A tangent PQ at a point P of a circle of radius. 5cm meets a line through the centre O at a point Q so that OQ = 12 cm. Length PQ is :
A)12 cm
B) 13 cm
C) 8.5 cm
D) √119 cm
Answers
Answer :
[tex]\boxed{D) \sqrt{119} \: cm}[/tex]
Solution :
In the above figure, the line that is drawn from the centre of the given circle to the targent PQ is perpendicular to PQ.
And So, OP ⊥ PQ
Using Pythagoras theorem in triangle ΔOPQ we get ,
[tex]\Longrightarrow\: OQ^2 = OP^2 + PQ^2[/tex]
[tex] \: \: \: \: \: \: \: \: \: \: \: \: [/tex]
[tex]\Longrightarrow\: (12)^2 = 5^2+PQ^2[/tex]
[tex]\: \: \: \: \: \: \: \: \: \: \: \: [/tex]
[tex]\Longrightarrow\: PQ^2 = 144-25[/tex]
[tex]\: \: \: \: \: \: \: \: \: \: \: \: [/tex]
[tex]\Longrightarrow\: PQ^2 = 119[/tex]
[tex]\: \: \: \: \: \: \: \: \: \: \: \: [/tex]
[tex]\Longrightarrow\: PQ = \sqrt{119} [/tex]
[tex]\: \: \: \: \: \: \: \: \: \: \: \: [/tex]
So, option D) √119 cm is the length of PQ.
Related Questions
Renting Cars Floppy Jalopy Rent-a-Car has 25 cars available for
rental-20 big bombs and 5 midsize cars. If two cars are selected at
random, what is the probability that both are big bombs?
Answers
The probability that both are big bombs is 19/30 or 0.63 if the renting Car's Floppy Jalopy Rent-a-Car has 25 cars available for rental-20 big bombs and 5 midsize cars. If two cars are selected at random.
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.
We have:
Renting Cars Floppy Jalopy Rent-a-Car has 25 cars available for rental-20 big bombs and 5 midsize cars. If two cars are selected at random.
Total number of outcomes = C(25, 2) = 300
Total number of favorable outcomes = C(20, 2) = 190
Probability = 190/300 = 19/30 or
= 0.63
Thus, the probability that both are big bombs is 19/30 or 0.63 if the renting Car's Floppy Jalopy Rent-a-Car has 25 cars available for rental-20 big bombs and 5 midsize cars. If two cars are selected at random.
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please answer this!!!
Answers
Step-by-step explanation:
sin60 =opp/hyp
0.86=y/20
y=17.2
cos60=adj/hyp
0.5=x/20
x=10
sin57=y/15
0.83=y/15
y=12.45
Explanation: a right angle adds to 90 degrees, meaning you would Add 57 and 15, then subtract that from 90. You would get -18, but turn that into a positive. Your answer will be 18 for Y on the second problem.
If overhead is applied to individual jobs at a rate of 50% of direct labor costs incurred per job, and $50,000 in direct materials were used and $25,000 of direct labor was required, what was the total cost of the job?
a) $25,000
b) $50,000
c) $12,500
d) $87,500
Answers
The total cost of the Job in the question is; D: $87,500
How to find the total Cost?
We are given that;
Direct Labor = $25000
Cost of direct materials used = $50000
Overhead is 50% of direct labor costs. Thus;
Overhead Cost = 50% * $25000 = $12500
Total Cost of Job = Overhead Cost + Materials Cost + Labor Cost
Total Cost of Job = $87,500
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In the past month, Joe rented 5 video games and 4 DVDs. The rental price for each video game was $2.60. The rental price for each DVD was $3.30. What is
the total amount that Joe spent on video game and DVD rentals in the past month?
Answers
Answer:
$26.2
Step-by-step explanation:
5*2.50 is 13 for video games
4*3.30 is 13.2 for DVD
Sum them up and you get 26.2
What is the eighth term of the sequence below?
5, 9, 13, 17, …
A. 33
B. 30
C. 29
D. 34
Answers
Answer:
A. 33
Step-by-step explanation:
Add 4 to each number
1. 5 is your first number
2. 5+4= 9 is your second number
3. 9+4= 13 is your third number
4. 13+4= 17 ...
5. 17+4= 21 ...
6. 21+4= 25 ...
7.25+4= 29 ...
8.29+ 4= 33 is your eight number
Enter the values for the highlighted variables that show how to subtract the rational expressions correctly: startfraction 2 over x squared minus 36 endfraction minus startfraction 1 over x squared 6 x endfraction = startfraction 2 over (x 6) (x minus 6) endfraction minus startfraction 1 over x (x a) endfraction. = startfraction b x over (x 6) (x minus 6) x endfraction minus startfraction x minus c over (x 6) (x minus 6) x endfraction. = startfraction d x minus x e over (x 6) (x minus 6) x endfraction. = startfraction x f over (x 6) (x minus 6) x endfraction. = startfraction g over x (x minus 6) endfraction a = b = c = d = e = f = g =
Answers
The values for the highlighted variables that show how to subtract the rational expressions correctly are a = 6, x^2 + 6x is equal to x(x+6), and b=2.
How to explain rational expressions?From the informaation, the denominator and numerator of the first term are multiplied by x.
The second term is multiplied by (x-6)/(x-6).
Now that they have the same denominator, the two terms are combined. 2 is the coefficient of the first term. In the same way as d is carried over from b, e is carried over from c.
We factor out the (x+6) from the numerator and denominator.
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Somebody please explain how to solve this by formula or theorem
Answers
[tex]\text{It is an equilateral triangle, so all angles are equal to}~ 60^{\circ}\\\\~~~~~~m\angle 2 = x+72\\\\\implies 60 = x+72\\\\\implies x = 60-72\\\\\implies x = -12[/tex]
Determine why the triangles are congruent. Choose from SSS, SAS, ASA, AAS, and HL. If the
triangles are not congruent type NC. (Use all capitals in your answer)
Answers
Answer:
Step-by-step explanation:
the distance lesley walks from home to school is 120 meters and 80 meters when he goes to church from home. gusion estimates that the distance lesley walks when he goes directly to church. coming frim school is 180 meters. guinevere's estimation is 210 meters which etimation is feasible? make a map of lesley ways from home to school and church justify.
Answers
Guinevere’s estimation of 210m is not feasible.
Gusion’s estimate is feasible if the locations form a triangle.
A water tank measures 1.4m by 8cm by 60cm. Find the capacity of the tank in litres
Answers
Answer:
672 litres.
Step-by-step explanation:
Convert the measurements to cm:
14 m = 1400 cm
The capacity = 1400 * 8 * 60
= 672,00 cm^3
There are 1000 cm^3 in 1 litre so the answer is
672 litres.
PLSSS HELP ME WITH MATH
Answers
Step-by-step explanation:
always remember, equations and inequalities are like a scale with 2 pans (left and right).
a variable is like a placeholder, an empty spot on the pans. and the expressions on both sides are kind of the conditions for the things to put in these empty spots so that the status of the scale stays unchanged.
for an equation the scale has to stay balanced all the time.
and in an inequality one side is heavier that the other (it normally does not matter how much heavier) with "<" or ">" signs, or the scale can be also balanced with "<=" or ">=" signs. just the other side must never be heavier.
A
so, in our case here
2x - 5 = 3
yes, the solution (the ONLY solution, actually) is x = 4. no other value of x allows the scale to be balanced.
2x - 5 >= 3
well, since it is a ">=" sign, we can be lazy and treat it like the equation above, and x = 4 is therefore a valid solution for the inequality too.
but so is every other value of x that makes the left side "heavier". what about e.g. 5 ?
2×5 - 5 >= 3
10 - 5 >= 3
5 >= 3
true, great ! so, e.g. x = 5 is also a valid solution.
what else ?
let's simplify the inequality
2x - 5 >= 3
2x >= 8
x >= 4
so, really every value of x that is greater or equal to 4 is a valid solution for the inequality.
B
-2x - 5 = 3
yes, the solution (the ONLY solution, actually) is x = -4. no other value of x allows the scale to be balanced.
-2x - 5 >= 3
well, since it is a ">=" sign, we can be lazy and treat it like the equation above, and x = -4 is therefore a valid solution for the inequality too.
but so is every other value of x that makes the left side "heavier". what about e.g. -5 ?
-2×-5 - 5 >= 3
remember, -×- = +
10 - 5 >= 3
5 >= 3
true, great ! so, e.g. x = -5 is also a valid solution.
what else ?
let's simplify the inequality
-2x - 5 >= 3
-2x >= 8
x <= -4
a multiplication or division by a negative value flips the inequality sign, because such an operation makes a light weight heavy and a heavy weight light.
so, really every value of x that is less or equal to -4 is a valid solution for the inequality.
If two supplementary angles are in the ratio of 7: 8 ,find them.
Answers
Answer:
84° and 96°Step-by-step explanation :
Given :
Two supplementary angles are in the ratio of 7: 8To Find :
The two anglesSolution :
Let the angles be 7x and 8x respectively
As We know that, Sum of supplementary angles is always 180°
So, Adding Both the angles,
→ 7x + 8x = 180°
→ 15x = 180°
→ x = 180/15
→ x = 12
Hence,
7x = 7(12) = 84° 8x = 8(12) = 96°Therefore,
The required angles are 84° and 96°Alizeh plans on leaving her $10,000 invested for 20 years. Write an equation representing her investment’s value, y, after x years. What is the value of Alizeh’s investment after 20 years?
Answers
Answer:
$38696.84
Step-by-step explanation:
7% interest
so *1.07 per year
10,000*1.07^x=y
10,000*1.07^20=$38696.84
The equation that represent the value of Alizeh’s investment after 20 years is y = 1000(b)^20
Exponential equationThe increase in the amount of his money can be represented using the exponential function as shown:
y = ab^x
Given the following
a = 1000
x = 20 years
Substitute
y = 1000(b)^20
Hence the equation that represent the value of Alizeh’s investment after 20 years is y = 1000(b)^20
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y
12
11
10
9
7
NWO0065
4
-12-11-10-9-8
-65
-3-2-1
1
2 3 4 5 6
8 9 10 11 12
-2
-9
-10
-11
-12
Answers
Answer:
y12111097
Step-by-step explanation:
because I know the answer
A sector whose central angle measures 72º has an area of 16.211 square feet. What is the radius of the circle?
Answers
Answer:
81.055 ft²
Step-by-step explanation:
A full circle has a central angle of 360°.
A sector with a central angle is 72° is 72/360 = 1/5 of a circle.
A full circle has 5 times the area of a sector with a 72° central angle.
A = 5 × 16.211 ft²
A = 81.055 ft²
Robert climbed 125 steps in five minutes at this rate how many steps did he average per minute
Answers
The solution is 62. We have to multiply the mixed number by the whole number. 12 1/2 is 25/2 so we now multiply by flipping the 25/2 to 2/25 and when you multiply you get 1550/25, which is 62
Which number sentence is not true?
A. | -1 | > 1/2
B. | -1 | = -1
C. | 1/2 | < | -1 |
D. | -1/2 | < | -1 |
Answers
Answer:
Option B
Step-by-step explanation:
|-1| [tex]\neq[/tex] -1
|-1| = 1
Answer:b
Step-by-step explanation: bc it’s right
A certain ore contains 9 percent gold. How much ore (in tons) is needed to obtain 126 tons of gold
Answers
Answer:
251,991 tons of ore are need to obtain 126 tons of gold.
Step-by-step explanation:
solve this using pythagorean theorem please and give me the right answer and i will give YOU brainliest and a like in return.
Answers
Answer:
[tex]They\ are\ 8.544\ feet\ apart[/tex]
Step-by-step explanation:
Step 1: Determine the important information
Math teacher 8 feet in front
Science teacher 3 feet to the right
Step 2: Determine how far apart the teachers are
Pythagorean theorem → [tex]a^2 + b^2 = c^2[/tex]
[tex](8)^2+(3)^2=c^2[/tex]
[tex]64 + 9 = c^2[/tex]
[tex]73 = c^2[/tex]
[tex]\sqrt{73} = \sqrt{c^2}[/tex]
[tex]8.544=c[/tex]
Answer: [tex]They\ are\ 8.544\ feet\ apart[/tex]
Tell whether a triangle with the side lengths 65 feet, 72 feet, and 97 feet is a right triangle.
Answers
Answer:
when the sum of the squares of the sides are equal to the square of the hypotenuse
Step-by-step explanation:
we use Pythagoras, 97 is the hypotenuse, 65 and 72 the sides.
97² = 65² + 72²
97² = 97²
it is a right triangle
VW has a midpoint at M(12, 0.5). Point V is at (10, -18). Find the coordinates of point W. Write the coordinates as decimals or integers.
Answers
[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ V(\stackrel{x_1}{10}~,~\stackrel{y_1}{-18})\qquad W(\stackrel{x_2}{x}~,~\stackrel{y_2}{y}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ x +10}{2}~~~ ,~~~ \cfrac{ y -18}{2} \right)~~ = ~~\stackrel{M}{(12~~,~~0.5)} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ x +10}{2}=12\implies x+10=24\implies \boxed{x=14} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ y -18}{2}=0.5\implies y-18=1\implies \boxed{y=19}[/tex]
Find the coordinates of the midpoint of the line segment with endpoints at ( 6, -7) and (-3,5)
Answers
Answer:
Coordinates of the midpoint are ( 9/2 , -6 )
subtract the quotient of 15 divided by 3 from the sum of 33 and 7
Answers
Answer:
(33+7)-(15/3) = 35
Step-by-step explanation:
35
Step-by-step explanation:
fancy way of saying (33+7) - (15/3)
33 + 7 = 40
15 / 3 = 5
40 - 5 = 35
#88 will give brainliest to the best response!
Answers
Answer:
Mean: 80
Mode: 81
Median:81
Step-by-step explanation:
First, let's get the set of numbers from this Stem-and-Leaf plot:
[60,61,73,75,79,81,81,81,92,96,98]. From here we can solve for the mean by adding all the numbers up and dividing it by the number of terms that we have: [tex]\frac{60+61+73+75+79+81+81+81+92+96+98}{11} = 80[/tex] when rounded to the nearest whole number. The median is the middle number of the set when arranged from least to greatest, in this case, the median is 81.
Hope this helps! :)
Emmet set up a bubble station for his little sister's birthday party. He filled a bubble machine and a bottle for kids to blow their own bubbles. In the bubble machine, Emmet mixed 12 ounces of dish soap and 24 ounces of water. In the bottle, he mixed 5 ounces of dish soap and 9 ounces of water. Which container had the greater ratio of dish soap to water?
Answers
Answer:
It's 5912
Step-by-step explanation:
It's 5912 cause 5912 is the answer.
Please help me its a math problem !! please see image
Answers
Answer:
y ≤ 4
Step-by-step explanation:
Solving :
Highest y-value is 4The other y-values are less than 4Hence, the range is : y ≤ 4A car travels a distance of D km at 80 km/h and arrives 20 min late. If the car travels at
120 km/h, the car will arrive 20 min early. Find the value of D.
Answers
What is the range for the following set of measurements? 7.1 g, 9.8 g, 2.3 g, 8.5 g, 7.4 g, 5.7 g
Answers
Answer:
7.5
Step-by-step explanation:
you take the largest number (9.8) and subtract with the smallest number (2.3)
9.8-2.3= 7.5You asked students the survey question: How many hours did you do homework last week? The responses were 3, 10, 5, 7, 4, 8, 3, 5, 4, and 2 hours. Which statement best represents the data?
1. Most of the friends who responded did homework for 5 or fewer hours last week.
2. Most of the friends who responded did homework for more than 8 hours last week.
3. Most of the friends who responded did homework for 6 or more hours last week.
4. Exactly half of the friends who responded did homework for fewer than 6 hours last week.
Answers
If you write it out in order of smallest number to largest number, you can count that only 3 people out of the ten total did over 5 hours of homework
I need help with part 2 on this question (Screenshot)
Answers
Hope this helps.