Directions: Write the slope form of the equation with the given information.

13) through (3,4) and (5,-2)

Using limit definition of the derivative, The value of f'(3) is 2.

By determining the limit of a slope expression, one can get the instantaneous rate of change (derivative).

The derivative of a function f at x is the instantaneous rate of change of the function at x since the derivative is defined as the limit that determines the slope of the tangent line to a function.

Given function

f(x) = x² - 4x.

derivate with respect to x

f'(x) = 2x - 4

put x = 6

f'(x) = 2(3) - 4

= 6-4

=2

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Answer:

Option D.

Step-by-step explanation:

We are given with three function.

Plug in x=-2 in first functionf(x)= 3 so f(-2) = 3Plug in x=-2 in second function.

The value of the smaller number is 5

From the question, we are to determine the value of the smaller number

Let one of the numbers be x and the other number be y

From the given information,

The difference of two numbers is 1

That is,

x - y = 1

and

Their sum is 11

That is,  

x + y = 11

Now, we will solve the equations simultaneously

From the first equation

x - y = 1

x = 1 + y     ------------- (3)

Substitute into the second equation

x + y = 11

1 + y + y = 11

1 + 2y = 11

2y = 11 - 1

2y = 10

y = 10/2

y = 5

Substitute the value of y into equation (3)

x = 1 + y

x = 1 + 5

x = 6

Hence, the number is 5

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Answer:

y = -2x.

Step-by-step explanation:

2y = x - 3

y = 1/2x - 3/2

- so, the slope of this line is 1/2

and the slope of a line perpendicular to it is - 1/ 1/2

= -2.

Using the point slope form of a line the equation of the required line is

y - y1 = m(x - x1)

m = -2, x1 = -1 and y1 = 2.

So,

y - 2 = -2(x - (-1))

y - 2 = -2x - 2

y = -2x - 2 + 2

y = -2x.

Answer:

Step-by-step explanation:

2100 - 1900 =  200

660(200) + 14,400

p = 146400

146,400 people

The answer is B

The original price of the toy is p.

An easier way to understand this problem is : The original price is 1, or 100%. Now, it's reduced by 15%, so the new price is 100% - 15% = 85%.

85% can be converted to 0.85, or 85/100. Therefore, the answer is 0.85p

If the first marble is not reinserted into the bag before the second draw, there is 1/15 probability of drawing two pink marbles.

When the result of one event affects the result of another, two events are said to be dependent. The likelihood of two connected events is the sum of the probabilities of the occurrences X and Y that happen after X.

It is given that there are two yellow, three pink and 5 blue marbles.

So, in the first draw, the probability of drawing pink marble is the ratio of the number of pink marbles to the total number of marbles in the bag.

[tex]p_1=\frac{3}{10}[/tex]

Now, in the second draw, the probability of drawing pink marbles will be affected as it is not kept back. So, in the second draw, the probability of drawing pink marble is the ratio of the number of remaining pink marbles to the remaining number of marbles in the bag.

[tex]p_2=\frac{2}{9}[/tex]

Given that both occurrences occur concurrently, multiply the likelihood of the first event by the probability of the second event.

[tex]p=p_1\times p_2\\\\=\frac{3}{10}\times\frac{2}{9}\\\\ =\frac{1}{15}[/tex]

So, If the first marble is not reinserted into the bag before the second draw, there is 1/15 probability of drawing two pink marbles.

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Answer:

5

Explanation:

When we divide A by B, we are calculating how many Bs fit into A. So, if we want to know how many 2/5s fit into 2 yds, we need to divide 2 by 2/5. So:

So, 2 yds of rope can be divide into 5 ropes of 2/5 yd.

The length of the arc whose central angle is 50° is 10.91.

Here, we are given that a circle has a circumference of 25π.

The length of the arc of a circle is given by the following formula-

(∅/360)*2πr

where ∅ is the measure of the angle that the arc subtends at the center and r is the radius of the circle.

Here, we are already given the circumference, thus, 2πr = 25π.

And, the central angle is given to be 50. Thus, ∅ = 50

Now, substituting the values in the above formula we can calculate the length of the arc as follows-

(50/360)*25π

= 5/36 × 25π

= 125/36 × 22/7

= 2,750/ 252

= 10.91

Thus, the length of the arc whose central angle is 50° is 10.91.

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Given:

A U.S. Geological Survey map has a scale of 1:24200

There are two buildings that are 3.38 miles apart.

We will find how they are inches apart on the map

First, convert from miles to inches

1 mile = 63 360 inches

So, 3.38 miles = 3.38 * 63 360 inches = 214156.8 inches

The map has a scale of 1:24200

So, using the ratio and the proportions, we will find the length on the map as follows:

Rounding to the nearest hundredth

So, the answer will be: 8.85 inches

Answer:

The right answer choices are B, C, and F

The equation of the line perpendicular to y = 6x -2 and passes through (6, -2) is y = - 1 / 6 x - 1

The equation of a linear graph can be represented in slope intercept form.

Therefore,

y = mx + b

where

Therefore,  the equation of the line is perpendicular to y = 6x -2 and passes through (6, -2).

Perpendicular lines follows the rule below:

m₁ m₂ = -1

6m₂ = -1

m₂ = - 1 / 6

Therefore, let's find the y-intercept using (6, -2)

y = - 1 / 6 x + b

-2  = - 1 / 6 (6) + b

- 2 + 1 = b

b = -1

Therefore, the equation of the line is y = - 1 / 6 x - 1

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Answer:

1) 267.45

2) 18.48

3) 3472

Answer:

6

Step-by-step explanation:

4-x/3=2

4-6/3=2

The area of the first and second circles is 36π m² and 9π m², respectively.

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Answer:

-6<v<3

Step-by-step explanation:

hope this helps

Given that g(x)=2x + 1,

therefore, the value of g(a+h) and g(a) can be written as,g(x)=2x + 1g(a+h)=2(a+h) + 1     
   = 2a + 2h + 1

g(x) = 2x + 1g(a) = 2(a) + 1   
   = 2a + 1

Now, the value of g(a+h)-g(a) will be,

g(a+h) - g(a)= (2a + 2h + 1) - (2a + 1)= 2a + 2h + 1 - 2a - 1= 2h

Hence, the value of g(a+h)-g(a) is 2h.

Step-by-step explanation:

146 × 48 = 48 × 146

due to the commutative law of multiplication the sequence of the operands of a multiplication does not matter.

a × b = b × a

this bases on the fact that a multiplication is nothing else than a special kind of addition

a × b = add a b times; or add b a times.

and as already the addition follows the commutative law

a + b = b + a

so, does then the multiplication.

The price after the discount but before tax, to the nearest dollar and cent, is $18.4.

Given Information:

Price on the tag = $23

Amount of Discount =20%

A % or Percentage is a figure or ratio that is stated as a fraction of 100 (from the Latin per centum, "by a hundred").  A % lacks dimensions and has no associated unit of measurement.

Percentage Formula =[tex]\frac{value}{Total value} *100[/tex]

Calculating the discount,

There is a 20 % discount on the camera

So, the amount of discount by using the percentage formula = [tex]\frac{20*23}{100} = 4.6[/tex]

Hence, the amount of discount is $4.6

Subtracting the discount to calculate the price after the discount =

Initial Price - Discount amount = $23-$4.6 = $18.4

Thus, the price after the discount is $18.4

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Answer:

{1, -5/6}

Step-by-step explanation:

(6a+5)(a-1) = 0

6a+5 = 0 (or) a-1 = 0

a = -5/6 (or) a = 1

If in lixue's garden the green pepper plants grew 5 inches in 3/4 months then at this rate they can grow 0.555 feet in one month

The problem is solved as per the unitary method

In lixue's garden the green pepper plants grew 5 inches in 3/4 months.

In 3/4 months the green pepper grew by 5 inches.

3/4 months can be written as 0.75 months

in 1 month the green pepper plant will grow by (5/0.75) 1

The green pepper plant will grow by 6.66 inches

1 foot is equals to 12 inches

1 inch = 1/12 foot

6.666 inches = (1/12) 6.666

= 0.0833 x 6.666

= 0.555

the plant grew 0.555 feet in 1 month

Therefore, if in lixue's garden the green pepper plants grew 5 inches in 3/4 months then at this rate,they can grow 0.555 feet in one month

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The most appropriate choice for function and domain and range of a function will be given by -

Domain of y = [tex]\mathbb{R} -[/tex] {[tex]-\frac{1}{2}[/tex]}

Range = [tex]\mathbb{R}-[/tex]{[tex]\frac{1}{2}[/tex]}

What is a function and domain and range of a function?

A function from A to B is a rule that assigns to each element of A a unique element of B. A is called the domain of the function and B is called the codomain of the function.

There are different operations on functions like addition, subtraction, multiplication, division and composition of functions.

The set of  values for which the function is defined is the domain of the function and the values obtained on substituting the values of domain in the function is the range of the function.

y = [tex]\frac{x -5}{2x + 4}\\[/tex]

For domain of y

y is not defined if 2x  +4 = 0

y is not defined if [tex]x = -\frac{1}{2}[/tex]

Domain of y = [tex]\mathbb{R} -[/tex] {[tex]-\frac{1}{2}[/tex]}

For range of y

let [tex]\frac{x -5}{2x + 4}\\[/tex] = z

[tex]x - 5 = z(2x +4)\\x - 5 = 2zx + 4z\\x - 2zx = 4z + 5\\x(1 - 2z) = 4z + 5\\x = \frac{4z + 5}{1 - 2z}[/tex]

If y = [tex]\frac{1}{2}[/tex]

[tex]\frac{x-5}{2x + 4} = \frac{1}{2}\\2x - 10 = 2x + 8\\-10 = 8\\[/tex]

Not possible

[tex]\frac{1}{2}[/tex] is not in the range of y

Range = [tex]\mathbb{R}-[/tex]{[tex]\frac{1}{2}[/tex]}

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Yes it is possible for a rectangle to have irrational sides and rational area.

What are rational numbers?

Ration numbers is an ordered pair of integers a, b written in the form a/b where b is not equal to zero.

We are given that sides of rectangle are irrational can the rectangle have rational area

Let us consider that sides of the rectangle be [tex]2\sqrt{2}[/tex] and [tex]\sqrt{2}[/tex]

Hence the area of the rectangle is the product of sides which is [tex]4[/tex] sq. units

Which is a rational number

Hence, Yes it is possible for a rectangle to have irrational sides and rational area

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Answer:

86995.5

Step-by-step explanation:

86995.499184 86995.49918

The fractional equivalent of the repeating decimal n = 0.1515... is 5/33, with two repeating digits.

A fractional equivalent is a fraction that shares the same equivalent value with a decimal.

For instance, the equivalent fraction of 0.1515 is 303/2000.  But for a repeating decimal like 0.1515..., the equivalent fraction is 5/33.

When numbers or values are said to be equivalent, it means that they are equal.

By their nature, repeating decimals continue endlessly.

Let x = 0.1515... equation 1

100x = 15.1515... equation 2

Subtract equation 1 from equation 2:

100x = 15.1515...

    x =   0.1515...

99x = 15

x = 15/99

x = 5/33

Thus, n = 0.1515... as a repeating decimal or 5/33 as a fraction.

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Step-by-step explanation:

option D is correct..

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