The ratio of two numbers is 7:5. The product of these numbers is 140. What is the smaller if these two numbers?

Answer:

See below ~

Step-by-step explanation:

Question 1

⇒ The given angles are supplementary (add up to 180°)

⇒ 6x + 6 + 8x - 22 = 180

⇒ 14x - 16 = 180

⇒ 14x = 196

⇒ x = 14

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Question 2

⇒ The given angles are complementary (Add up to 90°)

⇒ 3x + 5 + 40 = 90

⇒ 3x + 45 = 90

⇒ 3x = 45

⇒ x = 15

If y = y(x), then the slope of the tangent line to (1, 1) is equal to the value of the derivative dy/dx when x = 1 and y = 1.

Compute the derivative using implicit differentiation:

d/dx [xy ^2 + y] = d/dx [2x]

d/dx [xy ^2] + d/dx [y] = 2 d/dx [x]

(x d/dx [y ^2] + d/dx [x] y ^2) + dy/dx = 2

2xy dy/dx + y ^2 + dy/dx = 2

(2xy + 1) dy/dx = 2 - y ^2

dy/dx = (2 - y ^2) / (2xy + 1)

Plug in x = 1 and y = 1 :

slope = dy/dx = (2 - 1^2) / (2*1*1 + 1) = 1/3

Now use the point-slope formula to get the equation of the line:

y - 1 = 1/3 (x - 1)

y = x/3 + 2/3

Answer:

The answer is Gerald R. Ford, Jimmy Carter, Ronald Reagan, and lastly George H.W Bush

Step-by-step explanation:

Question 2

\(23=p \cdot 250\)

Question 3

\(p=\frac{23}{250}=0.092\)

A Reflection over the y-axis and a shift downwards by three units, which is consistent with the function f(x) = -|x| − 3.

The function f(x) = -|x| − 3 can be graphed by following these steps:

Therefore, the correct graph is an option (D). The graph of the option (D) shows a reflection over the y-axis and a shift downwards by three units, which is consistent with the function f(x) = -|x| − 3.

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Answer:

3 4/15

Step-by-step explanation:

A

The anwser would be 33 because 33=33 as an absolute value

The absolute value of a number is how far away the number is from zero. The absolute value is ALWAYS positive.

What is the absolute value of -33?

The negative version of the number is also | 33 |

The equation of the line best fit is y = 25x + 340

The term "line equation" typically refers to the equation of a straight line in the Cartesian coordinate plane.

To write an equation for the line passing through the given graph points (1, 360) and (8, 540), we can use the slope-intercept form of a linear equation, y = mx + c

To find the slope (m), we can use the formula:

\(m = \frac{(y_{2} - y_1)}{(x_2 - x_1)}\)

where (x₁, y₁) = (1, 360) and (x₂, y₂) = (8, 540)

m = (540 - 360) / (8 - 1)

m = 25.7 ≈ 25

Now we can use the slope-intercept form of the equation and plug in the slope and one of the given points to find the y-intercept (c):

y = mx + c

540 = 25×8 + c

540 = 200 + c

c = 340

Therefore, the equation of the line passing through the points (1, 360) and (8, 540) is: y = 25x + 340

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Answer:

622.08

Step-by-step explanation:

576 × (0.080 ÷ 1)

576 × 1.08

622.08

Answer:

622.08

Step-by-step explanation:

hope it helps you

To find the height of the shuttle, we can use trigonometry and the concept of similar triangles. The height of the shuttle is approximately 468.675 meters.

Let's assume that the height of the shuttle is represented by 'h' meters. From the information given, we know that the distance between the camera and the launch pad is 750 meters, and the angle of elevation from the camera to the shuttle is 32 degrees.

Using trigonometry, we can set up the following equation:

tan(32°) = h / 750

To find the value of h, we can rearrange the equation:

h = tan(32°) * 750

Using a calculator, we can find the value of tan(32°) ≈ 0.6249.

Now we can calculate the height of the shuttle:

h ≈ 0.6249 * 750

h ≈ 468.675 meters

Therefore, the height of the shuttle is approximately 468.675 meters.

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According to the equation the given all necessary math work are:

\(A: (x -f)^2 +(y -g)^2 = h^2\)

B:  domain: [-5, 11]; range: [-9, 7]

C:  yes, inside

The hypοtenuse's square is equal tο the sum οf the squares οf the οther twο sides if a triangle has a straight angle (90 degrees), accοrding tο the Pythagοras theοrem. Keep in mind that BC² = AB² + AC² in the triangle ABC signifies this. Base AB, height AC, and hypοtenuse BC are all used in this equatiοn. The lοngest side οf a right-angled triangle is its hypοtenuse, it shοuld be emphasized.

Part A:

Use οf the Pythagοrean theοrem gets yοu tο the equatiοn fοr a circle in essentially οne step:

sum οf squares οf sides = square οf hypοtenuse

\((x -f)^2 +(y -g)^2 = h^2\) . . . . . . circle cantered οn (f, g) with radius h

Part B:

The circle will be defined fοr values οf x in the dοmain f ± h, and fοr values οf y in the range g ± h.

dοmain: 3 ± 8 = [-5, 11]

range: -1 ±8 = [-9, 7]

Part C:

The distance frοm pοint (10, -4) tο (f, g) is ...

\(h^2 = (10 -3)^2 +(-4 -(-1))^2\)

\(h^2 = 7^2 +(-3)^2 = 49 +9 = 58\)

h = √58 < 8 . . . . the distance tο the pοint is less than h=8.

The pοint is inside the circle.

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The position vs. time connection is best described by equations is \(& -(0.15 \mathrm{~m}) \cos (3.65) t\) .

From the given data,

A student attaches a 3.0 kg mass to a spring with a spring constant of 40 N/m.

The student compresses the spring to the left by 0.15 m and then releases the mass allowing it to oscillate.

The position of the mass for the spring- mass oscillatory system is,

Where

The angular frequency of the system is,

The angular frequency refers to the angular displacement of any wave element per unit of time or the rate of change of the waveform phase.

Therefore, equation (1) changes as follows

\(x & =A \cos \left(\sqrt{\frac{k}{m}}\right) t \\\)

\(& =-(0.15 \mathrm{~m}) \cos \left(\sqrt{\frac{40 \mathrm{~N} / \mathrm{m}}{3.0 \mathrm{~kg}}}\right) t \\\)

\(& =-(0.15 \mathrm{~m}) \cos (3.65) t\)

Therefore, the position vs. time connection is best described by equations is \(& -(0.15 \mathrm{~m}) \cos (3.65) t\) .

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Answer:

wow-

Step-by-step explanation:

Bet he's doing a good job ;)

Angles in a triangle add up to 180 degrees

The value of x is 85 degrees

A triangle is a polygon which has  three sides and three vertices. It is one of the normal shapes in geometry. A triangle with vertices A, B, and C has three sides & three angles A, B, C.

here, we have,

How to determine the value of x

The total  sum of angles for a triangle is 180 degrees.

So, we have:

x + 35 + 60 = 180

Evaluate the sum

x + 95= 180

Subtract 95 from both sides

x = 85

Hence, the value of x is 85 degrees

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Full question: (SAT Prep) Find the value of x. 35° 60° X

x=?​

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data

circle

center (2,-2)

diameter = 8

point on the circle = ?

Step 02:

equation of a circle

(x - a)² + (y - b)² = r²

r = d / 2 = 8 / 2 = 4

(x - 2)² + ( y - (-2))² = 4²

(x - 2)² + ( y + 2)² = 16

Step 03:

We must verify the points with the equation.

A. If (0 , 1)

(x - 2)² + ( y + 2)² = 16

( 0 - 2)² + ( 1 + 2)² = 16

4 + 9 = 16

15 < 16 the point is inside of the circle

B. If ( 6, -2)

(x - 2)² + ( y + 2)² = 16

(6 - 2)² + ( -2 + 2)² = 16

16 = 16 the point is on the circle

The answer is:

B. (6 , -2)

Answer:

-2

Step-by-step explanation:

    \(\frac{(-2)^3+3 (4)}{-8+6}\)

 \(= \frac{-8 + 12}{-2}\)

 \(= \frac{4}{-2}\)    

 \(= -2\)

Answer:

2.3

Step-by-step explanation:

First we must get rid of the exponent, which is that little 3 at the top.

To do this, we will do:

(-2) × (-2) × (-2) = -8

Now we have -8 + 3.4, which equals -4.6

Next we will combine the numbers in the denominator, to get -2.

Now, all together, we have -4.6/-2.

Last but not least, we will divide -4.6 by -2, to get 2.3

And that's your answer, hope this helps you :)

Sorry if it doesn't, though.

Answer:

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Answer:

447

Step-by-step explanation:

Answer:

6.79

Step-by-step explanation:

you just divide 27.16 (the cost) by 4 (how many sandwiches were purchased)

Answer:

A. 6

Step-by-step explanation:

Using the Pythagorean theorem which states that: Hypotenus² = Opposite² + Adjacent²

Where: hypotenus = 10, opposite = x, adjacent = 8

So:

\( {10}^{2} = {x}^{2} + {8}^{2} \)

Solving for x

\(100 = {x}^{2} + 64\)

Collect like terms to make x the subject of formula

\(100 - 64 = {x}^{2} →36 = {x}^{2} \)

\(36 = {x}^{2} ⟹ {x}^{2} = 36\)

square root both sides of the equation to find the value of x

\( \sqrt{ {x}^{2} } = \sqrt{36} →x = 6\)

Therefore: Option A is correct

Answer: D=2/7 R=4/7

Step-by-step explanation: there are 7 parts and D is the 2nd part R is the 4th part.

Answer:

1/26

Step-by-step explanation:

There is 1 four of spades, and 1 ace of clubs.

So the probability is 2/52, or 1/26.

Answer:

P(four of spades or ace of clubs)= 1/26

Step-by-step explanation:

In a deck of 52 cards, there is one four of spaces and one ace of clubs. we want to find the probability of selecting those cards.

P(four of spades or ace of clubs)=four of spades+ace of clubs/total cards

There is 1 four of spades and 1 ace of clubs. 1+1=2

P(four of spades or ace of clubs)=2/total cards

There are 52 total cards in a deck.

P(four of spades or ace of clubs)=2/52

This fraction can be simplified. Both the numerator (top number) and denominator (bottom number) can be divided by 2.

P(four of spades or ace of clubs)= (2/2) / (52/2)

P(four of spades or ace of clubs)= 1/26

Answer:

2,-1,-2,-4

Step-by-step explanation:

The limit of the function as x approaches -2 is 20.To find the limit of the function (if it exists), we can substitute the given value into the function and simplify. Given function: f(x) = 4x² + 5x - 6x + 2

To find the limit as x approaches -2, we substitute -2 into the function:

f(-2) = 4(-2)² + 5(-2) - 6(-2) + 2
      = 4(4) - 10 + 12 + 2
      = 16 - 10 + 12 + 2
      = 20

Therefore, the limit of the function as x approaches -2 is 20.

To write a simpler function that agrees with the given function at all but one point, we can use a graphing utility. By plotting the given function and observing its behavior, we can create a simpler function that matches the original function except at one point.

However, without further information about the specific behavior of the given function, it is not possible to provide a more detailed explanation or a graph of the simpler function.

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Answer:

Here's an interesting project idea for mathematics that can relate three different topics:

Topic 1: Fractals

Topic 2: Chaos Theory

Topic 3: Differential Equations

Research Question: Can fractals be used to model chaotic systems described by differential equations?

In this project, you can explore the concept of fractals and their applications in modeling complex systems. You can also delve into chaos theory and differential equations to understand how they are used to describe chaotic systems. By combining these three topics, you can investigate whether fractals can provide a better understanding of chaotic systems by modeling them more accurately.

Your research paper can cover the following areas:

Introduction: Provide an overview of fractals, chaos theory, and differential equations, and explain their relevance to the research question.

Fractals: Discuss the properties of fractals and how they can be used to model complex systems. Provide examples of fractals in nature and technology.

Chaos Theory: Explain the concept of chaos and how it is described by differential equations. Discuss the importance of chaos theory in understanding complex systems.

Differential Equations: Provide an overview of differential equations and their applications in physics, engineering, and other fields. Explain how differential equations are used to model chaotic systems.

Combining the three topics: Explain how fractals can be used to model chaotic systems described by differential equations. Provide examples of fractals used in modeling chaotic systems and compare the results to traditional methods.

Conclusion: Summarize the findings of your research and discuss the implications of using fractals to model chaotic systems.

Overall, this project can be a challenging and rewarding exploration of the interplay between three different mathematical topics.

Step-by-step explanation:

a) the initial condition as 0 kg sugar in the tank at time = 0 (pure water)

b) with the net rate of change the amount of sugar after t minutes is S(t) = 236.8 [1 - e (t/740)]

c) time goes to infinity, the amount of sugar in is 236.8 kg.

a) Let A(t) denote the amount of sugar in the tank at time. The tank starts with only pure water, so A(0) = 0 OR you can say that you give the initial condition as 0 kg sugar in the tank at time = 0 (pure water)

b) Sugar flows in at a rate of (0.07 kg/L) * (7 L/min) = 0.49 kg/min = 49/100 kg/min and flows out at a rate of (A(t)/1080 kg/L) * (7 L/min) = 7A(t)/1080 kg/min, so that the net rate of change of is governed by the ODE, multiply both sides by the integrating factor  to condense the left side into the derivative of a product, if t = time and S(t) is the amount of sugar in the tank as a function of time, then the equation that we get is S(t) = 236.8 [1 - e (t/740)]

c) As t---> ∞, the exponential term converges to 0 and we're left with the means when time goes to infinity, the amount of sugar in is 236.8 kg.

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Answer:

\(2(y + 2) = 3(y - 7) \\ 2y + 2 \times 2 = 3y - 3 \times 7 \\ 2y + 4 = 3y - 21 \\ y \: terms \: togther \\ 3y - 2y = 4 + 21 \\ y = 25\)

\(thank \: you\)