Jenny is scuba diving on her trip to Hawaii she descends 3 feet below sea level. Then she descends the same distance 6 more times. What is Jenny’s final elevation?

Due to length restrictions, we kindly invite to read the explanation of this question for further details about the table and graph of the function.

In this problem we must plot the graph of a function on a Cartesian plane. The procedure is summarized below:

After following the procedure, we have the following result:

Input, x             x + 4                Output, y             (x, y)

   - 2               - 2 + 4                     2                    (- 2, 2)

     0                 0 + 4                     4                     (0, 4)

     2                 2 + 4                     6                     (2, 6)

     4                 4 + 4                     8                      (4, 8)

     6                 6 + 4                    10                      (6, 10)

     8                 8 + 4                    12                      (8, 12)

Lastly, we plot the graph of the linear function.

To learn more on functions: https://brainly.com/question/12431044

#SPJ1

Using the concept of ratio, the rate at which questions were answered correctly is 0.867 which is option B

Rate can be defined as comparing two or more ratio with a standard value.

The rate of correct answer can be calculated using the ratio between the number of correct answers to numbers of questions answered.

The rate is given as;

rate = 65 / 75

rate = 0.867

The rate of correct answers is 0.867

Learn more on rates here;

https://brainly.com/question/843074

#SPJ1

Answer:

2

Step-by-step explanation:

Answer:

The tree is 12.5ft Step-by-step explanation: 1.  TREE'S HEIGHT over TREE'S SHADOW equals WOMAN'S HEIGHT over WOMAN'S SHADOW

2.  TREE'S HEIGHT over WOMAN'S HEIGHT equals TREE'S SHADOW over WOMAN'S SHADOW

or some other ways as long as you pair them up by 'height', or pair them up by

'shadow'.  {But don't get them criss-crossed)

Let TREE's HEIGHT = t.

A tree casts a shadow 7.5 ft long

TREE'S SHADOW = 7.5

at the same time that

a woman 5 ft tall

WOMAN'S HEIGHT = 5

casts a shadow 3 ft long.

WOMAN'S SHADOW = 3

So if you use

1.  TREE'S HEIGHT over TREE'S SHADOW equals WOMAN'S HEIGHT over WOMAN'S SHADOW

cross-multiply:

3t = 37.5

 t = 12.5

or if you use

2.cross-multiply

3t = 37.5

 t = 12.5

Either way, the tree is 12.5 feet tall.    

Answer: I got 12.5 too

Step-by-step explanation:

Answer:

see below

Step-by-step explanation:

Modified problem

(x)^2-3/x

Step 1: Find f(x+h)

(x+h)^2-3/(x+h)

x^2 +2hx + h^2 -3/(x+h)

Step 2: Find f(x + h) − f(x)

x^2 +2hx + h^2 -3/(x+h) - ( x^2-3/x)

Distribute the minus sign

x^2 +2hx + h^2 -3/(x+h) -  x^2+3/x

Combine like terms and get a common denominator

2hx + h^2  -3x/(x(x+h)) +3(x+h)/(x(x+h)

2hx + h^2  +3h/(x(x+h))

Step 3: Find (f(x + h) − f(x))/h

(2hx + h^2+3h/(x(x+h)) )/h

2hx/h  + h^2/h+3h/(x(x+h)) /h

2x +h +3/(x(x+h))

Step 4: Find lim  h→0  (f(x + h) − f(x))/h

2x+0 +3/(x(x+0))

2x +3/x^2

the car is approximately 22.4 meters away from the tower.

What is Trigonometric Functions?

Trigonometry uses six fundamental trigonometric operations. Trigonometric ratios describe these operations. The sine function, cosine function, secant function, co-secant function, tangent function, and co-tangent function are the six fundamental trigonometric functions. The ratio of sides of a right-angled triangle is the basis for trigonometric functions and identities. Using trigonometric formulas, the sine, cosine, tangent, secant, and cotangent values are calculated for the perpendicular side, hypotenuse, and base of a right triangle.

we can write:

tan(55 degrees) = 32 / d

To solve for "d", we can rearrange the equation:

d = 32 / tan(55 degrees)

Using a calculator, we can evaluate the tangent of 55 degrees:

tan(55 degrees) = 1.428

d = 22.4 meters

Therefore, the car is approximately 22.4 meters away from the tower.

Learn more about  Trigonometric Functions, by the following link.

brainly.com/question/24349828

#SPJ1

Answer:

10

Step-by-step explanation:

AB+BC=AC

2x+32+6=x+27

x=_11

AB=2(_11)+32=10

Answer: To determine the unit price, we divide the price by the number of ounces.

For the 1.5-ounce bag:

Unit price = $0.65 / 1.5 ounces = $0.433 per ounce

For the 5.75-ounce bag:

Unit price = $1.30 / 5.75 ounces = $0.226 per ounce

For the 2-pack of 5.75-ounce bags:

Total ounces = 2 x 5.75 = 11.5 ounces

Total price = $2.45

Unit price = $2.45 / 11.5 ounces = $0.213 per ounce

Therefore, the 2-pack of 5.75-ounce bags has the lowest unit price and is the best buy based on price alone.

Step-by-step explanation:

Answer:

3n + 1 = 7n - 5

1 + 5 = 7n - 3n

6 = 4n

3/2 = n

2[x + 3(x - 1)] = 18

2[x + 3x - 3] = 18

2(4x - 3) = 18

8x - 6 = 18

8x = 12

x = 12/8

x = 3/2

6(y + 2) - 4 = -10

6y + 12 - 4 = -10

6y = -10 - 8

6y = -18

y = -3

2x² = 50

x² = 50/2

x = √25

x = 5

5 + 2(k + 4) = 5(k - 3) + 10

5 + 2k + 8 = 5k - 15 + 10

2k - 5k = -5 - 13

-3k = -18

k = 6

6 + 2x(x - 3) = 2x²

6 + 2x² - 6x = 2x²

-6x = 2x² - 2x² - 6

x = 1

2/3x - 18 = x/6

12(2/3x - 18 = x/6)

8x - 216 = 2x

8x - 2x = 216

6x = 216

x = 36

x - 2/3 = 2x + 1/4

12(x - 2/3 = 2x + 1/4)

4x - 8 = 6x + 3

4x - 6x = 8 + 3

2x = 11

x = 11/2

-TheUnknownScientist 72

In this scenario, the independent variable's scale of measurement is Ordinal. So the answer is option is B.

The independent variable in this study is the type of feedback given to the pilots during the simulated emergency landing procedure. They are randomly assigned to either the visual condition or the visual and auditory condition.

The scale of measurement for this variable is ordinal because it represents ordered categories. The visual condition represents one level of the variable, while the visual and auditory condition represents another level.

However, there is no inherent numerical value associated with these categories. It is not possible to determine the magnitude of the difference between the two conditions.

Therefore, the scale of measurement for the independent variable in this scenario is ordinal.

Learn more about Ordinal:

https://brainly.com/question/30648205

#SPJ1

The roots of the given quadratic equation are 5 and -4

Quadratics are the polynomial equation which has the highest degree of 2. Also, called quadratic equations.

Given is an equation 3x²-13x-10 = 0, we need to solve by using completing the square method,

The given equation is =

3x²-13x-10 = 0

3(x²-13x/3-10/3) = 0

3(x²-2x·13x/6-10/3) = 0

Adding and subtracting (13/6)²

3(x²-2x·13x/6+(13/6)²-(13/6)²-10/3) = 0

3[(x-13/6)²-169/36-10/3] = 0

3[(x-13/6)²-289/36] = 0

(x-13/6)²-289/36 = 0

(x-13/6)² = 289/36

Taking roots,

x-13/6 = ±17/6

x = 17/6+13/6

x = 5

Or,

x = -17/6+13/6

x = -4

Hence, the roots of the given quadratic equation are 5 and -4

Learn more about quadratic equation, click;

https://brainly.com/question/30098550

#SPJ9

Answer:

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

Collinear points are the points on the same line.

There are two lines in the diagram.

The collinear points:

The points that are collinear are  D,G and E  and another set of points which are collinear are L,G and J.

The points which lie on the same straight line are known as collinear points.

Similarly, if three or more number of points are collinear then they form a straight line.

If we observe the figure, the points D,G and E are collinear points as they are on same line.

Similarly the points L, G and H are in the straight line which makes them collinear.

Therefore , the points L,G and J are collinear points.

Hence, the points that are collinear are  D,G and E and another set of points which are collinear are L,G and J

To learn more on Coordinate Geometry click:

brainly.com/question/27326241

#SPJ1

Answer:

Option 2.

Step-by-step explanation:

Find the domain by finding where the function is defined. The range is the set of values that correspond with the domain.

Domain: \((- \infty} ,0)\) ∪ \((0, \infty} )\)

Range: \((- \infty} ,0)\)∪\((0, \infty} )\)

The surface area of the pyramid is 74.25 square meters.

Surface area is the total area that the surface of an object occupies. It is the sum of the areas of all the faces, sides, and curved surfaces of an object. Surface area is usually measured in square units, such as square meters, square feet, or square centimeters.

A pyramid is a polyhedron with a polygonal base and triangular faces that meet at a common vertex (known as the apex). Pyramids are named according to the shape of their base.

In the given question,

The area of the base is simply the area of a square, which is:

Area of base = length x width = 4.5m x 4.5m = 20.25 square meters

To find the area of each triangular face, we first need to find the length of the slant height (the height of the triangle).

We can use the Pythagorean theorem to do this:

h²= (1/2 x base)² + height²

h² = (1/2 x 4.5)² + 6²

h² = 2.25 + 36

h² = 38.25

h = √38.25

h = 6.18 meters (rounded to two decimal places)

Now that we know the slant height, we can find the area of each triangular face:

Area of one triangular face = (1/2 x base x height) = (1/2 x 4.5 x 6) = 13.5 square meters

Since there are four triangular faces on a square pyramid, we need to multiply this by 4 to find the total area of the triangular faces:

Total area of triangular faces = 4 x 13.5 = 54 square meters

Finally, we can find the surface area of the pyramid by adding the area of the base and the area of the triangular faces:

Surface area = Area of base + Total area of triangular faces

Surface area = 20.25 + 54

Surface area = 74.25 square meters

Therefore, the surface area of the pyramid is 74.25 square meters.

To know more about Surface area, visit:

https://brainly.com/question/29298005

#SPJ1

Answer:

A linear function would be the best type of equation to model this situation. The total cost of renting the truck increases linearly with the number of miles driven. The initial charge of $60 can be considered as the y-intercept of the linear function, and the additional fee per mile driven can be considered as the slope of the line. Therefore, the equation that models this situation can be written in the form y = mx + b, where y is the total cost of renting the truck, x is the number of miles driven, m is the additional fee per mile driven (the slope of the line), and b is the initial charge of $60 (the y-intercept).

Answer:

A linear function would be the best type of equation to model this function.

Step-by-step explanation:

The total cost of renting the truck is composed of two parts:

The initial charge of $60 is the fixed charge, and the additional fee is the variable charge that is proportional to the number of miles driven.

Let "x" be the number of miles driven and "y" be the total cost of the rental (in dollars), then the linear equation is:

y = mx + 60

where "m" is the additional fee (in dollars) per mile driven.

Therefore, a linear function, in the form y = mx + b, where m represents the slope or rate of change, and b represents the initial fixed charge, is the most appropriate function to model this situation.

Answer:

  a) maximum; the parabola opens downward

  b) positive; it must lie above the x-axis

  c) x = 1.5

Step-by-step explanation:

The x-intercepts of a function are the points where the graph of the function crosses the x-axis. The y-values there are zero.

The "differences" of a function are related to the average slope between adjacent points. Second differences are related to the rate of change of the slope of the function. When second differences are negative, as here, the slope of the quadratic function is decreasing, becoming more negative. We say the curvature of the function is negatve, and that it opens downward.

__

If the graph of the parabola opens downward, and it crosses the x-axis, it must have a maximum that is a positive value of y.

__

The graph of a parabola is symmetrical about its vertex. That means points on the same horizontal line are the same distance from the line of symmetry, which must go through the vertex. The x-coordinate of the vertex will be the x-coordinate of the midpoint between the two x-intercepts:

  x = (-2 +5)/2 = 3/2

The x-coordinate of the vertex is x = 1.5.

______

Additional comment

The attachment shows a table with three evenly-spaced points on the curve. The calculations show first differences (d1) and second differences (d2). You can see that the sign of the second diffference is negative, in agreement with the given conditions.

Answer:

The slope of a line is

\( \frac{y2 - y1}{x2 - x1} \)

Get 2 points off each line

(x1, y1)

(x2, y2)

And sub them into the formula.

The y intercept is where the line cuts the y axis (the vertical line)

From what I can make out the y intercept for the first part in question 12 is (0,-2) and for the third part is (0,0) but I can't see the second one.

It might help if you took a clearer photograph I'm so sorry but I can't really see it.

Let the length of the garden be x and the width be y.

It is given that the width of a rectangular garden is 11 feet longer than 3 times its length so it follows:

It is also given that the garden's perimeter is 150 feet so it follows:

Add equation (i) and (ii) to get:

Substitute x=16 in (ii) to get:

Therefore the dimensions are:

Length=16 feet

Width=59 feet.

Answer:

The slant height of the cone affected is two times the slant height of original cone

Step-by-step explanation:

we know that

If the height and base radius of a cone are increased by a factor of  to create a similar cone

then

the scale factor is equal to  

therefore

the slant height of the cone affected is equal to the slant height of the original cone multiplied by the scale factor

Find the slant height of the original cone

Let

l-----> slant height of original cone

la-----> slant height of the cone affected

Applying the Pythagoras theorem

so

The slant height of the cone affected is two times the slant height of original cone

(I GOT THIS FROM SOMEONE ELSES ANSWER IN 2017 SO I HOPE THIS HELPS)

The slant height of the larger cone is double the slant height of the smaller cone.

Option B is the correct answer.

It is a shape of a Christmas tree where there is a base of radius r and a top point called the apex.

The volume of a cone is 1/3 πr²h

We have,

The slant height of the cone is affected by a factor of 2.

When the height and base radius of a cone are multiplied by 2, the dimensions of the new cone are doubled.

Therefore,

The slant height of the larger cone is double the slant height of the smaller cone.

Learn more about cones here:

https://brainly.com/question/13798146

#SPJ5

The number of years of employment is A. Nikhil has been with the company for 16 years, while Mae has been there for 4 years.

The system of equations given is:

x = 4y

x = 8 + 2y

You can solve the system by setting the two expressions for x equal to each other:

4y = 8 + 2y

2y = 8

2y / 2 = 8 / 2

y = 4

Substitute y = 4 into the first equation to solve for x:

x = 4 x 4

= 16

So, Mae (y) has been at the company for 4 years and Nikhil (x) has been at the company for 16 years.

Find out more on system of equations at https://brainly.com/question/3978002

#SPJ1

Answer:

a. \( \frac{2}{3} \)

Step-by-step explanation:

The fraction, \( \frac{2}{3} \) is greater than \( \frac{1}{2} \) and less than \( \frac{3}{4} \).

How do we know this? See below how the fractions are compared together.

First, compare \( \frac{2}{3} \) and \( \frac{1}{2} \).

Find a common denominator for both fractions:

Common denominator of 2 and 3 would be 6. Therefore, multiply as follows:

\( \frac{2 \times 2}{3 \times 2} = \frac{4}{6}\) and

\( \frac{1 \times 3}{2 \times 3} = \frac{3}{6} \).

Compare the numerators. Which one is greater?

Form the calculation above:

\( \frac{2}{3} = \frac{4}{6} \) has a numerator of 4.

.

\( \frac{1}{2} = \frac{3}{6} \) has a numerator of 3.

Since 4 is greater than 3, therefore, the fraction, \( \frac{2}{3} \) is greater than \( \frac{1}{2} \).

✍️Compare \( \frac{2}{3} \) and \( \frac{3}{4} \).

Find a common denominator for both fractions

\( \frac{2 \times 4}{3 \times 4} = \frac{8}{12} \) and

\( \frac{3 \times 3}{4 \times 3} = \frac{9}{12} \)

Comparing their numerator, 8 is less than 9, therefore:

\( \frac{2}{3} \) is less than \( \frac{3}{4} \).

✔️We can conclude that:

\( \frac{2}{3} \) is greater than \( \frac{1}{2} \), and less than \( \frac{3}{4} \).

Answer:

Step-by-step explanation:

It is a vertical parabola. The equation of a vertical parabola can be written in the form y = a(x-h)² + k, where a>0 and (h,k) is the vertex.

You can eliminate G and I because the leading coefficient is negative.

The graph isn't marked with units, but both F and H say that the vertex is at (0,-2), so you know that each square on the graph is one unit.

Now look for another clue.

The x-intercepts are at (-1,0) and (1,0). Plug one of the points into F and H.

F: 0 = 2·1² - 2

H: 0 ≠ 1² - 2

So, F represents the graph.

The simple formula or rule that generates the terms of an integer sequence that begins with the given list is given below.

Sequence is the order in which elements, such as numbers, letters, or symbols, follow one another in a specific order. It is a fundamental concept in mathematics and computer science, and is used in many other areas including music, language, and art. In mathematics, it is often used to describe patterns or to represent numerical values. In computer science, it is used to represent data structures, such as lists and arrays.
a. The sequence can be expressed as 3x2^n, where n is the position of the number in the sequence. The next three terms are 127, 162, and 201.

b. The sequence can be expressed as 4n+3, where n is the position of the number in the sequence. The next three terms are 47, 51, and 55.

c. The sequence can be expressed as 2^n+n-1, where n is the position of the number in the sequence. The next three terms are 1111, 10000, and 10011.

d. The sequence can be expressed as the number of times the previous value is repeated, starting with 1. The next three terms are 5, 5, and 8.

e. The sequence can be expressed as 4x3^n, where n is the position of the number in the sequence. The next three terms are 5906, 17718, and 53154.

f. The sequence can be expressed as (n+1)!+(n-1)!+2, where n is the position of the number in the sequence. The next three terms are 27027025, 94594500, and 34459425.

g. The sequence can be expressed as the number of times the previous number is repeated, starting with 1. The next three terms are 0, 0, and 1.

h. The sequence can be expressed as 4^n, where n is the position of the number in the sequence. The next three terms are 4294967296, 17179869184, and 68719476736.

To know more about sequence click-
https://brainly.com/question/7882626
#SPJ4

Complete questions as follows-
For each of these lists of integers, provide a simple formula or rule that generates the terms of an integer sequence that begins with the given list. Assuming that your formula or rule is correct, determine the next three terms of the sequence.
a. 3, 6, 11, 18, 27, 38, 51, 66, 83, 102, . . .
b. 7, 11, 15, 19, 23, 27, 31, 35, 39, 43, . . .
c. 1, 10, 11, 100, 101, 110, 111, 1000, 1001, 1010, 1011, . . .
d. 1, 2, 2, 2, 3, 3, 3, 3, 3, 5, 5, 5, 5, 5, 5, 5, . . .
e. 0, 2, 8, 26, 80,242,728,2186,6560,19682, . . .
f. 1, 3, 15, 105, 945, 10395, 135135, 2027025, 34459425, . . .
g. 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, . . .
h. 2, 4, 16, 256, 65536, 4294967296, . . .

Answer:

I believe that the answer is D.

Step-by-step explanation:

Hope this helps!

The complete sequence is -24, 12, 6, 12, 3, -3.

What is a sequence?

A sequence is an enumerated collection of objects in which repetitions are allowed. Like a set, it contains members (also called elements, or terms).

To find the missing terms in the sequence, we need to identify the pattern or rule that relates to the given terms. We can start by looking at the differences between consecutive terms:

12 - (-24) = 36

6 - 12 = -6

_ - 6 = ?

3 - _ = ?

From the first and second terms, we can see that the difference is 36. From the second and third terms, we can see that the difference is -6. This suggests that the pattern alternates between adding and subtracting 6. Therefore, we can add 6 to 6 to get the missing term:

6 + 6 = 12

Then, we can subtract 6 from 3 to get the last missing term:

3 - 6 = -3

Hence, the complete sequence is:

-24, 12, 6, 12, 3, -3

To know more about sequence visit:

https://brainly.com/question/12246947

#SPJ1

less than zero

Step-by-step explanation:

when the discriminant is less than zero, then it has no real solutions. this can be written as

b²-4ac<0 has no real solutions.

The correct answers are A) 7cm, C) 9cm and D) 12cm

The process of changing a given quantity that is expressed in one unit of measurement to another unit of measurement that is equivalent in value is referred to as conversion of units.

If every 2 cm on a scale drawing is equal to 7 feet in real life, then we can use proportions to find out which lines on the drawing would be greater than 21 feet in real life.

Let x be the length of a line on the scale drawing in centimeters. Then, we can set up the following proportion:

⇒  \(\frac{2cm}{7 feet} = \frac{x cm }{yfeet}\)

where y is the length of the line in real life. Solving for y, we get:

⇒  \(y = \frac{7 feet} {2cm} *x\)  

⇒  \(y = 3.5 x feet\)

If we put x = 2cm (given) then, y = 7 feet

For y = 21 feet, the value of x = 6cm.

Therefore, any line on the scale drawing that is greater than 6cm in length corresponds to a length greater than 21 feet in real life.

So, the lines on the drawing that are greater than 21 feet in real life are:

A) 7cm, C) 9cm, D) 12cm

Therefore, the correct answers are A) 7cm, C) 9cm and D) 12cm

To know more about conversion, visit:
https://brainly.com/question/13016491
#SPJ1

(A) delta h(t) = 32

Step-by-step explanation:

Average rate of change delta h(t) is given by

\(delta \: h(t) = \frac{h(b) - h(a)}{b - a} \)

at t = 0, h(0) = 80

at t = 2, h(2) = -16(4) + 64(2) + 80 = 144

Plugging in the numbers

delta h(t) = (144 - 80)/(2 - 0)

= 32

Answer:

The greatest number of teams is 4, with each having 7 boys and 7 girls. There is a remainder of 7 boys.

Step-by-step explanation:

The standard absolute value graph has been shifted 7 units to the right and 3 units down to get this graph.  

That means we have answer B: f(x) = | x - 7 | - 3

Remember that the left-right shifts are opposite from what they would appear to be in the equation.

  | x - 7 | shifts it right 7 units.

  | x + 7 | shifts it left 7 units.