OA and OB are congruent. CD is a chord of both circles.2If a radius is 17 ft and CD = 16 ft, how long is AB?АB
Answers
Given the circles' A and B
As shown: the circles are congruent
CD is a chord of both circles, CD = 16 ft
The radius of the circle = 17 ft
Hint: connect AC
The intersection between AB and CD is the point E
So, for the triangle ACE:
CD will be perpendicular to AB
So, the measure of the angle AEC = 90
AC = 17 ft, CE = 0.5 * 16 = 8
so, the length of AE will be calculated using the Pythagorean theorem:
\(AE=\sqrt[]{17^2-8^2}=\sqrt[]{289-64}=\sqrt[]{225}=15\)So, the length of AB will be two times the length of AE
So, AB = 2 * 15 = 30
so, the answer will be AB = 30 ft
Related Questions
Given f(x) = -x² + 3x + 11, find f(−1)
Answers
Answer:
7
Step-by-step explanation:
Substitute the given value of x into the function:
f(-1) = \(-[(-1)^{2}] + 3(-1) + 11\)
Expand the parenthesis using the Distributive Law:
= \(-(1) -3 + 11\)
Since there are only addition and subtraction present in this expression, solve from the left to right:
= \(-1 -3 + 11\)
= \(-4+11\)
= 7
present ages of two children are 2 and 5 years the rspectively. After how long will the sum of their square ages be 45.
Answers
Using the concept of word problems and quadratic equation it will take 1 year until the sum of square of their ages be 45.
Calculating the duration to get the sum to 45Word problems are mathematical problems that are delivered in ordinary words, instead of mathematical symbols.
Part of the problem with dealing with word problems that they first need to be translated into mathematical equations, and then the equations need to be solved.In this problem;
let x represent the number of years from now when the sum of square of their respective age will be
45.(x + 2)² + (x + 5)² = 45
Expanding the brackets;
x² + 4x + 4 + x² + 10x + 25 = 45
2x² + 14x + 29 = 45
2x² + 14x + 29 - 45 = 0
2x² + 14x - 16 = 0
Solving the quadratic equation for x;
x = 1, x = -8
Taking the positive value, the value of x is 1
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The revenue of a company is represented by 3x² + 9x + 5 and the costs by 3x² + 3x + 21. If the profit can be found by subtracting cost from revenue, what expression could represent the profit? I
Answers
Subtract the cost equation from the revenue equation
The 3X^2 cancel each other out
9X-3X= 6X
And 5-21= -16
Leaving 6X-16
Two boys, Brady and Quinn, are running a 100 meter race. In the race, Brady beats Quinn by 5 meters.
They decide to race again. To make things fair, in the second race, Brady stands 5 meters behind the
starting line. The two boys run at the same speed as they did in the first racy. Who wins the second race?
Answers
Answer:
It states they ran the same speed in the first race so that means only the distance they ran would be different. Thus that means Brady only ran 95 meters instead of 100 meters. If Brady was put 5 meters back that means it will be a tie if they ran at the same speed the entire race.
Step-by-step explanation:
Have a great rest of your day
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It would be a tie. Brady is 5 meters faster then Quinn. So if Brady were to stay behind 5 meters and they ran the same speed as they did before, then it would be a tie.
What’s 0.4 divided by 2.56 i need help
Answers
Answer:
Step-by-step explanation:
0.15625
Find the value of the trigonometric ratio. Reduce the fraction when you can.
sin Z
Answers
Answer:
A.
Step-by-step explanation:
Recall, SOHCAHTOA.
Reference angle = Z
Opposite = 35
Adjacent = 12
Hypotenuse = 37
Sin Z = Opp/Hyp
Therefore,
Sin z = 35/37
Which of the following options have the same value as 40\%40%40, percent of 848484?
Choose 2 answers:
Choose 2 answers:
(Choice A)
A
40\cdot 8440⋅8440, dot, 84
(Choice B)
B
0.4\div 840.4÷840, point, 4, divided by, 84
(Choice C)
C
\dfrac{40}{100}\cdot 84
100
40
⋅84start fraction, 40, divided by, 100, end fraction, dot, 84
(Choice D)
D
84 \div 4084÷4084, divided by, 40
(Choice E)
E
0.4\cdot 840.4⋅840, point, 4, dot, 84
Answers
Answer:
\((c)\ \dfrac{40}{100}\cdot 84\)
\((e)\ 0.4\cdot 84\)
Step-by-step explanation:
Given
\(40\%\ of\ 84\)
Required
Two options with the same value
First, calculate the value of: \(40\%\ of\ 84\)
\(40\%\ of\ 84 = 0.40 * 84\)
\(40\%\ of\ 84 = 33.6\)
So, we have:
\((a)\ 40\cdot 84\)
\(40\cdot 84 = 40 * 84\)
\(40\cdot 84 = 3360\)
\((b)\ 0.4\div 84\)
\(0.4\div 84 = \frac{0.4}{84}\)
\(0.4\div 84 = 0.00476\)
\((c)\ \dfrac{40}{100}\cdot 84\)
\(\dfrac{40}{100}\cdot 84 =\dfrac{40}{100}*84\)
\(\dfrac{40}{100}\cdot 84 = 0.40*84\)
\(\dfrac{40}{100}\cdot 84 = 33.6\)
\((d)\ 84 \div 40\)
\(84 \div 40 = \frac{84}{40}\)
\(84 \div 40 = 2.10\)
\((e)\ 0.4\cdot 84\)
\(0.4\cdot 84 = 0.4 * 84\)
\(0.4\cdot 84 = 33.6\)
By comparison, we have:
\((c)\ \dfrac{40}{100}\cdot 84\)
\((e)\ 0.4\cdot 84\)
have the same value as: \(40\%\ of\ 84\)
- 8+ -7=
Pa help po
Integers po yan
Answers
Answer:
-8 + (-7) = -8 - 7 = -15
The sum of -8 and -7 is -15.
I hope this helps! Let me know if you have any other questions.
Step-by-step explanation:
In 2016, a school started its own aquarium with x fish. In 2019, there were x3 fish in the same aquarium. There were 512 fish in 2019. How many fish were there in 2016? Show your work.
Answers
Answer:
Step-by-step explanation:
We are given that in 2016, the aquarium had x fish, and in 2019, there were x3 fish. We also know that in 2019, there were 512 fish. So we can set up the equation:
x3 = 512
To solve for x, we need to take the cube root of both sides of the equation:
x = ∛512
Using a calculator or simplifying by prime factorization, we can find that:
512 = 2^9
So,
∛512 = ∛2^9 = 2^3 = 8
Therefore, there were 8 fish in the aquarium in 2016.
Answer:
Let's use algebra to solve the problem. We can start by using the information given to set up an equation relating the number of fish in 2016 (x) to the number of fish in 2019 (x3):
x3 = 512
To solve for x, we can isolate x by dividing both sides of the equation by 3:
x = 512/3
x = 170.67 (rounded to two decimal places)
Therefore, there were approximately 170.67 fish in the aquarium in 2016. However, since we cannot have a fraction of a fish, we can round up to the nearest whole number to get the final answer:
x ≈ 171
So there were 171 fish in the aquarium in 2016.
Step-by-step explanation:
You roll a fair six sided die twice. The first roll shows a six and the second row shows 3
Answers
Answer:
4/12 simplified to 1/3 of rolling 2 times.
Step-by-step explanation:
Joe earned 2,100$.He spent 1/5 on rent and 1/3 on food.How much money did he have left
Answers
Answer:
$980
Step-by-step explanation:
Step 1: Find \(\frac{1}{5}\) of 2100 = 420
\(\frac{1}{5}\times \:2100\)Convert 2100 to a fraction: \(\:2100=\frac{2100}{1}\)\(=\frac{1}{5}\times \frac{2100}{1}\)Cross Divide\(2100 \div 5 = 420\)Step 2: Find \(\frac{1}{3}\) of 2100 = 700
\(\frac{1}{3}\times \:2100\)Convert 2100 to a fraction: \(\:2100=\frac{2100}{1}\)\(=\frac{1}{3}\times \frac{2100}{1}\)Cross Divide\(2100 \div 3 = 700\)Step 3: Add both results together
\(420 + 700 = 1120\)
Step 4: Subtract the result from how much joe earns ($2,100)
\(2100 - 1120 = 980\)
Joe has $980 left
If Joe earned 2,100$ and He spent 1/5 on rent and 1/3 on food, Joe had $980 left after paying for rent and food.
Joe earned $2,100 and spent 1/5 of it on rent and 1/3 on food. To calculate the amount he spent on rent, we need to find 1/5 of $2,100, which is
(1/5) * $2,100 = $420.
Similarly, the amount he spent on food is found by calculating 1/3 of $2,100, which is (1/3) * $2,100 = $700.
To determine how much money Joe had left, we subtract the total amount he spent from his earnings. Adding the amounts spent on rent and food, we get $420 + $700 = $1,120.
To find the money Joe had left, we subtract the total spent from his earnings: $2,100 - $1,120 = $980.
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Find the h.c.f of
\( {x}^{3} + {y}^{3} \: and \: \: {x}^{2} - xy + {y}^{2} \)
Answers
The greatest common factor will be (x² – xy + y²).
Greatest common factorThis is a value or expression that can divide the given expressions without leaving a remainder.
Given the following expressions
x^3+^3 and x^2 - xy + y^2
Expand x^3+y^3
x^3+y^3 =(x + y)(x² – xy + y²).
Since (x² – xy + y²) is common to both expression, hence the greatest common factor will be (x² – xy + y²).
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The table shows a proportional relationship between the number of stars Roberto collects in a game and his total points.
Roberto's game
Number of stars Total points
888 121212
101010 151515
141414 212121
? ?
A row of values is missing in the table.
Which numbers of stars and total points could be used as the missing values in the table?
Choose 3 answers:
Choose 3 answers:
(Choice A)
A
222 stars and 333 points
(Choice B)
B
666 stars and 444 points
(Choice C)
C
161616 stars and 242424 points
(Choice D)
D
121212 stars and 181818 points
(Choice E)
E
444 stars and 555 points
Answers
Answer:
acd
Step-by-step explanation:
I WILL GIVE BRAINLIEST
Answers
Answer:
1. X-intercept=3/2
Y-intercept=3
2. X-intercept=5/2
Y-intercept=-5
3. X-intercept=5
Y-intercept=-3
Answer:
\(3x + 2y = 6 \\ \boxed{\frac{x}{2} + \frac{y}{3} = 1} \)
x-intercept=2y-intercept=3\(4x - 2y = 10 \\ \boxed{ \frac{x}{ \frac{5}{2} } + \frac{y}{ (- 5)} = 1}\)
x-intercept=5/2y-intercept=-5\( - 3x + 5y = - 15 \\ \boxed{ \frac{x}{5} + \frac{y}{( - 3)} = 1}\)
x-intercept=5y-intercept=-3What is the present value of R13 000 p.a. invested at the beginning of each year for 8years at 10%p.a. compound interest? (NB Use the compound interest tables provided or work to three decimal places only.)
Answers
Given statement solution is :- The present value of R13,000 per year invested for 8 years at 10% compound interest is approximately R69,776.60.
To calculate the present value of an investment with compound interest, we can use the formula for the present value of an annuity:
PV = A *\((1 - (1 + r)^(-n)) / r\)
Where:
PV = Present value
A = Annual payment or cash flow
r = Interest rate per period
n = Number of periods
In this case, the annual payment (A) is R13,000, the interest rate (r) is 10% per year, and the investment is made for 8 years (n).
Using the formula and substituting the given values, we can calculate the present value:
PV = \(13000 * (1 - (1 + 0.10)^(-8)) / 0.10\)
Calculating this expression:
PV = \(13000 * (1 - 1.10^(-8)) / 0.10\)
= 13000 * (1 - 0.46318) / 0.10
= 13000 * 0.53682 / 0.10
= 6977.66 / 0.10
= 69776.6
Therefore, the present value of R13,000 per year invested for 8 years at 10% compound interest is approximately R69,776.60.
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Work out the circumstances of this circle. take π to be 3.142 and give your answer to 1 decimal place. Radius is 4cm
Answers
Answer:
Step-by-step explanation:
The formula for the circumference of a circle is:
C = 2πr
where C is the circumference, π is pi, and r is the radius.
Substituting the given value of π = 3.142 and r = 4 cm, we get:
C = 2 x 3.142 x 4
C = 25.136 cm
Therefore, the circumference of the circle is 25.1 cm (rounded to 1 decimal place).
A dealer gains 16% by selling a mop for rs.78300.but due to competition in the market, he decides to make a profit of only 10%. what is it's new selling price?
Answers
Answer:
The correct answer is - 72,349.2
Step-by-step explanation:
Given:
selling price = 7234.92
Initial profit = 16%
we know:
selling price = cost price + profit
Solution:
78300 = cp + 16*cp/100
profit = 78300*16/100 = 12528
cost price = 78300 - 12528 = 65772
then the profit on 10%
= 65772*10/100
= 6577.2
the new selling price = 65772+6577.2
= 72,349.2
Enter an equation that expresses y in terms of x.
x 40 50 60 70
y 38 48 58 68
The equation is
Answers
The equation that expresses y in terms of x is y = x - 2.
To find an equation that expresses y in terms of x, we need to determine the relationship between the two variables. One way to do this is by finding the slope of the line that passes through the given points.
Using the two points (40, 38) and (70, 68), we can find the slope as:
slope = (change in y) / (change in x)
slope = (68 - 38) / (70 - 40)
slope = 30 / 30
slope = 1
This means that for every increase of 1 in x, y also increases by 1.
We can now use the point-slope form of a linear equation to find the equation of the line passing through these points:
y - 38 = 1(x - 40)
Simplifying:
y = x - 2
Therefore, the equation that expresses y in terms of x is y = x - 2.
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What is the missing section
Answers
Answer:
picture d is the answer
Step-by-step explanation:
but the first s should be nice
Niall bought 234 inches of nylon cord for rock climbing. There are 36 inches in 1 yard. How many yards of cord did Niall buy?
Answers
Answer:
6.5 yards of cord were bought
Step-by-step explanation:
234/36=6.5
In January, Joanna deposited $250into her savings account. InFebruary, she deposited anadditional $100. If her account hasan APR of 6% compounded monthly,how much interest did Joanna earnin the first two months?
Answers
Given:
In January Joanna deposited $250 into her savings account.
In February, she deposited an additional $100.
Her account has an APR of 6% compounded monthly.
Required:
We have to find how much interest did Joanna earn in the first two months.
Explanation:
For the month of January:
\(A=P(1+\frac{r}{100})^n\)Here, P=$250, r=6%, amd n= 1 month=1/12 year.
Then,
\(\begin{gathered} A=250(1+\frac{6}{100})^{\frac{1}{12}} \\ \\ A=250(\frac{106}{100})^{\frac{1}{12}} \end{gathered}\)\(\begin{gathered} A=250\times1.005 \\ A=\text{ \$}251.25 \end{gathered}\)Then the interest is
\(I=A-P=251.25-250=\text{ \$}1.25\)For the month of February:
P=251.24+100=351.25
Then we have
\(\begin{gathered} A=351.25(1+\frac{6}{100})^{\frac{1}{12}} \\ \\ A=351.25(\frac{106}{100})^{\frac{1}{12}} \end{gathered}\)\(\begin{gathered} A=351.5\times1.005 \\ A=\text{ \$}353.01 \end{gathered}\)Then the interest is
\(A=P-I=353.01-351.25=\text{ \$}1.76\)Therefore, the total interest is
\(1.25+1.76=\text{ \$}3.01\)Final answer:
Hence the final answer is
\(\text{ \$}3.01\)
find the measure of angle BAC
Answers
Answer:
a= 26
Step-by-step explanation:
180-130=50
total angle in triangle =180
4a+a+50=180
then proceed like norma algebra
Why does the equation (x-4)^2-28=8 have two solutions?
Answers
For your first answer it is because they are two different ways to solve the equation
Step-by-step explanation:For Example!
Solution 1:(x-4)² – 28 = 8The 8 is positive making it a different equation (this is like absolute value). (I am assuming you know the answer to the probelm)
Solution 2:(x-4)² – 28 = -8
The 8 could be negative meaning that when you add the 28 to the right side it is -8+28 which will be a negative!
I hope this helpsIF IT DOES HELP PLEASE GIVE IT A BRAINLIEST!Answer:
This is because it is a quadratic equation.
It can therefore be solved using either factorization method or completing of squares method.
the factorization method has been worked above.
672,829
Word Form
Expanded Form
Unit Form
Answers
Answer and Step-by-step explanation:
The Word form is:
Six hundred, seventy-two thousand, eight hundred and twenty nine.
The Expanded form is:
600,000 + 70,000 + 2,000 + 800 + 20 + 9
The Unit form is:
6 one hundred thousands, 7 ten thousands, 2 thousands, 8 hundreds, 2 tens and 9 ones.
#teamtrees #PAW (Plant And Water)
The area of a square is 36 sq.cm, then its perimeter is a) 24 cm b) 6 cm c) 144 cm d) 36 cm
Answers
Answer:
a
Step-by-step explanation:
the perimeter (P) of a square is the sum of the 4 congruent sides.
the area of a square is calculated as
area = s² ( s is the length of a side )
here area is 36 , then
s² = 36 ( take square root of both sides )
s = \(\sqrt{36}\) = 6
then
P = 4s = 4 × 6 = 24 cm
4. Daryll rides a bike 8 miles in 40 minutes. Isabella rides a bike 5 miles in 30
minutes. If they continue to ride at those speeds, who will bike the farthest
in 2 hours? How much father? Show your work.
5 A student sells 5 ears of corn for $2.00 how much will 9 ears cost show your work
6 A market sells 4 oranges for 2.45 how much will 8 oranges cost ? 12 oranges show your work
Answers
4. Daryl = 24 miles, Isabella = 20 miles
so Daryl bikes the farthest by 4 more miles in 2 hours (120 minutes)
5. $3.60 for 9 ears
6. $4.90 for 8 oranges, $7.35 for 12 oranges
_____________
Step by step
4.
Solve for Daryl
8 miles /40 min = x miles / 120 min.
Find rate 8/40 = .2 miles per minute
.2 x 120 minutes = 24 miles in 120 minutes
Solve for Isabella
5 miles / 30 minutes = x miles / 120 minutes
Find rate 5/30 = 1/6 rate x 120 = 20 miles in 120 minutes
5.
5 ears corn for $2.00
Find rate $2.00/5 = .40 per ear
Multiply .40 x 9 ears = $3.60 for 9 ears
6.
4 oranges for 2.45
Find rate $2.45 / 4 = .6125 per orange
.6125 x 8 oranges = $4.90
.6125 x 12 oranges = $7.35
Question Solve: s + 159 = 25.
Answers
We have to solve for s:
\(\begin{gathered} s+159=25 \\ s+159-159=25-159 \\ s=-134 \end{gathered}\)Answer: s = -134
A) Find an equation for the line perpendicular to the tangent line to the curve y=x^3-4x+6 at the point (2,6)
-The equation is y=
b) What is the smallest slope on the curve? At what point on the curve does the curve have this slope?
-The smallest slope on the curve is
-The curve has the smallest slope at the point
c) Find equations for the tangent lines to the curve at the points where the slope of the curve is 8.
Answers
Answer:
f(x) = x³ - 4x + 6
f'(x) = 3x² - 4
a) f'(2) = 3(2²) - 4 = 12 - 4 = 8
6 = 8(2) + b
6 = 16 + b
b = -10
y = 8x - 10
b) 3x² - 4 = 0
3x² = 4, so x = ±2/√3 = ±(2/3)√3
= ±1.1547
f(-(2/3)√3) = 9.0792
f((2/3)√3) = 2.9208
c) 3x² - 4 = 8
3x² = 12
x² = 4, so x = ±2
f(-2) = (-2)³ - 4(-2) + 6 = -8 + 8 + 6 = 6
6 = -2(8) + b
6 = -16 + b
b = 22
y = 8x + 22
f(2) = 6
y = 8x - 10
The equation perpendicular to the tangent is y = -1/8x + 25/4
-The smallest slope on the curve is 2.92
The curve has the smallest slope at the point (1.15, 2.92)
The equations at tangent points are y = 8x + 16 and y = 8x - 16
Finding the equation perpendicular to the tangentFrom the question, we have the following parameters that can be used in our computation:
y = x³ - 4x + 6
Differentiate
So, we have
f'(x) = 3x² - 4
The point is (2, 6)
So, we have
f'(2) = 3(2)² - 4
f'(2) = 8
The slope of the perpendicular line is
Slope = -1/8
So, we have
y = -1/8(x - 2) + 6
y = -1/8x + 25/4
The smallest slope on the curveWe have
f'(x) = 3x² - 4
Set to 0
3x² - 4 = 0
Solve for x
x = √[4/3]
x = 1.15
So, we have
Smallest slope = (√[4/3])³ - 4(√[4/3]) + 6
Smallest slope = 2.92
So, the smallest slope is 2.92 at (1.15, 2.92)
The equation of the tangent lineHere, we set f'(x) to 8
3x² - 4 = 8
Solve for x
x = ±2
Calculate y at x = ±2
y = (-2)³ - 4(-2) + 6 = 6: (-2, 0)
y = (2)³ - 4(2) + 6 = 6: (2, 0)
The equations at these points are
y = 8x + 16
y = 8x - 16
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A rectangular shaped parking lot is to have a perimeter of 656 yards if the width must be 82 yards because of a building code what will the length need to be
Answers
The length of the rectangular shaped parking lot will be: 246 yards.
What is the Perimeter of a Rectangular Shape?A rectangular shape has a width and a length. The perimeter of the rectangular shape is simply the sum of all its width and its length. The formula for the perimeter of the rectangular shape would therefore be:
Perimeter = 2(length + width).
Given the following:
Perimeter of the rectangular shaped parking lot = 656 yards
Width of the rectangular shaped parking lot = 82 yards
Length = x = ?
Plug in the values into the perimeter formula for a rectangular shape:
2(x + 82) = 656
Divide both sides by 2
2(x + 82)/2 = 656/2
x + 82 = 328
x + 82 - 82 = 328 - 82
x = 246
Length would need to be 246 yards.
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Michael bought a soccer ball for $15. it was 40% off the original price .what fraction represents the amount of the original price he paid
Answers
Answer:
Step-by-step explanation:
6/10 or 3/5