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The domain and the range of the function f(x) = log₂(x) are (6, ∞) and [0, ∞)

The equation of the function is given as

f(x) = log₂(x)

In this case, the argument of the logarithm is x - 6 must be greater than 0 for the function to be defined.

So, we have

x - 6 > 0

Adding 6 to both sides of the inequality, we get:

x > 6

This means that

Domain: (6, ∞)

The range of a logarithmic function is the set of all possible output values of the function.

In this case, the base of the logarithm is 2, which means that the function will not take negative values

Therefore, the range of the function is:

Range: [0, ∞)

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Answer: I’m sure the answer is 2.

Step-by-step explanation:

3 x = 7 − 1 3x=7-1 3x=7−1.3 x = 6 3x=6 3x=6.x = 2 x=2 x=2.

Answer:

I'm sure the answer is -2

Step-by-step explanation:

-3*-2+1=7

Therefore , the solution of the given problem of function comes out to be (x - 2)(x - 2) (x - 2)

The study of mathematics includes histology, architecture, and both actual and fictitious geographic locations, as well as arithmetic, numerals, and their divisions. A function explains the relationships between different components, each of which has a corresponding result. A function is made up of a variety of components that, when put together, produce specific outputs for each input. Each post is assigned a realm, which may be a city, a region, or even another region.

Here,

We know that (x - 1-) is a component of the polynomial if 1+ is the polynomial function's zero. Similarly, we know that (x - 2) is also a component of the polynomial because 2 is also a zero of the polynomial function.

Thus, the polynomial function's three components are:

= >(x - 1+)

=> (x - 1-)

=> (x - 2)

or

=> (x - 1+)

=>(x - 2)(x - 2) (x - 2)

or

=> (x - 1+)

=> (x - 1-)

=> (x - 2)(x - 2) (x - 2)

Depending on the needs of the issue, these can be further expanded or simplified.

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By answering the above question, we may state that As a result, the coordinates  graph's line has the equation y = (4/5)x + 11/5.

A coordinate system in geometry is a method that employs one or more integers or coordinates to identify the precise placement of points or other geometrical objects on a manifold, such as Euclidean space. Pairs of integers called coordinates are used to locate a point or object on a two-dimensional plane. The position of a point on a 2D plane is described by two integers known as the x and y coordinates. a group of numbers that represent precise positions. Usually, there are two numbers in the figure. The front-to-back distance is represented by the first number, while the top-to-bottom distance is represented by the second number. like in (12.5), when there are 12 units below and 5 above.

In order to determine the line's equation, we must first determine the slope (m) of the line using the following formula:

m = (y2 - y1) / (x2 - x1) (x2 - x1)

where the coordinates of the two sites the line travels through are (x1, y1) and (x2, y2), respectively.

In place of the values we hold:

m = (7 - 3) / (6 - 1) (6 - 1)

m = 4 / 5

Now that we have the slope, we can solve the equation of a line using the point-slope form, which is:

y - y1 = m(x - x1) (x - x1)

where one of the locations the line travels through is (x1, y1).

y - 3 = (4/5)(x - 1) (x - 1)

y = (4/5)x - 4/5 + 3 y = (4/5)x + 11/5 is equal to y - 3 = (4/5)x - 4/5.

As a result, the graph's line has the equation y = (4/5)x + 11/5.

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The statement that a factor goes into a larger number is true.

A factor is a number that can be divided into another larger number without leaving a remainder. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12, because these are the numbers that can be evenly divided into 12. Similarly, the factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24. 5 is a factor of 20 because 20 can be divided evenly by 5:

20 ÷ 5 = 4.

In contrast, 7 is not a factor of 20 because 20 ÷ 7 leaves a remainder:

Factors are important in mathematics because they are used to find common denominators, simplify fractions, and solve equations.

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The sοlutiοn tο the given prοblem οf expressiοn cοmes οut tο be  1.2516883 x 10⁴ is the abbreviated fοrmula in scientific nοtatiοn.

There is a need fοr mathematical οperatiοns like multiplying, splitting, adding, and even deleting. They wοuld result in the fοllοwing assertiοn if cοmbined: A mathematical fοrmula, sοme data, and an equatiοn A declaratiοn οf truth is made up οf values, elements, and mathematical οperatiοns like additiοns, erasures, algebraic expressiοns, and divisiοns. It is pοssible tο rate and analyze wοrds and sentences.

Here,

The priοr respοnse was cοndensed,

[tex]\frac{[(0.0070)(50)(55)]} {[(1.4)(0.0011)(.25)]} = 12516.883[/tex]

We can describe the following respοnse in scientific notatiοn as the sum of a decimal number between 1 and 10 and a pοwer of 10:

12516.883 = 1.2516883 x 10⁴

Therefοre, 1.2516883 x 10⁴ is the abbreviated fοrmula in scientific notation.

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A rectangle has 2 lines of symmetry.

What is a line of symmetry?

A line of symmetry is a line that divides a shape into two mirror-image halves. When a shape is divided by a line of symmetry, each half of the shape is a reflection of the other half, and they are said to be symmetric or mirror images of each other. In other words, if you were to fold the shape along its line of symmetry, the two halves would match up perfectly. The presence or absence of lines of symmetry is an important characteristic of shapes and can be used to identify and classify them.

Calculate the line of symmetry of a rectangle -

A rectangle has two lines of symmetry: one line that runs vertically down the center of the rectangle, and another line that runs horizontally across the center of the rectangle.

To understand why a rectangle has two lines of symmetry, consider that any line that runs down the center of a rectangle will divide it into two halves that are mirror images of each other. This is true for lines that run vertically or horizontally through the center of the rectangle.

In contrast, a rectangle does not have diagonal lines of symmetry. That is, there is no line that can be drawn from one corner of the rectangle to another corner that will divide it into two mirror-image halves.

Overall, a rectangle has two lines of symmetry, and these lines are important to its geometry and properties.

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Where the above conditions exist:

(a) To find the weight of each type of coffee in 800g of X, we can use the ratio of P coffee to Q coffee in the blend, which is 3:13.

Let the weight of P coffee in 800g of X be 3x, then the weight of Q coffee in 800g of X is 13x.

The total weight of X is 800g, so we have:

3x + 13x = 800

16x = 800

x = 50

Therefore, the weight of P coffee in 800g of X is:

3x = 3(50) = 150g

And the weight of Q coffee in 800g of X is:

13x = 13(50) = 650g

(b) To find the weights of type P coffee and type R coffee in 800g of Y, we can use the ratio of the three types of coffee in the blend, which is 1:7:12 by weight.

Let the weight of P coffee in 800g of Y be x, then the weight of Q coffee in 800g of Y is 7x and the weight of R coffee in 800g of Y is 12x.

The total weight of Y is 800g, so we have:

x + 7x + 12x = 800

20x = 800

x = 40

Therefore, the weight of P coffee in 800g of Y is:

x = 40g

And the weight of R coffee in 800g of Y is:

12x = 12(40)

= 480g

(c) To find the ratio of the three types of coffee in a third standard blend Z, formed by mixing equal weights of X and Y, we first need to find the total weight of X and Y that will be used to make Z. Since we are mixing equal weights of X and Y, the total weight of X and Y in Z will be:

800g + 800g = 1600g

The ratio of P coffee to Q coffee in Z can be found by adding the weights of P coffee in X and Y, and then dividing by the total weight of X and Y:

(150g + 40g) / 1600g = 0.1125

Similarly, the ratio of Q coffee to the total weight in Z can be found by adding the weights of Q coffee in X and Y, and then dividing by the total weight of X and Y:

(650g + 7(40g)) / 1600g = 0.5063

The ratio of R coffee to the total weight in Z can be found by adding the weights of R coffee in Y, and then dividing by the total weight of X and Y:

(12(40g)) / 1600g = 0.3

Therefore, the ratio of the three types of coffee in Z is approximate:

P : Q : R = 0.1125 : 0.5063 : 0.3

(d) To find the weight of type P coffee in 800g of Z, we can use the ratio of P coffee to the total weight in Z, which is 0.1125.

Therefore, the weight of P coffee in 800g of Z is:

0.1125 * 800g = 90g

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Full Question:

Two types of coffee, P and Q, are blended in the ratio 3:13 by weight to form a standard blend X. A second standard blend, Y, is formed by blending type P coffee, type Q coffee, and type R coffee in the ratio 1:7:12 by weight. Find:

a) The weight of each type of coffee in 800 g of X

b) The weights of type P coffee and type R coffee in 800 g of Y

c) The ratio of the three types of coffee in a third standard blend Z, formed by mixing equal weights of X and Y

d) The weight of type P coffee in 800 g of Z.

Answer:

To determine which supermarket offers the best value for money, we need to compare the cost per kilogram (kg) of potatoes from both supermarkets.

For Supermarket A:

4.5 kg cost R20, so 1 kg costs R20/4.5 kg = R4.44 per kg (excluding VAT)

For Supermarket B:

1.8 kg cost R8, so 1 kg costs R8/1.8 kg = R4.44 per kg (excluding VAT)

As both supermarkets offer potatoes at the same cost per kg, they are equal in terms of value for money. Therefore, Betty and Valencia can choose either supermarket to purchase their potatoes for the mini tuck shop.

Step-by-step explanation:

15% of the people in the city visited the food pantry last month.

What is the percentage?

A percentage is a way of expressing a number as a fraction of 100. It is a ratio that compares a number to 100, and it is often denoted using the % symbol. For example, if there are 25 blue marbles in a jar of 100 marbles, we can say that 25% of the marbles are blue. This means that 25 out of every 100 marbles are blue.

To calculate the percentage of people who visited the food pantry last month, we can use the following formula:

Percentage = (Part / Whole) x 100%

where "Part" is the number of people who visited the food pantry last month, and "Whole" is the total number of people in the city.

Plugging in the given values, we get:

Percentage = (150 / 1,000) x 100%

Percentage = 0.15 x 100%

Percentage = 15%

Therefore, 15% of the people in the city visited the food pantry last month.

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The total area of the given figure is found to be 96 m².

Total area = area of rectangle  +  area of triangle

Total area = length x breadth + 1/2 x base x height

Total area = 12 x 7 + 1/2 x 6 x (11 - 7)

Total area = 84 + 12

Total area = 96

Thus, the total area of the given figure is found to be 96 m².

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There are 10,000 different telephone numbers possible in city A.

Since the first three digits of the telephone number are fixed to be 719, we only need to consider the possible combinations for the last four digits.

Each of the last four digits can be any of the ten digits 0 through 9, so there are 10 choices for each of the four digits. Therefore, the total number of possible telephone numbers is:

10 × 10 × 10 × 10 = 10,000

Therefore, there are 10,000 different telephone numbers possible in city A.

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Answer:

40% chance

I hope I'm right srry if its wrong

Fabian has $0.05x + $0.01y in total.

If Fabian has 130 nickels, his collection is worth:

130 nickels at $0.05 each translate to $6.50.

Moreover, if he has 120 cents, the total amount is:

120 pennies multiplied by the price of a penny ($0.01) equal $1.20.

Combining these two numbers, Fabian has:

$6.50 + $1.20 = $7.70

Fabian now has $7.70 in total.

If Fabian owns x nickels, the worth of those nickels is:

x nickels * 0.05 cents each nickel = 0.05x

Moreover, if he possesses y cents, the total worth is:

y pennies * $0.01 per penny = $0.01y

Combining these two numbers, Fabian has:

$0.05x + $0.01y

Fabian therefore has a total of $0.05x + $0.01y.

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The percent increase in the vaIue οf the parceI οf Iand is 8%.

Tο find the percent increase in the vaIue οf the parceI οf Iand, we need tο determine the difference between the current vaIue and the οriginaI vaIue, and then express that difference as a percentage οf the οriginaI vaIue.

percent increase = (new vaIue - οId vaIue) / οId vaIue x 100%

PIugging in the vaIues given in the prοbIem, we get:

percent increase = ($15,444 - $14,300) / $14,300 x 100%

percent increase = $1,144 / $14,300 x 100%

percent increase = 0.08 x 100%

percent increase = 8%

Therefοre, the percent increase in the vaIue οf the parceI οf Iand is 8%.

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Answer:

K = 13

Step-by-step explanation:

We must solve for K

K - 3 / 10 = 1

Multiply both sides by 10

K - 3 = 10

K = 10 + 3

K = 13

By using the future value of a series formula, you can calculate the future value of your investment. In this case, if you invest $600 annually in a 401k mutual fund with a 9% annual return, you will have approximately $132,204.02 after 40 years.

To solve this problem, we can use the future value of a series formula (also known as an annuity), which is common in business finance. The formula is:

FV = P * [((1 + r)^n - 1) / r]

Where:
FV is the future value of the money you have invested.
P is the annual investment (in this case, $600).
r is the annual rate of return (which is 9% or 0.09 as a decimal).
n is the number of years the money is invested (which is 40 in this scenario).

Applying these numbers to the formula we get:

FV = 600 * [((1 + 0.09)^40 - 1) / 0.09]

After performing the calculations, the future value (which is the amount of money you'll have at the end of 40 years) comes out to be approximately $132,204.02. Thus, if you invest $600 annually in a 401k which invests in an international stock mutual fund with a 9% annual rate of return, you will have $132,204.02 in the fund when retiring in 40 years.

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The members that did not use the stepper and treadmill is 190.

A circle graph is a graph that displays information in a circle. The circle is divided into slices which represent a numerical proportion. The sum of angles in a circle graph is 360 degrees. The percentages add up to 100 percent.

Members that do not use the stepper or treadmill = (100 - percentage that represents the number of people that use the treadmill and stepper) x number of people that used the cardio equipment

= [100 - (42% + 20%)] x 500

(100 - 62%) x 500

38% x 500

= 38/100 x 500 = 190

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Answer:

the answe will be -71 I think

sorry if I got it wrong

Therefore , the solution of the given problem of equation comes out to be the  2 * √6 is the positive value of the square root of the sum of the roots.

Mathematical formulas frequently use the same variable letter to try to impose uniformity between two claims. Many academic numbers are shown to be equal using mathematical expression, also known as assertions. The normalise divides 12 and b + 6 into two parts using the result y + 6 = 12 as an illustration. It is possible to determine the connection between each sign component and the number of lines. The significance of a symbol usually contradicts itself.

Here,

By modifying the equation y2 + 24 = -11y, we can first convert it to standard quadratic form:

=> y^2 + 11y + 24 = 0

Using the quadratic formula, we can now determine the quadratic's roots:

=> y = (-11 ± √11^2 - 4(1)(24)))/(2(1))

=>   ( -11 ± √(121 - 96))/2

=>  (-11 ± √(25))/2

Thus, y = -8 and y = -3 are the solutions.

What the roots produce is:

(-8) * (-3) = 24

Additionally, the product's square root's positive number is:

=> √(24) = 2 * √(6)

In light of this, 2 * √6 is the positive value of the square root of the sum of the roots.

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The solutions for θ between 0 and 2π are:

θ = π/4, 3π/4, 5π/4, 7π/4.

Trigonometry is the branch of mathematics which set up a relationship between the sides and angles of right-angle triangles.

Starting with the equation:

√2sinθ + 1 = 0

Subtracting 1 from both sides, we get:

√2sinθ = -1

Squaring both sides, we get:

2sin²θ = 1

Dividing both sides by 2, we get:

sin²θ = 1/2

Taking the square root of both sides, we get:

sinθ = ± √2/2

Using the unit circle, we know that sinθ = √2/2 at π/4 and 3π/4, and sinθ = -√2/2 at 5π/4 and 7π/4.

Therefore, we have:

sinθ = √2/2 at θ = π/4 + 2πn, 3π/4 + 2πn

sinθ = -√2/2 at θ = 5π/4 + 2πn, 7π/4 + 2πn

Thus, the solutions for θ between 0 and 2π are:

θ = π/4, 3π/4, 5π/4, 7π/4.

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Answer:

Step-by-step explanation:

Let [tex]x[/tex] be the total points on the quiz, then

[tex]\frac{60}{100}[/tex] × [tex]x[/tex] = 15

[tex]60x=1500[/tex] (multiplied both sides by 100)

[tex]x=25[/tex] (divided both sides by 60)

So there were 25 points on the quiz

Answer:

To solve for x, we can cross-multiply:

1/5x = 3/10

10(1/5x) = 10(3/10)

2x = 3

x = 3/2

Therefore, the solution is x = 3/2.

Answer:

To solve the equation 1/5x = 3/10 for x, we need to isolate x on one side of the equation.

First, we can simplify the equation by multiplying both sides by the reciprocal of 1/5, which is 5/1 or simply 5:

(1/5)x = 3/10

5(1/5)x = 5(3/10)

x = 3/2

Therefore, the solution to the equation 1/5x = 3/10 is x = 3/2 or 1.5.

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The volumes of the complex figure are;

A complex figure is a figure that comprises of shapes that can often be evaluated as the sum of the simple parts of the figure.

1. The volume of the object can be found by finding the volumes of the component parts as follows;

The volume of the vertical rectangular prism = 3 ft × 7 ft × 7 ft = 147 ft³

The volume of the adjacent prism is found as follows;

Height of the prism = 7 ft - 5 ft =2 ft

Volume = 2 ft × 2 ft × 7 ft = 28 ft³

Volume of the prism = 147 ft³ + 28 ft³ = 175 ft³

2. The volume of the rectangular prism at the top = 1 m × 2 m × 3 m = 6 m³

Volume of the larger rectangular prism at the base = 6 m × 3 m × 3 m = 54 m³

Volume of the figure = 6 m³ + 54 m³ = 60 m³

3. Volume of the prism on the bottom left = 3 m × 4 m  × 7 m = 84 m³

Volume of the higher rectangular prism on the right = 2 m × 4 m × 7 m = 56 m³

The volume of the solid is therefore;

4. The dimensions of the  chimney are;

The rectangular prism at the left base 3 inches by 4 inches by 2 inches

The volume of the rectangular prism = 3 in × 4 in × 2 in = 24 in³

Rectangular prism to the right of the chimney = 4 in × 4 in × 12 in = 192 in³

The volume of the complex figure = 24 in³ + 192 in³ = 216 in³

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The cost of $28 for 1 jacket. This can be expressed as a rate of $28 per 1 jacket or $28/jacket, where the unit is "jacket".

A unit rate is a rate that compares a quantity to one unit of another quantity. In other words, it is a rate that describes how much of one quantity there is per one unit of another quantity.

For example, if you drive 200 miles in 4 hours, the unit rate of your speed is 50 miles per hour, or 50 miles/hour. This means that you traveled 50 miles for every one hour of driving.

Unit rates are commonly used in many real-life situations, such as calculating miles per gallon in a car, the cost per pound of food at the grocery store, or the rate of interest on a loan.

A unit rate is a rate that compares a quantity to one unit of another quantity.

Out of the options given, the unit rate is:

Therefore, The cost of $28 for 1 jacket. This can be expressed as a rate of $28 per 1 jacket or $28/jacket, where the unit is "jacket".

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The distance from frank's house to john's house and then back to frank's house is less than a mile by 1/5 units.

Simply multiplying the distance between two points while travelling from one location to another and back will give you the total distance travelled when travelling from one location to another and returning to the starting point.

The distance from frank's house to john's house = 4/10.

The distance back to Frank's house = 4/10.

Total distance = 4/10 + 4/10

Total distance = 8/10

The distance is thus,

1 - 8/10

Take the LCM:

(10 - 8) / 10

2/10 = 1/5

Hence, the distance from frank's house to john's house and then back to frank's house is less than a mile by 1/5 units.

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Angle AXC is congruent to both angle CAX (78 degrees) and angle CDX (102 degrees), its measurement is also 102 degrees.

To find the measurement of angle AXC, we need to consider that it is an inscribed angle subtended by the same arc CX as arc CA and arc DB.

Inscribed angles that subtend the same arc are congruent. Therefore, we can conclude that angle AXC is congruent to both angle CAX and angle CDX.

Since angle CAX and angle CDX are supplementary angles (they add up to 180 degrees) and we know the measurement of angle CAX, we can find the measurement of angle CDX.

angle CAX + angle CDX = 180 degrees

78 degrees + angle CDX = 180 degrees

angle CDX = 180 degrees - 78 degrees

angle CDX = 102 degrees

Since angle AXC is congruent to both angle CAX (78 degrees) and angle CDX (102 degrees), its measurement is also 102 degrees.

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The required slope of the tangent line to the graph of the function at the point (-1, 5) is -2.

A line that only touches a circle or an ellipse at one place is said to be tangential in geometry. If a line touches a curve at point P, that place is referred to as the point of tangency. In other words, it is described as the line that, at that particular point, depicts the slope of a curve.

The slope of the tangent line to the graph of a function at a given point is equal to the derivative of the function at that point.

So, to find the slope of the tangent line to the graph of the function f(x) = -2x at the point (-1, 5), we need to find the derivative of the function at x = -1.

Using the power rule for derivatives, we can find the derivative of f(x) = -2x as:

[tex]$f'(x) = \frac{d}{dx}(-2x) = -2$$[/tex]

So, the slope of the tangent line to the graph of the function f(x) = -2x at x = -1 is:

f'(-1) = -2

Therefore, the slope of the tangent line to the graph of the function at the point (-1, 5) is -2.

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Answer:

Let's assume Pena's favorite number as "p".

According to the problem, Tonya's number is 9 more than Pena's favorite number, so Tonya's favorite number would be p + 9.

But Tonya says her favorite number is 44, so we can write:

p + 9 = 44

This equation represents the relationship between Pena's and Tonya's favorite numbers.