−x + y = 6
2x + y = −12

Find the inverse of each of the given functions. f(x) = 4x − 12 f−1(x) = x +

first one is 1/4

second one is 3

Answer:

first box is 1/4
second box is 3

for the next question on the page ( h(x) = (2x-4)/3 ) the answer is C (h^-1(x) = (3x+4)/2 )

Step-by-step explanation:

Answer:

Find the GCD (or HCF) of numerator and denominator

GCD of 76 and 75 is 1

Divide both the numerator and denominator by the GCD

76 ÷ 1

75 ÷ 1

Reduced fraction:  

76

75

Therefore, 76/75 simplified to lowest terms is 76/75.

Step-by-step explanation:

hope this helps

Answer:

the answer is 5,700

Step-by-step explanation:

Answer:

When you are bored then, that time you can try many things like spinning pen , drawing and also gossiping with friends

The value of the iterated integral using polar coordinates is π.

What is Polar Coordinates?

a polar coordinate system is a two-dimensional coordinate system in which each point in a plane is specified by a distance from a reference point and an angle from a reference direction. The reference point is called the pole, and the ray from the pole in the reference direction is the polar axis.

To evaluate the iterated integral ∫∫ e^(-x^2 - y^2) dy dx using polar coordinates, we need to convert the Cartesian coordinates (x, y) to polar coordinates (r, θ).

In polar coordinates, x = r cos(θ) and y = r sin(θ), where r represents the distance from the origin and θ represents the angle with the positive x-axis.

To convert the integral limits, we consider the region of integration. Since no limits are provided in your question, let's assume the integral is over the entire xy-plane.

In Cartesian coordinates, the entire xy-plane covers the range -∞ to +∞ for both x and y. In polar coordinates, this corresponds to the entire range of r from 0 to ∞ and the entire range of θ from 0 to 2π.

The Jacobian determinant for the conversion from Cartesian to polar coordinates is r, so we have dy dx = r dr dθ.

Now, let's express the integrand e^(-x^2 - y^2) in terms of polar coordinates:

e^(-x^2 - y^2) = e^(-(r cos(θ))^2 - (r sin(θ))^2)

= e^(-r^2(cos^2(θ) + sin^2(θ)))

= e^(-r^2)

Substituting the variables and the Jacobian into the original integral, we get:

∫∫ e^(-x^2 - y^2) dy dx

= ∫[0 to 2π] ∫[0 to ∞] e^(-r^2) (r dr) dθ

Now, we can evaluate this integral using polar coordinates. The inner integral with respect to r is a standard integral:

∫[0 to 2π] ∫[0 to ∞] e^(-r^2) (r dr) dθ

= ∫[0 to 2π] (-1/2) e^(-r^2) ∣∣[0 to ∞] dθ

= ∫[0 to 2π] (-1/2) (e^(-∞^2) - e^(0^2)) dθ

= ∫[0 to 2π] (-1/2) (0 - 1) dθ

= ∫[0 to 2π] (1/2) dθ

= (1/2) θ ∣∣[0 to 2π]

= (1/2) (2π - 0)

= π

Therefore, the value of the iterated integral using polar coordinates is π.

To learn more about Polar Coordinates from the given link

https://brainly.com/question/15865602

#SPJ4

Answer:

Chris has $40 left.

Step-by-step explanation:

Answer:

$20

Step-by-step explanation:

96 ÷ 2 = 48

48 ÷ 2 = 24

24 ÷ 2 = 12

160 ÷ 2 = 80

80 ÷ 2 = 40

40 ÷ 2 = 20

You have the following expression:

(a + 2b)/ 5

In order to evaluate the previous expression for a = 1 and b = 2, you proceed as follow:

(a + 2b)/ 5 = ( 1 + 2(2) )/5

= ( 1 + 4 )/5

= (5)/5

= 1

Hence, the answer is 1.

The Solution to the given questions are:

A central angle is an angle whose vertex is at the centre of a circle and whose sides intersect the circle at two distinct points. The measure of a central angle is equal to the measure of the arc intercepted by the angle, where the arc is the portion of the circle between the two points of intersection.

An intercepted arc is a segment of a circle's circumference that is bounded by two points on the circle and contains all the points of the circle's circumference that lie between those two points. In other words, it is the portion of the circle that is "cut out" or intercepted by two points on the circle.

In this given question,

The circumscribed angle can be measured by dividing the central angle by 2.

Hence,

112°/2= 56°.

Therefore, the measurement of circumscribed angle is 56°.

To know more about Circles visit:

https://brainly.com/question/11833983

#SPJ1

The likely percentage that Maggie will get pregnant again 2 years after the first baby's birth is not predictable as it depends on various factors.

It's important to note that individual circumstances can vary greatly, and predicting an exact percentage of Maggie's likelihood of getting pregnant again in 2 years isn't possible. However, some factors that may influence her chances include her age, contraceptive use, and personal choices.

Teenagers have a higher fertility rate, but using effective contraceptives and making informed decisions can reduce the likelihood of a subsequent pregnancy. It's crucial for Maggie to consult with a healthcare professional for personalized advice and support.

While research suggests that the chances of getting pregnant in the first year after childbirth are relatively high, the likelihood decreases over time, and after two years, it may be lower than the chances of getting pregnant for the first time.

To learn more about percentage, click here:

https://brainly.com/question/29306119

#SPJ11

Answer:

c

Step-by-step explanation:

Fluid Ounces would be likely to use to measure the capacity of a mug.

The unit to measure the volume of a mug is required.

The best suitable unit is fluid ounces.

Let us convert each unit to liters which will help us compare the units.

\(1\ \text{teaspoon}=0.00493\ \text{l}\)

\(1\ \text{quart}=0.95\ \text{l}\)

\(1\ \text{fluid ounce}=0.0296\ \text{l}\)

A teaspoon is to small to measure a mug's volume, while a quart is too large.

So, the best suitable unit is fluid ounces.

Learn more:

https://brainly.com/question/17271202

The derivative of the function f(x) = 390 by using the rules of differentiation is f'(x) = 0.

To find the derivative of the function f(x) = 390, we can apply the rules of differentiation.

In this case, the function f(x) = 390 is a constant function, which means it does not depend on the variable x. The derivative of a constant function is always zero.

Therefore, the derivative f'(x) of the function f(x) = 390 is:

f'(x) = 0

The derivative of a constant function is zero because a constant value does not change with respect to the variable x. So regardless of the value of x, the rate of change of the function is always zero.

To know more about derivative, click here: brainly.com/question/29144258

#SPJ11

Answer:

Select all of the coefficients in the expression. 12xy^3+ 2x^5y +4x^5y^2 +7x^5y.

If we take an equation like 2xyz = 0 then,

The coefficient of x in 2xyz is term that is multiplied by x. so here the coefficient of x will be 2yz.

So here in the equation 12xy^3 +2x^5y +4x^5y^2 +7x^5y = 0 the coefficients will be:

First we take the common factor form the equation:

So we get form the equation is as ;

= xy * (12y^2 + 2x^4 + 4x^4y + 7x^4) so this basically represents multiplicative distribution law

if we simplify using exponent rule with same base

a^n . a^m = a^n+am

That is 12xy^(2+1) + 2x(4+1)y + 4x(4+1)y(1+1) + 7x(4+1)y

so,

12xy^3 +2x^5y +4x^5y^2 +7x^5y = 0

xy * (12y^2 + 2x^4 + 4x^4y + 7x^4) =0

So the coefficients are : xy and (12y^2 + 2x^4 + 4x^4y + 7x^4)

Know more about “coefficients in the expression” here: https://brainly.com/question/28316633

#SPJ4

Disclaimer: The question was given incomplete on the portal. Here is the complete question.

Question: Select all of the coefficients in the expression. 12xy^3+ 2x^5y +4x^5y^2 +7x^5y.

The coefficient in the expressions 12xy³, 2x⁵y, 4x⁵y²  and 7x⁵y. will be 12, 2, 4 and 7 respectively.

We are given the expressions:

12xy³

2x⁵y

4x⁵y²

7x⁵y.

We need to identify the coefficients for the expression.

For the expression 12xy³, the coefficient will be 12 as it is the numerical value written with the variable.

Similarly, for the expression 2x⁵y , the coefficient will be 2 for the variable x⁵y.

For the expression 4x⁵y², the coefficient will be 4 for the variable x⁵y².

For the expression 7x⁵y, the coefficient will be 7 for the variable x⁵y.

Therefore, we get that, the coefficient in the expressions 12xy³, 2x⁵y, 4x⁵y²  and 7x⁵y. will be 12, 2, 4 and 7 respectively.

Learn more about coefficients here:

https://brainly.com/question/4219149

#SPJ4

Answer:

wouldn't this be 4,2?

Step-by-step explanation:

i remember doing this in school last year and dilation means you would multiple the coordinates by what ever the dilation factor was, in this case its 2.

The value of x is equal to 0.8603 units.

In order to determine the adjacent side (value of x), we would apply the law of tangent because the given side lengths represent the opposite side and angles of a right-angled triangle.

tan(θ) = Opp/Adj

Where:

Based on the information provided in the image, we can logically deduce the following parameters:

Adj = x units.

Opp = 8.3 units.

By substituting the parameters into the tangent ratio formula, we have the following;

Tan16 = 8.3/x

x = 3tan16

x = 0.8603 units.

Read more on right-angled triangle here: brainly.com/question/2223099

#SPJ1

In a binomial distribution, the number of ways of arranging all trials to be failures is 1. This means that there is only one way to have all trials result in failures, as each trial can only have one possible outcome - a failure.

1. In a binomial distribution, each trial can result in either a success or a failure. Let's assume that there are n trials in total.

2. To arrange all trials to be failures, we need to ensure that no trial results in a success. Therefore, for each trial, there is only one possible outcome - a failure.

3. The number of ways of arranging all trials to be failures can be calculated using combinations. In this case, we need to select 0 successes from n trials. The number of ways to do this is given by the combination formula: C(n, 0) = 1, where C represents the combination.

Therefore, the number of ways of arranging all trials to be failures in a binomial distribution is given by the combination formula, C(n, k) = n! / (k! * (n-k)!).

To know more about binomial distribution visit:

https://brainly.com/question/29137961

#SPJ11

The number of ways of arranging all trials to be failures in a binomial distribution is always 1. This is because there is only one way to have no successes in a set of trials.

Regardless of the number of trials or the probability of success, the number of ways of arranging all trials to be failures in a binomial distribution is always 1.

The number of ways of arranging all trials to be failures in a binomial distribution can be determined using the formula for the binomial coefficient.
The binomial coefficient, often denoted as nCk or n choose k, represents the number of ways to choose k items from a set of n items, without considering their order. In the context of a binomial distribution, n represents the total number of trials and k represents the number of successes (in this case, 0).
To find the number of ways of arranging all trials to be failures, we can use the binomial coefficient formula:
nCk = n! / (k!(n-k)!)
In this case, since we want all trials to be failures, k is equal to 0. Thus, the formula simplifies to:
nC0 = n! / (0!(n-0)!) = n! / (0! * n!) = 1

For example, if we have 5 trials and we want all of them to be failures, there is only one possible arrangement: FFFFF, where F represents a failure.

Learn more about probability from the given link:

https://brainly.com/question/13604758

#SPJ11

Answer:

5y=9x-2

y=mx-b

m=slope

y=9/5x-2/5

m=9/5=1.8 slope of pArallel

slope of pARALLEL=-1/M SLOPE OF A LINE PERPENDICULAR

m=-5/9 slope of a line perpendiculr

Answer:

B 397,331

Step-by-step explanation:

215+182=397                                  322+009=331

397,331

For the equilibrium, the value of supply and the value of demand will be equal. Then the value of price (p) is 58.

A Linear system is a system in which the degree of the variable in the equation is one. It may contain one, two, or more than two variables.

The demand and supply equations for overhead projectors in a certain market.

In these equations, p represents price, D represents demand, and S represents supply.

\(\rm S = \dfrac{3}{4}p - 28 \\\\D = -2 p + 131\)

For the equilibrium, the value of supply and the value of demand will be equal. Then we have

\(\begin{aligned} \dfrac{3}{4}p - 28 &= -2 p + 131\\\\3p- 112 &= -8p + 524\\\\11p &= 636\\\\p &= 57.81818 \approx 58 \end{aligned}\)

More about the linear system link is given below.

https://brainly.com/question/20379472

Answer: B. 15

Step-by-step explanation: edge 2022 i got it right

The probability that x < y is 1/8 or 0.25 .

What is probability of an event?
The possibility or chance of an event happening is commonly believed to be the probability of it happening. In the most basic scenarios, the probability that a specific event 'A' will occur as a result of an experiment is calculated by dividing the number of ways that 'A' can happen by the total number of possible outcomes.
P(A) = Number of events concerning 'A' / Total events in consideration.

Given, the vertices of the rectangle are (0, 0), (4, 0), (4, 1), (0, 1).
On carefully analyzing and plotting the vertices roughly, we get that the given rectangle has a width of 4 units and a height of 1 unit.
Therefore, the area of the given rectangle = Width*Height = 4*1 = 4 units²
Also, it can be assessed that the line x = y passes through the points of the rectangle at (0, 0) and (1, 1).
Thus, the area for which x < y will be an isosceles triangle with side length of 1 units and co-ordinates of vertices as (0, 0), (0, 1) and (1, 1).
The area of the isosceles triangle thus assumed = 0.5 × 1² = 0.5 units²
Probability that x < y is P(E): 0.5/4 = 1/8 = 0.25
Therefore, the probability that x < y is 1/8 or 0.25 .

To learn more about probability, tap on the link below:
https://brainly.com/question/24756209

#SPJ4

If a group consists of 3 men and 2 women, what is the probability that all the men end up sitting next to each other is 60%.

The first step in understanding the probability that the set of 3 men will end up sitting next to each other, we have to determine the number of seating arrangements and divide by the likely number of seating arrangements. Like this:

Then, based on this data, we can build our permutation, which will be:

Therefore, the probability found for the set of men to sit next to each other is 0.6 or 60%.

Find out more about probability at:

https://brainly.com/question/13604758

#SPJ4

The margin of error for the survey, rounded to the nearest tenth, is approximately 4.0% when expressed as a percentage.

To determine the margin of error for a survey at the 95% confidence level, we need to calculate the standard error. The margin of error represents the range within which the true population proportion is likely to fall.

The formula for calculating the standard error is:

Standard Error = sqrt((p * (1 - p)) / n)

where p is the sample proportion and n is the sample size.

In this case, the sample proportion is 64% (or 0.64) since 64% of the 1350 surveyed residents support the plan.

Plugging in the values:

Standard Error = \(\sqrt{(0.64 * (1 - 0.64)) / 1350)}\)

\(= \sqrt{(0.2304 / 1350)} \\= \sqrt{(0.0001707)}\)

≈ 0.0131

Now, to find the margin of error, we multiply the standard error by the appropriate critical value for a 95% confidence level. The critical value corresponds to the z-score, which is approximately 1.96 for a 95% confidence level.

Margin of Error = z * Standard Error

= 1.96 * 0.0131

≈ 0.0257

Finally, to express the margin of error as a percentage, we divide it by the sample proportion and multiply by 100:

Margin of Error as Percentage = (Margin of Error / Sample Proportion) * 100

= (0.0257 / 0.64) * 100

≈ 4.0%

Therefore, the margin of error for this survey, expressed as a percentage to the nearest tenth, is approximately 4.0%.

For more question on margin visit:

https://brainly.com/question/15691460

#SPJ8

Answer:

2/3

Step-by-step explanation:

17/21-1/7

17/21-3/21

14/21=2/3

Answer:

Volume of the given pyramid = 1122.37 cubic feet

Step-by-step explanation:

Volume of the regular hexagonal pyramid = \(\frac{1}{3}(\text{Area of the base})(\text{Base})\)

Measure of internal angle of a polygon = \(\frac{(n-2)\times 180}{n}\)

Here, n = number of sides of the polygon

For a hexagon, n = 6

Measure of interior ∠C = \(\frac{(6-2)\times 180}{6}\)

                                       = 120°

Measure of ∠BCD = \(\frac{120}{2}\)

                              = 60°

By applying tangent rule in ΔCED,

tan(∠ECD) = \(\frac{\text{Opposite side}}{\text{Adjacent side}}\)

tan(60°) = \(\frac{DE}{CE}\)

\(\sqrt{3}=\frac{DE}{6}\)

DE = \(6\sqrt{3}\) feet

And cos(60°) = \(\frac{EC}{CD}\)

\(\frac{1}{2}=\frac{6}{CD}\)

CD = 12 feet

Area of ΔBCD = \(\frac{1}{2}(\text{Base})(\text{Height})\)

                        =  \(\frac{1}{2}(6\sqrt{3})(12)\)

                        = \(36\sqrt{3}\) feet

Area of hexagonal Base of the pyramid = \(6(36\sqrt{3})\)

                                                                  = 216√3 square feet

Since, lateral height of the pyramid (AC) = 15 feet

By applying Pythagoras theorem in ΔADC,

AC² = AD² + CD²

(15)² = AD² + (12)²

AD = \(\sqrt{225-144}\)

AD = 9 feet

Volume of the given pyramid = \(\frac{1}{3}(216\sqrt{3})(9)\)

                                                 = 648√3 cubic feet

                                                 = 1122.37 cubic feet

Answer:

A (2,-1)

B (-3,-2)

C (-2,1)

Step-by-step explanation:

A (-2,-1), B (3, - 2), and C (2,1)

Image of triangle ABC reflexión over the y: opposite of the x-coordinates. The y coordinates stay the same.

A’ (2,-1), B’ (-3, -2), and C’ (-2,1)

Answer:

  1.4×10¹⁸ m³

Step-by-step explanation:

You want 1.4×10⁹ km³ expressed in terms of m³.

1 km = 10³ m. Substituting that value for km in the given expression, we find the volume is ...

  1.4×10⁹ km³ = 1.4×10⁹×(10³ m)³ = 1.4×10¹⁸ m³

<95141404393>

Therefore, The given value of 1.4 × 109 km3 is converted into m3 by multiplying it with the conversion factor of (109 m3/km3), which gives 1.4 × 1018 m3.

The given value is 1.4 × 109 km3 to be converted into

m3.1 km = 1000 m.

Hence,

1 km3 = (1000 m)3 = 109 m3.

Therefore,

1.4 × 109 km3 = 1.4 × 109 × (109 m3/km3) = 1.4 × 1018 m3.

Hence, 1.4 × 109 km3 is equal to

1.4 × 1018 m3.

To convert

1.4 × 109 km3

into m3, the given value is multiplied by

(109 m3/km3), as 1 km3 = (1000 m)3 = 109 m3.

Therefore,

1.4 × 109 km3 = 1.4 × 109 × (109 m3/km3) = 1.4 × 1018 m3.

Hence, the conversion factor from km3 to m3 is 109, and this factor is multiplied by the given value. In the final answer, the value is expressed as 1.4 × 1018 m3.

Therefore, The given value of 1.4 × 109 km3 is converted into m3 by multiplying it with the conversion factor of (109 m3/km3), which gives 1.4 × 1018 m3.

To learn more about scale factor visit:

https://brainly.com/question/29967135

#SPJ11

Sarah will need 392 square inches of wood to make all the supports for the 4 shelves which are each 14 inches deep.

Each support is in the shape of a right isosceles triangle, so the area of each support can be calculated using the formula for the area of a triangle:

(1/2)*b*h,

Where, b is the base of the triangle and h is the height.

If the shelf is 14 inches deep, the height of the triangle will be 14 inches and the base will be half the height, or,

Base = 14/2 = 7 inches.

So the area of each triangle = (1/2)*(7)*(14) = 49 square inches.

Since each shelf has 2 supports, the total area of the supports for one shelf is 2 * 49 = 98 square inches.

Since Sarah is building 4 shelves,

The total area of all the supports = 4 * 98 = 392 square inches.

So Sarah will need 392 square inches of wood to make all the supports for the 4 shelves.

Learn more about isosceles triangle here brainly.com/question/29774496

#SPJ4

To create a sphere, a cross-section would need to be revolved around the y-axis line (y = 1). Given the circle on a coordinate plane with the center at (0,0) and a radius of 2, the equation of the circle is x² + y² = 4.

This circle is perpendicular to the x-axis and the y-axis. A cross-section of this circle would be a semi-circle with its diameter as the x-axis. If this semi-circle is revolved around the y-axis, it would create a sphere of radius 2. The y-axis line (y = 1) passes through the center of the semi-circle and is perpendicular to the diameter of the semi-circle (which lies along the x-axis).

Therefore, this semi-circle needs to be revolved around the y-axis line (y = 1) to create a sphere.Hence, a cross-section would need to be revolved around the y-axis line (y = 1) to create a sphere.

To know more about equation of the circle visit:

https://brainly.com/question/29288238

#SPJ11

Answer:

(5,7   6,2   4,8   1,3) and (7,1  5,3   4,8   6,2)

Answer: 5,7 6,2 4,8 1,3 7,1 5,3 4,8 6,2

Step-by-step explanation:

In light of our responses to the presented questions, using equations, we can deduce that the person's estimated height is 0.0225 meters, or 2.25 centimeters.

A mathematical equation is a sentence that suggests that other equations are equivalent. The two sides of an equation are separated by the algebraic symbol (F).

For example, the statement "\(2x+3=9\)" states that the value "9" in the total is indicated by the combination "\(2x + 3\)". The goal of equation solving is to determine the value or values of the fact(s) that will allow an equation to be true.

Equations can be simple or complicated, linear or nonlinear, and they can involve one or more variables. For example, in the equation "\(2x^2+2x-3-0,\) *the variable x is raised to the power of 2 for the solution. Lines are frequently used in geometry, algebra, and equations.

We may determine the person's height in meters using the scale diagram. Assume the individual's height is "h" metres.

As a result, the ratio of the length of the lorry to the height of the person in the diagram is:

\(900cm : 4.5cm\)

When we simplify this ratio, we get:

\(20 : 01\)

As a result, the individual's height in metres is:

\((4.5cm) \times (1metre/100cm) \times (1/200)=0.0225m\)

As a result, the person's estimated height is 0.0225 metres or 2.25 Centimetres.

Learn more about equation here:

brainly.com/question/29273511

#SPJ1

Answer: choices for the number in hundreds place =  7 , 8, 9,0

Step-by-step explanation:

Given: Dinesh wrote a number greater than 4699 and less than 5100.

Numbers greater than 4699 = 4700, 4701,.....

Numbers less than 5100 = 5099, 5098 , .....

From 4700 to 5099 , the possible values for hundreds place = 7 , 8, 9,0

So, the choices for the number in hundreds place =  7 , 8, 9,0