1. draw the graphs of:
a. g(x) = -4x - 5

b. h(x) = - 4x - 12

c. j(x)= -4x -15

2. Write an equation for the linear function with a gradient of - 4 and an
unknown y-intercept of k.

The length of the arc AB is 6 cm when BC is 2 cm, ∠BOC = 32°, and ∠AOB = 96°.

The arc length is the portion of the circumference of a circle. It is directly proportional to the central angle formed by an arc.

The center of the circle is O, where BC = 2 cm, ∠BOC = 32°, and ∠AOB = 96°. Draw the diagram as per the given data.

As 96° = 3×32°, it follows that ∠AOB = 3×∠BOC.

As the central angle formed by an arc is proportional to its length. It follows that AB = 3×BC.

Since, BC = 2 cm, it can be got that AB = 3×2 cm = 6 cm.

Therefore, the required answer is 6 cm.

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Answer:

5X^4 + 2X^2 – 8

Step-by-step explanation

Its quadratic form is 5(x²)² +2x² -8

Let be X²=p, so the final expression is 5p²+2p-8

hope this help's

Answer:

Step-by-step explanation:

Number of guests who called for room service = 45

Total number of guests = 45 + 200 = 245

Percentage of guests who called for room service = (45/245) x 100% ≈ 18.4%

Therefore, approximately 18.4% of the hotel's guests called for room service.

Answer:

To add different quantities of liquids with different units of measurements, we need to convert them all to the same unit of measurement. In this case, let's convert everything to quarts since that is what we want the final answer to be in.

2 gallons = 8 quarts (since 1 gallon = 4 quarts)

5 quarts of pineapple juice = 5 quarts (no conversion needed)

4 pints of cranberry juice = 8 cups = 2 quarts (since 1 pint = 2 cups and 1 quart = 4 cups)

6 cups of apple juice = 1.5 quarts (since 1 cup = 0.25 quarts)

Now we can add up all the quantities:

2 + 5 + 2 + 1.5 = 10.5

Maya made 10.5 quarts of fruit punch in all

The value of the variables y and z are 18

From the question, we have the following parameters that can be used in our computation:

The special right triangle

The special right triangle has one of its angles to be 45 degrees

This means that

Legs = Hypotenuse/√2

Using the above as a guide, we have the following:

Legs = 18√2/√2

Evaluate

Legs = 18

Hence, the value of y and z are 18

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Ill try my best to "show my work" in text

First, we need to calculate the total amount of time Ron spent watching TV over the weekend.

On Saturday, he watched TV for 1 hour and 0 minutes from 9:30-10:30AM, 2 hours and 30 minutes from 1:00-3:30PM, and 2 hours from 8:00-10:00PM, for a total of 5 hours and 30 minutes on Saturday.

On Sunday, he watched TV for 1 hour and 30 minutes from 1:00-2:30PM, and 2 hours from 8:00-10:00PM, for a total of 2 hours and 30 minutes on Sunday.

The total time he spent watching TV over the weekend is 5 hours and 30 minutes on Saturday + 2 hours and 30 minutes on Sunday = 8 hours.

Next, we need to calculate the time he spent watching sports programs and movies.

He watched sports programs for half of the total time he spent watching TV, so he spent 8 hours / 2 = 4 hours watching sports programs.

He watched movies for one third of the total time he spent watching TV, so he spent 8 hours / 3 = 2 hours and 40 minutes watching movies.

Finally, we can calculate the time he spent watching cartoons with his sister.

He spent 8 hours watching TV total, and 4 hours watching sports programs and 2 hours and 40 minutes watching movies, so he spent 8 hours - 4 hours - 2 hours and 40 minutes = 1 hour and 20 minutes watching cartoons.

Since there are 60 minutes in an hour, the total time Ron spent watching cartoons is 1 hour and 20 minutes = 80 minutes.

Answer:

So Ron spent 1 hour and 40 minutes watching cartoons with his sister Ronnette.

Step-by-step explanation:

First, we need to calculate the total time that Ron spent watching TV. On Saturday, he watched TV for 1 hour in the morning, 2 hours and 30 minutes in the afternoon, and 2 hours in the evening, which adds up to 6 hours and 30 minutes. On Sunday, he watched TV for 1 hour and 30 minutes in the afternoon and 2 hours in the evening, which is a total of 3 hours and 30 minutes. So over the weekend, Ron watched TV for 6 hours and 30 minutes on Saturday and 3 hours and 30 minutes on Sunday, which adds up to a total of 10 hours.

Since Ron watched sports programs for half the time he watched TV, he spent 10 hours / 2 = 5 hours watching sports.

And since he watched movies for one-third of the time he watched TV, he spent 10 hours / 3 = 3 hours and 20 minutes watching movies.

Finally, we can calculate the time Ron spent watching cartoons by subtracting the time he spent watching sports and movies from the total time he spent watching TV:

10 hours - 5 hours - 3 hours and 20 minutes = 1 hour and 40 minutes

So Ron spent 1 hour and 40 minutes watching cartoons with his sister Ronnette.

The correct option regarding the estimate of the percentage is of:

The answer should be close to 1/3 of 120, which is 40.

The percentage is estimated applying the proportions in the context of the problem.

To estimate 30% of 123, we must multiply the total amount of 123 by the decimal equivalent of the percentage of 30%, which is 30/100 = 0.3, hence the estimate is given as follows:

0.3 x 123 = 36.9.

This is close to 1/3 of 120, which is of 40, hence the last option is correct.

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Cluster sampling is a sampling technique used in statistics and research methodology where a population is divided into groups, or clusters, and a sample is randomly selected from each cluster to be included in the study.

This method is often used when it is difficult or impractical to obtain a simple random sample of individuals from a large and diverse population. For example, in a study of public schools in a state, it may be easier to randomly select a sample of schools and then include all students in those schools in the study, rather than attempting to randomly select individual students from the entire state.

The advantages of cluster sampling include lower costs and greater efficiency than other sampling techniques, particularly when working with large populations. However, it can also increase the risk of sampling bias and decrease the precision of estimates if the clusters are not representative of the larger population. Therefore, it is important to carefully choose clusters that are as heterogeneous as possible within and as similar as possible between clusters.

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Answer:

I think its

Step-by-step explanation:

2^(n+1) is the explicit form

Answer:

acute angle

Step-by-step explanation:

The equation y =-2/3x+7 , 4x+6y=42 has many solution.

System of equation can be solved using different method such as elimination method, substitution method and graphical method. Let's solve the system of equation using substitution method.

y = -2/3 x + 7

4x + 6y = 42

Let's substitute the value of y in equation 2

Therefore,

4x + 6(- 2/3 x + 7) = 42

4x - 12 / 3 x + 42 = 42

4x - 4x + 42 = 42

4x - 4x = 42 - 42

0 = 0

Therefore, it numerous solution

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The error she made is option c. Jamie did not factor the variable from the second term.

Expressions are mathematical statements which consist of two or more terms and terms are connected to each other using mathematical operators like addition, multiplication, subtraction and so on.

Given expression is 15x - 20xy.

We have to factor the expression.

Common factor of both the terms 15x and 20xy is 5x.

Taking the term 5x outside and using the distributive property,

15x - 20xy = 5x (3 - 4y)

But Jamie got it as 5x (3 - 4xy)

So the variable in the second term has not been factored correctly.

Hence the error in the process is that She did not factor the variable from the second term.

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The correct matching according to the given question is given in the image below.

The value of an expression is obtained by substituting the variables with the specific values. The value may be any real number if the specific values are constants.

Substitute x=6 into the expression -2+2x/3.

-2+(2×6)/3=-2+12/3

=-2+4

=2

Substitute x=-3 into the expression 5-x/3.

5-(-3)/3=5-(-1)

=5+1

=6

Substitute x= 6 into the expression -3+x/2.

-3+6/2=-3+3

=0

Substitute x=4 into the expression 2-3x/4.

2-(3×4)/4=2-12/4

=2-3

=-1

Therefore, the answers are correctly matched by an arrow line.

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Answer:

Step-by-step explanation:

The statement that correctly compares the values of the 7s in 7.825 and 3.7 is:

The 7s in 7.825 are greater than the 7s in 3.7.

The 7s refer to the units place (the "ones" place) in decimal numbers. In 7.825, the 7s are 7 and in 3.7, the 7s are 7. When comparing the two numbers, we can see that the number 7.825 is greater than 3.7, which means the 7s in 7.825 are greater than the 7s in 3.7.

a) Relationship between corresponding sides: the corresponding sides are parallel and have a ratio of k in length.

b) Relationship between corresponding sides' orientations: The corresponding sides will still be parallel to the original sides.

c) Relationship between corresponding angles:the corresponding angles are congruent.

What do you mean by congruent angles?

Congruent angles are angles that have the same measure or size. In other words, if two angles have the same number of degrees or radians, they are said to be congruent. When we say that two angles are congruent, it means that they are exactly the same shape and size, and they can be superimposed on each other without any rotation or scaling. Congruent angles play an important role in geometry, as they allow us to prove that two figures are similar or congruent.

To apply a dilation with scale factor k centered at the origin, we multiply the coordinates of each vertex by k. So, to find the coordinates of A', B', and C', we will multiply the coordinates of A, B, and C by the scale factor.

a) The relationship between corresponding sides in terms of their lengths:

Let's denote the scale factor by k. The distance between two points (x1, y1) and (x2, y2) is given by the distance formula, which is:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

When we multiply each coordinate by k, the distance between the two points is multiplied by k as well. So, if AB has length dAB and A'B' has length dA'B', we have:

dA'B' = k * dAB

Similarly, we can find the relationship between the lengths of BC and B'C', as well as between the lengths of AC and A'C'.

b) The relationship between corresponding sides in terms of their orientations:

The orientation of a line is given by its slope. If two lines have the same slope, they are parallel or collinear. If they have slopes that are negative reciprocals of each other, they are perpendicular. When we multiply the coordinates of a point by k, the slope of any line passing through that point is multiplied by k as well. So, if the slope of AB is mAB and the slope of A'B' is mA'B', we have:

mA'B' = k * mAB

We can use this to find the relationship between the slopes of BC and B'C', as well as between the slopes of AC and A'C'.

c) The relationship between corresponding angles in terms of their measures:

The measure of an angle is determined by the slope of the line that contains the angle. When we multiply the coordinates of a point by k, the slope of any line passing through that point is multiplied by k as well. This means that the measure of any angle that includes the origin is unchanged by the dilation. However, the measure of any angle that does not include the origin is multiplied by a factor of k. So, if angle ABC has measure x and angle A'B'C' has measure y, we have:

y = k * x

We can use this to find the relationship between the measures of angles BAC and B'A'C', as well as between the measures of angles CBA and C'B'A'.

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Answer:

350x + 200y - 4200 = 0

x intercept is (12,0)

y intercept (0,21)

steps:

ii

350x + 200y - 4200 = 0

Therefore, the equation in standard form that models the number of funnel cakes, x, and the number of deep-fried Oreos, y, Francis can buy if he spends $42.00 is:

350x + 200y - 4200 = 0

To find the x-intercept, we set y to zero and solve for x:

350x + 200(0) - 4200 = 0

350x = 4200

x = 12

Therefore, the x-intercept is 12. This means that if Francis only buys deep-fried Oreos (y = 0), he can buy 12 funnel cakes with $42.00.

Answer:

350x + 200y - 4200 = 0

x intercept is (12,0)

y intercept (0,21)

steps:

3.50x + 2.00y = 42.00

3.50x + 2.00y - 42.00 = 0

Multiplying both sides by 100 to eliminate the decimals, we get:

350x + 200y - 4200 = 0

x-intercept means what is x when y is 0

350x + 200(0) - 4200 = 0

350x = 4200

x = 12

y-intercept means what is y when x is 0

350(0) + 200y - 4200 = 0

200y = 4200

y = 21

So the x-intercept is (12, 0) and the y-intercept is (0, 21).

ChatGPT

To find the y-intercept, we set x to zero and solve for y:

350(0) + 200y - 4200 = 0

200y = 4200

y = 21

Therefore, the y-intercept is 21. This means that if Francis only buys funnel cakes (x = 0), he can buy 21 deep-fried Oreos with $42.00.

So the x-intercept is (12, 0) and the y-intercept is (0, 21).

ChatGPT

Answer:

22

Step-by-step explanation:

(11 x 4) / 2 x 1

= 44/2 x 1

= 22 x 1

= 22

The study of population growth is important because it helps us understand the factors that drive changes in population size, and the impacts that population growth can have on the environment, economy, and human well-being.

Understanding population dynamics is essential for developing sustainable policies and managing natural resources effectively.

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The Equation of Circle is (x+ 6)² + (y - 3)² = 9².

The equation for a circle is given by:

(x-h)² +(y-k)² = a²

Where (h,k) is the center and a is the radius of the circle.

Given:

We have the points A(-6, 3), B(-15, 3), and C(3,3).

Using Distance Formula

AB = √(-15 + 6)² + (3-3)²

AB = √9²

AB= 9 unit

BC= √(3 + 15)² + (3-3)²

BC = 18 unit

and, AC = √(3+6)² + (3-3)²

AC = 9 unit

As, AB = AC then A has to be the center (-6, 3) with radius 9 unit.

Thus, the Equation of Circle is

(x+ 6)² + (y - 3)² = 9²

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The balance amount when compounded daily at a rate of 4.075% after 6 months is  $269,320.60.

What is meant by compound interest?

The interest you earn on interest is known as compound interest. Compound interest, also known as interest on principal & interest, is the practice of adding interest to the principal amount of a loan or deposit. Compound interest is calculated for an amount based on both the principal and cumulative interest. The major distinction between compound and simple interest is this. If we examine our bank statements, we will typically see that our account is credited with interest on a yearly basis. Even while the principal remains the same, the interest changes annually. We can observe that interest rises over time. Thus, we can infer that the interest the bank charges is compound interest rather than simple interest.

Given,

Principal amount P = $263,000

Rate of interest r = 4.075%

Time period t = 6 months = 0.5 years

Final amount =  [tex]A = P(1 + \frac{r}{n})^{nt}[/tex]

where n = 365

A = [tex]P(1 + \frac{r}{n})^{nt} =263000(1 + \frac{0.04075}{365})^{365*0.5}[/tex]  = $269,320.60

Therefore the balance amount when compounded daily at a rate of 4.075% is  $269,320.60.

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Answer:

= 15x + 1.

Step-by-step explanation:

Sum and the length of all three sides

8x - 4 + x + 5 + 6x

8x + x + 6x - 4 + 5

15x + 1.

The number of packets of dimensions 16 cm by 9 cm by 4 cm in a cubical box will be 3,000.

Volume is a measurement of three-dimensional space that is utilized. It is frequently mathematically quantified using SI-derived units or different imperial or US traditional units. The concept of length is linked to the notion of capacity.

The volume of each packet is given as,

v = 16 x 9 x 4

v = 576 cubic cm

The volume of the cubical box is given as,

V = (1.2 x 100) x (1.2 x 100) x (1.2 x 100)

V = 120 x 120 x 120

V = 1,728,000 cubic cm

Then the number of packets is given as,

n = V / v

n = 1,728,000 / 576

n = 3,000

The number of packets of dimensions 16 cm by 9 cm by 4 cm in a cubical box will be 3,000.

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To calculate the z-score, the formula is: z-score = (x - μ)/σ, where x is the value, μ is the mean, and σ is the standard deviation. Once the z-score is calculated, it can be used to look up the area, or probability, in the table.

A unit normal table is a type of probability table that is used to determine the area, or probability, under the normal curve. It is based on the standard normal probability distribution, which is a normal distribution with a mean of 0 and a standard deviation of 1. To use the unit normal table, one first needs to calculate the z-score, which is the number of standard deviations away from the mean a given value is. To calculate the z-score, the formula is: z-score = (x - μ)/σ, where x is the value, μ is the mean, and σ is the standard deviation. Once the z-score is calculated, it can be used to look up the area, or probability, in the table.

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Answer:

There are two possible solutions for angle Θ, as cosine is negative in the second and third quadrants.

Using the inverse cosine function on a calculator, we can find the two possible solutions for Θ:

Θ = 120° (in the second quadrant)

Θ = 240° (in the third quadrant)

Therefore, the possible angles for Θ are 120° and 240°.

Answer: To find the point on the directed line segment that partitions it into a ratio of 4 to 5, we can use the formula for a point on a line given two endpoints and a ratio. The formula is:

(x, y) = (1 - t) * (x1, y1) + t * (x2, y2)

where (x1, y1) and (x2, y2) are the coordinates of the endpoints of the line segment, and t is a value between 0 and 1 that determines the location of the point along the line.

In this case, (x1, y1) = (-1, -9) and (x2, y2) = (8, 9), and we want the point that partitions the line segment into a 4 to 5 ratio, so:

t = 4 / (4 + 5) = 4 / 9

Plugging in the values into the formula:

x = (1 - t) * x1 + t * x2 = (1 - 4/9) * (-1) + (4/9) * 8 = (5/9) * 8 - (4/9) * 1 = 44/9 - 4/9 = 40/9

y = (1 - t) * y1 + t * y2 = (1 - 4/9) * (-9) + (4/9) * 9 = (5/9) * 9 - (4/9) * (-9) = 45/9 + 36/9 = 81/9

So the point that partitions the line segment into a 4 to 5 ratio is (40/9, 81/9).

Step-by-step explanation:

Answer: c

Step-by-step explanation:

A parabola is a mirror-symmetrical, roughly U-shaped planar curve in mathematics. Many seemingly unrelated mathematical descriptions that all correlate to the same curves can be used to define it.

In mathematics, a parabola is a roughly U-shaped, mirror-symmetrical planar curve.

The same curves can be defined by a number of seemingly unrelated mathematical definitions, which all correspond to it.

A line and a point (the focus) are two components of one definition of a parabola (the directrix).

The directrix is not the main focus.

The locus of points in that plane that are equally spaced apart from the directrix and the focus is known as the parabola.

A right circular conical surface and a plane parallel to another plane that is tangential to the conical surface intersect to form a parabola, which is also known as a conic section.

Therefore, a parabola is a mirror-symmetrical, roughly U-shaped planar curve in mathematics. Many seemingly unrelated mathematical descriptions that all correlate to the same curves can be used to define it.

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Complete question:

What is a parabola?

We can find the variance of a uniform distribution, using the following formula: Variance = (b - a)² / 12. Here: a is the lower limit of the uniform distribution, b is the upper limit of the uniform distribution.

The formula for the variance of a uniform distribution is based on the fact that the variance of a continuous uniform distribution is equal to the square of the range (i.e., the difference between the upper and lower limits) divided by 12.

For example, let's say we have a uniform distribution between 0 and 10. To find the variance, we would use the formula:

Variance = (10 - 0)² / 12

Variance = 100 / 12

Variance = 8.33

Therefore, the variance of a uniform distribution between 0 and 10 is 8.33.

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Answer: Two triangles are congruent if and only if all corresponding sides are equal in length. So, to find the values of x and y for which ΔABC and ΔXYZ are congruent, we need to equate the corresponding side lengths:

4x + 3 = 6x - 1

5 = 5

8y - 1 = y + 6

Solving the first equation for x:

4x + 3 = 6x - 1

2x = -4

x = -2

Solving the third equation for y:

8y - 1 = y + 6

7y = 7

y = 1

So, the values of x and y that make ΔABC and ΔXYZ congruent are x = -2 and y = 1.

Step-by-step explanation: