georgianna wants to use the linear model associated with the data in the table to make a prediction. which range of time values describes the entire interval over which she would be interpolating?

The solutions to the equation y/ (y- 4) - 4/ (y + 4) = 32/ y are approximately 30.948, 4.627 and -3.575.

The given equation is y/ (y- 4) - 4/ (y + 4) = 32/ y

Let us simplify the left hand side (LHS) :

Make the denominator same to (y - 4)(y + 4)

y/ (y- 4) - 4/ (y + 4) = (y/ (y- 4))×((y + 4)/(y + 4)) - (4/ (y + 4))×((y - 4)/(y - 4))

y/ (y- 4) - 4/ (y + 4) = ( y(y + 4) - 4(y - 4))/ (y - 4)(y + 4)

y/ (y- 4) - 4/ (y + 4) = (y² + 4y - 4y + 16)/ (y² - 16)

y/ (y- 4) - 4/ (y + 4) = (y² + 16)/ (y² - 16)

Now plugging this simplified version in LHS

(y² + 16)/ (y² - 16) = 32/ y

y(y² + 16) = 32(y² - 16)

y³ - 32y² + 16y + 32×16 = 0

The solutions are approximately 30.948, 4.627 and -3.575.

To know more on cubic polynomial

https://brainly.com/question/1417425

#SPJ4

The vertices of the polygon before and after dilation are shown below

preimage         Image

J (-5, 3)            J' (-5/2, 3/2)

K (2, 3)            K' (1, 3/2)

L (2, -3)           L' (1, -3/2)

M (-5, -3)        M' (-5/2, -3/2)

Dilation is a method of transformation that magnify or shrink the preimage depending on the scale factor

The rule used in  transformation is as follows

(x, y) for a scale factor of r → (rx, ry)

Applying the rule to the vertices  of the polygon we have

preimage                                  Image

J (-5, 3)      (1/2 * -5, 1/2 * 3)      J' (-5/2, 3/2)

K (2, 3)       (1/2 * 2, 1/2 * 3)       K' (1, 3/2)

L (2, -3)      (1/2 * 2, 1/2 * -3)       L' (1, -3/2)

M (-5, -3)    (1/2 * -5, 1/2 * -3)     M' (-5/2, -3/2)

Learn more about dilation at:

https://brainly.com/question/30239118

#SPJ1

Answer:

Perpendicular Bisector

Answer:

[tex]k { { { {y6444396}^{46446?} }^342{?} }^66 {6 { { {6636163 \\ }^{2} }^{2} }^{2} }^{2} {?} }^{?} \times \4166441frac{?}{?} [/tex]

Step-by-step explanation:

djdkkwkwnsjididjfjrje

On solving the provided question we can say that any triangle's perimeter is the sum of its three sides' lengths = [tex]\x = 360/6 = > x = 60[/tex]

A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.

Triangle's sides are x, 2x, and 3x Plus 2 ft. Respectively.

Radius is 362 feet.

Any triangle's perimeter is the sum of its three sides' lengths.

[tex]362 = x + 2 x + 3x +2\\6 x +2=362\\6 x= 362-2\\6 x=360\\x = 360/6\\x = 60[/tex]

Triangle's shortest side measures 60 feet.

Middle side = 2 x 2 x 60 ft = second side

Third side equals 3 x + 2 and is measured as 360+2=180+2=182 ft.

To know more about triangle visit:

https://brainly.com/question/2773823

#SPJ4

Answer: C

Step-by-step explanation:

Yes, the conditions for constructing a t confidence interval are met. The sample size is 10, which is greater than 30, and the sample is a random sample of 10 deliveries from a large number of deliveries made.

1. Constructing a t confidence interval requires that the sample size is greater than 30, so the first condition that must be met is that the sample size is greater than 30.

2. The second condition that must be met is that the sample is a random sample of the population of interest. In this case, the sample is a random sample of 10 deliveries from a large number of deliveries made.

Since both conditions are met, the conditions for constructing a t confidence interval are met.

Yes, the conditions for constructing a t confidence interval are met. The sample size is 10, which is greater than 30, and the sample is a random sample of 10 deliveries from a large number of deliveries made.

Learn more about sample here

https://brainly.com/question/25894237

#SPJ4

Answer:

C. y = 30x + 130    D. 5 people  Q3. The 1st number is 25

     y = 20x +180                                 The 2cnd number is 7

Step-by-step explanation:

C. The x represents the amount of people attending.

     30 and 20 are the price per person.

D. 30 x 5 + 130 = 280

    20 x 5 = 180 = 280

Q3. 32 + 18 = 50

50/2 = 25

25 + y = 32

y = 32 - 25

y = 7

hope this helps =)

y = 30x + 130 and y = 20x + 180 is the  system of equations that represents the model and The two numbers are 25 and 7 in second question.

Two or more expressions with an Equal sign is called as Equation.

Let y represents the total cost of the party, and x represents the number of the people attending the party.

The hockey suite costs $130 to rent the room and $30 per person.

y=130+30x

The basketball suite costs $180 to rent the room and $20 per person.

y=180+20x

So option c is correct and

If there was going to be a total of 4 people attending the party,

y=130+30(4)=250

y=180+20(4)=260

basket ball is most cost efficient.

If there was an amount of people that could attend the party so that both games would cost the same

130+30x=180+20x

10x=50

x=5

So 5 people could attend the party.

The sum of two numbers is 32

The difference is 18

x+y=32

x-y=18

x+y+x-y=32+18

2x=50

Divide both sides by 2

x=25

y=7

The two numbers are 25 and 7.

Hence, y = 30x + 130 and y = 20x + 180 is the  system of equations that represents the model and The two numbers are 25 and 7 in second question.

To learn more on Equation:

https://brainly.com/question/10413253

#SPJ1

On solving the provided question, we can say that by linear equation we have 2.5x * cereals = y

A linear equation is one that has the form y=mx+b in algebra. B is the slope, and m is the y-intercept. It's usual to refer to the previous clause as a "linear equation with two variables" because y and x are variables. The two-variable linear equations known as bivariate linear equations. There are several instances of linear equations: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3.

2.5 cups of this particular cereal,

the following linear equation, you could calculate how many calories and grams of fiber you were eating.

let x = cereals we eat y = calories

so, equation - 2.5x * cereals = y

To know more about linear equation visit:

https://brainly.com/question/11897796

#SPJ4

Transformations that have been applied to function f(x) to get g(x) are translation, reflection, and dilation.

The process of transforming the existing graph or graphed equation, to create a variation of the following chart is called graph conversion. Transformations such as translation, reflection, and dilation have been applied to function f(x) to produce g(x).

Therefore, the answer is "translation , reflection , and dilation".

To learn more about transformation of graphs, visit the link:

brainly.com/question/12202719

#SPJ4

Answer:

A) Translation

B) Reflection

C) Dilation

Step-by-step explanation:

Two types of transformations that can be used to transform f(x) to g(x) are horizontal and vertical stretching/shrinking.

What is transformation ?

A transformation is a function that changes the position, size, or shape of an object or a graph. In mathematics, transformations are often used to map a function from one coordinate space to another. There are several types of transformations, including translations, rotations, reflections, and scalings.

Part A: Two types of transformations that can be used to transform f(x) to g(x) are horizontal and vertical stretching/shrinking.

Part B:

Horizontal stretching/shrinking: k is the horizontal scale factor.

Vertical stretching/shrinking: k is the vertical scale factor.

Part C:

Horizontal stretching/shrinking: g(x) = f(kx)

Vertical stretching/shrinking: g(x) = kf(x)

Two types of transformations that can be used to transform f(x) to g(x) are horizontal and vertical stretching/shrinking.

To learn more about transformation visit : brainly.com/question/11709244

#SPJ4

Answer:

a = 0

(0,3)

Step-by-step explanation:

The possible length of the third side of the triangle is x>52 inches.

The sum of the lengths of any two sides of a triangle is always greater than the length of the third side. If the sum of the two sides is equal to the third side, then the two sides will coincide with the third side so a triangle cannot be formed. Hence, the sum of the two sides must be greater than the third side for the triangle to be formed.

Given: Sides of two sides of a triangle as 15 and 37 inches.

let the third side of the triangle be x.

then x>15+37

       x>52 inches.

Hence, The possible length of the third side of the triangle is x>52 inches.

Learn more about triangles here:

https://brainly.com/question/2456591

#SPJ1

On solving the provided question, we can say that by equation 15+4 = total minutes, they can talk 19 minute

An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.

x= total minutes -4    the 1st 4 minutes are included in the .30

total cost = .3 + .18 x  

[tex]3 = .3 +.18 x\\2.7 = .18x\\2.7/.18 = x\\15 = x[/tex]

x = total minutes -4

15+4 = total minutes

they can talk 19 minute

To know more about equation visit:

https://brainly.com/question/649785

#SPJ4

Answer:

16

Step-by-step explanation:

The side lengths of the original square was 2.  2 x 2 = 4

.25 x 2 = .5

The squares are now 1/2 x 1/2.  One of the 4 original squares will now need 4 new smaller size squares to cover the one square.

4 x 4 = 16

Answer: The answer is C hope this helps :)

Step-by-step explanation:

The approximate height of the ball from where it is dropped will be 115 cm. Then the correct option is C.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

The height of a ball after its second bounce was 80 cm. The ball had a rebound factor of 0.7. Then the height of the ball from where it is dropped is given as,

0.7h = 80

h = 80 / 0.7

h = 14.3 cm

h ≈ 115 cm

The approximate height of the ball from where it is dropped will be 115 cm. Then the correct option is C.

More about the Algebra link is given below.

https://brainly.com/question/953809

#SPJ2

Answer:

|1|

Step-by-step explanation:

Because absolute value measures the positive distance from the numeral to 1, the answer could be negative or positive one, which is what the graph shows. So, |1| is the answer.

Answer: C. 3

Step-by-step explanation:

Using the trapezoid midsegment theorem,

[tex]\frac{4x+8x+3}{2}=4x+7.5\\\\\frac{12x+3}{2}=4x+7.5\\\\12x+3=8x+15\\\\4x+3=15\\\\4x=12\\\\x=3[/tex]

Answer:

Probably  c:  f(x) = y + 3

Step-by-step explanation:

See attached worksheet

Given the polynomial Q(x)=4x^3-3x+1,

P(x) = 8x^3 - 6x + 2

Generally, To find P(x), we can start by substituting

P(x) = 2*(Q(x) + P(x)) into the equation:

P(x) = 2*(Q(x) + P(x))

This simplifies to:

P(x) = 2*(4x^3 - 3x + 1 + P(x))

Expanding and rearranging the equation gives:

P(x) = 8x^3 - 6x + 2 + 2P(x)

Subtracting 2P(x) from both sides of the equation gives:

P(x) - 2P(x) = 8x^3 - 6x + 2

This simplifies to:

-P(x) = 8x^3 - 6x + 2

Adding P(x) to both sides of the equation gives:

0 = 8x^3 - 6x + 2 + P(x)

Therefore, the polynomial P(x) that satisfies the equation

P(x) = 2*(Q(x) + P(x)) is:

P(x) = 8x^3 - 6x + 2

Read more about polynomial

https://brainly.com/question/11536910

#SPJ1

There are 22 different types of functions based on range, element, equation, and domain.

Based on the range it includes Modulus Function, rational function, signum function, even and odd functions, periodic functions, greatest integer function, inverse function, and composite functions. On the basis of elements, it includes One One function, many one functions, onto function, one one and onto function, into function, and constant function. On the basis of the equation, it includes the identity function, linear function, quadratic function, cubic function, and polynomial functions. On the basis of the domain, it has algebraic functions, trigonometric functions, and logarithmic functions.

Learn more about functions here:

https://brainly.com/question/12431044

#SPJ4

Answer:

b.

y = 3x + 11, y = 3x + 15

Step-by-step explanation:

Both lines have the same slope, so they are parallel.

Answer:

[tex]-\frac{1}{64}[/tex]

Step-by-step explanation:

We have:

[tex][( \frac{1}{15} - \frac{2}{5}) * (-\frac{3}{4})^{3}] / (-9)[/tex]

Now, we will multiply the second fraction in the first parentheses by [tex]\frac{3}{3}[/tex] so we can subtract it from the [tex]\frac{1}{15}[/tex]. Then, we will multiply all of the [tex]\frac{3}{4}[/tex]'s. This gives us:

[tex][( \frac{1}{15} - \frac{2}{5} * \frac{3}{3} ) * (-\frac{3}{4} * -\frac{3}{4} * -\frac{3}{4})] / (-9)[/tex]

Which simplifies to:

[tex][( \frac{1}{15} - \frac{6}{15} ) * (-\frac{27}{64})] / (-9)[/tex]

Simplifying:

[tex][(-\frac{5}{15} ) * (-\frac{27}{64})] / (-9)[/tex]

Multiplying in our brackets gives us:

[tex]\frac{9}{64} / (-9)[/tex]

Now, using the rule of KCF (Keep, Change, Flip), we will keep our first fraction, change our division sign to a multiplication sign, and make the last number its reciprocal. This gives us:

[tex]\frac{9}{64} * -\frac{1}{9} = -\frac{1}{64}[/tex]

So, the equation simplified is [tex]-\frac{1}{64}[/tex].

Hope this helped!

Answer:

Step-by-step explanation:

substitute p for 8, because p=8

question 1 :    8+4=12    ----Yes

question 2: 8x8 =64-------Yes

question 3  5x8=35, not 8----No

question 4 2+8=10, not 12----No

Answer: a = 9

Step-by-step explanation:

The given figure formed is a rectangle.

Area of given region (Yellow region) = 24 [tex]unit^{2}[/tex]

Length (l) = 6-2 = 4 units

Breadth (b) = a-3 units

Area = l×b

24 = 4 x (a-3)

6 = a-3

a = 9 units

85.41  cubic inches of the treasure chest is taken up by the coins

a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.

Remember that the volume of a cylinder is given by:

volume = (height)×pi×(radius)²

Where pi = 3.14

Then here the volume of each coin is:

V = (0.0625)(3.14)(1.6)²

= 0.5024 in³

And there are 170 coins, so the total volume is:

170×0.5024

85.408 in³

85.41 in³

Hence, 85.41  cubic inches of the treasure chest is taken up by the coins

To learn more on Three dimensional figure click:

https://brainly.com/question/2400003

#SPJ1

Answer:

c or 85.41

Step-by-step explanation: its simple

Therefore , the solution of the given problem of function comes out to be the function f(x) = x³ + 2x² + 7x - 11  = -1 and g(x) = 3f(x) = -3

The subject of mathematics includes quantities and their variations, equations and related structures, shapes and their locations, and places where they can be found. The term "function" refers to the relationship between a set of inputs, each of which has an associated output. A connection between inputs and outputs in which each input leads to a single, distinct result is known as a function. Each function is given a domain and a codomain, or scope.

Here,

Given:

we have been provided with -

f(x) = x³ + 2x² + 7x - 11  

so, x = 1

f(x) = 1 +2 +7 -11= -1

g(x) = 3f(x) = -3

Therefore , the solution of the given problem of function comes out to be the function f(x) = x³ + 2x² + 7x - 11  = -1 and g(x) = 3f(x) = -3

To know more about function visit:

brainly.com/question/28193995

#SPJ1

To reduce your department by 15%, you would need to let go of 33 workers.

Reducing a department by 15% means that 15% of the current workforce in that department will be let go. To calculate this, you first need to determine the percentage of the total workforce that your department represents. In this case, your department has 220 workers out of 512 workers in the whole company, which represents 43% of the total workforce.

Then, you can calculate the number of workers that need to be let go by multiplying the total number of workers in your department by the percentage that needs to be cut. In this case, that would be

220 x 0.15 = 33 workers

This means that 33 out of the 220 workers in your department would need to be let go in order to achieve a 15% reduction.

To know more on percentage

https://brainly.com/question/29763752

#SPJ4

Assuming an isosceles right triangle whose legs measure 6 is continuously rotated about one of its legs to form a three-dimensional object, the three-dimensional object is a: D. cone with a diameter of 12.

In Geometry, there are five (5) major types of triangle based on the length of their sides (side lengths) and angles, and these include the following;

In Mathematics, a right angle can be defined as a type of angle that is formed by the intersection of two (2) straight lines at 90 degrees (90°).

Generally speaking, the resulting three-dimensional (3-D) geometric object that is formed when a right-angled triangle is continuously rotated about a leg would be a cone. Additionally, the radius of this cone would be equal to 6 because the base of the right-angled triangle is 6.

Therefore, the diameter of this cone can be calculated as follows;

Diameter of cone = 2 × radius of cone

Diameter of cone = 2 × 6

Diameter of cone = 12 units.

Read more on right angle here: brainly.com/question/28453423

#SPJ1

Complete Question:

An isosceles right triangle whose legs measure 6 is continuously rotated about one of its legs to form a three-dimensional object. The three-dimensional object is a

answer choices

cylinder with a diameter of 6

cylinder with a diameter of 12

cone with a diameter of 6

cone with a diameter of 12

The hypotenuse side of the right triangle is 7 units.

The value of x in the triangle is 5.92 units.

A right triangle is a triangle with one of its angles as 90 degrees. The sum of angles in a triangle is 180 degrees.

The side of a right triangle can be found using Pythagoras's theorem as follows:

using Pythagoras's theorem,

c² = a² + b²

where

Therefore,

hypotenuse = 7

Let's find x.

7² - (√14)² = x²

49 - 14 = x²

x² = 35

square root both sides

x = √35

x = 5.9160797831

x = 5.92 units

learn more on right triangle here: https://brainly.com/question/28523734

#SPJ1