y = ex²+¹ find dy/dx​

Answer:  x₁=2   x₂=-(1/4)   x₃=-(2/3)

Step-by-step explanation:

View image attached

Answer:

Step-by-step explanation:

Given the equation 4n^2 +28n +49, to get the factors of the equation, we need to factorize the equation completely as shown;

= 4n² +28n +49

Using the general formula n = -b±√b²-4ac/2a

from the equation: a = 4, b = 28 and c = 49

n =  -b±√b²-4ac/2a

n = -28±√28²-4(4)(49)/2(4)

n =  -28±√784-784/8

n = -28±√0/8

n = -28/8

n = -7/2

The factor of the given function is -7/2

The constant of variation of the given problem is calculated as; 240 miles

A constant of variation (k) is defined as a ratio that represents the relationship between the independent variable (x) and the dependent variable (y).

Now, we are told that average speed, s, in miles per hour is inversely proportional to the time, t, the trip takes in hours. Thus;

s ∝ 1/t

Thus;

s = k(1/t)

where k is the constant of proportionality

we are told that If the train takes 2 hours, and the average speed is 120 mph. Thus;

120 = k(1/2)

Multiply both sides by 2 to get;

240 miles = k

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The sets of figures shown are debits and credits into Henry's account. The Credit entry means money has been added (+) and the debit entry means money had been deducted (-).

This is shown as follows;

Opening balance - 200

Deposits - 175

Lunch expense - 15

Lunch expense - 15

Loan to brother - 85

Therefore, Henry's balance on saturday was $260

Answer:

6

Step-by-step explanation:

Given,

x = 15

To find : The value of x - 9 = ?

Solution : -

Substitute x = 15 in x - 9,

x - 9

= 15 - 9

= 6

Hence, evaluated.

Answer:

Yes, 9 is the answer.

Step-by-step explanation:

This is a one step equation so you only have to preform one operation to solve. You do the inverse operation of what the equation is doing. In this case you are multiplying, which means you will divide to solve.

63/7 = 9

The perimeter of the rectangle is 62 square units.

The perimeter of a rectangle can be calculated using the formula:

P = 2(L + W)

Where:

L is the length of the rectangle

W is the width of the rectangle

We have:

L = 20 units

W = 11 units

Substituting into the formula:

P = 2(20 + 11)

P = 2(31)

P = 62 square units

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Question in English

What is the perimeter of a rectangle if it is 20 long and 11 wide?

Answer

12r2 +r − 7

Step-by-step explanation:

Answer:

mn

Step-by-step explanation:jhhh

Answer:

slope = 3/1 or 3

Step-by-step explanation:

Using the rise and run method we see the line rises up 3 and runs sideways 1 unit.

This means that the slope is 3/1 or 3

If you continue along the line this pattern will continue

Hope this helps :)

Answer:

The slope is 3/1

Step-by-step explanation:

The slope is 3 over 1 because the line moves the right by 1 unit and moves up by 3 units.

The obtained function is :

The question for the 3rd part is, how long will it be to have $14500 in the account.

Substitute A = 14500 and solve for the value of t :

Rounded to 2 decimal places, the value of t will be :

For the next question, the value of t when the amount is doubled :

The answer is 9.90 years

Hey mate!!!!

We know that area =

lxb

Here we should find the factors of 18.

Factors of 18 are

1, 2, 3, 6, 9, 18

Now the sides could be long as 18 itself.

Examples:

1 x b

1) 1 x 18

2) 2 × 9

3) 3 x 6

4) 9× 2

5) 18 x 1

6) 6 x 3

Hope it helps dear friend

The bench costs $375, and the garden table costs $295. Together, they amount to $670, with the table being $80 cheaper than the bench.

Let the cost of the bench be x. Then the cost of the garden table is x-80. The sum of the costs of both items is $670. So we have the equation: x + (x-80) = $670.

Simplifying this, we get 2x - 80 = $670  + 80 2x = $750  x = $375. So the cost of the bench is $375. The garden table costs $375 - $80 = $295. A garden table and a bench cost $670 combined.

The garden table costs $80 less than the bench. To find the cost of the bench, we can use algebraic equations. Let the cost of the bench be x. Then, the cost of the garden table is x - 80.

The sum of both costs is $670. Using this information, we can form an equation: x + (x - 80) = $670. Simplifying, we get 2x - 80 = $670 + 80. Solving for x, we get x = $375.

Therefore, the cost of the bench is $375, and the cost of the garden table is $295.

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The line tangent to the graphs are y = 77 and y = -74/49(x - 2) + [f(2)/g(2)].

Function (1)

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

y = 4x+ 3 and y = 6x - 5

At x = 2, we have

y = 4(2) + 3 and y = 6(2) - 5

So, we have

y = 11 and y = 7

So, we have:

Tangent line: y = 11 * 7

y = 77

Function 2

Here, we have

The derivative of the quotient of two functions:

(d/dx)(f(x)/g(x)) = (g(x) * df/dx - f(x) * dg/dx) / g(x)^2

Substituting the tangent lines for f and g, we get:

(d/dx)(f(x)/g(x)) = (6x - 5 * 4 - (4x + 3) * 6) / (6x - 5)^2

Evaluating at x = 2, we get:

(d/dx)(f(x)/g(x)) = (-16 - 18) / (-3)^2 = -74/49

Hence, the line tangent to the graph of y = f(x)/g(x) at x = 2 is y = -74/49(x - 2) + [f(2)/g(2)].

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Answer:

B. Freedom in Industry

Step-by-step explanation:

The Kyoto Protocol is a commitment between countries to limit the amount of greenhouse gases produced. Nuclear, Sun, Wind, and Tidal energy are all renewable energy sources.

Answer:

0

Step-by-step explanation:

The given expression is :

\(8.29 \times \frac{ - 5.62 + 5.62}{5.62}\)

We can solve the expression as follows :

\(\frac{ - 5.62 + 5.62}{5.62}=\dfrac{0}{5.62}\) (As -5.62+5.62 equals to 0)

Any number multipled to 0 gives 0.

Hence, the value of the given expression is equal to 0.

The correct answer is F. (8,-2). When a triangle is rotated about the line y=-3, the location of the vertex will be shifted downwards.

A triangle is a closed, three-sided geometric shape. It is one of the simplest shapes known to mankind and is widely used in mathematics and architecture. The three sides of a triangle are joined together by three angles, which add up to 180 degrees.

This means that the coordinates of the new triangle A'B'C' will be shifted downwards by 3 units for each vertex. Therefore, the coordinates of C' will be (8,-2).

To understand this, let’s look at the coordinates of the original triangle ABC. The coordinates of A are (2,-2), B is (6,-2) and C is (8,-5). As we can see, the x-coordinate of vertex C is 8 and its y-coordinate is -5. Now, when the triangle is rotated about the line y=-3, the x-coordinate of vertex C will remain the same (i.e. 8) but the y-coordinate will be shifted downwards by 3 units. This means that the coordinates of C' will be (8,-2).

This explains why the correct answer is F. (8,-2). All the other given options (G. (8,-3), H. (8-5), J. (8-8) and K. (8-10)) are incorrect because they do not follow the logic of the rotation.

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Answer:

Interest = Nu 600

Amount = Nu 5600

Step-by-step explanation:

P = Nu 5000

R = 12%

T = 1

\(Interest = \frac{PRT}{100} = \frac{5000 \times 12 \times 1}{100} = Nu \ 600\)

\(Amount = P + Interest = 5000 + 60 0 = Nu \ 5600\)

Answer:

The answer is C

Step-by-step explanation:

The work is shown in the attached images. Each equation is labeled for slope intercept and standard form

y=-1/5x +18/5

5y+x=18

The equation of line passing through point (-2,4) and parallel to x+5y=7 in

standard form is \(x+5y =18\)

slope intercept form is \(y = \frac{-1}{5}x + \frac{18}{5}\)

The equation of line is  a linear equation with degree of one and an algebraic form of representing the set of points, which together form a line in a coordinate system.

\((y-y_{1} ) = m(x-x_{1} )\)

where,

\((x_{1}, y_{1} )\) are the points through which  the line passes

m is the slope of line

(slopes of parallel lines are equals)

According to the given question

we have

Equation of line x+5y=7

a point (-2,4)

slope of the line x+5y = 7 by placing it into slope intercept form:

x+5y = 7

⇒ 5y = -x+7

⇒ y = \(\frac{-x}{5} +\frac{7}{5}\)

the slope of the line, m=\(\frac{-1}{5}\)

here, the point (-2,4) and slope is  m= \(\frac{-1}{5}\)  

therefore the equation of line which is parallel to x+5y =7 and passing through (-2,4) is:

\((y-4)=\frac{-1}{5}(x-(-2))\)

⇒\((y-4) = \frac{-1}{5} (x+2)\)

⇒ \(5(y-4)= -x-2\)

⇒\(5y-20 = -x-2\)

⇒\(x+5y= 20-2\)

⇒ \(x+5y = 18\)

so,

(a). the equation of line in slope intercept form is given by

\(5y= -x+18\)

\(y = \frac{-1}{5}x+\frac{18}{5}\)

(b). the standard form of line is x+5y = 18.

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It's asking  would not be a solution soo

(-10, -9) as you can see

You're welcome thank me later

Answer:

42 squared is 1764

Step-by-step explanation:

Answer: (x + 42)(x - 42)

Step-by-step explanation:

factorise: x^2 - 42^2

. x^2 - 42^2 have ^2 in common (so you can ignore that).

. put in brackets (x - 42)(x + 42)

. +/- any order really doesn't matter :D

The graph of an exponential function shows a geometric increase or decrease using a curve

Exponential functions are inverse of logarithmic functions. The standard exponential function is expressed as:

y = ab^x

where

a is the base

x is the exponent

The graph of an exponential function shows a geometric increase or decrease using a curve. According to the function given there will a decrease rate due to the value of the rate value given which is less than 1. The graph of the function given is attached below;

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Answer:

9-4/5

5/5 = 1

Step-by-step explanation:

Answer:

1

9-4/5 is equal to 5/5 which is equal to 1

Answer:

Lets express this as equations to get a better idea of this situation.

let f represent February, m represent march and so on

60 mangoes in feburary

(60)2=m

m=120

120 mangoes in march

A=120+60+20

a=200

m+f+a=total amount of mangoes

60+120+200=t

380=total

Step-by-step explanation:

The total mangoes harvested by Martin is 380 kilograms.

A word problem in math is a math question written as one sentence or more that requires children to apply their math knowledge to a 'real-life' scenario.

Given that, Martin harvested 60 kilograms of mangoes last February, twice as much in March, and 20 kilograms more in April than the combined harvest in February and March.

We need to find the total harvested mangoes,

Let f represent February, m represent march and April be a

February = 60 mangoes

So, in March,

(60) 2 = m

m = 120

Therefore, 120 mangoes in March

A = 120+60+20

a = 200

Now, the total mangoes = 60+120+200 = 380

Hence the total mangoes harvested by Martin is 380 kilograms.

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Answer: It is C

Step-by-step explanation:

The slop for Kitten A is 1/4 or 4

Kitten B has a slop of 2/6 or 3 so the answer is,

Answer:

9

Step-by-step explanation:

(-2+5)^2

3^2

9

\(~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{a~is~negative}{op ens~\cap}\qquad \stackrel{a~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} h=0\\ k=0\\ \end{cases}\implies y=a(~~x-0~~)^2 + 0\hspace{4em}\textit{we also know that} \begin{cases} x=3\\ y=18 \end{cases} \\\\\\ 18=a(3-0)^2+0\implies 18=9a\implies \cfrac{18}{9}=a\implies 2=a \\\\\\ y=2(~~x-0~~)^2 + 0\implies \boxed{y=2x^2}\)