what is the example for the Y-intercept, slope, two points, and the ordered pair

The following algebraic expressions are factorized using their highest common factor HCF:

a) x² - 2x = x(x - 2)

b) 6x² + 12x = 6x(x + 2)

c) 3x³ - 9x = 3x(x² - 3)

d) 4x² + 28x³ = 4x²(1 + 7x)

The H.C.F. defines the highest common factor present in between given two or more numbers or mathematical expression.

x² and 2x have HCF as x such that;

x² - 2x = x × x - 2 × x

x² - 2x = x(x - 2)

6x² and 12x have HCF as 6x such that;

6x² + 12x = x × 6x + 2 × 6x

6x² + 12x = 6x(x + 2)

3x³ and 9x have HCF as 3x such that;

3x³ - 9x = x² × 3x - 3 × 3x

3x³ - 9x = 3x(x² + 3)

4x² + 28x³ have HCF as 4x² such that;

4x² + 28x³ = 1 × 4x² + 7x × 4x²

4x² + 28x³ = 4x²(1 + 7x)

Therefore, the algebraic expressions are factorized using their highest common factor HCF to be:

a) x² - 2x = x(x - 2)

b) 6x² + 12x = 6x(x + 2)

c) 3x³ - 9x = 3x(x² - 3)

d) 4x² + 28x³ = 4x²(1 + 7x)

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The solution for the system of inequalities is (-0.83,-1.34).

What is an inequality?

In algebra, the inequality symbol is used to show how two expressions are related in an inequality assertion. Uneven expressions can be seen on both sides of a sign of inequality.

We are given a graph on which two inequalities are plotted

So, first, we will have to frame the equations from the points.

For the blue line, we have points (0,-3) and (-1.5,0)

So, using slope-intercept form, we get the equation as

y + 2x ≥ -3

For the red line, we have points (-1,-2) and (0,2)

So, using slope-intercept form, we get the equation as

y - 4x ≥ 2

For finding the solution, we will subtract both the equations

On subtracting, we get

⇒(y+2x) - (y-4x) = -3 - 2

⇒y+2x - y + 4x = -5

⇒6x = -5

⇒x = -0.83

Substituting this value in the equation, we get

⇒y+2(-0.83) = -3

⇒y-1.66 = -3

⇒y = -1.34

Hence, the solution for the system of inequalities is (-0.83,-1.34).

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1. Total 30 4th year children travel.

2. Total 40 children from 5th year travel.

3. Total 10 adults travel.

4. Total 40 students from 6th year travel.

5. The fraction of the total number of passengers together represent the students of 4th and 5th years who traveled is 7/12.

6. The fraction of the total does not have students of 4th or 5th is 5/12.

7. The fraction of the total number of travelers are adults is 1/12.

Total passenger = 120

4th year student = 1/4 × 120

4th year student = 30

5th year student = 1/3 × 120

5th year student = 40

Now the remaining passenger

Remaining passenger = Total passenger - (4th year student + 5th year student)

Remaining passenger = 120 - (30 + 40)

Remaining passenger = 120 - 70

Remaining passenger = 50

Adults = 1/5 × 50

Adults = 10

Now the 40 passengers are left that are 6th year students.

Now we determine fraction of the total number of passengers together represent the students of 4th and 5th years who traveled.

Fraction = (4th year student + 5th year student)/Total passenger

Fraction = (30 + 40)/120

Fraction = 70/120

Fraction = 7/12

Now we determine fraction of the total does not have students of 4th or 5th.

Fraction = (Adults + 6th year passenger)/Total Passenger

Fraction = (10 + 40)/120

Fraction = 50/120

Fraction = 5/12

Now we determine fraction of the total number of travelers are adults.

Fraction = Adults/Total Passenger

Fraction = 10/120

Fraction = 1/12

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The complete question is:

In a school excursion 120 passengers travel: 1/4 of the total: 4th year students, 1/3 of the total: 5th year students and the rest, 1/5 are adults.

1. How many 4th year children travel?

2. How many children from 5th year travel?

3. How many adults travel?

4. How many students from 6th year travel?

5. What fraction of the total number of passengers together represent the students of 4th and 5th years who traveled?

6. Which fraction of the total does not have students of 4th or 5th?

7. What fraction of the total number of travelers are adults?

(a) the sample mean is 0.0494 and the sample variance is 0.000016, (b) the upper quartile is 0.04775, and the lower quartile is 0.0510, (c) the sample median is 0.04975, (d) boxplot is attached, and (e) the 5th and 95th percentiles of the inside diameter are 0.03974 and 0.056995 respectively.

(a) The mean = sum of all values divided by the number of values

μ = (x1 + x2 + ..... + xn)/n

n = 20

μ = (0.0395 + 0.0443+ 0.0450 + ... + 0.0550 + 0.0571)/20

μ = 0.9878/20

μ = 0.0494

(b) Variance = sum of squared deviations from the mean divided by n-1

s² = {(x1-μ)² + (x2-μ)² + .... (xn - μ)²)/(n-1)

s² = {(0.0395-0.0494)² + (0.0443-0.0494)² + .... +(0.0571-0.0494)²}/19

s² = 0.000016

(b) The minimum is 0.0395 and the maximum is 0.0571.

since the number of data is even, the median will be the average of two middle values.

M = Q2 = (0.0496+0.0499)/2 = 0.04975

Now, the first quartile is the median of the data values below the median

so Q1 = (0.0470+0.0485)/2 = 0.04775

And third quartile will be the median of the data values above the median

Q3 = (0.0504+0.0516)/2 = 0.0510

(c) Since we know that the number of data values is even, the median will be the average of the two middle values of the data set

so M = (0.0496+0.0499)/2

or M = 0.04975

(d) The boxplot is at maximum and minimum values. It will start in Q1 and end in Q3 and has a vertical line at the median or Q2.

The boxplot is attached.

(e) The 5th percentile means 0.05(n+1)th data value

or = 0.05(20+1) = 1.05th data value

5th percentile = 0.0550 + 0.05(0.0443-0.0395) = 0.03974

similarly,

95th percentile = 0.0550 + 0.95(0.0571-0.0550) = 0.056995

Therefore, (a) the sample mean is 0.0494 and the sample variance is 0.000016, (b) the upper quartile is 0.04775, and the lower quartile is 0.0510, (c) the sample median is 0.04975, and (e) the 5th and 95th percentiles of the inside diameter are 0.03974 and 0.056995 respectively.

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1. At least 4 ordered pairs that comply with the conditions are (0, 25), (6, 20.5), (12, 16) and (16, 13)

2. Graph is drawn according to the points and equation which is given below.

Alegria have total money $20.

The cost of one pound rice = $0.60

The cost of one pound sugar = $0.80

Let Algeria buy x pound rice and y pound sugar.

So the total cost of x pound rice is 0.60x.

The total cost of y pound sugar is 0.80y.

Now the required equation is:

0.60x + 0.80y = 20

Now we find the values buy putting the values as x = 1, 2, 3, ...

x       0         6         12          16

y      25      20.5      16          13

The graph of the values are given below:

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The complete question is:

Alegria goes to the store to buy rice and sugar, but only has $ 20. If each pound of rice costs $ 0.60 and sugar costs $ 0.80, how many pounds does each pound cost to buy?

a. Write at least 4 ordered pairs that comply with the condition

b. Realize the graphics.

A square rotated about its center by 360º maps onto itself at 4  different angles of rotation. You can reflect a square onto itself across 4  different lines of reflection.

It is important to note that a square has 4 angles of rotation and 4 lines of symmetry.

The 4 angles of rotation implies that you can tend to  rotate it  4 times so as to have it line up with its main  image before hitting 360°.

The 4 lines of symmetry which are:

Therefore the first and second blank is both 4.

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Answer:  C. proportion

Reason:

A fraction or ratio is something like [tex]\frac{2}{3}[/tex]

Something like [tex]\frac{2}{3} = \frac{4}{6}[/tex] is a proportion that ties together two fractions.

Answer:

C. proportion

Step-by-step explanation:

It is statement of equality of two ratios

A. fraction

B. ratio

C. proportion

D. rate

(I think the word should be "equality", not "quality".)

The ratio of a to b can be written as:

a to b, a:b, a/b

When you set a ratio equal to another ratio, then you have a proportion.

If ratio a/b is equal to ratio c/d, then you can write

a/b = c/d,

and now you have a proportion.

If three inches are cut off each piece, the expression represents the new total length of all five pieces of wood will be 5 x (initial length) - 15 .

To derive the expression:

Multiply 5 (the number of pieces) times the initial length of each piece
5 x (initial length)

Subtract 3 (the amount cut off each piece) times 5 (the number of pieces)

5 x (initial length) - (3 x 5)

Simplify

5 x (initial length) - 15

New total length of all five pieces of wood:

5 x (initial length) - 15

Hence the required expression is 5 x (initial length) - 15.

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(b) The probability of a positive test result is 0.0159.

(c) The probability that a person has the HIV antibody, given a positive test result, is 0.735. In this case, that would be 0.8 x 0.9 = 0.72.

This means that, if someone tests positive for the HIV antibody, there is a 73.5% chance that they actually have the HIV antibody. This number is determined by taking into account the false positive rate and true positive rate of the test.

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In option B Charlie get more money. So he picks the option B that will give him $700 more after 10 years and deposits $10,000.

A bank offers two interest-rate options.

First we check which option can give more amount after 10 years by solving the options. Then we determine how much more money Charlie will have after 10 years.

Option A gives 6% annual interest compounded quarterly.

There are 4 quarters in a year. So n = 4

So r = 6/4 = 3/2%

The formula of compound interest is

A = P(1 + r/100)^n

From the question P = 10,000, Now putting the value

A = 10000(1 + 3/200)^4

A = 10000(203/200)^4

A = 10000(1.015)^4

A = 10000(1.0614)

A = $10,614

Option B gives 7% annual interest compounded yearly.

r = 7%, P = $10000, n = 1

The formula of compound interest is

A = P(1 + r/100)^n

Now put the values.

A = 10000(1 + 7/100)^1

A = 10000(107/100)

A = 10000 × 1.07

A = $10,700

Now we can see that in option B Charlie get more money.

More Money after 10 years = 10,700 - 10,000

More Money after 10 years = $700

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The solution to the system of equations is (7.5, 1)

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

2x−3y=12

−12y+8x=48

divide the first equation by 2

So, we have

x - 1.5y = 6

This gives

x = 6y + 1.5

By substitution, the second equation becomes

-12y + 8 (6y + 1.5) = 48

So, we have

-12y + 48y + 12 = 48

Evaluate

36y = 36

Divide by 36

y = 1

So, we have

x = 6 + 1.5

x = 7.5

Hence, the solution is (7.5, 1)

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Complete question

What is the solution to this system?

2x−3y=12

−12y+8x=48

Enter the solution as an ordered pair, (x, y).

The equations c = 18z, 3s = P, and L = 60w represent a proportional relationship, but A = s² does not represent a proportional relationship.

The equation that represents a proportional relationship, or a line, is y = kx, where k is the constant of proportionality.

If we take the first equation, Volume measured in cups (c) vs The same volume measured in ounces (z): c = 18z

Here, 18 is a constant

∴It is a proportional relationship.

If we take the second equation, the Area of a square (A) vs The side length of the square (s): A = s²

This is a quadratic equation.

∴It is not a proportional relationship.

If we take the third equation, Perimeter of an equilateral triangle (P) vs The side length of the triangle (s): 3s = P

Here, 3 is a constant

∴It is a proportional relationship.

Finally, If we take the fourth equation, Length (L) vs Width (w) for a rectangle whose area is 60 square units: L = 60 w

Here, 60 is a constant

∴It is a proportional relationship.

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Answer:

Joe graphed the wrong y-axis. The y-axis is (0,2) Also the x-axis is wrong, its supposed to be (4,0).

Step-by-step explanation:

30.6% of survey respondents do not like both hamburgers and burritos, with the strongest association being that customers who like hamburgers are more likely to not like burritos.

Part A: The number of survey respondents that do not like hamburgers is 205 - 81 = 124.

Of these 124 respondents, 38 do not like burritos as well, so the percentage of respondents that do not like both hamburgers and burritos is 38 / 124 * 100% = 30.6%.

Part B: The marginal relative frequency of all customers who like hamburgers is 81 / (81 + 205) = 28.2%.

Part C: The conditional relative frequency of customers that like burritos given they like hamburgers is 49 / 81 = 60.5%.

The conditional relative frequency of customers that do not like burritos given they like hamburgers is 32 / 81 = 39.5%.

The conditional relative frequency of customers that like hamburgers given they like burritos is 49 / 141 = 34.8%.

The conditional relative frequency of customers that do not like hamburgers given they like burritos are 92 / 141 = 65.2%.

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Answer:

No.

Step-by-step explanation:

A linear function can be identified if the function is a line when graphed or if the x is to the first power. X is to the third power, so it's not linear.

Hope it helped!

The given are two scalene triangles are similar with a scale of 2:3. The correct option is 4th i.e, PQ/GH = 3/2.

The triangles GHI and PQR are similar with a scale of 2:3.

The corresponding sides of similar triangles are proportional and the corresponding angles are congruent.

GH/PQ = HI/QR = GI/PR = 2/3

∠G ≅ ∠P

g = p

g/p = 1

So, the third option is incorrect.

∠H ≅ ∠Q

h = q

∠I ≅ ∠R

i = r

i/r = 1

So, the second option is incorrect.

Now,

HI/QR = 2/3 ≠ 3/2

So, the first option is incorrect.

PQ/GH = 3/2

Thus, fourth option is correct.

The question is incomplete. The figures are attached in the below attachment. The options are missing. They are ' A. HI/QR = 3/2 B.i/r = 2/3

C.g/r = 1 D. PQ/GH = 3/2'

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Answer: c. a = 2y and b = -3

Step-by-step explanation:

To find the values of a and b in this division problem, we need to perform polynomial division. Starting with the dividend, 8y^2 – 12y + 4, we divide the leading term of the dividend, 8y^2, by the leading term of the divisor, 4y. This gives a quotient of 2y.

Next, we multiply the divisor, 4y, by 2y and subtract it from the dividend, 8y^2 – 12y + 4. This gives a remainder of -3.

So, in this division problem, the values of a and b are a = 2y and b = -3.

Answer:

To solve this problem we can use the formula for future value of an investment, which is:

FV = PV(1+r)^t

Where PV is the present value, r is the interest rate, t is the number of years, and FV is the future value.

In this case, we know that PV = $4,900, r = 3% = 0.03, and FV = $5,920.

So we can rearrange the formula to solve for t:

t = log(FV/PV) / log(1+r)

t = log($5,920 / $4,900) / log(1+ 0.03)

t ≈ 10.3 years

Therefore, it would take approximately 10.3 years for the account to reach $5,920.

The average rate of change of f(x) from x = 1 to x = 3 is 0.5

The average rate of change of a function over an interval is the change in the function value (y) divided by the change in the input value (x) over that interval.

To find the average rate of change of f(x) = [tex]x^{3}[/tex] - [tex]4x^{2}[/tex] + 5 from x = 1 to x = 3, we can use the following formula:

(f(3) - f(1)) / (3 - 1)

substituting the function value, we get

([tex]3^{3}[/tex] - 4[tex](3)^{2}[/tex] + 5 - ([tex]1^{3}[/tex] - 4[tex](1)^{2}[/tex] + 5)) / (3 - 1)

= (27 - 36 + 5 - (1 - 4 + 5)) / 2

= (1) / 2

So the average rate of change of f(x) from x = 1 to x = 3 is 0.5

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Answer:

  zero

Step-by-step explanation:

You want the rate of change between the points (3, 1) and (4, 1).

The "rate of change" is also known as the "slope" of the line between the points. That is given by the formula ...

  m = (y2 -y1)/(x2 -x1)

For your points, this is ...

  m = (1 -1)/(4 -3) = 0/1 = 0

The rate of change is zero.

__

Additional comment

The y-value is constant. That means the equation of the line is y=1, a horizontal line. It does not rise or fall. Its rate of change is zero.

10.8 m = 10*(8/10)=54/5 m

1.5 h = 3/2 h

distance = 54/5

time = 3/2 h

Speed = distance /time

= 54/5 ÷ 3/2 = 7.2 m/h

how far will the snail travel in 5 minute ?

5 min = 5/60 = 1/12 h

In 1/12 h the snail will travel

7.2 * 1/12 m = 0.6 m = 60 cms

Rigid motions and dilations are transformations in Euclidean space. They are both types of transformations that preserve distances and angles.

Similarities between Rigid motions and Dilations:

Both preserve the length of lines and distances between points.

Both preserve angles between lines.

Differences between Rigid motions and Dilations:

Rigid motions are a combination of rotations, translations, and reflections, while dilations are just scaling transformations.

Rigid motions preserve orientation, while dilations change it.

Rigid motions preserve the shape of figures, while dilations change the size of figures but preserve the ratio of lengths of corresponding sides.

Properties and the transformations that preserve them:

Length of lines: Rigid motions and dilations preserve the length of lines.

Distances between points: Rigid motions and dilations preserve distances between points.

Angles between lines: Rigid motions and dilations preserve angles between lines.

Orientation: Rigid motions preserve orientation, while dilations change it.

Shape of figures: Rigid motions preserve the shape of figures, while dilations change the size of figures but preserve the ratio of lengths of corresponding sides.

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The equation of the line passing through M and perpendicular to PR would be y = -x + 6.

What is the equation of the line?

An equation of a line is a mathematical expression that describes the relationship between the variables x and y that defines the position of a point on the line. There are several ways to write the equation of a line, including slope-intercept form (y = mx + b), point-slope form (y - y1 = m(x - x1)), and standard form (ax + by = c).

The midpoint of a line segment is the point that is exactly halfway between the two endpoints of the line. To find the midpoint of a line segment, you need to take the average of the x-coordinates and the y-coordinates of the two endpoints.

Given the line segment Q(-6, 2) and R(10, 6), the midpoint is:

((-6+10)/2 , (2+6)/2) = (2,4)

So the midpoint of the line segment Q(-6, 2) and R(10, 6) is (2,4).

Now find the slope of PR = 6-(-4)/10 = 10/10=1

Hence, the slope of the line passing through M and perpendicular to PR would be = -1.

Now we can form the equation of the line:

y - 4 = -1(x - 2)

y - 4 = -x + 2

y = -x + 6

Hence, the equation of the line passing through M and perpendicular to PR would be y = -x + 6.

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You can use this trigonometry calculator in two common situations when trigonometry is required. Use the calculator's first section to get the values of sine, cosine, tangent, and their reciprocal functions.

A subfield of mathematics is trigonometry. In particular, it describes and applies the connections and ratios between angles and sides in triangles. Trigonometry largely works with angles and triangles. Thus, solving triangles exactly correct triangles as well as any other kind of triangle you choose is the main application.

Numerous difficulties in daily life, such figuring out the height or separation between two objects, can be solved using trigonometry. Other uses include the satellite navigation system, astronomy, and geography.

Additionally, sine and cosine functions are essential for explaining periodic events; with their help, we can explain oscillatory movements (like those in our straightforward pendulum calculator) and waves like sound, vibration, and light.

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[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{Looking for improper or mixed fraction:}[/tex]

[tex]\mathsf{310\% \rightarrow \dfrac{310}{100} \rightarrow 3.1}[/tex]

[tex]\mathsf{\rightarrow 3.1 \times \dfrac{10}{10}}[/tex]

[tex]\mathsf{\rightarrow \dfrac{3.1}{1}\times\dfrac{10}{10}}[/tex]

[tex]\mathsf{\rightarrow \dfrac{3.1\times10}{1\times10}}[/tex]

[tex]\mathsf{\rightarrow \dfrac{31}{10}}[/tex]

[tex]\mathsf{\rightarrow 3 \dfrac{1}{10}}[/tex]

[tex]\huge\text{Therefore, your answers should be:}[/tex]

[tex]\huge\boxed{\mathsf{Fraction \rightarrow \dfrac{310}{100}\ \& \ Mixed\ Number \ \rightarrow 3\dfrac{1}{10}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Allan would need to sell 427 boxes to make 1600 dollars in total sales. The number line representation of the number of boxes sold is 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, ..............., 1600].

A pair of coordinates’ vertical value. How high or low the point is. In an ordered pair of coordinates (x,y), the Y Coordinate is always written second, as in (12,5). In this case, the Y Coordinate is “5”. Also known as “Ordinate” Pick x and solve the equation for y to locate points on the line y = mx + b, or choose y and solve for x.

When you know the slope of the line to be investigated and the point supplied is also the y intercept, you may utilize the slope intercept formula y = mx + b. (0, b). The y value of the y intercept point is represented by b in the formula. Exemplification 2: Determine the equation.

In the given question,

a. The point on the graph that represents 1600 dollars in total sales is (427, 1600).

b. Allan would have to sell 427 boxes to make 1600 dollars in total sales.

c. The number line representation of the number of boxes sold when the total sales is equal to 1600 dollars would be:

[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, ................., 1600].

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Based on the constant rate of painting, Owen will paint 1600 square feet in 80 minutes.

The expression for calculation to find the area painted in 80 minutes is -

Area to be painted in 80 minutes = area painted in one minute × time spent

Keep the values in formula to find the area painted

Area to be painted in 80 minutes = 20 × 80

Performing multiplication on Right Hand Side of the equation

Area to be painted in 80 minutes = 1600 square feet

Thus, the painted area by Owen will be 1600 square feet.

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Mary's speed, given the kilometers she rode in 7 hours, can be found to be 12. 8 km / hr

To find the speed that Mary was going in order to have been able to travel 89.6 kilometers in 7 hours, you can use the speed formula which is:

= Distance / Time

Distance =  89. 6 kilometers

Time = 7 hours

The speed that Mary was going at is therefore :

= 89. 6 km / 7 hours

= 12. 8 km / hr

In conclusion, the speed that Mary was going at was 12. 8 km / h.

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The measure of angle m∠EDC = 25°, round to the nearest tenth.

For the given question

As the both diagonal of the rectangle are equal.

ΔAED is isosceles triangle.

Then,

m∠ADE = m∠DAE = 50°

As all 4 angles of the triangle are equal.

m∠EDC = 90 - m∠ADE

             = 90 - 65

m∠EDC = 25°

Thus, the measure of the angle m∠EDC = 25°, round to the nearest tenth.

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The diagram for the question is attached.