the question is
on the image. ​

The Question Is On The Image.

Answers

Answer 1

Answer:

PR = 7.99 cm (2 dp)

Step-by-step explanation:

Pythagoras' Theorem:  a² + b² = c²

(where a and b are the legs, and c is the hypotenuse, of a right triangle)

From inspection of the triangle:

a = PRb = PQ = 12.1 cmc = RQ = 14.5 cm

Substituting the given values into the formula;:

⇒ a² + b² = c²

⇒ PR² + 12.1² = 14.5²

⇒ PR² + 146.41 = 210.25

⇒ PR² = 210.25 - 146.41

⇒ PR² = 63.84

⇒ PR = ±√(63.84)

⇒ PR = ±7.99 (2 dp)

As distance is positive, PR = 7.99 cm (2 dp) only


Related Questions

There are a total of 12 bicycles and tricycles in a parking lot. If there are 31 wheels in all, how many of them are bicycles?

Answers

Answer:

5 bicycles

Step-by-step explanation:

5 * 2 = 10 wheels

7 * 3 = 21 wheels

10 + 21 = 31

Hope this helped! Brainliest :)

find the value of x

Answers

[tex]\textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2 \qquad \begin{cases} c=\stackrel{hypotenuse}{11 + x}\\ a=\stackrel{adjacent}{x}\\ b=\stackrel{opposite}{17}\\ \end{cases}\implies (11+x)^2=x^2+17^2 \\\\\\ (11+x)(11+x)=x^2+17^2\implies \stackrel{F~O~I~L}{121+22x+x^2}~~ = ~~x^2+289 \\\\\\ 121+22x=289\implies 22x=168\implies x=\cfrac{168}{22}\implies x=\cfrac{84}{11}\implies x=7\frac{7}{11}[/tex]

Select the reason that best supports Statement 7 in the given proof.

Answers

Answer:

the guy above if right it is D

Step-by-step explanation:

I did the work on Acellus and pick D IT GAVE ME A CHECK MARK

The reason that supports the statement 7 in the given proof is D. Subtraction property of equality.

What is Subtraction property of equality?

Subtraction property of equality is defined as, if an equation is of the form,

a = b,

then any number subtracted from both sides makes the equation same.

a - c = b - c

Here, given a proof for the value of x.

In the 6th step, by substitution,

55 = 5x + 10

This is an equation.

We need term in x on one side and a constant term on other side.

For that, if we subtract both sides by 10,

55 - 10 = 5x + 10 - 10

45 = 5x

So here the subtraction property of equality is used.

Hence the correct option is D.

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Your younger brother is getting stickers from a vending machine at the local supermarket. A proportion of stickers have the
phrase "Girls Rule!" If there are eight stickers with this message in a sample of 36 stickers, what is the 95% confidence interval
for this proportion? (1 point)
0 (0.0864, 0.3580)
0 (0.0862, 0.3578)
0 (0.0847, 0.3553)
0 (0.0812, 0.3256)

Answers

Answer:

p^​=368​=0.2222.95%CI=(0.2222−1.960.2222(1−0.2222)36,0.2222+1.960.2222(1−0.2222)36)=95%CI=(0.2222−1.96360.2222(1−0.2222)​​,0.2222+1.96360.2222(1−0.2222)​​)==(0.0864,0.3580).

=(0.0864,0.3580).

Step-by-step explanation:

flvs?

The 95% confidence interval for the given proportion is  (0.864, 0.3580).

What is a confidence interval?

In statistics, a confidence interval describes the likelihood that a population parameter would fall between a set of values for a given percentage of the time. Confidence ranges that include 95% or 99% of predicted observations are frequently used by analysts.

Given total samples = E = 36

number of outcomes  = 8

probability = p = 8/36 = 0.2222

value of z for 95% confidence interval = 1.96

intervals = p ± z([tex]\sqrt{\frac{p(1 - p)}{E} }[/tex])

taking positive sign

= 0.2222 + 1.96[tex](\sqrt{\frac{0.2222(1 - 0.2222)}{36} })[/tex] = 0.3580

taking negative sign

= 0.2222 - 1.96[tex](\sqrt{\frac{0.2222(1 - 0.2222)}{36} })[/tex]  = 0.0864

Hence, the intervals are  (0.864, 0.3580), and option A is a suitable answer.

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The half-life of a particular radioactive substance is 10 seconds. If you started with 100 grams of this substance, how much of it would remain after 60 seconds?

Answers

Answer:
100(1-0.50)^6
remaining amount is:

1.56

There are 1.5625 grams of the radioactive substance that would remain after 60 seconds.

What is an exponent?

The exponent of a number represents the total time required to multiply that number. 8 8 8 may be stated as 83 since 8 is multiplied by itself three times. In this case, 3 is the 'exponent' or 'power' that indicates how many times 8 is multiplied by itself, and 8 is the 'base' that represents the integer being multiplied.

The exponent is given as:

y = a (1 - r)ˣ

As per the question, we have

a = 100, and r = 0.50 and x = 6

Substitute the known values in the above formula, and we get

y = 100 × (1-0.50)⁶

y = 100 × (0.50)⁶

y = 100 × 0.015625

Apply the multiplication operation, a

y = 1.5625

So, after 60 seconds, 1.5625 grams of the radioactive substance would remain.

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based on the experimental probability about how many times will yosef draw a green marble if he draws a total of 75 marbles

Answers

35 if you want to count purple but 12 if your from orange

Simplify the following variable expressions ​

Answers

a. 6x-1
b. 3x-12
Hope this helps!!

Katie practiced her flute for 45 mins Then she ate a snack for 15 mins Next She watched televosion for 30 mins until 6:00 p.m at what time did Katie start practicing the flute

Answers

I want to assume at 4:30
Katie practiced the flute at 5:15 pm

First we add 30 and 15 which is 45 then subtract that from 60 because 60 minutes make up an hour. 60-45= 15 therefore, Katie practiced the flute at 5:15 pm

find perimeter of a semicircle that has radius of 6cm (give answer in 2 d.p)​

Answers

Answer:

30.84 cm

Step-by-step explanation:

Formula for perimeter of semi-circle = πr + 2r

Radius (r) = 6 cm

π = 3.14

Perimeter

= πr + 2r

= 3.14(6) + 2(6)

= 3.14(6) + 12

= 18.84 + 12

= 30.84 cm

_________

Hope it helps ⚜

Answer:

30.85 cm to 2 d.p.

Step-by-step explanation:

The perimeter is made up of the diameter ( = 2*radius) and half a full circle

= 6*2 + 1/2 * π* 6

= 12 + 3π

= 30.849

will give brainliest!!

Evaluate [(40 + 5) – 321 = 9.2
- 9.3
- 8.6
- 8
- 2

Answers

Answer:

The answer should be 9.2

Step-by-step explanation:

Im lowkey kinda lost in this one ngl

find the volume of a right circular cone that has a height of 3.2 m and a base with a radius of 14.1 m

Answers

Answer: 666.22 m^3

Step-by-step explanation:

The formula for the volume of a right circular cone is: V = π*r^2*(h/

3)

Therefore, plugging in 14.1 for "r" and 3.2 for "h" yields 666.22

A 20-inch pizza has an area of 314 in? That pizza is
divided into eight equal slices. What is the area of two slices of
that pizza?

A. 3114 in2
B. 78.5 in2
C. 39.25 in2
D. 314 in2

Answers

The area of each pizza is gotten by dividing the total area by the number of slices. Therefore, the area of two slices of that pizza is 31.4 inches².

What is area?

Area is the amount of space occupied by a two-dimensional figure. In other words the area is the space occupied by a flat shape or the surface of an object.

Therefore, 20 inch pizza has an area of 314 inches². The pizza is divided into 8 equal slices.

Each area of the slices = 314 / 20

Each area of the slices = 15.7 inches²

Therefore, the area of two slices of the pizza is as follows:

area of two slices = 15.7 + 15.7 = 31.4 inches²

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The figure below is composed of eight circles, seven small circles and one large circle containing them all. Neighboring circles only share one point, and two regions between the smaller circles have been shaded. Each small circle has a radius of 5 cm.

Answers

The figure below is composed of eight circles, seven small circles and one large circle containing them all. Neighboring circles only share one point, and two regions between the smaller circles have been shaded. Each small circle has a radius of 5 cm.

what numbers can you make ?

Answers

169 is the number closest to 200 that you can make using three of those numbers

Answer:

196

Step-by-step explanation:

their sum is -11 and difference is 41

Answers

Answer:

15 and -26.

Step-by-step explanation:

Answer:

15 and -26

Step-by-step explanation:

just bc

What is an estimate of 37.9% of 192.3?
A 57
B 02
C 80
D 100

Answers

Answer:

C.80

Step-by-step explanation:

37.9% of 192.3

=37.9/100 × 192.3

=0.379×192.3

=72.8817

≈80 (possible answer)

Which statements are true for the following expression?
(9 + 1) · 5

Answers

Answer:

50

Step-by-step explanation:

add

9 + 1 = 10

multiply

10 * 5 = 50

Answer: 50

The length and width of the park are measured in linear units. inches, miles, meters, etc the area is measured in square units. explain the reason for using square units for area of the park. (please hurry and make it not too long please )​

Answers

The area is measured in square units because it is the product of two units which gives square unit.

What is area?

Area is the amount of space occupied by a two dimensional shape or object.

The area of a rectangular park is gotten from the productiif the width and length, hence:

Area = length * width

The area is measured in square units because it is the product of two units which gives square unit.

Find out more on area at: https://brainly.com/question/25292087

Evaluate the function graphically.

Find f(3)

Answers

f(3) means what is y when, x = 3

It is 6 because at x=3, y =6

A circular swimming pool has a radius of 20 feet. The family that owns the pool wants to put up a circular fence that is 5 feet away from the pool at all points. Which is closest to the circumference of the fence they will need?

Answers

Answer:

157.08 ft

Step-by-step explanation:

R = 20+5 = 25

Circumfrence = 2*pi*r = 2*pi*25 = 157.079 ft

factorise: x^4– 5x^2 + 4​

Answers

Answer:

(x - 2)(x - 1)(x + 1)(x + 2)

Step-by-step explanation:

[tex] {x}^{4} - 5 {x}^{2} + 4 \\ \\ = {x}^{4} - 4 {x}^{2} - {x}^{2} + 4 \\ \\ = {x}^{2} ( {x}^{2} - 4) - 1( {x}^{2} - 4) \\ \\ = ( {x}^{2} - 4)( {x}^{2} - 1) \\ \\ = (x + 2)(x - 2)(x + 1)(x - 1) \\ \\ = (x - 2)(x - 1)(x + 1)(x + 2)[/tex]

Answer:

[tex](x+1)(x-1)(x+2)(x-2)[/tex]

Step-by-step explanation:

To factorise  [tex]x^4-5x^2+4[/tex] :

Let [tex]x^2=u[/tex]

[tex]\implies x^4-5x^2+4=u^2-5u+4[/tex]

Now factorise  [tex]u^2-5u+4[/tex]

[tex]\textsf{for} \ ax^2+bx+c \ \textsf{find} \ v, w \ \textsf{such that} \ v \cdot w=a \cdot c \ \textsf{and} \ v+w=b[/tex]

[tex]\textsf{and group into} \ (ax^2+vx)+(wx+c)[/tex]

[tex]\implies v=-1, w=-4[/tex]

[tex]\implies u^2-u-4u+4[/tex]

Break into groups

[tex]\implies (u^2-u)+(-4u+4)[/tex]

Factor each parentheses:

[tex]\implies u(u-1)-4(u-1)[/tex]

Factor out common term [tex](u-1)[/tex]:

[tex]\implies (u-1)(u-4)[/tex]

Substitute back [tex]u=x^2[/tex] :

[tex]\implies (x^2-1)(x^2-4)[/tex]

Factor both parentheses using the Difference of Two Squares: [tex]a^2-b^2=(a+b)(a-b)[/tex]

[tex]\implies (x+1)(x-1)(x+2)(x-2)[/tex]

Therefore, the factorisation of [tex]x^4-5x^2+4[/tex] is

[tex](x+1)(x-1)(x+2)(x-2)[/tex]

Need help with this, I’ll give brainliest for an explaining response :)

Answers

Answer:

d

Step-by-step explanation:

The answer must be a multiple of 4, because 4q⁵rs⁴ is divisible by 4. Only option d has this condition.

9,000 were divided equally among a certain no of persons . had there been 20 more person each would have got rupees 160 . find the original no of persons​

Answers

Answer:

let the number of persons be " x "

and , let each person get [tex]\frac{9000}{x}\\[/tex]rupees.

______________________________________

let's first see why each person got [tex]\frac{9000}{x}\\[/tex] rupees ,

let us suppose each person gets an amount of " r " rupees.

then ,

[tex]x \times r = amount \: we \: have \: with \: us \\ \dashrightarrow{xr = 9000} \\ \dashrightarrow{ r = \frac{9000}{x}} [/tex]

_____________________________________

According to Question ,

hαd thєrє вєєn 20 mσrє pєrѕσnѕ, єαch pєrѕσn wσuld'vє gσt rupєєѕ 160 lєѕѕ.

hєncє, wє αrє nσw ín α ѕtαtє tσ frαmє αn єquαtíσn whích íѕ αѕ fσllσwѕ -

[tex]\fbox{(x + 20)(r - 160) = 9000}[/tex]

lєt'ѕ nσw plug ín thє vαluє σf r αѕ [tex]\frac{9000}{x}\\[/tex]

[tex](x + 20)( \frac{9000}{x} - 160) = 900 0\\ \\ \cancel{9000} + \frac{180000}{x} - 160x - 3200 =\cancel{ 9000} \\ \\ taking\:LCM, \\ \\ - 160x {}^{2} - 3200x + 180000 = 0 [/tex]

on dividing the complete equation by (- 160)

[tex]x { }^{2} + 20x - 1125 = 0[/tex]

now , use the method of splitting the middle term so that we get the value of x.

[tex]x {}^{2} + 45x - 25x - 1125 = 0 \\ \\ x(x + 45) - 25(x + 45) \\ \\ (x + 45)(x - 25) = 0 \\ \\ \fbox{x = - 45 \: \: or \: \: 25}[/tex]

since number of persons can't be negative. therefore ,

number of persons = x = 25

_____________________________

_____________________________

hope helpful :D

Which expression is equivalent to 125 x 15,??
y
O 5x®y3z
0 5x²y5z
O 25x²y3z
O 25x²y5z

Answers

Answer:

25²×3is the equivalent answer

Please answer I am stuck on this problem

Answers

Answer:

20+2C

Step-by-step explanation:

sum means addition

if Craig's age is c than twice his age is 2xC, also expressed as 2C

20+2C

Please help its decimals

Answers

Each line they are adding 4.96


11.72 + 4.96 = 16.68

Answer:

the correct answer is 16.68

A mother shared $400 amongst her three daughters Amy, Beatrice and Claire in the ratio of 3:2:5 respectively. How much money did Amy receive?

Answers

Answer:

$120

Step-by-step explanation:

Total Parts = 3+2+5 = 10

400 / 10 = $40 per part

Amy = 40 x 3 = 120

Ivanna needs to buy some pencils. Brand A has a pack of 36 pencils for 8.52 . Brand B has a pack of 48 pencils for 9.98 . Find the unit price for each brand. Then state which brand is the better buy based on the unit price. Round your answers to the nearest cent.

Answers

Answer:

Brand B is better

Step-by-step explanation:

Brand A's unit price is $0.24

Brand B's unit price is $0.21

Is -2 a whole number or irrational number?

Answers

Answer:

It is neither.

Step-by-step explanation:

A whole number is all numbers is 0, 1, 2, 3, 4.... you get it

An irrational number is a number that cannot be written as a fraction and -2 can be written as -2/1

solve for x:
-3(x-2)^2+17=0
round your answer to the nearest hundredth

Answers

Answer:

-3(x-2)×2+17=0

-3x+6×2+17=0-3x+12+17=0-3x+29=0-3x=0-29=-29-3x=-2929÷3=9.700 to the nearest hundredth
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