Find the largest domain of f(x)=x²+1
​

Step-by-step explanation:

9x-7i > 3(3x-7u)

-9x-7i > 9x-21u

-7i > -21u

-i > -3u

i < 3u

Charlie's utility function is given by U(A, B) = AB, where A is the number of apples he consumes and B is the number of bananas he consumes. The price of apples is $1, and the price of bananas is $2.

If Charlie's income is $120, he has a budget constraint given by:

1A + 2B = 120

To maximize his utility subject to this budget constraint, Charlie must use his income to purchase the combination of apples and bananas that gives him the greatest value of U(A, B).

The solution to this problem can be found by using the method of Lagrange multipliers. From the budget constraint, we can solve for A in terms of B:

A = 120 - 2B

Substituting this into the utility function, we have:

U(B) = (120 - 2B)B = 120B - 2B^2

To maximize U(B), we must find the value of B that maximizes this expression. Taking the derivative of U(B) with respect to B and setting it equal to zero, we find that:

dU/dB = 120 - 4B = 0

Solving for B, we find that:

B = 30

Thus, if Charlie chose the bundle that maximizes his utility subject to his budget constraint, he would consume 30 units of bananas. The answer is therefore a. 30.

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The situation that can be represented using the equation x + 14 = 25 is

illustrated below.

An equation of degree one is known as a linear equation.

A linear equation of two variables can be represented by ax + by = c.

Given an equation x + 14 = 25.

A situation can be represented as,

Joy and John are two friends, Joy has 14 chocolates, and together they have a total of 25 chocolates, How many chocolates John has?

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The sequences of translations, rotations, and reflections bthat would take polygon P to polygon Q will be:

C Translate so that Ais taken to J. Then reflect over line BA

E Reflect over line BAand then translate by directed line segment BA.

A function is translated when it is moved from where it was before. In geometry, a function that moves an object a specific distance is referred to as translation. Nothing else is done to change the object.

It is not scaled, reflected, rotated, or refracted. Every point of the object must be translated by the same amount and in the same direction.

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To find 4f(-2) + 5f(1), we need to first find the values of f(-2) and f(1). Using the given equation, we have:

An easy definition of a function

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output.

f(-2) = -(-2) - 11 = 9

f(1) = -1 - 11 = -12

So, 4f(-2) + 5f(1) = 4 * 9 + 5 * -12 = 36 - 60 = -24.

To find 3f(5) * 2, we need to first find the value of f(5). Using the given equation, we have:

f(5) = -5 - 11 = -16

So, 3f(5) * 2 = 3 * -16 * 2 = -96

To find -5f(12) - 2f(-9), we need to first find the values of f(12) and f(-9). Using the given equation, we have:

f(12) = -12 - 11 = -23

f(-9) = -(-9) - 11 = 2

So, -5f(12) - 2f(-9) = -5 * -23 - 2 * 2 = 115 + 4 = 119

To find f(9)/f(-6), we need to first find the values of f(9) and f(-6). Using the given equation, we have:

f(9) = -9 - 11 = -20

f(-6) = -(-6) - 11 = 5

So, f(9)/f(-6) = -20 / 5 = -4.

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The angle in radians in simplest form is 2π/3 radians.

A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point. The line of reflection symmetry is formed by all lines that traverse the circle. Additionally, every angle has rotational symmetry around the center.

Given the radius of the circle = 8

and length of arc = 16π/3

the relation between angle and arc is given by,

s = rθ

where r = radius, s = arc length and θ = angle in radians,

so, θ = s/r

θ = (16π/3)/8

θ = 2π/3 radians

Hence the angle is 2π/3 radians.

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Answer:

3 cm

Step-by-step explanation:

Given

Triangle ABC and Triangle DEF are similar

BC=4cm

EF = 16cm

FD = 12cm

ED = 10cm

Since we know that the triangles are similar,

AB/DE = BC/EF = CA/FD as they are the corresponding sides of the similar triangles

or

BC/EF = AC/FD

or

4/16 = AC/12

1/4 = AC/12

12/4 = AC

3 = AC

Therefore the value of AC is 3 cm

Answer:

Step-by-step explanation:

You want the domain and range of the function ...

  F(x) = (x -6)/(x² -3x -18)

We can simplify the function to ...

  [tex]F(x) = \dfrac{x-6}{x^2-3x-18}=\dfrac{x-6}{(x-6)(x+3)}\\\\F(x)=\dfrac{1}{x+3}\quad x\notin\{-3,6\}[/tex]

The domain is the set of x-values for which the function is defined. It is undefined where the denominator is zero. So, x=-3 and x=6 are excluded from the domain, which would otherwise be all real numbers.

The range is the set of values that the function may have. Here, the function can have any y-value except 0 (the value of the horizontal asymptote), and 1/9, the location of the "hole" at x=6.

The range is all real numbers except 0 and 1/9.

the given function  y = 3(4)ˣ, is an exponential function.

The opposite of an exponential function is a logarithmic function. A log function and an exponential function both use the same base. An exponent is a logarithm. f(x) = bx is how the exponential function is expressed. The formula for the logarithmic function is f(x) = log base b of x.

Given a function y = 3(4)ˣ

An exponential function is defined by the formula f(x) = a, where the input variable x occurs as an exponent. The exponential curve depends on the exponential function and it depends on the value of the x.

The exponential function is an important mathematical function which is of the form

f(x) = aˣ

therefore, we can say that the given function is an exponential function.

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Answer:

To turn -5/7 and 8 into a quadratic equation, we first need to convert 8 into an equation by adding 8 to both sides. The equation becomes: -5/7 = x^2 + 8. Then, we can expand the right side into a complete square, using the formula (b/2)^2. The equation becomes:

-5/7 = (x^2 + 8) + (4/2)^2

-5/7 = x^2 + 8 + 4

-5/7 = x^2 + 12

Finally, we can rearrange the equation to make the right side equal to 0, and then factor it. The final equation is:

x^2 + 12 + 5/7 = 0

x^2 + 12 + 5/7 = (x + 6/√7)(x + 6/√7) = 0

Step-by-step explanation:

In the first step, we added 8 to both sides to make the equation -5/7 = x^2 + 8. In the next step, we added 4 to the right side to complete the square. The purpose of completing the square is to get a perfect square on the right side, which will make it easier to factor the equation.

Next, we rearranged the equation to make the right side equal to 0, so that we can factor the equation. The equation x^2 + 12 + 5/7 = 0 can be factored as (x + 6/√7)(x + 6/√7) = 0, where (x + 6/√7) is a binomial that satisfies the equation.

Answer:

Australian dollar = n * 100 / 88

Step-by-step explanation:

n = American dollars

1 Australian dollar = 88 cents American

The values of triangle ABC are

The angles in triangle ABC is calculated using the sine rule which sates that the ratio of a side and the opposite angles are equal to  each other

This represented by the formula

Sine A / a = Sine B / b = Sine C / c

applying the formula for the problem

Sine B / b = Sine C / c

Sine 48 / 121 = Sine C / 162

cross multiplying

Sine C = 162 * Sine 48 / 121

Sine C = 0.99495

C = arc sine (0.99495)

C = 84.2

Applying sum of angles in a triangle

< A + < B + < C = 180

< A + 48 + 84.2 = 180

< A = 180 - 48 - 84.2

< A = 47.8 degrees

side a

Sine A / a = Sine B / b

Sine 47.8 / a = Sine 48 / 121

121 * sine 47.8 / Sine 48  =  a

a = 120.6

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The counterexample proves that the converse of the theorem is not always true, and we have to be careful when making statements about limit points and convergence of sequences.

A sequence is a set of numbers that are generated one after the other in a specific pattern.

The theorem states that if a sequence converges, it will have exactly one limit point. In other words, if a sequence is getting closer and closer to a certain number, there will be only one number that it approaches. This is a fundamental idea in mathematics, and it is important to understand why it is true.

To prove this theorem, let's consider a sequence (a_n) that converges to a limit L. If there were two different limit points, say L1 and L2, then there would be a contradiction. This is because by definition, the sequence (a_n) would be getting closer and closer to L1 and L2 at the same time, which is not possible. Hence, it must be true that the sequence (a_n) has exactly one limit point, L.

The converse of this theorem is not always true. In other words, just because a sequence has exactly one limit point, it doesn't necessarily mean that it converges to that limit. To see why this is the case, let's consider the following sequence:

(2, 3, 4, 5, 6, ...)

In this sequence, the limit point is 6. However, the sequence does not converge to 6 because it is not getting closer and closer to 6 as it goes on. Instead, it is increasing by 1 with each term, and therefore it does not converge.

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The value of sin( tetha) is -2/√5

Point of intersection is the point where two lines meet.

a+2b = 0 can be related to x+2y = 0

Line x + 2y = 0 is end side of angle θ and cos θ < 0 means x < 0. Line is y = -x/2, slope -1/2 and the Line intersects unit circle when :

b = -1/2 a

therefore the slope is -1/2

Line intersect unit circle when:

x²+y² = 1

a²+b² = 1

a² +( - 1/2a)² = 1

a²+ a²/4 = 1

5a²/4 = 1

a² = 4/5

a = √ 4/5

the value of sin(tetha) at the point of intersection is y

y = -1/2a

y = -1/2√4/5

y = -2/√ 5

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The rate of change of the table is 3

From the question, we have the following parameters that can be used in our computation:

The table of values

On the table, we have the following ordered pairs

(9, -6)  and (11, -12)

The rate of the table is then calculated using the following slope equation

Slope = (y₂ - y₁)/(x₂ - x₁)

Where

(x, y) = (9, -6)  and (11, -12)

Substitute the known values in the above equation

So, we have the following equation

Slope = (-12 + 6)/(11 - 9)

Evaluate

Slope = -3

Hence, the rate of the table is -3

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Antonia will have to wait 42 days before she gets to do both activities on the same day again.

The smallest positive integer that is a multiple of both 6 and 7 is the least common multiple (LCM) of 6 and 7. This is the number of days that will pass before Antonia does both of these activities on the same day again.

We can find the LCM of 6 and 7 using the formula as follows -

LCM(6, 7) = 6 * 7 / GCD(6, 7)

where GCD is the greatest common divisor.

The GCD of 6 and 7 is 1, so we can write -

LCM(6, 7) = 6 * 7 / 1 = 42

Therefore, Antonia will have to wait 42 days before she gets to do both activities on the same day again.

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Answer:

first convert 2mins to seconds

60sec=1 min

which is 2×60=120sec

then70/120sec=0.583

convert 50mis to sec

5×60=300sec

so therefore 300sec×0.583=174.9words

HOPE IT HELPS

Answer: 175 words

Step-by-step explanation:

First start out by dividing how many amount (5 min) you are looking for by the amount (2 min) that we already know.

5 / 2  = 2.5

This gives us the key to finding our final answer.

Use this new number (2.5) and multiply it by 70 to get our answer.

70 x 2.5 = 175

The approximate percent increase in consumption from 1986 to 1997 is:

B. 20%

The initial consumption level for the year, 1986 is 62 million barrels per day and by 1997, the percent increase in consumption shot up to 74 million barrels per day.

When we subtract the latter consumption levels from the former, we will have a total of 12 million barrels per day. So, the percentage increase will be:

12 million barrels per day/ 62 million barrels per day × 100

= 19.35 %

Thus, we can arrive at the conclusion that the total consumption levels per day increased by 19.35%, which is approximately 20%.

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5% as a ratio not in simplified form is 5/100 or 5:100.

To write a percent as a ratio, we can divide it by 100 and express the result as a fraction. For example, 5% can be written as 5/100.

So, according to the U.S. Census Bureau, 5% of Americans age 25 or older had completed a bachelor's degree or higher in 1940 can be written as a ratio as:

= 5/100

This fraction represents the ratio of Americans age 25 or older who had completed a bachelor's degree or higher in 1940 to the total number of Americans age 25 or older.

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If the surface of the area of a cylinder is 372π square centimeters. Then the height of the cylinder is 31 centimeters.

Let r be the radius and h be the height of the cylinder. Then the surface area of the cylinder will be given as,

SA = 2πrh square units

The surface of the area of a cylinder is 372π square centimeters the radius is 6 cm. Then the height of the cylinder is given as,

SA = 2πrh

372π = 2π x 6 x h

h = 372 / 12

h = 31 centimeters

The height of the cylinder is 31 centimeters.

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Answer:

Step-by-step explanation:

We can use the proportionality relationship between force and acceleration, which is given as:

force = constant × acceleration

Let's call the constant of proportionality k. Then we can write:

40 N = k × 4 m/s^2

Solving for k, we get:

k = 40 N / 4 m/s^2 = 10 Ns^2/m

Now we can use this value of k to find the force required for an acceleration of 9 m/s^2:

force = k × acceleration = 10 Ns^2/m × 9 m/s^2 = 90 N

Therefore, the force required for an acceleration of 9 m/s^2 is 90 N.

The volume of a cone with a diameter of 8 cm and a height of 6 cm is

100.48 cm³.

A cone is a three-dimensional geometric shape with a smooth and curving surface and a flat base, with an increase in the height radius of a cone decreasing to a certain point.

The volume of a cone is (1/3)πr²h.

The total surface area of a cone is πr(r + l).

The curved surface area is πrl.

Given, The height of the cone is 6 cm.

Also given the diameter of the base 2r = 8 cm hence r = 4 cm.

Therefore, The volume of this cone is,

= (1/3)π(4)²×6 cm³.

= 32π cm³.

= 100.48 cm³

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Answer: C. The most accurate measure of center to represent the data in this case is the median of 20.

Step-by-step explanation: The median is the middle value in a dataset when the data is arranged in ascending or descending order. In this case, the donations are: 10, 10, 10, 10, 15, 15, 15, 19, 20, 20, 20, 25, 25, 25, 30, 30, 55, 55.

When we arrange these values in ascending order, we get: 10, 10, 10, 10, 15, 15, 15, 19, 20, 20, 20, 25, 25, 25, 30, 30, 55, 55.

The median is the value that separates the dataset into two equal halves. In this case, there are 18 values, so the middle value is the 9th value, which is 20.

The reason the median is the most accurate measure of center to use in this case is because the data is skewed. Skewness refers to the asymmetry in the distribution of data. In this case, the data is skewed to the right because there are a few large values (55) that pull the mean higher than the majority of the values.

Using the mean, which is calculated by summing all the values and dividing by the total number of values, would be influenced by these large values and may not accurately represent the typical donations received by the charity.

The root mean square speed of a carbon dioxide molecule at mentioned average kinetic energy is 1.57× [tex] {10}^{-11} [/tex].

The formula to find root mean square speed of carbon dioxide molecule using average kinetic energy is as follows -

c = ✓2KE/m, where c is root mean square speed, KE is kinetic energy and m is molecular mass

Keep the values in formula to find the root mean square speed.

c = ✓2×5.44×[tex] {10}^{-21} [/tex]/44

Performing multiplication and division on Right Hand Side of the equation

c = ✓2.47×[tex] {10}^{-22} [/tex]

Taking square root on Right Hand Side of the equation

c = 1.57× [tex] {10}^{-11} [/tex]

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22 MB in 5 seconds

how many MB per second

divide the 5 out

22/5 = 4.4 MBPS

30 MB in 6 seconds

30/6 = 5 MBPS

5 MBPS > 4.4 MBPS

No, they aren't equivalent because one is greater than the other.

Hope this helps,

- Jeron :- )

Answer:

pls give more detail

Step-by-step explanation:

The timesheet of Rick's working hours is given below.

Combining objects and counting them as one big group is done through addition. In arithmetic, addition is the process of adding two or more integers together. Addends are the numbers that are added, and the sum refers to the outcome of the operation.

From the given data points of Rick's working hours:

Date      Start Time     End Time  Time away  Regular hours

Dec. 9,   7:30 am        4:30 pm     30 minutes     8.5  

Dec. 10,  7:00 am        4:30 pm     30 minutes     8.5

Dec. 11,   11:30 am        5:00 pm      -                       5.5

Dec. 12,   7:30 am        5:30 pm      60 minutes      9

Dec. 13,   7:30 am        7:00 pm      90 minutes       10

Dec. 14,   8:00 am        5:00 pm      90 minutes       4.9

Dec. 15,    -                       -                   -                      -

Therefore, the timesheet is given.

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The complete question:

Make a timesheet for the following dates and times: Dec. 9, Rick...

Make a timesheet for the following dates and times:

Dec. 9, Rick worked from 7:30am to 4:30 p.m. He took a 30 min lunch break

Dec. 10, Rick worked from 7 am to 4:30 p.m. He took a 30 min lunch break

Dec. 11, Rick worked from 11:30 am to 5:00 p.m. He didn't take a lunch break

Dec. 12, Rick worked from 7:30 am to 5:30 p.m. He took an hour lunch break

Dec. 13, Rick worked from 7:30 am to 7:00 p.m. He took an hour and a half lunch break

Dec. 14, Rick worked from 8 am to 5 p.m. He took an hour and a half lunch break

Dec. 15,  Rick did not work.

Answer:

12% of the items in the group are red and have stripes.

Step-by-step explanation:

Aassume that there is 100 items, 40 items red.

In the 40 items, 30% are striped.

40×(30/100)=12%

12% of the items in the group are red and have stripes. This is found by multiplying the proportion of red items (40%) by the proportion of these red items that also have stripes (30%).

We are given that 40% of items in a group are red. This is represented as 40/100, or 0.40. The question mentions that out of these red items, 30% also have stripes. This can be represented as 30/100, or 0.30. The question requires us to find out what percentage of the total items in the group are red and have stripes. To find this, we multiply 0.30 (the proportion of red items that are striped) by 0.40 (the proportion of items that are red).

So, 0.30 x 0.40 = 0.12 or 12%.

Therefore, 12% of the items in the group are red and have stripes.

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Answer:

4

Step-by-step explanation:

18 = 3x + 6

18 - 6 = 3x

12=3x

12/3 = x

4 = x

Hope this helped, please mark the brainliest if it did! I put a lot of effort into my answers

Answer:

Step-by-step explanation:

If Carlos is 6ft tall and looks up at the tree that is 275 ft tall, subtract those two.

275 - 6 = 269

Use tangent with the given angle and the new height. The distance is x.

tan15 = 269/x

x = 269/tan15

x = 1004ft

The distance from Carlos to the tree, given he is 6 feet tall and looks up at a 15° angle of elevation to see the top of a 275-foot tall tree located in Sequoia National Park, is 1026.

Hence option C is correct.

According to the information given,

We can set up a right triangle with Carlos's eye level, the top of the tree, And the base of the tree as the three points of the triangle.

Carlos's height of 6 feet can be used as one side of the triangle,

And we can use the tangent function to find the length of the adjacent side.

A tangent of 15 degrees is equal to the opposite side (height of the tree) divided by the adjacent side (distance from Carlos to the tree).

So, we can solve for the adjacent side by multiplying the height of the tree by the tangent of 15 degrees:

tan(15) = height of the tree / distance from Carlos to the tree

Distance from Carlos to the tree = height of the tree / tan(15)

Plugging in the values given:

Distance from Carlos to the tree = 275 / tan(15)

                                                      ≈ 1026

Therefore,

The nearest foot to the distance from Carlos to the tree is option C. 1026.

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