what is the gradient of the straight line AB in the figure above​

Answer:

y < 3

Step-by-step explanation:

2y + 1 < 7

~Subtract 1 to both sides

2y < 6

~Divide 2 to both sides

y < 3

Best of Luck!

The derivative formula for the division of two functions is equal to d [θ(x)] / dx = [g(x) · f'(x) - f(x) · g'(x)] / [g(x)]², where θ(x) = f(x) / g(x).

In this problem we need to derive the formula for the derivative of the division of two functions, that is, the expression θ(x) = f(x) / g(x). First, we write the definition of the derivative for the given expression:

\(\frac{d}{dx} [\theta (x)] = \lim_{h \to 0} \frac{\theta(x + h) - \theta (x)}{h}\)

Second, substitute and expand the expression by algebra properties:

\(\frac{d}{dx} [\theta (x)] = \lim_{h \to 0} \frac{\frac{f(x + h)}{g(x + h)} - \frac{f(x)}{g(x)} }{h}\)

\(\frac{d}{dx}[\theta (x)] = \lim_{h \to 0} \frac{f(x + h) \cdot g(x) - f(x) \cdot g(x + h)}{h\cdot g(x + h)\cdot g(x)}\)

Third, expand and simplify the expression one more time by algebra properties and limit properties:

\(\frac{d}{dx} [\theta (x)] = \lim_{h \to 0} \frac{f(x + h) \cdot g(x) - f(x) \cdot g(x) + g(x) \cdot f(x) -f(x) \cdot g(x + h)}{h \cdot g(x + h) \cdot g(x)}\)

\(\frac{d}{dx}[\theta (x)] = \lim_{h \to 0} g(x) \cdot \frac{f(x + h) - f(x)}{h\cdot g(x+h)\cdot g(x)} - \lim_{h \to 0} f(x) \cdot \frac{g(x + h) - g(x)}{h\cdot g(x+h)\cdot g(x)}\)

\(\frac{d}{dx}[\theta (x)] = \lim_{h \to 0} \frac{g(x)}{g(x + h) \cdot g(x)} \cdot \lim_{h \to 0} \frac{f(x + h) - f(x)}{h} - \lim_{h \to 0} \frac{f(x)}{g(x+ h) \cdot g(x)} \cdot \lim_{h \to 0} \cdot \frac{g(x + h) - g(x)}{h}\)

Fourth, simplify the resulting expression by evaluating the limits:

d [θ(x)] / dx = [g(x) / [g(x)]²] · f'(x) - [f(x) / [g(x)]²] · g'(x)

d [θ(x)] / dx = [g(x) · f'(x) - f(x) · g'(x)] / [g(x)]²

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Answer: I think it’s 22 May 2021

Step-by-step explanation:-

First Step ) August 2020 + 9 Months = May 2021

Second Step ) 4 + 7*2 ( two weeks has 14 days ) or 4 + 7 + 7 = 18

Third Step ) 18 + 4 Days Later = 22

So final answer would be 22 May 2021.

Hope it helps, Good Day! And happy reading

( P.S ) The bed set took a lot of time to arrive xD

Answer:

-2

Step-by-step explanation:

The answer for this question is A:

A = x = –t + 1 and y = 0.5t + 4 when –2 ≤ t ≤ 6

The parametric equations of the curve are:

x = –t + 1 and y = 0.5t + 4 when –5 ≤ t ≤ 3

The parametric equation of the line is, \(x=x_0+at,y=y_0+bt\) where \((x_0,y_0)\) is the point on the line and \(\frac{b}{a}\) is the slope of the line with a, b are real numbers.

If (a, b) and (c, d) are any two points on the line then, slope of the line is:

m = (d - b)/(c - a)

For given situation,

a line goes from (-5, 7) to (3, 3).

Using the formula of slope, the value of m i.e., slope of the line  would be,

⇒ m = (7 - 3)/(-5 - 3)

⇒ m = 4/(-8)

⇒ m = 1/(-2)

⇒ m= 0.5/(-1)

Comparing with m = b/a,

b = 0.5 and a = -1.

From the graph of the line given below,

A point (1, 4) is also on the line.

Let \(\bold{(x_0,y_0)=(1,4)}\)

Using the parametric equation of the line,

\(x=x_0+at\)

⇒ x = 1 + (-1)t

⇒ x = -t + 1

and \(y = y_0+bt\)

⇒ y = 4 + (0.5)t

⇒ y = 0.5t + 4

Therefore, the parametric equations of the curve are:

x = –t + 1 and y = 0.5t + 4 when –5 ≤ t ≤ 3

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Answer:

52% is the answer

52%

all decimals can convert to percentages easily. For example:

0.76 = 76%

0.4 = 40%

0.093 = 9.3%

just move the decimal point 2 places backwards.

Answer:

Down payment is when you are trying to by something that is expensive up front like a house or a car.  It is usually paid in cash or equivalent at the time of finalizing the transaction. A loan of some sort is then required to finance the remainder of the payment.

Step-by-step explanation:

Answer:

x = 3

Step-by-step explanation:

\(In\: \triangle PQT,\: \overline{PQ}|| \overline {RS}...(Given)\\\\\implies\frac{PS}{ST}=\frac{QR}{RT}\\(By\: Proportionality\: Theorem) \\ \\\implies\frac{2x+4}{5}=\frac{3x+5}{7}\\\\ \implies \: 7(2x + 4) = 5(3x + 5) \\ \\ \implies \:14x + 28 = 15x + 25 \\ \\ 14x - 15x = 25 - 28 \\ \\ - x = - 3 \\ \\ x = 3\)

Answer:

it should be 378 = w(241 - 223)

∆ADB is congruent to ∆ADC . Because,

{ If any two sides and angle included between the sides of one triangle = The corresponding two sides and the angle between the sides of the second triangle, then the two triangles are said to be congruent by SAS rule. }

What is a right-angle triangle?

It is a triangle in which one of the angles is 90 degrees and the other two are sharp angles. The sides of a right-angled triangle are known as the hypotenuse, perpendicular, and base.

BD = DC = 3cm.

AD ⟂ BC .

So,

in ∆ADB and ∆ADC, we have,

→ AD = AD (common)

→ ∠ADB = ∠ADC (AD ⟂ BC so, 90°)

→ DB = DC (given both 3cm.)

Thus,

→ ∆ADB ~ ∆ADC (By SAS) { If any two sides and angle included between the sides of one triangle = The corresponding two sides and the angle between the sides of the second triangle, then the two triangles are said to be congruent by SAS rule. }

Hence, ∆ADB is congruent to ∆ADC .

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Answer:

2\(\frac{1}{3}\)x5=11\(\frac{2}{3}\)

Step-by-step explanation:

5x2=10

\(\frac{1}{3}\)x5=\(\frac{5}{3}\)

\(\frac{5}{3}\)=1\(\frac{2}{3}\)

10+1\(\frac{2}{3}\)=11\(\frac{2}{3}\)

It would cost approximately $52.18 to drive from Statesville, NC to Washington, DC with a car that gets 29 miles per gallon on the interstate, considering a gas cost of $3.89 per gallon.

To calculate the time it would take to drive from Statesville, NC to Washington, DC, we can divide the distance of 389 miles by the average speed of 65 mph.

Time = Distance / Speed

Time = 389 miles / 65 mph

Time ≈ 5.98 hours

Therefore, it would take approximately 5.98 hours to drive from Statesville, NC to Washington, DC on interstates with an average speed of 65 mph.

To calculate the cost of driving to Washington, DC, we need to know the number of gallons of gas required for the trip. We can find this by dividing the distance by the car's mileage, which is 29 miles per gallon.

Number of gallons = Distance / Mileage

Number of gallons = 389 miles / 29 miles per gallon

Number of gallons ≈ 13.41 gallons

The cost of gas can be calculated by multiplying the number of gallons by the cost per gallon, which is $3.89.

Cost = Number of gallons * Cost per gallon

Cost ≈ 13.41 gallons * $3.89/gallon

Cost ≈ $52.18

Therefore, it would cost approximately $52.18 to drive from Statesville, NC to Washington, DC with a car that gets 29 miles per gallon on the interstate, considering a gas cost of $3.89 per gallon.

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Answer: Here is the calculation:

The cost of the wings is $0.25 per wing

The cost of the pitcher of beverage is $5

The cost of the ranch dip is $1.50

Sales tax is 8.5%, so you need to add 8.5/100 * (5+1.5) = 0.0825 to the cost of the beverage and dip.

The cost of the beverage and dip after tax is 5+1.5+0.0825 = 6.5825

The total cost of the wings, beverage, and dip before tip is 6.5825 + 20 = 26.5825

You need to leave a 20% tip, so you need to add 0.2*26.5825 =5.31650 to the total cost

The total cost of the wings, beverage, dip and tip is 26.5825+5.31650 = 31.899

So you have $20 and you want to spend $31.899 including tax and tip, you can purchase 20/0.25 = 80 chicken wings.

Step-by-step explanation:

The general solution of the partial differential equation is:

U(x, t) = Σ [Aₙ*sin((nπ/3)x)]*e^(-(nπ/3)²t)

The partial differential equation (PDE) is given as:

Uxx = (1/2)Ut with the boundary and initial conditions as 0< X <3 with U(0,t) = U(3, t)=0, U(0, t) = 5sin(4πx)

Assume that the solution can be written as a product of two functions:

U(x, t) = X(x)T(t)

Substituting this into the PDE, we have:

X''(x)T(t) = (1/2)X(x)T'(t)

Dividing both sides by X(x)T(t), we get:

(X''(x))/X(x) = (1/2)(T'(t))/T(t)

Since the left side only depends on x and the right side only depends on t, both sides must be equal to a constant, denoted as -λ²:

(X''(x))/X(x) = -λ²

(1/2)(T'(t))/T(t) = -λ²

Simplifying the second equation, we have:

T'(t)/T(t) = -2λ²

Solving the second equation, we find:

T(t) = Ce^(-2λ²t)

Applying the boundary condition U(0, t) = 0, we have:

U(0, t) = X(0)T(t) = 0

Since T(t) ≠ 0, we must have X(0) = 0.

Applying the boundary condition U(3, t) = 0, we have:

U(3, t) = X(3)T(t) = 0

Again, since T(t) ≠ 0, we must have X(3) = 0.

Therefore, we can conclude that X(x) must satisfy the following boundary value problem:

X''(x)/X(x) = -λ²

X(0) = 0

X(3) = 0

The general solution to this ordinary differential equation is given by:

X(x) = Asin(λx) + Bcos(λx)

Applying the initial condition U(x, 0) = 5*sin(4πx), we have:

U(x, 0) = X(x)T(0) = X(x)C

Comparing this with the given initial condition, we can conclude that T(0) = C = 5.

Therefore, the complete solution for U(x, t) is given by:

U(x, t) = Σ [Aₙsin(λₙx) + Bₙcos(λₙx)]*e^(-2(λₙ)²t)

where:

Σ represents the summation over all values of n

λₙ are the eigenvalues obtained from solving the boundary value problem for X(x).

To find the eigenvalues λₙ, we substitute the boundary conditions into the general solution for X(x):

X(0) = 0: Aₙsin(0) + Bₙcos(0) = 0

X(3) = 0: Aₙsin(3λₙ) + Bₙcos(3λₙ) = 0

From the first equation, we have Bₙ = 0.

From the second equation, we have Aₙ*sin(3λₙ) = 0. Since Aₙ ≠ 0, we must have sin(3λₙ) = 0.

This implies that 3λₙ = nπ, where n is an integer.

Therefore, λₙ = (nπ)/3.

Substituting the eigenvalues into the general solution, we have:

U(x, t) = Σ [Aₙ*sin((nπ/3)x)]*e^(-(nπ/3)²t)

where Aₙ are the coefficients that can be determined from the initial condition.

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Using the least common factor, it is found that:

The number of minutes it takes for them to complete a sign at the same time is the least common factor of 6 and 8, hence:

6 - 8|2

3 - 4|2

3 - 2|2

3 - 1|3

1 - 1

lcm(6,8) = 2³ x 3 = 24

They work for 30 minutes, then, since lcm(6,8) = 24 < 30, Mai and Clare will complete a sign at the same time.

Following the same logic, for Mai and Noah:

6 - 5|2

3 - 5|3

1 - 5|5

1 - 1

lcm(6,5) = 2 x 3 x 5 = 30

Since lcm(6,5) = 30 = 30, Mai and Noah will complete a sign at the same time.

For Clare and Noah:

5 - 8|2

5 - 4|2

5 - 2|2

5 - 1|5

1- 1

lcm(5,8) = 2³ x 5 = 40

Since lcm(5,8) = 40 > 30, Clare and Noah will not complete a sign at the same time.

Since Clare and Noah will not complete a sign at the same time, all three students will not complete a sign at the same time.

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Answer:

the vertex is the highest point on the graph — called the maximum, or max.

Step-by-step explanation:

hope this hoped

2x and 2 + x are not equivalent, because 2x is product of 2 and x and 2+x is sum of 2 and x.

Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable.

The given expressions are 2x and 2+x.

Here, 2x is product of 2 and x.

2+x is sum of 2 and x.

Thus, 2x≠2+x

Therefore, 2x and 2 + x are not equivalent, because 2x is product of 2 and x and 2+x is sum of 2 and x.

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The inequality that represents the value of x is (b)  x > 80

from the question, we have the following parameters that can be used in our computation:

The figure

The general rule is that

The larger the side length, the larger the angle opposite it

using the above as a guide, we have the following:

1/8x > 10

So, we have

x > 80

Hence, the inequality is x > 80

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Answer:

answer is c Find the optimum production quantity maximize profit

Notice that they give us the actual linear equation that represents the savings of Jim for week:

y = 120 x + 250

The rate here is given by the "slope"of this linear equation (the slope is the numerical factor that multiplies the variable "x" of the number of weeks).

Then the RATE of savings per week for Jim is: $120 per week.

Now, we need to obtain the rate for Josh based on the values given in the table. We use for example:

2 weeks --> $520

4 weeks --> $740

and we calculate the rate using the slope formula:

rate per week for Josh = (740 - 520) / (4 - 2) = 220 / 2 = $110 per week.

Then, Vivian is right (Jim is saving at a higher rate)

Complete the square in the denominator:

\(x^2 - 8x + 39 = x^2 - 8x + 16 + 23 = (x-4)^2 + 23\)

Then in the integral, substitute \(x - 4 = \sqrt{23} \tan(t)\) and \(dx = \sqrt{23} \sec^2(t) \, dt\).

\(\displaystyle \int \frac{dx}{x^2 - 8x + 39} = \int \frac{\sqrt{23} \sec^2(t) \, dt}{\left(\sqrt{23}\tan(t)\right)^2 + 23} = \frac1{\sqrt{23}} \int \frac{\sec^2(t)}{\tan^2(t)+1} \, dt\)

Recall that tan²(x) + 1 = sec²(x) for all x (such that cos(x) ≠ 0, anyway). Then the integral reduces to the trival

\(\displaystyle \frac1{\sqrt{23}} \int dt = \frac1{\sqrt{23}} t + C\)

and putting the result back in terms of x, we get

\(\displaystyle \int \frac{dx}{x^2 - 8x + 39} = \boxed{\frac1{\sqrt{23}} \tan^{-1}\left(\frac{x-4}{\sqrt{23}}\right) + C}\)

If you want to proceed via partial fractions, there's more work involved. We can use the complete-square expression to easily find the roots of the denominator:

\((x-4)^2 + 23 = 0 \implies (x-4)^2 = -23 \implies x - 4 = \pm i \sqrt{23} \implies x = 4 \pm i \sqrt{23}\)

Then we factorize

\(x^2 - 8x + 39 = \left(x - 4 - i\sqrt{23}\right) \left(x - 4 + i \sqrt{23}\right)\)

and the PFD would be

\(\dfrac1{x^2-8x+39} = \dfrac a{x - 4 - i\sqrt{23}} + \dfrac b{x - 4 + i\sqrt{23}}\)

Solve for the coefficients:

\(1 = a\left(x - 4 + i\sqrt{23}\right) + b\left(x - 4 - i\sqrt{23}\right)\)

\(\implies \begin{cases}a+b = 0 \\ \left(-4+i\sqrt{23}\right) a - \left(4+i\sqrt{23}\right) b = 1 \end{cases} \implies a = \dfrac i{2\sqrt{23}}, b=-\dfrac i{2\sqrt{23}}\)

Then the integral is

\(\displaystyle \int \frac{dx}{x^2-8x+39} = \dfrac i{2\sqrt{23}} \ln\left|x - 4 - i\sqrt{23}\right| - \dfrac i{2\sqrt{23}} \ln\left|x - 4 + i\sqrt{23}\right| + C\)

and we can condense the logarithms to

\(\displaystyle \int \frac{dx}{x^2-8x+39} = \dfrac i{2\sqrt{23}} \ln\dfrac{\left|x - 4 - i\sqrt{23}}{\left|x - 4 + i\sqrt{23}\right|} + C\)

Now we fight the urge to be discouraged by the presence of imaginary numbers in this result. The two antiderivatives are one and the same!

For any complex number z, the following identity holds:

\(\tan^{-1}(z) = -\dfrac i2 \ln \left(\dfrac{i-z}{i+z}\right)\)

With some rewriting, we have for instance

\(\dfrac i{2\sqrt{23}} \ln\dfrac{\left|x - 4 - i\sqrt{23}\right|}{\left|x - 4 + i\sqrt{23}\right|} = -\dfrac1{\sqrt{23}} \times -\dfrac i2 \ln \left|\dfrac{\frac{x-4}{\sqrt{23}} - i}{\frac{x-4}{\sqrt{23}} + i}\right| \\\\ = -\dfrac1{\sqrt{23}} \tan^{-1}\left(-\dfrac{x-4}{\sqrt{23}}\right) \\\\ = \dfrac1{\sqrt{23}} \tan^{-1}\left(\dfrac{x-4}{\sqrt{23}}\right)\)

Admittedly, I skip over a bunch of details, but the point is that both methods end with the same result, but the first method is much simpler to  follow and execute, in my opinion.

Answer:

11

Step-by-step explanation:

Substituting the values of x, y, and z into the expression, we get:

2x² - y + 2(z-1) = 2(2)² - 3 + 2(4-1)

= 2(4) - 3 + 2(3)

= 8 - 3 + 6

= 11

Therefore, if x = 2, y = 3, and z = 4, then the value of the expression 2x² - y + 2(z-1) is 11.

Answer:

11

Step-by-step explanation:

if x = 2, y = 3, and z = 4.

2x²-y + 2(z-1)

Substituting the given values of x, y, and z, we get:

2x² - y + 2(z-1) = 2(2)² - 3 + 2(4-1)

= 2(4) - 3 + 2(3)

= 8 - 3 + 6

= 11

Therefore, the value of the expression when x = 2, y = 3, and z = 4 is 11.

BODMAS (Brackets, Order, Division, Multiplication, Addition, Subtraction) is used to determine the sequence of operations in a mathematical expression. It is used to avoid confusion and ensure that everyone obtains the same answer from a mathematical expression. The rule states that the operations inside the brackets must be done first, followed by orders, then division and multiplication (from left to right), and finally addition and subtraction (from left to right).

The additive inverse of the polynomial is A' = - ( 1.3t³ - 0.2t² - 6t - 8 )

Given data ,

Let the polynomial be represented as A

Now , the value of A is

A = ( 1.3t³ + 0.4t² - 24t ) - ( 0.6t² + 8 - 18t )

On simplifying the equation , we get

A = 1.3t³ + 0.4t² - 24t - 0.6t² - 8 + 18t

A = 1.3t³ - 0.2t² - 6t - 8

Now , the additive inverse of the polynomial is

A' = - ( 1.3t³ - 0.2t² - 6t - 8 )

Hence , the polynomial is solved

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Answer:

Step-by-step explanation:

360 people can fit in 8 buses.

First we need to find how many people fit in 1 bus, so we can divide 495, the total number of people, by 11, the number of buses.

495/11=45

Now we know 45 people can go on 1 bus, and we have 8 of them, so we multiply these 2 numbers.

45*8=360

360 people.

Answer:
8 buses can carry 360 passengers

If this help please set brainliest.

Step-by-step explanation:

To find out how many people can fit in 8 buses, you need to multiply the number of people that can fit in one bus by the number of buses. Since 11 buses can carry 495 passengers and each bus can carry the same number of passengers, one bus can carry 495/11=45 45 passengers.

Therefore, 8 buses can carry 360 passengers.

Answer:

2%

Step-by-step explanation:

If 300 minutes is 100%, how much percent is 306 minutes?

we need to use the rule of three

306 minutes x 100% / 300 minutes = 102%

Therefore the percent of the increase is 102%-100%= 2%

Answer:

1unit scale on map is equal to 100.16 km in real life

Step-by-step explanation:

since in map 12.cm =1262km in real life

1cm=(1262/12.6) km

therefore it gives us 100.158km which is approximately 100.16 km .

Answer:

Concave

Step-by-step explanation:

Answer:

\(y = - \frac{7}{2} x + \frac{47}{2}\)