Dylan, eli and fabian share some sweets.
the amount of sweets dylan gets to the amount of sweets eli gets is in the ratio 7:3
the amount dylan gets to the amount fabian gets is in the ratio 4:5
given fabian gets 21 more sweets than dylan.
work out how many sweets eli gets.

The value of the sides are;

x = 20.4

x = 13.84

There are six different trigonometric identities. They include;

Given that the ratios are;

sin θ = opposite/hypotenuse

cos θ = adjacent/hypotenuse

tan θ = opposite/adjacent

Using the tangent identity, we have;

tan 64 = 42/x

cross multiply the values

x = 42/2. 050

x = 20. 4

Using the sine identity;

sin 70 = 13/x

cross multiply the values

x = 13/0. 939

x = 13. 84

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Answer:

24°

Step-by-step explanation:

Supplementary angles: 2 angles that add up to 180°.

We are given that one angle is 156°, so we can write an equation:

180=156+x

subtract both sides by 156

24=x

So, the measure of the supplementary angle is 24°.

Hope this helps!

The value of k = 2

Substituting into the integral:

k ∫₀^(π/2k) sec²(u) du

= k [tan(u)]₀^(π/2k)

= k [tan(π/2k) - tan(0)]

= k [∞ - 0]

= ∞

This means that the integral diverges unless k = 0.

∫₀^(π/2k) sec²(x/k) dx

= ∫₀^(π/2k) (1 + tan²(x/k)) dx

= [x + k tan(x/k)]₀^(π/2k)

= π/2

So we have:

π/2 = [π/2k + k tan(π/2k)] - [0 + k tan(0)]

= π/2k + k tan(π/2k)

Multiplying through by k:

π/2 = π/2 + k² tan(π/2k)

Subtracting π/2 from both sides:

0 = k² tan(π/2k)

The only way for this equation to hold for k > 0 is if tan(π/2k) = 0. This occurs when π/2k is an integer multiple of π/2, i.e., when k is an even integer.

Therefore, the value of k that satisfies the original integral is k = 2.

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b(x) = 6x² and m(x) = -1/3x²- 4 have similarities and differences as quadratic functions with different coefficients and signs.

We can look at the similarities and differences to compare b(x) = 6x² and m(x) = -1/3x² - 4

Both b(x) and m(x) are quadratic functions, which means they have an x² term.

They both have a constant term, with b(x) having a constant of 0 and m(x) having a constant of -4.

The coefficients of the x² term are different: b(x) has a coefficient of 6, while m(x) has a coefficient of -1/3.

The signs of the coefficients are different: b(x) has a positive coefficient, while m(x) has a negative coefficient.

Overall, b(x) and m(x) have some similarities in their form as quadratic functions, but their coefficients and signs are different, which means they will have different shapes and behaviors.

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The area of the triangle is (a-6, b-12) square units 6 sq unit.

A triangle is described as  a polygon with three sides having three vertices. The angle formed inside the triangle is equal to 180 degrees.

This means that the sum of the interior angles of a triangle is equal to 180°

Now that we have  the points they make a 3-4-5 triangle.

The two legs are 3 and 4, so the hypotenuse has to be 5.

We  could also use the Pythagorean theorem a² + b² = c² 3² + 4² = c² 25 = c² c = 5

We then calculate the area

Area =1/2 b*h

Area = 1/2(3*4)

Area =  6 sq unit

The area of the triangle is (a-6, b-12) square units 6 sq unit.

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The coordinates of the points in the table indicates that the coordinates of the image following the reflections, can be presented on the coordinate plane as shown in the attached graph created with MS Excel.

A reflection transformation is one in which the mirror image of the preimage is created across a line of reflection.

The coordinate points of the image after the specified reflections can be presented as follows;

Original   [tex]{}[/tex]Reflection across the x-axis   Reflection across the y-axis   y = -x

(0, 15)      [tex]{}[/tex] (0, -15)                                      (0, 15)                                   (-15, 0)

(1,  15)      [tex]{}[/tex] (1, -15)                                       (-1, 15)                                   (-15, -1)

(1, 13)      [tex]{}[/tex]  (1, -13)                                       (-1, 13)                                    (-13, -1)

(3, 15)      [tex]{}[/tex] (3, -15)                                      (-3, 15)                                   (-15, -3)

(3, 12)      [tex]{}[/tex] (3, -12)                                      (-3, 12)                                   (-12, -3)

(1, 10)      [tex]{}[/tex]  (1, -10)                                      (-1, 10)                                     (-10, -1)

(1, 8)      [tex]{}[/tex]   (1, -8)                                        (-1, 8)                                      (-8, -1)

(3, 10)      [tex]{}[/tex](3, -10)                                      (-3, 10)                                    (-10, -3)

(3, 7)      [tex]{}[/tex]  (3, -7)                                       (-3, 7)                                      (-7, -3)

(1, 5)      [tex]{}[/tex]  (1, -5)                                        (-1, 5)                                      (-5, -1)

(1, 2)      [tex]{}[/tex]  (1, -2)                                        (-1, 2)                                      (-2, -1)

(4, 4)      [tex]{}[/tex] (4, -4)                                       (-4, 4)                                      (-4, -4)

(5, 7)      [tex]{}[/tex] (-5, 7)                                       (5, -7)                                      (-7, -5)

(7, 8)      [tex]{}[/tex] (7, -8)                                       (-7, 8)                                      (-8, -7)

(6, 5)     [tex]{}[/tex]  (6, -5)                                      (-6, 5)                                      (-5, -6)

(8, 6)     [tex]{}[/tex]  (8, -6)                                      (-8, 6)                                      (-6, -8)

(9, 9)     [tex]{}[/tex]  (9, -9)                                      (-9, 9)                                      (-9, -9)

(11, 10)     [tex]{}[/tex] (11, -10)                                   (-11, 10)                                    (-10, -11)

(10, 7)     [tex]{}[/tex]  (10, -7)                                   (-10, 7)                                     (-7, -10)

(12, 8)     [tex]{}[/tex]  (12, -8)                                   (-12, 8)                                    (-8, -12)

(13, 6)     [tex]{}[/tex]  (13, -6)                                   (-13, 6)                                    (-6, -13)

(11, 5)      [tex]{}[/tex]  (11, -5)                                    (-11, 5)                                     (-5, -11)

(14, 4)      [tex]{}[/tex] (14, -4)            [tex]{}[/tex]                       (-14, 4)                                     (-4, -14)

(12, 3)     [tex]{}[/tex]  (12, -3)                                   (-12, 3)                                     (-3, -12)

(9, 4)      [tex]{}[/tex]  (9, -4)                                    (-9, 4)                                       (-4, -9)

(7, 3)      [tex]{}[/tex]  (7, -3)                                     (-7, 3)                                       (-3, -7)

(10, 2)    [tex]{}[/tex]  (10, -2)                                   (-10, 2)                                     (-2, -10)

(8, 1)      [tex]{}[/tex]  (8, -1)                                      (-8, 1)                                       (-1, -8)

(5, 2)     [tex]{}[/tex]  (5, -2)                                     (-5, 2)                                      (-2, -5)

(2, 0)     [tex]{}[/tex]  (2, 0)                                      (-2, 0)                                      (0, -2)

The above coordinate points can be used to plot the graphs showing the image of the points following the specified reflections across the x-, y-, and y = -x, axis.

Please find attached the required graph of the coordinate points following the reflection transformations, created with MS Excel.

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The approximate value of x using the newton method is 0.7

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

[tex]\frac{x}{x^2+1}-\sqrt{1-x}[/tex]

Also, we have the function f(x) to be

[tex]f(x) = x(x^2+1)^{-1} -\sqrt{1-x}[/tex]

And we have the differentiated function to be

[tex]f'(x) = \frac{1}{x^2+1} - \frac{2x^2}{(x^2 + 1)^2} + \frac{1}{2\sqrt{1-x}}[/tex]

The value of x using the newton method is given as

[tex]x_n = x_{n-1} - \frac{f(x_{n-1})}{f'(x_{n-1})}[/tex]

Set [tex]x_{n-1}[/tex] = 0

So, we have

x₁ = 0 - -1/1.5 = 0.67

x₂ = 0.67 - undefined = undefined

So, we have

x₁ = 0.67

When approximated, we have

x = 0.7

This means that the value of x using the newton method is 0.7

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p + q + 36 = 0 is the equation that is true. From this equation, we can say that p + q = -36.

If we substitute x = 1 in the given function, we get:

f(1) = [tex](1)^4 + 5(1)^3 + p(1)^2 + q(1) + 30[/tex]

= 1 + 5 + p + q + 30

= p + q + 36

We are given that f(1) = 0. Therefore, we have:

p + q + 36 = 0

This is the equation that is true. From this equation, we can say that p + q = -36.

Now, let's see why this is the case. When we substitute x = 1 in the given function and get f(1) = 0, it means that (1, 0) is a point on the graph of the function. This point lies on the x-axis, which means that the function intersects the x-axis at x = 1. Since the x-axis is the line y = 0, this means that f(x) = 0 when x = 1.

Using this information, we can write an equation in terms of p and q. If we substitute x = 1 in the given function and get f(1) = 0, it means that:

f(x) = [tex](x - 1)(x^3 + 6x^2 + (6+p)x + (30-q))[/tex]

Therefore, we have:

[tex](x - 1)(x^3 + 6x^2 + (6+p)x + (30-q)) = 0[/tex]

Since (1,0) is a point on the graph of the function, we know that x = 1 is a root of this equation. Therefore, we have:

[tex](x - 1)(x^3 + 6x^2 + (6+p)x + (30-q)) = (x - 1)(x^2 + (7+p)x + (36-p-q))[/tex]

We know that (x - 1) is a factor of this equation, so we can use polynomial long division to divide the expression [tex](x^2 + (7+p)x + (36-p-q))[/tex] by (x - 1). The quotient will give us the other two roots of the equation. However, we do not need to find these roots to answer the question. All we need to know is that p + q = -36.

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The simplified expression is (n - 3) / (n - 2).

The expression is simplified as follows;

(n² - 5n + 6) / (n² - 4n + 4)

n² - 5n + 6 can be factored as (n - 2) (n - 3)

n² - 4n + 4 can be factored as (n - 2) (n - 2)

Therefore, the expression becomes:

[(n - 2) (n - 3)] / [(n - 2) (n - 2)]

We can cancel the (n - 2) factor in the numerator and denominator, leaving us with:

(n - 3) / (n - 2)

So the simplified expression is (n - 3) / (n - 2).

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The length of the shadow cast by the 5 foot 6 inch student is approximately 1.83 feet.

To solve this problem, we'll set up a proportion using the principles of similar triangles. The two triangles in this case are the building and its shadow, and the student and their shadow.

Convert the height of the student to feet. 5 feet 6 inches is equal to 5.5 feet.

Set up the proportion. Let x represent the length of the shadow cast by the student. We have the following proportion:

(height of building) / (length of building's shadow) = (height of student) / (length of student's shadow)
60 / 20 = 5.5 / x

Cross-multiply and solve for x:

60 * x = 20 * 5.5
60x = 110
x = 110 / 60
x = 1.83 (rounded to two decimal places)

The length of the shadow cast by the 5 foot 6 inch student is approximately 1.83 feet.

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The calculated perimeter of the square from the side length is 17.2x + 8

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

A square that has a side length of 4.3x + 2 inches.

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

Perimeter = 4 * side length

Substitute the known values in the above equation, so, we have the following representation

Perimeter = 4 * (4.3x + 2)

When teh brackets are opened, we have

Perimeter = 17.2x + 8

Hence, the perimeter is 17.2x + 8

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A function that can be used to find y, the mass of the substance in grams remaining after x hours is [tex]P(x) = 963(0.63)^x[/tex]

In Mathematics and Statistics, a population or substance that decreases at a specific period of time represent an exponential decay. This ultimately implies that, a mathematical model for any population or substance that decreases by r percent per unit of time is an exponential equation of this form:

[tex]P(x) = I(1 - r)^x[/tex]

Where:

By substituting given parameters into the , we have the following:

[tex]P(x) = I(1 - r)^x\\\\P(x) = 963(1 - 0.27)^x\\\\P(x) = 963(0.63)^x[/tex]

In conclusion, we can reasonably infer and logically deduce that the decay rate is equal to 63%.

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The slope of the line that represents the proportional relationship between x and y in the given table is 1/6. To graph the line, we can plot the points from the table and connect them with a straight line passing through the origin (0,0).

The relationship between x and y is proportional, which means that there is a constant ratio between the two variables. We can find the slope of the line that represents this relationship by calculating the ratio of the change in y over the change in x between any two points on the line. Let's use the first and last points

slope = (y2 - y1) / (x2 - x1) = (2.0 - 0) / (12 - 0) = 2/12 = 1/6

So, the slope of the line that represents this proportional relationship is 1/6.

To graph the line, we can plot the points from the table and connect them with a straight line. The line will pass through the origin (0,0) and have a slope of 1/6. The graph will look like.

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Answer: x-0.5y=1.5

Step-by-step explanation:

Answer:

$10.8

Step-by-step explanation:

We know that 3 books are $2.70, so 1 book is 2.70/3 which is $0.9

1 dozen = 12

To find the price of 12 books, we multiply by the cost of 1 book

12 * 0.9 = $10.8

The primary reason many present-day African nations struggled to unite their people is F. Because many African peoples have strong tribal ties.

The strong tribal identities and loyalties that exist among various ethnic groups inside African states today are one of the main causes of the effort to bring people together. Through colonisation, many African nations were developed, and many of them contained numerous groups with various cultural, linguistic, and ethnic origins.

Therefore, as a result, it has been challenging to forge a strong sense of national identity among many individuals who still identify primarily with their own tribe or ethnic group. This has occasionally resulted in disputes and hostilities amongst various diverse groups, impeding efforts to create a community that is more unified.

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The mark-up value percentage is 25 %

Given data ,

The markup amount is the selling price minus the cost price, so:

Markup = $8630 - $6900 = $1730

The markup percentage is the markup amount divided by the cost price, expressed as a percentage:

Markup percentage = (Markup / Cost price) x 100%

Markup percentage = ($1730 / $6900) x 100%

Markup percentage = 0.25 x 100%

Markup percentage = 25%

Hence , the markup percentage is 25%

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The set of all points in quadrant I not including the axis's can be represented by the following system of inequalities:

x > 0

y > 0

Inequalities are useful in modeling situations where there are constraints or limitations. For  illustration, in real- life  scripts, there may be limited  coffers or capacity, or certain variables must fall within a specific range. Systems of inequalities are  frequently used to represent these constraints or limitations graphically.   One common  operation of systems of inequalities is in optimization problems, where the  thing is to maximize or minimize a particular function subject to certain constraints.

In these situations, the  doable region, or the set of all points that satisfy the constraints, is  frequently represented as a shadowed region on a graph. The optimal  result is  also  set up by  relating the point( s) within this region that maximize or minimize the function.

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The area of the playground include the following: 900 square yards.

In Mathematics and Geometry, the area of a regular polygon can be calculated by using this formula:

Area = (n × s × a)/2

Where:

In Mathematics and Geometry, the area of a parallelogram can be calculated by using the following formula:

Area of a parallelogram, A = base area × height

Area of playground, A = 45 × 20

Area of a playground, A = 900 square yards.

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The pool is draining at a rate of 1.36% per hour according to Inayah's claim.

According to Inayah's claim, the pool is experiencing a draining at a rate of 1.36% per hour. This means that for every hour that passes, the pool's water level decreases by 1.36% of its total volume.

Understanding the rate at which a pool is draining is essential for monitoring and managing water levels. If the rate of drainage is accurate, it can help estimate how long it would take for the pool to reach a certain level or completely drain. Additionally, it aids in determining the necessary actions to maintain the pool's water balance and prevent potential issues such as overflow or inadequate water supply.

It is crucial to verify the accuracy of the claim by monitoring the pool's water level over a specific period. This can be done by measuring the change in water volume or using other reliable methods to ensure the drainage rate aligns with the claimed percentage.

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Answer: it will need to be rewritten so that the variable is only on one side of the equation

Step-by-step explanation:f the equation contains fractions, you may elect to multiply both sides of the equation by the least common denominator

Answer:

m = -4

Step-by-step explanation:

Slope = rise/run or (y2 - y1) / (x2 - x1)

Pick 2 points (-3,12) (-2,8)

We see the y decrease by -4, and the x increase by 1, so the slope is

m = -4

So, the slope of the line representing by the data is -4.

Answer:

Point in the original figure: (5,4)

Point in the final figure: (0,-2)

Step-by-step explanation:

hope this works and helps! :)

Answer:47.25

Step-by-step explanation:

Answer:

48.5

Step-by-step explanation:

To find the first quartile (Q1) of the data set, we need to arrange the numbers in ascending order:

42, 46, 51, 53, 66, 70, 79, 90

Q1 is the median of the lower half of the data set. Since we have 8 data points, the lower half will be the first four numbers.

42, 46, 51, 53

To find the median of these numbers, we take the average of the two middle numbers:

(Q1) = (46 + 51) / 2 = 48.5

Therefore, the first quartile (Q1) of the data set is 48.5.

Steve paid $10 more than Cole for gas, regardless of the actual prices of gas at the two gas stations.

To answer this question, we need to know the prices of gas at both gas stations. Let's assume that Cole bought 10 gallons of gas at the gas station with the lowest price, and that the price difference between the two gas stations is $x per gallon.

If we denote the price per gallon of gas at the gas station where Cole bought gas as "c", then the total amount Cole paid for gas is:

10c

If we denote the price per gallon of gas at the gas station where Steve bought gas as "s", then the total amount Steve paid for gas is:

10s

The difference between the two amounts is:

10s - 10c

But we know that Steve bought gas at the gas station with the highest price, so we can assume that s = c + x.

Substituting this expression for s into the equation above, we get:

10s - 10c = 10(c + x) - 10c = 10x

So Steve paid $10 more than Cole for gas, regardless of the actual prices of gas at the two gas stations.

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The function that is increasing and has a domain of (1, infinity) is A. F(x) = log(x - 1) + 2.


To determine the increasing function with the specified domain, let's analyze each option:

A. F(x) = log(x - 1) + 2
This function is increasing because the logarithm of a positive number is always increasing. The domain is (1, infinity), which matches the requirement.

B. F(x) = -log(x - 2) + 1
This function is decreasing because the negative sign in front of the logarithm inverts the increase. The domain is (2, infinity), which does not match the requirement.

C. F(x) = -log(x - 1) + 2
This function is also decreasing because of the negative sign in front of the logarithm. The domain is (1, infinity), which matches the requirement, but the function is not increasing.

D. F(x) = log(x - 2) + 1
This function is increasing because the logarithm of a positive number is always increasing. However, the domain is (2, infinity), which does not match the requirement.

The function that is increasing and has a domain of (1, infinity) is A. F(x) = log(x - 1) + 2.

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The least number of packages of plates, napkins, and cups Maria has to buy is 15 packages .

To find the least number of packages, we need to find the least common multiple (LCM) of the three package sizes: 8 (plates), 10 (napkins), and 12 (cups).

The prime factors of 8 are 2x2x2, of 10 are 2x5, and of 12 are 2x2x3. To find the LCM, we multiply the highest powers of each prime factor: 2³x3x5 = 120.

This means Maria needs 120 of each item. She will buy 120/8 = 15 packages of plates, 120/10 = 12 packages of napkins, and 120/12 = 10 packages of cups.

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