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3 years ago

How can I solve 16,18,20, and 22?

Mathematics

1 answer:

juin [17]3 years ago

3 0

Problem 16 Begin by setting corresponding positions equal to each other.
9 = x + 2y and 13 = 4x + 1
The second equation only has one variable so you should solve it first.
13 = 4x + 1
13 - 1 = 4x + 1 - 1
12 = 4x (divide both sides by 4)
3 = x
you can use this value to find y in the other equation
9 = 3 + 2y
9 - 3 = 3 - 3 + 2y
6 = 2y
3 = y

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What is the equation of the quadratic graph with a focus of (8, −8) and a directrix of y = −6?

yarga [219]

The vertex is exactly half way between directrix and focus. In this case the vertex is (8,-7)
(h,k)

P is the distance between the vertex and either the directrix or focus, in this case p = 1.

a = 1/(4p) or 1/(4*1) or 1/4

write the equation in vertex form

y = a(x-h)^2 + k

y = 1/4(x-8)^2 -7

4 0

3 years ago

Dwayne drove 18 miles to the airport to pick up his father and then returned home. On the return trip he was able to drive an av

Nesterboy [21]

Answer:

30 mph

Step-by-step explanation:

Let d = distance (in miles)

Let t = time (in hours)

Let v = average speed driving to the airport (in mph)

⇒ v + 15 = average speed driving from the airport (in mph)

Using: distance = speed x time

$\implies t=\dfrac{d}{v}$

Create two equations for the journey to and from the airport, given that the distance one way is 18 miles:

$\implies t=\dfrac{18}{v} \ \ \textsf{and} \ \ t=\dfrac{18}{v+15}$

We are told that the total driving time is 1 hour, so the sum of these expressions equals 1 hour:

$\implies \dfrac{18}{v} +\dfrac{18}{v+15}=1$

Now all we have to do is solve the equation for v:

$\implies \dfrac{18(v+15)}{v(v+15)} +\dfrac{18v}{v(v+15)}=1$

$\implies \dfrac{18(v+15)+18v}{v(v+15)}=1$

$\implies 18(v+15)+18v=v(v+15)$

$\implies 18v+270+18v=v^2+15v$

$\implies v^2-21v-270=0$

$\implies (v-30)(v+9)=0$

$\implies v=30, v=-9$

As v is positive, v = 30 only

So the average speed driving to the airport was 30 mph

(and the average speed driving from the airport was 45 mph)

8 0

2 years ago

Read 2 more answers

At what time the sum Rs. 5000 will be doubled at the interest of 10% per annum?

FromTheMoon [43]

Answer:

Time= $10$ years

Step-by-step explanation:

Let total time $=t$

Initial Amount $=5000$

Final Amount $=10000$

Total interest = Final Amount - Initial Amount

$=10000-5000\\=5000$

Simple Interest $=\frac{Initial Amount\times time\times rate}{100} \\\\5000=\frac{5000\times t \times 10}{100}\\\frac{t}{10} =1\\t=10 \ years$

7 0

3 years ago

Last year the manager of a health care facility served 36,500 dinners. The manager estimates an increase of 5% in the number of

EastWind [94]

Answer:

38,325 dinners.

Step-by-step explanation:

We have been given that last year the manager of a health care facility served 36,500 dinners. The manager estimates an increase of 5% in the number of dinners to be served next year.

The estimated number of dinners next year would be 36,500 plus 5% of 36,500.

$36,500+(\frac{5}{100}\times 36,500)$

$36,500+(0.05\times 36,500)$

$36,500+1,825$

$38,325$

Therefore, 38,325 dinners will be served next year.

6 0

3 years ago

Can anyone help me with this math problem?

wariber [46]

Lemme give you a cheap answer, by simply using the "compound interest formula", which is what that is, 2% compounded yearly

thus $\bf \qquad \textit{Compound Interest Earned Amount}
\\\\
A=P\left(1+\frac{r}{n}\right)^{nt}
\qquad 
\begin{cases}
A=\textit{current amount}\to&\boxed{y}\\
P=\textit{original amount deposited}\to &\$23000\\
r=rate\to 2\%\to \frac{2}{100}\to &0.02\\
n=
\begin{array}{llll}
\textit{times it compounds per year}\\
\textit{per year, meaning once}
\end{array}\to &1\\

t=years\to &\boxed{x}
\end{cases}$

plug in those values, and simplify

3 0

3 years ago

Read 2 more answers