y2=2x2−1 is a function

To find the inverse of a function:

\(f(x)= 2x-\dfrac{9}{4}\)

⇒ Replace f(x) with y:

\(y= 2x-\dfrac{9}{4}\)

⇒ Switch around y and x:

\(x= 2y-\dfrac{9}{4}\)

⇒ Isolate y:

\(x+\dfrac{9}{4}= 2y\\\\\dfrac{1}{2}(x+\dfrac{9}{4})= 2y(\dfrac{1}{2})\\\\\dfrac{1}{2}x+(\dfrac{1}{2}*\dfrac{9}{4})= y\\\\\dfrac{1}{2}x+\dfrac{9}{8}= y\\\\y=\dfrac{1}{2}x+\dfrac{9}{8}\)

⇒ Replace y with f⁻¹(x):

\(f^{-1}(x)=\dfrac{1}{2}x+\dfrac{9}{8}\)

\(f^{-1}(x)=\dfrac{1}{2}x+\dfrac{9}{8}\)

the area of the rectangle will be 1.5w².

What is a rectangle?

Rectangles are quadrilaterals having four right angles in the Euclidean plane of geometry. Various definitions include an equiangular quadrilateral, A closed, four-sided rectangle is a two-dimensional shape. A rectangle's opposite sides are equal and parallel to one another, and all of its angles are exactly 90 degrees.

Area of rectangle is A = a*b

The given length of the rectangle is w

The width will be 1.5w

So the rectangle of the white figure is Area = w*1.5w = 1.5 w²

hence the area of the rectangle will be 1.5w².

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The flour and sugar coral that will be use to make the cookies is 2 1/4 cups.

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.

In this situation, Tucker is making cookies the recipe called for 1/3/4 cups of flour and 1/2cup of sugar.

The flour and sugar coral that will be use to make the cookies will be:

= 1 3/4 + 1/2

= 2 1/4

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The annualized return for the entire period is the closest to 10.5%.

To calculate the annualized return for the entire period, we need to consider the returns for each year and the return in the first quarter of Year 4. Since the returns are given for each period, we can use the geometric mean to calculate the annualized return.

The formula for calculating the geometric mean return is:

Geometric Mean Return = [(1 + R1) * (1 + R2) * (1 + R3) * (1 + R4)]^(1/n) - 1

Where R1, R2, R3, and R4 are the returns for each respective period, and n is the number of periods.

Given the returns:

Year 1 return: 5% or 0.05

Year 2 return: 12% or 0.12

Year 3 return: -6% or -0.06

First quarter of Year 4 return: 2% or 0.02

Using the formula, we can calculate the annualized return:

Annualized Return = [(1 + 0.05) * (1 + 0.12) * (1 - 0.06) * (1 + 0.02)]^(1/3) - 1

Annualized Return = (1.05 * 1.12 * 0.94 * 1.02)^(1/3) - 1

Annualized Return = 1.121485^(1/3) - 1

Annualized Return ≈ 0.105 or 10.5%

Therefore, the annualized return for the entire period is approximately 10.5%.

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Answer:

In explanation

Step-by-step explanation:

x= -1

3(-1)^2+7=0

= 10

x= 0

3(0)^2+7

y=7

x=1

3(1)^2+7

y=10

x=2

3(2)^2+7

=3(4)+7

=12+7

y=19

Navern's manufacturing cycle efficiency (MCE) for its elevators is: 41.4%

The formula for obtaining the manufacturing cycle efficiency is value-added time divided by the production cycle time * 100. In the data given, the process and inspection times qualify as a value-added time

Process time = 23 days

Inspection time = 13 days

Value added time = 23 + 13 = 36days

The production cycle time = Move time + process time + queue time + inspection time + wait time

= 22 + 12 + 23 + 13 + 17 days

= 87 days

So, the manufacturing efficiency time = 36/87 * 100

= 41.4%

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Answer:

Step-by-step explanation:

Answer:

Quan runs a maximum of 5.3 miles and a minimum of 4.7 miles every day.

Step-by-step explanation:

Let x= the actual measurement.

|actual − ideal|≤ tolerance

Use an absolute value inequality to express this situation.

|x−5|≤0.3

Rewrite as a compound inequality.

−0.3≤x−5≤0.3

Solve the inequality.

4.7≤x≤5.3

Answer the question. Quan runs a maximum of 5.3 miles and a minimum of 4.7 miles every day.

Answer:

I hope it works for u

Step-by-step explanation:

if u want for week 2 than its

Please Brain-list if its help-full

Answer:

\(\frac{2}{3}x^{12}\)

Step-by-step explanation:

\(\displaystyle \frac{6x^{18}}{9x^6}=\frac{6}{9}*\frac{x^{18}}{x^6}=\frac{2}{3}*x^{18-6}=\frac{2}{3}x^{12}\)

\(\\ \rm\Rrightarrow \dfrac{6x^{18}}{9x^6}\)

\(\\ \rm\Rrightarrow \dfrac{2}{3}x^{18-6}\)

\(\\ \rm\Rrightarrow \dfrac{2}{3}x^{12}\)

\(\\ \rm\Rrightarrow \dfrac{2x^{12}}{3}\)

The boldface numbers in the quote represent measures of relative risk.

One way to measure the likelihood of an event happening in a particular group is to calculate the relative risk, which compares the probability of the event occurring in that group to the likelihood of the same event occurring in a different group.

The phrase highlighted in bold font, "20 times greater," denotes the proportionate hazard that female smokers face in comparison to their non-smoking counterparts. The second significant figure, which indicates a "10-fold increase," indicates the comparative risk for male smokers compared to non-smokers.

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                 Statement                               Reason                  

⇒ ∠2 = ∠5 = ∠6 = 3x + 7

Looking at the picture, we can see that ∠6 and 4x + 5 are a linear pair.

Finding the value of x:

⇒ ∠6 + 4x + 5 = 180

⇒ 3x + 7 + 4x + 5 = 180

⇒ 7x + 12 = 180

⇒ 7x = 180 - 12

⇒ 7x = 168

⇒ 7x/7 = 168/7

⇒ x = 168/7 = 24

Now, substitute the value of x into the expression "3x + 7" to find ∠6.

Finding the measure of ∠6:

⇒ ∠6 = 3x + 7

⇒ ∠6 = 3(24) + 7

⇒ ∠6 = 72 + 7

⇒ ∠6 = 79°

Answer:

cos θ = -5/13

Step-by-step explanation:

sin θ = -12/13

Use Pythagorean identity.

sin²θ + cos²θ = 1

(-12/13)² + cos²θ = 1

144/169 + cos²θ = 1

cos²θ = 25/169

cos θ = ±5/13

θ is in the 3rd quadrant, so cos θ < 0.

cos θ = -5/13

The amount natalya will spend constructing the patio with concrete and brick is $4320, the correct option is D.

We are given that;

The concrete portion of the patio cost=$3 per square

To construct and the brick portion of the patio cost= $6 per square

Now,

The area of a rectangle is given by length times width. The concrete portion of the patio is a rectangle with length 6 cm and width 3 cm. Using the scale, we can convert these to feet:

6 cm = 6 x 4 ft = 24 ft 3 cm = 3 x 4 ft = 12 ft

Therefore, the area of the concrete portion is:

24 ft x 12 ft = 288 ft^2

The brick portion of the patio consists of two identical rectangles with lenth 3 cm and width 6 cm. Using the scale, we can convert these to feet:

3 cm = 3 x 4 ft = 12 ft 6 cm = 6 x 4 ft = 24 ft

Therefore, the area of one brick rectangle is:

12 ft x 24 ft = 288 ft^2

Since there are two brick rectangles, the total area of the brick portion is:

2 x 288 ft^2 = 576 ft^2

Now we can multiply the areas by their costs per square foot to get the costs of each portion:

Concrete cost = $3 x 288 ft^2 = $864 Brick cost = $6 x 576 ft^2 = $3456

The total cost of constructing the patio is the sum of the costs of each portion:

Total cost = $864 + $3456 = $4320

Therefore, by area the answer will be $4320.

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Answer:

78 buttons left

Step-by-step explanation:

I multiplied 24 children by 3 buttons because each child took 3 buttons and I got 72 buttons taken.

Then I subtracted 150 buttons which is the starting number by 72 buttons (the amount taken by the child's) to get 78 buttons left in the box. ( I just separated negative 72 buttons into -50 and -22 to make it easier)

For the quadrilateral PQRS, the value for its diagonal is obtained to be 74.36 meters.

What is a quadrilateral?

A quadrilateral is a flat shape with four edges and four corners, also known as vertices. The quadrilateral has angles at each of its four vertices, or corners. The angles at the vertices of a quadrilateral ABCD are ∠A, ∠B, ∠C, and ∠D. A quadrilateral has the following sides: AB, BC, CD, and DA.

We can use the law of cosines to find the length of the diagonal PS in the quadrilateral PQRS.

Let's first find the measure of angle PQR in radians -

angle PQR = 95 degrees

= (95/180)π radians

≈ 1.66 radians

Similarly, angle QRS = 115 degrees

= (115/180)π radians

≈ 2.01 radians

Using the law of cosines, we have -

PS² = PQ² + QS² - 2(PQ)(QS)cos(angle PQR + angle QRS)

PS² = (43)² + (34)² - 2(43)(34)cos(1.66 + 2.01)

PS ≈ 74.36 m

Therefore, the length of the diagonal PS is approximately 74.36 meters.

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Answer:

(3,2)

Step-by-step explanation:

The equation of the line graphed is

y = 2/3x + 2

Parallel lines have the same slope.

y = mx + b

y = 2/3x + 0  P tells me that the y-intercept is 0

y = 2/3 x  Which point would make this true?

Point (3,2)  We plug in 3 for x and 2 for y

2 = 2/3(3)

2 = 2 This is a true statement, so the point (3,2) is on the line.

Coverage Error results from the exclusion of certain groups of subjects from a population frame. The answer for the given statement is Coverage Error.

Coverage errors come from failure to cover sufficiently all components of the population being studied. Incomplete sampling frames usually result in coverage errors. Coverage errors happen because of the divergences between the target population and the frame.

Coverage error also may happen when not all members of the population of interest have an equal chance of being selected for the survey. For example, if we use e-mail lists or phone lists to build the sample and not all potential respondents are on those e-mail or phone lists.

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Note that the notation   "∪C = {x : x ∈ for some S ∈ C} = ∪ { S:S ∈ C}" represents a mathematical statement involving sets.

∪C : This represents the  union (∪) of the sets in C.

{x : x ∈ for some S ∈ C}: This is the description or definition of the elements in the set formed by the union of sets in C.

It states that an element x belongs to the union of   sets in C if and only if x belongs to at least one set S that is an   element of the set C.

= ∪{ S:S ∈ C}   : This means that the union (∪) of sets in C is equal to the union of all sets S that belong to the set C.

In summary,  the statement is saying that the union of sets in C consists of all elements that belong to at least one set in C. It is the combined collection of elements from all sets in C.

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Answer:

-------------------------

Initial value of the toy is €450.

After 10% increase the value is:

After further 10% decrease the value becomes:

The final value of the toy is €445.50.

Pie graphs can be used to display percentages of an entire group and depict percentages at a certain moment. Customers contacted via the web = x(let) then.as a result, customers contacted online (chart = x = 100), 25 customers were reached by social media, or x/4

Pie charts can be used to show percentages for the whole group or for a specific time period.

In contrast to bar and line graphs, pie charts do not show changes over time.

The following pages provide descriptions of the various pie chart elements.

Since the slices of a pie chart represent different parts of the whole, their sum must always equal 100%.

Number of customers overall = 250 clients were contacted via email for every 500 customers contacted via phone, or 50% of phone contacts.

=(50÷100)×250

=125

Customers reached via social media

= total customers + 250 + 125 + x+1 = 500 x+1

=125 × 5

T=125

x=100.

Customers contacted via the web = x(let) then.

as a result, customers contacted online (chart = x = 100)

25 customers were reached by social media, or x/4

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Answer:

Therefore, the solution to the equation -x + 3y = 11 is x = -34/11 and y = 29/11.

Step-by-step explanation:

The given equation is:

-x + 3y = 11

To solve this equation by elimination, we need to add or subtract one or both equations to eliminate one of the variables. In this case, we can eliminate the variable x by adding the equation with another equation that has x with the same coefficient, but opposite sign.

Let's suppose we have another equation with x, for example:

2x + 5y = 7

We can eliminate x by multiplying the first equation by 2 and the second equation by 1, so that the coefficients of x are opposite:

-2x + 6y = 22 (multiply the first equation by -2)

2x + 5y = 7 (the second equation)

Now we can add the two equations to eliminate x:

-2x + 2x + 6y + 5y = 22 + 7

Simplifying the equation, we get:

11y = 29

Dividing both sides by 11, we get:

y = 29/11

Now that we know the value of y, we can substitute it back into one of the original equations to find the value of x. Let's use the first equation:

-x + 3y = 11

Substituting y = 29/11, we get:

-x + 3(29/11) = 11

Simplifying the equation, we get:

-x + 87/11 = 11

Subtracting 87/11 from both sides, we get:

-x = 11 - 87/11

Multiplying both sides by -1, we get:

x = 87/11 - 11

Simplifying the equation, we get:

x = (87 - 121)/11

x = -34/11

Answer:

9

Step-by-step explanation:

She bet 9 each time, you can find this by doing 27 ÷ 3 :)

Answer:

she bet $9 each time and x is the number of bets

Step-by-step explanation:

27/3=9

$9 per bet

9x

x=number of bets

The exponential function obtained from the table is represented by the formula y is 650(1.045)x.

A function with the exponential shape is:

y = abˣ

where an is y's initial value, b are multipliers, and y and x are variables.

The bacterial population at x hours should be represented by y.

With 650 bacteria cells at the beginning, the group.

a = 650

4.5% is the growth rate.

b = 100% + 4.5% = 104.5% = 1.045

The exponential function obtained from the table is represented by the formula y = 650(1.045)x.

The exponential function obtained from the table is represented by the formula y is 650(1.045)x.

Thirty hours later:

y = 650(1.045)³⁰ = 2434.

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Answer:

there is no correct answer given

Step-by-step explanation:

look at image

The number of feet above the submarine is the shark is 23 feet.

Given that, a submarine is 42 feet below the surface of the water and shark is 19 feet below the surface of the water.

Here, location of shark = 42-19

= 23 feet

Therefore, the number of feet above the submarine is the shark is 23 feet.

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"Your question is incomplete, probably the complete question/missing part is:"

A submarine is 42 feet below the surface of the water a shark directly above the submarine is 19 feet below the surface of the water how many feet above the submarine is the shark.

The weighted average of the numbers 0 and 4 with their respective weights is 8/3

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

The formula to calculate weighted average is:

weighted average = (w₁x₁ + w₂x₂ + ... + wₙxₙ) / (w₁ + w₂ + ... + wₙ)

Where x₁, x₂, ..., xₙ are the values being averaged, and w₁, w₂, ..., wₙ are their corresponding weights.

So, we have

weighted average = (0 * 1/3 + 4 * 2/3)/(1/3 + 2/3)

Evaluate

weighted average = 8/3

Hence, the weighted average is 8/3

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Answer:

(0,

3) (1, -1)

Step-by-step explanation: