graph each linear equation y=3x+7

Part a: The equation of the tangent line is: y - 5 = -15(x - 0)

Part b:The second derivative is a constant value, -15. Since the second derivative is negative, it means the function is concave down at (0, 5).

Part c:The particular solution is y = -10cos(x² + 3x + π) + 15(x² + 3x + π) - 5 - 15π

Part A: To find the equation of the line tangent to the solution curve at the point (0, 5), to follow these steps:

Step 1: Find the derivative of the given differential equation.

Given differential equation: dy/dx = 5(2x + 3)sin(x² + 3x + π)

Differentiate both sides with respect to x:

dy/dx = d/dx (5(2x + 3)sin(x²+ 3x + π))

dy/dx = 5 × (2(sin(x² + 3x + π)) + (2x + 3)cos(x² + 3x + π))

Step 2: Evaluate the derivative at the point (0, 5).

To find the slope of the tangent line at (0, 5), substitute x = 0 into the derivative:

dy/dx = 5 × (2(sin(π)) + (2×0 + 3)cos(π))

dy/dx = 5 × (2(0) + 3(-1)) = -15

Step 3: Use the point-slope form of the equation to write the equation of the tangent line.

The point-slope form of the equation is: y - y1 = m(x - x1), where m is the slope and (x1, y1) is the point (0, 5).

Simplifying, we get: y = -15x + 5

Part B: To find the second derivative at (0, 5) and determine the concavity of the solution curve at that point, follow these steps:

Step 1: Find the second derivative of the given differential equation.

Given differential equation: dy/dx = 5(2x + 3)sin(x² + 3x + π)

Differentiate the previous result for dy/dx with respect to x to get the second derivative:

d²y/dx² = d/dx (-15x + 5)

d²y/dx² = -15

Step 2: Determine the concavity.

Part C: To find the particular solution y = f(x) with the initial condition f(0) = 5,  to integrate the given differential equation:

dy/dx = 5(2x + 3)sin(x² + 3x + π)

Step 1: Integrate the equation with respect to x:

∫dy = ∫5(2x + 3)sin(x² + 3x + π) dx

y = ∫(10x + 15)sin(x² + 3x + π) dx

Step 2: Use u-substitution:

Let u = x² + 3x + π, then du = (2x + 3) dx

Now the integral becomes:

y = ∫(10x + 15)sin(u) du

Step 3: Integrate with respect to u:

y = -10cos(u) + 15u + C

Step 4: Substitute back for u:

y = -10cos(x² + 3x + π) + 15(x² + 3x + π) + C

Step 5: Apply the initial condition f(0) = 5:

Substitute x = 0 and y = 5 into the equation:

5 = -10cos(π) + 15(0² + 3(0) + π) + C

5 = 10 + 15π + C

Simplifying,

C = 5 - 10 - 15π

C = -5 - 15π

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To find the missing side of an AAS triangle, use the Pythagorean Theorem and the known lengths of the other two sides to calculate the length of the missing side.

An AAS triangle (angle-angle-side) is a triangle where two angles and one side length are known. To find the missing side, the Pythagorean Theorem must be used. The Pythagorean Theorem states that in a right triangle, the sum of the squares of the two sides must equal the square of the hypotenuse. To use this theorem, the two known sides must be squared and added together. The resulting number must then be equal to the square of the missing side. Once the result is equal, the square root of the result will give you the length of the missing side. For example, if two sides of a triangle are given as 3 and 4, the Pythagorean Theorem can be used to calculate the missing side. Squaring and adding the two sides together (3^2 + 4^2) will result in 25. Taking the square root of this result will give you the length of the missing side, which is 5.

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Answer:So for an isosceles right triangle with side length a , the hypotenuse has a length of a√2 . Similarly, if the hypotenuse of an isosceles right triangle has length of a , the legs have a length of a√2ora√22 each

Step-by-step explanation:

An isosceles triangle is a special triangle due to the values of its angles. These triangles are referred to as triangles and their side lengths follow a specific pattern that states that one can calculate the length of the legs of an isoceles triangle by dividing the length of the hypotenuse by the square root of 2.

FOR EXAMPLE What is the length of the legs of an isosceles right triangle if the hypotenuse is 8 units?

2 Answers By Expert Tutors. For an isoceles right trangle, the legs each have length x and the hypotenuse has length x √2. Therefore, since the hypotenuse has length 8√2, the legs must each be of length 8.

Answer:

The figures are congruent because a 270° rotation about the origin and then a reflection over the x-axis will map ΔABC onto ΔLMN.

Answer:

j = 2

Step-by-step explanation:

Slope of a line is given by:
\(\medium \text{$\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}$}\)

where (x₁, y₁) and (x₂, y₂) are two points on the line

This is commonly referred to as rise/run

Given the two points (6, 1) corresponding to (x₁, y₁) and (9, j) corresponding to (x₂, y₂)

\(\text{Slope = }\dfrac{\ensuremath{j}-1}{9-6}=\dfrac{j-1}{3}\)

But we are given the slope as 1/3

So we get
\(\dfrac{j-1}{3} = \dfrac{1}{3}\)

Multiplying by 2 on both sides gives us:

j - 1 = 1

Adding 1 to both sides gives us

j - 1 + 1 = 1 + 1

j = 2

Answer:

(5,-2)

Step-by-step explanation:

(x, y)=(y, -x)

(2,-5)=(5,-2)

90° clockwise=(5,-2)

Mark the brainiest if correct

-0.45 x + 0.33 = -0.66

Adding -0.33 to both sides

-0.45 x = -0.99

Dividing both sides by -0.45

x = -0.99 / -0.45 = 2.2

Answer: x = 2.2, last choice

Answer: 22

Step-by-step explanation:

11 - 6 = 5

4 x 5 = 20

20 + 2 = 22

' pls can i have brainliest? i need it for my goal'

Answer:

22

Step-by-step explanation:

Solve whats in the paranthesis: (11-6) = 5

New problem: 4(5) + 2

Then multiply: 20+2

Finally add both numbers together: 22

Answer:

I think you have it

Step-by-step explanation:

It's not -4.44, and if it was -3.14 it would be closer to the -3 tick on the line. With the negative square root of 17 being 4.12 it's not that either. -11/3 is 3.6666667 or something along those lines so it would be closer to the -4 tick on the line, so I'm pretty sure you got it.

Answer:

-28

Step-by-step explanation:

Given that the resistance remains constant, if the voltage decreases to one-third of its original amount, the resulting current in the circuit is 0.4A

Ohm’s law states that the potential difference between two points is directly proportional to the current flowing through the resistance.

It is expressed as;

V = IR

Where V is the voltage or potential difference, potential difference, I is the current and R is the resistance.

Given that;

Initially, A circuit has a current I = 1.2A

V = IR

R = V/I

R = V/1.2A ...... let this be equation 1

Next, voltage decreases to one-third of its original amount while the resistance remains constant.

Meaning Voltage = 1/3 of V = V/3

Hence;

V = IR

V/3 = IR

From equation 1 ( R = V/1.2A )

V/3 = I × V/1.2A

V/3 = IV/1.2A

We cross multiply

V1.2A = 3IV

I = V1.2A / 3V

I = 1.2A / 3

I = 0.4A

Therefore, given that the resistance remains constant, if the voltage decreases to one-third of its original amount, the resulting current in the circuit is 0.4A

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Answer:

0.4 A

Step-by-step explanation:

When resistance is constant, current is proportional to voltage. When 1/3 the voltage is applied, 1/3 the current will result. (1/3)* (1.2 A) = 0.4 A The resulting current will be 0.4 A.

The probability that the landing gear will survive a 10,000 landing design life without damage is approximately 0.905.

Given, The probability of an aircraft landing gear being damaged due to excessive impact is 10-5 per landing.In other words, the probability of the landing gear being damaged due to excessive impact is 1 out of 100,000.

Therefore, the probability of the landing gear not being damaged due to excessive impact is

1 - (1/100,000) = 99,999/100,000.

To find the probability that the landing gear will survive a 10,000 landing design life without damage, we need to find the probability that the landing gear will not be damaged in each of the 10,000 landings.

Using the formula for independent events, we can find the probability of the landing gear not being damaged in 10,000 landings: P(surviving 10,000 landings)

= (99,999/100,000)^10,000

= 0.905

Thus, the probability that the landing gear will survive a 10,000 landing design life without damage is approximately 0.905.

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Answer:To find a translation image of a shape, you can use the following rule or formula. Suppose you want to translate or slide point P a units horizontally and b units vertically. Then, change the x-values and y-values of the coordinates of P. The points of the triangle of are A(-3, 1), B(-4, 3), and C(-2, 4).

Step-by-step explanation:This all i can remember to help you out

Answer:

Question 1: -5, -4.9, -4.35, -4.3, -4

Question 2: -3, -2\(\frac{1}{2}\), -2\(\frac{2}{5}\), -2\(\frac{3}{10}\). -2

Question 3: -1, \(\frac{-3}{4}\), \(\frac{-5}{8}\), -\(\frac{1}{20}\), 0

Step-by-step explanation:

Negative numbers are the direct opposite of positive. If the number looks bigger than another, and they are both negative the one that looks lager is actually smaller.

Answer:

the first picture...

1. -5, -4.9, -4.35, -4.3, -4

Second pic

2. -3, -2 3/5, -2 1/2, -2 3/10, -2

third pic

3.  -1, -3/4, -5/8, -1/20, 0

your welcome.

Answer:

Hey! here is the answer!

Step-by-step explanation:

C! 10 = ∎ × 60

i know this becuase i did the equation in reverse, then used my calculator to make sure all the numbers added up.

Answer: B)

Step-by-step explanation:

First we need to find the value of the black sqaure. The value of the black square is 6 because 60 / 10 = 6. A) cannot be the answer because 6 does not equal 60. C) cannot be the answer because 10 does not equal 360. The only answer can be B) because 6 x 10 does equal 60.

The given statement is True. A discrete probability distribution can be expressed in a graph, table, or formula, as long as it gives the probability associated with each value of the discrete random variable.

A Discrete probability distribution is a statistical term used to describe the probability distribution of a random variable that can take on a finite or countably infinite number of distinct outcomes. In other words, a discrete random variable is one that can only take on a specific set of values, while a continuous random variable can take on any value within a specified range.Examples of discrete random variables include the number of children in a family, the number of accidents that occur in a given day, and the number of red cars that pass through an intersection in an hour. A discrete probability distribution is a way of describing the probabilities associated with each of these possible outcomes.In summary, a discrete probability distribution can be expressed in a graph, table, or formula, as long as it gives the probability associated with each value of the discrete random variable. This is because a discrete random variable can only take on a specific set of values, making it easy to calculate the probabilities associated with each outcome.

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Answer:

=The opposite angles of a parallelogram are equal

=(3x+4)

=(5x-2)

=-2x=-6

=x=6+2

=x=3=

1st angle=3x+4=13

3rd angle=5x-2=13

=sum of adjacent side of angle is 180°

=Let the adjacent (2nd angle ) be y=

y+13°=180°

=y=180°-13°

=y=167°=

2nd angle=4th angle

=2nd angle=167° 

=4th angle=167°

Step-by-step explanation:

This might be confusing, but I hope it helps <3

Answer:

2

Step-by-step explanation:

Answer:

rational numbers

Step-by-step explanation:

all numbers are rational, but not all numbers are integers or whole numbers.

Answer: 5

Step-by-step explanation:

weights =   pounds

Answer: Jackie has two puppies. One weighs 5 9/16 pounds and the other weighs 6 1/4 pounds. Find the difference in their weights.

Step-by-step explanation:

"DIFFERENCE" means to subtract their weights. We will subtract lesser amount from the greater amount to get our answer.

Also, we need to first make these mixed numbers into improper fractions by using the rule below:

If a number is given in this form:

We can do the operation below to make it improper fraction:

The bigger number is . So we subtract the other from this after changing to improper fraction.

and

Now, we subtract via doing LCM and get our answer: The difference in weight is 11/16 pounds

Answer: The area of a rectangular room is 750 square feet and the width of the room is 5 feet less than the length of the room.

Three equations that can be used to solve for y, the length of the room are:

y(y + 5) = 750: This equation uses the formula for the area of a rectangle, which is length x width. Since the width is 5 feet less than the length, we can substitute y-5 for the width.

750 – y(y – 5) = 0: This equation uses the same method as the first equation, but it is rearranged to solve for y.

(y + 25)(y – 30) = 0: This equation uses the quadratic formula to solve for the length of the room, this equation is also useful when the length is an irrational number.

Note that the fourth equation y(y – 5) + 750 = 0 is not valid because it is not possible to have negative area, hence y(y-5) should not be added to 750.

The fifth equation (y+25)(y-30)=0 is also not valid because it gives y = -25 and y = 30 as solutions but the length of the room can't be negative.

Step-by-step explanation:

Answer:

x-intercepts: x=3, -5

Step-by-step explanation:

y = x^2 + 2x − 15

y = x^2 + 5x - 3x − 15  ==> 5*(-3)=-15 and 5+(-3) = 5-3=2

y = x^2 + 5x - 3x − 15

y = x(x+5) - 3(x+5)

y = (x-3)(x+5)

x-3=0  ==> x=3

x+5=0 ==> x=-5

x-intercepts: x=3, -5

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Answer:

Finding the dilation's center point is the first step in determining the scale factor. Next, we measure the distances between the center point and various points on the preimage and the image. We may determine the scale factor by dividing these distances by 2.

Step-by-step explanation:

Answer:

1,500 balloons in 20 packages

Step-by-step explanation:

75 x 20 = 1500

(a) The domain closed and bounded.

(b) The domain bounded.

(c) The domain closed.

(d) The domain bounded.

(e) The domain closed and bounded.

(f) The domain closed and bounded.

In this question, we have been given some domains.

We need to check which domains are closed and which are bounded.

A domain of function is said to be closed if the region R contains all boundary points.

A bounded domain is nothing but a domain which is a bounded set.

(a) {(x,y)∈R2:x^2+y^2≤1}

The domain of x^2+y^2≤1 contains set of all points (x, y) ∈R2

so, the domain closed and bounded.

(b) {(x,y)∈R2:x2+y2<1}

The domain of x^2+y^2 < 1 contains set of all points (x, y) ∈R2

so, the domain is bounded.

(c) {(x,y)∈R2: x ≥ 0}

The domain of x ≥ 0 is R2 - {x < 0}

So, the domain is closed.

(d) {(x, y) ∈ R2 : x > 0,y > 0}

The domain is R2 - {(x, y) ≥ 0}

So, the domain is bounded.

(e) {(x, y) ∈ R2 : 1 ≤ x ≤ 4, 5 ≤ y ≤ 10}

The domain is closed and bounded.

(f) {(x,y)∈R2:x>0,x^2+y^2≤10}

The domain is closed and bounded.

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