Find the domain of the function. Express the exact answer using interval notation.

f(x) = 2/3x+8

The expression 2ab + [tex]c^2[/tex]  represents the area of the figure as the sum of the area of the shaded triangles and the area of the white square.

The equivalent expression [tex]a^2 +b^2+2ab[/tex] use the length of the figure to represent the area.

[tex]2ab +c^2=a^2+b^2+2ab[/tex]

Subtracting 2ab from both sides

[tex]c^2=a^2+b^2[/tex]

Figure of a square with some shaded triangles.

Area of the triangle formula is 1/2 times base times height

base =a and height =a

Area of one triangle = 1/2ab

There are 4 shaded triangles

Area of 4 shaded triangles = 4 x 1/2ab

Area of the square = side times side

Now we find the area of outer square. side length is a+b

Area of outside square = (a + b)(a + b) = [tex](a+b)^2[/tex] = [tex]a^2 +b^2+2ab[/tex]

Using the length of the figure to represent the area.

Thus, now set both the areas equal to each other.

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Your question seems incomplete, the probable complete question is

8.1 CO: oxide

8.2 CO₂: dioxide

8.3 SO₂: dioxide

8.4 CaCO:

8.5 NaOH:

8.1 CO: oxide

CO represents carbon monoxide, which is composed of one carbon atom (C) and one oxygen atom (O). It is classified as an oxide because it consists of oxygen combined with another element.

8.2 CO₂: dioxide

CO₂ represents carbon dioxide, which consists of one carbon atom (C) and two oxygen atoms (O). It is classified as a dioxide because it contains two oxygen atoms per molecule.

8.3 SO₂: dioxide

SO₂ represents sulfur dioxide, composed of one sulfur atom (S) and two oxygen atoms (O). It is also classified as a dioxide because it contains two oxygen atoms per molecule.

8.4 CaCO: This formula is incomplete or incorrect. It seems to be missing a subscript or superscript to indicate the number of atoms or ions involved. Please provide the correct formula, and I'll be happy to match it with its type.

8.5 NaOH: hydroxide

NaOH represents sodium hydroxide, which consists of one sodium ion (Na⁺) and one hydroxide ion (OH⁻). It is classified as a hydroxide because it contains the hydroxide ion, which is composed of one oxygen atom and one hydrogen atom.

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In solving the sequence using the provided rules, we have:

A) Sequence 1: 13, 16, 19, 22, 25.

    Sequence 2: 15, 13, 11, 9, 7.

    Ordered Pair: (13, 15), (16, 13), (19, 11), (22, 9), (25, 7)

B) Sequence 1: 1, 5, 17, 53, 159.

Sequence 2:  6, 15, 33, 69, 141.

Ordered Pair: (1, 6), (5, 15), (17, 33), (53, 69), (159, 141).

Using the given rules, we can solve the sequence as follows:

A. Rule 1: Add 3 starting from 13

The first five terms in Sequence 1 would be:

13, 13 +3 = 16, 16 +3 = 19, 19 + 3 = 22, 22 + 3 = 25.

13, 16, 19, 22, 25

Using Rule 2: 25-2x, where x is equal to 5, 6, 7, 8, 9

The first five terms in Sequence 2 would be:

25 - 2(5) = 25 - 10 = 15

25 - 2(6) = 25 - 12 = 13

25 - 2(7) = 25 - 14 = 11

25 - 2(8) = 25 - 16 = 9

25 - 2(9) = 25 - 18 = 7

The ordered pairs for each numerical pattern would be:

(13, 15), (16, 13), (19, 11), (22, 9), (25, 7)

B.  Rule 1: Multiply by 3, then add 2, starting from 1

The first five terms in Sequence 1:

1, (1 * 3) + 2 = 5, (5 * 3) + 2 = 17, (17 * 3) + 2 = 53, (53 * 3) + 2 = 159

Using Rule 2: Multiply by 2, then add 3, starting from 6

The first five terms in Sequence 2:

6, (6 * 2) + 3 = 15, (15 * 2) + 3 = 33, (33 * 2) + 3 = 69, (69 * 2) + 3 = 141

The ordered pairs for each numerical pattern would be:

(1, 6), (5, 15), (17, 33), (53, 69), (159, 141)

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If a top travels 8 centimeters each time it is spun and it is spun 7 times, the total distance it travels is 56 centimeters.

The total distance is determined by multiplication of the distance traveled per spin and the number of spins.

Multiplication involves the multiplicand, the multiplier, and the product.

The traveling distance per spun = 8 centimeters

The number of spinning of the top = 7 times

The total distance = 56 centimeters (8 x 7)

Thus, using multiplication, the total distance the top travels after the 7th spin is 56 centimeters.

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Answer:

[tex]-61[/tex]

Step-by-step explanation:

[tex]\mathrm{We\ have\ f(}x)=-3x^2-2x+4\\\mathrm{Put}\ x=-5,\\\mathrm{f}(-5)=-3(-5)^2-2(-5)+4=-3(25)+10+4=-75+10+4=-61[/tex]

The similar triangles for this problem are given as follows:

RST and VUT.

Then the measure VT is given as follows:

VT = 5.4 units.

Similar triangles are triangles that share these two features listed as follows:

Hence the similar triangles for this problem are given as follows:

RST and VUT.

The proportional relationship for the side lengths is given as follows:

6/14 = (x + 2)/(4x - 1).

Applying cross multiplication, the value of x is obtained as follows:

14(x + 2) = 6(4x - 1)

14x + 28 = 24x - 6

10x = 3.4

x = 3.4.

Then the length VT is given as follows:

VT = 3.4 + 2

VT = 5.4 units.

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Answer:

P(d) = 0; 14 days

Step-by-step explanation:

First part of answer:  Setting P(d) = 0 would allow us to find the day Sandra finishes since P represents the pages remaining the book will be finished when there are 0 pages left to read.

Second part of answer:  We can solve the equation P(d) = 0 = 420 - 30d to see how it would take 14 days to finish the book and have 0 pages left to read:

Step 1:  Subtract 420 from both sides:

(0 = 420 - 30d) - 420

-420 = -30d

Step 2:  Divide both sides by -3 to solve for d:

(-420 = -30d) / -30

14 = d

The area of the shaded region, obtained by finding the area of the composite figure is the difference between the area of the square and the area of the triangle and semicircle composite figure.

5. The area of the shaded region is about 205.8 cm squared. The correct option is therefore;

D. 205.8 cm squared

A composite figure is a figure that is composed two or more regular figures.

The area of the shaded region can be found by considering the unshaded region as a composite figure consisting of a triangle and a semicircle.

The area of the unshaded semicircle = π × 24²/8 = 72·π

The area of the triangular part of the unshaded region = (1/2) × 24 × 12 = 144

Area of the square = 24 × 24 = 576

Therefore, the area of shaded region = 576 - (72·π + 144) ≈ 205.8

The area of the shaded region ≈ 205.8 cm squared

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Answer:

4. 4155.3cm³

5. 783m³

6. 1962.44821094mm³

#4 Explanation:

First, you would separate the 2 shapes it consists of, a cylinder and a cone.

For the cone, you would use the equation (1/3)πr²h. Fill in the appropriate variables with the numbers from the formula. Pi, π, is a number itself so you leave it as it is.

r = radius = 8cm

h = height = 14cm

(1/3)(π)(8)²(14)

Put this equation into a calculator, it's important to include the parentheses or it might give you the incorrect answer, this is so that it separates the different values while multiplying. After inputting it, it should give you:

v = 938.289005872cm³

Then, you would have to find the volume of the cylinder, using the equation; πr²h.

The radius would be the same as the cone, and the height is as the problem states, 16cm.

Solve the problem after inputting the values:

π(8)²(16)= 3216.99087728cm³

Then, add the values to get the total volume.

938.289005872cm³ + 3216.99087728cm³ =

4155.27988315cm³

Round to nearest tenth: 4155.3cm³

#5 Explanation:

Again, you would separate the shapes into 2 separate ones.

The top one is a triangular prism and uses the equation (1/2)bh.

b = base = 9m

h = 12m

(1/2)(9)(12) = 54m³

The bottom shape is a rectangular prism, where we use the equation L×W×H.

Length = 9m

Width = 9m

Height = 9m

Substitute the numbers into the equation.

9×9×9 = 729m³

Add both of them together to get the total volume:

54m³ + 729m³ = 783m³

#6 Equation:
In this figure, we are looking for the outer shape, so we will have to subtract the smaller cone.

First, we find the total volume, and we will use the same equation, (1/3)πr²h.

radius = half of diameter = 20/2 = 10mm

h = 20mm

(1/3)π(10)²(20) = 2094.39510239mm³

Second, we find the volume of the smaller cone, using the same equation, (1/3)πr²h.

In order to find the diameter, we will have to subtract the 7 mm that are on either side of the cone, so 20 - 14 = 6, then divide it by 2 so we can get the necessary radius. 6/2 = 3

r = 3mm

h = 14mm

Substitute values into equation and use calculator to solve.

(1/3)π(3)²(14) = 131.946891451mm³

Subtract the value of the smaller cone from total volume in order to get the volume for this figure.

2094.39510239mm³ - 131.946891451mm³ =

1962.44821094mm³

Answer:

Step-by-step explanation:

The exact solutions for the equation 2sec²x - tan²x = -1 in radians are:

x = π/4 + πk, where k is an integer

x = 3π/4 + πk, where k is an integer

These solutions represent all the values of x that satisfy the given equation.

The number 1.3 is both a rational and an irrational number.

The number 1.3 is a rational number because it can be expressed as the quotient of two integers, namely 13/10.

The number 1.3 an irrational number because it cannot be expressed as the ratio of two integers, without repeating or terminating decimals, and its decimal representation goes on forever without repeating.

So we can conclude that the number 1.3 is both rational and irrational number.

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The function f(x) = 1/x³ is indeed a decreasing function for x > 0.

To show that the function f(x) = 1/x³ is a decreasing function, we need to demonstrate that the derivative of f(x) is negative for all x > 0.

Let's calculate the derivative of f(x) with respect to x:

f'(x) = d/dx (1/x³)

Using the power rule for differentiation, we can rewrite the expression as:

[tex]f'(x) = (-3) / x^{(3+1)[/tex]

Simplifying further, we have:

f'(x) = -3 / x⁴

Now, to show that f(x) is decreasing, we need to prove that f'(x) < 0 for all x > 0.

Substituting x = 1 in f'(x), we get:

f'(1) = -3 / 1⁴ = -3

Since -3 is negative, we can conclude that f'(x) < 0 for all x > 0.

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Answer:

11.9 sq cm, answer choice C.

Step-by-step explanation:

Area of a parallelogram = base x height.

The base is 4.25 cm, and the height is 2.8 cm. The other measurement is not needed.

area = 4.25 x 2.8 = 11.9 sq cm, answer choice C.

The vector representing the radius at the given position is  -13i - j  - 5k.

The magnitude of the radius vector is 13.96 units.

The vector representing the radius at the given position is calculated as follows;

center of the sphere = (11, 5, 2)

The point of the radius = ( -2, 4, -3 )

The radius vector = ( - 2 - 11) , ( 4 - 5), ( -3 - 2)

r = ( -13, - 1, - 5)

r = -13i - j  - 5k

The magnitude of the radius vector is calculated as follows;

| r | = √ x² + y² + z²

where;

| r | = √[ ( -13²) + ( -1)² + ( -5 )² ]

| r | = √ ( 169 + 1 + 25 )

| r | = √ ( 195 )

| r | = 13.96 units

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The standard notation for the given scientific notation[tex]5.397 * 10^2[/tex] is 539.7

To convert the given scientific notation [tex]5.397 * 10^2[/tex]to standard notation, you simply need to multiply the coefficient (5.397) by the power of [tex]10 (10^2).[/tex]

The power of 10 indicates how many places the decimal point should be moved to the right. In this case, [tex]10^2[/tex] means moving the decimal point two places to the right.

Multiplying the coefficient 5.397 by

[tex]10^2[/tex]

gives us:

[tex]5.397 \times 10^2 = 5.397 \times \ 100 = 539.7[/tex]

Therefore, the standard notation for the given scientific notation 5.397 x [tex]10^2[/tex]  is 539.7.

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The probabilities are: 1a) P(A) = 12, 1b)P(B) = 1.055 + 1,160 = 1,161.055 . 1c) P(A and B) = P(AB) = 1.055

P(A) = 12

P(B) = 1.055 + 1,160 = 1,161.055

P(A and B) = P(AB) = 1.055

To determine if the events A and B are independent, we need to check if P(A and B) = P(A) * P(B).

P(A) * P(B) = 12 * 1,161.055 = 13,932.66

Since P(AB) = 1.055 is not equal to P(A) * P(B) = 13,932.66, the events A and B are not independent.

P(A | B) = P(AB) / P(B) = 1.055 / 1,161.055 ≈ 0.0009098

To convert this probability to a percentage, we multiply by 100:

Percentage chance = P(A | B) * 100 ≈ 0.0009098 * 100 ≈ 0.091%

Therefore, the company should report a percentage chance of approximately 0.091% to the person as an estimate of their risk of developing the disease based on the study.

The reasoning behind this estimation is that among those who have the genetic variation (B), the probability of having the disease (A) is approximately 0.0009098, which corresponds to 0.091% when expressed as a percentage.

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Given statement solution :- The correct proportion to make the best estimate for the number of beats in 60 seconds is:

A. 48/40 = 60/x

To make the best estimate for the number of beats in 60 seconds, we need to find the proportion that relates the beats per second in the given scenario to the desired duration of 60 seconds.

Let's set up the proportion using the given information:

Heart beats per second (beats/sec) = 48 beats / 40 seconds

We want to find the number of beats in 60 seconds (x beats / 60 seconds).

The correct proportion would be:

48 beats / 40 seconds = x beats / 60 seconds

Therefore, the correct proportion to make the best estimate for the number of beats in 60 seconds is:

A. 48/40 = 60/x

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Answer:

  100

Step-by-step explanation:

You want the value of --(5-1)(5²).

The even number of leading minus signs cancel each other, so the effect is as if there were no leading minus signs.

  --(5 -1)(5²)

  = --(4)(25)

  = --(100)

  = -(-100)

  = 100

__

Additional comment

As always, the value of a numeric expression can be found using a calculator.

<95141404393>

i) Compute the autonomous investment, government the MPM is 0.4.

AI = 1 / (1 - 0.35) = 1 / 0.65 ≈ 1.538 (approximately)

GM = 1 / (1 - 0.35) = 1 / 0.65 ≈ 1.538 (approximately)

XM = 1 / (1 - 0.4) = 1 / 0.6 ≈ 1.667 (approximately)

TM = -0.35 / (1 - 0.35) ≈ -0.538 (approximately)

ii) The equilibrium income is approximately 709.52.

To compute the autonomous investment (A), government expenditure (G), export (X), and tax (T) multipliers, we need to use the following formulas:

Autonomous Investment Multiplier (AI):

AI = 1 / (1 - MPC)

where MPC is the marginal propensity to consume.

Government Expenditure Multiplier (GM):

GM = 1 / (1 - MPC)

Export Multiplier (XM):

XM = 1 / (1 - MPM)

where MPX is the marginal propensity to import.

Tax Multiplier (TM):

TM = -MPC / (1 - MPC)

Now let's calculate these multipliers using the given information:

i). Compute the multipliers:

MPC = change in consumption / change in income

Here, we can see that the consumption function is given by C = 40 + 0.35Y.

So, the MPC is 0.35.

MPM = change in imports / change in income

Here, we can see that the import function is given by M = 45 + 0.4Y.

So, the MPM is 0.4.

AI = 1 / (1 - 0.35) = 1 / 0.65 ≈ 1.538 (approximately)

GM = 1 / (1 - 0.35) = 1 / 0.65 ≈ 1.538 (approximately)

XM = 1 / (1 - 0.4) = 1 / 0.6 ≈ 1.667 (approximately)

TM = -0.35 / (1 - 0.35) ≈ -0.538 (approximately)

ii). Find the equilibrium income:

To find the equilibrium income, we set aggregate demand (Y) equal to aggregate supply (Y) and solve for Y.

Aggregate demand (Y):

Y = C + I + G + (X - M)

Substituting the given values, we have:

Y = (40 + 0.35Y) + (70 - 2r) + 400 + (240 - (45 + 0.4Y))

Simplifying the equation:

Y = 40 + 0.35Y + 70 - 2(0.5) + 400 + 240 - 45 - 0.4Y

Combining like terms:

Y = 745 - 0.05Y

Bringing Y terms to one side:

1.05Y = 745

Dividing both sides by 1.05:

Y = 745 / 1.05 ≈ 709.52 (approximately)

Therefore, the equilibrium income is approximately 709.52.

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Answer:

Step-by-step explanation:

Answer:

can i have a photo, please?

Step-by-step explanation:

The statement that "the coldest temperature ever recorded on earth was - 89. 2 ° " is True.

The Soviet Union's Vostok Station in Antarctica recorded the coldest temperature ever observed on Earth, measuring at -89.2°C on July 21, 1983 via satellite and weather station data.

This natural occurrence saw a temperature that presents significant risks to animal and human life due to poor insulation available against such extreme colds. Without suitable warming tools, survival is near impossible.

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The values of the angles a, b and c are 60°, 110° and 80° respectively.

Given is a figure we need to find the measure of the angles given,

a, b, c.

So,

70° + 50° + a = 180° [making linear pair angles]

120° + a = 180°

a = 60°

50° + a = b [corresponding angles between parallel lines]

b = 50° + 60°

b = 110°

a + 40° + ∠HFE = 180° [angle sum property of a triangle]

60° + 40° + ∠HFE = 180°

∠HFE = 80°

∠HFE = c [alternate angles between parallel lines]

c = 80°

Hence the values of the angles a, b and c are 60°, 110° and 80° respectively.

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1) The value of x = 12°

2) For any real value of n, y = n and  x = (3/2)n

And the measure of angle B is 68°

3) The measure of angle A is 26° and the measure of angle B is 154°

4) The coordinates of vertex D(4, 0)

1)

We know that a linear pair of angles always add up to 180°

168° + x° = 180°

x = 180° - 168°

x = 12°

2)

Here, in parallelogram ABCD, the measure of angle A = 112°

We know that the opposite angles of a parallelogram are equal.

So, m∠C = 112°

Let measure of angle B and D is p degrees.

∠A + ∠B + ∠C + ∠D = 360°

2p + 2(112) = 360°

p = (360 - 224)/2

p = 68°

so, the measure of angle B is 68°

The opposite sides of a parallelogram are equal.

So, side AD = side BC

(2x + 4) = (3y + 4)

2x = 3y

x = (3/2)y

For any real value of n,

y = n

then x = (3/2)n

3)

Consider parallelogram ABCD.

Let us assume that one of the interior angle measures x and then other interior angle be y.

x is 50 degrees more than 4 times the measure of y

x = 4y + 50

We know that the sum of two interior angles (non-opposite) is 180°

⇒ x + y =  180°

⇒ 4y + 50 + y =  180°

⇒ 5y = 130°

⇒ y = 26°

And the value of x would be,

x = 4(26) + 50

x = 154°

So, the measure of angle A is 26° and the measure of angle B is 154°

4)

Let the fourth vertex be D(a,b)

Since ABCD is a parallelogram, the diagonals bisect each other.

coordinates of midpoint of AC = coordinates of midpoint of BD

By midpoint formula,

((1 + 6)/2, (2 + 4)/2) = ((3 + a)/2 , (6 + b)/2)

comparing x and y coordinates,

(3 + a)/2 = (1 + 6)/2

3 + a = 7

a = 4

(6 + b)/2 = (2 + 4)/2

6 + b = 6

b = 0

So, the coordinates of vertex D(4, 0)

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The 10,100 cards will be necessary to build a 100-story card tower.

To build a 100-story card tower, we can use the triangular number formula to calculate the total number of cards needed. The formula is:

Triangular number = (n * (n + 1)) / 2

In this case, n represents the number of stories in the tower (100). Plug in the value for n:

Triangular number = (100 * (100 + 1)) / 2
Triangular number = (100 * 101) / 2
Triangular number = 10,100 / 2
Triangular number = 5,050

Additionally, each story requires two cards, so we multiply the triangular number by 2 to get the total number of cards:

Total cards = 5,050 * 2
Total cards = 10,100

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The first two steps in solving the radical equation, √x+1-4 = 8  is D. Add 4 to both sides and then square both sides.

We can solve the radical equation by adding 4 to both sides and then squaring both sides.

Given equation: √x+1 - 4 = 8.

The First step: add 4 to both sides of the equation:

√x+1 - 4 + 4 = 8 + 4

Simplifying the equation:

√x+1 = 12

The Second step: square both sides of the equation to eliminate the square root:

(√x+1)² = 12²

Squaring both sides gives:

x + 1 = 144

Finally, subtract 1 from both sides to isolate x:

x + 1 - 1 = 144 - 1

x = 143

So, adding 4 to both sides and then squaring both sides are the first two steps in solving the equation.

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Postulate is an assumption, presumed to be true, that is used as the basis for a logical argument.

We have,

A postulate is a statement or proposition that is accepted as true without proof.

It is an assumption or starting point in a logical argument that is considered to be self-evident or evident based on previous experience or observation.

In mathematics,

Postulates are used to define the basic concepts and axioms that form the foundation of a particular system of thought.

They are often used as the starting point for deriving other mathematical concepts and theorems.

Postulates are also known as axioms or assumptions.

Thus,

Postulate is an assumption, presumed to be true, that is used as the basis for a logical argument.

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The radius of the cone with the given volume which is is terms of π would be = 18m

To determine the radius of the cone, the formula that should be used in the formula for the volume of cone which would be given below;

Volume of cone =1/3πr²h

where;

radius = ?

volume = 5,400π

height = 50m

That is;

5,400π = 1/3×π×r²×50

make r² the subject of formula;

r² = 5400π×3/50π

= 108×3

= 324

r = √324

= 18

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The decreasing interval of function is (-∞ , 0) .

The decreasing interval in the function is said to be when the value of the derivative f' (x) ≤ 0 .

Decreasing interval is when f(x) is decreasing as x is increasing.

Here the graph is of a parabola the equation of a upper parabola is

f(x) = x²

Now doing derivation of the parabola equation, we get

f'(x) = 2x

As for decreasing interval we will put

f'(x) ≤ 0

Putting the value of f'(x) in the equation

2x ≤ 0

x ≤ 0

Decreasing interval (-∞ , 0)

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