How long do eyes stay dilated?

Replace -0.5 with the fraction -1/2 if needed.

======================================================

Explanation:

The legs of any right triangle are always perpendicular. They meet up to form a right angle, aka 90 degree angle.

The line y = 2x+4 goes through (2,8). This can be confirmed with a graph. Or note how plugging x = 2 leads to y = 8.

Therefore, y = 2x+4 forms one of the legs of this triangle.

The slope here is 2 = 2/1; the negative reciprocal is -1/2 = -0.5, which is the slope of the perpendicular line. We want this line to go through (2,8)

So,

y = mx+b

8 = -0.5*2+b

8 = -1+b

8+1 = b

9 = b

b = 9

The equation of the perpendicular line is y = -0.5x+9

Replace -0.5 with the fraction -1/2 if needed.

Check out the graph below.

The scatter plot for the given data (See full and correct details attached) is appended accordingly.

A scatter plot is a collection of dots drawn on two axes, horizontal and vertical. Scatter plots are useful in statistics because they illustrate the amount, if any, of correlation between the values of observed quantities or events (called variables).

Scatter plots aid in the visual representation of correlations between economic factors such as employment and production, inflation and retail sales, and taxes and economic growth.

As you can see there is a slight positive correlation between the number of hours meditated and the numberr of hours slept.

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The price of a sweater bought by Rahul before the discount is Rs. 80.

Let us assume the price of the sweater before the discount to be x.

Given that,

The money saved by Rahul will be equal to the discount given for the sweater.

Therefore, we can say that Rs. 20 will be equal to 25% of the price of the sweater before the discount.

The equation we would obtain from the language above would be,

25% of x = 20

Solving this equation further, we can see that,

=> 25% of x = 20

=> 25* 1/100 * x = 20

=> x/4 = 20

=> x = 80

As we assumed x to be the price of the sweater before the discount,

So, the price of a sweater bought by Rahul before the discount is Rs. 80.

Complete question: Rahul bought a sweater and saved Rs. 20 when a discount of 25% was given. What was the price of the sweater before the discount?

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Jon should solve for y in the first equation because the coefficients can be reduced by a common factor to eliminate the coefficient of y.

Linear equations are equation involving one or more expressions including variables and constants and the variables are having no exponents or the exponent of the variable is 1.

Given linear equations are,

6x + 3y = 27

5x + 2y = 21

The coefficients of the first equation are multiples of 3.

Hence dividing throughout the first equation by the common factor 3, coefficient of y will be eliminated.

6x/3 + 3y/3 = 27/3

2x + y = 9

y = 9 - 2x

Solving by substitution, the second equation becomes,

5x + 2(9 - 2x) = 21

5x + 18 - 4x = 21

x = 3

y = 9 - 2x = 3

Hence Jon should could solve the problem by eliminating the coefficient of y in the first equation by a common factor 3.

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The residual square sum may equal 0. Your model will fit your data more closely if the residual sum of squares is small; conversely, if the residual sum of squares is large, your model will match your data less closely. A value of 0 indicates that your model fits the data perfectly.

What Exactly Is Residual Value?

The estimated value of an asset that is fixed at the end of its useful life or lease term is its residual value, which is often referred to as salvage value. In lease agreements, the residual value is one of the lessor's main methodologies for calculating the lessee's periodic lease payments.

A good residual value is what?

Check out the Car Lease Ratings section of our Lease Kit for a complete list of high-residual vehicle brands and models.

                   A car is probably not a good lease deal if the lease-end residual value is less than 50% of the MSRP (for a 36-month lease). 55% to 65% of MSRP would be a nice residual.

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The complete table is,

x             3/8         0         1         3

g(x)          0            3        -5       -21

Each term in a linear equation has an exponent of 1, and when this algebraic equation is graphed, it always produces a straight line. It is called a "linear equation" for this reason.

Given equation g⁡(x) = 3 − 8⁢x

1. when g(x) = 0

0 = 3 - 8x

8x = 3

x = 3/8

2. when x = 0

g⁡(x) = 3 − 8⁢x

g⁡(x) = 3 − 8⁢(0)

g(x) = 3

3. when g(x) = -5

-5 = 3 - 8x

8x = 3 + 5

8x = 8

x = 1

4. when x = 3

g⁡(x) = 3 − 8⁢x

g⁡(x) = 3 − 8⁢(3)

g(x) = -21

Hence the missing values of x are  3/8 and 1,

missing values of g(x) are 3 and -21.

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While writing the coordinates in the coordinate plane the coordinate that comes first coordinate is represented by x-coordinate.

As given in the question,

In the coordinate plane:

Therefore, the first coordinate in the coordinate plane is represented by x-coordinate.

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No, 1 1 2 3 5 8 is not an arithmetic sequence. An arithmetic sequence is a sequence of numbers in which each term is obtained by adding a constant to the previous term.

Thus, the difference between successive terms is the same. In the given sequence, the difference between terms 1 and 2 is 0, between terms 2 and 3 is 1, between terms 3 and 5 is 2, and between terms 5 and 8 is 3. Therefore, the difference between successive terms is not the same and hence, 1 1 2 3 5 8 is not an arithmetic sequence.

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The measure of each interior angle of the polygon is 156°.

In a regular polygon, all interior angles are equal. The interior angle of a polygon = sum of interior angles and the number of sides is the formula for determining the size of an interior angle. A polygon's exterior angles add up to 360°.

Given that the number of sides of the polygon is 15. The sum of the interior angles of the polygon is calculated by the formula:-

Sum = ( n - 2 ) x 180

Sum = ( 15 - 2 ) x 180

Sum = 2340

The measure of each angle is calculated as:-

Angle = 2340 / 15

Angle = 156°

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Answer:

Step-by-step explanation:

The commutative property of addition states that the order of the numbers being added does not affect the result. For example, the sum of 2 + 3 is the same as the sum of 3 + 2, which is 5.

The commutative property of addition does not work for subtraction because subtraction is not commutative. In subtraction, the order of the numbers being subtracted does affect the result. For example, the difference of 3 - 2 is 1, but the difference of 2 - 3 is -1.

The reason for this is that subtraction is the inverse operation of addition and the inverse operation of a commutative operation is not always commutative. In addition, subtraction is not commutative because when we subtract the smaller number from the larger number, we get a positive result but when we subtract the larger number from the smaller number we get a negative result.

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The term "exponential of 10" means the numbers in which the base is 10 and the exponent is an integer.

The Exponential of 10 or the "powers of 10" means when the number 10 is multiplied a certain number of times, then the  product is expressed using exponents.

These numbers which are written as the exponents are exponents of 10.

For example : 10² , 10³ represents different exponents of 10 .

In general form of the exponent of 10 or power of 10 is represented as 10ⁿ .

For Example : 10 to the exponent of 5 can be written as 10⁵, and

it's value is calculates as :

⇒ [tex]10^{5}=10\times\ 10 \times 10\times 10\times 10[/tex]

⇒[tex]10^{5}= 100000[/tex] .

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The image of A After a reflection in y=x followed by a reflection in x=−3. is (0. 7).

There are two ways of reflection.

Along x-axis:

(x, y) – (x, -y)

Along y-axis:

(x, y) - (-x, y)

We have,

A = (7, -6)

Reflection rules over y = x.

(x, y) → (y, x)

So,

(7, -6) = (-6, 7)

Now,

Reflection in x = -3

Reflection rules over the y-axis.

(x, y) → (-x, y)

So,

x = -3

There are 3 units between -3 and -6.

So,

3 + 3 = 6 units will be added during reflection over y = -3

i.e

3 units on the left side of y = -3

3 units on the right side of y = -3

So,

(-6, 7) = (-6 + 6, 7) = (0, 7)

Thus,

The image of A is (0. 7).

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The reflection of image of point in y = x is (-6, 7),

and  reflection in x = −3 is (-13, -6).

The transformation, or f: X X, is the name given to a function, f, that maps to itself. After the transformation, the pre-image X becomes the picture X. Any operation, or a combination of operations, such as translation, rotation, reflection, and dilation, can be used in this transformation.

Given a point  A(7, −6)

A. a reflection in y = x

Flipping is the term for reflection. A reflection is the shape's mirror image. The line of reflection is the path taken by an image when it reflects.

reflection in y = x

x changed to y and y changed to x

x = -6 and y = 7

coordinates are A'(-6, 7)

B. a reflection in x = −3.

let the coordinates be (a, b)

reflection in x = k

image coordinates will be A" (2k - a, b)

here a = 7, k = -3, and b = -6

2k - a = 2(-3) - 7

2k - a = -13

image coordinates will be A"(-13, -6)

Hence the coordinates are A'(-6, 7),

and reflection in x = -3,

coordinates aere A"(-13, -6).

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Answer:

a

Step-by-step explanation:

(x,, y,) is a point on the line in the point-slope formula, and m is the slope.

When you know the slope of the line to be investigated and the point supplied is also the y intercept, you may utilize the slope intercept formula y = mx + b. (0, b). The y value of the y intercept point is represented by b in the formula.

The equation of a line can be written in several different formats:

Standard form

Ax+ By = C

A, B, and C must be real numbers and A and B cannot both be zero.

Slope-intercept form

Y = MX + b

M is the slope and b is the y-intercept.

Point-slope form

y-y₁ = m(x-x1)

In the point-slope formula, (x,, y,) is a point on the line and m is the slope.

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rotation then reflection.

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Answer: 1/3x

Step-by-step explanation:

Hey there!

f(x) = 1/3x

f(x) = 1/3(-3)

f(x) = 1/3(-3/1)

f(x) = 1(-3)/3(1)

f(x) = -3/3

f(x) = -1

Therefore, your answer should be:

f(x) = -1

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Answer:

Slope = 1.25

Y-intercept = -1.5

Step-by-step explanation:

Slope:

[tex]\displaystyle m=\frac{y_2-y_1}{x_2-x_1}=\frac{11-(-14)}{10-(-10)}=\frac{11+14}{10+10}=\frac{25}{20}=1.25[/tex]

Y-intercept:

[tex]y=mx+b\\\rightarrow y=1.25x+b\\\rightarrow 11=1.25(10)+b\\\rightarrow 11=12.5+b\\\rightarrow -1.5=b[/tex]

Final Equation:

[tex]y=1.25x-1.5[/tex]

The solution of the partial differential equation 7.7.2 is given by

u(x,t) = t^2 sin(2πx) + c,u(0.3,1.5) = 1.96 + c, where c is an arbitrary constant.

Partial differential equations are mathematical equations used to describe how a function changes as its inputs change. The equation 7.7.2 is a linear second order partial differential equation in two independent variables. It has the form of a generalized wave equation, in which a wave propagates through a medium with varying physical properties.

To calculate partial differential equations u(x,t) for given values of x and t:

Let x = 0.3 and t = 1.5

Substituting these values into the equation, we get:

u(0.3,1.5) = (1.5)^2 sin(2π(0.3)) + c

= 2.25 sin(0.6π) + c

= 2.25(0.87) + c

= 1.96 + c

Therefore, u(0.3,1.5) = 1.96 + c, where c is an arbitrary constant.

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The value of x in the equation 8 (x - 3) + 7 = 2x (4 - 17) is x = 1/2.

An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side

The given equation is,

8 (x - 3) + 7 = 2x (4 - 17)

Distributive property : p (q + r) = p q + p r

Applying the property here,

8x - (8 × 3) + 7 = 2x × (-13)

8x - 24 + 7= -26x

8x - 17 = -26x

8x + 26x = 17

34x = 17

x = 17/34

x = 1/2

The mistake of Lin happened in the second step where 4 - 17 = -13 but she wrote 13.

Hence the value of x is 1/2 not -1/2 as the solution of Lin.

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Yes, x³ is an exponential function. An exponential function is a function in which the variable (x) is in the exponent.

The general form of an exponential function is f(x) = a^x, where a is the base and x is the exponent. In the case of x³, the variable (x) is in the exponent. x³ represents x raised to the power of 3, where x is the base and 3 is the exponent.

Exponential functions are often used to model growth and decay in a variety of natural phenomena, such as population growth, radioactive decay, and compound interest. Understanding exponential functions is important for solving mathematical problems, especially in algebra, calculus, and applied fields such as physics and engineering.

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The number of mosquitoes that will inhabit the city on May 23, given the increase in population, is 563, 048 mosquitos

The formula for finding the number of mosquitoes after May 11, is given as:

y​ = 250,000 ( 1. 07 ) ˣ

Given that x is the number of days since May 11, the number of days till May 23 is :

= 23 - 11

= 12 days

The number of mosquitoes is therefore:

= 250, 000 x ( 1. 07 ) ¹²

= 250, 000 x 2.252191588960823337718801

= 563, 048 mosquitos

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Answer:

x=2

Step-by-step explanation:

2(4x-1)= -10(x-3)+4

(2×4x)-(1×2 )=(-10×x) -(3×-10) +4

8x -2 = -10x -(-30)+4

8x -2 = -10x +30+4

8x-2= -10x+ 34

8x+10x=34+2

18x=36 we do ÷18

x=2

Any value inside an absolute value in a problem or equation indicates that the value is always positive.

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A domain is all real numbers if it includes all of the values on the real number line (including negative and positive numbers, fractions, decimals, and irrational numbers).

1. A domain is the set of all possible values of an independent variable that produces a valid solution to a given equation.

2. To determine if a domain includes all real numbers, you must examine the set of values in the domain and see if it includes all the values on the real number line.

3. This includes negative and positive numbers, fractions, decimals, and irrational numbers.

4. If the domain includes all of these, then it is all real numbers.

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Based on the information provided, the price of each DVD is $11.

To calculate the price of the DVD, two main variables must be considered:

Tax is a compulsory amount that is levied on goods and services by the government. Tax serves as a form of transfer of wealth from the private individuals to the government.

Taxes increase the cost of a good or service.

Now, let's calculate the cost of each DVD:

The price of each DVD = (total cost - tax) / number of DVDs bought

The price of each DVD = (61 - 6) / 5

The price of each DVD = 55 / 5

The price of each DVD = $11

Based on this, the price of each DVD was $11, you can double-check this below
$11 x 5 = $55 (prices for the DVDs) + 6 = $61 (total price)

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Isosceles right angled triangle XYZ is constructed with the given measure of ∠Y =90° , YX = 5cm and YZ = 5cm each using steps of construction.

Constructed diagram is attached.

As given in the question,

Given measurement to construct a isosceles right angled triangle are:

Measure of ∠Y =90°

Measure of side length

YX = 5cm and YZ = 5cm

Constructed diagram is attached.

Step of construction :

Therefore, construction of isosceles right angled triangle is done as per the above steps of construction.

The above question is incomplete, the complete question is :

Construct an isosceles right-angled Triangle 'XYZ' in which angle Y=90° and two side are 5cm each.

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The constant of proportionality for respective problems is 2/7, 15, 2.75, 13, 4/3.

A) In the first block,

Using points we can find the equation of line ,

Using the formula (y - y₀) = m (x - x₀)

where m is the slope of the equation

The equation of line becomes 2x = 7y

⇒ y = 2/7x

⇒ 2/7 is the constant of proportionality

B) From the graph given,

Again Using the formula (y - y₀) = m (x - x₀)

If we consider two points,

(2,30) and (4,60)

The equation of line becomes

15x = y

Here, the constant of proportionality is 15.

C) It is given the equation is y = 2.75x

The constant of proportionality here is 2.75

D) It is given that,

The price of 5 games is $65.00

The price of 1 game will be 65 / 5

= $13.00

The equation becomes

y = 13x

So, the constant of proportionality becomes 13.

E) Let us consider 2 points (3,12) and (6,24)

The equation of line using the formula (y - y₀) = m (x - x₀) becomes 4x = 3y

⇒ y = 4/3 x

The constant of proportionality becomes 4/3.

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Answer:

780.

Step-by-step explanation:

I cant explain Its just the answer.

Answer: (a * b) - 12

Step-by-step explanation:

      We will pull details for the sentence given to write an expression representing this situation.

      In this case, these words mathematically mean:

             less ➜ subtraction

             product ➜ multiplication

      Using this information, we will write our expression.

(a * b) - 12