True or False? In a circle, radius OP intersects chord AC in point B so that AB = 8 units and BC = 8 units. This means that OP is perpendicular to AC.

Answers

Answer 1

Answer: True.

Because, OAC forms a triangle where:

- the base is AC,
- the other two sides are OA and OC with same length equal to OP (the radius of the circle)
- when you trace the bisectriz of AC you realize it is a line perpedicular to AC that intersects the center of the the circle, O

Answer 2

Answer:

Answer:

TRUEEE

Step-by-step explanation:

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Which of the following statements describes circumscribing? Choose all correct answers.A) One figure is drawn around the other.
B) One figure must be a circle.
C) The figure on the inside circumscribes the figure on the outside.
D) Circumscribing can be done as a construction.
E) The figures intersect.

Answers

In circumscribing,
One figure is drawn around the other and Circumscribing can be done as a construction.

Answer:

A and D are correct options.

Step-by-step explanation:

Circumscribing some figure means to draw one figure around another in such a way that all the sides should touch the outside figure. Like if we circumscribe a circle around a triangle, all the vertices must touch the circle.

Based on the definition, the following statements are correct answer.

A) One figure is drawn around the other.

D) Circumscribing can be done as a construction.

Many figures can be circumscribed like - a right triangle around a square, a circle around a triangle or a square etc.

Allie deposited $300.00 into a new savings account that earns 13% interest compounded quarterly. How long will it take for the balance to grow to $995.00? Round your answer to the nearest month. years and months

Answers

Answer:

9 years 4 months

Step-by-step explanation:

To find out how long it will take for Allie's initial deposit of $300to grow to $995 in a savings account with a 13% annual interest rate compounded quarterly, we can use the compound interest formula:

$\boxed{\begin{array}{l}\underline{\textsf{Compound Interest Formula}}\n\nA=P\left(1+(r)/(n)\right)^(nt)\n\n\textsf{where:}\n\phantom{ww}\bullet\;\;\textsf{$A$ is the final amount.}\n\phantom{ww}\bullet\;\;\textsf{$P$ is the principal amount.}\n\phantom{ww}\bullet\;\;\textsf{$r$ is the interest rate (in decimal form).}\n\phantom{ww}\bullet\;\;\textsf{$n$ is the number of times interest is applied per year.}\n\phantom{ww}\bullet\;\;\textsf{$t$ is the time (in years).}\end{array}}$

In this case:

A = $995
P = $300
r = 13% = 0.13
n = 4 (quarterly)

Substitute the values into the formula and solve for t:

$995=300\left(1+(0.13)/(4)\right)^(4t)$

Simplify the expression inside the bracket:

$995=300\left(1.0325\right)^(4t)$

Divide both sides of the equation by 300:

$(995)/(300)=\left(1.0325\right)^(4t)$

Take natural logs (ln) of both sides of the equation:

$\ln\left((995)/(300)\right)=\ln\left(1.0325^(4t)\right)$

$\textsf{Apply the power law:} \quad \ln x^n=n \ln x$

$\ln\left((995)/(300)\right)=4t\ln\left(1.0325\right)$

Divide both sides of the equation by 4ln(1.0325) to isolate t:

$(\ln\left((995)/(300)\right))/(4\ln\left(1.0325\right))=t$

$t=(\ln\left((995)/(300)\right))/(4\ln\left(1.0325\right))$

Evaluate using a calculator:

$t=9.37184241...$

Therefore, it will take 9.37 years for the balance to grow to $995.00.

To determine the number of months, subtract 9 from the value of t and multiply by 12:

$\textsf{Months}=12(9.37184241...-9)=4.46210895...$

Therefore, it will take 9 years and 4 months (rounded to the nearest month) for the balance to grow to $995.00.

Additional comments

In the case of quarterly compounding, the interest is calculated and added to the account balance every three months (once every quarter). So, even though it will take 9 years and 4 months for the balance to reach $995.00, Allie's account will not show this exact amount at that specific time. It will show a balance of $979.61 at 9 years and 3 months, and a balance of $1,011.45 at 9 years and 6 months, so technically, the account balance will still show as $979.61 at 9 years and 4 months.

Answer:

9 years and 4 months

Step-by-step explanation:

In order to calculate the number of years and months it will take for Allie's savings account balance to grow to $995.00, we can use the following compound interest formula:

$\sf A = P\left(1 + (r)/(n)\right)^(nt)$

where:

A is the future value
P is the present value
r is the annual interest rate
n is the number of compounding periods per year
t is the number of years

We can use the following values for the variables in the formula:

P = $300.00

r = 13% = 0.13

n = 4 (compounding quarterly)

A = $995.00

Substituting value, we get

$\sf 995 = 30000\left(1 + (0.13)/(4)\right)^(4\cdot t)$

$\sf 995 = 300.00\left(1.0325\right)^(4\cdot t)$

$\sf (995)/(300)=\left(1.0325\right)^(4\cdot t)$

$\sf 3.316 = \left(1.0325\right)^(4\cdot t)$

In order to solve the exponential equation, we can take the natural log of both sides:

$\sf ln(3.316) = ln(1.0325) ^ {4t}$

Using the properties of logarithms, we can bring the exponent down in front of the log:

$\sf 4t * ln(1.0325) = ln(3.316)$

Dividing both sides by ln(1.0325), we get:

$\sf t =( ln(3.316) )/(4ln(1.0325))$

Evaluating this expression, we get:

$\sf t = 9.3702710709672$

In the nearest hundred:

$\sf t \approx 9.37$

Therefore, year = 9 year

month = 37% of 12 = 4.44≈ 4 month

So, it will take Allie 9 years and 4 months for her savings account balance to grow to $995.00.

Y is eleven times the value of x.

The equation is y =____

Answers

Answer:

Your answer will be y = 11x

The same thing as multiplying 11 by x

Or you could say y = 11*x

Hope this comes to help someone! :)

(02.02 HC)Andrew makes $6 an hour plus $9 an hour for every hour of overtime. Overtime hours are any hours more than 40 hours for the week.

Part A: Create an equation that shows the amount of wages earned, W, for working x hours in a week when there is no overtime. (3 points)

Part B: Create an equation that shows the amount of wages earned, S, for working y hours of overtime. Hint: Remember to include in the equation the amount earned from working 40 hours. (3 points)

Part C: Andrew earned $330 in 1 week. How many hours (regular plus overtime) did he work? (4 points)

Answers

A) 6x=W
B)(6 x 40) + 9y = s
240 + 9y = s
C) 240 +9y = 330
9y = 90
y=10

Andrew worked 40 hours plus 10 hours of overtime.
He worked a total of 50 hours

Which of the following represents "The product of the abscissa and ordinate is ten"?a)xy = 10
b)10x = y
c)10y = x

Answers

Hello,
if x represents the abscissa
and y the ordinate then
the product is x*y
Answer A

Chin correctly translated the following phrase into an algebraic expression.“one-fifth less than the product of seven and a number”

Which expression represents Chin’s phrase?
7 n + one-fifth
StartFraction 7 n minus 1 Over 5 EndFraction
StartFraction 7 n + 1 Over 5 EndFraction
7 n minus one-fifth

Answers

Answer: C = b7 + bc

Step-by-step explanation:

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