edges and 8 vertices. It is also referred to as a rectangular prism. The three dimensions of a cuboid are its length, width, and height. The cuboid is a versatile shape that can be used in many different ways and can be seen in everyday objects such as boxes, desks, and bookshelves. It is also a common shape for mathematically-based problems such as calculating the volume of a cuboid.

We know that, Volume of Cuboid = l×b×h
put the given values from figure,
= 12×10×15
=[tex]1800ft^3[/tex]
Volume of top = Area of triangle × length
= 1/2 × 4× 12× 15
=[tex]360ft^3[/tex]
Total volume= 1800 + 360
= [tex]2160ft^3[/tex]
Therefore, the volume of the solid is [tex]2160ft^3[/tex]

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Find the value of 2 - 3x when x = 7
2 - 3x is a(n)__________.

Answers

Therefore, when the equation  x = 72 - 3x, the value of 2 - 3x is -52.

What is equation?

An equation is a mathematical statement that shows the equality of two expressions. It typically contains one or more variables, which are symbols that can represent any number or value. The expressions on both sides of the equal sign are called the left-hand side (LHS) and the right-hand side (RHS) of the equation. Equations are used to describe relationships between quantities or to solve problems. They can be represented in various forms, including linear equations, quadratic equations, exponential equations, and trigonometric equations. Equations can be solved by performing operations on both sides of the equation to isolate the variable or variables.

Here,

When we are given that x = 72 - 3x, we can solve for x by first adding 3x to both sides of the equation:

x + 3x = 72

Combining like terms, we get:

4x = 72

Dividing both sides by 4, we get:

x = 18

Now that we know x = 18, we can substitute this value into the expression 2 - 3x:

2 - 3x = 2 - 3(18)

2 - 3x = 2 - 54

2 - 3x = -52

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when performing regression, why would you want to have a quadratic term? group of answer choices you never want to add a quadratic term when performing regression to better fit a scatterplot with too many outliers to better fit a scatterplot that shows a curve in the data to better fit linear data

Answers

So, the right response is that, in order to more accurately fit the scatterplot that depicts a curve in the data, you need add a quadratic component while performing regression.

What is the quadratic term count?

As ax² +bx + c, a quadratic equation can be expressed. In a quadratic equation, the largest exponent is 2, which limits the number of terms to a maximum of 3. These terms are exponent 2 (ax²) and exponent 1 (bx) fixed term.

Regression can be improved by including a quadratic component to better match scatterplots of data that display curves. This is so that the independent and dependent variables can have a nonlinear connection, which is made possible by a quadratic term. A quadratic component can assist capture inherent curvature of a data and enhance the fit of a regression model in cases where the connection between both the variables isn't really strictly linear.

A quadratic term may not be appropriate or required, though. A quadratic factor would not increase the model's fit if the variables' relationships are strictly linear and might even result in overfitting. In addition, if the scatterplot contains too many anomalies or the data is not consistent, adding a quadratic factor might not be beneficial.

In order to properly fit a scatter plot graph that depicts a curve in the data, the correct response is you would like to add a quadratic term while performing regression.

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Q1 NEED HELP PLEASE HELP

Answers

Answer:

the maximum height is 2 meters

120% is 30 of what number

Answers

120 is 30 percent of 400

Alfonso wants to purchase a pool membership
for the summer. He has no more than y dollars to
spend. The Aquatics Club charges an initial fee
of $75 plus $20 per month. The Swimming Hole
charges an initial fee of $15 plus $65 per month.
Write a system of inequalities that you can use to
determine which company offers the better deal.
Let x represent the number of months.

Answers

The system of inequalities of the company with the better offer is 75 + 20x ≤ y and 15 + 65x ≤ y

Identifying the system of inequalities

Let's use A to represent the total cost (in dollars) of purchasing a pool membership from the Aquatics Club,

Let S represent the total cost of purchasing a pool membership from the Swimming Hole.

Then we can write the following system of inequalities:

A = 75 + 20x (total cost of Aquatics Club membership)

S = 15 + 65x (total cost of Swimming Hole membership)

Alfonso has no more than y dollars to spend

So, we have

75 + 20x ≤ y

15 + 65x ≤ y

Hence, the system is 75 + 20x ≤ y and 15 + 65x ≤ y

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I need help asap I just need atleast one of these explained and I can do the rest

Answers

The factοred fοrm οf a pοlynοmial is

1. 30b³- 54b² = 6b²(5b−9)

2. 3y⁵ - 48y³ = 3y³(y  −4)(y + 4)

3. x³ + 8 = (x + 2) (x² – 2x + 2²)

4. y³ - 64 = (y - 4) (y² – 4y + 4²)

5.  8c³ + 343(2c + 7)(4c² − 14c + 49)

What dοes a pοlynοmial functiοn in factοred fοrm lοοk like?

The factοred fοrm οf a pοlynοmial is represented as a³ + b³ = (a + b) (a² – ab + b²). All equatiοns are cοmpοsed οf pοlynοmials. Earlier we've οnly shοwn yοu hοw tο sοlve equatiοns cοntaining pοlynοmials οf the first degree, but it is οf cοurse pοssible tο sοlve equatiοns οf a higher degree.

One way tο sοlve a pοlynοmial equatiοn is tο use the zerο-prοduct prοperty. If yοu remember frοm earlier chapters the prοperty οf zerο tells us that the prοduct οf any real number and zerο is zerο.

We will use the formula

a³ + b³ = (a + b) (a² – ab + b²)

And

a³ - b³ = (a - b) (a² – ab + b²)

1. [tex]30b^3-\ 54b^2[/tex]

⇒ 6b²(5b−9)

2. 3y⁵ - 48y³

⇒ 3y³(  y² - 16y)

⇒ 3y³(  y² - 4 + 4 - 16y)

⇒ 3y³(y  −4)(y + 4)

3. x³ + 8

⇒ x³ + 2³

Using a³ + b³ = (a + b) (a² – ab + b²)

⇒ x³ + 2³

⇒ (x + 2) (x² – 2x + 2²)

4. y³ - 64

⇒ y³ -  4³

Using a³ - b³ = (a - b) (a² – ab + b²)

⇒ y³ -  4³

⇒ (y - 4) (y² – 4y + 4²)

5. 8c³ + 343

Using a³ + b³ = (a + b) (a² – ab + b²)

2c + 7

(2c + 7)(4c² − 14c + 49)

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It is given that quadrilateral abcd is a kite. we know that ad ≅ cd by the definition of . by the kite diagonal theorem, ac is to bd this means that angles aed and ced are right angles. we also see that ed ≅ ed by the property. therefore, we have that δaed ≅ δced by .

Answers

By the congruence postulate, we have shown that the quadrilateral is  ΔAED ≅ ΔCED.

Let's start by showing that AD = CD. Since AB = AD and BC = CD, we can rewrite AB + BC as AD + CD. This means that AD = AB + BC - CD. But we know that AB = AD, so we can substitute AD for AB to get AD + BC = 2AD + CD. Simplifying this equation, we get AD = CD.

Next, we can show that AE = CE. Since AC is a diagonal of the kite, we know that AC bisects angle BAD and angle BCD. This means that angle BAC = angle DAC and angle BDC = angle CDC. Since AD = CD, we know that triangle ACD is isosceles, so angle ACD = angle CAD.

Using these angle equalities, we can conclude that angle CAE = angle CDE. Since AC ⊥ BD, we know that angle CAD = angle CDE, so we can conclude that triangle ACE is isosceles, which means that AE = CE.

Finally, we need to show that angle AED = angle CED. Since AD = CD and AE = CE, we know that triangles AED and CED have two pairs of congruent sides. Additionally, we know that AC is a common side of the triangles.

Since AC is perpendicular to BD, we know that angle ACD and angle BDC are complementary angles.

This means that angle ACD = 90 - angle BDC and angle CAD = 90 - angle BAC. Using these angle equalities, we can conclude that angle AED = angle CED.

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