Use synthetic division to divide.
(x^3-12x^2+15x+7)/(x+4)

a) Jill receives £45

b) Jack receives £20 the following Christmas

c) Jack will be 5/4 years old, which is equivalent to 1 year and 3 months when he receives £25 from Uncle Fred.

Explain the term years

Years are a unit of time measurement used to quantify the duration of one complete orbit of the Earth around the sun. A year consists of 365 days, except in a leap year when an extra day is added. The concept of a year is used in various fields, including astronomy, geology, and history.

According to the given information

(a) Let's first find the total ratio of their ages:

1 + 3 = 4

So Jack's share will be:

1/4 x £60 = £15

And Jill's share will be:

3/4 x £60 = £45

Therefore, Jill receives £45.

(b) The next Christmas, Jack will be 2 and Jill will be 4. We can use the same ratio to find Jack's share:

2/6 x £60 = £20

So Jack receives £20.

(c) Let x be the age of Jack when he receives £25 from Uncle Fred. We know that:

1/4 x £60 = £25

Multiplying both sides by 4/60, we get:x = 5/4

So Jack will be 5/4 years old, which is equivalent to 1 year and 3 months, when he receives £25 from Uncle Fred.

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Answer:two lines are parallel if their slopes are equal and they have different y-intercepts

Step-by-step explanation:

Answer: 1.75

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

Since the garden bed looks like the shape of a trapezoid the equation to find the area of a trapezoid is A = 1/2h (base 1 + base 2)

The area is already given so you can just plug it in. Also you can plug in the bases.

21 = 1/2h (3 + 4)

21 = 1/2h (7)  rewrite

21 = 1/2(7)h

21 = 3.5h  Divide both sides by 3.5

6 = h

To determine if (2, 6) is a solution to the system of equations:

y = 3/2x + 3 ... (equation 1)

y = -9x + 1 ... (equation 2)

We need to substitute x = 2 and y = 6 into both equations and check if they are true.

Substituting x = 2 and y = 6 into equation 1, we get:

6 = 3/2(2) + 3

6 = 3 + 3

6 = 6

This equation is true.

Substituting x = 2 and y = 6 into equation 2, we get:

6 = -9(2) + 1

6 = -18 + 1

6 = -17

This equation is false.

Since (2, 6) does not satisfy equation 2, it is not a solution to the system of equations. Therefore, the answer is: no.

I hope this helps you.

Vector a: start at (1, 3) and end at (-4, -2) in blue.

Vector b: start at (-4, -2) and end at (1, 3) in red.

Vector a+b: start at (1, 3) and end at (2, 7) in green.

To represent a+b using the parallelogram method,

we must draw vectors representing a and b.

The initial point of vector a is (1, 3), and its terminal point is (-4, -2). The initial point of vector b is (-4, -2), and its terminal point is (1, 3).

Using the vector tool, we then  draw the vectors a and b. We start at the initial point of each vector and select the terminal point.

Vector a: start at (1, 3) and end at (-4, -2)

Vector b: start at (-4, -2) and end at (1, 3)

We the diagonal, we start at the initial point of vector a, (1, 3), and draw a line parallel to vector b that passes through the initial point of vector b, (-4, -2). This line intersects the line parallel to vector a that passes through the initial point of vector b at point (2, 7). This point is the terminal point of the diagonal vector, which is a+b.

We use the vector tool, we can draw vector a in blue, vector b in red, and vector a+b in green.

Vector a: start at (1, 3) and end at (-4, -2) in blue.

Vector b: start at (-4, -2) and end at (1, 3) in red.

Vector a+b: start at (1, 3) and end at (2, 7) in green.

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The best percentage bar graph that represents Camryn's data is:

C Winter | Spring | Summer | Fall

0% 20% 40% 60% 80% 100%

A bar graph's purpose is to visually convey relational information quickly. The bars show the value for a specific type of data.

This is because the graph correctly shows the percentage of students who prefer each season, with the bar for each season extending to the appropriate percentage mark on the graph. It also clearly labels each season under the corresponding bar.

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The result of adding -3 (row 1) to row 2 is determined as (0  10) |-14.

The result of the row multiplication in the matrix is calculated by applying the following method;

row 1 in the given matrix = [1  -4] | 8

To multiply row1 by -3, we will multiply each entity by -3 as shown below;

= -3(1  -4) | 8

= (-3  12) | -24

To add the result to 3;

(-3  12) | -24  +  (3   -2)|10

= (0  10) |-14

Thus, the result of the row multiplication is determined by multiplying each entry in row 1, by - 3.

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From the circle graph of the survey, 52 more people prefer pigs than chickens.

A sort of data visualisation tool used to depict data as a circular chart is a circle graph, commonly referred to as a pie chart. Each slice of the circle graph, also known as a sector, represents a certain category or chunk of the entire. Each slice's size is proportional to how much data or what percentage it represents, and the sum of all slices is 100%.

Circle graphs are frequently used to depict percentages or categorical data, and they are especially helpful for comparing and illustrating relative proportions among several categories within a data collection.

From the circle graph we see that the percentage of people who prefer chickens are 29%.

Thus, 29/100 (400) = 116 people

Also, 16% people prefer pig:

Thus, 16/100 (400) = 64 people

Thus, the difference is:

116 - 64 = 52

Hence, from the circle graph of the survey, 52 more people prefer pigs than chickens.

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The complete question is:

Answer:

(-8.89, -26.69)

Step-by-step explanation:

To find the point with coordinates of the form (a, 3a) that is in the third quadrant and is a distance 5 from P(2,1), we can use the following steps:

[tex]\sqrt{(2 - (-|a|))^2 + (1 - (-3|a|))^2} = 5\\\sqrt{(2 + |a|)^2 + (1 + 3|a|)^2} = 5[/tex]

[tex]a^2 + 8a - 8 = 0[/tex]

[tex]a = \frac{-8 ±\sqrt{8^2 - 4(1)(-8)}} {(2(1))}\\a = \frac{-8 ± \sqrt{96}}{ 2}\\a = -4 ± 2\sqrt{6}[/tex]

[tex]a = -4 - 2\sqrt(6)[/tex]

(x, y) =[tex](-|-4 - 2\sqrt(6)|, -3|-4 - 2\sqrt(6)|)[/tex]

(x, y) ≈ (-8.89, -26.69)

Therefore, the point with coordinates of the form (a, 3a) that is in the third quadrant and is a distance 5 from P(2,1) is approximately (-8.89, -26.69).

After answering the presented question, we may conclude that  As a percentage result, around 74.43 grammes of the drug will remain after 18 hours.

In mathematics, a percentage is a number or ratio expressed as a fraction of 100. The abbreviations "pct.," "pct," and "pc" are also used on occasion. However, it is commonly indicated using the percent symbol "%." The % amount has no dimensions. Percentages are just fractions with a denominator of 100. Place a percent sign (%) next to a number to indicate that it is a percentage. For example, if you answer 75 out of 100 questions properly on a test (75/100), you score a 75%. Divide the money by the total and multiply the result by 100 to calculate percentages. The percentage is derived by multiplying (value/total) by 100%.

A substance's radioactive decay rate is expressed as a percentage per unit time. This indicates that the amount of material left after each unit of time will be lowered by the set percentage.

We may use the exponential decay formula to this problem:

[tex]N(t) = N_0 * e^{(-kt)}[/tex]

where:

N₀  = starting drug quantity

N(t) = the amount of material that remains after time. t k = decay constant (related to decay rate)

t = the amount of time that has passed

To calculate the amount of material left after 18 hours, we must first determine the value of k. Using the rate of decay stated in the issue, we may accomplish the following:

[tex]3.75% = k * 1 hour\\k = 0.0375/hour\\N(18) = 150 * e^{(-0.0375*18)}\\N(18) = 74.43 grams \\[/tex]

As a result, around 74.43 grammes of the drug will remain after 18 hours.

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An equation that best models this set of data is: D. y = 9.74x - 0.06

In this scenario, the hours worked would be plotted on the x-axis (x-coordinate) of the scatter plot while the earnings would be plotted on the y-axis (y-coordinate) of the scatter plot through the use of Microsoft Excel.

On the Microsoft Excel worksheet, you should right click on any data point on the scatter plot, select format trend line, and then tick the box to display a linear equation for the line of best fit (trend line) on the scatter plot.

From the scatter plot (see attachment) which models the relationship between the hours worked and earnings, an equation for the line of best fit is given by:

y = 9.74x - 0.06

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Answer:

Vertically opposite angles are always same.

Straight angle=180°

Angle MQN=70°

Thus, the length of chord BD of the given circle is found to be 8.5 units.

A chord is indeed a straight line that connects two points on a circle's circumference. Because it connects to points on the circle's perimeter, the diameter is thought to be the chord with the longest length.

The lengthiest chord in a circle is called the diameter, and the chord's perpendicular distance to the circle's centre is zero.

Given that: From diagram.

Now, in right triangle, MAD, using the Pythagorean theorem:

(AD)² = (AM)² + (MD)²

(9.5)² = (4)² + (MD)²

(MD)² = 9.5² -  4²

(MD)² = 90.25  - 16

(MD)² = 74.25

MD = 8.5

Thus, the length of chord BD of the given circle is found to be 8.5 units.

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Answer:

Since there are only yellow and green balls in the tub, there is no possibility of picking a red ball. Therefore, the probability of picking a red ball is zero.

(i) The probability of picking a yellow ball can be calculated by dividing the number of yellow balls by the total number of balls. In this case, there are two yellow balls and three green balls, so the total number of balls is 2 + 3 = 5. The probability of picking a yellow ball is 2/5 or 0.4, which is 40%.

(ii) Similarly, the probability of picking a green ball can be calculated by dividing the number of green balls by the total number of balls. In this case, there are three green balls and five total balls. Therefore, the probability of picking a green ball is 3/5 or 0.6, which is 60%.

(iii) As mentioned earlier, there are no red balls in the tub. Hence, the probability of picking a red ball is 0.

The solution to the system of equations is:

x = -19/5, y = 2, z = 1/10

4x + 6y - 2z = 2 (multiply first equation by 2)

x + 2y - 3z = -5 (third equation)

Add the two equations, we get:

5x + 8y = -3 (eliminated z)

-7x + 7y - 6z = -33 (multiplying second equation by 3 and subtracting from the first)

3x + y + 2z = 12 (second equation)

Add these two equations, we have:

-4x + 8y = -21 (eliminated z)

5x + 8y = -3

5x = -8y - 3

x = (-8y - 3)/5

Substituting this expression for x into the second equation, we get:

3((-8y - 3)/5) + y + 2z = 12

z = (39/10) - (19/10)y

Finally, substituting these expressions for x and z into any of the original equations (let's use the first one), we can solve for y:

2((-8y - 3)/5) + 3y - ((39/10) - (19/10)y) = 1

Simplifying and solving for y, we get:

y = 2

x = (-8(2) - 3)/5 = -19/5

z = (39/10) - (19/10)(2) = 1/10

In conclusion, the solution to the system of equations is:

x = -19/5, y = 2, z = 1/10

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The solution to the given system of linear equations is

x = 3, y = -1 and z = 2

From the question, we are to solve the given system of linear equations.

The given system of linear equations is

2x + 3y − z = 1

3x + y + 2z = 12

x + 2y − 3z = −5

Multiply the third equation by 2

x + 2y − 3z = −5 ) ×2

2x + 4y - 6z = -10

Subtract the first equation from the resulting equation

  2x + 4y - 6z = -10

- (2x + 3y − z = 1

----------------------------------------

y - 5z = -11     ---------- (1)

Now,

Multiply the third equation by 3

x + 2y − 3z = −5 ) ×3

3x + 6y -9z = -15

Subtract the second equation from the resulting equation

 3x + 6y -9z = -15

- (3x + y + 2z = 12

-----------------------------------------

5y - 11z = -27     ----------- (2)

Solve equations (1) and (2) simultaneously

y - 5z = -11         ------------ (1)

5y - 11z = -27     ------------ (2)

Multiply equation (1) by 5

y - 5z = -11  ) ×5

5y - 25z = -55

Subtract the resulting equation from equation (2)

  5y - 11z = -27

-( 5y - 25z = -55

-----------------------------

14z = 28

Divide both sides by 14

14z/14 = 28/14

z = 2

Substitute the value of z into equation (1)

y - 5z = -11

y - 5(2) = -11

y - 10 = -11

Add 10 to both sides of the equation

y - 10 + 10 = -11 + 10

y = -1

Substitute the value of y and z into the third equation

x + 2y − 3z = −5

x + 2(-1) − 3(2) = −5

x - 2 - 6 = -5

x - 8 = -5

Add 8 to both sides of the equation

x - 8 + 8 = -5 + 8

x = 3

Hence,

The solution is

x = 3, y = -1 and z = 2

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Answer:

no solution

Step-by-step explanation:

3r + 10 - 3r = 15 ← collect like terms on left side

10 = 15 ← false statement

this false statement indicates the equation has no solution

The statement that is false, given the table of Ms Stewart's class would be A. 15 % of her students are in biology.

The table shows that out of all he students, Ms. Stewart has 35 % that are doing Biology and not 15 %. But, she does have 15 % of Freshmen doing Biology and not of all her students.

30 % of the students are indeed engaged in doing physical science, and 35 % of her students are in chemistry from the table. 45 % of the total cohort that Ms. Stewart teaches are freshmen.

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Answer: 228[tex]cm^2[/tex]

Step-by-step explanation:

The lateral area is 2lh + 2wh

= (2 * 14 * 6) + (2 * 5 * 6)

= 228[tex]cm^2[/tex]

The mean of the data set is 25, the median is 25, the range is 20, the variance is 20, and the standard deviation is 4.47.

Given the dataset:

x = 30, 20, 35, 25, 15

N = 5

Mean of the data set is the average of the dataset. To find the average, we add up all the numbers and divide by the total number of values:

Mean (Xbar) = (30 + 20 + 35 + 25 + 15) / 5 = 25

Median is the number that fall at the middle of the dataset. To find the median of the data set, we need to arrange the numbers in order from smallest to largest:

15, 20, 25, 30, 35

The median is the middle number, which is 25 in this case.

Range of the data set can be calculated by subtract the smallest value from the largest value:

Range = 35 - 15 = 20

Standard Deviation and Variance

First find the deviations of each value from the mean:

(x - Xbar) = d

30 - 25 = 5

20 - 25 = -5

35 - 25 = 10

25 - 25 = 0

15 - 25 = -10

To find the variance, we square each deviation, add them up, and divide by the number of values:

Variance = d²/N

               = (5² + (-5)² + 10² + 0² + (-10)²) / 5

               = 100/5 = 20

To find the standard deviation, we take the square root of the variance:

Standard Deviation = sqrt(variance)

                                 = sqrt(20)

                                 = 4.47 (rounded to two decimal places)

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The percentage of Kira's free throws is 68%.

We have,

From the grid,

We can see that,

There are 25 boxes.

Now,

The number of shaded boxes = 17

Now,

The percentage of the shaded boxes.

= 17/25 x 100

= 17 x 4

= 68%

Thus,

The percentage of Kira's free throws is 68%.

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The complete question.

The shaded area on the grid represents the part of Kira's free throws that she made in the basketball practice today.

Find the percentage of Kira's free throws.

Answer:

x = [tex]\frac{53}{40}[/tex]

Step-by-step explanation:

18 7/8 + __ = 20 1/5

18 7/8 = 151/8

20 1/5 = 101/5

[tex]\frac{151}{8}[/tex] + x = [tex]\frac{101}{5}[/tex]

x = [tex]\frac{101}{5}[/tex] - [tex]\frac{151}{8}[/tex]

x = [tex]\frac{53}{40}[/tex]

So, the answer is [tex]\frac{53}{40}[/tex]

There are 25  persons who actually voted, the 95% confidence interval for the population of registered voters who voted in the most recent school board election is 0.2±0.07 that is (0.13, 0.27).

In statistics, a confidence interval, means  the probability which a population parameter will fall between a set of values for a certain proportion of times. Confidence intervals measure the degree of uncertainty or certainty in a sampling method. There are various types of confidence interval such as 90%, 95%, 99% etc.

A certain randomly selected sample of 125 registered voters showed that 20% of them voted in the most recent school board election.

So in 125persons the persons who actually voted are

                (125×20)/100

              = 2500/100

              = 25

For 95% confidence interval the z value is 1.96.

If we take p as probability of success that is the persons who actually voted then 1-p denotes the probability of failure.

p= 25/125= 1/5 = 0.2          n= 125

1-p= 1-(1/5)

    = 1-0.2= 0.8

The formula for confidence interval is

p± z√{p(1-p)/n}

0.2 ±1.96√{(0.2×0.8)/125}

= 0.2 ± 1.96√(0.16/125)

= 0.2± 1.96 ×0.035777

= 0.2±0.07012

Hence , the 95% confidence interval for the population of registered voters who voted in the most recent school board election is 0.2±0.07

that is (0.13, 0.27).

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The expressions that are equivalent to 6x²y + 2xy⁵; are 2(3x²y + xy⁵), 2xy(3x + y⁴), xy(6x + 2y⁴) and 4xy(3/2x + 1/2y⁴). So, the correct options are a, b, e and g.

Algebra is known to be a branch of mathematics in which problems are represented as mathematical expressions using letters or variables (x, y, z, etc.) to represent unknown values ​​that may change. The purpose of algebra is to understand what the unknown values ​​are in order to find solutions to problems. The degree of an algebraic equation is the largest power that exists for the variables in the equation. Algebraic equations can be classified by degree as follows:

Equation A: 2(3x²y + xy⁵) = 6x²y + 2xy⁵

Equation B: 2xy(3x + y⁴) = 6x²y + 2xy⁵

Equation C: 2x²y(6 + 5y) = 12x²y + 10x²y²

Equation D: 6x²y.2xy⁵

Equation E: xy(6x + 2y⁴) = 6x²y + 2xy⁵

Equation F: 2y(3x + xy⁴)⁰ = 2y

Equation G: 4xy(3/2x + 1/2y⁴) = 6xy + 2xy⁵

Hence, Equation A, B, E and G are the equations found equivalent to the given equation, 6x²y + 2xy⁵.

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Answer:

[tex]\frac{sin(A)}{a}[/tex]

Answer:

According to the Pythagorean Theorem, in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. So we have:

c^2 = a^2 + b^2

where c is the length of the hypotenuse and a and b are the lengths of the other two sides.

Substituting the given values, we get:

c^2 = 14^2 + 48^2

c^2 = 196 + 2304

c^2 = 2500

Taking the square root of both sides, we get:

c = 50

Therefore, the length of the hypotenuse is 50 units.

Answer: The area of circle is 28.26 cm^2

Step-by-step explanation: As the diameter of the given circle is 6 cm, the radius of the same would be 3 cm.

Area of circle = pi r^2

And the value of pi is to be taken 3.14

The area of the given circle is 28.26cm^2.

Answer:

We need to convert both measurements to the same unit in order to compare them. Let's convert 6 1/3 feet to inches:

1 foot = 12 inches

6 feet = 6 x 12 = 72 inches

1/3 foot = (1/3) x 12 = 4 inches

6 1/3 feet = 72 + 4 + (1/3) x 12 = 76 inches

Therefore, the plumber has 76 inches of piping.

Since the plumber needs 75 inches of piping, we can see that she does have enough piping.

Step-by-step explanation:

Answer: A. 251.3 in.

Step-by-step explanation:

        We can use this formula to solve for the circumference of a circle. r is equal to the radius, or half of the circle's width.

                 C = 2πr

C = 2πr

C = 2π(40)

C ≈ 251.3

                 A. 251.3 in.

The difference in volume between the two boxes would be = 156in³

To calculate the difference in volume between the boxes is the find the individual volume of the boxes using the formula ;

Volume = length×width×height.

For box 1 = length = 12in, width = 7¾in, height= 2in

Vol = 12×7¾×2 = 186in³

For box 2; length = 3⅔in, width = 3½in, height= 2⅓in

Volume = 3⅔×3½×2⅓ = 30

The difference = 186-30 = 156in³

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