Find the midpoint of points A(-9, -3) and B(1, 7) graphically.
Plot the line segment AB

The derivative and domain of the function f(x) = x²-2x³  is :[tex](-\infty, \infty)[/tex].

The slope of a function's graph or, more precisely, the slope of the tangent line at a point can be used to interpret a function's derivative.

Its computation actually stems from the slope formula for a straight line, with the exception that curves require the employment of a limiting procedure.

Calculation for the derivative:

Step 1: Use the definition of the derivative. Remember that f(x+h) means plug (x+h) into everywhere there is an "x" in f(x).

[tex]\begin{aligned}f^{\prime}(x) &=\lim _{h \rightarrow 0} \frac{f(x+h)-f(x)}{h} \\&=\lim _{h \rightarrow 0} \frac{(x+h)^{2}-2(x+h)^{3}-\left(x^{2}-2 x^{3}\right)}{h} \\&=\lim _{h \rightarrow 0} \frac{\left(x^{2}+2 h x+h^{2}\right)-2(x+h)(x+h)^{2}-x^{2}+2 x^{3}}{h} \quad \text { cancel } x^{2}\end{aligned}[/tex]

       [tex]\begin{aligned}&=\lim _{h \rightarrow 0} \frac{\left(2 h x+h^{2}\right)-2(x+h)\left(x^{2}+2 h x+h^{2}\right)+2 x^{3}}{h} \\&=\lim _{h \rightarrow 0} \frac{\left(2 h x+h^{2}\right)-2\left(x^{3}+2 h x^{2}+h^{2} x+h x^{2}+2 h^{2} x+h^{3}\right)+2 x^{3}}{h} \\&=\lim _{h \rightarrow 0} \frac{2 h x+h^{2}-2 x^{3}-4 h x^{2}-2 h^{2} x-2 h x^{2}-4 h^{2} x-2 h^{3}+2 x^{3}}{h}\end{aligned}[/tex]

       [tex]=\lim _{h \rightarrow 0} \frac{2 h x+h^{2}-6 h x^{2}-6 h^{2} x-2 h^{3}}{h}[/tex]

Step 2: Cancel out a factor of h from each term in the numerator with the h in the denominator. Then direct substitute h=0.

      [tex]\begin{aligned}&=\lim _{h \rightarrow 0}\left(2 x+h-6 x^{2}-6 h x-2 h^{2}\right) \\&=2 x+0-6 x^{2}-6(0) x-2(0)^{2} \\&=2 x-6 x^{2}\end{aligned}[/tex]

f and f' are polynomials, so their domains are all real numbers.

Therefore,  for f(x) = x²-2x³      domain of f and f' :[tex](-\infty, \infty)[/tex].

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The complete question is -

Find the derivative of the function using the definition of derivative. State the domain of the function and the domain of its derivative f(x) = x²-2x³.

Type of sequence: arithmetic progression

Explicit formula: 5n

Recursive formula: [tex]5_{n-1}[/tex] + 5

A Sequence is a series of numbers in a regular pattern of increment. A sequence can be arithmetic or geometric in nature.

Given that a total value of a collection of nickels can be described by this sequence: 5, 10, 15, 20, 25, 30, .....

The difference in the sequence above is 10 - 5 = 5. There is an increment of 5 in each term.

Therefore, the type of sequence is arithmetic progression

The difference d = 5 and the first term is also 5

An explicit formula will be

a + (n - 1)d

substitute a and d into the formula

5 + (n - 1)5

5 + 5n - 5

5n

Therefore, 5n gives the value of a specific term based on the position

A recursive formula will be

[tex]a_{n-1}[/tex] + d

substitute a and d into the formula

[tex]5_{n-1}[/tex] + 5

Therefore, [tex]5_{n-1}[/tex] + 5 gives the value of a specific term based on the previous term

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The additional information which would be sufficient to conclude that LMNO is a parallelogram is; ML ∥ NO, LO ≅ MN, and ML ≅ LO.

The condition for a quadrilateral to be a parallelogram is that; the opposite pairs must be parallel and consequently opposite pairs are congruent as they have equal length measures.

On this note, it can be concluded that the additional information which would be sufficient are; ML ∥ NO, LO ≅ MN, and ML ≅ LO.

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(A.) ML ∥ NO,

(C.) LO ≅ MN.

Have a great day and hydrate!! <3

The mass of the same nickel which is 5 grams in milligrams is 5,000 milligram.

Weight of a nickel = 5 gram

Weight of same nickel in milligram = 5 grams × 1000

= 5,000 milligram

Therefore, the mass of the same nickel is 5,000 milligram

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Answer:

See below

Step-by-step explanation:

The larger is  

7-6 = 1 unit bigger than the smaller....and this unit = 24 gallons

   each unit is 24 gallons

larger barrel holds   24 * 7 = 168 gal

smaller barrel holds  24 * 6 = 144 gal

Answer:

Small barrel=144 large barrel=168

Step-by-step explanation:

The ratio is 6 to 7 so lets assign x as a factor.

6x=Small barrel (S)

7x=Large barrel (L)

7x-6x=x

x is the difference so x is 24

x=24

6*24=144=S

7*24=168=L

Answer:

Option B: 3

Step-by-step explanation:

#1: Substitute in 6 for [tex]y[/tex] and 3 for [tex]x[/tex]: [tex]13=(3)(6)-5[/tex]

#2: Multiply 3 and 6: [tex]13=18-5[/tex]

#3: Evaluate the equation: [tex]13=18-5[/tex] → [tex]13=13[/tex]

#4: Check if the solution is equal: [tex]13=13[/tex] ✓

[tex]x[/tex] is equal to 3 (Option B).

Answer:

A. y= cos x - 1

Step-by-step explanation:

short answer: this is basically the parent graph cos(x), just vertically shifted down 1 unit.

longer answer:

standard form is y = a cos(bx-c) +d

a = amplitude

b = 2pi/period

c = horizontal shift

d = vertical shift (also equal to midline)

for this graph

a=1

period is 2pi, so b=1

there is no horizontal shift so c=0

d= -1 because it is shifted down one unit from axis (midline is at -1)

The graph that shows the minimum amount due for a credit amount of x given that the credit limit is $2,000 is graph B.

Let x represent the credit amount  and y represent the minimum amount due.

For a bill of less than $100, the entire amount is due. That is for 0 ≤ x < $100, y = x

For a bill of at least $100 but less than $500, the minimum due is $100. That is for $100 ≤ x < $500, y = 100

For a bill of at least $500 but less than $1,000, the minimum due is $300. That is for $500 ≤ x < $1000, y = $300

For a bill of $1,000 or more, the minimum due is $500. But the credit limit is $2000. That is For $1000 ≤ x < $2000, y = $500

The graph that shows the minimum amount due for a credit amount of x  is graph B.

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For the following pair of functions, the vertex of g(x) 2 units to the right of f(x),

f(x) = x² and g(x) = (x - 2)²

What are functions?

Defining a relationship between an independent variable and a dependent variable using mathematical expressions, rules, or laws is known as a function. Mathematics is rife with functions, and the sciences depend on them for constructing physical relationships.

Determining the Correct Pair of Functions

For a given function f(x), its horizontal translation would be f(x + a). Here, a is the distance translated, owing to which f(x + a) is generated.

If a > 0, then it indicates a right translation of a units.

If a < 0, then it indicates a left translation of a units.

The required functions are to be such that the vertex of g(x) is 2 units to the right of the vertex of f(x).

Thus, if f(x) = x², then g(x) = (x - 2)²

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The surface area of the composite figure is 444m²

Given a composite figure which is shown in the question.

The  area of ​​a shape (in square units) is the number of unit squares required to cover the entire area without gaps or overlaps. If a hologram has planes, those faces are called faces. Area is the sum of the areas of the faces.

Firstly, we will find the area of front and end triangles by using the formula

Area=(1/2)×b×h and we will multiply this area by 2 because we are finding the area of two same triangles.

Here, h=6 and b=16 and substitute these values in the formula, we get

A₁=2×(1/2)×16×6

A₁=2×8×6

A₁=96m²

Now, we will find the area of the left and right side rectangles which joined both the triangles.

We will find the area by using the formula Area=l×b and we will multiply this area by 2 because we are finding the area of two same rectangles.

here, l=10 and b=5 and substitute these values in the formula, we get

A₂=2×10×5

A₂=100m²

Further, we will find the area of the front and end side rectangles that joined both by the base of the triangles.

We will find the area by using the formula Area=l×b and we will multiply this area by 2 because we are finding the area of two same rectangles.

here, l=16 and b=4 and substitute these values in the formula, we get

A₃=2×16×4

A₃=128m²

Furthermore,  we will find the area of the left and right side rectangles which joined by the front and end rectangles.

We will find the area by using the formula Area=l×b and we will multiply this area by 2 because we are finding the area of two same rectangles.

here, l=4 and b=5 and substitute these values in the formula, we get

A₄=2×4×5

A₄=40m²

Now, we will find the area of the base of the composite figure which is rectangle.

We will find the area by using the formula Area=l×b.

here, l=16 and b=5 and substitute these values in the formula, we get

A₅=16×5

A₅=80m²

So, the surface area of the given composite figure will be

Surface area=A₁+A₂+A₃+A₄+A₅

Surface area=96m²+100m²+128m²+40m²+80m²

Surface area=444m²

Hence, the surface area of the given composite figure is 444m².

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Answer:

5 hours 20 minutes.

Step-by-step explanation:

8 * 2/3

= 16/3

= 5 1/3

= 5 hours 20 minutes.

Answer: 8r + 9.8s + 8.1

Step-by-step explanation:

   Given:

-(-8r-9.8s)+8.1

   Distribute:

   ↳ A - times a - becomes a +, a -times a + stays a -

8r + 9.8s + 8.1

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Step-by-step explanation:

123456 less then 7

unlimited greater then 7

The numbers from negative infinity to 7, excluding 7."are less than 7 and "all numbers from 7 to positive infinity, excluding 7" are more than 7.

The combination of positive, negative numbers including 0  are called as integers.

The numbers less than 7 are:

This set includes all real numbers that are strictly less than 7.

It can be denoted as (-∞, 7), which means "all numbers from negative infinity to 7, excluding 7."

The numbers greater than 7 are:

This set includes all real numbers that are strictly greater than 7. It can be denoted as (7, +∞), which means "all numbers from 7 to positive infinity, excluding 7."

Thus, there are infinite numbers which are less than 7 and more than 7.

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The type of bacterial pneumonia is most often seen in children and young adults is; Pneumococcal infection.

The correct type of Bacterial pneumonia that is most often seen in children and young adult is called Pneumococcal infection. This is because it is a name for any infection caused by bacteria called Streptococcus pneumoniae, or pneumococcus.

Thus, we can conclude that the type of Bacterial pneumonia here is called Pneumococcal infection.

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The three stages that have to do with fluency, progression and automaticity are found in the Number Sense and Operations .

This is the part of mathematics that is known to teach the student basic ways to carry out number operations in mathematics. This has to do with representation of numbers as well as solving for the existing relationships in these numbers.

Having a sense of numbers is a very important ability skill that has to be developed early is students to enable them progress in the subject.

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The value of f⁻¹(f(58)) is 58 and the value of the function f(f(5)) is 11

As a general rule, we have:

f⁻¹(f(x)) = x

Substitute 58 for x

So, we have:

f⁻¹(f(58)) = 58

Hence, the value of f⁻¹(f(58)) is 58

Also, we have:

f(f(5))

From the table, we have:

f(5) = 9

So, we have:

f(f(5)) = f(9)

From the table, we have:

f(9) = 11

So, we have:

f(f(5)) = 11

Hence, the value of the function f(f(5)) is 11

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Jasmine will not have enough for the car. The amount more that she needs is $520.

The first step is to convert the fraction that represents the amount needed as a deposit to percentage.

(2/5) x 100 = 40%

Difference in the deposit and the amount Jasmine's father deposited: 40% - 30% = 10%

Amount more that she needs : 10% x 5200 = $520

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The piecewise defined function is formed by the following three functions: y = 40, for 0 ≤ x < 15, y = 0.0425 · x² - 3.8 · x + 87.438, for 15 ≤ x < 65 and y = 0.4 · x - 6, for x ≥ 65.

In this problem we have a piecewise defined function formed by three functions: (i) Linear equation, (ii) Quadratic equation, (iii) Linear equation. The first function is y = 40, for 0 ≤ x < 15.

The second function can be found based on the knowledge of three points:

y = a · x² + b · x + c

(x₁, y₁) = (15, 40)

40 = 225 · a + 15 · b + c

(x₂, y₂) = (45, 2.5)

2.5 = 2025 · a + 45 · b + c

(x₃, y₃) = (65, 20)

20 = 4225 · a + 65 · b + c

And the quadratic equation is y = 0.0425 · x² - 3.8 · x + 87.438, for 15 ≤ x < 65.

And the latter linear equation is:

y = m · x + b

m = (30 - 20)/(90 - 65)

m = 0.4

And the x-intercept is:

b = y - m · x

b = 20 - 0.4 · 65

b = - 6

The linear equation is y = 0.4 · x - 6, for x ≥ 65.

The piecewise defined function is formed by the following three functions: y = 40, for 0 ≤ x < 15, y = 0.0425 · x² - 3.8 · x + 87.438, for 15 ≤ x < 65 and y = 0.4 · x - 6, for x ≥ 65.

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Answer:

( 3 , 4 )

Step-by-step explanation:

Midpoint Formula: ( (x1+x2)/2 , (y1+y2)/2 )

Distance Formula: d = √[(x1-x2)^2 + (y1-y2)^2]

Gradient (Slope) Formula: (y2-y1) / (x2-x1)

Midpoint Formula:

( (x1+x2)/2 , (y1+y2)/2 )

(2,3) and (4,5)

( (2+4)/2 , (3+5)/2 )

( (6)/2 , (8)/2 )

( 3 , 4 )

wyzant sean w

Answer: D

Step-by-step explanation:

If the original price was p, a price reduction would be p- the amount. Per the given answers, $275 is used for the reduction amount.

Answer:

A) Equation of the line of best fit: y = -5x + 62

B) y = -3

Explanation:

Given points: {(5, 38), (6, 34), (7, 27), (8, 21), (9, 17), (10, 14)}

Plot these points on the graph and draw a straight line between them.

A)

The points (7, 27), (9, 17)

Find slope:

[tex]\sf slope: \dfrac{17-27}{9-7} = -5[/tex]

Equation:

[tex]y - y_1 = m(x - x_1)[/tex]

[tex]\sf y - 27= -5(x - 7)[/tex]

[tex]\sf y = -5x + 35 + 27[/tex]

[tex]\sf y = -5x + 62[/tex]

B) If x = 13, then approximate value of y is

insert x = 13 in equation

y = -5x + 62

y = -5(13) + 62

y = -3

The answers are :

A) y = -5x + 64

B) -1

Part (A) :

Finding the slope : Take the points (6, 34) and (10, 14)

m = Δy/Δx

m = 14 - 34 / 10 - 6

m = -20/4

* m = -5 *

Using point slope formula to find equation :

y - y₁ = m (x - x₁)

y - 34 = -5 (x - 6)

y - 34 = -5x + 30

y = -5x + 64

Part (B) :

Substitute x = 13 in the line of best fit equation

y = -5(13) + 64

y = -65 + 64

y = -1

The numbers : 4,-10 and -4 are integers.

A number without a decimal or fractional element is known as an integer, which can be both positive and negative, including zero.

The Latin word "integer" signifies "whole" or "intact." Thus, fractions and decimals are not included in integers.

All whole numbers and negative numbers are considered integers. This means that if we combine negative numbers with whole numbers, a collection of integers results.

"Negative 1 and one-third" includes a fractional part, so it is not an integer.

"2.5" and "0.ModifyingAbove 13 with Bar" contain a decimal, so it is also not an integer.

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Bob eats a 171 days sweetened cereal and 194 days he eat unsweetened cereal.

According to the statement

we have given that the Bob rolls a composite number, he eats sweetened cereal. If he rolls a prime number, he eats unsweetened cereal.

and we have to find that the expected value of the difference between the number of days.

So, the total number of days in a year is 365 days.

Chance to get a prime number on a die = 3/6

Chance to get a prime number on a die = 1/2.

and chances to get a composite number = 2/6

chances to get a composite number = 1/3

and chances to get a 1 on a die = 1/6.

Then the expected value =

so, expected value = 365(1/6) + 365(1/3) + 365(1/2)

then after calculating

Expected value = 1+2+1

then the value become is 4

and by this way he eat 171 days sweet cereal and other days he eat unsweetened.

So, Bob eats a 171 days sweetened cereal and 194 days he eat unsweetened cereal.

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Here, Given

h= 8ft

a=144 * ft^2

then,

A=L*H

144=L*8 or 144/8 =L

L=18

now, P=2(L+H)

P=2(18+8)

P=52m

Perimeter and area are two important and basic mathematical subjects. They help quantify the physical space and also provide a more advanced foundation of mathematics in algebra, trigonometry, and calculus. Perimeter is a measure of the distance around a shape, and area indicates how much area the shape covers.

The perimeter of a 2D shape is the distance around the shape. You can imagine wrapping a string around a triangle. The length of this cord is around the triangle. Or, if you're traveling outside the park, take a route that goes around the edge of the park.

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The relationship of the data can be classified as a fairly strong positive correlation.

Correlation is a statistical measure used to measure the relationship that exists between two variables.

Positive correlation is when two variables move in the same direction. If one variable increases, the other variable also increases. When there is a positive correlation, the graph of the variables is upward sloping

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Answer:

20 units

Step-by-step explanation:

As you know that the quadrilateral is a square, you’ll just have to find the length of one side and multiply it by four. We can count and see that one side is 5 units.

5 * 4 = 20 units

You can also add the length of each of the four sides.

5 + 5 + 5 + 5 = 20

Hope that helps you! Please let me know if you need more help with this question. Have a great day!

The volume of the shape will be 50cm3.

It should be noted that the volume van be found by multiplying the area by the height. The volume will be:

= 10 × 5

= 50cm³

The standard deviation volume will be:

= 0.1 × 50

= 5cm

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The value of x in the trapezoid is 11.

Therefore, the angle 9x and 7x + 4 are supplementary.

Hence,

9x + 7x + 4 = 180

16x + 4 = 180

16x  = 180  - 4

16x = 176

x = 176 / 16

x = 11

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Answer:11

Step-by-step explanation:Easy

The school building's actual length is 40 m.

Length exists as a measure of distance. In the International System of Quantities, length exists as a quantity with dimension distance. In most systems of measure a base unit for length is selected, from which all other units exist derived. In the International System of Units system, the base unit for length exists as the meter.

Given: School building length is given 40 cm on the map

scale used is 1 cm = 1 m

The scale utilized exists 1 cm = 1 m

1 cm in map = 1 m in actual

⇒ 40 cm in map = 40 m in actual

School building length in map = 40 cm

⇒ Actual Length of the school building is 40 m

Therefore, the school building's actual length is 40 m.

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