The water pressure on a submerged object is given by P = 64d, where P is the pressure in pounds per square foot, and d is the depth of the object in feet.
a. solve the formula for d.


b. Find the depth of a submerged object if the pressure is 672 pounds per square foot.

The equation has two solutions [tex]x_{1}[/tex] =  [-4 + 2√13]/3] and

[tex]x_{2}[/tex] = [-4 - 2√13]/3]

Given the question:

(x + 4)^2 = 15 - 2x^2.

To solve the above Equation by using Quadratic Formula:
Solving Steps of Equation:

[tex](x+4)^2 = 15 -2x^2[/tex]

Expand the expression

[tex]x^{2} +8x+16=15-2x^2[/tex]

Move the expression to the left

[tex]x^{2} +8x+16-15+2x^2[/tex] = 0

Collect like terms

[tex]3x^{2} +8x+1=0[/tex]

Use the Quadratic formula:

x = [-b ± √(b2 – 4ac)]/2a

x = [-8 ± √(8^2 – 4x3x1)]/2x 3

Multiply and evaluate :

x = [-8± √(64 – 12)]/6]

Calculate:

x = [-8± 2√13]/6]

Separate the solutions

[tex]x_{1}[/tex] =  [-4 + 2√13]/3]

[tex]x_{2}[/tex] = [-4 - 2√13]/3]

Hence, The equation has two solutions [tex]x_{1}[/tex] =  [-4 + 2√13]/3] and

[tex]x_{2}[/tex] = [-4 - 2√13]/3]

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Answer: i think b

Step-by-step explanation:

Okay, here we have this:

Considering the provided expression, we are going to solve it, so we obtain the following:

Finally we obtain that the expression is equal to 0.95°.

f(x) = lx – 5l

x-5, if x-5 ≥ 0, x ≥5

-(x-5) = -x + 5 if x-5<0, x < 5

As given by the question

There are given that expression:

Now,

First, multiply the numbers:

In the given solution of the question, there are perform addition, so this is the first error.

Now,

Hence, the correct answer is :

After evaluating, we get

In the given question, we are given two expressions that include numerical in Roots. We have to calculate their values for each.

These are examples of Products. Product is when two numbers or terms are multiplied together.

The first expression is represented by:

=> 3 *√25, Calculating this expression we get

=> 3 * 5

=> 15

The second expression is represented by:

=> √(2 * 50), calculating this expression we get

=> √(100)

=> 10

Hence, after calculating both A. and B. expressions we get values 15, and 10 respectively

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Let x represent the weight of the comic book to be sold

Let y represent the weight of the appraised book to be appraised

There are 15 copies of the comic book the individual wants to sell (S), and 8 copies of a comic book the individual wants appraised (A), with a combined weight of 49.9 oz. It means that

15x + 8y = 49.9 equation 1

If the individual brings 10 copies of the comic book he wants to sell (S), 4 copies to be appraised (A), the combined weight would be 30.2 oz, it means that

10x + 4y = 30.2 equation 2

Multiplying equation 2 by 2, it becomes

20x + 8y = 60.4 equation 3

Subtracting equation 3 from equation 1, it becomes

20x - 15x + 8y - 8y = 60.4 - 49.9

5x = 10.5

x = 10.5/5

x = 2.1

Substituting x = 2.1 into equation 2, it becomes

10(2.1) + 4y = 30.2

21 + 4y = 30.2

4y = 30.2 - 21 = 9.2

y = 9.2/4

y = 2.3

Weight of the comic(S) to be sold = 2.1 oz

Before carrying out rotation transformation, the coordinates of the vertices of the pre-image are;

A (3, -6)

B(1, 2)

C (7, -1).

We are given the coordinates of the transformed image as:

A'(6, 3),

B'(–2, 1),

C'(1, 7).

We need to find the coordinates of the pre-image A, B and C.

The rule for rotation of 90° about the origin is (x,y) ---> (-y,x).

But we need to find the coordinates of the vertices of the pre-image.

So, we need to apply rule (-y,x) ---->(x,y).

Applying the 90 degrees clockwise rotation rule,

A'(6, 3) -----> A (3, -6)

B'(–2, 1) -----> B(1, 2)

C'(1,7) -----> C (7, -1).

Therefore, coordinates of the vertices of the pre-image are

A (3, -6)

B(1, 2)

C (7, -1).

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Complete question is;

After a rotation of 90° about the origin, the coordinates of the vertices of the image of a triangle are A'(6, 3), B'(–2, 1), and C'(1, 7). What are the coordinates of the vertices of the pre-image?

We have the following:

1. Similar By SSS similarity

4/2= 2

7.3.5 = 2

6/3 = 2

2. Similar by AA similarity, same angles, 90°, 70° and 50°

3. Similar by SAS similarity

, same angles and related sides.::

4/2 = 2

6/3 = 2

4. Similar by SAS similarity, same angles and related sides:

12/6 = 2

8/4 = 2

Principal = $3000

Rate = 5%

time = 2

Amount after 2 years =

= $3307.5

Option D is the correct answer

Answer:

-1.5 ≤ r < 9.5

Step-by-step explanation:

All you have to do is just insert the numbers

we use ≤ as it says in the question "no less"

For given function f(x)=8/(x+2) , g(x)=4x² +2 then evaluation of the composition of function (fog)(-1) =1.

As given in the question,

Given function:

f(x) = 8 / (x+2)

g(x) = 4x² +2

Evaluation of the composition of function f(x) and g(x) we get,

(fog)(x)

= f(g(x))

Substitute g(x) = 4x² + 2

= f(4x² +2)

= 8/(4x² +2+2)

= 8/(4x²+4)

= 2/(x²+1)

Substitute x =-1 in the above function

(fog)(-1) = 2/ ((-1)² +1)

            = 2/ 2

            =1

Therefore, for given function f(x) = 8/ (x+2) , g(x) = 4x² +2 then evaluation of the composition of function (fog)(-1) =1.

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A specific type of graphic or mathematical diagram known as a "scatter plot" employs Cartesian coordinates to display values for typically two variables for a group of data.

A scatter graph, scatter chart, scattergram, or scatter diagram are other names for it.

The scatter graph can be represented by the line of best fit which is calculated by taking the average of all the  x -coordinates and the y-coordinates.

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If the ham costs $6.24 per pound, and the cheese costs $4.80 per pound. You spend twice as much on ham as you do on cheese. The amount spent in total is: $187.20.

Let number of ham bought = x + 4

Let number  of cheese bought = x - 3

Price of ham = $6.24

Price of cheese = $4.80

Hence,

Amount spent on ham = (x+4)×6.24

Amount spent on ham =6.24x + 24.96

Amount spent on cheese = (x−3)×4.80

Amount spent on cheese =4.80x−14.40

So,

6.24 x + 24.96 = 2 (4.80 x - 14.40)

6.24x + 24.96 = 9.60 x - 28.80

Combine like terms

24.96 + 28.80 = 9.60 x - 6.24 x

3.36 x = 53.76

Divide both side by 3.36x

x = 53.76/3.36

= 16x

Now let find the total money spent where x is 16

Total amount = 6.24(16) + 24.96+ 4.80(16) - 14.40

Total amount = $187.20

Therefore the amount of $187.20 was spent in total.

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The boat that sailed in the direction closest to due north is the both that has lesser angle to the vertical ,which is the boat that that sailed 30 miles west and 22 miles north.

Given data

One boat sails 30 miles west and 22 miles north

Another boat sails 55 miles west and 40 miles north

Say boat A sail 30 miles west and 22 miles north while boat B sails 55 miles west and 40 miles north

Boat A

let the angle boat A made with the vertical be a. This is given as

tan a = 30 / 22

a = arc tan ( 30 / 22 )

a = 53.746 degrees

Boat B

let the angle boat B made with the vertical be b. This is given as

tan b = 55 / 40

b = arc tan ( 55 / 40 )

b = 53.973 degrees

Comparing angle a and angle b shows that angle a is lesser hence boat A is the boat that sailed in the direction closest to the north

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Original price: $16

Discount: 40%

First, multiply the original price by the percentage discount in decimal form (divided by 100)

16 x 40/100 = 16 x 0.4 = $6.4 ( discount amount)

Subtract the discount amount to the original price

16-6.4 = $9.6 new price

multiply by 7 :

9.6 x 7 = $67.2

The most appropriate choice for relation, domain and range will be given by-

Domain of S = {3, 1, 4}

Range of S = {0 , 2, -1, 9}

What is relation, domain and range?

A relation over set A and B is the subset of the cartesian product A x B.

Domain of a relation is the set of values for which the relation is defined.

Range is the set of solution obtained on putting the values of domain.

The relation S is defined as follows

S = {(3, 0), (1, 2), (4, -1), (3, 9)}

Now the set of values for which the relation is defined is the domain of the relation

For each ordered pair, the first number gives the values to be put in S. So the first number of every ordered pair is the domain.

So domain of S = {3, 1, 4}

Now, the second number gives the solution after putting the numbers in S.

So the second number of every ordered pair represents the range.

So, range of S = {0 , 2, -1, 9}

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When the ratio of the number of miles run to the number of miles biked is equivalent for each row in the table, the value for A is C. 2 3/4.

It should be noted that based on the information, the table has been given and the appropriate figures have been put into it.

The constant rate will be:

7 / 3 1/2 = 2

Now we can then write the relationship and this is illustrated as:

B = 2R

where B is the distance biked

R = the distance that's run.

We want to find the missing value of A. This is illustrated as:

5 1/2 = 2 × A

2A = 5 1/2

A = 2 3/4

Therefore, based on the information given, the correct option is C.

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The ratio of the number of miles run to the number of miles biked is equivalent for each row in the table.

Complete the table for A

A 2 1/4

B 2 2/4

C 2 3/4

D 3 3/4

Given:

AB = 14

SO = 24

To find:

a) the volume

b) the area of the lateral surface

c) the total surface area

a) To find the volume of the cone, we will use the formula:

r = radius

diameter = AB = 14

diameter = 2(radius)

radius = diameter/2 = 14/2

radius = 7

height = SO = 24

let π= 3.14

b) To get the lateral surface, we will apply the formula:

c) The total surface area formula:

The probabilities are (a) 0.4228, and (b) 0.8382

Define probability?

Probability is an area of mathematics that deals with numerical representations of how probable an event is to occur or how likely a statement is to be true. The probability of an occurrence is a number between 0 and 1, where 0 denotes the event's impossibility and 1 represents certainty. The greater the likelihood of an occurrence, the more probable it will occur. Tossing a fair (unbiased) coin is a basic example. Because the coin is fair, the two possibilities ("heads" and "tails") are equally likely; the chance of "heads" equals the probability of "tails," and because no other outcomes are possible, the probability of either "heads" or "tails" is 1/2.

(a) probability of drawing first a white marble and then a red marble

= 4/(4+10+3) x 3(3+10+3) = 4/17 + 3/16 = 0.4228

(b) probability of drawing first a green marble and then a blue marble

= 10/(10+3+4) x 4(9+3+4) = 10/17 + 4/16 = 0.8382

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It is given that,

By using parallelogram method,

The graph is as shown below:

{(2,9), (2,-5),(-6,3), (4, -7)} this pair doesn't represent a function

A mathematical function is a relationship that is established between two sets, through which each element of the first set is assigned a single element of the second set or none at all. The initial set or starting set is also called the domain; the final set or arrival set is called the rank.

Since in this set two elements of the range are associated with the same element of the domain [(2,9) and (2,-5)], we can conclude that it is not a function

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \:-\dfrac{1}{\sqrt{3-2x}} [/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

We newd to find the derivative of given function :

[tex]\qquad \tt \rightarrow \: y = \sqrt{3 - 2x} [/tex]

[tex]\qquad \tt \rightarrow \: y = (3 - 2x) {}^{ \frac{1}{2} } [/tex]

[tex]\qquad \displaystyle \tt \rightarrow \: \frac{dy}{dx} = \frac{d}{dx} (3 - 2x) {}^{ \frac{1}{2} } [/tex]

[tex]\qquad \displaystyle \tt \rightarrow \: \frac{dy}{dx} = \frac{1}{2} \sdot(3 - 2x) {}^{ - \frac{1}{2} } \sdot( - 2)[/tex]

[tex]\qquad \displaystyle \tt \rightarrow \: \frac{dy}{dx} = \frac{1}{ \cancel2} \sdot\frac{1}{(3 - 2x) {}^{ \frac{1}{2} } }\sdot( - \cancel2)[/tex]

[tex]\qquad \displaystyle \tt \rightarrow \: \frac{dy}{dx} = \frac{ - 1}{ \sqrt{ (3 - 2x) {}^{ }} }[/tex]

Correct option : B

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

The distance of each flight is 60 miles and the time taken is 40 minutes.

Distance is the total path covered by an object or species in a particular time period.

At x = 0 minutes after takeoff,

f(x)=60−1.5x                  (given)

= 60-1.5*0                     (at 0 minutes)

= 60 miles                     (distance between the helicopter and destination)

So, the distance of the flight is 60 miles.

When the helicopter reaches the destination, distance left is 0 miles

Thus, f(x) = 0 in x minutes.

Putting the above data in the equation, we get

0 = 60 - 1.5x

1.5x = 60                        (bringing unlike terms on different sides)

x = 60/1.5

x = 40 minutes

Therefore, the distance of each flight is 60 miles and the time taken is 40 minutes.

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The money she saved is 700.

Given:

Aunt's food budget = 3500

Fraction of the budget she saved = 1/5

So, the total money she saved  = 1/5 of the food budget

                                                    = 1/5 × 3500

                                                    = 700

Therefore, the money she saved is 700.

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Distributive property is illustrated in Step 2.

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If a submarine was situated 800 feet below sea level. ​If it ascends 275 feet, its new position relative to the sea level is: -525 feet.

Given :

Initial position of the submarine = 800ft below sea level

Ascending =275ft.

Hence, the New position relative to the sea level  is calculated as:

New position relative to the sea level = (-800+ 275)

New position relative to the sea level = - 525 feet

Therefore the new position is: -525 feet.

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The values of x and y of the solution to the system of equations are 2 and -5, respectively.

We are given three matrices. The matrices are A, Ax, and Ay.

The determinant of the matrix A is [(4*-2)-(-6*8)] = 40.

The determinant of the matrix Ax is [(38*-2)-(-6*26)] = 80.

The determinant of the matrix Ay is [(4*26)-(38*8)] = -200.

We need to find the values of x and y of the solution to the system of equations.

The value of x is |Ax|/|A| = 80/40 = 2.

Hence, the value of "x" is 2.

The value of y is |Ay|/|A| = -200/40 = -5.

Hence, the value of "y" is -5.

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