Answers
Answer:
16 meters
Step-by-step explanation:
[tex] In\: \odot F, \: \overline {RS} [/tex] is tangent to the circle at point R and FR is radius.
[tex] \therefore RF\perp RS[/tex] (Tangent radius theorem)
[tex] \therefore m\angle FRS = 90\degree [/tex]
So, [tex] \triangle FRS[/tex] is right angled triangle and FS is its hypotenuse.
Let FR = FT = r
FS = FT + ST = r + 9
Now, by Pythagoras theorem:
[tex]FR^2 + RS^2 = FS^2 \\ \therefore r^2 + (15)^2 = (r + 9)^2 \\ \therefore \cancel{ r^2} +225 = \cancel{ r^2} + 18r + 81\\ \therefore \: 225 = 18r + 81 \\ \therefore \: 225 - 81= 18r \\ \therefore \: 144= 18r \\ \therefore \: r = \frac{144}{18} \\ \therefore \: r =8 \: m\\ \implies \: d = 2r = 2(8) = 16 \: m[/tex]
Thus, the diameter of the fountain is 16 meters.
Related Questions
Write the equation of this line from the table provided.
SOMEONE PLEASE HELP ASAP I WILL GIVE YOU BRAINLIEST!!!
Answers
Answer:
y=2x-1
Step-by-step explanation:
If you are supposed to write the equation in slope-intercept format, (y=mx+b), then y=2x-1 would be the answer. 2 is the slope(m), and -1 is the y-intercept(b). I hope thus helped :).
Jane will rent a car for the weekend she can choose one of the two plans the first plan has an initial fee of $42 in cost of additional $.12 per mile driven the second plan has an initial fee of $55 in cost additional seven cents per mile driven
Answers
Answer:
260m
$73.2
Step-by-step explanation:
For what amount of driving do the plans cost the same?
What the cost when the two plans cost the same?
first plan = 42 + 0.12m
second plan = 55 + 0.07m
42 + 0.12m = 55 + 0.07m
collect like terms
55 - 42 = 0.12 - 0.07m
13 = 0.05m
m = 260
42 + 0.12(260) = 73.2
Samantha has chocolate bars and lollipops in the the ratio 4:5. If she has 12 chocolate bars,how many lollipops does she have?
Answers
5 • 3 = 15
she has 15 lollipops
Someone help me please with this ? Like right now please
Answers
Answer: 6472
Step-by-step explanation:
You have to multiply and add
A train travels a total of 67 km at a constant speed of 110 km/h.
How long is its journey? Give your answer in minutes and seconds, to the nearest second.
Answers
Answer:
36 m 32 s
Step-by-step explanation:
67 /110 = 0.609 hour
0.609 × 60 minutes = 36.54 minutes
36 minutes + 0.54×60 second
= 36 minutes 32 seconds
Answer:
36 mins 32 secs
Step-by-step explanation:
Is knowing the coordinates of the vertex of a parabola enough to determine the domain and range? a. No: we would have no information about the domain. c. Yes: if the vertex is at (m,n), then the domain is all reals and the range is y ≤ n. b. No: we would need to know if the vertex is a minimum or a maximum. d. Yes: if the vertex is at (m,n), then the domain is all reals and the range is y ≥ n.
Answers
Answer:
The answer would have to be B
Step-by-step explanation:
explains itself
Answer:it’s B
Step-by-step explanation:
600 raffle tickets were sold for $5 each. There is one $500 first prize and three $200 second prizes. The remainder of the tickets do not win anything. What is the expected value of this raffle?
Answers
Answer:
its -$3.17
Step-by-step explanation:
500-5=495
200-5=195
the remainder of the tickets is -$5
the expected value is $495 x 1/600 + $ 19583/600 + (-$5) 596/600= -$3.17
it takes luis 4.5 minutes to read 3 pages. how long will it take him to read 32 pages?
Answers
Answer:
48 minutes
Step-by-step explanation:
4.5/3 = 1.5
1.5 x 32 = 48
Joseph runs 2 miles on Monday. Each day after that, he runs the same 1 1/3 mile route every
morning. His goal is to run at least 6 miles by the end of the week.
Which inequality represents the least number of days after Monday that Joseph needs to run
to reach his goal? *
Answers
Answer:
2 + 1 1/3x ≥ 6
x ≥ 3 days
Step-by-step explanation:
Monday = 2 miles
Other days = 1 1/3 miles
x = least number of days after Monday that Joseph needs to run
to reach his goal
Total miles = 6 miles
The inequality is
2 + 1 1/3x ≥ 6
1 1/3x ≥ 6 - 2
1 1/3x ≥ 4
4/3x ≥ 4
Divide both sides by 4/3
4/3x ÷ 4/3 ≥ 4 ÷ 4/3
x ≥ 4 × 3/4
x ≥ 3 days
Which would it be please?Help if you can.
Answers
Answer:
B
Step-by-step explanation:
Area = length times width, in this case, both length and width is x.
While 5 and 2 are the lengths and widths for the unshaded part.
x^2 = whole square
x^2 - (5)(2) = area of shaded region
PLEASE HURRY! i’ll give brainliest
Answers
Answer:
1
Step-by-step explanation:
What is the value of 1,608 divided by 10 cubed
Answers
Answer:
16 2/25
Step-by-step explanation:
1608 / 10^2
1608/100
16 8/100
16 4/50
16 2/25
Answer:
1.608
Step-by-step explanation:
1608 ÷ 1000 = 1.608
Find the measure of angle 1
HELP
Answers
Answer:
75°
Step-by-step explanation:
The chord- chord angle is half the sum of of the arcs intercepted by the angle and its vertical angle, then
∠ 1 = [tex]\frac{1}{2}[/tex] (110 + 40)° = 0.5 × 150° = 75°
No one wants to help me ! :(((( need help on algebra: modeling dot plots Box plots and histograms.!
Answers
Ms. Benton drew a right angle and split it into 2 angles. one of the labels inside was labeled 5x and the other angle was labeled 4x. what does x equal?
Answer choices:
5°
10°
15°
20°
please help
Answers
Answer:
B-10⁰
Step-by-step explanation:
5 x 10 is 50, 4 x 10 is 40, add those and you get 90⁰
Find the value of -8 - 12 - (-20).
24
-40
16
0
Answers
Answer:
it's = 0
you have to use the steps of maths
Hope that helped!
Type the missing number that makes these fractions equal: 4/?=8/14
Answers
Answer:
4/7 = 8/14
Step-by-step explanation:
Answer:
7
Step-by-step explanation:
[tex]\frac{4}{x} =\frac{8}{14} \\[/tex]
cross multiply
8x = 14 x 4
8x = 56
x = 7
The curve
[tex]y = \sqrt{x - 3} [/tex]
has a tangent with gradient
[tex] \frac{1}{2} [/tex]
at point N.
Find the coordinates of N.
Answers
Answer:
Point N(4, 1)
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityAlgebra I
Coordinates (x, y)FunctionsFunction NotationTerms/CoefficientsAnything to the 0th power is 1Exponential Rule [Rewrite]: [tex]\displaystyle b^{-m} = \frac{1}{b^m}[/tex] Exponential Rule [Root Rewrite]: [tex]\displaystyle \sqrt[n]{x} = x^{\frac{1}{n}}[/tex]Calculus
Derivatives
Derivative Notation
Derivative of a constant is 0
Basic Power Rule:
f(x) = cxⁿ f’(x) = c·nxⁿ⁻¹Derivative Rule [Chain Rule]: [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]
Step-by-step explanation:
Step 1: Define
[tex]\displaystyle y = \sqrt{x - 3}[/tex]
[tex]\displaystyle y' = \frac{1}{2}[/tex]
Step 2: Differentiate
[Function] Rewrite [Exponential Rule - Root Rewrite]: [tex]\displaystyle y = (x - 3)^{\frac{1}{2}}[/tex]Chain Rule: [tex]\displaystyle y' = \frac{d}{dx}[(x - 3)^{\frac{1}{2}}] \cdot \frac{d}{dx}[x - 3][/tex]Basic Power Rule: [tex]\displaystyle y' = \frac{1}{2}(x - 3)^{\frac{1}{2} - 1} \cdot (1 \cdot x^{1 - 1} - 0)[/tex]Simplify: [tex]\displaystyle y' = \frac{1}{2}(x - 3)^{-\frac{1}{2}} \cdot 1[/tex]Multiply: [tex]\displaystyle y' = \frac{1}{2}(x - 3)^{-\frac{1}{2}}[/tex][Derivative] Rewrite [Exponential Rule - Rewrite]: [tex]\displaystyle y' = \frac{1}{2(x - 3)^{\frac{1}{2}}}[/tex][Derivative] Rewrite [Exponential Rule - Root Rewrite]: [tex]\displaystyle y' = \frac{1}{2\sqrt{x - 3}}[/tex]Step 3: Solve
Find coordinates
x-coordinate
Substitute in y' [Derivative]: [tex]\displaystyle \frac{1}{2} = \frac{1}{2\sqrt{x - 3}}[/tex][Multiplication Property of Equality] Multiply 2 on both sides: [tex]\displaystyle 1 = \frac{1}{\sqrt{x - 3}}[/tex][Multiplication Property of Equality] Multiply √(x - 3) on both sides: [tex]\displaystyle \sqrt{x - 3} = 1[/tex][Equality Property] Square both sides: [tex]\displaystyle x - 3 = 1[/tex][Addition Property of Equality] Add 3 on both sides: [tex]\displaystyle x = 4[/tex]y-coordinate
Substitute in x [Function]: [tex]\displaystyle y = \sqrt{4 - 3}[/tex][√Radical] Subtract: [tex]\displaystyle y = \sqrt{1}[/tex][√Radical] Evaluate: [tex]\displaystyle y = 1[/tex]∴ Coordinates of Point N is (4, 1).
Topic: AP Calculus AB/BC (Calculus I/II)
Unit: Derivatives
Book: College Calculus 10e
Ahmad picked up a toy with a mass of 7/12 kilograms. Then picked up another of 1/12 kilograms. What's the total Write your answer as a fraction in simplest form
Answers
Answer:
2/3
Step-by-step explanation:
7/12+1/12=8/12
8 / 4 2
12 / 4 3
Final answer 2/3
A hiking trail is 2 3/5 miles long. Lucy walks 1/2 of the trail before stopping for a water break. How many miles does Lucy walk before stopping?
Answers
Answer:
look at the picture I have sent
Answer:
1.3
Step-by-step explanation:
First you simplify 2 3/5, which can be 2.6. You will find half of it so 2.6 divided by 2 equals 1.3. She traveled 1.3 miles or 1 3/10 miles before she stopped.
y= 4x + 2
y= 4x + 6
How many Solutions
Answers
So no solution
Which triangle makes this statement true?
Answers
Answer:
A.
Step-by-step explanation:
i pretty sure
What is the length of the missing side of the triangle? The figure is not drawn to scale.
15
9
08
06
O 24
O 12
Answers
Answer:
Step-by-step explanation:
add all the numbers together to get your answer and divide it by two.
Answer:
Hello! answer: 12
Step-by-step explanation:
Assuming this is the Pythagorean theorem we would usually solve for c but c is already found so we have to work backwards so... 15 × 15 = 225
9 × 9 = 81 225 - 81 = 144 √144 = 12 therefore 12 is the answer Hope that helps!
Plz help I will give BRAINLY
Answers
Answer:
I believe it is C
Step-by-step explanation:
Sorry if I got it wrong but hopefully you got it right
Write the recursive formula for the sequence
37, 67, 97, 127, 157
Answers
Answer:
The recursive formula for this arithmetic sequence would be [tex]a_{1} = 37[/tex], [tex]a_{i} = a_{i-1} + 30[/tex].
Step-by-step explanation:
A recursive formula is a formula that defines each term of a sequence using the preceding term(s). Recursive formulas must always state the initial term, or terms, of the sequence, as well as an equation defining [tex]a_{i}[/tex] in terms of preceding terms. Since the first term of this sequence is 37, that means [tex]a_{1} = 37[/tex]. The pattern in this arithmetic sequence between each term in ascending order would be 30 more than the previous term, so you can create the function [tex]a_{i} = a_{i-1} + 30[/tex]. So the recursive formula for this arithmetic sequence would be [tex]a_{1} = 37[/tex] and [tex]a_{i} = a_{i-1} + 30[/tex].
4/5 divided by 3/4
I need help please!! :)
Answers
Answer:
1 1/5 in fraction form :))
HELP ME IM STUCK PLEASE QUICK
Answers
Answer:
C) 24>x
Step-by-step explanation:
The inequality is just turned around. 24>x is thw same thing as x<24.
Hope this helped :)
Answer:
D
Step-by-step explanation:
x+3≥12
<=> x≥8
so 8 is less than x
x is less than 24 means 24>8 but in this case we must follow a model so x is less than 24 can be write 24≥x (read x is less than 24 or is equal to 24)
You are planning to build a walkway that surrounds the area of a rectangular garden. The width of the walkway around the
garden is the same on every side. Which of the following polynomials represents the total area of the garden and
walkway?
Answers
Answer:
B. (2x + 10)(2x + 9)
Step-by-step explanation:
Length (L) of the garden and walkway = x + 10 + x = (2x + 10) ft
Width (W) of the garden and walkway = x + 9 + x = (2x + 9)
Area of the garden and walkway = area of rectangle = L*W
= (2x + 10)(2x + 9)
The polynomial representing the total area of the garden and walkway = (2x + 10)(2x + 9)
Jamal's friends toss 12 balls to him at the same time. Three balls are red, 3 are green, 3 are blue, and 3 are white. Jamal manages to catch 5 of the balls.
What is the probability that he catches 2 red balls and 1 ball of each of the other colors?
Answers
Answer:
81/792 or 9/88 or 10.2%
Step-by-step explanation:
Possibility: nCr(12,5) = 792
Red: nCr(3,2) = 3
Blue, Green, White: nCr(3,1) = 3
3 * 3 * 3 * 3 = 81
81/792 simplified is 9/88 percentage is 10.22%
The probability that Jamal will catch 2 red balls and 1 ball of each of the other colors is 0.1025.
What is probability?Probability is the branch of Mathematics that deals with the measurement of the chance of occurrence of a random event.
The probability of any event always lies in the close interval of 0 and 1 [0,1].
The zero value of probability indicates that the event will not happen while its value equal to one indicate that it will happen.
The total numbers of balls are 12.
Each color has 3 balls.
If total 12 balls are tossed, the number of ways of catching 5 of them is,
¹²C₅ = 792
The number of ways of catching 2 red balls out of 3 is ³C₂ = 3
The number of ways of catching 1 green ball out of 3 is ³C₁ = 3
The number of ways of catching 1 blue ball out of 3 is ³C₁ = 3
The number of ways of catching 1 white ball out of 3 is ³C₁ = 3
Thus, the probability as per the question is given as follows,
(3 × 3 × 3 × 3)/792
= 81/792
= 0.1025
Hence, the probability of catching 2 red balls and 1 ball of each of the other colors is 0.1025.
To know more about probability click on,
https://brainly.com/question/11234923
#SPJ2
What inverse operation is used to solve the equation?
2x=10
Addition Property: add 2 to both sides
Division Property: divide both sides by 2
Multiplication Property: multiply both sides by 2
Subtraction Property: subtract 2 from both sides
Answers
Answer:
Division Property: divide both sides by 2
Step-by-step explanation:
[tex]2x = 10[/tex]
[tex] \frac{2x}{2} = \frac{10}{2} [/tex][tex]x = \frac{10}{2} [/tex][tex]x = 5[/tex]
Hope it is helpful....