solve the following proportion

The slope of the line tangent to the graph of h(x) = 1/x + 3 at the point when x is -6 is -1/36.

To determine the slope of the line tangent to the graph of the given function when x = -6;

Using alternative form of the definition of derivative.

f'(a) = lim (h->0) [f(a+h) - f(a)] / h

Using this formula for the given function;

h'(a) = lim (h->0) [h(a+h) - h(a)] / h

Now, substitute a = -6 into the formula:

h'(-6) = lim (h->0) [h(-6+h) - h(-6)] / h

Next, simplify the expression by plugging in the values:

h'(-6) = lim (h->0) [1/(-6+h) + 3 - (1/-6 + 3)] / h

Simplifying further:

h'(-6) = lim (h->0) [1/(-6+h) - 1/-6] / h

Now, let's combine the fractions with a common denominator:

h'(-6) = lim (h->0) [(-6 - (-6+h))/((-6+h)(-6))] / h

Simplifying the numerator:

h'(-6) = lim (h->0) [-h / ((-6+h)(-6))] / h

Canceling out the h's:

h'(-6) = lim (h->0) [-1 / ((-6+h)(-6))]

Taking the limit as h approaches 0:

h'(-6) = -1 / ((-6)(-6))

Simplifying further:

h'(-6) = -1 / 36

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If the consumer raises their credit score by 60 points to 705, they will qualify for interest rate of 8.132%. The Option C

To know new interest rate, we have to get new credit score range and corresponding interest rate. The consumer's current credit score is 645, which falls within the range of 580-669.

To calculate the new credit score, we add 60 points to the current credit score:

= 645 + 60

= 705

The new credit score of 705 falls within the range of 670-739.  According to the given table, this range corresponds to a simple interest rate of 8.132%

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Answer:

A= 158

B=158

D=22

Step-by-step explanation:

An isosceles trapezoid has 2 pairs of equal angles.

A=B

C=D

Also A+C=180

So we have that A=158

B=158 and D=22

By using the parallelogram method, the addition of the vectors [tex]\vec a + \vec b[/tex] is (3, 1).

In Mathematics, a vector typically comprises two (2) points. First, is the starting point which is commonly referred to as the "tail" and the second (ending) point that is commonly referred to the "head."

Furthermore, the head to tail method of adding two vectors requires drawing the first vector ([tex]\vec a[/tex]) on a graph and then placing the tail of the second vector ([tex]\vec b[/tex]) at the head of the first vector. Finally, the resultant vector would be drawn from the tail of the first vector ([tex]\vec a[/tex]) to the head of the second vector ([tex]\vec b[/tex]).

Furthermore, the head to tail method of adding two (2) vectors requires drawing the first vector ([tex]\vec a[/tex]) on a graph and then placing the tail of the second vector ([tex]\vec b[/tex]) at the head of the first vector. Finally, the resultant vector would be drawn from the tail of the first vector ([tex]\vec a[/tex]) to the head of the second vector ([tex]\vec b[/tex]).

By adding the given vectors algebraically, we have the following:

[tex]\vec a + \vec b[/tex] = (4, -3) + (-1, -2)

[tex]\vec a + \vec b[/tex] = [(4 + (-1)), (-3 + (-2))]

[tex]\vec a + \vec b[/tex] = [(4 - 1), (-3 - 2)]

[tex]\vec a + \vec b[/tex] = (3, -5).

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1. We can see here that  the initial flounder population will be = [tex]\frac{220}{0.6t + 1}[/tex].

2. The P'(11) in 2 decimal places is: 28.95.

Population refers to the total number of people residing in a given region or area. In most cases, it is expressed as the number of people in relation to a unit of area, like a square kilometer or square mile. A census, which is a count of every person residing in a specific area, can be used to estimate the population of a nation or region.

Many variables, such as birth, mortality, and migration rates, can have an impact on population size.

1. The initial flounder population:

[tex]\frac{4t + 216}{0.6t^{2} + 1 } = \frac{4 + 216}{0.6t + 1} = \frac{220}{0.6t + 1}[/tex]

2. The P'(11) will be:

where t = 11

[tex]\frac{220}{0.6(11) + 1} = \frac{220}{7.6} = 28.9473[/tex]

= 28.95 (2d.p.)

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Answer:

please see detailed answers below

Step-by-step explanation:

1) circumference = πd = 16π inches.

arc length = (15/360) X πd = (2/3)π inches.

area of circle = πr² = π(8)² = 64π square inches.

area of sector = (15/360) X 64π = (8/3)π square inches.

2) circumference = πd = 30π inches.

minor arc length = (60/360) X 30π = 5π inches.

major arc length = (300/360) X 30π = 25π inches.

area of circle = πr² = π(15)² = 225π square inches.

area of minor sector = (60/360) X πr² = (75/2)π square inches.

area of major sector = (300/360) X πr² = (375/2)π square inches.

3) circumference = πd = 40π inches.

arc length = (125/360) X 40π = (125/9)π inches.

area of circle = πr² = π(20)² = 400π square inches.

area of sector = (125/360) X 400π = (1250/9)π square inches.

1). 140cm²

2). angle QRT

3). angle ACB= 65°

4). radian measure of d°

Dian's family is 3 times old now.  

Let's call Dian's family's age" x" now.

 According to the problem,

Dian is 8 times aged than his family, so Dian's age is x 8 now.  

In 5 times, Dian's age will be x 8 5, and his family's age will be x 5.  

The problem also states that in 5 times, Dian will be  doubly as old as his family,

so we can set up the equation

 x+ 8+ 5 =  2( x +5)  

Simplifying the equation  x +13 =  2x+ 10  

Obtaining x from both sides  

13 =  x +10  

Obtaining 10 from both sides  

3 =  x  

thus,X=3

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The equation for the line of best fit is given as follows:

y = 50x/3.

The slope-intercept equation for a linear function is presented as follows:

y = mx + b.

The parameters of the definition of the linear function are given as follows:

From the graph, when x = 0, y = 0, hence the intercept b is given as follows:

b = 0.

Hence:

y = mx.

When x = 3, y = 50, hence the slope m is given as follows:

3m = 50

m = 50/3.

Hence the equation is:

y = 50x/3.

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Answer:

The set M of all square numbers less than 80 is:

M = {0, 1, 4, 9, 16, 25, 36, 49, 64}

The set N of all non-negative even numbers that are under 30 is:

N = {0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28}

Answer:

All elements of the set M in ascending order are:

All elements of the set N in ascending order are:

Step-by-step explanation:

A square number, also known as a perfect square, is a non-negative integer that is obtained by multiplying an integer by itself. In other words, it is the result of squaring an integer.

The square numbers less than 80 are:

An even number is an integer that is divisible by 2 without leaving a remainder.

The non-negative even numbers that are under 30 are:

Therefore:

All elements of the set M in ascending order are:

All elements of the set N in ascending order are:

Answer:

4/3 ×π×r³

4/3 × 22/7 ×3³

88/21 ×27

Answer:

The graph of the parent function y = 2^x can be transformed to create the graph of y = 2^(3x) by horizontally compressing by a factor of 3. Therefore, the correct answer is C.

Check the picture below.

so the part on the left is a template for transformations, and we can look at g(x) like this

[tex]{\Large \begin{array}{llll} g(x)=\stackrel{A}{-3} ~~ (\stackrel{B}{1}x+\stackrel{C}{4})^2 ~~ \stackrel{D}{-3} \end{array}}[/tex]

now, if you look at the template, we do +4 first, then -3 shift down, then 3 vertical shrink, and then the negative of -3, landing at g(x) from our parent f(x).

Step-by-step explanation:

Volume  = 24 ft^3 = L x W x H

                  24 = 6 x 2 x H

                     H = 24 / ( 6 x 2) = 2 ft

We know the volume is 24, we can rearrange the formula to find the height: h = V/A. Plugging in the given values, we get h = 24/πr^2.

If the volume of a cylinder B2 is 24 cubic centimeters, there are a few things we can determine about the cylinder's dimensions. To find the radius of the cylinder, we first need to calculate the area of the base.

We can use the formula A = πr^2, where A is the area and r is the radius. If we know the volume of the cylinder, we can use the formula V = Ah, where V is the volume,

A is the area of the base, and h is the height of the cylinder. However, we do not have enough information to find the radius, as there are infinite combinations of radius and height that can give us a volume of 24 cubic centimeters.

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Answer:

1 South African Rand is equal to 100 cents. Therefore, 349 South African Rands is equal to 34900 cents.

Answer:

349 South African Rand equals

United States Dollar

17.95

South African Rand

349

Answer:

The correct answer is C. Net income refers to your take-home pay after taxes and other deductions have been taken out of your gross income. It is an important financial measure because it represents the actual amount of money you have available to save, invest, or spend on your expenses and bills.

Step-by-step explanation:

Answer:

If the height and radius of a cone are both 9 yards, then you can use the formula for the volume of a cone to calculate its volume. The formula for the volume of a cone is V = (1/3)πr^2h, where r is the radius of the base and h is the height of the cone. Plugging in the values for r, h, and π gives us:

V = (1/3)πr^2h

 = (1/3)(3.14)(9 yd)^2(9 yd)

 = (1/3)(3.14)(81 yd^2)(9 yd)

 = (1/3)(254.34 yd^3)

 ≈ 84.78 yd^3

So, the volume of a cone with a height and radius of 9 yards is approximately 84.78 cubic yards, rounded to the nearest hundredth.

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Step-by-step explanation:

work he in a department store

Answer:

8

Step-by-step explanation:

(5² + 7) ÷ 4 ← evaluate terms in parenthesis

= (25 + 7) ÷ 4

= 32 ÷ 4

= 8

Step-by-step explanation:

This graph shows a vertical asymptote at x = 0  

                                           this is where it is not continuous

The angle pairs are given as follows:

a) Alternate exterior: <2 and <8.

b) Corresponding angles: <2 and <6.

c) Alternate interior: <3 and <5.

Item a:

Alternate exterior angles are two angles that are on the exterior of the two parallel lines, on opposite sides of the transversal line, hence they are given as follows, for item a:

Item b:

Corresponding angles are angles that are on the same position relative to the transversal line, but on different parallel lines, hence one example is given as follows, for item b:

<2 and <6.

Item c:

The two alternate interior angles are positioned on the inside of the two parallel lines, and on opposite sides of the transversal line, hence they are given as follows, for item c:

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Solution of expression 12 - |2x + 15| > 3 are,

⇒ - 12 < x < 3

And, Solution of (x - 3)² - x² + 3)/ (x² + 1) ≥ 0 is,

⇒ x ∈ [2, ∞) - {i, - i}

We have to given that;

Expressions are,

⇒ 12 - |2x + 15| > 3

And, (x - 3)² - x² + 3)/ (x² + 1) ≥ 0

Now, We can simplify as;

⇒ 12 - |2x + 15| > 3

⇒ 12 - 3 > |2x + 15|

⇒ 9 > |2x + 15|

⇒ |2x + 15| < 9

⇒ - 9 < 2x + 15 < 9

This gives,

⇒ - 9 < 2x + 15

⇒ - 9 - 15 < 2x

⇒ - 24 < 2x

⇒ - 12 < x

And, 2x + 15 < 9

⇒ 2x < 15 - 9

⇒ 2x < 6

⇒ x < 3

Hence, Solution of expression 12 - |2x + 15| > 3 are,

⇒ - 12 < x < 3

And, Simplify the expressions ,

⇒ (x - 3)² - x² + 3)/ (x² + 1) ≥ 0

⇒ (x - 3)² - x² + 3) ≥ 0

⇒ x² + 9 - 6x - x² + 3 ≥ 0

⇒ 12 - 6x ≥ 0

⇒ 12 ≥ 6x

⇒ 2 ≥ x

Hence, Solution of (x - 3)² - x² + 3)/ (x² + 1) ≥ 0 is,

⇒ x ∈ [2, ∞) - {i, - i}

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To find the area of a sector, you can use the formula A = (θ/2π) × πr^2 = (θ/2) × r^2.

The area of a circle is given by the equation A = πr^2, where r is the radius of the circle. The arc length of a circle is given by the equation L = rθ, where θ is the central angle in radians and r is the radius of the circle.

To find the arc length of a portion of a circle, you can use the formula L = (θ/2π) × 2πr = (θ/2π) × C, where C is the circumference of the circle. This formula is useful when you have a fraction of a circle, such as a sector.

These equations are fundamental in geometry and are used in many applications such as architecture, engineering, and physics.

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Answer:

Vicky uses 400 ml of lemon juice in the salad dressing.

The greatest number of children that can distribute the mangoes equally is 481. Each child will receive 481/481 = 1 mango.

In order to distribute the mangoes equally among children, we first need to determine the total number of mangoes in the bag.

If there are 215% (or 2.15) of 224 mangoes in the bag, we can calculate the total number of mangoes by multiplying these values: 2.15 * 224 = 481.6 mangoes.

Since we cannot have fractional mangoes, we round down to the nearest whole number, which gives us a total of 481 mangoes in the bag.

To distribute these mangoes equally among the children, we divide the total number of mangoes by the number of children. Let's assume there are 'x' children.

Each child will receive 481/x mangoes.

To determine the greatest number of children, we need to find a value for 'x' that evenly divides 481. We can do this by finding the factors of 481. The factors of 481 are 1, 13, 37, and 481.

Therefore, the greatest number of children that can distribute the mangoes equally is 481. Each child will receive 481/481 = 1 mango.

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To find the first four terms of the infinite sequence u_n = 1/(7n - 2), we substitute the values of n from 1 to 4 into the formula:

For n = 1:

u_1 = 1/(7(1) - 2) = 1/5

For n = 2:

u_2 = 1/(7(2) - 2) = 1/12

For n = 3:

u_3 = 1/(7(3) - 2) = 1/19

For n = 4:

u_4 = 1/(7(4) - 2) = 1/26

Therefore, the first four terms of the infinite sequence are:

u_1 = 1/5

u_2 = 1/12

u_3 = 1/19

u_4 = 1/26

Answer:

x = 4

Step-by-step explanation:

the angle immediately to the left of 20x must be 25x. that's because the two lines with double arrows at the top are parallel lines.

the angle to the left of 20x and the 25x are called alternate angles. they are equal.

also, 20x and the angle to the left of it are on a straight line. angles on a straight line add up to 180°.

so, we now have 20x + 25x = 180.

45x = 180

divide both sides by 45:

x = 180/45

= 4.

x = 4.

The cardinality of set A (n(A)) is 3.

The cardinality of set B (n(B)) is 4.

To find the cardinality of a set, we count the number of elements in that set.

For set A, we need to count the number of integers between -6 and -4 (inclusive).

The integers in this range are -6, -5, and -4.

Therefore, the cardinality of set A (n(A)) is 3.

For set B, we simply count the number of elements given in the set. From the given set B = {-29, 20, 28, 29}, we have 4 elements.

Therefore, the cardinality of set B (n(B)) is 4.

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Hello

What is the value of x?^

[tex]\frac{3x}{4x} = \frac{3x+7}{5x-8} \\\\\frac{3}{4} = \frac{3x+7}{5x-8}\\\\\frac{3}{4}(5x-8) = 3x+7\\\\\frac{3(5x-8)}{4} = 3x + 7\\\\\frac{15x-24}{4} = 3x + 7\\\\15x - 24 = 4(3x + 7)\\\\15x - 24 = 12x + 28\\\\15x - 12x = 28 + 24\\\\3x = 52\\\\\boxed{x = 52/3}[/tex]