MATHEMATICS HIGH SCHOOL

Which equation represents the line that passes through the point (1, 5) and has a slope of -2?

Answers

Answer 1

Answer:

Answer:

y=-2x+7

Step-by-step explanation:

y-y1=m(x-x1)

y-5=-2(x-1)

y=-2x+2+5

y=-2x+7

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Which of the following functions is not written in explicit form? y=x
x^2-6xy-9y^2=0
y=0
y=-squrt (1-x2)

Answers

Answer:

Option 2 and 3 are not written in explicit form.

Step-by-step explanation:

We have four functions we have to find which one of them are not written in explicit form:

Explicit form is the form in which we can finc the value of n.

Option 1 is correct

y=x because

we can calculate y and x by substituting different values.

Option 2 is incorrect because we can not calculate y from the given equation

$x^2-6xy-9y^2=0$

Option 3 is incorrect because y=0 we can not find anything.

Option 4 is correct because we can find values of y by substituting different values of x in the given equation that is $y=-\sqrt{(1-x^2)$ .

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.

Darnelle drew this figure and the accompanying equations. w + x + y = 180 y + z = 180Which equation must also be true?
A
w + z = 180
B
y – x = w
C
w + x + z = 180
D
w + x = z

Answers

Answer:

The correct option is D w + x = z

Step-by-step explanation:

Consider the provided equations.

$y + z = 180$

Solve the equation for y.

$y= 180-z$

Now substitute the vlaue of y in $w + x + y = 180$

$w + x + 180-z = 180$

Subtract 180 from both sides.

$w + x + 180-180-z = 180-180$

$w + x -z = 0$

Add z to both sides.

$w + x -z+z = z$

$w + x= z$

Hence, the correct option is D w + x = z

180=w+x+y and 180=y+z so

w+x+y=z+y so subtract y from both sides

w+x=z

Put these in order of size, smallest first 0.1. 30% 1/5

Answers

well put it in percentage
so you know 30 % is the same so then do
0.1 and that is 1/10 and that is also 10/100
also there is 1/100 is out of 100 %
so that means that 0.1 is 10 %
and 1/5 is the same as 2/10 and the same as 20/100 also the same as 20%
so the oder is 0.1 , 1/5 , 30%

0.1 1/5 30%

I hope this helps. If doesn't please tell me :)

5 + 3 + 52 × 5 − 2 =

Answers

Answer:

164 With the parenthesis

266 without parenthesis

A spool of ribbon is 85 inches long. riley needs to cut strips of ribbon that are 17 inches long. what are the possible numbers of strips that riley can cut?

Answers

Answer:

80/14=5.7 OR 5 14 IN.

Step-by-step explanation:

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