From the diagram below, if AC is a tangent line, and if PD = 8 and DC = 9, find the length of BC.

The tension in the string at rest calculating the force and friction is  approximately 2 N.

For particle A ,

The forces perpendicular to the plane is

R - 3cos 30° = 0

⇒R = 3cos 30°

The resultant force acting horizontally is  

T cos 30° - R  sin 30°

Now we substitute the value of R and T we get:

⇒ [tex]\frac{3(1+\sqrt3)}{4} cos 30 -3cos30\text{ }sin30[/tex]

⇒3√3 / 8 + 9/8 -3√3 / 4

⇒0.475 N

For the particle B.

The forces perpendicular to the plane is

R - 3cos 60° = 0

⇒R = 3cos 60°

The resultant force acting horizontally is  

T cos 60° - R  sin 60°

Now we substitute the value of R and T we get:

Force = 0.275 N

Resultant tension in the string:

0.475 -0.275 = 0.2

The given tension in the string is 3/4(1+√3) N

or, tension =2.049..N

or, tension ≈ 2 N approx

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Answer:

3.2 m/s

Step-by-step explanation:

If we use the equation distance/time=speed, we can find this pretty quickly.

Our distance is 400 m.

Our time is 125 s.

400/125=

3.2 m/s

EXPLANATION

Given the cubic root:

Rewriting 8 as 2^3:

Applying the property of roots:

Given

The given formula

The base is circle

Now back to the given formula

The final answer

Explanation:

1) C = 5/9 f + 32

The start value is the constant = 32.

The start value = 32

Growth value = rate of change

Growth value = 5/9

2) y = 4000 - 250x

The start value is the constant = 4000

The start value = 4000

To evaluate it at x = -2 substitute x by -2 in p(x)

Now let us find its value

(-2)^3 = -2 * -2 * -2

In the exercise we first formulate and then replace values ​​to find an unknown;

It is important to first look at what data the exercise gives us and then place them in the correct way, it must coincide with what the graph shows us.

The component form of vector v with initial point (-6,2) and terminal point (7,-3) is (13,-5).

The component form of a vector is represented as x, y >, where x denotes the direction of travel (right or left) and y denotes the direction of travel (up or down) of the vector. Any two-dimensional vector may be conceived of as exerting influence in two separate directions. In other words, it can be considered to have two pieces. Components are the individual pieces that make up a two-dimensional vector. A vector's elements show how that vector will act in a specific direction.

Here,

initial point A=(-6,2)

terminal point B=(7,-3).

AB=(Bx-Ax, By-Ay)

=(7-(-6), -3-2)

= (13, -5)

The component form of the vector v with the starting points (-6, 2) and terminal points (7, -3) is (13,-5).

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The graph that represents the systems of linear equations 2x - y ≥ -3 and y < -2x + 4 is option d

information gotten from the question include

inequality graph showing shaded regions

rearranging the equation to be in the form

y = mx + c

2x - y ≥ -3

2x + 3 ≥ y

y ≤ 2x + 3

The two equations are

y ≤ 2x + 3

y < -2x + 4

some interpretation on the information from the question include

The both inequalities are less than hence the shading for the both will be below the line

This interpretation helps to conclude that last options is the best choice

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The three division expressions that are each equivale to 35.78 ÷ 6 is 0.5933[tex]\times10^1[/tex], 59.33[tex]\times10^{-1}[/tex] and 59.33[tex]\times10^{-2}[/tex].

In the given question we have to use the powers of 10 to write three division expressions that are each equivale to 35.78 ÷ 6.

The given expression is 35.78 ÷ 6

To express in power of 10 we have to firstly simplify the given expression.

To simplify the given expression we have to divide the 35.78 by 6.

So 35.78 ÷ 6 =5.9633

To express in the power of 10 we move the decimal point left and right.

When we move left the power is positive and when move right power is negative.

The first expression is 0.5933[tex]\times10^1[/tex]

The second expression is 59.33[tex]\times10^{-1}[/tex]

The third expression is 593.3[tex]\times10^{-2}[/tex]

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[tex]\huge\red{\mid{\underline{\overline{\textbf{EQUATION AND ANSWER}}}\mid}}[/tex]

_________________

Let's solve this simple percentage problem,

Percentage - Percentages are essentially fractions where the denominator is 100. To show that a number is a percent, we use the percent symbol (%) beside the number.

Cross Multiplication - In mathematics, specifically in elementary arithmetic and elementary algebra, given an equation between two fractions or rational expressions, one can cross-multiply to simplify the equation or determine the value of a variable.

Division - Division, otherwise known as the inverse of multiplication separates a certain number into what it has been divided by.

_________________

Now that we understand the definition we can further solve this equation

[tex]\large\red{\mid{\underline{\overline{\textbf{Values}}}\mid}}[/tex]

________________

Now we will add to solve this equation

[tex]\large\red{\mid{\underline{\overline{\textbf{Equtation}}}\mid}}[/tex]

[tex]\frac{x}{100}=\frac{231}{330}[/tex]

Now we will do cross multiplication

[tex]231\cdot100\\x\cdot330[/tex]

[tex]330x=231000[/tex]

Finally, we will do some division

[tex]x=70[/tex]

[tex]\large\red{\mid{\underline{\overline{\textbf{Answer}}}\mid}}[/tex]

The answer is [tex]70%[/tex]%

Answer:

Multiplicative inverse property (because 6 is the inverse of 1/6)

Answer:

5, 6, 7, 8

Step-by-step explanation:

substitute the values of x from the table into f(x)

f(1) = 1 + 4 = 5

f(2) = 2 + 4 = 6

f(3) = 3 + 4 = 7

f(4) = 4 + 4 = 8

the values of f(x) are 5, 6, 7, 8

Answer:

0.25

Step-by-step explanation:

3 / 12 = 0.25

Answer:  0.60

Step-by-step explanation:

The value of the expression  ctg 30° + 2 csc 60° - 3 cos 30° is 5√3/6

The expression is calculated using trignometic values

ctg 30° + 2 csc 60° - 3 cos 30°

1/tan 30 + 2/sin 60 - 3 cos 30

1/(1/√3) + 2/(√3/2) - 3 (√3/2)

√3 + 4/√3 - 3√3/2

LCM is 2√3

(√3(2√3) + 2(4) - 3√3(√3) )/2√3

(6 + 8 - 9)/2√3

5/2√3

5√3/6

The value of the expression  ctg 30° + 2 csc 60° - 3 cos 30° is 5√3/6

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ANSWER

2325 cans

EXPLANATION

We are given that 31 students each brought 75 aluminum cans to class.

To find how many cans the class collected, we have to multiply the number of students by the number of cans collected by each student.

That is:

Number of cans = 31 * 75 = 2325

Therefore, 2325 cans were collected by the class.

If the coordinates of the points are (x, y), then the point lies in the 1st quadrant

If the coordinates of the point are (-x, y), then the point lies in the 2nd quadrant

If the coordinates of the point are (-x, -y), then the point lies in the 3rd quadrant

If the coordinates of the point are (x, -y), then it lies in the 4th quadrant

Since the given point is (-3, 6), then it should be in the 2nd quadrant

Since point B is in the 2nd quadrant, then

The answer is B the third answer

(

By using division of decimal numbers, it is obtained that cost of 1 pound of coffee is $8.99

What is decimal number and division?

Decimal numbers are those numbers which consist of an integer part and a fractional part.

Decimal are of two types-

Terminating decimals are those decimals which has finite number of figures after decimal point

Non terminating decimals are those decimals which has infinite number of figures after decimal point.

Division is the process by which value of single unit can be calculated from the value of multiple unit

The number which is divided is the dividend, the number by which dividend is divided is the divisor, the result obtained is the quotient and the remaining part is the remainder.

There is a well known formula in division

Divisor x Quotient + Remainder = Dividend

Here, division of decimal will be used

Cost of 5 pounds of coffee = $44.95

Cost of 1 pound of coffee = $[tex]\frac{44.95}{5}\\[/tex]

                                          = $8.99

Cost of 8 pounds of coffee = $71.92

Cost of 1 pound of coffee = $[tex]\frac{71.92}{8}\\[/tex]

                                          = $8.99

Cost of 14 pounds of coffee = $125.86

Cost of 1 pound of coffee = $[tex]\frac{125.86}{14}\\[/tex]

                                          = $8.99

Cost of 20 pounds of coffee = $179.80

Cost of 1 pound of coffee = $[tex]\frac{179.80}{20}\\[/tex]

                                          = $8.99

So cost of 1 pound of coffee = 8.99

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The triangle ABC undergoes a dilation of scale factor 2 centered at the origin.

Dilation About the Origin

Given a point P(x,y), its dilation about the origin by a scale factor of k maps the point to a point P'(kx,ky).

If we are given the dilated point, then we can find the original point by dividing by the scale factor.

Triangle ABC was dilated by a scale factor of 2 about the origin mapping it to triangle A'B'C' with vertices A'(-4,4), B'(-4,6), and C(2,4).

The coordinates of triangle ABC are:

A=(-4/2,4/2) = (-2,2)

B=(-4/2,6/2) = (-2,3)

C=(2/2,4/2) = (1,2)

The coordinates of ABC are respectively (-2,2), (-2,3), and  (1,2).

Hence the answer is the triangle ABC undergoes a dilation of scale factor 2 centered at the origin.

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Answer:i'm pretty sure it's the one to the right of the example

Step-by-step explanation:

Seven hundredths is:

Fifteen hundredths is:

Answer:

No, Anthony is not correct.

Step-by-step explanation:

K is at (-4, 8), L is at (-7, 4), M is at (-2, 1)

KL

[tex] \sqrt{ {( - 4 - ( - 7))}^{2} + {(8 - 4)}^{2} } [/tex]

[tex] \sqrt{ {3}^{2} + {4}^{2} } = \sqrt{9 + 16} = \sqrt{25} = 5[/tex]

LM

[tex] \sqrt{ {( - 7 - ( - 2))}^{2} + {(4 - 1)}^{2} } [/tex]

[tex] \sqrt{ {( - 5)}^{2} + {3}^{2} } = \sqrt{25 + 9} = \sqrt{34} [/tex]

KM

[tex] \sqrt{ {( - 4 - ( - 2))}^{2} + {(8 - 1)}^{2} } [/tex]

[tex] \sqrt{ {( - 2)}^{2} + {7}^{2} } = \sqrt{4 + 49} = \sqrt{53} [/tex]

From these, it follows that KLM is not an isoceles triangle.

Answer:

B

Step-by-step explanation:

If you see two negatives next to each other, just think of them as adding. So add 8 and 7, you get 15.

If the homeowner helps the professional roofer they will do the job in  2.53 days

Let the number of days to complete the job be x

The rate at which the homeowner will roof is x / 16

The rate at which the professional roofer will roof is x / 3

Adding the rates together gives

x / 16 + x / 3

19x / 48

The rate it will take them both to finish the job is

= 48 / 19

= 2.53 days

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Considering the given triangle is a right-angled triangle. Therefore, one side of the triangle is [tex]11\sqrt{2}[/tex] and the other side of the triangle is [tex]22\sqrt{2}[/tex]. Since we have to find one of the legs of the triangle, we can assume [tex]22\sqrt{2}[/tex] is the length of the hypotenuse and [tex]11\sqrt{2}[/tex] the length of one of the sides of the right-angled triangle.

Therefore, by Pythagoras' theorem,

[tex]\sqrt{ (22\sqrt{2}) ^{2} - (11\sqrt{2} )^{2} } =[/tex] length of one leg of the triangle = 26.95 units

Therefore, The length of one leg of the triangle is 26.95 units.

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Answer:

b…22

Step-by-step explanation:

#28

The given expression is

At first, we will simplify each square bracket

Note that, the + sign does not change the terms in the bracket but the - sign change the signs of the terms inside the bracket

Now, we will multiply the 2 brackets

Now we will add the like terms

Answer:

Step-by-step explanation:

Ok1

1. Put percent into numbers

25/100*8=

200/100=

2

2. Add

There was a increase of 2 dollars from 8$

8$+2$=

10$

Answer: 10$

Answer:10

note: please tell me if I'm wrong

The probability that any given person is a universal donor is 7.2%. This means that the probability that a person is not a universal donor is 92.8%.This indicates that there is a 0.65 percent chance that at least 1 out of every 10 randomly selected individuals is a universal donor.

Now, if we choose 10 people at random, we can use the binomial distribution to calculate the probability that at least 1 of them is a universal donor. The binomial distribution tells us that the probability of getting exactly k successes in n trials is:

P(k; n, p) = (n choose k) p^k (1-p)^(n-k)

where n is the number of trials, p is the probability of success on a single trial, and k is the number of successes.

plugging in our values, we get:

P(1; 10, 0.072) = (10 choose 1) (0.072)^1 (1-0.072)^9

P(1; 10, 0.072) = 10(0.072) (0.928)^9

P(1; 10, 0.072) = 0.65

This means that the probability that at least 1 out of 10 people chosen at random is a universal donor is 0.65.

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Given:

5, 11, 2, 12, 4, 2

Required:

To find the mean of the given numbers.

Explanation:

Consider the given numbers

5, 11, 2, 12, 4, 2

Now the mean is

Final Answer:

The mean is 6.

The sum of all the possible events is 1, which means that all the events are independent of the others, in that case

P(A or C) = P(A)+P(C) = 0.1 + 0.8 = 0.9

P(B and C) = P(B)*P(C) = 0.1 * 0.8 = 0.08