Use the definition of the derivative to find the derivative of the function with respect to x. Show steps

Step-by-step explanation:

we have the 2 numbers x and (x+2).

x × (x + 2) = 143

x² + 2x = 143

x² + 2x - 143 = 0

the general solution to such a quadratic equation

ax² + bx + c = 0

is

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case this is

x = (-2 ± sqrt(2² - 4×1×-143))/(2×1) =

= (-2 ± sqrt(4 + 572))/2 = (-2 ± sqrt(576))/2 =

= (-2 ± 24)/2 = (-1 ± 12)

x1 = -1 + 12 = 11

x2 = -1 - 12 = -13

so, we have 2 solutions : 11 and 13, -13 and -11

11× 13 = 143

-11×-13 = 143

Answer:

11.67 yards

Explanation:

From the above figure, we can use the Pythagorean theorem to find the width of the pool as shown below;

Step 1

Given;

Step 2

When repeated random samples of a certain size n are taken from a population of values for a categorical variable, the mean of all sample proportions equals the population percentage (p).

Thus;

checking properly, the sample proportion =0.30, because

Answer; Option D

Answer:

$35,708.4

Explanation:

His net income will be the total that he earns less the taxes.

So, we need to calculate how much money does Rob pays for each tax.

Therefore, 6.2% of 4200 is equal to:

It means that Rob pays $260.4 each month for social security,

In the same way, 1.45% of 4200 is equal to:

16% of 4200 is equal to:

5.5% of 4200 is equal to:

Now, we can calculate the net income per month as:

$4200 - $260.4 - $60.9 - $672 - $231 = $2975.7

Finally, his annually net income will be the net income per month multiplied by 12 months:

$2975.7 x 12 = $35,708.4

So, the answer is $35,708.4

Answer:

Step-by-step explanation:

This question can be solved using a rule of three.

For each configuration, we need the perimeter and the amount of bags of mulch.

For a square of side s, the perimeter is P = 4s

If the 10 x 10 garden took 3 1/2 bags of mulch:

10x10 means that s = 10.

So the perimeter is:

P = 4*10 = 40

The number of bags of mulch is:

3 1/2 = 3 + (1/2) = 3 + 0.5 = 3.5

15 x 15 garden

15x15 means that s = 15.

The perimeter is: P = 4*s = 4*15 = 60.

The number of bags is X.

Now applying the rule of three:

With the number of bags and the perimeter.

3.5 bags - 40'

X bags - 60'

Now we apply cross multiplication:

Step 1:

Concept

Number of way of arranging n different objects = n!

Step 2:

Word = NEWFOUNDLAND

N = 3

E = 1

W = 1

F = 1

O = 1

U = 1

D = 2

L = 1

A = 1

Step

Number of ways of arranging the word NEWFOUNDLAND

In the cosine equation

A is the amplitude

B is using it to find the period

C is the phase shift

D is the vertical shift

Since the given function is

A = 1

B = 1

C = 0

D = 2

The amplitude is 1

The answer is 1

Use the slope formula to find the slope of a line that goes through two points:

Substitute the coordinates (6,-10) and (3,-13) into the slope formula:

Therefore, the slope of a line that passes through those points, is 1.

The given question is

Use the identity

Then replace the denominator by sec^2 (x)

Since sec is the reciprocal of cos, then

Replce sec^2(x) by 1/cos^2(x)

Since denominator of denominator will be a numerator

Use the value of tan

Replace tan by sin/cos

Reduce cos(x) up with cos(x) down

Use the identity

Replace 2 sin(x)cos(x) by sin(2x)

The answer is

2 sin(2x)

For this problem we know that y=f(x) at x=0 is 5 units above y=g(x). So then the best solution for this case it seems to be:

And solving for g(x) we got:

From the figure we can obtain 2 equations:

and

first lets simplify both equations:

for the first;

and for the second one:

Now we have that x=15 and we can substitute x for 15 in the first equation to find y:

so the final answe is: x=15 and y=63

To determine if the equation is true we multiply the expression on the right side by the denominator on the left; if the result is the numerator on the left then the equation is true:

Since the result is the numerator on the left side we conclude that the equation is true.

Solution:

Given the expression below

Applying the combination formula below

The binomial coefficient will be

Hence, the answer is 56

Answer:

m = 2 and m = 3

Explanation:

To find the solutions to the inequality, we need to isolate m. So, we can subtract 7 from both sides as:

7 + m < 20

7 + m - 7 < 20 - 7

m < 13

Therefore, any number that is less than 13, is a solution of the inequality.

For example: 2 and 3 are solutions of the inequality.

Given:

Required:

We need to find the points are included in the solution

Explanation:

Recall that the solution of the system of inequalities is the intersection region of all the solutions in the system.

The points G and F lie inside the intersection.

The points in the solution are G and F.

Final answer:

Points F and G.

The value of (f+g)(x) from the given functions is 4x³+x²+5x+2.

The given functions are f(x)=4x²+ 5x - 3 and g(x)=4x³ - 3x² + 5.

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

Now, (f+g)(x)=f(x)+g(x)

= 4x²+ 5x - 3+4x³ - 3x² + 5

= 4x³+4x²- 3x²+5x+5-3

= 4x³+x²+5x+2

Therefore, the value of (f+g)(x) from the given functions is 4x³+x²+5x+2.

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Compound Shape

The shape of the figure attached consists on four triangles and one square.

The base of each triangle is B=12 cm and the height is H=10 cm, thus the area is:

Calculating:

The area of each triangle is 60 square cm.

Now for the square of a side length of L=12.

The area of a square of side length a, is:

Calculate the area of the square:

The total surface area is:

A = 60*4 + 144

A= 240 + 144

A = 384 square cm

A diagram of the situation is shown below:

In order to determine the angle of elevation x, use the sine function, as follow:

sin x = opposite side/hypotenuse

the opposite side is the distance from the ground to the wi

Lets call x to the number of ducks

and y the number of pigs.

Then:

Because there are 2 legs per duck and 4 legs per pig.

If the total of animals is 37, then:

Then:

And replacing on the first equation we get:

There are 12 pigs and therefore 25 ducks.

The two unit vectors orthogonal to both j-k and i+j  are [tex]\frac{i}{\sqrt{3} }- \frac{j}{\sqrt{3} } -\frac{k}{\sqrt{3} }[/tex]

Let a bar = j- k  = < 0,1,-1>

b bar = i+j = <1,1,0>

the cross product a x b bar is orthogonal to both a and b bar

= i ( 0-(-1) ) -j ( 0-(-1) ) + r (0-1)

= i-j-k

A unit vector is a vector whose length is 1 unit

There the unit vector is :

[tex]\frac{i-j-k}{\sqrt{1^2+(-1)^2+(-1)^2} } = \frac{i-j-k}{\sqrt{3} }[/tex]

= [tex]\frac{i}{\sqrt{3} }-\frac{j}{\sqrt{3} }-\frac{k}{\sqrt{3} }[/tex]

The second unit vector orthogonal to both a and b bar would be negative of the previous vector.

= [tex]-\frac{i}{\sqrt{3} }-\frac{j}{\sqrt{3} }-\frac{k}{\sqrt{3} }[/tex]

Hence the two unit vectors orthogonal to both j-k and i+j are  [tex]\frac{i}{\sqrt{3} }- \frac{j}{\sqrt{3} } -\frac{k}{\sqrt{3} }[/tex]

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Given the ordered pairs:

(-12, -16), (-3, -4), (0, 0), (9, 12)

Let's say that the first coordinate corresponds to x, and the second one corresponds to y. Then, the constant of variation k relates x and y as:

Using the ordered pairs:

We conclude that the constant of variation is:

In this problem

we have an exponential growth function

where

a=2500 ----> initial value of the number of referrals at the start of the model

b=1.50 ---> the base of the exponential function (growth factor of the number of referrals each year

therefore

The answer Part 1 is the last option

Part 2

Find out the annual percent increase

we know that

b=1+r

b=1.50

1.50=1+r

r=1.50-1

r=0.50

therefore

r=50%

ANSWER:

$104.37

STEP-BY-STEP EXPLANATION:

To calculate the total profit, we must add the amount he earned each day, multiplying the salary by the number of hours, like this:

Therefore, he earned in the last three days a total of $104.37

Given that a box is 12 inches long 8 inches wide and 2 inches high, the area of wrapping paper needed to wrap the gift box​ is equal to the total surface area of the box.

The total surface area of the box can be calculated using the formula;

Tenemos una foto de 4 x 6 pulgadas.

Tenemos un marco con borde de ancho constante, lo que significa que alrededor de la foto siempre tenemos un "espesor" constante, que llamaremos "e".

También sabemos que el area total del marco es 80 pulgadas cuadradas.

Podemos dibujar esto así:

El marco tiene un ancho total de 4+2e y un largo de 6+2e.

Entonces, podemos calcular el espesor "e" a partir de calcular el area del marco e igualarlo a 80 pulgadas cuadradas. El area del marco sera igual al ancho por el largo:

Debemos aplicar la ecuación cuadrática para calcular e:

e=-7 no es una solución válida, ya que el espesor debe ser positivo.

Entonces, la solución es e=2.

Respuesta: el ancho del borde es 2 pulgadas.

The area of the circle can be calculated with the following formula

First let's find the radius

The answer would be 200.96 square yards

Answer:

The vertical shift is of 2 units up

Step-by-step explanation:

We have a function in the following format:

F(x) = a(x+b) + c

The vertical shift is given by c.

If c > 0, the shift is up.

If c < 0, the shift is down.

In this question:

F(x) = 9|x+1| + 2

So c = 2

The vertical shift is of 2 units up

We have the following equation:

We want to rewrite it in a way 'C' is a function of 'r'. We can accomplish that, if we divide both sides by 2pi.

From this, we have our result.

the given series is 4 -16 64 -256

that is

4 x -4 = -16 = -4^2

-16 x -4 = 64 = 4^3

64 x -4 = -256 = -4^4

so we can say that is every time the number is multiplied with -4,

for a7, as 7 is an odd number so the negative sign will be there from the above observations

-4^7 = -16384

the recursive rule will be'

The sand box is rectangular with

Wide= 5feet

Length= 7feet

He wants to fill the box with a depth of 2 feet