Simplify the following using trigonometric identities:
( - tan² (x) + sec² (x) ) - sin² (x)

The length and width of the wall of the barn are 12 feet and 6 feet respectively.

The formula for area of rectangle is -

Area of rectangle = length × width

Let the width of rectangle be x. So, the length of rectangle = x + 6. Keep the values in formula to find the length and width of the barn.

x × (x + 6) = 72

Performing multiplication

x²+ 6x - 72 = 0

x² + 12x - 6x - 72 = 0

x (x + 12) -6(x + 12) = 0

x = 6 and - 12

Thus, width of rectangle = 6 feet

Length of rectangle = x+ 6

Length of rectangle = 6 + 6

Length of rectangle = 12 feet

Thus, length and width are 12 and 6 feet.

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The complete question is -

The area of a rectangular wall of a barn is 72 square feet. Its length is 6 feet longer than the width. Find the length and width of the wall of the barn.

The line that represent the graph have the equation of y = 4x  + 42 .

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

Equations with graphs as the unknowns are known as graph equations. The concept of isomorphism is one of the key issues in graph theory. When are two graphs identical, we inquire Different graph equations may be used to express the aforementioned graphs.

We must determine the slope and the y-intercept in order to graph this line. Y=mx+b, where m is the slope and b is the y-intercept, is the equation's slope-intercept form.

From the graph we can 2 points on the graph are

(0, 42) and (6, 18)

The equation of the graph will be

y - 42 = 18 - 42 /(6 - 0) *(x - 0)

⇒ (y -42)*6 = 24x

⇒y-42 = 4x

⇒y = 4x + 42.

The line that represent the graph have the equation of y = 4x  + 42 .

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Answer:

32

Step-by-step explanation:

The area of a parallelogram is bh where b = base, h = height

This is one of the questions where plotting the points and seeing the parallelogram is vital

See the attached figure

height h = |difference between x-coordinates of A and C| =

= |6 - 2| = 4.

This will be the same as |difference between x-coordinates of B and D

base b = |difference between y-coordinates of A and B| =  |1-(-7)| = 8.

This will be same as |difference between y-coordinates of C and D|

Area = bh = 8 x 4 = 32

Tickets are sold by airlines based on availability and demand. To increase their amount of earnings, they consider things like flight capacity, the time of year that people travel, the number of tickets available, and pricing.

Tickets are sold by airlines based on availability and demand. To choose the best course of action for their firm, they carefully analyse variables including aeroplane capacity, travel season, seat availability, and cost. Airlines assess the current market and forecast future trends using sophisticated mathematical models. This aids them in figuring out the ideal quantity of tickets to market and the finest selling price. To make sure that their tickets are reasonably priced, airlines also take into account the demand for their flights and the competition from other airlines. In order to make their tickets appealing to customers, airlines may consider promotional activities and unique offers. Airlines may increase their revenue by selling tickets at the proper price by studying the data and making wise judgements.

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The volume of the cylinder tank is 179530L and the standard deviation of the result is 5.869 L.

For the open cylindrical tank, the volume of the cylinder is given by:

V = (πd^2 h)/4

Where d is the diameter of the base and h is the height of the cylinder.

As there are four measurements for the diameter, the mean of the diameter is:

d = (5.2+5.7+5.3+5.5)/4=5.425

As there are three measurements for the heigh, the mean of the height is:

h = (7.9+7.8+7.6)/3=7.767

Hence, the volume of the cylinder is:

V = (π〖5.425〗^2 (7.767))/4 = 179.53 m^3 or 179530 L

In order to calculate the standard deviation of volume, calculate the standard deviation of diameter and height and calculate the volume.

SD = √(∑▒(di-d)^2 )/(N-1)

SD = √(∑▒〖(5.2-5.425)^2+(5.7-5.425)^2+(5.3-5.425)^2+(5.5-5.425)^2 〗)/(4-1) = 0.221

SD = √(∑▒(hi-h)^2 )/(N-1)

SD = √(∑▒〖(7.9-7.767)^2+(7.8-7.767)^2+(7.6-7.767)^2 〗)/(3-1) = 0.153

Hence, the SD of the volume is:

SD = (π(0.221)^2 (0.153))/4 = 0.005869 m^3 or 5.869 L

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As per the concept of reasoning, the conditional statement is false.

The term reasoning in math is called as students who genuinely make sense of mathematical ideas can apply them in problem solving and unfamiliar situations and can use them as a foundation for future learning.

Here we have the conditional statement "if a human being has 7 heads, then they have 11 arms".

And here we need to find out whether this statement is true or false.

While we looking into the given statement we have identified that this is false because this statement is missing the necessary or sufficient words.

Simply said that it is not possible situation.

Therefore the statement is false.

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a) The speed of car is, 56 miles per hour.

b) The time to complete 100 miles is, 25/14 hour.

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

We have to given that;

A car goes 42 miles in 45 minutes (3/4 of an hour).

Now, We know that;

⇒ Speed = Distance / Time

Substitute the given values, we get;

⇒ Speed = 42/(3/4)

⇒ Speed = 42 × 4/3

⇒ Speed = 56 miles per hour

Thus, The speed of car is, 56 miles per hour.

And, At the same rate, the time to complete 100 miles is,

⇒ Speed = Distance / Time

⇒ 56 = 100 / Time

⇒ Time = 100 / 56

⇒ Time = 25/14 hour

Thus, The time to complete 100 miles is, 25/14 hour.

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Answer:

r= 45 s=5

5(r-s)= 45-5= 40

Step-by-step explanation:

5(9-1) <--- You substitute the values

(5*9-5*1)<--- Multiply

45-5<--- Subtract

40 <-- Answer

r= 45

s=5

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

[tex]\mathsf{5(r - s)}\\\mathsf{= 5(9 - 1)}\\\mathsf{= 5(9) + 5(-1)}\\\mathsf{= 45 - 5}\\\mathsf{= 40}\\\\\huge\text{Therefore your answer should be:}\\\huge\boxed{\mathsf{40}}\huge\checkmark[/tex]

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

At the instant when dp/dt=41 and c = 15, the value of dc/dt is -0.273333.

The derivative of p with respect to time t is given by:

dp/dt = 2p dp/dc * dc/dt

Since dp/dt = 41, we have:

41 = 2p dp/dc * dc/dt

To find dp/dc, we can use the relationship between p and c:

p^2 = (20-c)^3

Taking the derivative of both sides with respect to c, we get:

2p dp/dc = -3(20-c)^2

Substituting this expression into the equation for dp/dt, we get:

41 = 2p * (-3(20-c)^2) * dc/dt

Plugging in the value of c = 15, we find:

41 = 2 * p * (-3(5)^2) * dc/dt

Using the relationship p^2 = (20-c)^3, we can find p:

p = sqrt((20-c)^3) = sqrt((20-15)^3) = sqrt(5^3) = 5

Substituting the value of p into the equation for dp/dt, we get:

41 = 2 * 5 * (-3(5)^2) * dc/dt

Solving for dc/dt, we find:

dc/dt = 41 / (2 * 5 * (-3(5)^2)) = 41 / (2 * 5 * (-3 * 5^2)) = 41 / (-150) = -41/150 = -0.273333...

So the value of dc/dt at the instant when dp/dt = 41 and c = 15 is approximately -0.273333.

Correct Question :

the positive variables p and c change with respect to time t. the relationship between p and c is given by the equation p2= (20−c)3. at the instant when dp/dt=41 and c = 15 what is the value of dc/dt?

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Answer:

[tex]-\frac{82\sqrt{5} }{15}[/tex]

Step-by-step explanation:

[tex]p^{2} =(20-c)^{3}[/tex]

[tex]2p(\frac{dp}{dt}) =3(20-c)^{2}(-\frac{dc}{dt} )[/tex]

Took the derivative of both sides ^

It gives you [tex]\frac{dp}{dt} =41[/tex] and [tex]c=15[/tex], so you just need [tex]p[/tex]

[tex]p=\sqrt{(20-15)^{3} } =5\sqrt{5}[/tex]

Now plug in

[tex]2(5\sqrt{5} )(41)=3(20-15)^{2} (-\frac{dc}{dt} )[/tex]

[tex]-\frac{410\sqrt{5} }{75} =\frac{dc}{dt}[/tex]

[tex]-\frac{82\sqrt{5} }{15} =\frac{dc}{dt}[/tex]

The relationship between ACT scores and gender varies depending on the data and analysis performed.

ACT scores are an important aspect in the college admissions process. They measure a student's knowledge and skills in English, mathematics, reading, and science.

In the first scenario, it states that the largest percentage of both genders' ACT scores are above 25. It also mentions that more male students have scores under 20 than female students.

In the second scenario, it mentions that the largest percentage of both genders' ACT scores are in the 20 to 25 range and that more female students have scores under 20 than male students.

In the third scenario, it states that the largest percentage of both genders' ACT scores are under 20 and that more male students have scores above 25 than female students.

In the fourth scenario, it mentions that the largest percentage of both genders' ACT scores are in the 20 to 25 range and that more male students have scores under 20 than female students.

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The length of the sides of the rhombus JKLM is 12 units.

A rhombus is one of parallelograms. The opposite sides of a rhombus are parallel, and the opposite angles are equal. Furthermore, all of the sides of a rhombus are the same length, and the diagonals intersect at right angles.

In the problem, the sides of rhombus JKLM are:

JK = 2x + 4

JM = 3x

Since the length all of the sides of a rhombus are the same, then:

JM = JK

3x = 2x + 4

Substract both sides by 2x:

3x - 2x = 2x + 4 - 2x

x = 4

To find the length of a side, substitute x = 4 into:

JM = 3x

JM = 3(4) = 12

Hence, the length of the sides of the given rhombus is 12.

The picture in your question is missing. Most likely it was like on the attached picture.

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Answer:

12

Step-by-step explanation:

JK = JM

2x + 4 = 3x

x = 4

JK = JM = 3 x 4 = 12

The numbers are 19 and 71 respectively

Let's call the smaller number "y".

The larger number would be 3 times y plus 14,

Which we can write as 3y + 14.

From the problem, we know that the sum of the two numbers is 90, so we can write an equation:

y + (3y + 14) = 90

Remove the brackets

y + 3y + 14 = 90

So, we have

4y + 14 = 90

4y = 76

Divide both sides by 4

y = 19

So the smaller number is 19 and the larger number is 3 times that plus 14, which is 3 * 19 + 14 = 71.

So the two numbers are 19 and 71.

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Haven't answered an inequality question in a while so this
might be complete bullhonkey.

Answer:

154 minutes of talktime.

Step-by-step explanation:

To find out how many minutes of talktime John can have per month, we need to set up an equation using the information given.

Let x be the number of minutes of talktime John can have per month.

The equation for John's monthly phone bill is:

26.50 + 0.35x = 80

To find the value of x, we can solve for x by subtracting 26.50 from both sides:

0.35x = 53.50

To find the number of minutes, we can divide both sides by 0.35:

x = 153.57

To the nearest whole number, John can have 154 minutes of talktime per month.

Answer:

x = 3

Step-by-step explanation:

2x + 5 = 3x + 2

-5 -5

2x = 3x + 2 - 5

-3x -3x

2x - 3x = 2 - 5

-x = -3

x = 3

The derivative of y with respect to x exist for all values of y, that is it does not exist for no value of y.

Therefore the answer is d. for no values of y

The curve y^2 = x is a parabolic function and its derivative is continuous for all x in its domain, which is x >= 0. The derivative of this function, which is y' = (dy/dx) = 1/2 * √x, is well-defined for all x >= 0 and therefore, the derivative exists for all values of y, including y = 0 and y = -1.

In general, a function is said to be differentiable at a point if its derivative exists at that point, and the derivative provides information about the rate of change of the function at that point.

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The amount of gallium-67  remain after 6.5 days = 2.5 grams

We know that the half-life of the radioactive isotope is nothing but the time needed for the isotope to be half of its initial value of mass.

This means, with each half-life, the isotope will be halved of its initial value.

The formula for the numbers of half-lives:

numbers of half-lives = total time passed / the half-life of the isotope

Here, total time passed  = 6.5 days

                                        = 156 hours

the half-life of the isotope = 98 hours

Let n represents the number of half lives.

Using above formula,

numbers of half-lives n =  156 / 98

numbers of half-lives n = 1.59

numbers of half-lives n ≈ 2

So, the remaining mass would be,

remainig mass m = initial mass / [tex]2^n[/tex]

m = 10 / 2²

m = 2.5 g

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Terms = 3x² , 6x , 7

Coefficients = 3,6

Neither One  = x²

A quantity or number that is combined with a variable is known as a coefficient.

Adding a variable to a number produces a coefficient.

The variable next to it is often multiplied by an integer.

Three terms make up the trinomial: 3x² + 6x + 7

3x²

6x

7

Enter the first column as a result.

The coefficients at and are respectively 3 and 6.

The second column should have these two integers.

x² is not a term (because 3x² is a term) and is not a coefficient, because coefficients are numbers.

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Mira's scale factor of 7 in would not be reasonable because it would make the dimensions of A' too small.

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Answer:x=-4

Step-by-step explanation

1. Set y as 0. Doing so will help you solve for x

3x +20(0)=-12 aka 3x=-12

2. Divide each sides by 3

3x(divided by three) = -12 (divided by three)

x=-4

(your answer would be negative because a negative divided by a postitive is negative.)

Answer:

Similar by SAS

Step-by-step explanation:

:)

The statement that is not true is the fourth one.

"Other points that are on line f are also solutions of the system".

We know that the graphs of lines f and g intercept at the point (4, 5). So trivially, the point (4, 5) belongs to both graphs.

That also means that (4, 5) is the solution of the system of equations:

y = f(x)

y = g(x).

And because these two are lines, these will intercept only once, then (4, 5) is the only solution of the system.

That means that the correct option (the false statement) is the fourth one.

"Other points that are on line f are also solutions of the system".

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The sample size is: n=39

Class        frequency
120-125           1
125-130            3
130-135             7
135-140             13
140-145             10
145-150               3
150-155               2

Total                   39

∵Therefore, The sample size is: n=39


A histogram is a graphical representation of a frequency distribution with continuous classes that has been grouped. It is an area diagram with bases and intervals between class boundaries, and areas proportional to frequencies in the corresponding classes. Because the base spans the intervals between class boundaries, all rectangles in such representations are adjacent.  

How Do You Plot a Histogram?

Answer: 1 1/3

Step-by-step explanation: To find this answer, we simply divide the people by the oranges. So, 4 / 3 is 1.3333333333333...... We round this to about 1.3. So, that as a fraction is 1 1/3. So, each person gets 1 1/3. To check, we multiply 1 1/3 by 3 (people) and we get 4. I hope this helped!

The sine of an angle's complementary angle is equal to the cosine of that angle, and the reverse is true for the other direction.

Identity :

[tex]{cosec}^2 \mathrm{~A}-\cot ^2 \mathrm{~A}=1$[/tex]

LHS  [tex]$=\left(1+\cot ^2 \mathrm{~A}\right) \sin ^2 \mathrm{~A}$[/tex]

[tex]{cosec}^2 \mathrm{~A} \times \sin ^2 \mathrm{~A}$[/tex]

[tex]$=\frac{1}{\sin ^2 A} \times \sin ^2 A$[/tex]

= 1

= RHS

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Answer:250(0.6)

Step-by-step explanation:

The value of the function is f ( x ) = 250 ( 0.6 )ˣ

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

The values of x are in set x = { 0 , 1 , 2 , 3 , 4 , }

The values of y are in set y = { 250 , 150 , 90 , 54 , 32.4 }

Now , the equation will be y = 250 ( 0.6 )ˣ

when x = 0

y = 250 ( 0.6 )⁰

y = 250 ( 1 )

y = 250

when x = 1

y = 250 ( 0.6 )¹

y = 250 ( 0.6 )

y = 150

when x = 2

y = 250 ( 0.6 )²

y = 250 ( 0.36 )

y = 90

when x = 3

y = 250 ( 0.6 )³

y = 250 ( 0.216 )

y = 54

when x = 4

y = 250 ( 0.6 )⁴

y = 250 ( 0.1296 )

y = 32.4

Hence , the function is y = 250 ( 0.6 )ˣ

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Answer:

a) (0,1)

b) k = 6.5

Step-by-step explanation:

When a line crosses the y-axis at a point, the point's x-coordinate must be 0. Let's substitute the value of x into the equation of the line to find its y-coordinate.

y - 4x = 1

Rearrange terms to isolate y.

y = 4x + 1

Substitute x = 0 into the equation.

When x = 0, y = 4(0) + 1

y = 0 + 1

y = 1

Thus, the coordinates of the point is (0, 1).

---

The second question uses the general equation of a straight line which is y = mx + c where m is the gradient of the line and c is the y-intercept of the line. As you can see from the graph drawn, the line cuts the y-intercept at (0, -3) so c = -3. You are given the y-coordinate of the point (which is 10) so you can find the x-coordinate (k) by substituting the value of y into the equation of the line once again.

y = 2x + c

You know the value of c from the y-intercept. c = -3

y = 2x - 3

Substitute y = 10 into the equation.

When y = 10, 10 = 2x - 3

10 + 3 = 2x

2x = 13

x = 6.5 when y = 10

Thus, the value of k is 6.5.

After solving, the lower number is 9 and the larger number is 41.

The sum of two number is 50.

The larger number is 4 less than 5 times the lower number.

Let the lower number is x.

Five times the lower number = 5x

Larger number 4 less than five times the lower number = 5x - 4

Sum of number = 50

Lower Number + Larger number = 50

x + 5x - 4 = 50

Simplify

6x - 4 = 50

Add 4 on both side, we get

6x = 54

Divide by 6 on both side, we get

x = 9

Now finding the number.

Lower Number = x = 9

Larger Number = 5x - 4

Larger Number = 5(9) - 4

Larger Number = 45 - 4

Larger Number = 41

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The complete question is:

The sum of two number is 50. The larger number is 4 less than 5 times the lower number. Find the number.

The competitor drive 804.672 or 800 Km to complete the race​.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

The Indianapolis 500 race takes 200 laps to complete.

and, 1 lap = 4 Km

Then, for 200 laps the competitor need to drive

= 200 x 4

= 800 Km

also, Indianapolis 500 race is to cover 500 miles in 200 laps then we can write it as

1 miles = 1.60934 Km

and 500 miles= 804.672 Km

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Answer:

Step-by-step explanation:

=0.25