GCM for 16 and 32 I- resdy

After burning for x hours, the candle's length, y, is calculated using the formula: y = 9 - (1/2)x.

Let y represent the length of the candle that is still burning after burning for x hours.

Since the candle burns at a rate of 1/2 inch per hour, we can use the following equation to explain the connection between the candle's length and the number of hours burned:

y = 9 - (1/2)x

Here, 9 represents the original length of the candle, and (1/2)x represents the length of the candle burned after x hours.

By subtracting the length burned from the original length, we obtain the length remaining after x hours.

Therefore, the function that determines the length of the candle, y, after burning for x number of hours is:

y = 9 - (1/2)x

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The numbers closest to the middle of the squares of consecutive integers around 69² are 4624 and 4761, which are at the squares of 68 and 69, respectively.

To find the number closest to the middle of the squares of consecutive integers around 69², we can use the fact that the squares of consecutive integers increase by an odd number. Specifically, the difference between the squares of consecutive integers n and n+1 is

(n+1)² - n² = 2n + 1

Therefore, the squares of consecutive integers around 69² are

67² = 4489

68² = 4624

69² = 4761

70² = 4900

71² = 5041

The middle of these squares is between 69² and 70², which is

(69² + 70²)/2 = 9674.5

So, we want to find the squares of the integers closest to 9674.5. Since 69 is closer to 9674.5 than 70, the two squares that are closest are

68² = 4624

69² = 4761

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--The given question is incomplete, the complete question is given

" What Interferes are closest to the number in the middle of 69²? "--

The volume of C.a .cylinder is twice the volume of a cone.

The formula fro the cylinder is πr²h and that of the cone is ⅓ the volume It should be noted that the volume of a cone can be equated to theone-third of the volume of a cylinder , this can be established when they are having same base radius and height.

The cylinder's volume  can be expressed as π r² h,  along with the surface area  which can be expressed as 2π r h + 2π r² and this can be used to get the values.

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The length of arc on equator is 69.08 miles.

We have

Radius of Earth = 3960 miles

Angle = 1 degree

So, the length of arc on equator is

= θ/360 x 2πr

= 1/360 x 2 (3.14) (3960)

= 69.08 miles

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Two years ago, an investment of R1 500000 has increased to R1 700000 and has delivered R40 000 worth of dividends over the two years. Then the return on investment would be 16%.

We can use the following formula to calculate ROI:

ROI = (gain from investment - cost of investment) / cost of investment

where, gain from investment is the total value of the investment (including dividends), and cost of investment is the initial investment.

Using the values given in the question, we can calculate the ROI as:

ROI = ((R1,700,000 + R40,000) - R1,500,000) / R1,500,000 = R240,000 / R1,500,000

ROI = 0.16 or 16%

Therefore, the return on the investment is 16%.

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The solution to the set of equations are:

x = 17/7

y = 20/7

We have,

The two equations are:

x + y = 7 ______(1)

x² - y² = 15 _______(2)

We can use the method of substitution.

From the first equation.

y = 7 - x

We can substitute this expression for y into the second equation.

x² - (7 - x)² = 15

Expanding the square in the second term gives:

x² - (49 - 14x + x²) = 15

Simplifying this equation.

-14x + 34 = 0

Solving for x gives:

x = 17/7

Substituting this value of x into the first equation.

y = 7 - x = 20/7

Therefore,

The solution to the set of equations are:

x = 17/7

y = 20/7

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The complete question:

Solve the set of algebraic equations.

x + y = 7

x² - y² = 15

4ab² is the simplified value of the given expression.

To simplify the expression, we can divide the coefficients and variables separately:

[tex]12a^3b^6c^5 / 3a^2b^4c^5\\\\= (12/3) * (a^3/a^2) * (b^6/b^4) * (c^5/c^5)\\\\= 4 * a^{3-2}* b^{6-4} * c^{5-5}\\\\= 4a * b^2 * 1\\\\= 4ab^2\\[/tex]

Therefore, the simplified expression is 4ab².

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The indefinite integral of ∫ (4x⁴ - 5)⁵ . 32x³ dx is (4x⁴ - 5)⁶/3 + C.

The solution of the indefinite integral is calculated by using substitution method.

Let u = 4x⁴ - 5

du/dx = 16x³

dx = du/(16x³)

Substituting into the integral;

∫ (4x⁴ - 5)⁵ . 32x³ dx =  ∫ u⁵ . 32x³ du/(16x³)

∫ u⁵ . 32x³ du/(16x³) =  ∫ 2u⁵ du

∫ 2u⁵ du =  2∫u⁵ du

2∫u⁵ du = 2 (u⁶/6 + C)

2 (u⁶/6 + C)  = u⁶/3 + C

Substituting back for u;

∫ (4x⁴ - 5)⁵ . 32x³ dx = (4x⁴ - 5)⁶/3 + C

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The required graph has been attached below that represents the function f(x) = 5 cos (2x).

The graph of the function f(x) = 5 cos(2x) is a periodic function that oscillates between its maximum and minimum values as x changes.

Specifically, the function is a cosine function with amplitude 5 and period π, since the coefficient of x is 2 in the argument of the cosine function.

The graph of the function f(x) = 5 cos(2x) has a maximum value of 5 when cos(2x) = 1 (i.e., at 2x = 0 + 2πk, where k is an integer), and a minimum value of -5 when cos(2x) = -1 (i.e., at 2x = π + 2πk, where k is an integer).

Thus, the graph has been attached below that represents the given function.

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The construction of an equilateral triangle is shown in the solution.

Steps -

When the length of three sides of the triangle is given, then follow the below steps to construct the required triangle.

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The multiplication of the given two matrices A and B gives,

AB = [tex]\left[\begin{array}{ccc}-9&0\\9&9\end{array}\right][/tex]

Given two matrices,

A = [tex]\left[\begin{array}{ccc}1&3&-1\\3&0&3\end{array}\right][/tex] and B = [tex]\left[\begin{array}{ccc}3&0\\-4&1\\0&3\end{array}\right][/tex]

We have to find the product of these matrices.

We have to multiply each row of A with each column of B.3

(AB)₁₁ = (1 × 3) + (3 × -4) + (-1 × 0) = -9

(AB)₁₂ = (1 × 0) + (3 × 1) + (-1 × 3) = 0

(AB)₂₁ = (3 × 3) + (0 × -4) + (3 × 0) = 9

(AB)₂₂ = (3 × 0) + (0 × 1) + (3 × 3) = 9

Hence the product is,

AB = [tex]\left[\begin{array}{ccc}-9&0\\9&9\end{array}\right][/tex]

Hence the product is AB = [tex]\left[\begin{array}{ccc}-9&0\\9&9\end{array}\right][/tex].

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The domain and range of the exponential function for the given graph is equal to Domain = [ -1 , 3 ) and range = [ -36 , -1/36 ).

For the plotted graph of exponential function f(x),

Plotted graph represents the endpoints.

In the fourth quadrant ( -1 , -36 ) represents the closed interval.

In the first quadrant ( 3 , -1/36 ) represents the open interval.

Domain of the function is represented by all input values.

Here x-values represents the domain.

Domain of the exponential function = [ -1 , 3)

Or -1 ≤ x < 3

Range of the function is all output values.

Here y-values represents the range.

Range of the exponential function = [ -36 , -1/36 ).

Therefore, the domain and range of the exponential function of the graph is equal to [ -1 , 3 ) and  [ -36 , -1/36 ).

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The lateral area of the triangular prism is 288 square inches and the surface area is 336 square inches

The lateral area of a right triangular prism is given by:

LA = perimeter of base triangle * height

LA = (a + b + c) * h    (check attached image for labeling)

where a, b and c are the bases of the rectangular faces and h is the total height of the prism.

a = 10 in, c = 8 in and h = 12 in

b = √(10² - 8²)      (Pythagoras)

b = 6 in

LA = (10 + 6 + 8) * 12

LA =  288 square inches

The surface area of a right triangular prism is sum of the areas of the faces that make the prism.

The surface area of a right triangular prism is given by:

SA = (a + b + c)h + bc

SA = [(10 + 6 + 8)*12] + [6 * 8]

SA = 288 + 48

SA = 338 square inches

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Complete Question

Check image

Answer:

6

Step-by-step explanation:

y2=144 +81 = 225

225 sqaure root =. 15

so the triangle lenghts are 9 12 15  

the other ones lenghts are x 8 10

to find how they changed you could use cross multiplication.

so you will get 12 x = 72 and simply it to get x = 6

Answer:8.52%

Step-by-step explanation:

There are 14 utensils in the drawer, and then there will be one less in the bowl after each successive utensil is removed. There are then 3 possibilities for the same kind being removed on all pulls:

P(3 spoons) = (6/14)*(5/13)*(4/12)

P(3 forks) = (5/14)*(4/13)*(3/12)

P(3 knives) = (3/14)*(2/13)*(1/12)

Add all of these outcomes together and you'd get about 8.52%

The possible perimeter for the rectangle would be 28(Letter D)

Answer:

[tex]x=4.865[/tex]

Step-by-step explanation:

We know the area of a rectangle to be [tex]base*height[/tex]. In this instance, [tex]base=(2x+10)in[/tex], [tex]height=(3x) in[/tex], and [tex]area=288in^2[/tex]

The next step is to plug these known values into the [tex]area=base*height[/tex] equation. It'll look like this:

[tex]288=(2x+10)*(3x)=6x^2+30x[/tex]

This simplifies to:

[tex]48=x^2+5x[/tex]

Next, we want to rewrite the equation so we can apply the quadratic formula to it. We are going to do this by subtracting 48 from each side. The new equation looks like this:

[tex]x^2+5x-48=0[/tex]

Next, we plug this into the quadratic formula:

[tex]x=\frac{-(5)+\sqrt{5^2-4(1)(-48)} }{2(1)}=4.865[/tex]

[tex]x=\frac{-(5)-\sqrt{5^2-4(1)(-48)} }{2(1)}=-9.865[/tex]

The second value of x is negative, and since a side length cannot be negative this leaves us with just the first answer of [tex]x=4.865[/tex].

Answer:

[tex]\Large \boxed{\boxed{\textsf{$\therefore x=4.87 $ in}}}[/tex]

Step-by-step explanation:

The area of a rectangle is equal to the base × height:

[tex]\large \textsf{$\rm A $ $= (2x+10)\times(3x)$}\\ \\\large \textsf{$\rm \phantom{A}=$ $6x^2+30x$, and since A = 288,}\\ \\\large \textsf{$\therefore 288 = 6x^2+30x$}[/tex]

Rearranging this equation, we get:

[tex]\large \textsf{$6x^2+30x-288=0$}\\\\\large \textsf{$6(x^2+5x-48)=0$}\\\\\large \textsf{$\therefore x^2+5x-48=0$}[/tex]

Here we are left with a quadratic equation, which we can solve using the quadratic formula:

[tex]\Large \boxed{\textsf{$x = \frac{-b\pm \sqrt{b^2-4ac}}{2a}$}} \textsf{ where $ax+bx+c=0$}[/tex]

Plugging values into the formula, we get:

[tex]\Large \textsf{$x = \frac{-(5)\pm \sqrt{(5)^2-4(1)(-48)}}{2(1)}$} \\\\\Large \textsf{$x=4.87, -9.87$,} \large \textsf{ but length cannot be negative.}\\\\\Large \boxed{\boxed{\textsf{$\therefore x=4.87 $ in}}}[/tex]

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The Cartesian equation of the polar equation r = 4 sin(θ)cos(θ) is:

x = 4 cos²θ sinθ

y = 4 sin²θ cosθ

We have,

We can use the following conversions from polar to Cartesian coordinates:

x = r cosθ

y = r sinθ

To convert the polar equation r = 4 sin(θ)cos(θ) into Cartesian coordinates, we substitute r with its equivalent value 4 sin(θ)cos(θ) and use the above conversions:

x = (4 sinθ cosθ) cosθ

y = (4 sinθ cosθ) sinθ

Simplifying these expressions, we get:

x = 4 cos^2θ sinθ

y = 4 sin^2θ cosθ

The Cartesian equation of the polar equation r = 4 sin(θ)cos(θ) is:

x = 4 cos^2θ sinθ

y = 4 sin^2θ cosθ

or, in standard form:

x = 4xy

This is the Cartesian equation in terms of x and y, obtained by replacing sinθ and cosθ with x and y, respectively.

Thus,

The Cartesian equation of the polar equation r = 4 sin(θ)cos(θ) is:

x = 4 cos²θ sinθ

y = 4 sin²θ cosθ

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The number of students have not paid for the trip is 0.

Given that, there are 30 students in her class.

⅕ paid for the trip with a check.

That is, 1/5 ×30=6 students

½ paid for the trip with cash.

Now, 1/2 ×30 =15 students

30% have paid half of their money.

Here, 30% of 30

30/100 ×30

= 900/100

= 9 students

Total students = 6+15+9

= 30

So, rest of students = 30-30=0

Therefore, the number of students have not paid for the trip is 0.

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The number of blue cars and the number of red cars are 3 and 5 respectively

Let b and r represent the number of blue cars and  the number of red cars respectively.

There are a total of 8 cars, we have:

b + r = 8

There are 135 clowns in total. Blue cars hold 20 clowns and red cars only hold 15, we have:

20b + 15r = 135.

Thus, we have a system of equations with two variables:

b + r = 8   ---- (1)

20b + 15r = 135  ---- (2)

We can use elimination to solve for b and r.

Let's use elimination. Multiplying the first equation by 20 and second equation by 1:

20 * (b + r = 8)                  = 20b + 20r = 160  (subtract)

1 * (20b + 15r = 135)         = 20b + 15r = 135

                                      ...............................................

                                                      5r = 25

                                      ...............................................

r = 25/5

r = 5

Using (1):

b + r = 8

b + 5 = 8

b = 8 - 5

b = 3

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The measure of arc CFE is 246⁰.

The measure of arc FED is 190⁰.

The value of the angle CFE is 57⁰.

The value of the angle DEF is 85⁰.

The value of the angles is calculated by applying intersecting chord theorem.

This theorem states that the angle at tangent is half of the arc angle of the two intersecting chords.

angle CFE = 180 - 123 (opposite angles of a cyclic quadrilateral)

angle CFE = 57

arc CDF = 2 x 57

arc CDF = 114

arc CFE = 360 - 114 = 246⁰

angle DEF = 180 - 95

angle DEF = 85

arc DCF = 2 x 85 = 170

arc FED = 360 - 170 = 190

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Sharon's employer deducts taxes from her salary to pay the federal government directly, which is a type of payroll tax. Nelson's company pays taxes based on a percentage of profits for the year, which is a type of corporate tax.

Priscilla pays more than the value listed on the price tag of a summer dress, which is a type of sales tax. Lincoln pays taxes directly to the government for the land he owns, which is a type of property tax.

Payroll taxes are levied on the earnings of employees and are used to fund social security, Medicare, and other federal and state programs. Corporate taxes are taxes on the profits earned by businesses.

Sales taxes are levied on the price of goods or services sold to consumers. Property taxes are levied on real estate owned by individuals or businesses based on the assessed value of the property.

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The image of A after a reflection using the y-axis is (-2, -1).

Given that, the coordinate of point A is (2, -1).

The image of A after a translation 2 units to the right.

Translation rules:

When the shape is moved towards the right by k units, then replace x with x + k.

Here, (2+2, -1)=(4, -1)

The image of A after a reflection using the y-axis.

The reflection of point (x, y) across the y-axis is (-x, y).

So, the image of point A is (-2, -1)

The image of A after a rotation of 180° using center (0, 0)

Rule: (x, y) becomes (-y, x)

So, the image of point A is (1, 2)

Therefore, the image of A after a reflection using the y-axis is (-2, -1).

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Answer:

[tex]m = \frac{29 - 20}{33 - 8} = \frac{9}{27} = \frac{1}{3} [/tex]

[tex]20 = \frac{1}{3} (8) + b[/tex]

[tex] \frac{60}{3} = \frac{8}{3} + b[/tex]

[tex]b = \frac{52}{3} [/tex]

[tex]y = \frac{1}{3} x + \frac{52}{3} [/tex]

[tex]3y = x + 52[/tex]

[tex] - x + 3y = 52[/tex]

[tex]x - 3y = - 52[/tex]

The total value of the annuity in 26 years is 179163.85 dollars.

Given that, Deandre deposits $97 each month in an annuity that pays 7.7 % interest, compounded quarterly.

The formula used to find the compound interest = [tex]A=P(1+\frac{r}{100})^{nt}[/tex].

Here, 26 years = 26×4

= 104

Now, A=97(1+7.5/100)¹⁰⁴

A=97(1+0.075)¹⁰⁴

A=97(1.075)¹⁰⁴

A=97×1847.05

A=$179163.85

Therefore, the total value of the annuity in 26 years is 179163.85 dollars.

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Answer:

(p + 2)(3b - 7)

Step-by-step explanation:

3b(p + 2) - 7(p + 2) ← factor out common factor (p + 2) from each term

= (p + 2)(3b - 7)

The value of x is 2√14 mi

Pythagoras theorem states that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse.

Therefore, if a and b are the legs of the triangle and c is the hypotenuse, then

c² = a²+b²

here, x and 5 are the legs and 9 is the hypotenuse of the triangle.

therefore;

x² = 9²-5²

x² = 81-25

x² = 56

x = √56

x = √4×14

x = 2√14

Therefore the value of the Missing side is 2√14 mi

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The value of angle k is 129⁰.

The value of angle b is 64.5⁰.

The value of angle b and angle k is calculated by applying the following principle of intersecting chord theorem.

k + 113 + 118 = 360 (sum of angles in a circle)

k + 231 = 360

k = 360 - 231

k = 129⁰

The value of angle b is calculated by applying the principle of intersecting chord theorem.

b = ¹/₂ arc k

b = ¹/₂ x 129

b = 64.5⁰

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Öncelikle verilen A ve B ifadelerinin değerlerini hesaplayalım:

A = (sin x . sec x)² - (tan x . cosec x)²

A = (sin x / cos x)² - (sin x / cos x)²

A = sin² x / cos² x - sin² x / cos² x

A = 0

B = 2 - 2cos² x + cos⁴ x - sin⁴ x

B = 2 - 2cos² x + (cos² x)² - (sin² x)²

B = (cos² x)² - 2cos² x + 2

Şimdi 2A + 3B'yi hesaplayalım:

2A + 3B = 2(0) + 3[(cos² x)² - 2cos² x + 2]

2A + 3B = 3cos⁴ x - 6cos² x + 6

Bu şekilde 2A + 3B ifadesinin ayrıntılı hesaplanması tamamlanmış oldu.

Being male and preferring Brand A are independent, as:

P(male|Brand A) = P(male).

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

From the table, we are already given the relative frequencies, hence we must simply identify the desired outcomes and the probability of being male is given as follows:

0.5 + 0.15 = 0.65.

The conditional probability of being male, given that the person prefers brand A, is given as follows:

P(male|Brand A) = P(male and Brand A)/P(Brand A) = 0.5/0.8 =  0.625.

As the probabilities are equal, the events are independent.

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