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Activity
A submarine is at a depth of 100 feet below sea level. Then it starts to dive at a rate of 50 feet per minute. Use this information to answer the following questions.

Question 1
Part A
For this situation, what is the independent variable (include units)?

Part B
What is the dependent variable (include units)?

Part C
What is the slope of the line that models this situation?

Part D
What is the y-intercept of the line that models this situation?

Question 2
Write the equation of the line that models the situation using the slope and y-intercept found in parts C and D of question 1.

Answer:

151, 29, 151

Step-by-step explanation:

[tex]m\angle 2=29^{\circ}[/tex] (vertical angles)

[tex]m\angle 1=m\angle 3=151^{\circ}[/tex] (linear pair)

Answer:

[tex]m \angle 1= \boxed{151}\;^{\circ}\\\\m \angle 2= \boxed{29}\;^{\circ}\\\\m \angle 3= \boxed{151}\;^{\circ}[/tex]

Step-by-step explanation:

Angles on a straight line sum to 180°.

⇒ m∠3 + m∠4 = 180°

⇒ m∠3 + 29° = 180°

⇒ m∠3 = 151°

Vertical Angle Theorem

When two straight lines intersect, the opposite vertical angles are congruent.

Applying the Vertical Angle Theorem:

Answer:

1. Slope= 2

2. [tex] \frac{b - 2}{4 - 2} = 2[/tex] or [tex] \frac{8 - 2}{a - 2} = 2[/tex]

3. a= 5

4. b= 6

Step-by-step explanation:

The slope of a straight line between any two points of the line would be the same. This means that calculating the slope of the line using point (2, 2) and (6, 10) would give us the same slope value when calculating with points (4, b) and (6, 10) for example.

Formula

[tex]\boxed{\text{slope} = \frac{y_1 - y_2}{x_1 - x_2} }[/tex]

Q1. Since we two pairs of known coordinates, let's make use of them in the slope calculation.

Slope of line

[tex] = \frac{10 - 2}{6 - 2} [/tex]

[tex] = \frac{8}{4} [/tex]

= 2

Q2-4. Since in the subsequent parts we will eventually have to find the value of a and b, let's form an equation for each of them.

Slope between (2, 2) and (4, b)= slope between (2, 2) and (6, 10)

[tex] \frac{b - 2}{4 - 2} = 2[/tex]

[tex] \frac{b - 2}{2} = 2[/tex]

Multiply both sides by 2:

b -2= 2(2)

b -2= 4

b= 4 +2

b= 6

Using (2, 2) and (a, 8):

[tex] \frac{8 - 2}{a - 2} = 2[/tex]

Multiply both sides by (a -2):

6= 2(a -2)

Expand:

6= 2a -4

Add 4 to both sides:

2a= 10

Divide both sides by 2:

a= 10 ÷2

a= 5

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Answer:

C) infinite solutions

Step-by-step explanation: hope this helps have an amazing rest of ur day <3 ^ ^ :>

Any value of y makes the equation true. All real numbers Interval Notation: (−∞,∞)

The equation given has no solution because they will cancel out each other.

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

Given the equation is;

0.3(6y + 15) = 1.8y + 4.5.

Solving for the variable y;

0.3(6y + 15) = 1.8y + 4.5

Open the bracket;

1.8y + 4.5 = 1.8y + 4.5

Here we can conclude that the equation given has no solution because they will cancel out each other.

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The value of angle T is 65°

In this question, we have been given sin 25=cos T

We need to find the value of T.

Assuming angle in degrees the value of trigonometric function would be,

sin 25 =  0.4226

As we have been given sin 25=cos T,

cos T =  0.4226

So angle T would be,

⇒ T = arccos( 0.4226)

⇒ T = cos^(-1)( 0.4226)

⇒ T = 65°

Therefore, the value of angle T is 65°

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the Algebraic representation of the expression "product of 2 and the cube of a number" is 2x³

Algebra is the system for computation using letters or other symbols to represent numbers, with rules for manipulating these symbols.

The product of 2 and the cube of a number

So,

product of 2 and the cube of a number

= 2 × x³

= 2x³

For instance, if x = 2

2x³

= 2×(2)³

= 2 × (2 × 2 × 2)

= 2 × 8

= 16

Therefore, the expression "product of 2 and the cube of a number" can be written as 2x³

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The length of the course is 480 m.

Length is used to measure distance. According to the International System of Quantities, length has the dimension of distance. In most measurement systems, length is represented by a base unit from which all other units are derived. The International System of Units (SI) system's fundamental unit of length is the meter.

From the given figure we can infer that W is the mid-point of AB. Therefore we know that AW = WB

Now the distance is given by

5x -110 = 2x +100

or, 5x - 2x = 100 + 110

or, 3x = 210

or, x = 70

Therefore total length = 5x -110 + 2x +100 = 7x - 10 = 490 - 10 = 480 m

Therefore the length is 480 m.

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Answer:

11.4 pounds

Step-by-step explanation:

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{3c + 6d + 3d}\\\large\text{COMBINE the LIKE TERMS}\\\mathsf{= (3c) + (6d + 3d)}\\\mathsf{= 3c + 6d + 3d}\\\mathsf{= 3c + 9d}\\\huge\text{Therefore, your answer should be: \boxed{\mathsf{3c + 9d}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

New function that is a horizontal stretch of F(x)=[tex](x+2)^{3} + 5[/tex] is F([tex]\frac{x}{k}[/tex])=[tex](\frac{x}{k} +2)^{3} + 5[/tex]

The point (x, y) on the graph of f(x) is changed to the point (x/k, y) on the graph of g when the graph is stretched or contracted horizontally by a factor of 1/k (x).Only when the input value is also increased by a, can a graph be stretched horizontally by a factor of 1/a. The x-coordinates should be multiplied by a once f(x) has been stretched horizontally to f(ax). Keep the y-intercepts where they are. The resulting function might have a different domain, but it will have the same range. If a point (m, n) is stretched horizontally, it becomes (am, n).

F(x)=[tex](x+2)^{3} + 5[/tex]

F([tex]\frac{x}{k}[/tex])=[tex](\frac{x}{k} +2)^{3} + 5[/tex]ch visit :
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The sine of the angle based on the information about the cosine is D. ✓91 / 10.

It should be noted that cos is calculated as:

= adjacent / hypothenuse.

This was given as 3/10.

It should be noted that sine = Opposite / Hypothenuse

The opposite will be:

Opp² + Adj² = Hyp²

Opp² + 3² = 10²

Opp² + 9 = 100

Opp² = 100 - 9

Opp² = 91

Opp = ✓91

Therefore, the sine of the angle will be ✓91 / 10

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Answer:

-5

Step-by-step explanation:

[tex]-3t+4=19 \\ \\ -3t=15 \\ \\ t=-5[/tex]

When the person picks 170 beads, the number of red beads will be 57.

It should be noted that based on the information, the following can be deduced:

Number of red beads = 139

Number of yellow beads = 167

Number of green beads = 107

Total number of beads = 139 + 167 + 107 = 413

Therefore, when one selects 170 beads, the number of red beads will be:

= Number of red beads / Total number × 170

= 139 / 413 × 170

= 57

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Answer:

Slope = -1

Step-by-step explanation:

m = second y - first y / second x - first x

second y = 1

first y = 9

second x = 9

first x = 1

1 - 9 = -8

9 - 8 = 8

-8/8 = -1

Find the slope of a line.

We mark the points: (x₁ = 1, y₁=9) and (x₂ = 8, y₂ = 1)

We have that the formula is:

          [tex]\boldsymbol{\sf{m=\dfrac{Y_{2}-Y_{1} }{X_{2}-X_{1}} }}[/tex]

Now we apply the formula and solve:

                    [tex]\boldsymbol{\sf{m=\dfrac{1-9}{8-1} =\dfrac{-8}{7} }}[/tex]

                   [tex]\boldsymbol{\sf{m=\dfrac{-8}{7} }}[/tex]

The slope of the line through (1, 9) and (8, 1) is -8/7.

Answer:

7560 meters

Step-by-step explanation:

42 meters a second -> 2520 meters a minute -> 7560 meters for 3 minutes

Answer:

The airplane will be 7560 meters after three minutes of flying.

Step-by-step explanation:

one minute= sixty seconds

42*1800=7560

3*60=1800

Not sure if I did the math right but I'm positive I got the right answer.

Answer:

Only 6 match your answer choices.

Step-by-step explanation:

Solve for x:

x^3 - 5 x^2 - 8 x + 12 = 0

The left-hand side factors into a product with three terms:

(x - 6) (x - 1) (x + 2) = 0

Split into three equations:

x - 6 = 0 or x - 1 = 0 or x + 2 = 0

Add 6 to both sides:

x = 6 or x - 1 = 0 or x + 2 = 0

Add 1 to both sides:

x = 6 or x = 1 or x + 2 = 0

Subtract 2 from both sides:

Answer: x = 6 or x = 1 or x = -2

Twenty-four equals the sum of 10.5 and the quotient of a number and 4.5 is given by 24 = 10.5 + x/4.5

An expression can be defined as a mathematical equation which is used to show the relationship existing between two or more variables and numerical quantities.

Quotient can be defined as a mathematical expression that is simply used to represent the division of a number by another number. As a general rule, the smaller the divisor (denominator) of an expression, the larger would be the quotient.

In order to translate this word problem, we would assign a variable to the unknown number and then translate the word problem into algebraic equation as follows:

Let n represent the unknown number.

Translating the word problem into an algebraic equation, we have;

24 = 10.5 + x/4.5

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Answer:

14.077 appr. 14.1

Step-by-step explanation:

183/13=

18÷13=1 remainder 5

53÷13=4 remainder 1

therefore the answer is 14.1

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After 2.57 hours, the distance between Steve and Elsie will be 25 miles.

So, let t (hours) represent the amount of time Elsie needs to travel before they are 25 miles apart.

Steve takes longer because he is 2 hours earlier, so his time is t + 2.

So, according to the formula the distance between Steve and Elsie will be:

Solve for t as follows:

[tex]\begin{aligned}&(2(t+2))^2+(2.5 t)^2=25^2=625 \\&4(t+2)^2+6.25 t^2=625 \\&4\left(t^2+4 t+4\right)+6.25 t^2=625 \\&10.25 t^2+16 t-609=0 \\&t=\frac{-b \pm \sqrt{t^2-4 a x}}{2 a} \\&t=\frac{-16 \pm \sqrt{(16)^2-4 *(10.25) *(-109)}}{2 *(10.25)} \\&t=\frac{-16 \pm 68.74}{20.5}\end{aligned}[/tex]

So, t = 2.57 or t = -4.13.

Therefore, after 2.57 hours, the distance between Steve and Elsie will be 25 miles.

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The correct question is given below:

Steve and Elsie are camping in the desert, but have decided to part ways. Steve heads north, at 8 AM, and walks steadily at 2 miles per hour. Elsie sleeps in and starts walking west at 2.5 miles per hour starting at 10 AM. When will the distance between them be 25 miles?

The distance between the two points is 13 unit.

A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the display style for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a singular triangle and a singular plane (i.e. a two-dimensional Euclidean space). In other words, every triangle is contained in a plane, and there is only one plane that contains that triangle. All triangles are enclosed in a single plane if all of geometry is the Euclidean plane, however this is no longer true in higher-dimensional Euclidean spaces. Except when otherwise specified, this article discusses triangles in Euclidean geometry, namely the Euclidean plane.

Given that,

A right triangle can be drawn using the grid lines for legs and the line segment between the two points as the hypotenuse. You can count grid squares or subtract coordinates to find the vertical leg is 12 units and the horizontal leg is 5 units. The Pythagorean theorem tells you the length of the hypotenuse (distance between the points) is d² = 12² +5² = 144 +25 = 169

d = √169 = 13

The distance between the two points is 13 unit

This set of dimensions, {5, 12, 13}, is one of several "Pythagorean triples" that often show up in math problems. Other common triples are {3, 4, 5}, {7, 24, 25}, {8, 15, 17}, {9, 40, 41}, and multiples of these.

Therefore, distance between the two points is 13 unit.

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Answer:

x = -4

Step-by-step explanation:

3(x-5) becomes 3x-15

5x-(3-x) becomes 6x-3

3x - 15 = 6x - 3

    + 15        + 15

3x = 6x + 12

-6x  -6x

-3x = 12

    divide -3 on both sides

X = - 4

Answer:

x = -4.

Step-by-step explanation:

3(x-5) = 5x-(3-x)

3x - 15 = 5x - 3 + x

3x - 5x - x = -3 + 15

-3x = 12

x = -4.

The speed of the cyclist and the walker is 25 miles per hour and 16.67 miles per hour, respectively.

Speed describes how fast an object moves. It can be measured as distance over time.

speed = distance / time

Let x be the speed of the walker and 1.5x is the speed of the cyclist.

If they start "moving simultaneously in the same direction" from the same point and, after 1.5 hours, the distance between them is 12.5 miles, then

distance traveled by cyclist = distance traveled by the walker + 12.5 miles

cyclist's speed(time) = walker's speed(time) + 12.5

1.5x(1.5 hours) = x(1.5 hours) + 12.5

2.25x - 1.5x = 12.5

x = 50/3

walker's speed = 50/3 or 16.67miles per hour

cyclist's speed = 1.5(50/3)

cyclist's speed = 25 miles per hour

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Answer:

p=+/- 5/3 or

p =+/- 1 2/3  or

p = +/- 1.66666667

Step-by-step explanation:

Equation

What you have is a quadratic. I am taking the 9 to be a 9 and not a q. So the equation, as I read it, is

9p^2 - 9 = 16                   Add 9 to both sides of the equation

Solution

-9+9 + 9p^2 = 16 +9        Combine

9p^2 = 25                        Divide by 9

9 p^2 /9 = 25/9               Combine

√p^2 = √(25/9)               Take the Square Root of both sides.

p = +/- 5/3

Gil is out purchasing CDs and books. He spends $32 on 4 books but not any CDs. A standard form equation y=-8n and x=0.

Given that,

Gil is out purchasing CDs and books. He spends $32 on 4 books but not any CDs.

We have to create a standard form equation to show the connection between the price of a book (y) and the price of a CD (x).

The equations in standard form for Gil's change in money after purchasing a book (y) and his change in money after selling a CD (x).

Gil spends $32 on 4 books.

4 books = $32

1 book = $8

If n is the total number of books bought, the change in currency equals

y=-8n.

Here, the negative sign stands for a decline in currency. Here, a slope of -8 indicates that after purchasing each book, the money declined by $8.

There are no CDs so x=0.

Therefore, y=-8n and x=0.

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Answer:

Your answer is [tex]70[/tex].

Step-by-step explanation:

[tex]10[/tex] ÷ [tex]\frac{1}{7}[/tex] [tex]= 70[/tex]

The volume of the Oblique pyramid is 19 [tex]ft^{2}[/tex]

We know, the volume of a pyramid is [tex]\frac{1}{2}[/tex] × B × h

where B is the area of the base and h is the height of the pyramid.

Given:  The pentagonal base has an edge length of 2.16 ft and an area of 8 [tex]ft^{2}[/tex] and angle ACB measures 30°.

Consider triangle ACB

tan30° = [tex]\frac{AB}{CB}[/tex]

[tex]\frac{1}{\sqrt{3} }[/tex] = [tex]\frac{AB}{7\sqrt{3} }[/tex]

AB = 0.58 × [tex]7\sqrt{3}[/tex]

AB = 0.58 × 12.12

AB = 7.03

Now, the volume of the oblique pyramid will be

V = [tex]\frac{1}{2}[/tex] × 8 × 7.03

V = 18.75

V ≈ 19 [tex]ft^{2}[/tex]

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Answer:19

Step-by-step explanation: