5.2 Two concentric circles have radii 7cm and 4cm respectively. PQ, a chord to the larger circle, is 13cm. 5.2.1 Draw the sketch. (2) 5.2.2 Calculate AB (a chord to a smaller circle), correct to 2 decimal places. (6)​

Answers

Answer 1

The length of the chord AB will be 6.08 cm

A chord of a circle is a section of a straight line whose ends both fall on an arc of a circle. A secant line, often known as secant, is a chord's infinite line extension. A chord is, more broadly speaking, a line segment connecting two points on any curve, such as an ellipse.

Given two concentric circles have radii 7cm and 4cm respectively. PQ, a chord to the larger circle, is 13cm

We have to find the length of chord AB drawn to smaller circle

Given:

PQ = 13 cm

R = 7 cm

r = 4 cm

The formula to find length of chord is as follow:

Length of chord = 2 x √(R²-d²)

Where,

R = radius of circle

D = Perpendicular distance from center of circle to chord

So,

PQ = 2 x √(R²-d²)

13 = 2 x √(7²-d²)

d = 2.59 cm

Now,

AB = 2 x √(r²-d²)

AB = 2 x √(4²-2.59²)

AB = 6.08 cm

Hence the length of chord AB will be 6.08 cm

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Related Questions

Given the graph of the pre-image and image, identify the correct
coordinate transformation.

Answers

The preimage was shifted to the image by a translation 2 units right and 2 units up, so the answer is [tex](x,y) \longrightarrow (x+2, y+2)[/tex]

Suppose you want to test the effectiveness of a certain drug for treating a disease that said you wanted to see if using the drug is better the standard treatment used to like 150 patients to give the drug and 150 patients to give the standard treatment name at least five factors you should control for in your samples to make the test more random

Answers

Five factors that should be controlled are the dose of the medicine, the time the patients take this medicine, their diet, the stage of this disease and medicine composition.

Why should some factors be controlled?

This is done to avoid bias or imprecise results.

What factors should be controlled?

Factors related to the medicine itself and factors that can affect the results should be controlled. This includes:

The dose given to the patients.The stage of the disease that should be similar for all patients.The medicine compositon and manufacturer.The number of day patients take the medicine.The patients' diet.

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The vehicle preference of police officers and firefighters is given in the table.
Police Officers Firefighters
Cars 12
Trucks 9
SUVS 15
3
4
2
Based on the information in the table, which of the following is an example of independent events.

Answers

An example of independent events is P(Police Officers and choose cars).

Which pair of events are called independent events?

When one event's occurrence or non-occurrence doesn't affect the occurrence or non-occurrence of another event, then such events are called independent events.

Symbolically, we have:

Two events A and B are said to be independent if we have:

P(A ∩ B) = P(A)P(B)

                    Police Officers         Firefighters

Cars               12                             3

Trucks            9                              4

SUVs              15                             2

Let  P(A) = Firefighters choose cars

P(B) = Firefighters choose Trucks

P(A ∩ B)  =  Police Officers choose cars

Thus,

P(A ∩ B) = P(A)P(B)

12 = (4) ( 3)

Hence,  an example of independent events is P(Police Officers and choose cars).

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A bag of 20 marbles consists of 5 blue marbles, 4 red marbles and 9 yellow marbles. You draw a marble out of the bag, put it back then draw out another marble. Calculate the probability you will draw a blue marble on your first draw and then draw a blue marble on your second draw? Write your answer a percentage to the nearest hundredth.

Answers

The probability you will draw a blue marble on your first draw and then draw a blue marble on your second draw is 0.063.

What is probability?

It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

Total marbles = 20

Number of blue marbles = 5

P(blue) = 5/20

P(blue∩blue) = P(blue)×P(blue)

= (5/20)(5/20)

= 25/400

= 1/16

= 0.0625 ≈ 0.063

Thus, the probability you will draw a blue marble on your first draw and then draw a blue marble on your second draw is 0.063.

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Use the zero x = 5, to help find the remaining zeros of x4 - 4x3 - 14x² + 36x + 45. Select one:
O a. x = 5, 3, and -3
O b. x = -1, 3, and -3
O c. None of these
O d. x = 1, 3, and -3​

Answers

Answer:

huh

Step-by-step explanation:

Ratio of men to women working for a company is 7to5 there are 75 women working for the company what is total number of employees

Answers

Answer:

There is a total of 180 employees.

Step-by-step explanation:

men : women

  7    :       5

5 units = 75

   1 unit = 15

12 units = 180

In a statistics class with 36 students the professor wanted to know the probability that at least two students share the same birthday. The probability would be

Answers

The probability that at least two students share the same birthday is 83.22 %.

Probability of sharing the same birthdayLet P(A) = Probability that no two students share same birthdayLet P(A') = Probability at least two students share same birthday

There are 365 days in year and there 36 students in the class.

Total sample space, n = 365³⁶

36 students will be selected as [tex]365P_{36}[/tex]

[tex]P(A) = \frac{365P_{36}}{365^{36}} = 0.1678[/tex]

Probability at least two students share same birthday

P(A') = 1 - P(A)

P(A') = 1 - 0.1678

P(A') = 0.8322

P(A') = 83.22 %

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f(x)=7; find f(-3) and f(0.1)

Answers

Answer:

f(-3) = 7

f(0.1) = 7

Step-by-step explanation:

The function f(x)=7 gives an output of 7 for all inputs. In other words, no matter what we plug in for x, f(x) will equal 7.

When graphed, f(x)=7 produces a horizontal line at y=7. From there, you can also see that any value of x gives an output of 7.

why is smallest possible angle of a 36-gon 5 degrees instead of 4.72222222222?

Answers

The smallest interior angle of the given regular polygon with 36 sides is; 170°

How to find the sum of interior angles of a polygon?

The formula for calculating the sum of interior angles of a regular polygon is; S = (n − 2) × 180°

where n is number of sides of the polygon

We are told that number of sides of ploygon is 36. Thus;

S = (36 - 2) × 180°

S = 6120°

Thus;

Smallest possible angle of polygon = 6120/36 = 170°

Sum of external angles of a regular polygon is;

S = 360/n

S = 360/36

S = 10°

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use the point–slope formula to write an equation of the line that passes through(-5, -16 )and has a slope of m = 3 . Write the answer in slope–intercept form (if possible).

Answers

Answer:

y + 16 = 3(x + 5)

Step-by-step explanation:

When you write an equation in point-slope form, you only need two things: a point and a slope.

Given:

point: (-5, -16)slope (m): 3

The standard point-slope equation is

y - y₁ = m(x - x₁)

Plug in what you know.

y - (-16) = 3(x - (-5))

Simplify.

y + 16 = 3(x + 5)

This is your equation.

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16 Let f(x) and g ) are function such that f () = x+5 and g(x) x+4, what is domain of f(x)+g(x)?​

Answers

Answer: all real numbers

Step-by-step explanation:

I assume you meant to write:

Let f(x) and g(x) be functions such that f(x) = x+5 and g(x) = x+4. What is domain of f(x)+g(x)?​

[tex]f(x)+g(x)=(x+5)+(x+4)=2x+9[/tex]

Since this is a linear function, the domain is all real numbers.

what is it asap please​

Answers

There is a 70% probability that a pupil who uses the swimming pool and gym will be selected. How do I know this? Well, since 30 pupils use neither, this means at least 50/80 pupils use both. This reduces to 5/8, so 5/8 pupils use both the gym and swimming pool. 5/8 as a decimal is equal to 70%, because 80% would be 6/8, 90% would be 7/8, and 100% would be 8/8.

That’s one way to do it.


Another way to solve this is as follows:

Since 22 pupils use the swimming pool and 34 use the gym, that means 56 pupils use both total. 56/80 reduces to 7/10, which as a decimal is 70% or 0.7.

Your final answer: Probability = 70%

If you need more help, let me know and I will gladly assist you!

In parallelogram ABCD, diagonals AC and BD intersect at point E, AE = x^2 - 12, and CE = 4x What is AC?

Answers

The length of the AC is x^2  + 4x  - 12.

What is a parallelogram?

That quadrilateral in which opposite sides are parallel is called a parallelogram.

Thus, a parallelogram is always a quadrilateral but a quadrilateral can or cannot be a parallelogram.

Given :

In Parallelogram ABCD, diagonals AC and BD intersect at point E.

such that

AE = x^2 - 12,

CE = 4x

We know that the diagonal of a parallelogram bisect each other.

x^2 - 12 = 4x

x^2  - 4x  - 12= 0

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

Hence, the value of x = 6, 2.

AC = AE + CE = x^2  + 4x  - 12.

The length of the AC is x^2  + 4x  - 12.

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Quick please!
Will give brainliest
100 points
3(4j + 7 + 2j) or 3(6j +7) b. Use the distributive property to create an equivalent expression.

Answers

Answer:

3(4j + 7 + 2j)

12j + 21 + 6j

12j + 6j + 21

18j + 21 ----- (1)

3(6j +7)

18j + 21 --------(2)

eq 1 = eq. 2

both are equal

round 0.3391 to the nearest thousandth

Answers

Answer:

0.339

Step-by-step explanation:

Hope it helped!

Hii!

___________________________________________________________

Answer: 0.339

Explanation:

Rounding Rules

There are two rounding rules that will help us whenever we need to round a number! These are the rules.

If the number that you need to round is followed by a digit that is less than 5, you round down.If the number that you need to round is followed by a digit that is either greater than or equal to 5, you round up.

---

Now that we know the rules, let's get down to solving our problem! ^^

The nearest thousandth is 3 decimal places.

_._ _ _ <==== Nearest thousandth

The third number after the decimal point is 9. After it is a digit that is less than 5. According to the rounding rules, we should round down.

[tex]\boldsymbol{0.3391=== > 0.339}[/tex]

--

Hope that this helped! Best wishes.

--

Use the five numbers 12, 11, 19, 16, and 12 to complete parts a) through e) below.
a) Compute the mean and standard deviation of the given set of data.
The mean is x = and the standard deviation is s =
(Round to two decimal places as needed.)

Answers

Answer:

mean = 14 and standard deviation = 3.03

Step-by-step explanation:

mean = sum of all numbers ÷ by the numbers available

= (11 + 12 + 12 + 16 + 19) ÷ 5

= 70 ÷ 5

= 14

FOR STANDARD DEVIATION * USE A SCIENTIFIC CALCULATOR THEY WON'T PENALIZE YOU*

follow these steps:

1. press mode then STAT

2. then press 1-VAR

3. put all the numbers on the table in ascending order

4 after press AC

5. press shift then 1

6. you will see many things but we are only interested in standard deviation, press *Var*

7. then select the standard deviation sign and press the equal sign

Solve x:

3x + 99x= 1224

10 pts




Answers

Answer is 12
Reason
Combine like terms
3x + 99 x = 1224
102x = 1224
Now solve for x
Divide both sides by 102
x= 12

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

[tex]\mathsf{3x + 99x = 1,224}\\\\\large\textbf{COMBINE the LIKE TERMS}\\\\\mathsf{(3x + 99x) = 1,224}\\\mathsf{3x + 99x = 1,224}\\\mathsf{\bold{102x} = 1,224}\\\\\large\textbf{DIVIDE 102 to BOTH SIDES}\\\\\mathsf{\dfrac{102x}{102} = \dfrac{1,224}{102}}\\\\\large\textbf{SIMPLIFY IT!}\\\\\mathsf{x = \dfrac{1,224}{102}}\\\\\mathsf{x = 12}\\\\\\\huge\text{Therefore, your answer should be: \boxed{\mathsf{x = 12}}}\huge\checkmark[/tex]

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

~[tex]\frak{Amphitrite1040:)}[/tex]


Use a real number line to define la.
Choose the correct answer below.
OA. |a| = -a for any real number a.
B. The midpoint of the origin and a is la for any real number a.
OC. The distance from the origin to a is la for any real number a.
D. The distance from a to a is |a| for any real number a.

Answers

A number line is just that – a straight, horizontal line with numbers placed at even increments. The distance from the origin to a is |a| for any real number a. Thus, the correct option is C.

What is a number line?

A number line is just that – a straight, horizontal line with numbers placed at even increments along the length. It’s not a ruler, so the space between each number doesn’t matter, but the numbers included on the line determine how it’s meant to be used.

As we know that in the given function |a|, when any value is given to a, then the value that the function is written is equal to a.

Let a=-5, then the value that the function will return is 5. Which is the distance borigin and a, on the number line.

Hence, The distance from the origin to a is |a| for any real number a. Thus, the correct option is C.

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solve the system of equations for one of the variables x+4y=5 x-4y=5

Answers

Answer:

x=5 y=0

Step-by-step explanation:

cancel out the 4y's and then add the x's together. also add the 5s together. 2x = 10, x = 5, and plug it in, and 5 cancels out, leaving y by itself.

A survey of 600 randomly selected high school students determined that 290 play organized sports. what is the probability that a randomly selected high school student plays sports

Answers

Answer:

29/60

Step-by-step explanation:

probability of playing is 290/600 which when simplified is29/60

find the binomial expansion of (2+3x)^5 - (2 - 3x)^5

Answers

 The binomial expansion of (2+3x)^5 - (2 - 3x)^5 is 480x + 2160x^3 + 486x^5

Concept: Binomial expansion is to expand and write the terms which are equal to the natural number exponent of the sum or difference of two terms.

For two terms x and y the binomial expansion to the power of n is (x + y)n = nC0 0 xn y0 + nC1 1 xn - 1 y1 + nC2 2 xn-2 y2 + nC3.

Binomial expansion of (2+3x)^5 =32+240x+720x^2+1080x^3+810x^4+243x^5

Binomial expansion of (2-3x)^5 = 32-240x+720x^2-1080x^3+810x^4-243x^5

Combining both the expansions,=32+240x+720x^2+1080x^3+810x^4+243x^5 - (32-240x+720x^2-1080x^3+810x^4-243x^5)

= 32+240x+720x^2+1080x^3+810x^4+243x^5 - 32+ 240x - 720x^2 +1080x^3 -810x^4 +243x^5

=480x + 2160x^3 + 486x^5

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find y please help meeee :)

Answers

Answer:

the interior angle of a triangle = 180- 89 ( forming linear pair)

= 91°

y = 91 + 23

Y = 114° ( sum of interior angle of a triangle ls equal to its outer angle)

Answer:

114

Step-by-step explanation:

Angle A + 89 = 180 (Sum ofAngles in a straight line)

Angle A = 180 - 89 = 91

Angle B + Angle A + 23 = 180 (Sum of angles in a triangle)

Angle B + 91 + 23 = 180

Angle B = 180 - 114 = 66

Angle B + y = 180 (Sum of angles in a straight line)

66 + y = 180

y = 180 - 66 = 114

Refer to the attached picture.

If f(x)=16x- 30 and g(x)= 14x-6, for which value of x does (f-g)(x)=0?

Answers

Answer:

x=12

Step-by-step explanation:

16x-30-(14x-6)=2x-24=0. add 24 on both sides to get 2x=24. divide by 2 on both sides to get x=12


Given the function f(x) = 8x^2-3x+2 Calculate the following values

Answers

[tex]1) \text{ } f(-2)=8(-2)^{2}-3(-2)+2=\boxed{40}\\\\2) \text{ } f(-1)=8(-1)^{2}-3(-1)+2=\boxed{13}\\\\3) \text{ } f(0)=8(0)^{2}-3(0)+2=\boxed{2}\\\\4) \text{ } f(1)=8(1)^{2}-3(1)+2=\boxed{7}\\\\5) \text{ } f(2)=8(2)^{2}-3(2)+2=\boxed{28}[/tex]

Find the area of the shaded portion of the
figure. All angles are right angles.
Dimensions are in inches.
3
8
5

Answers

Answer:  22 square inches

======================================================

Explanation:

The white rectangle is 3 by 6 with area of 3*6 = 18 square inches.

The larger rectangle is 8 by 5 with area of 8*5 = 40 square inches.

The difference of these will get us the shaded area:

40 - 18 = 22 square inches

Need help with this geometric question

Answers

Answer: QN=19

Step-by-step explanation:

Diagonals of an isosceles trapezoid are congruent, so NQ=PM.

By the segment addition postulate, NQ=QR+RN=3x+7.

So,

[tex]6x-5=3x+7\\\\3x-5=7\\3x=12\\\\x=4[/tex]

So, [tex]QN=3(4)+7=\boxed{19}[/tex]


[tex]4x {}^{2} + 20x + 25[/tex]
using appropriate identity factories the following​

Answers

[tex] \sf{\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Let's Solve ~

[tex]\qquad \sf  \dashrightarrow \: 4 {x}^{2} + 20x + 25[/tex]

[tex]\qquad \sf  \dashrightarrow \: 4 {x}^{2} + 10x + 10x + 25[/tex]

[tex]\qquad \sf  \dashrightarrow \: 2x(2x + 5) + 5(2x + 5)[/tex]

[tex]\qquad \sf  \dashrightarrow \: (2x + 5) (2x + 5)[/tex]

[tex]\qquad \sf  \dashrightarrow \: (2x + 5) {}^{2} [/tex]

or

[tex] \sf{\qquad \sf  \dashrightarrow \: 4x² + 20x + 25 } [/tex]

[tex] \sf{\qquad \sf  \dashrightarrow \: (2x)² + (2 \sdot 2x \sdot 5) + (5)²} [/tex]

[ it's similar to expression - a² + 2ab + b² that is equal to (a + b)² ]

so, let's use this identity here to factorise :

[tex] \sf{\qquad \sf  \dashrightarrow \: (2x + 5)²} [/tex]

I hope it was helpful ~

(3x+7)(x+7)=0
What are the two possible values?​

Answers

For the given equation, either 3x + 7 = 0 or x + 7 = 0

Now,

3x + 7 = 0

3x = -7

x = -7/3

or

x + 7 = 0

x = -7

So, possible values of x is : -7 and -7/3

[tex](3x + 7)(x + 7) = 0 \\ \\ \\3x + 7 = 0 \\ \\ 3x = - 7 \\ \\ x = \frac{ - 7}{3} . \\ \\ \\ x + 7 = 0 \\ \\ x = - 7.[/tex]

Samantha is 9 years younger than her brother Maurice. In 10
years, Maurice will be 1.5 times older than his sister. Find their
present ages.

Answers

Step-by-step explanation:

hope you can understand

Answer:

Samantha is 8 years and Maurice is 17 years

Step-by-step explanation:

First represent Samantha's brother's age with a variable, x.

Secondly, find Samantha's age. since shes 9 years younger, then it will be her brother's age which is x minus 9

Thirdly, in ten years, they will all age hence 10 will be added to all their ages.

Fourthly, once 10 has been added to their after 10 years, rhen we realise Maurice age will be 1.5 timess Samantha's age... Then you solve the resulting equation.

Solve x^2 - 10x = 30x

Answers

[tex]x^2-10x=30x\\x^2-40x=0\\x(x-40)=0\\x=0 \vee x=40[/tex]

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