How would you write the equation with a slope of 1 and a y-intercept is 7?

The inverse function [tex]f^{-1}[/tex](8) = 3/2

A function that "undoes" another function is known as an inverse in mathematics. In other words, if f(x) produces y, then introducing y into the inverse of f produces x. An invertible function has an inverse, which is represented by the symbol.[tex]f^{-1}[/tex]

The function given is

f(x) = 2x + 5

We have to find the inverse

Let us consider f(x) as y

y = 2x + 5

Now by replacing x to y and y to x

x = 2y + 5

By solving for y and replacing f-1(x)

2y = x - 5

y = (x - 5)/2

[tex]f^{-1}[/tex](x) = (x - 5)/2

We have to find [tex]f^{-1}[/tex](8)

[tex]f^{-1}[/tex](8) = (8 - 5)/2 = 3/2

So

The inverse function [tex]f^{-1}[/tex](8) = 3/2

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After six years, the population will grow to 586,455 if compounded annually at a rate of 7.5%.

This is exactly like a compound interest problem where the interest rate is 7.5% compounded annually for 6 years.

If we use the compound interest formula A = P(1+r/n)nt where A is the end amount to be found, p = initial amount (p= 380,000), n = number of times the interest is compounded annually (n= 1) and t is the time in years (t=6)

A = 380,000(1 + .075/1)1(6)

A = 380,000(1.075)6

A = 586,454.58 people

Rounded to the nearest whole number

the population after 6 years should be

586,455 people

Hence we get the required answer.

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Your question is incomplete. Please find the missing content below.

A city has a population of 380,000 people. suppost that each year the population grows by 7.5%. what will be the population after 6 years.

Therefore the directional derivative of f at a in the direction of the vector ad is grad F( x, y ) ×ad(u)  =64/10

Any function's rate of change at a given location in a fixed direction is known as its directional derivative. Any derivative is thought of in this way: as a vector form. It provides information on the function's immediate rate of variation.

Here,

The terms "directional derivative" and "gradient of a function" must be used in order to respond to this question.

Grad F(x, Y) = 64/10 ad(u)

A function's gradient is a vector with the following definitions:

Grad f(x,y) is equal to f(x,y)/x I + f(x,y)/y j.

where the definition of the directional derivative in the direction of ab is

Grad f(x,y) = Uab(u), where Uab is a unitary vector pointing in the direction of ab.

Consequently, Uab (u) = Uab/|ab|

If f (x,ydirectional )'s derivative in the direction of vector ab is 5, then.

A (7, 3), B (12, 3), and vector ab is then:

ab = [ 12 - 7 , 3 - 3 ] ⇒ ab = [ 5 , 0 ] as well as |ab| = (5)2 (0)2 |ab| = 5

a unitary vector in the direction of ab is:

ab(u) = 5×i/ 5 and according to equation (1)

δf(x,y) / δx × i  × 5 × i / |5| = 5

δf(x,y) / δx × i  × 5 × i = 25

δf(x,y) / δx = 5       then   f( x,y ) = 5 × x  + ????

We go on to calculate the component on j of f(x,y)

Following the same procedure

ac = ( 7 , 7 ) - ( 7 , 3 )     ⇒   ac = [ 0 ,  4 ]      |ac| = √(4)² + (0)²

|ac| = 4

In the direction of ac(u), the unitary vector is:

ac/|ac| = 4 × j / 4

Then :

j / 4 + f(x,y) / y = 4

16 is equal to f(x,y) / y j + 4 j.

both f(x,y) = -4y & f(x,y) / y = - 4

f(x,y) = 5 × I + 4 × j

Finally:

((15 - 7, 9 - 3)) as the vector ad ⇒ ad = ( 8 , 6 ) ( 8 , 6 )

a unitary vector in the direction of

ad(u) = (8 ×i + 6 ×j) / √ (8)² Plus (6)

² ⇒ ad(u) = (8 ×i + 6 ×j) /√ (8)² + (6) ²

ad(u) = (8 ×i + 6 ×j) /10

Currently, we have f (x, y) = 5 I + 4 j and ad(u) = 8 I + 6 j /10.

We can calculate the directional derivative of f(x,y) in the direction of ad with the use of equation (1)

grad F( x, y ) ×ad(u)  = ( 5 × i + 4 × j ) × ( 8 ×i  + 6 ×j ) /10

grad F( x, y ) ×ad(u)  = 4 + ( 24/10)

grad F( x, y ) ×ad(u)  =64/10

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Answer:

To solve this equation, we can first rewrite it in a form that is easier to work with. We can do this by dividing both sides by 9^2, which gives us:

(9^2x+1)/9^2 = 27^x-3

We can then simplify the left side of the equation by taking the square root of both sides, which gives us:

3x+1/3 = 3^x-3

We can then rearrange the terms on the left side of the equation to get:

3x = 3^x-6

We can then subtract 3^x from both sides of the equation, which gives us:

3x-3^x = -6

We can then divide both sides of the equation by 3-3^x, which gives us the final solution:

x = -6 / (3-3^x)

This is the value of x that satisfies the original equation.

Step-by-step explanation:

Answer:

-2b - 7/2

Step-by-step explanation:

solve for e: -4b+1=8+2e

-4b + 1 = 8 + 2e

-4b + 1 -8 = 2e

-4b - 7 = 2e

-2b - 7/2 = e

Answer:

f(x) = 5x^(2)-3

Step-by-step explanation:

graph each equation

The probability that in the resulting coloring, no two adjacent edges have the same color is 1/24.

It is given that the edges of a regular pentagon are colored res, blue or green at random, so that each edge has an equally likely chance of being painted with any color.

So you can't have 0 reds.

You can have 1 red and there are 2 scenarios for that.

You can have 2 reds and there are 8 scenarios for that.

You can't have 3+ reds.

In total there are 10 scenarios that work.

Therefore there are 3⁵ - 3 total cases.

i.e there are 240 total cases.

So the probability that no two adjacent edges have the same color is,

total scenarios/total cases = 10/240 = 1/24.

Therefore the probability that no two adjacent edges have the same color is 1/24.

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The SSS( Side-Side-Side) Congruance theorem can be used to prove that

△MLQ ≅ △NPQ.

So, The correct option is option (B).

We have given that,

The above figure shows three triangles .

Also, MQ = NQ

Q is mid point of Side LP .

or LM~= PN => LM = PN

we have to show that △MLQ ≅ △NPQ

Mid point is defined as a point which divide the side into to equal parts i.e if P is mid point of AB then AP = BP.

Using this fact , we have

LQ = QP --(1) ( because Q is mid point)

MQ = NQ (given)

LM = PN ( given)

That's we see that all three sides of triangle are

equivalents to corresponding sides of second triangle.

Therefore, these two triangles are congruent by SSS rule of congruance, i. e △MLQ ≅ △NPQ.

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Complete Question

Given: MQ = NQ; Q is the midpoint of LP; LM ≅ PN

Which congruence theorem can be used to prove △MLQ ≅ △NPQ?

a) AAS

b) SSS

c) ASA

c) SAS

The expression that is equivalent to the given expression is 4√5.

What is simplification?

Simplifying procedures is one way to achieve uniformity in work efforts, expenses, and time. It reduces diversity and variety that is pointless, harmful, or unnecessary.

Here, we have

Given: √80

We have to find which expressions are equivalent to the given expression.

For this, we first evaluate all options and see which option is suitable for the given expression.

160 ≠ √80

4√10 = 16 ×10 = 160 ≠ √80

4√5 = 16 × 5 = √80

8√5 = 64 × 5 ≠ √80

Hence, the expression that is equivalent to the given expression is 4√5.

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Medical institution 64 grams of bismuth-214 must be prepared.

A medical institution is a facility in which medical care is provided. It can be a hospital, clinic, nursing home, or other type of health care facility. Medical institutions provide a wide range of services including diagnosis, treatment, and preventive care. In addition to providing direct patient care, they also provide educational opportunities, research, and administrative services. Medical institutions are staffed by a variety of healthcare professionals such as doctors, nurses, allied health professionals, and administrative staff. They are responsible for providing quality care to their patients and ensuring the safety and wellbeing of their staff and visitors.

Given: 2 hours = 20 minutes

If each half life is 20 minutes, and 2 hours (120 minutes) go by,

then n = 6 ( [tex]\frac{120}{20}[/tex] )

The setup is as follows:

[tex]1g=m_{i}(\frac{1}{2}) ^{\frac{120}{20} }[/tex]

[tex]1g=m_{i}(0.015625)[/tex]

[tex]\frac{1}{0.015625} =64g[/tex]

Hence, 64 grams of bismuth-214 must be prepared if the shipping time is 2 hours.

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Answer:180 minutes

Step-by-step explanation:

We choose an infinitive in a sentence; It is "to + 1st form of verb" in the case of the infinitive, "1st form of the verb + -ing", and "1st form of the verb + both the first and third form of the verb" in the case of gerunds.

In the given question we have to explain how we choose an infinitive in a sentence.

The verb form called as an infinitive can be used as a noun, adjective, or adverb. They can be helpful when talking about activities without actually performing the activity because they are typically created by adding the word to before the underlying verb.

It is "to + first form of the verb" in the case of the infinitive, "1st form of the verb + -ing" that serves as a noun, and "1st form of the verb + both the 1st and 3rd form of the verb" in the case of gerunds that the first form with –ing. "To do" is the infinitive in this sentence.

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The equation of a line in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. The equation of a line that is perpendicular to Y = -3x^2 is: X = -3y^2/2

The equation of a line that is perpendicular to a given line is found by changing the sign of the slope of the given line and taking the reciprocal of the slope.

The slope of the given line Y = -3x^2 is -3, so the slope of the line perpendicular to it is 3.

The equation of a line in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Therefore, the equation of a line that is perpendicular to Y = -3x^2 is: x = 3y + b

We can now solve for the y-intercept, b, by substituting the point (0,0) into the equation:

x = 3y + b

0 = 3(0) + b

b = 0

Therefore, the equation of a line that is perpendicular to Y = -3x^2 is: x = 3y^2/2

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The flux of the vector-field F = 1i + 1j + 3k across the surface S is 2. We find out the flux of the vector-field using Green's Theorem.

Flux form of Green's Theorem for the given vector-field

φ = ∫ F.n ds

= ∫∫ F. divG.dA

Here G is equivalent to the part of the plane = 2x + 1y + z = 2.

and given F = 1i + 1j + 2k

div G = div(2x + 1y + z = 2) = 2i + 4j + k

Flux = ∫(1i + 1j + 3k) (2x + 1y + z) dA

φ = ∫ (2 + 4 + 2 ) dA

= 8∫dA

A = 1/2 XY (on the given x-y plane)

2x+4y =2

at x = 0, y = 1/2

y = 0, x = 1

1/2 (1*1/2) = 1/4

Therefore flux = 8*1/4 = 2

φ = 2.

Green's theorem has numerous applications. One method is to solve two-dimensional flow integrals, which state that the sum of fluid outflows from a volume equals the total outflow summed around an enclosing area.

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The difference between the two lengths is 2.8284 inches

What is cube?

The six square faces of a cube, which has six sides that are all the same length, make it a solid object in three dimensions. One of the five platonic solids, it is additionally referred to as a regular hexahedron. Twelve edges, eight vertices, and six square faces make up the form. Given that the three-dimensional object is a square with equal-length sides, the lengths of the cube's length, breadth, and height are all the same. The edge, which is regarded as the edge's bounding line, divides a cube's faces along a shared border.

Cube's surface area is equal to 6 * (sides)2 where side2 = surface area / 6 and side = sqrt (surface area / 6)

The cube's 1200 square inch surface area is as follows:

side = (surface area / 6)

side = sqrt(1200/6)

size equals 14.1421 inches.

Using the 768-square-inch cube as an example:

side = (surface area / 6)

side = sqrt(768 / 6)

dimension is 11.3137 inches.

Hence the difference between the two lengths is 2.8284 inches

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Note that this line is in form y = mx + b, where b is the y intercept and m is the slope.

Y intercept is the value of y at x = 0

The function starts at y = 6

Slope is 1/4, meaning that for every 4 x the line travels, it goes up 1.

This is what the graph would look like:

(see image)

Hope this helps :)

If you need any more explanation, feel free to ask.  If this really helps, consider marking brainliest.

- Jeron

68.26% of students out of 500 would score between 68 and 82  if the mean is 75 and standard deviation is 7.

A low standard deviation suggests that values are often close to the mean (also known as the anticipated value) of the collection, whereas a large standard deviation suggests that values are dispersed over a wider range.

Standard deviation, often known as SD, is most frequently represented in mathematical texts and equations by the lower case Greek letter (sigma), for the population standard deviation, or the Latin letter s, for the sample standard deviation.

Given,

Mean μ=75

σ=7

By using normal distribution,

P(68<x<82)=P(((68-μ)/σ)<z<((82-75)/7))

P(-1<z<1)

P(z<1)-P(z< -1)

By using z-table, we get

=0.8413-0.1587

=0.6826

P(68<x<82)=0.6826≈68.26

P(68<x<82)=68.26%

Therefore, 68.26% of students out of 500 would score between 68 and 82 if the mean is 75 and standard deviation is 7.

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The best and most correct answer is 2x greater then zero which satisfy the condition.

The absolute value function is defined by the following piecewise rule, depending on the input of the function:

If x ≥ 0, then we need to find x+|x|

Since {x | x < 0} and {x | x > 0} there is no number that is less than zero and greater than zero at the same time.

WE need to add here;

x+|x|  = 2x

Therefore, we can see that 2x is greater then zero which satisfy the condition.

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Function can be solved easily by f(x)= mx + c.

function

A function produces one output per input. Learn about function notation, tables of values, and more.

Function is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

A function is uniquely represented by the set of all pairs (x, f (x)), called the graph of the function, a popular means of illustrating the function. When the domain and the codomain are sets of real numbers, each such pair may be thought of as the Cartesian coordinates of a point in the plane.

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Answer:

Step-by-step explanation:

Line 1: -3y = 2x + 6 Line 2: (2/9)y - 4 = (1/3)(x - 18)

Answer:

25

Step-by-step explanation:

Let x be the mystery number.

The minimum number of factors a number can have is two:

(These numbers are called prime numbers).

If a number has exactly 3 factors, it must be an perfect square number since every perfect square has an odd number of factors and any number that is not a perfect square will have an even number factors..

Odd square numbers between 20 and 30:

Factors of 25:  1, 5 and 25.

Therefore, Grey's mystery number is 25.

Proof:

The measurement of <B is 121 degree.

The sum of a triangle's three internal angles is 180 degrees, as stated by the angle sum Property of a triangle.

According to the triangle's "angle sum property," a triangle's angles add up to 180 degrees.

Given:

let the measure of <A be x.

So, m<G= x- 9

and, m<B = 4x- 15

Using Angle Sum Property

m<A+ m<B+ m<G= 180

x+ 4x- 15 + x- 9 = 180

6x - 24 = 180

6x = 180+ 24

x= 204/6

x= 34

So, m<A = 34

m<B= 4(34) - 15 = 121

and, m<G = 34 - 9= 25 degree.

Hence, the measure of <B is 121 degree.

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Answer: 24 cm

Step-by-step explanation:

51cm is the hypotenuse, so that it will be C in the equation!

45^2 + b^2 = 51^2

2025 + b^2 = 2601

b^2 = 576

b = 24 cm

The vertices of the image of triangle ABC after the transformations are given as follows:

A'(4,-2), B'(4,2), C'(0,-1).

The vertices of triangle ABC are given as follows:

A(1,1), B(1,5), C(5,2).

The first transformation is the translation defined as follows:

(x,y) -> (x - 5, y - 3).

Hence the translated vertices are given as follows:

A'(-4, -2), B'(-4, 2), C'(0, -1).

The second transformation is the reflection over the x-axis, hence the rule is:

(x,y) -> (x, -y).

Then the vertices of the translated and reflected triangle are given as follows:

A'(-4, 2), B'(-4,-2), C'(0,1).

The final transformation is the rotation of 180º clockwise around the origin, for which the rule is of:

(x,y) -> (-x,-y).

Then the vertices of the image, after all the transformations, are given as follows:

A'(4,-2), B'(4,2), C'(0,-1).

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The first rider the displacement is, 17 km.

And the 2nd river the displacement is 20.22 km.

What is right triangle?

A right triangle, also known as a right-angled triangle, right-perpendicular triangle, orthogonal triangle, or formerly rectangled triangle, is a triangle with one right angle, or two perpendicular sides. The foundation of trigonometry is the relationship between the sides and other angles of the right triangle.

It is asked in this problem is who's displacement is greater (not distance) it means that the shortest distance of starting and ending point with direction from start and end.

Here we have two triangle with two arm know for both.

So we have to find the 3rd arm for both triangle.

Now we have for a right triangle

a^2 + b^2 = c^2

For other triangle we know the cosine law of triangle is,

a^2 + b^2 - 2ab cosθ = c^2

θ is the opposite angle of c

For the first rider the displacement is,

[tex]c = \sqrt{a^2 +b^2} = \sqrt{8^2 + 15^2} = 17 km[/tex]

For the 2nd river the displacement is

[tex]c = \sqrt{a^2 + b^2 - 2abcostheta}[/tex]   θ = 120°

[tex]c = \sqrt{a^2 - b^2 - 2ab cos(120)} \\c = \sqrt{(8^2 + 15^2 - (2*8*15cos(120))} \\c = \sqrt{289 - 240 cos(120)} \\c = \sqrt{289- (-120)} \\c = \sqrt{409}\\ c = 20.22 km[/tex]

Hence, the first rider the displacement is, 17 km.

And  the 2nd river the displacement is 20.22 km.

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Answer:

1.25 hours  (1 and 1/4 hours)

Step-by-step explanation:

Kiran;s aunt bikes at an average rate of 8 miles/hr.  Assuming it is an average day, we can determine the time it will take her to bike 10 miles by dividng the miles by her average speed:

  (10 miles)/(8 miles/hr)

The miles cancel and the hr comes to the top:

 (10/8) hours or 1.25 hours  1 and 1/4 hours

Kiran's aunt takes 1.25 hours to cover the distance of 10 miles at the average speed of 8 miles per hour.

In unit time, the distance covered by any object is called speed.

In mathematical term, Speed is express as S = D/T,

where S=speed, D=distance, T= time.

Given that,

Distance that Kiran's aunt plans to bike = 10 miles.

The average speed of bike = 8 miles per hour.

To find the time taken by Kiran' aunt to cover 10 miles distance,

Use Formula

Time = Distance / speed

Time = 10 / 8

Time = 1.25

The time taken by Kiran's aunt to cover 10 miles distance is 1.25 hours.

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In a shipment of 3500 tomatoes can be expected to weight from 0.32 lb to 0.92 lb is 3340. When A vegetable distributor knows that during the month of august, the weights of its tomatoes are normally distributed with a mean Of 0.62 lb and a standard deviation of 0.15.

A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed. In contrast, a high or low standard deviation indicates that the data points are, respectively, above or below the mean. A standard deviation that is close to zero implies that the data points are close to the mean. The standard deviation measures the degree of dispersion of a set of data. Each data point is compared to the average of all the data points, and standard deviation gives a determined value that indicates whether the data points are clustered together or dispersed. The standard deviation of a normal distribution indicates how far values deviate from the mean.

Given,

A vegetable distributor knows that during the month of august, the weights of its tomatoes are normally distributed with a mean Of 0.62 lb and a standard deviation of 0.15.

Normal variable of x = 0.32

Z = X - mean/ standard deviation

Z = 0.32 - 0.62/0.15

Z = -2

Now, normal variable of x = 0.92

Z1 = X - mean/ Standard deviation

Z1 = 0.92 - 0.62/ 0.15

Z1 = 2

Required area,

P(-2 ≤ z ≤ 2)

2P(0 ≤ z ≤2 )

2 × 0.4772

0.9542

Weight of 3500 tomatoes

3500 × 0.9542

3340

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Answer:

2.7x +2y

Step-by-step explanation:

Why because  u distribute the 2 to get  1.2x + 1.5x + 2y. CBL and get

2.7x +2y

Answer:

a = 2[tex]w^{2}[/tex] + 3w

Step-by-step explanation:

Area = length time width

A= (2w + 3) w

a = 2[tex]w^{2}[/tex] + 3w

Carla's behavior of putting in extra practices to become faster can be seen as an example of (Option A.) compensation. This is because she is trying to make up for her perceived lack of speed by working harder to become as fast as her teammates.

Carla's behavior of putting in extra practices to become faster can be seen as an example of compensation. This is because she is trying to make up for her perceived lack of speed by working harder to become as fast as her teammates.

By engaging in extra practices, Carla is attempting to compensate for her lack of speed and improve her performance. This is different from rationalization, which is the act of making excuses for one's behavior, or from regression, which is the act of reverting to a younger age in response to a stressful situation.

Finally, displacement is the act of redirecting one's emotions or anger onto another person or object.

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