Write an equation of the line that passes through (2, 7) and (0, −5)


y=

Quadrilateral JKLM is a rhombus because its sides are all equal in length. By using the midpoints of the rectangle EFGH, we find that JK and LM are both 2a in length, and KL and MJ are both 2b in length, confirming that all four sides are equal.

To prove that quadrilateral JKLM is a rhombus, we find the lengths of its sides.

Since J, K, L, and M are midpoints of the sides of rectangle EFGH, the segments connecting them will be parallel to the sides of EFGH and half the length.

We can use the coordinates of F(-a,b), G(a,b), H(a,-b), and E(-a,-b) to find the lengths:

JK is parallel to EH and GH, so its length is half of EH and GH, and since E and G are on the same vertical line, the length of JK is a - (-a) = 2a.

KL is parallel to EG and FH, so its length is also half of EG and FH, and since E and F are on the same horizontal line, the length of KL is b - (-b) = 2b.

LM is parallel to EH and GH, hence its length is the same as JK which is 2a.

MJ is parallel to EG and FH, hence its length is the same as KL which is 2b.

Given that JK = LM and KL = MJ, and all are equal to 2a or 2b, quadrilateral JKLM has all sides of equal length. Therefore, it is a rhombus.

The probable question may be:

Points J, K, L, and M are midpoints of the sides of the rectangle EFGH. Prove that quadrilateral JKLM is a rhombus by finding the lengths of the sides. The diagram is not drawn to scale.

F(-a,b)

G(a,b)

H(a,-b)

E(-a,-b)

J(-a,0)

K(0,b)

L(a,0)

M(0,-b)

Using algebraic equation, the negative number that is squared is: -9.

An algebraic equation can be used to find an unknown value, by making the unknown value the variable.

Let the negative number that would be squared be represented by the variable, x. Thus, we have -x². Therefore:

2x² - 5 = 157

2x² = 157 + 5

2x² = 162

x² = 162/2

x² = 81

x = √81

x = -9

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Answer:

$ 17,200

Step-by-step explanation:

Given,

The amount of down payment = $ 10000,

Also, monthly payment = $ 450,

Number of months = 36,

So, the total payment ( except down payment ) = number of months × monthly payment

= 36 × 450

= $ 16200,

Hence, the total amount paid for the car = down payment + total payment

= $ 1,000 + $ 16,200

= $ 17,200

Answer:

y > 2x - 4 and y ≤ [tex]\frac{x}{2}-1[/tex]

Step-by-step explanation:

In this question we will find the equations of the lines first then decide the inequality sign.

Dotted line in the graph passes through two points (2, 0) and (0, -4)

Let the equation of the line is y = mx + c

Where m = slope and c = y-intercept

Slope (m) of the line will be = [tex]\frac{y-y'}{x-x'}[/tex]

m = [tex]\frac{0+4}{2-0}[/tex]

m = 2

y-intercept of the line = (-4)

So, equation of the line will be y = 2x - 4

Now we see the shaded area is above the dotted line so inequality will be

y > 2x - 4

Now for the bold line

Let the equation of this line is y = m'x + c'

This line passes through points (2, 0) and (0, -1)

then slope of the line m' = [tex]\frac{y-y'}{x-x'}[/tex]

m = [tex]\frac{0+1}{2-0}[/tex] = [tex]\frac{1}{2}[/tex]

y-intercept = c = -1

Then equation of the line will be

y = [tex]\frac{x}{2}-1[/tex]

Since shaded area is below the bold line therefore, inequality sign will be "less than equal to"

Inequality of the bold line will be y ≤ [tex]\frac{x}{2}-1[/tex]

System of the linear inequalities will be

y > 2x - 4 and y ≤ [tex]\frac{x}{2}-1[/tex]

Planes Q and R are parallel. Lines a and b are shown on planes Q and R, respectively.

Which statement is true about lines a and b?

To solve the expression, you should substitute the provided values for y and z then simplify the resulting expression. The solution is 11.

To evaluate the expression 3/2y - 3 + 5/3z when y = 6 and z = 3, first, we should substitute the values of y and z into the expression.

So, the expression becomes 3/2*6 - 3 + 5/3*3. Multiply to reduce fractions: 9 - 3 + 5. This simplifies to 11.

So the value of the given expression when y = 6 and z = 3 is 11.

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Answer:

x=18 degrees

Step-by-step explanation:

Hello

by definition, two angles are called complementary angles, if the sum of their degree measures is 90. Each angle is called complement of the other.

A = angle 1=x

B=angle 2 =4x

A and B are complementary angles,hence

A+B=90

replacing

[tex]x+4x=90\\\\5x =90\\x=\frac{90}{5} \\x=18\ degrees[/tex]

A=18 degrees

B=4*x

B=72 degrees

x=18 degrees

The value of 2.1e-10 = 0.00000000021

An exponent refers to the number of times a number is multiplied by itself.

Here e is used when the number is too large and small for the calculator.

We know 'e' represent exponents

2.1e-10, represents [tex]2.1* 10^{-10}[/tex]

= 2.1 x [tex]\frac{1}{10^{10}}[/tex]

= 2.1 x [tex]\frac{1}{10000000000}[/tex]

= 0.00000000021

Hence, 2.1e-10 = 0.00000000021

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Answer:

Option C. $94.49

Step-by-step explanation:

Jaime had a balance in his bank account on Sunday = $37

The table shows his account activity for the next four days.

From the given table we add all the deposits to his balance and then subtract all the withdrawals.

Balance on Sunday + Deposits

= 37.00 + 17.42 + 62.29 =  $ 116.71

Now we subtract all the withdrawals

= 116.71 - (12.60 + 9.62)

= 116.71 - 22.22 = $94.49

The balance would be $94.49 in Jaime's account after his deposit on Thursday.

Answer: [tex]w+s=4500[/tex]

[tex] w=1.25s[/tex]

Step-by-step explanation:

Let w be the number of bottles of water and let s be the number of bottles of soda.

Since , the manager needs to buy a total of 4,500 drinks.

Then , we have [tex]w+s=4500[/tex]

Also, the they have 25% more water than soda.

Since 25%=0.25

Then, [tex]w=s+0.25s=s(1.25)[/tex]

[tex]\Rightarrow\ w=1.25s[/tex]

Hence, the  system of equations for w in terms of s that the manager could use to find out how many bottles of water and soda to buy.

[tex]w+s=4500[/tex]

[tex] w=1.25s[/tex]

Using the exchange rate of USD/EUR 1.3847, you need to multiply your €100 by 1.3847 to determine the amount in US dollars, which is USD 138.47. Therefore, you will receive USD 138.47 for your €100.

You are returning from a trip to England with €100 euro, and the exchange rate is USD/EUR 1.3847. To calculate how much in US dollars you should receive, you use the exchange rate to convert euros to USD.

Therefore, you should receive USD 138.47.

The value the given expression x + 20 – 1 is, the solution is A. 28.

An expression is any mathematical statement which consists of numbers, variables and an arithmetic operation between them. In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

here, we have,

w = 13, x = 9, y = 1.9, z = 0.5

x + 20 – 1

Since X Is 9 ,

You're Problem Would Now Be

= 9 + 20 - 1

Then You Subtract 20

And 1 Which Will Give You 19

Then , You're Left With 9 + 19

Which Is 28.

Hence, the solution is A. 28.

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Answer:

The simplified form will be:  [tex]x\sqrt[5]{x^3}[/tex]

Step-by-step explanation:

The given expression is:   [tex]\sqrt[5]{x^4}*\sqrt[5]{x^4}[/tex]

Simplifying the above expression......

[tex]\sqrt[5]{x^4}*\sqrt[5]{x^4}\\ \\ =\sqrt[5]{x^4*x^4}\\ \\ =\sqrt[5]{x^4^+^4}\ [Exponents\ gets\ added\ while\ multiplication]\\ \\ =\sqrt[5]{x^8}\\ \\ =\sqrt[5]{x^5*x^3}\ [As\ 5+3=8] \\ \\ =\sqrt[5]{x^5}*\sqrt[5]{x^3}\\ \\ =x\sqrt[5]{x^3}[/tex]

So, the simplified form will be:  [tex]x\sqrt[5]{x^3}[/tex]

The large sphere is 64 times the surface area of the small sphere.

A sphere is a geometrical object that is a three-dimensional analogue to a two-dimensional circle. A sphere is the set of points that are all at the same distance r from a given point in three-dimensional space. That given point is the centre of the sphere, and r is the sphere's radius.

Given that, the radius of a large sphere is 8 times the radius of a small sphere.

Let the radius of a small sphere be x, then the radius of a large sphere is 8x.

We know that, the surface area of a sphere is 4πr².

Here, surface area of a small sphere = 4πx²

The surface area of a large sphere = 4π(8x)²

= 256πx²

Now, 256πx²/4πx² =64

Therefore, the large sphere is 64 times the surface area of the small sphere.

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Answer:

IS D

Step-by-step explanation:

The student wrongly calculated the value of [tex]\rm tan\theta[/tex], [tex]\rm sin\theta[/tex], [tex]\rm cosec\theta[/tex], and [tex]\rm cot\theta[/tex] and this can be determined by using the Pythagorean theorem and trigonometric functions.

GIven :

The point (-7, -24) is on the terminal ray of angle θ which is in standard position.

To determine the trigonometric function first determine the value of the hypotenuse and to determine the value of the hypotenuse, the Pythagorean theorem can be used.

[tex]\rm H^2 = P^2 + B^2[/tex]

where H is the hypotenuse, B is the base, and P is the perpendicular.

Now, substitute the value of known terms in the above equation.

[tex]\rm H^2 = 7^2+24^2[/tex]

[tex]\rm H^2=49+576[/tex]

[tex]\rm H^2 = 625[/tex]

H = 25

Now, the values of the trigonometric functions are as follows:

[tex]\rm cos\theta=\dfrac{-7}{25}[/tex]

[tex]\rm sin\theta=\dfrac{-24}{25}[/tex]

[tex]\rm tan\theta=\dfrac{24}{7}[/tex]

[tex]\rm cosec\theta=\dfrac{25}{-24}[/tex]

[tex]\rm sec\theta=\dfrac{25}{-7}[/tex]

[tex]\rm cot\theta=\dfrac{7}{24}[/tex]

The student wrongly calculated the value of [tex]\rm tan\theta[/tex], [tex]\rm sin\theta[/tex], [tex]\rm cosec\theta[/tex], and [tex]\rm cot\theta[/tex].

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To find the six trigonometric values for angle θ (-7, -24) on the terminal ray, we can use sine, cosine, tangent, cosecant, secant, and cotangent ratios.

The given point (-7, -24) lies on the terminal ray of an angle in standard position, denoted by θ. To find the six trigonometric values for angle θ, we can use the values of the coordinates of the point. The coordinate (-7) represents the x-value (adjacent side) and the coordinate (-24) represents the y-value (opposite side).

We can use the trigonometric ratios: sine (sin), cosine (cos), tangent (tan), cosecant (csc), secant (sec), and cotangent (cot), to find the values.

Here, sinθ = y/r = (-24)/7.6, cosθ = x/r = (-7)/7.6, tanθ = y/x = (-24)/(-7), cscθ = 1/sinθ, secθ = 1/cosθ, and cotθ = 1/tanθ. By substituting the respective values, we can find all six trigonometric values.

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The median salary for the given data set of four salaries ($20,000, $22,000, $24,000, and $26,000) is calculated by averaging the two middle values ($22,000 and $24,000), resulting in a median of $23,000

To calculate the median salary from an ordered data set, you first need to determine if the number of data points is even or odd. In this scenario, there are four data points: $20,000, $22,000, $24,000, and $26,000. As the number of data values is even, the median is the average of the two middle values.

Steps to Calculate Median Salary

Therefore, the median salary for this data set is $23,000

Answer:

4 to the power of 3, square root of 40, square root of 13, square root of 7, 14 over 9

Step-by-step explanation:

i took the test

it's the other way around.

Answer:

A

Step-by-step explanation:

x + y-1 = 0

 if x = 6

 replace x with 6 to get

6 +y-1 =0

subtract 6 from each side

y-1 =-6

add 1 to each side

y = -5

Final answer:

The volta in Sonnet 73 is a shift that occurs between lines eight and nine, serving to transition from metaphors of aging to considering their impact on love. This turn is common in sonnets, marking a change in argument or tone.

Explanation:

Finding the Volta in Sonnet 73

The volta, or the turn, in a sonnet marks a shift in thought or argument and is crucial to understanding the poem's structure and meaning. In Sonnet 73, the volta can be identified between lines eight and nine, where the poet moves from reflecting on the images that convey the passage of time and coming to terms with mortality, to directly addressing the beloved and discussing the importance of this realization for their relationship. The logical relationship between the octet (the first eight lines) and the following sestet (the last six lines) in Sonnet 73 is that the octet sets up a series of metaphors about aging and the passage of time, which the sestet then responds to by contemplating the impact of these realizations on love and connection.

The Petrarchan sonnet typically follows a structure with an octave that presents a problem that is resolved or responded to in the following sestet. Although the rhyme scheme might vary, the purpose of the volta remains the same across different sonnets: it signifies a pivot or shift in the argument or mood of the poem.

The reference to Shakespearian and Petrarchan sonnet styles in the question helps us understand that the student likely confuses the structure. Sonnet 73 is a Shakespearian sonnet that consists of three quatrains and a concluding couplet, with the volta being a conceptual rather than structural shift in Shakespeare's sonnets, typically occurring at the start of the third quatrain or the couplet.