A right triangle has a hypotenuse of 12√2 and one leg equal to 9√2. What is
the length of the other leg?

Answer: (3, -9)

Step-by-step explanation:

The equation of P is \((x-3)^2 +(y+2)^2 =49\)

Substituting the coordinates of each of the points into the equation, we see that only (3, -9) satisfies the equation.

The general solution of the given differential equation x dy = y + (x^2 - y^2)/y is given by y^2 + 2x^2 + C1y = C2, where C1, C2 are constants.

General solution of the given differential equation is given by :

The general solution of the given differential equation x dy = y + (x^2 - y^2)/y is y^2 + 2x^2 + C1y = C2, where C1, C2 are constants. We will now find the general solution of the given differential equation  x dy = y + (x^2 - y^2)/y,  x > 0 as follows:

The given differential equation is of the form dy/dx + P(x)y = Q(x)/y.

Here, P(x) = 1/x and Q(x) = (x^2 - y^2)/y.

Multiplying the equation by y, we get xydy - y^2dy/dx = xy + x^2 - y^2.

We now rearrange the equation as follows : xdy/dx - y/x = (x^2 - y^2)/(xy).

We now assume that y^2 + 2x^2 = v and differentiating with respect to x gives 2y dy/dx + 4x = dv/dx.

Substituting the given value of the differential equation and then reducing the equation to standard form using suitable transformations, we get the value of constant as y^2 + 2x^2 + C1y = C2.

Therefore, the general solution of the given differential equation x dy = y + (x^2 - y^2)/y is given by y^2 + 2x^2 + C1y = C2, where C1, C2 are constants.

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Answer:

1/4 or .25

Step-by-step explanation:

You cross multiply which would give you 4x=1.

Answer:

y = 2x - 12

Step-by-step explanation:

(y-4)/(-4-4) = (x-8)/(4-8)

(y-4)/-8 = (x-8)/-4

y-4 = 2x - 16

y = 2x - 16 + 4

y = 2x - 12

Answer:

Step-by-step explanation:

its 100%

9514 1404 393

Answer:

Step-by-step explanation:

The price difference is found by subtracting Emma's price from DeShawn's price. Each price is the product of the number of square feet and the price per square foot.

The number of square feet is already given in the answer form, so you only need to fill in the per square foot prices. Those are found in the table. Both the window name and the window area give clues as to which is the right price to choose.

The expression is (4² × 33) - (3² × 27).

__

For the second fill-in, you need to actually do this arithmetic. For many calculators, you can enter this expression directly.

DeShawn paid $285 more for his window than Emma.

The change in air pressure when the pure tone is produced is mathematically given as

p(1/2000) =0 mP

This pressure is referred to as the atmospheric pressure, air pressure, or simply pressure. It is the force that is exerted on a surface by the air that is above it due to the gravitational pull that gravity has on the surface. A barometer is an instrument most often used to measure the pressure of the atmosphere. When the pressure in the atmosphere changes, a column of mercury contained inside a glass tube in a barometer will either rise or sink.

Generally, the equation for is pressure  mathematically given as

\(p(t) =2sin (4000\pi t)\)

Therefore

p(1/2000) =2sin (4000\pi *1/2000)

p(1/2000) = 2sin (2\pi)

p(1/2000) = 2*0

p(1/2000) =0 mP

In conclusion, the pressure

p(1/2000) =0 mP

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Answer:

x=-4544

Step-by-step explanation:

- 71 = x/64

Multiply each side by 64

- 71 *64 = x/64 *64

x=-4544

Answer:

x=−4544

Step-by-step explanation:

Answer:

Answer should be 33

Step-by-step explanation:

\(7 + 19 = 26\)

\(26 \times 2 = 52\)

\(52 - 19 = 33\)

\(33 \div 5 = 6.6\)

\(by \: the \: of \: 7 \: she \: does \: exceed \: \\ her \: fathers \: age \: slightly \: \\ more \: than \: \frac{1}{5} \: of \\ \: 33 \: which \: would \: be \: 6.6\)

Answer:

Palladium

Step-by-step explanation:

Its on the periodic table, periods are vertical, groups are horizontal

The element in group 10 and period 5 is,  Palladium (Pd).

The periodic table of chemical elements, often called the periodic table, organizes all discovered chemical elements in rows (called periods) and columns (called groups) according to increasing atomic number.

We know that;

The elements of group 10 are consists of Nickel (Ni), Palladium (Pd), Platinum (Pt), Darmstadt (Ds) which reside in a period of 4, 5, 6, and 7 respectively in a periodic table.

Hence, The element in a group 10 and period 5 is Palladium (Pd).

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The type of variable that represents the names of the automobile manufacturers would be the categorical variable.

A variable is defined as the quantity that may change within the context of a mathematical problem, research work or an experiment.

There are various types of variables that include the following:

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Answer:

g(x)=2x+1

Step-by-step explanation:

(2x+1)^2+1=4x^2+4x+2

Answer:

will change by 12% because of the loan.

Step-by-step explanation:

okay so since the area is 22cm^2 , you will need to simplify it.

Which you will get 22*22 and the total would be 484. Which u will divide by 4 ( Square) to get each of the side your looking for.

So your answer is... 121

Answer:

-12degrees Celsius

Step-by-step explanation:

-3+5=2 1:00pm

2-2=0 6:00pm

(10-6=4)

4(3)=12, 0-12=-12 10:00pm

i hope this helps!

Answer:

-12° C

Step-by-step explanation:

Temperature at 8 a.m.: -3° C

From 8 a.m. to 1 p.m. the temperature went up 5° C.

-3° C + 5° C = 2° C

Temperature at 1 p.m.: 2° C

By 6 p.m. the temperature was 2° C colder than at 1 p.m.

2° C - 2° C = 0° C

Temperature at 1 p.m.: 0° C

The temperature decreased 3° C per hour from 6 p.m. to 10 p.m.

From 6 p.m. to 10 p.m., it's 4 hours. The temperature decreased 3° C per hour for 4 hours. 4 * 3° C = 12° C. The temperature went down 12° C altogether from 6 p.m. to 10 p.m.

0° C - 12° C = -12° C

Temperature at 10 p.m.: -12° C

Answer: -12° C

Answer:

y = 2.35x

Step-by-step explanation:

(21.15-16.45)/(9-7) = Slope = 2.35

------

y = ax + b

y = 2.35x + b

------

Plug it in

------

16.45 = 2.35(7) + b

16.45 = 16.45 + b

b = 0

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

y = 2.35x

The rate, in inches per minute, at which the radius of the sphere is changing when the radius is 4 inches is 2.83

What is the Volume of a Sphere?

The capacity of a sphere is its volume. It is the area that the sphere occupies. Cubic measurements of a sphere's volume include m3, cm3, in3, etc. The sphere has a circular, three-dimensional form. Its form is determined by three axes: the x, y, and z axes. Sports like basketball and football are all instances of spheres with volume.

Since the cross-section of the sphere is a circle, the volume in this case is dependent on the diameter of the sphere's radius. The area or region of a sphere's outer surface is known as its surface area. We may use the following formula to get the volume of a sphere whose radius is "r":

Here, In the question, It is given that:

Radius = 4inch.

Rate of increase = 569 cubic inches;

So, using the Volume of Sphere, formula:

\(\begin{aligned}v=\frac{4}{3} \pi r^3 \\\frac{d v}{d t} &=\frac{d}{d t}\left[\frac{4}{3} \pi r^3\right] \\&=\frac{4 \pi}{3}\left(3 r^2\right) \frac{d r}{d t} \\\frac{d v}{d t} &=4 \pi r^2 \frac{d r}{d t}\end{aligned}\)

\(\begin{aligned}&\frac{d r}{d t}=\frac{\frac{d v}{d t}}{4 \pi r^2}\\&\left.\frac{d r}{d t}=\frac{569}{(4 \pi)(4)^2}=\frac{d}{d t}_{r=4}^{d r^2}=569\right]\\&\frac{d v}{d t}=\frac{569}{64 \pi} \sim 2.83\end{aligned}\)

Hence,  the rate, in inches per minute, at which the radius of the sphere is changing when the radius is 4 inches is 2.83

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Answer:

Hello,

\(\boxed{Answer: 75}\)

Step-by-step explanation:

x,y integers, x,y >0 ,x≠y

\(\dfrac{1}{x} +\dfrac{1}{y} =\dfrac{1}{18}\\\\\dfrac{x+y}{xy} =\dfrac{1}{18}\\\\x+y=\dfrac{xy}{18}\\\\x=\dfrac{18y}{y-18}\\x=\dfrac{18y-324 +324}{y-18}\\x=18+\dfrac{324}{y-18}\\\)

\(\dfrac{1}{x} +\dfrac{1}{y} =\dfrac{1}{18}\\\\\dfrac{x+y}{xy} =\dfrac{1}{18}\\\\x+y=\dfrac{xy}{18}\\\\x=\dfrac{18y}{y-18}\\x=\dfrac{18y-324 +324}{y-18}\\x=18+\dfrac{324}{y-18}\\\begin{array}{|c|c|c|c|}y-18&y&x&x+y\\---&---&---&---\\1&19&18+324=342&362\\2&20&18+162=180&200\\3&21&126&147\\4&22&99&121\\6&24&108&132\\12&30&45&75\\18&36&36&72\\\end{array}\\\\\\\boxed{Answer: 75}\\\\\)

Answer: A. The compromise allowed California to join the United States as a free state but would allowed slavery in the southwestern territories.

Step-by-step explanation:

As the abolitionist North and the pro-slavery South saw their rivalry intensify with the lobbying by the South that slavery should be allowed in the western territories, Congress decided to pass the compromise of 1850 which was several acts that would calm both sides for the time being.

With this compromise, California was allowed to join the United States as a free state but in return, the Southwestern territories were allowed to decide their slavery status in an election which meant that if the territories so pleased, they could allow slavery in their territories.

Answer: Some times

Step-by-step explanation:

I did the quiz and I got the answer right, I hope this helps and everyone have a great day!

Answer:

sometimes

Step-by-step explanation:

Answer:

Step-by-step explanation:

8 and 47

False, each objective function line is unique and not necessarily parallel to every other objective function line in a problem.

In a multi-objective optimization problem, each objective function represents a different optimization criterion or goal. These objectives can have different slopes and directions, resulting in objective function lines that are not necessarily parallel to each other. The objectives may have conflicting or complementary relationships, leading to different trade-offs and possibilities in the optimization process. Therefore, it is incorrect to assume that all objective function lines are parallel in a problem.

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Answer:

19 times

Step-by-step explanation:

8000 - 1200 - 2000 ÷ 250 = 19.2

Answer:

Perimeter = 54

Step-by-step explanation:

Since AC = RP, then the following also applies:

AB = RB

CB = PB

So, in order to determine this, you first need to find a common ratio in order to find the missing side of PB which you need for the perimeter.

To determine the ratio you do the following:

AB = 21 (14 + 7)

RB = 7

21: 7   = 3: 1

This means in finding a smaller side you can divide by the value 3 to find it.

It also means that side CP is 2/3 of the value of CB which means that we need 1/3 of the value left in order to determine PB:

CP = 10 = 2/3, which means 1/3 is 5, so

PB = 5

Therefore: CB = 15

Perimeter = CB + AC + AB

15 + 21 + 18 = 54

Answer:

The color of painting 31 is RED

Step-by-step explanation:

it should be red :)

Vincent vanThat answer is 37

Answer:

D. 240

Step-by-step explanation:

6 types of backpacks = 6

4 types of binders = 4

5 types of pencils = 5

2 types of notebook paper= 2

6×4×5×2=

24×10=

240

The number of possible outcomes will be 240. The correct option is D.

Expression in maths is defined as the relation of numbers variables and functions by using mathematical signs like addition, subtraction, multiplication and division.

Given that there are 6 types of backpacks, 4 types of binders, 5 types of pencils, and 2 types of notebook paper.

6 types of backpacks = 6

4 types of binders = 4

5 types of pencils = 5

2 types of notebook paper= 2

The number of possible outcomes will be calculated as:-

N = 6×4×5×2

N = 24×10

N = 240

Therefore, there will be 240 possible outcomes. The correct answer is D.

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Answer:

A U B ={2,5,6,7,8,15}

C U D ={3,11,21,26}

Answer: x=14

Step-by-step explanation: The total is 180 degrees. The right angle is 90, the given angle is 76, so x is 14.