A line passes through point (5, –3) and is perpendicular to the equation y = x. What's the equation of the line?

Question 26 options:

y = –x + 2


y = x


y = x + 3


y = –x – 7

Answer:the general form of a hyperbola is 6x^2-5y^2+12x+50y-149=0 the answer is (x+1)^2/5 -((y-5)^2/6=1

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

Divide 4 by [tex]2/3[/tex]

[tex]\frac{4}{2/3}[/tex] =[tex]\frac{4*3}{2}[/tex]

=6

By using  ε - δ  definition of limit, the proof of

The limit of a function exists at a cluster point c if and only if the left- and right-handed limits both exist at c and are equal

has been shown below.

What is ε - δ  definition of limit?

Let the function be f(x), cluster point be c and the limit be l. Then

the limit of a function exists at a cluster point c if

For every [tex]\epsilon[/tex] > 0, there exist a [tex]\delta[/tex] > 0 such that |x − c |< δ ⟹ |f(x) − l| < ε

Let the limit exist at a cluster point c. Let the limit be l

For every [tex]\epsilon[/tex] > 0, there exist a [tex]\delta[/tex] > 0 such that |x − c |< δ ⟹ |f(x) − l| < ε

For every [tex]\epsilon[/tex] > 0, there exist a [tex]\delta[/tex] > 0 such that 0 < c - x < δ ⟹ |f(x) − l| < ε or

                                                                         0 < x - c < δ ⟹ |f(x) − l| < ε

For every [tex]\epsilon[/tex] > 0, there exist a [tex]\delta[/tex] > 0 such that c - δ < x < c ⟹ |f(x) − l| < ε or

                                                                         c < x < c + δ ⟹ |f(x) − l| < ε

For every [tex]\epsilon[/tex] > 0, there exist a [tex]\delta[/tex] > 0 such that c - δ < x < c ⟹ |f(x) − l| < ε  and

For every [tex]\epsilon[/tex] > 0, there exist a [tex]\delta[/tex] > 0 such that   c < x < c + δ ⟹ |f(x) − l| < ε

So the left hand and right hand limit exist and are equal.

Let the left hand and right hand limit exist and are equal.

For every [tex]\epsilon[/tex] > 0, there exist a [tex]\delta[/tex] > 0 such that c - δ < x < c ⟹ |f(x) − l| < ε  and

For every [tex]\epsilon[/tex] > 0, there exist a [tex]\delta[/tex] > 0 such that   c < x < c + δ ⟹ |f(x) − l| < ε

Let [tex]\delta_3 = min\{\delta_1, \delta_2\}[/tex]

For every [tex]\epsilon[/tex] > 0, there exist a [tex]\delta[/tex] > 0 such that c - [tex]\delta_1[/tex] < x < c ⟹ |f(x) − l| < ε  and

For every [tex]\epsilon[/tex] > 0, there exist a [tex]\delta[/tex] > 0 such that   c < x < c + [tex]\delta_2[/tex] ⟹ |f(x) − l| < ε

For every [tex]\epsilon[/tex] > 0, there exist a [tex]\delta[/tex] > 0 such that c - [tex]\delta_1[/tex] < x < c or  c < x < c + [tex]\delta_2[/tex]⟹ |f(x) − l| < ε  

For every [tex]\epsilon[/tex] > 0, there exist a [tex]\delta[/tex] > 0 such that |x - c| < [tex]\delta_3[/tex] ⟹ |f(x) − l| < ε  

The limit of a function exists at a cluster point c and the limit is l

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Details scalcets,

a) If u is unit vector , then, ⃗u.⃗v = 1/2 and ⃗u.⃗w = - 1/2 where v and w also unit vectors.

b) Exact value of angle between the vectors is 34.3803442 and Approximation value, 34.4..

c) Exact value of the angle between the vectors, a = 71 - 2j + k, b = 3i - k is 30.60889766 ~ 30.61 (approximation value).

In mathematics, a unit vector is defined as a normed vector space is a vector of length one.

a) If u is a unit vector , we have to calculate ⃗u.⃗v and ⃗u.⃗w where v and w are also unit vectors.

We know that, Angle between two vectors θ is

Cosθ = u⃗ .⃗v/|u| |v|

=> cos 60° |u| |v| = ⃗u.⃗v

=> ⃗u.⃗v = 1/2(1)(1) = 1/2

Also, Cosθ = ⃗u.⃗v/|u| |w|

=> Cosθ |u| |w| = ⃗u.⃗w

=> ⃗u.⃗w = cos 120° (1)(1)

=> ⃗u.⃗w = -1/2

So, ⃗u.⃗v = 1/2 and ⃗u.⃗w = - 1/2

b) We have, a = (7,2), b = (3,-1)

Cosθ = a.b/|a| |b|

|a| = √(7)²+ (2)² = √49+4 = √53

|b| = √(3)²+ (-1)²= √9+1 = √10

a.b = 7×3 - 2×1 = 21 - 2 = 19

so, Cos θ = 19/√10 (√53) = 19/√530

=> θ = Cos⁻¹( 19/√530)

=> θ = 34.3803442 ~ 34.4

c) We have, a = 7i - 2j + k, b = 3i - k

Cos θ = a.b/|a| |b|

|a| = √(7)² + (-2)² +(1)² = √49+4+1 = √54

|b| = √(3)²+ 0 +(-1)² = √9+1 = √10

a.b = (7i - 2j + k).(3i - k) = 21 -0 - 1 = 20

Cosθ = 20/√10√54 = 20/√540

θ = cos⁻¹(20/√540) = 30.60889766 ~ 30.61

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Answer:

1,150 cubic feet.

Step-by-step explanation:

The volume of a hemisphere with a radius of 6.4 feet can be calculated using the formula 4/3 * pi * r^3, where r is the radius of the hemisphere. Plugging in the values, we get 4/3 * pi * 6.4^3 = approximately 1,153 cubic feet. Rounded to the nearest tenth, the volume of the hemisphere is 1,150 cubic feet.

The value of x nearest hundredth of an inch is 18.19 inches.

Area is the quantity that expresses the extent of a region on the plane or on a curved surface. The area of a plane region or plane area refers to the area of a shape or planar lamina, while surface area refers to the area of an open surface or the boundary of a three-dimensional object.

Given that total area of the window is 463 square inches

We will need to write an equation using area of a square an area of a semi circle to find the approximate value of x and we know the total area of the window.

Area of square = [tex]x^{2}[/tex]

The area of the semicircle = [tex]\frac{1}{2}[/tex]πr²

So the radius squared would be 1/4 X squared

And the total area is 463.

We've got to clean this up two times pi times 1/4 that would be 1/8 times pi .

Combine like terms which would be 1.4 x squared.

Divide both sides by 1.4 and take the positive square root.

182x=18

Round to the nearest 100th which would be 18.19.

So value of x which is diameter of semicircle nearest 100th is = 18.19

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a matrix is a collection of integers that have been put in rows and columns to make a rectangular array. The entries of the matrix are the integers, which are referred to as its elements.

Linear algebra is a subfield of mathematics that mostly uses matrices. When you start solving linear equation systems, linear algebra first starts to seem good. You may concentrate on the figures and greatly simplify the procedure by condensing all the information into a single large chart and leaving out the rest.

Almost as their name implies, square, symmetric, triangular, and diagonal matrices. All-zero identity matrices except along the major diagonal, where the values are

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A continuous function is the one in which the function is continuous is the interval given for the function.

A continuous function that does not satisfy the conclusion of the mean value theorem on a closed interval is the function f(x) = |x| on the interval [-1, 1].

This function is continuous on the interval [-1, 1], but it does not have a derivative at x = 0. Therefore, the mean value theorem does not apply at this point, and there is no value c in the interval [-1, 1] such that f'(c) = (f(1) - f(-1))/(1 - (-1)).

This is an example of a function that is continuous on a closed interval, but does not satisfy the conclusion of the mean value theorem.

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The sum of the x-coordinates of the points that lie in the region above the straight line y = 2x + 7 in coordinate plane is thirty-eight.

A point lies above the straight line , y = 2x + 7 in co-ordinate plane . If its y -coordinate is greater than two times its x-coordinate plus 7. Now, we are checking the each ordered pair one by one ,

(i) plug x = 3 and y = 10

2x + 7 = 3×2 + 7 = 13 > 10

(ii) plug x = 6 in 2x+7

=> 2× 6 + 7 = 19 < 20

(iii) x = 12

=> 2x + 7 = 2× 12 + 7 = 31 < 35

(Iv) x = 18

=> 2x + 7 = 2× 18 + 7 = 43 > 40

(v) x = 20

2x + 7 = 2×20 + 7 = 47 < 50

We see (6, 20) , ( 12,35) and (20,50) satisfy this condition. Now, we determine the sum of x-coordinates . The sum of the x-coordinates of these points is 6 + 12 + 20 = 38 . So, required sum of x-coordinates is 38.

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Complete question:

Of the five points (3, 10), (6, 20),(12, 35), (18, 40)and (20, 50), what is the sum of the x-coordinates of the points that lie in the region above the line

y = 2x + 7 in coordinate plane.

The number of cell phones sold in 2015 is (0.29)(1.28x)

The correct answer is A) (0.29)(1.28x).

What is a linear equation?

A linear equation is an equation in which the highest power of the variable is 1. Linear equations can be written in the form ax + b = 0, where a and b are constants and x is the variable. Linear equations are called "linear" because they represent a straight line when plotted on a graph.

We are told that the number of cell phones Hongbo sold in 2014 was 128% greater than in 2013, which means that he sold 128/100 = 1.28 times as many cell phones in 2014 as he did in 2013. This can be represented by the equation x * 1.28 = number of cell phones sold in 2014.

We are also told that the number of cell phones Hongbo sold in 2015 was 29% greater than in 2014, which means that he sold 29/100 = 0.29 times as many cell phones in 2015 as he did in 2014. This can be represented by the equation (number of cell phones sold in 2014) * 0.29 = number of cell phones sold in 2015.

Substituting the first equation into the second equation, we get:

(x * 1.28) * 0.29 = number of cell phones sold in 2015

This simplifies to:

(0.29)(1.28x) = number of cell phones sold in 2015

Hence, the number of cell phones sold in 2015 is (0.29)(1.28x)

the correct answer is A) (0.29)(1.28x).

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The following statements are correct,

a.) Is used to determine the fit of a model.

b.) Can be inflated by adding more variables.

c.) Referred to as the coefficient of determination

d.) Represents the percent of variability in y that can be explained by the model.

e.) In simple linear regression, it is equal to the correlation coefficient r².

Define Regression Analysis

Regression analysis is a set of statistical processes for estimating the relationships between a dependent variable and one or more independent variables.

R² ≡ 1 - SS(res) / SS(tot)

SS(res) + SS(reg) = SS(tot)

R² = SS(reg) / SS(tot) = (SS(reg)/n) / ( SS(tot)/n )

Where,

    SS(tot) = ∑ (y - y(bar) )₂

     SS(reg) =  ∑ (f(i) - y(bar) )²

      SS(res) =  ∑ (y(i) - f(i) )² = ∑e²(i)

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Answer:

$16.50

Step-by-step explanation:

$110 * 15% =

$110 * 15/100 =   ==> percent value is 100 times greater than the fraction

$1650/100 =  ==> multiply 110 and 15

$16.50

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Answer:

Tip=[tex]16.50[/tex]

Step-by-step explanation:

Tip%=15

Bill=$110

Tip=[tex]\frac{15}{100}[/tex]x[tex]110[/tex]

Tip=[tex]16.50[/tex]

Hope this helps u

Answer:

The coordinates would be (12,1)

Step-by-step explanation:

A. The graph of the absolute value function is V-shaped, with the features given as follows:

B. The transformation is that the function was shifted right two units, hence the features are given as follows:

The absolute value function, with vertex (h,k), is defined as follows:

y = |x - h| + k.

The features of the function are given as follows:

For the first item, the function is |x + 3|, hence we just have to identify the features.

For the second function, the definition if h(x) = |x - 2|, with vertex at (2,0), meaning that the function was shifted two units right from the parent absolute value function y = |x|. The shift just changes the turning point of the graph, not altering domain and range.

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The two relations that are also functions are:

A relation is a function if and only if each point in the domain is mapped into a single value of the range.

So for example, the following relation:

{ (a, b), (a, c), (d, f)}

The input a is mapped into two different outputs, thus, this is not a function.

Then from the given options the ones that can be functions are:

S = { (-1, 0), (3, 2), (5, 4), (8, 9), (15, 12)}

R = {(0, -1), (2, 1), (5, 4), (7, 9), (14, 12)}

In all the other relations we can see inputs mapped into more than one output.

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Answer:

The pattern is in the order of even number being added or subtracting (takes turns)

Step-by-step explanation:

12,18,10,20,8

12 to 18 is plus 6

18 to 10 is minus 8

10 to 20 is plus 10

20 to 8 is minus 12

[tex]12 + 6 = 18 \\ 18 - 8 = 10 \\ 10 + 10 = 20 \\ 20 - 12 = 8 \\ 8 + 14 = 22 \\ 22 - 16 = 6 \\ = 24 \\ = 4 \\ = 26 \\ = 2 \\ ..[/tex]

For the regression equation, ŷ = b₀ + b₁x where b₁ is slope of this line and it is equals to (n∑xy - ∑x∑y)/(n∑x² - (∑x)²) and b₀ is y-intercept which is equals to (∑y - b₁ ∑x)/n .

A regression line indicates the linear relationship between the dependent variables on the y-axis and the independent variables on the x-axis. Correlation is determined by analyzing the data pattern formed by the variables.

The regression line is plotted closest to the data points in the regression plot. We use the ordinary least squares estimation method (O.L.S.E), to find the formulas to calculate the slope and intercept of the regression line, which minimizes the sum of squares due to the error. A simple linear regression model is given by y = b₀ + b₁x --(*)

where y : dependent variable

x: independent variable

b₁ --> slope of regression line

b₀ --> y-intercept

We have , regression line is ,

ŷ = (slope )x+ (y intercept)

ŷ represet the predicted value.

The formulas to compute slope(b₁) value and y-intercept (bo) value of regression line are following:

b₁ = (n∑xy - ∑x∑y)/(n∑x² - (∑x)²) and

b₀ = ŷ - b₁x = (∑y - b₁ ∑x)/n

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Answer:

B

Step-by-step explanation:

[tex]3x {}^{2} - 7x + 14 + 5 {x }^{2} + 4x - 6 = 8 {x}^{2} - 3x + 8[/tex]

Answer:

$47.25

Step-by-step explanation:

First we find how much the tax will be

45x0.05

2.25

and now we add to find the total

45+2.25

47.25

hopes this helps

Answer:

45

Step-by-step explanation:

two negative numbers multiplied equals a positive number

Answer:

5%

Step-by-step explanation:

Interest = deposit * annual rate * years

 1500   = 3000 * rate * 10 yrs

1500/(3000*10)  = rate in decimal form = .05   = 5 %

Answer:

x = -9; y = 1

Step-by-step explanation:

       x - 3y = -12

-     5x - 3y = -48

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

      -4x      = 36

x = -9

-9 - 3y = -12

-3y = -3

y = 1

Answer:

  P/Q = (-3x +2)/(3(3x -1))

  PQ = 12/((3x -1)(-3x +2))

Step-by-step explanation:

You want the quotient and product of P(x) = 2/(3x -1) and Q(x) = 6/(-3x +2).

The quotient is found by multiplying by the inverse of the denominator:

  [tex]P(x)\div Q(x)=\left(\dfrac{2}{3x-1}\right)\div\left(\dfrac{6}{-3x+2}\right)=\left(\dfrac{2}{3x-1}\right)\times\left(\dfrac{-3x+2}{6}\right)\\\\\\\dfrac{2(-3x+2)}{6(3x-1)}=\boxed{\dfrac{-3x+2}{3(3x-1)}}[/tex]

As with multiplying any fractions, the numerator is the product of the numerators, and the denominator is the product of the denominators.

  [tex]P(x)\times Q(x)=\left(\dfrac{2}{3x-1}\right)\times\left(\dfrac{6}{-3x+2}\right)=\dfrac{2\cdot 6}{(3x-1)(-3+2)}\\\\\\=\boxed{\dfrac{12}{(3x-1)(-3x+2)}}[/tex]

__

Additional comment

Usually the simplified form would contain no parentheses. The indicated products would be multiplied out.

The value of the property at the end of year 7 is 15,324,111$. for a detailed answer read below.

The net operating income (NOI) formula determines a company's revenue after operating costs have been subtracted, but before interest and taxes have been subtracted.

The net operating income of the property is given for years 1 to 8 in the question. Z Corporation wants to own the property for seven years and then sell the property in the 8th year. The growth rate in NOI is 3%, and the expected return on property is 12%.

The "going-in" capitalization rate should be calculated as follows: So, using first-year NOI as the basis, the cap rate is. 8.29%

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The segment joining the midpoints of two sides of a triangle is parallel to the third side and half as long as the third side.

According to Midpoint theorem, if the midpoints of two sides of a triangle are joined by the segment, then resultant segment is parallel to the third side of the triangle and is half of the length of the third side. Consider the triangle ABC, as shown in the figure. Let the midpoints of the sides AC and AB be given as E and D. Then the line DE is said to be parallel to the side BC, whereas the side DE is half of the side BC i.e., DE || BC and DE = (1/2 BC).

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Answer: 12

Step-by-step explanation:

7(3)-2(4)-1=12

The length of the mid-segment of the trapezoid is 6

The trapezium is a quadrilateral where 1 pair of sides are parallel and the sum of angle pairs between parallel lines is 180 degrees.

We have,

The vertices of a trapezoid:

E = (-3, 3)

F = (1, 3)

G = (3, -3)

H = (-5, -3)

The figure can be considered as,

            E____________F

             /                           \

      M /                                \ N

     /                                        \

H/_____________________\G

MN is the mid-segment of the trapezoid.

MN = (EF + HG) / 2

EF = √(4² + 0) = 4

HG = √(8² + 0) = 8

MN = (4 + 8) / 2

MN = 12/2

MN = 6

Thus,

6 is the length of the mid segment of the trapezoid.

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