a grant that your professor received includes funds for three graduate students to attend a conference to present their work. if your professor has eight graduate students and three students can go to the conference, how many choices does your professor have?

Hello!

Let's convert the equation, 3x + 4y = 7, into slope-intercept form:

  ⇒ slope-intercept form is where the y-variable is isolated to one side

    [tex]3x + 4y = 7\\\\4y=-3x + 7\\\\y=-\dfrac{3}{4}x +7[/tex]

The other line that is parallel to the equation: has the same slope

  ==> thus this other's line slope is -3/4

Let's set up the point-slope form for this other line:

 [tex](y-y_0)=m(x-x_0)[/tex]

       [tex](y+9)=-\dfrac{3}{4} (x+3)\\\\y + 9=-\dfrac{3}{4}x-\dfrac{9}{4} \\\\y=-\dfrac{3}{4}x-\dfrac{9}{4} -9\\\\y=-\dfrac{3}{4}x-\dfrac{9}{4} -\dfrac{36}{4} \\\\[/tex]

       [tex]y = -\dfrac{3}{4}x -\dfrac{45}{4}[/tex]   <== Answer

Hope that helps!

Answer:

  C)  180°

Step-by-step explanation:

You want the angle of rotation between triangle ABC and triangle A'B'C' given that the center of rotation is point P.

The angle of rotation will be the measure of the angle APA'. We see that this angle is a straight angle with a measure of 180°.

The angle of rotation is 180°.

__

Additional comment

Another clue regarding the answer is that 90° CW is equivalent to (and indistinguishable from) 270° CCW, and vice versa. This means each of the other answer choices is repeated, so one is as good as the other. The only possible single answer choice is 180°.

The angle of rotation can always be found this way. Form an angle between a preimage point, the center of rotation, and the corresponding image point. The measure of that angle is the angle of rotation.

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Let's solve figure by figure

Figure A

This figure has a total of 5 sides, therefore it is a pentagon.

Figure B

This figure has a total of 8 sides, therefore it is an octagon.

Figure C

This figure has a total of 3 sides, therefore it is a triangle.

According to the answer table, it would be

Pentagon: Figure A

Octagon: Figure B

Hexagon: None

Step-by-step explanation:

discretion data is something that will never change

continous data is data that will continue to become either larger or smaller

discret = ticket sales, number of employees

continuous = age,height

Answer:

12.106$

Step-by-step explanation:

20/100×60.53

1210.6/100

=12.106

Answer:

You will pay $457.56.

Step-by-step explanation:

600 x .18 = 108  This is the amount taken off

600 - 108 = 492 Now we will take 7% off of 492

492 x .07 = 34.44

492 - 34.44 = 457.56

Martin's answer is wrong. The afternoon temperature in Westfield city is  -10°F.

Given,

The temperature in Westfield city in morning = -2°F

The drop down temperature by afternoon = 8°F

We have to find the temperature in afternoon:

Temperature in afternoon = Temperature in morning - Drop down temperature

= -2 - 8 = -10

The afternoon temperature in Westfield city is -10°F

Martin subtracted like:

-2 - (-8) = -2 + 8 = 6

This is wrong.

That is,

We can conclude like:

Martin's answer is wrong. The temperature in Westfield city in afternoon is -10°F

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The equivalent expression of  (3d^4)² is 9d^8. Option B

Algebraic expressions are defined as expressions made up of terms, constants, factors, coefficients and variables.

They also consist of some mathematical operations, such as;

Equivalent expressions are defined as expressions that have the same solution but usually differ in the arrangement of the values.

Given the expression;

(3d^4)²

Now, let's expand the bracket, we have

(3)²(d)^4×2

Find the squares

9d^8

Thus, the expression is 9d^8

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The complete question:

Select the expression that is equivalent to (3d^4)²

The system of equations has two solutions, that is (4, 2).

Given,

There is a system of equations:

Equation 1: 2x + 4y = 16

Equation 2: (1/2)x - 2y = 4

The solution to the system of equations = (4, 2)

Lets check for the solution:

The equations are in the form of,

a₁x + b₁y + c₁ = 0

a₂x + b₂y + c₂ = 0

Here,

a₁ = 2 , a₂ = 1/2

b₁ = 4 , b₂ = 2

c₁ = 16 , c₂ = 4

Now we know that,

a₁/a₂ = b₁/b₂ = c₁/c₂

So,

a₁/a₂ = 2 / (1/2) = 4/1 = 4

b₁/b₂ = 4/2 = 2

c₁/c₂ = 16/4 = 4

Therefore, the system of equations has two solutions, that is (4, 2).

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The vertex of the function is (4, 0) and the range of the function is [0, 7]

The range of a function is the set of output values of the graph.

This in other words mean the range of a function is the set of y values of the graph.

The table of values represents the given parameter

As a general rule, the vertex of a function is the smallest or the largest value of the function

On the table of values, we have the smallest function value is 0

The corresponding x value is -4

When these values are paired, we have

(x, y) = (4, 0)

This means that the vertex of the function is (4, 0)

The table of values represents the given parameter

Using the definition of range stated above, we have

Smallest function value = 0

Largest function value = 7

This means that the range of the function is [0, 7]

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Answer:

$18.4

Explanation:

At the end of the year, Ryan will have the initial saving plus the interest earned.

So, to calculate the interest earned we will use the given equation:

i = p*r*t

So, replacing p by 16, r by 0.15, and t by 1, we get:

i = 16 x 0.15 x 1

i = 2.4

Then, after 1 year, she will have:

$16 + $2.4 = $18.4

Therefore, the answer is $18.4

Answer: 35 mile/hour

Step-by-step explanation:

[tex]r=\frac{d}{t}[/tex]

∴ [tex]r=\frac{227.5}{3.5}=65[/tex]

= 65 mile/hour

Answer:

These pairs are called vertical angles, and they always have the same measure. ∠1 and ∠3 are vertical angles. ∠2 and ∠4 are vertical angles.

Angle 1 and angle 3 are on the same side of the two parallel lines with a transversal line on them.

The special angle pair relationship between 1 and 3 is called the corresponding angles.

Corresponding angles are angles that occur on the same side of the transversal line and are equal in size.

We have,

Angle 1 and Angle 3.

The angles are on the same side of the two parallel lines with a transversal line on them.

The angles can be called the corresponding angles.

Thus,

The special angle pair relationship between 1 and 3 is called the corresponding angles.

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Answer:

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

Proportional relationship has the form of:

The value of k should be same for any pair of coordinates:

Equation of the line in slope form that is perpendicular to the line y =5x +6 and passes through the point (-3, 3) is equal to y = -5x -12.

As given in the question,

Equation of the given line :

y = 5x + 6

Slope of the given line m₁ = 5

Required line is perpendicular to the given line

Slope of the required line is m₂ = -5

Required line is passing through the point (x₁ , y₁) = (-3, 3)

Equation of the required line in slope form

y -y₁ = m₂( x -x₁ )

⇒ y - 3 = -5(x - (-3))

⇒ y -3 = -5x -15

⇒ y = -5x -12

Therefore, equation of the line in slope form that is perpendicular to the line y =5x +6 and passes through the point (-3, 3) is equal to y = -5x -12.

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128 feet³ is the volume of a cord of wood.

What is volume in maths?

l =  8 feet

b = 4 feet

h = 4 feet

volume of a cord of wood  = l × b × h

                                             = 8 × 4 × 4

                                              = 128 feet³

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The two essential characteristics of functions are domain and range. Function has a domain of (-1, ∞) and a range of (-∞, ∞), f(x) = log₂x - 1.

Mathematical procedures are comparable to those of a soda vending machine. You can choose from a variety of sodas after you deposit a particular sum of money. Similar to how we enter different numbers into functions, we also receive new numbers as the outcome. The two essential characteristics of functions are domain and range.

A soda can be purchased using quarters and one dollar bills. If pennies are put into the machine, no soda flavor will be provided. As a result, domain depicts the possible inputs, which are quarters and one-dollar bills. No matter how much you pay, a Coke machine won't give you a cheeseburger. As a result, range refers to potential outputs, or in this case,  soda tastes in machine. Let's discover how to graph and determine domain and range of a given function.

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Answer:

Hope this helps

fist add three to both sides

then subtract 4x from both sides

then divide both side with the same factor

Using multiplication, we know that 6,603 bottles of water were sold in march by the store.

Multiplication's characteristics. Commutative Multiplication Property.

So, bottles of water the store sells in march:

Therefore, using multiplication, we know that 6,603 bottles of water were sold in march by the store.

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If the solution set S ={3}, then the equation 1 is false

The solution set S = {3}

Equation 1

-28 = 2(4p-4)

4p-4 = -28/2

4p-4 = -14

4p = -14+4

4p = -10

p = -10/4

p = -5/2

This equation is false

Equation 2

5(b+3) = 30

b+3 = 30/5

b+3 = 6

b = 6-3

b = 3

This equation is true

Equation 3

7 = 3y-2

3y = 7+2

3y = 9

y = 9/3

y = 3

This equation is true

Equation 4

(1/3)x+18 = 19

(1/3)x = 19-18

(1/3)x = 1

x = 1 ÷1/3

x = 1×3

x = 3

This equation is true

Hence, If the solution set S ={3}, then the equation 1 is false

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[tex] - 2y = 8 - 3x \\ \frac{ - 2y}{ - 2} = \frac{8}{ - 2} - \frac{3x}{ - 2} \\ y = \frac{3}{2} x - 4[/tex]

AS WE SEE IN THE EQUATION ABOVE THE GRADIENT IS

[tex] \frac{3}{2} [/tex]

IT MEANS THE GRADIENT OF THE NEW EQUATION IS ALSO

[tex] \frac{3}{2} [/tex]

NOW GIVEN THE POINTS WE CAN USE THE KNOWNS TO GET THE VALUE OF C IN THE NEW EQUATION.

[tex] - 3 = \frac{3}{2} (6) + c \\ - 3 = 9 + c \\ - 3 - 9 = c \\ c = - 12[/tex]

[tex]y = \frac{3}{2} x - 12[/tex]

Answer:

x = 4

The two interior angles are

14x + 6 = 14 x 4 + 6 = 62°

16x + 4 = 16 x 4 + 4 = 68°

Step-by-step explanation:

The exterior angle of a triangle is the sum of the interior angles:

Here the exterior angle is 130° and the interior angles are
16x + 4 and 14x + 6

So 16x + 4 + 14x + 6 = 130

Gathering like terms and simplifying:
16x + 14x + 4 + 6 =  130

30x + 10 = 130

30x = 120           (subtract 10 from both sides)

x = 4

The two interior angles are

14x + 6 = 14 x 4 + 6 = 62°

16x + 4 = 16 x 4 + 4 = 68°

The expression represented by the mathematical sentence is 3/5a - 7 = –36

Expressions are mathematical statements that are represented by variables, coefficients and operators

The expression is given as

"The difference between three-fifths of a number and 7 is –36."

Three-fifths of a number a means multiply 3/5 and the number i.e. 3/5 * a

So, we have

The difference between three-fifths of a number and 7 is –36 ⇒ The difference between 3/5a and 7 is –36

difference means subtraction

So, we have

The difference between three-fifths of a number and 7 is –36 ⇒ 3/5a - 7 is –36

"is" means =

So, we have

The difference between three-fifths of a number and 7 is –36 ⇒ 3/5a - 7 = –36

Hence, the expression represented by the difference between three-fifths of a number and 7 is –36 is 3/5a - 7 = –36

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Answer:

what level math is this I am not too familiar with it

Based on the solution set S:{3} the equation which is false is

-28 =2(4p -4).

As given in the question,

Given solution set S:{3}

Equation which is false based on the solution set

1. −28 = 2(4p − 4)

Divide by 2 from both the sides

⇒ -14 = 4p -4

⇒ p = -10/4 ≠ 3

2. 5(b + 3) = 30

Divide by 5 from both the sides

⇒b + 3 =6

⇒ b = 3

3. 7 = 3y − 2

⇒ 3y = 9

⇒ y = 3

4. One third times x plus 18 equals 19

(1/3)x + 18 = 19

⇒(1/3)x =1

⇒x =3

Therefore, based on the solution set S:{3} the equation which is false is

-28 =2(4p -4).

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The factored expression of the expression given as xy - 9x - 3y + 27 is (x - 3)(y - 9)

Expressions are mathematical statements that are represented by variables, coefficients and operators

The expression is given as

xy - 9x - 3y + 27

Factor out the common factor from the expression

So, we have

xy - 9x - 3y + 27 = x(y - 9) - 3(y - 9)

Factor out (y - 9) from the expression

So, we have

xy - 9x - 3y + 27 = (x - 3)(y - 9)

The expression above cannot be further simplified

This means that the expression has been completely factored and cannot be further factored

Hence, the equivalent expression of the expression given as xy - 9x - 3y + 27 when it is factored by grouping is (x - 3)(y - 9)

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