What two positive real numbers whose product is 50 have the smallest possible sum?

Answers

Answer 1

Answer: x * y = 50
y = 50 / x
S = x + y = x + 50 / x
S` = 1 - 50 / x²
1 - 50 / x² = 0
50 / x² = 1
x² = 50
x = √ 50 = 5 √2
y = 50 / 5√2 = 5 √2
Answer:
Those numbers are: x = 5√2 and y = 5√2.

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Subtract 14 inches from 4 feet, 2 inches.10 inches3 feet34 inches5 feet
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Laura fills a bucket with water at a rate of 6 L/min. At the same time, Sarah empties a bucket holding 30 L of water at a rate of 9 L/min. Let l represent the number of liters of water and let t represent time in minutes. The system models this situation.How many minutes will it take for the buckets to hold equal amounts of water, and how much water will that be?l = 6tl = 30 – 9tIt will take ____ minutes for both buckets to hold equal amounts of water. They will each hold ____ liters.

Select all of the following points that lie on the graph of f(x) = 7 - 3x.(-2, 1)
(-1, 10)
(0, 7)
(1, 5)
(2, 1)

Answers

We know that

if the point belongs to the graph, then it must satisfy the given function.

We proceed to verify each of the points

we have

$f(x) = 7 - 3x$

case a) $(-2, 1)$

$x=-2\ny=1$

Substitute the value of x in the given function and compare the value of f(x) with the value of the coordinate y of the point

$f(x) = 7 - 3*(-2)$

$f(x) = 13$

$13\neq 1$ --------> the point not lie on the graph

case b) $(-1, 10)$

$x=-1\ny=10$

Substitute the value of x in the given function and compare the value of f(x) with the value of the coordinate y of the point

$f(x) = 7 - 3*(-1)$

$f(x) = 10$

$10=10$ --------> the point lie on the graph

case c) $(0, 7)$

$x=0\ny=7$

Substitute the value of x in the given function and compare the value of f(x) with the value of the coordinate y of the point

$f(x) = 7 - 3*(0)$

$f(x) = 7$

$7=7$ --------> the point lie on the graph

case d) $(1, 5)$

$x=1\ny=5$

Substitute the value of x in the given function and compare the value of f(x) with the value of the coordinate y of the point

$f(x) = 7 - 3*(1)$

$f(x) = 4$

$4\neq 5$ --------> the point not lie on the graph

case e) $(2, 1)$

$x=2\ny=1$

Substitute the value of x in the given function and compare the value of f(x) with the value of the coordinate y of the point

$f(x) = 7 - 3*(2)$

$f(x) = 1$

$1=1$ --------> the point lie on the graph

therefore

the answer is

Points that lie on the graph are

$(-1, 10)$

$(0, 7)$

$(2, 1)$

see the attached figure to better understand the problem

Answer:

So the person above me got it right (I think) but im small brain and dont wanna read all that so for all the ppl like me the answer is

(-1, 10)

(0, 7)

(2, 1).

Your welcome fellow lazy ppls :3

mr. pollack's biology class observed the growth of pea plants. if 5 pea plants grew to 30 cm and 15 pea plants grew to 50 cm, what was the overall average height of the pea plants

Answers

u do 5 times 30 and get 150 then take 15 times 50 and get 750 last take 750 plus 150 and u get 900 cm

Final answer:

To find the overall average height of the pea plants, we need to calculate the total height and divide it by the total number of plants. The overall average height of the pea plants is 45 cm.

Explanation:

To find the overall average height of the pea plants, we need to calculate the total height of all the plants and divide it by the total number of plants. Let's calculate:

The total height of the 5 plants that grew to 30 cm is 5 multiplied by 30, which equals 150 cm.
The total height of the 15 plants that grew to 50 cm is 15 multiplied by 50, which equals 750 cm.
The overall total height of all the plants is 150 cm + 750 cm, which equals 900 cm.
The overall average height of the pea plants is 900 cm divided by the total number of plants, which is 5 + 15 = 20 plants. So, the overall average height is 900 cm divided by 20, which equals 45 cm.

Therefore, the overall average height of the pea plants is 45 cm.

Learn more about Average Height of Pea Plants here:

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The Spartan Bike Shop has a credit card that they use for business transactions. Their starting amount is 4,500. Create a balance sheet similar to the one created in class which include: Date, Transaction, deposit withdraw and balance

Answers

Answer:

Step-by-step explanation:

Here is a sample balance sheet for the Spartan Bike Shop credit card transactions:

Date | Transaction | Deposit | Withdraw | Balance

--------------------------------------------------------------

01/01/2022 | Starting balance | - | - | $4,500

01/15/2022 | Purchase of supplies| - | $500 | $4,000

02/05/2022 | Payment received | $1,000 | - | $5,000

02/20/2022 | Equipment purchase | - | $2,500 | $2,500

03/10/2022 | Refund received | $300 | - | $2,800

In this example:

- The starting balance on 01/01/2022 is $4,500.

- On 01/15/2022, the shop made a purchase of supplies, resulting in a withdrawal of $500 from the credit card account, leaving a balance of $4,000.

- On 02/05/2022, the shop received a payment of $1,000, which was deposited into the credit card account, increasing the balance to $5,000.

- On 02/20/2022, the shop made an equipment purchase, resulting in a withdrawal of $2,500 from the credit card account, leaving a balance of $2,500.

- On 03/10/2022, the shop received a refund of $300, which was deposited into the credit card account, increasing the balance to $2,800.

This balance sheet provides a clear record of the credit card transactions for the Spartan Bike Shop, including the dates, transaction details, deposits, withdrawals, and the resulting balance after each transaction. It helps the shop keep track of their credit card activity and maintain an accurate record of their financial transactions.

Find the area of the trapezoids. What is the Area of the trapezoids

A= Square units

Answers

Answer:

$area = area \: of \: rectangle + area \: of \: triangles \n = (6 * 2) + ( (1)/(2) * 6 * 2) + ( (1)/(2) * 6 * 4) \n = 12 + 6 + 12 \n = 30 \: sq \: units$

Answer:

Step-by-step explanation:

Write the given expression in terms of x and y only tan(sin−1 x + cos−1 y)

Answers

Answer:

$\tan \left ( \sin ^(-1)x+ \cos ^(-1)y\right )=(xy+√(\left ( 1-x^2 \right )\left ( 1-y^2 \right )))/(y√(1-x^2)-x√(1-y^2))$

Step-by-step explanation:

We need to express $\tan \left ( \sin ^(-1)x+ \cos ^(-1)y\right )$ in terms of x and y .

Let $\sin ^(-1)x=\theta \,,\,\cos ^(-1)y=\phi$ , we get

$x=\sin \theta \,,\,y=\cos \phi$

Formulae Used:

$\sin ^2\theta +\cos ^2\theta =1\n\sin ^2 \phi +\cos ^2 \phi =1$

$\cos \theta =√(1-\sin^2 \theta)=√(1-x^2)\n\sin \phi=√(1-\cos ^2 \phi)=√(1-y^2)$

$\tan \theta =(\sin \theta )/(\cos\theta )=(x)/(√(1-x^2))\n\tan \phi =(\sin \phi)/(\cos\phi)=(√(1-y^2))/(y)$

We know that $\tan \left ( \theta +\phi\right )=(\tan \theta +\tan \phi )/(1-\tan \theta \,\tan \phi )$

$\tan \left ( \sin ^(-1)x+ \cos ^(-1)y\right )=((x)/(√(1-x^2))+(√(1-y^2))/(y))/(1-(x√(1-y^2))/(y√(-x^2)))\n\therefore \tan \left ( \sin ^(-1)x+ \cos ^(-1)y\right )=(xy+√(\left ( 1-x^2 \right )\left ( 1-y^2 \right )))/(y√(1-x^2)-x√(1-y^2))$

Substract (9g3 13g2 - 7g - 10) - (7g3 - 11g2 - 6g - 9)

Answers

2g^3+24g^2-g-1 is the answer

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