tan(-x)cos(-x) simplify

The Distance from point A to point B is: 3.4 ft when θ = 28° and The value of θ is: 54.8°

According to the question,

A spring is attached at one end to support B and at the other end to collar A.

Part A: Given that : Reference angle (θ) = 28°

We have to find out the distance of point A to point B.

Adjacent = 3 ft (given)

To find AB, apply the trigonometry function which is:

cos θ = adj / hypotenuse

Substituting all the values ,

=> cos 28°= 3/AB

=> AB = 3/cos 28°

=>  AB = 3.4 ft (nearest tenth of a foot)

Part B:

It is given that Distance  from point A to point B is 5.2 feet

We have to calculate the Value of θ

adj = 3 ft

hypotenuse = AB = 5.2 ft

To find θ , We will again apply the trigonometry function

cos θ = adj/hypotenuse

Substituting all the given values

=> cos θ = 3/5.2

=> θ = cos⁻¹ ( 3 / 5.2)

=> θ = 54.8°

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Answer:

A) 14

Step-by-step explanation:

Nuts:

[tex]\frac{6}{\frac{1}{3} }[/tex] = [tex]\frac{6}{1}[/tex] ÷ [tex]\frac{1}{3}[/tex]  Get a common denominator of 3 and divide

[tex]\frac{18}{3}[/tex] ÷ [tex]\frac{1}{3}[/tex] = [tex]\frac{\frac{18}{1} }{\frac{3}{3} }[/tex] = [tex]\frac{18}{1}[/tex] = 18

We can make 18 bags with the amount of nuts given.

Raisins:

[tex]\frac{8}{\frac{1}{4} }[/tex] = 8 ÷[tex]\frac{1}{4}[/tex]  Gert a common denominator of 4 and divide

[tex]\frac{32}{4}[/tex] ÷ [tex]\frac{1}{4}[/tex] = [tex]\frac{\frac{32}{1} }{\frac{4}{4} }[/tex] = [tex]\frac{32}{1}[/tex] = 32

We can make 32 bags with the amount of raisins given.

32 - 18 = 14

14 more bags need nuts agged.

Answer:

Jeff is Incorrect

Step-by-step explanation:

If x ≤ 1/2, the value will either be 2 or less than 2.

x = 1/2 =>  2(1/2)+1 = 2

x = 0 =>  2(0)+1 = 1

x = -1 =>  2(-1)+1 = 0

The number of bracelets and the number of necklaces will be 10 and 5, respectively.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

A gem dealer had a proper measure of gold to make wristbands and pieces of jewelry. The amount of gold in every armband is 5 grams and the amount of gold in every accessory is 16 grams. A goldsmith utilized 130 grams.

Let 'x' be the number of Bracelets and 'y' be the number of Necklaces. Then the equation is given as,

5x + 16y = 130

The term 16y in the equation should be a multiple of 5 to get the whole value.

If the value of y is 5. Then the number of bracelets is given as,

5x + 16(5) = 130

5x + 80 = 130

5x = 50

x = 10

The number of bracelets and the number of necklaces will be 10 and 5, respectively.

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Answer:

  2378 m

Step-by-step explanation:

You want the ground distance from the takeoff point to an airplane that has flown 2500 m in the air at a takeoff angle of 18°.

The cosine relation tells you ...

  Cos = Adjacent/Hypotenuse

  Adjacent = Hypotenuse · Cos

Here, the hypotenuse of the right triangle model is 2500 m, the angle is 18°, and we want to find the side of the triangle adjacent to the angle:

  AD = AP·cos(18°) = 2500·0.9510565 ≈ 2377.64 ≈ 2378 . . . . meters

The ground distance is about 2378 m.

The derivative of a whole number, like 1 is always zero as a whole number is constant.

In order to understand this answer, it is first necessary to realize that in calculus, a function's derivative is a formula that expresses the rate at which the function's value changes instantaneously in relation to x.

To get the derivative of a particular function, we can use specific rules like a whole number's derivative is always zero. To figure this out, we may apply the following calculus rule.

The derivative of f(x) is 0 if f(x) = a, where 'a' is any constant integer.

We can observe that the derivative of all constant functions is zero. This rule states that if f(x) = a, where 'a' is a whole number, then the derivative of f(x) equals 0, as 'a' whole number is a constant.

OR

We may infer from the graph below that for all values of x, the value of f(x) will stay constant (equal to 1). In light of the fact that f(x₂) = f(x₁), the derivative will be zero.

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Answer:

10 yrs old and 35 yrs old

Step-by-step explanation:

I figured it out by trial and error but here's the thinking process.

10 + 35= 45

Son becomes dad's age so 35-10=25, so plus 25 year to each age.

10+25=35

35+25= 60

35+60=95

I hope that makes enough sense!

The average speed in mile per hour is  5.455  miles per hour    .

In the question ,

it is given that ,

the 1 mile distance is covered in 11 minutes ,

So , in 1 minute the distance covered is = 1/11 miles

So , the speed in miles per minute is 1/11 miles per minute .

To convert speed in miles per minute to miles per hour ,

we multiply it by 60 ,

So , we get ,

Average Speed in miles per hour  is = 60 * (1/11)

= 60/11

= 5.45454

≈ 5.455

Therefore , the average speed is 5.455  miles per hour .

The given question is incomplete , the complete question is

What is your average speed in mile per hour and in feet per second if you travel a mile in 11 minute ?

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Calculating the cost of 4.25 kilogram(kg) is £2.38, by multiplying it by 4.25 kg by 1 kg.

Costs are the expenses incurred in the manufacture, marketing, or preparation of a good or asset for regular use. In other terms, it's the cost incurred to produce a good, buy inventories, sell goods, or prepare equipment for use in a commercial activity.

Given,

2.5 kg cost  £1.40 i.e,

2.5 kg = £1.40

For 1 kg= [tex]\frac{1.40}{2.5}[/tex]

= £0.56

To find the cost of 4.25 kg:

Then,

1 kg = £0.56

4.25 kg = 0.56 x 4.25

= £2.38

£2.38 is the cost of 4.25kg after calculating it.

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The illustration based on the Gestalt principles of grouping are:

(A) Closure principle.

(B) Proximity principle.

(C) Continuity principle.

(E) Similarity principle.

The principles of grouping, also known as the Gestalt rules of grouping, are a collection of psychological concepts first put out by Gestalt psychologists to explain why people naturally perceive items as structured patterns and objects, or Prägnanz.

Gestalt psychologists asserted that these principles hold true because the mind is predisposed to recognize patterns in the stimulus based on predetermined rules.

Gestalt grouping guidelines include:

Continuity principle.

Similarity principle.

Proximity principle.

Closure principle.

Common region principle.

Figure-ground principle.

Focal point principle.

Therefore, the illustration based on the Gestalt principles of grouping are:

(A) Closure principle.

(B) Proximity principle.

(C) Continuity principle.

(E) Similarity principle.

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If the original quantity is 8 and the new quantity is 2, then the correct answer is 75%.

For this question we need to subtract and multiply the numbers. We know that 2 = 25% of 8 so:

[tex]\boxed{8-2=6}\\\boxed{6/2=3}[/tex]

We are going to take that 25% and multiply it with 3 to get are final answer.

[tex]\boxed{25*3=75}\\\boxed{So,2=75}[/tex]

Therefore, If the original quantity is 8 and the new quantity is 2, then the correct answer is 75%.

There is no such a number whose absolute value is -2. This is because the absolute value of any number is its distance from 0 irrespective of the direction.

An absolute value of a number is the distance of the number from 0 on a number line irrespective of the direction.

Consider the number "x".

Then its absolute value is written as

|x| = x if x ≥ 0;

   = 0 if x = 0;

   = -x if x < 0;

For example x = -9; then its absolute value is

|(-9)| = -(-9) = 9; (Since x = -9 < 0; we applied |x| = -x)

So, we can conclude that irrespective of the direction (positive or negative), the absolute value of any number remains positive.

We know that the absolute value of any number is calculated by

|x| = x if x ≥ 0;

   = 0 if x = 0;

   = -x if x < 0;

And the absolute value of any number irrespective of its direction on the number line remains positive.

So, no such number has a negative absolute value.

Hence, the answer is none for the given question.

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Answer: 45 dogs will eat 135 pounds of dog food.

Step-by-step explanation:

The amount of food required for 45 dogs in a week will be equal to 135 pounds.

The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or even more items.

Included in them is the study of integers, especially the order of operations, which is important for all other areas of mathematics, notably algebra, data management, and geometry.

As per the data mentioned in the question,

Total number of dogs = 9

Amount of food eaten by dogs in a week = 27 pounds

Now, the number of dogs is 45.

Let the amount of food eaten by 45 dogs in a week is x.

So,

x = (27 × 45)/9

x = 1215/9

x = 135 Pounds.

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Answer:1/6 barrels=1 batch

Step-by-step explanation:

4/.666666666666666=6 batch's came from one barrel

6 batch's came from one barrel

1/6= 1 batch

Length of wall = 10km

side of square= 10km

area of square= 10²= 100km²

radius of circle = 10/2 = 5km

area of circle = 3.14 × 5²

area of circle = 3.14 × 25

area of circla = 78.5 km²

area of square >>> area of circle

y = 25x + 263 this equation represents how much money she will have, including her saving.

What is the linear equation?

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are present. The variables in the above equation are y and x, and it is occasionally referred to as a "linear equation of two variables."

We have,

The saved amount of $263 by Jenna,

and also she earns $25 per day

if x represents the number of days she works,

and let's take y as the total amount she will have.

Then the equation becomes:
y = 25x + 263

Hence, y = 25x + 263 this equation represents how much money she will have, including her saving.

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Answer:

first option

Step-by-step explanation:

given a quadratic equation in standard form

ax² + bx + c = 0 ( a ≠ 0 )

then the nature of the roots can be found using the discriminant

Δ = b² - 4ac

• If b² - 4ac > 0 , then the 2 roots are real and irrational

• If b² - 4ac > 0, and a perfect square, then 2 roots are real and rational

• If b² - 4ac = 0 , then 2 roots are real and equal

• If b² - 4ac < 0 , then 2 roots are not real

3x² + 4x - 2 = 0 ← is in standard form

with a = 3, b = 4 and c = - 2 , then

b² - 4ac = 4² - (4 × 3 × - 2) = 16 - (- 24) = 16 + 24 = 40

since b² - 4ac > 0 , then 2 real and irrational roots

Answer:

2. d = 40; 2 rational

Step-by-step explanation:

The discriminant (d) of a quadratic equation [tex]ax^2 + bx + c = 0[/tex] is:

[tex]\boxed{\mathrm{d =} \ b^2 - 4ac}[/tex].

If:

• d > 0, then there are two real solutions

• d = 0, then there is a repeated real solution

• d < 0, then there is no real solution.

In this question, we are given the quadratic equation [tex]3x^2 + 4x - 2 = 0[/tex]. Therefore, the discriminant of the equation is:
b² - 4ac = (4)² - 4(3)(-2)

             = 16 - (-24)

             = 40

Since the discriminant, 40, is greater than zero, the quadratic equation has 2 rational solutions.

Answer:

Monthly cost with 11 slices: $28.75

Monthly cost with x slices: C = 15 + x * 1.25

Step-by-step explanation:

If Austin bought 11 slices of pizza this month, he would have to pay the pizza shop a total of $15 + 11 * $1.25 = 28.75. This includes the cost of the membership fee of $15 and the cost of the 11 slices of pizza at the discounted price of $1.25 per slice.

The monthly cost for x slices of pizza can be represented by the equation C = 15 + x * 1.25, where C is the total cost and x is the number of slices of pizza purchased. This equation shows that the total monthly cost is equal to the membership fee of $15 plus the cost of the x slices of pizza at the discounted price of $1.25 per slice.

Answer:You consume 14 pounds of turkey annually. At a discount store, the price of turkey is $0.99 less per pound than at a supermarket. How much would you save annually, in dollars, if you bought all of your turkey at the discount store?

Step-by-step explanation:

The result of the expression is 60.

The given expression can be solved by applying the principle of BODMAS.

BODMAS stands for Bracket, Of, Division, Multiplication, Addition, and Subtraction. The BODMAS is used to explain the order of operation of a mathematical expression.

This indicates that numerous operator expressions must only be spelled out in this order, from left to right. We begin by resolving the brackets, then move on to powers or roots, division or multiplication (depending on which comes first from the left side of the expression), and lastly subtraction or addition (depending on which comes on the left side).

Given, 50+20/10*5 = 50+2*5=50+10=60

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The derivative of the function at P0 in the direction of A is,

([tex]\frac{df}{dx}[/tex])[tex]p_{0}[/tex] = -3 , ([tex]\frac{df}{dy}[/tex])[tex]p_{0}[/tex] = -1 , ([tex]\frac{df}{dz}[/tex])[tex]p_{0}[/tex] = 0

Geometrically, the derivative of a function can be interpreted as the slope of the graph of the function or, more precisely, as the slope of the tangent line at a point. Its calculation, in fact, derives from the slope formula for a straight line, except that a limiting process must be used for curves.

Given that,

The derivative of the function at P0 in the direction of A.

f(x, y, z) =

f(x, y, z) = (1,-1,-2)

x = 1

y = -1

z = -2

Derivative of f(x, y, z) = xy + yz + zx

[tex]\frac{df}{dx}[/tex] = y + z

[tex]\frac{df}{dy}[/tex] = x + z

[tex]\frac{df}{dz}[/tex] = x + y

We can substitute f(x, y, z) = (1,-1,-2) values,

([tex]\frac{df}{dx}[/tex])[tex]p_{0}[/tex] = y + z

([tex]\frac{df}{dx}[/tex])[tex]p_{0}[/tex] = -1 + (-2)

([tex]\frac{df}{dx}[/tex])[tex]p_{0}[/tex] = -3

([tex]\frac{df}{dy}[/tex])[tex]p_{0}[/tex] = x + z

([tex]\frac{df}{dy}[/tex])[tex]p_{0}[/tex] = 1 + (-2)

([tex]\frac{df}{dy}[/tex])[tex]p_{0}[/tex] = 1-2

([tex]\frac{df}{dy}[/tex])[tex]p_{0}[/tex] = -1

([tex]\frac{df}{dz}[/tex])[tex]p_{0}[/tex] = x + y

([tex]\frac{df}{dz}[/tex])[tex]p_{0}[/tex] = 1 + (-1)

([tex]\frac{df}{dz}[/tex])[tex]p_{0}[/tex] = 1-1

([tex]\frac{df}{dz}[/tex])[tex]p_{0}[/tex] = 0

Therefore,

The derivative of the function at P0 in the direction of A is,

([tex]\frac{df}{dx}[/tex])[tex]p_{0}[/tex] = -3 , ([tex]\frac{df}{dy}[/tex])[tex]p_{0}[/tex] = -1 , ([tex]\frac{df}{dz}[/tex])[tex]p_{0}[/tex] = 0

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The probability that it takes Emma more than 5 minutes to wait for the train is 0.8571.

Given :

the amount of time emma must wait for the train is continuous and uniformly distributed between 4 minutes and 11 minutes.

Let the random variable X denotes the amount of time it takes Emma to wait for the train is continuous and uniformly distributed between 4 minutes and 11 minutes.

the distribution function of X is:

F ( x ) = x - 4 / 11 - 4

4 < x < 11

P ( X > 5 ) = 1 - P ( X < 5 )

= 1 - F ( 5 )

= 1 - 1 / 7

= 7 - 1 / 7

= 6/7

= 0.8571

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Answer:

D

Step-by-step explanation:

A Hyperbola looks like a Parabola and its reflection, each Parabola curving opposite directions.

Answer:

D.  Hyperbola

Step-by-step explanation:

A conic is the intersection of a plane and a right circular cone.

Formed when a cone is intersected by a plane so that the plane is parallel to the circular base.

Formed when a cone is intersected by a plane so that the plane is at an angle with respect to the circular base.

Formed when a cone is intersected by a plane so that the plane is parallel to an edge.

Formed when a double-cone is intersected by a plane so that the plane is perpendicular to the circular bases.

Answer:

256

Step-by-step explanation:

((2*2)²)²

(((4)²)²)

(16)²

256

Answer: y = 4x + 1

Step-by-step explanation: Simple...

You have your equation... y=mx+b

You are given a coordinate. That is your x and y, and "m" is given already, and it's your slope.

First, you plug them in. You are solving for the unknown y-intercept or the "b".

5=4(1)+b

Then, you solve!

5=4+b

1=b

Parallel lines have the same slope, so the equation would be...

y=4x+1

From the statistical point of view , the type I error was made , the correct option is (c) .

In the question ,

it is given that ,

the machine was working well, but on the basis of our statistical hypothesis test, it was concluded that the machine was under-filling or over-filling and hence it was shut down .

but after examination by the engineers , there was nothing wrong with the filling machine .

that means that the null hypothesis was rejected when it was actually true .

which refers to the type I error .

Therefore , the correct option is (c) A Type I error was made.  

The given question is incomplete , the complete question is

The result of a hypothesis test is used to prevent a machine from under-filling or overfilling quart size bottles of olive oil. on the basis of sample, the hypothesis is rejected and the machine is shut down for inspection. a thorough examination reveals to engineers there is nothing wrong with the filling machine. from a statistical point of view:

(a) correct decision was made.

(b) Both, a Type I and a Type II errors were made.

(c) A Type I error was made.

(d) A Type II error was made.

(e) None of these answers.

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The evaluation of the composite figures, distances and coordinates in the question indicates;

24. The volume of the figure is about c) 1440 cm³

25) The distance of the airport from the plane is about c) 41,043.6 feet

26) The coordinates of the vertex U are c) (-5, -7)

A composite figure is a figure that is composed of two regular figures.

24. The figure is a composite figure comprising of a cylinder and a cone.

Volume of the cylinder = π × 5² × 15 = 375·π

Volume of the cone = (1/3) × π × 5² × (25 - 15) = (83 1/3)·π

The volume of the figure is therefore; 375·π + (18 1/3)·π ≈ 1440

25) The height of the plane = 12,000 ft

The angle of elevation to the airplane = 17°

Let r represent the direct distance of the airport from the plane, we get;

sin(17°) = 12000/r

x = 12000/(sin(17°) ≈ 41,043.6

The direct distance from the plane to the airport which is the hypotenuse side of the right triangle in the figure is about; d) 41,036.6 feet

26) The coordinates of the vertices of the triangle are; R(-6, -3), S(3, 3), and T(4, -1)

The type of quadrilateral represented by quadrilateral RSTU = A parallelogram

The slope of the side ST = (-1 - 3)/(4 - 3) = -4

Equation of the side RU is therefore;

y - (-3) = (-4) × (x - (-6)) = -4·x - 24

y = -4·x - 24 - 3 = -4·x - 27

y = -4·x - 27

The slope of the side RS = (3 - (-3))/(3 - (-6)) = 2/3

Equation of the side TU = y - (-1) = (2/3)·(x - 4) = (2/3)·x - (8/3)

y = (2/3)·x - (8/3) - 1 = (2/3)·x - (11/3)

y = 0.2·x - 1.8

The x-coordinate of the point U can be therefore obtained from the equation;

-4·x - 27 = (2/3)·x - (11/3)

x = -5

y = -4×(-5) - 27 = -7

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Therefore, the volume of the given cone is V=33.51 [tex]ft^{3}[/tex]

A three-dimensional space's occupied volume is measured. It is frequently expressed as a numerical value using SI-derived units, other imperial units, or US customary units. Volume and length definitions are connected.

Here,

Cone has a radius of 4ft

A height of 2ft.

Thus,

The formula for volume of cone is used

V=π[tex]r^{2} \frac{h}{3}[/tex]

V=3.14*[tex]4^{2}[/tex]*2/3

V=50.24*2/3

V=100.48/3

V=33.51 [tex]ft^{3}[/tex]

Therefore, the volume of the given cone is V=33.51 [tex]ft^{3}[/tex]

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The combined length for three shortest jumps is 43 feet. We can find out by analyzing the graph and its entities.

What are graph and entities ?

A graph can be defined as a pictorial representation or a diagram that represents data or values in an organized manner.

Entity is any data or any existing object .

From the graph:

14*1/4 feet = by 2 students

14*1/2 feet = by 3 students

14*3/4 feet = by 1 student

15 feet = by 1 student

So the three shortest jumps are 14*1/4 , 14*1/4 , 14*1/2.

Total distance = 57/4 + 57/4 + 58/4

                        = 43 feet.

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