The figure shows two parallel lines, j and k, cut by two transversals, t₁ and t₂.

What is the value of m<3, in degrees, if m<5 = 70° and m<2 = 60°?

Equation of the line for the given graph in slope-intercept form is given by  y = 5x -1.

As given in the question,

From the given graph,

Consider pair of two coordinates we have,

(x₁ , y₁) = (1, 4)

(x₂ , y₂) = (0,-1)

Equation of the line for the given graph in slope-intercept form is given by:

(y -y₁) / (x -x₁)= (y₂ -y₁) / (x₂ -x₁)

⇒ ( y - 4)/ (x -1) = (-1-4)/(0-1)

⇒(y-4)/(x-1) = 5

⇒y-4 = 5(x-1)

⇒y = 5x -5 +4

⇒ y= 5x -1

Therefore, equation of the line for the given graph in slope-intercept form is given by  y = 5x -1.

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The solution of the system of equation by substitution is x = 3 and y = -1.

System of equation can be solved using different techniques such as substitution method, elimination method and graphical method.

Let's solve the system of equation by substitution method

Therefore,

3x + 2y = 7

x = 3y + 6

Substitute equation(ii) in equation(i)

3(3y + 6) + 2y = 7

9y + 18 + 2y = 7

9y + 2y + 18 = 7

11y = 7 - 18

11y = -11

y = -11 / 11

y = -1

Hence, let's find x

x = 3(-1) + 6

x = -3 + 6

x = 3

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The solution to these are in form of equation as follows.

What is equation?

In arithmetic, an equation may be a formula that expresses the equality of 2 expressions, by connecting them with the sign =.

Main body:

x= number of HD headphones           y= number of basic headphones

z = price of HD headphones.             w = price of basic headphones

a)

110 (70) + y*w = 10,000

7,700+ y*w = 10,000

y*w = 2,300

y = 2,300/w

b)

x*z+ 55(20) = 2000

x*z = 2000 -1100

x*z = 900

z = 900/x

c)

x*z+y*w = 800

x*z+8(80) = 800

x*z+640=800

X*z=160

Hence the values to the equation are as follows.

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The answer is not a linear function, and the evaluation of the partial derivatives was done to a point. Thus, options (a) and (c) are correct. The correct equation for the tangent plane is  z = 3x - 108y - z + 241 = 0.

In a given point (x₀, y, z₀) the equation of the tangent plane to a surface given by the function S = f(x, y)can be obtained by

z-z₀ = f ₓ (x₀, y₀, z₀) (x - x₀) + fᵧ (x₀, y₀, z₀) (y - y₀) ... (i)

where  f ₓ (x₀, y₀, z₀) and fᵧ (x₀, y₀, z₀) (y - y₀) are the partial derivatives of f(x, y) with respect to x and y respectively. These two derivatives are evaluated at the point (x₀, y₀, z₀) .

Thus, we need to find two missing inputs, the z₀ coordinate and the two partial derivatives, in our problem in order to use equation (i).

In the case of z₀, evaluation of the given function gives us z = -80.

The partial derivatives are thus-

δf(x,y) / δx = fₓ (x, y) = 3x²

fₓ (x₀, y₀) = fₓ (1, 3) = 3

δf(x,y)/δxy= fᵧ (x, y) = -4y³

fᵧ (x₀, y₀) = fᵧ (1, 3) = -108

Now, arranging these values in equation (i) we obtain:

z-z₀ = f ₓ (x₀, y₀, z₀) (x - x₀) + fᵧ (x₀, y₀, z₀) (y - y₀)

z +80 = 3x² (x -1) - 4y³ (y - 3)

z = -80 +3x² (x -1) - 4y³ (y - 3)

Now, we will substitute the values of the partial derivatives at the given point:

z = -80 + 3x² (x -1) - 4y³ (y - 3)

z = 3x² (x -1) - 108 (y - 3)

z = 241 + 3x -108y

i.e., 3x - 108y - z + 241

Thus, the correct equation is 3x - 108y - z + 241.

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The complete question is-

A student was asked to find the equation of the tangent plane to the surface z = x³−y⁴ at the point (x, y) = (1, 3). The student's answer was z = −80 + 3x²(x−1)−(4y³)(y−3).

(a) At a glance, how do you know this is wrong? What mistakes did the student make? Select all that apply. A. The (x - 1) and (y - 3) should be x and y. B. The -80 should not be in the answer. C. The partial derivatives were not evaluated at this point. D. The correct answer is not a linear function. E. All of the above.

(b) What is the correct equation for the tangent plane? z=

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Answer:

x = 1/4p

y = 3/2p

Step-by-step explanation:

2x + 3y =5p__________________equ 1

y = 2x + p____________________equ 2

sub equ 2 for y in equ 1

2x + 3(2x + p) = 5p_______________open brackets

8x = 2p______________________divide both sides by 8

x = 1/4p

sub 1/4p for x in equ 2

y = 2(1/4p) + p___________________open brackets

y = 3/2p

Answer:

$3.70

Step-by-step explanation:

12 dimes, and dimes are ten cents each. So we will multiply 10*12=120. Which is $1.20.

10 quarters, and quarters are twenty-five cents each. So we will multiply 10*25=250. Which is $2.50

Now we take our two totals and add them together. 1.20+2.50=3.70.

So we have $3.70.

I hope this helps!!!

Step-by-step explanation:

ratios are special fractions and follow therefore all the fraction rules.

e.g. they follow the rule that for transformations the same multiplications or divisions have to happen for the denominator and the numerator when bringing them to the same denominator.

and they follow the same division and multiplication rules.

2/3 : 1/6 : 5/2 = (2/3)×(2/2) : 1/6 : (5/2)×(3/3) =

4/6 : 1/6 : 15/6 = 4 : 1 : 15

The equation for the vertical line that goes through point M(−2, 6) is x = -2.

Answer:

The equation of a straight line is:

y = mx + b;

y, x are variables, m is the slope of the line and b is the y intercept.

The slope of a vertical is undefined. Since the line passes through the point M(−2, 6), hence the equation of the vertical line is:

x = -2

Answer:

<ABD = 67.17

Step-by-step explanation:

Comment

This requires 2 steps.

Finding <A

<A is found by taking the inverse tangent of the ratio 8/19.

<A = tan-1*(8/19)

<A = 22.83 degrees. We'll round it later.

Finding <ABD

You have to use 2 facts here.

All triangle angles add up to 180 degrees.

You find the third angle by subtracting the other 2.

<A = 22.83                                       Found above

<ADB = 90 degrees                        Given

<ABD = ?

Equation

< A + <ADB + <ABD = 180

Solution

22,83 + 90 + <ABD = 180                 Combine the left

112.83 + <ABD = 180                         Subtract 112.83 from both sides.

112.83-112.83 +<ABD = 180 - 112.83  Combine

<ABD = 67.17

The answer to the nearest degree is 67.

When the divisor is missing, you divide the dividend (3.472) by the quotient (0.112)

So, we will do 3.472 divided by 0.112

3.472/0.112 = 31

Another method is multiplication. Multiplication is the opposite of division. We'd multiply 0.112 by 31.

0.112 x 31 = 3.472

In conclusion,

3.472/31 = 0.122

If you need extra help, use this video as a reference

https://youtu.be/9ui8Yh0bwCI?t=83

Answer: 3.472/31 = 0.122

Step-by-step explanation: I hope this helps:)

Answer:

see explanation

Step-by-step explanation:

(a)

AB = 4 + x

(b)

the area (A) of rectangle ABCD is calculated as

A = length × breadth

   = AB × AD

   = (4 + x)(6 + x) ← expand using FOIL

   = 24 + 10x + x²

given A = 28 , then

x² + 10x + 24 = 28 ( subtract 24 from both sides )

x² + 10x = 4 ← in the form x² + ax = b

with a = 10 and b = 4

The linear functions representing the systems of equations in each case are given as follows:

8. (D) 6x − y = 8 3x + 2y = 9

9. (C) a + o = 72 a = o + 8.

10. (C) 4x + 3y = −12 2x − 5y = 10.

The slope-intercept representation of a linear function is presented by the rule as follows:

y = mx + b

The coefficients of the function and their meaning are listed as follows:

For the line m, we have that when x increases by 6, y increases by 36, hence the slope is:

m = 36/6 = 6.

Considering the positive slope of 6, at x = 0, the numeric value is 12 less than the numeric value at x = 2, hence the intercept is:

b = 4 - 2 x 6 = -8.

Hence the equation is:

y = 6x - 8.

6x - y - 8.

Thus option d is correct.

For item 9, we use the variables a and o. The total is of 72, hence:

a + o = 72.

Suppose that a crate has 8 more apples than oranges, hence:

a = o + 8.

Thus option c is correct.

For line r in item 10, when x increases by 3, y decays by 4, hence the slope is:

m = -4/3.

When x = 0, y = -4, hence the intercept is:

b = -4.

Thus the equation is:

y = -4x/3 - 4

3y = -4x - 4.

4x + 3y = -12.

Meaning that option c is correct.

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The monthly budget for rent is $1,627.33 ≤ m ≤ $2,441.00

An equation is an expression that shows the relationship between two or more numbers and variables.

Let m represent the monthly rent of the shop.

The average yearly revenue is $195,280. Hence:

Monthly revenue = $195,280 / 12 = $16273.33

If the monthly budget for rent is 10%, hence:

m = 10% of $16273.33 = 0.1 * $16273.33 = $1627.33

If the monthly budget for rent is 15%, hence:

m = 15% of $16273.33 = 0.15 * $16273.33 = $2441.00

$1,627.33 ≤ m ≤ $2,441.00

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The slope of line 1 and line 2 are equal. Then the lines are parallel to each other.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The slope of the parallel lines will be equal.

The equations are given below.

5x − 3y = 2             ...1

5x − 3y = 8            ...2

The slope of line 1 is given as,

5x − 3y = 2

y = (5/3)x − 2/3

The slope of line 1 is 5/3.

The slope of line 2 is given as,

5x − 3y = 8

y = (5/3)x − 8/3

The slope of line 2 is 5/3.

The slope of line 1 and line 2 are equal. Then the lines are parallel to each other.

The graph is given below.

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The value a = 2 and b = 5 is makes the expression (5x²y²){-4xªy³) =−20xªyᵇ as true.

Expression:

An expression is set of numbers or variables combined using the operations +, -, * and /.

Given,

Here we have the expression (5x²y²){-4xªy³) =−20xªy°.

Now, we have to the value of a and b which make both equation as equal.

In order to get the value a and b, first, we have to solve the expression in the left hand side,

To solve this type of equation, the first step is to combine the like terms, then we get,

=> (5x²y²){-4xªy³)

=> (5 x -4) (x² xᵃ) (y² y³)

Now, we have to do the multiplication on it, then we get,

=> -20 xᵃ⁺² y²⁺³

=> -20xᵃ⁺²y⁵

Now, we have to equate both LHS and RHS, then we get,

=> -20xᵃ⁺²y⁵ = -20xᵃyᵇ

While we looking into the equation, we have identified that the value of a is 2 and the value of b is 5.

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Ty has  2 5/6 pounds of coffee left after giving 5/6 pounds of coffee to his grandma

Fraction is a numerical quantity that is not a whole number

From the question,

Ty bought 3 4/6 pounds of coffee

converting 3 4/6 to improper fraction

we have 22/6

Ty gave his friend 5/6 pound of coffee to his grandma

To estimate how much coffee Ty has left

We substract Coffee given to his grandma from Coffee bought

That is,

22/6 - 5/6

= 17/6

= 2 5/6 pounds of coffee left

Ty has 2 5/6 pounds of toffee left. He gave 5/6 of what he bought to his grandma.

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The probability of favorable  outcomes  P(E) = 37/256

What is probability in math?

Given,

      8 coins are faced simultaneously .

total outcomes = 2 * 2 * 2* 2 * 2 * 2 * 2 * 2

                             = 2⁸

                             = 256

favorable outcomes = 6 heads + 7 heads + 8 heads

                      = ⁸C₆ + ⁸C₇  + ⁸C₈

                       = 28 + 8 + 1   = 37

the probability of favorable  outcomes =            

              P(E) = 37/256

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The inequality of the graph represented in the figure is y ≥ 1/2x

The graph represents the given parameter

On the graph, we have the following points

(x, y) = (0, 0) and (2, 1)

This can be re-expressed as

(x, y) = (2, 1)

The slope is then calculated as

Slope = y/x

This gives

Slope = 1/2

The equation is then calculated as

y = Slope * x

So, we have

y = 1/2x

On the graph, we can see that the upper part of the graph is shaded and the line is a thick line

This means that the inequality expression is ≥

So, we have

y ≥ 1/2x

Hence, the inequality of the graph is y ≥ 1/2x

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The residual of a theatre performance with a revenue of $700 and 70 seats occupied is 45.

From the information illustrated, the theater director recorded the number of seats occupied at past performances and the total revenue per performance.

The equation is given as:

y = -325 + 14x

y = actual performance for 70 seats occupied

For x = 70

y = -325 + 14x

= 325 + 14(70)

= -325 + 980

= 655

Therefore, the residual will be:

= 700 - 655

= 45

The residual is 45.

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Answer:

[tex] {x}^{4} + 4 {x}^{3} + 6 {x}^{2} + 4x + 1[/tex]

Step-by-step explanation:

as shown in photo attached :")

The expected number of customers that get back their own hat is 1.

Utilizing indicator random variables, we resolve this issue. For 1 ≤ i ≤ n,

Let .

Xi = I {Customer 'i' who gets his hat back itself}.

The number of clients that receive their own hats back should be the random variable X. We want to figure out E[X].

Clearly,

      n

X = ∑ Xi

    i=1

It is clear that 1/n represents the likelihood that customer 'I' will receive his own hat.

Due to the fundamental characteristics of indicator random variables, this means that E[Xi] = 1/n.

                   n

  E[X] = E [ ∑ Xi  ]

                  i=1

                   n

           =  ∑ 1/n

                  i=1

Put the limits.

  E[X] = 1

As a result, 1 consumer is anticipated to have their own hats back.

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Function [tex]-3x^2+18x+3[/tex] has maximum value at x = 3 and its maximum value is 30.

How do you find the maximum and minimum value of the function?

Calculus can be used to find the critical point, or the x-value of the vertex, by taking the derivative of the function, or f'(x). To determine the critical point, we shall set the function's first derivative to zero and solve for x. This point's maximum or minimum value can be determined by taking the second derivative, or f"(x). The second derivative will have a minimal value if it is positive. The second derivative will be the highest value if it is negative.

Given function:

[tex]-3x^2+18x+3[/tex]

To find the maximum and minimum value of the function use second derivative test.

On differentiating the above function we get,

-6x + 18

Now, find critical point

-6x + 18 = 0

-6x = - 18

x = - 18/-6 = 3

x = 3

Here, x = 3 is the critical point. Now again differentiate the above function we get,

-6

As , [tex]f^{''}(x)[/tex] < 0 , therefore x = 3 will given a maximum value of function and maximum value is

f(3) = [tex]-3(3)^2+18x+3 = -3(9) + 18(3) + 3 = -27 + 54 + 3 = 27 + 3 = 30[/tex]

Hence , function [tex]-3x^2+18x+3[/tex] has maximum value at x = 3 and its maximum value is 30.

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The explicit formula is a_n = 3+4n

From the question, we have

a1 = 7

We know that,

a_n = a_1 +(n-1)d

a_n = 7 +(n-1)4

a_n = 7+4n-4

a_n = 3+4n

Subtraction:

Subtraction represents the operation of removing objects from a collection. The minus sign signifies subtraction −. For example, there are nine oranges arranged as a stack (as shown in the above figure), out of which four oranges are transferred to a basket, then there will be 9 – 4 oranges left in the stack, i.e. five oranges. Therefore, the difference between 9 and 4 is 5, i.e., 9 − 4 = 5. Subtraction is not only applied to natural numbers but also can be incorporated for different types of numbers.

The letter "-" stands for subtraction. Minuend, subtrahend, and difference are the three numerical components that make up the subtraction operation. A minuend is the first number in a subtraction process and is the number from which we subtract another integer in a subtraction phrase.

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21/8 must be added to the terms to give the result as 6. The answer will be in a fraction.

What is a fraction?

In general, any number of equal pieces is represented by a fraction, which is a portion of the entire. In ordinary English, a fraction refers to the number of parts of a specific size.

Main Body:

Let the term to be added be x.

3+3/8+x =6

on solving this we will get the value of  x= 21/8

Hence the answer of this question is 21/8.

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The inequality that can be used to solve for x, the number of minutes it will take Amy to finish typing her paper is D. 38x + 1,450 > 4,000.

Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.

Since Amy types at an average speed of 38 words per minute and has already typed 1,450 words of her final paper, which will be more than 4,000 words.

Let the number of minutes be x.

This will be:

1450 + 38(x) > 400

1450 + 38x > 4000

In conclusion, the correct option is D.

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The terms of the algebraic equation 3+6ab+c are (d) 3, 6ab  and c

The algebraic equation is given as

3 + 6ab + c

Consider an equation represented as

x + y

The terms of the equation are x and y

Also, for an equation represented as

x + y + z;

The terms are x, y and z

Using the above as a guide, the terms of 3 + 6ab + c are 3, 6ab  and c

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The function f(x) = [tex]-3x^2[/tex] + 18x + 3 has the maximum value of 30 at x = 3

The quadratic function is

f(x) = [tex]-3x^2[/tex] + 18x + 3

The general form of the quadratic function is

y = [tex]ax^2[/tex] + bx + c

If a < 0, the quadratic function has maximum value

Here the value of a = -3

Therefore the function has maximum value.

Maximum value will be at x = -b / 2a

= -18 / 2(-3)

= -18 / -6

= 3

The maximum value of quadratic function will be (4ac - [tex]b^2[/tex]) /4a

Substitute the value in the equation

(4ac - [tex]b^2[/tex]) /4a = (4×-3×3 - 18×18) / 4×-3

= (-36 - 324 / -12

= -360 / -12

= 30

Hence, the function f(x) = [tex]-3x^2[/tex] + 18x + 3 has the maximum value of 30 at x = 3

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The equation of the parabola that similar to f(x) = [tex]7x^2[/tex] but the vertex is (3, 5) in the standard form is y = [tex]7(x-3)^2[/tex] + 5

The equation of the parabola

f(x) = [tex]7x^2[/tex]

The standard vertex form of a parabola is

y = [tex]a(x-h)^2[/tex] + k

The coordinates of the vertex of a parabola = (3, 5)

Where (h, k)  is the coordinates

From the given function of the parabola f(x) =  [tex]7x^2[/tex]

The value of a = 7

Substitute the values in the vertex form of a parabola

y = [tex]7(x-3)^2[/tex] + 5

Hence, the equation of the parabola that is similar to f(x) = [tex]7x^2[/tex] but the vertex is (3, 5) in the standard form is y = [tex]7(x-3)^2[/tex] + 5

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By using the diagram and the given angle measure we get that:

if, m∠1 = 143°

then, m∠2 = 37°

         m∠3 = 143°

         m∠4 = 37°

What is angles?

An angle is formed when two straight lines or rays meet at a common endpoint.

What is Properties of Congruence?

       For all angles A ,

        ∠A≅∠A .

       An angle is congruent to itself.

        For any angles A  and  B ,

        if ∠A≅∠B , then ∠B≅∠A .

         Order of congruence does not matter.

        For any angles A,B,  and  C ,

        if ∠A≅∠B and ∠B≅∠C , then ∠A≅∠C .

        If two angles are both congruent to a third angle, then the first two        angles are also congruent.

I assume that, this refers to two intersecting lines which form four angles.

         ∠1 + ∠2 = 180°

          143° + ∠2 = 180°

          ∠2 = 180° - 143°

          ∠2 = 37°.

         It means that,  ∠1 = ∠3 =143° (properties of congruency)

         and ∠2 = ∠4 =37° (properties of congruency).

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