You spent $24 more than Pam. If you spent $82, how much money did Pam spend?Write and solve an equation.

The value of the derivative at the maximum or minimum for a continuous function must be zero.

So, remember that the derivative at a given value gives the slope of a tangent line to the curve at that point.

Now, also remember that maximums or minimums are points where the behavior of the curve changes (it stops going up and starts going down or things like that).

If you draw the tangent line to these points, you will see that you end with horizontal lines. And the slope of a horizontal line is zero.

So we conclude that the value of the derivative at the maximum or minimum for a continuous function must be zero.

If you want to learn more about maximums and minimums, you can read:

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Answer:

f(x) = 2x3 + 4

Stretch vertically be a factor of 2:

f(x) = 2*2x3 + 4 = 4x3 + 4

Shift 5 units to the left:

f(x) = 4(x+5)3 + 4

[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]

Let's solve ~

[tex]\qquad \sf  \dashrightarrow \: - \frac{ 3}{5} m + 8 = 20[/tex]

[tex]\qquad \sf  \dashrightarrow \: - \frac{ 3}{5} m = 20 - 8[/tex]

[tex]\qquad \sf  \dashrightarrow \: - \frac{ 3}{5} m =12[/tex]

[tex]\qquad \sf  \dashrightarrow \: - \frac{ }{} m =12 \times \frac{5}{3} [/tex]

[tex]\qquad \sf  \dashrightarrow \: - m = 4 \times 5[/tex]

[tex]\qquad \sf  \dashrightarrow \:m = - 20[/tex]

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Answer:

Hope the picture will help you

Solution :-

This triangle is a right angled triangle as we can see ∠POC, has a right angled sign. Now, we will assume the missing angle to be x, thus,

25° + 90° + x = 180° ( Angle sum property of a triangle )

115° + x = 180°

x = 180° - 115°

x = 65°

Thus, the measure of missing angle is 65°.

Hope that helps. :D

Using linear function concepts, it is found that the true statements are as follows:

A linear function is modeled by:

[tex]y = mx + b[/tex]

In which:

In this problem, for psychology, the model for the number of graduated students in t years after 2000 is:

P(t) = 2,376t + 73,219.

For biology, it is given by:

B(t) = 2,414t + 56, 545

Hence, the correct statements are:

More can be learned about linear function concepts at https://brainly.com/question/24808124

Answer:

[tex](-3)[/tex].

Step-by-step explanation:

Over this interval, the change in the value of this function is:

[tex]f(-5) - f(2) = 22 - 1 = 21[/tex].

The corresponding change in the value of [tex]x[/tex]:

[tex](-5) - 2 = -7[/tex].

The average rate of change of function [tex]f[/tex] over this interval is equal to the change in the function value divided by the corresponding change in [tex]x[/tex]:

[tex]\begin{aligned}& (\text{average rate of change}) \\ =\; & \frac{(\text{change in function value})}{(\text{change in $x$})} \\ =\; & \frac{f(-5) - f(2)}{(-5) - 2} \\ =\; & \frac{22 - 1}{-7} \\ =\; & \frac{21}{-7} \\ =\; & -3\end{aligned}[/tex].

Thus, the average rate of change of [tex]f(x) = x^{2} - 3[/tex] over the interval [tex][-5,\, 2][/tex] would be [tex](-3)[/tex].

The only interval with a negative rate of change is the last one:

[1, 2.5]

For an interval (a, b) and a function f(x), the rate of change is defined as:

[tex]r = \frac{f(b) - f(a)}{b - a}[/tex]

So the rate of change is only negative when the function evaluated on the first value of the interval is larger than the function evaluated in the second one.

For example, on the interval [1, 2.5} we can see that:

f(1) = 3

f(2.5) = -1

Then on this interval, the rate of change will be negative, meaning that this is the correct option.

If you want to learn more about rates of change, you can read:

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Answer:

It's D: 1 to 2.5

Step-by-step explanation:

It's D: 1 to 2.5

[tex]\boxed{\bold{x = 2, 3}}[/tex]

Stepwise Solving:

[tex]\rightarrow \sf x^2-5x + 6 = 0[/tex]

[tex]\sf use \ the \ formula : x = \dfrac{ -b \pm \sqrt{b^2 - 4ac}}{2a} \ \ when \ ax^2 + bx + c = 0[/tex]

Identify the coefficients:

Solve for x:

[tex]\dashrightarrow \ \sf x=\dfrac{-\left(-5\right)\pm \sqrt{\left(-5\right)^2-4 \ x \ 1 \ x \ 6}}{2 \ x \ 1}[/tex]

[tex]\dashrightarrow \ \sf x=\dfrac{\left5\right\pm \sqrt{\left25-24}}{2}[/tex]

[tex]\dashrightarrow \ \sf x=\dfrac{\left5\right\pm \sqrt{1}}{2}[/tex]

[tex]\dashrightarrow \ \sf x=\dfrac{\left5\right\pm1}{2}[/tex]

[tex]\dashrightarrow \ \sf x=\dfrac{\left5\right+ 1}{2} \ , \dfrac{\left5\right- 1}{2}[/tex]

[tex]\dashrightarrow \ \sf x=\dfrac{6}{2} \ , \ \dfrac{4}{2}[/tex]

[tex]\dashrightarrow \ \sf x= 3, \ 2[/tex]

Step-by-step explanation:

f(x) = x√(x+8)

When f(x) = 0,

0 = x√(x+8)

x = 0, x + 8 = 0

x = -8

f'(x) = (1)√(x+8) + x • ½(x+8)^(-½) = 0

0 = √(x+8) + 1/[2√(x+8)] (x)

-2(x+8) = x

-2x - 16 = x

x = -16/3

(-8 < -16/3 < 0)

Therefore, x-intercept of f'(x) = 0 is somewhere between the two x-intercepts, ranging from -8 to 0.

Answer:

Step-by-step explanation:

here.

Step-by-step explanation:

Therefore, there are projected to be approximately 1541 computer viruses in the year 2021.

Exponential growth is a pattern of growth where a quantity grows at a constant percentage rate per unit of time. In other words, the rate of growth is proportional to the current value of the quantity. This type of growth is often seen in natural phenomena such as population growth, the spread of diseases, and the growth of financial investments. Exponential growth can be described mathematically by an exponential function of the form y = abˣ, where a is the initial value, b is the growth factor, and x is the time variable.

Here,

To solve this problem, we can use exponential growth formula:

A = P(1 + r)ˣ

where:

A = final amount

P = initial amount

r = growth rate

t = time (in years)

Let's first calculate the number of years from 1995 to 2021:

2021 - 1995 = 26 years

Using the given information, we can plug in the values into the formula:

A = 501(1 + 0.57)²⁶

A = 501(3.08)

A = 1540.68

Rounding to the nearest whole number, we get:

A ≈ 1541

To know more about exponential growth,

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#SPJ1

Answer: Your solution is 34206

Hope this helps you!!!!

Step-by-step explanation:

please mark me as brainlest

Answer: 30 units^2

Step-by-step explanation:

[tex]\mathrm{From \ the \ figure \ we \ know \ this \ is \ a \ right \ triangle. \ The \ area \ of \ the \ triangle}:[/tex]

[tex]A = \frac{1}{2}bh \\= \frac{1}{2} \times 6 \times 10\\= 30 \ units^2[/tex]

(Formula for area of right triangle: Half of the product of two right edges)

Therefore, the area of the triangle is 30 units^2

Mr. Bartley expression of the ticket cost function is an illustration of equations

The true statement is (a) Tickets cost $52 each, and there are 25 students and 2 teachers going n trip

The equation of the total cost is given as:

Total Cost = 52 * (25 + 2)

The above can be rewritten generally as:

Total Cost = Cost per each * (Student + Teachers)

By comparison, we have:

Cost per each = $52

Students = 25

Teachers = 2

Hence, the true statement is (a) Tickets cost $52 each, and there are 25 students and 2 teachers going n trip

Read more about cost functions at:

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Let's recall that, the potential difference between any two points X(x,y,z) and Y(a,b,c) is given by ;

So, here ;

[tex]{:\implies \quad \sf \overrightarrow{E}=3x\hat{i}-2y\hat{j}+5z\hat{k}}[/tex]

So, now our second component of the Integrand will just be ;

[tex]{:\implies \quad \sf \overrightarrow{dr}=dx\hat{i}+dy\hat{j}+dz\hat{k}}[/tex]

So, now the whole integrand will just be ;

[tex]{:\implies \quad \sf \overrightarrow{E}\cdot \overrightarrow{dr}=(3x\hat{i}-2y\hat{j}+5z\hat{k})(dx\hat{i}+dy\hat{j}+dz\hat{k})}[/tex]

[tex]{:\implies \quad \sf \overrightarrow{E}\cdot \overrightarrow{dr}=3xdx-2ydy+5zdz}[/tex]

Now, Let's move to the final answer ;

[tex]{:\implies \quad \displaystyle \sf V_{Y}-V_{X}=-\int_{X}^{Y}3xdx-2ydy+5zdz}[/tex]

As,X is the point (1,3,5) and Y being (3,2,7) , so seperate the integral into three integrals with limits as follows respectively;

[tex]{:\implies \quad \displaystyle \sf V_{Y}-V_{X}=-\bigg(\int_{1}^{3}3xdx-\int_{3}^{2}ydy+\int_{5}^{7}zdz\bigg)}[/tex]

[tex]{:\implies \quad \displaystyle \sf V_{Y}-V_{X}=-\bigg(3\int_{1}^{3}xdx-2\int_{3}^{2}ydy+5\int_{5}^{7}zdz\bigg)}[/tex]

[tex]{:\implies \quad \displaystyle \sf V_{Y}-V_{X}=-\bigg\{3\bigg(\dfrac{x^2}{2}\bigg)\bigg|_{1}^{3}-2\bigg(\dfrac{y^2}{2}\bigg)\bigg|_{3}^{2}+5\bigg(\dfrac{z^2}{2}\bigg)\bigg|_{5}^{7}\bigg\}}[/tex]

[tex]{:\implies \quad \displaystyle \sf V_{Y}-V_{X}=-\bigg\{2\bigg(\dfrac{9}{2}-\dfrac12\bigg)-2\bigg(\dfrac{4}{2}-\dfrac92\bigg)+5\bigg(\dfrac{49}{2}-\dfrac{25}{2}\bigg)\bigg\}}[/tex]

[tex]{:\implies \quad \displaystyle \sf V_{Y}-V_{X}=-\{3(4)-(-5)+5(12)\}}[/tex]

[tex]{:\implies \quad \displaystyle \sf V_{Y}-V_{X}=-\{12+5+60\}}[/tex]

[tex]{:\implies \quad \displaystyle \boxed{\bf{V_{Y}-V_{X}=-77\:\: Volt}}}[/tex]

Hence, this is the required answer

Answer:

y=2x-4

Step-by-step explanation:

y-y1=m(x-x1)

y-(-4)=2(x-0)

y+4=2x-0

y=2x-0-4

y=2x-4

Step-by-step explanation:

If the equation is

[tex] \sqrt{x + 2} [/tex]

Then, here is the answer.

The definition of a derivative is

[tex] \frac{f(x + h) - f(x)}{h} [/tex]

Also note that we want h to be a small, negligible value so we let h be a value that is infinitesimal small.

So we get

[tex] \frac{ \sqrt{x + h + 2} - \sqrt{x + 2} }{h} [/tex]

Multiply both equations by the conjugate.

[tex] \frac{ \sqrt{x + h + 2} - \sqrt{x + 2} }{h} \times \frac{ \sqrt{x + h + 2} + \sqrt{x + 2} }{ \sqrt{x + h + 2} + \sqrt{x + 2} } = \frac{x + h + 2 - (x + 2)}{h \sqrt{x + h + 2} + \sqrt{x + 2} } [/tex]

[tex] \frac{h}{h \sqrt{x + h + 2} + \sqrt{x + 2} } [/tex]

[tex] \frac{1}{ \sqrt{x + h + 2} + \sqrt{x + 2} } [/tex]

Since h is very small, get rid of h.

[tex] \frac{1}{ \sqrt{x + 2} + \sqrt{x + 2} } [/tex]

[tex] \frac{1}{2 \sqrt{x + 2} } [/tex]

So the derivative of

[tex] \frac{d}{dx} ( \sqrt{x + 2} ) = \frac{1}{2 \sqrt{x + 2} } [/tex]

Part 2: If your function is

[tex] \sqrt{x} + 2[/tex]

Then we get

[tex] \frac{ \sqrt{x + h} + 2 - ( \sqrt{x} + 2) }{h} [/tex]

[tex] \frac{ \sqrt{x + h} - \sqrt{x} }{h} [/tex]

[tex] \frac{x + h - x}{h( \sqrt{x + h} + \sqrt{x}) } [/tex]

[tex] \frac{h}{h( \sqrt{x + h} + \sqrt{x} ) } [/tex]

[tex] \frac{1}{ \sqrt{x + h} + \sqrt{x} } [/tex]

[tex] \frac{1}{2 \sqrt{x} } [/tex]

So

[tex] \frac{d}{dx} ( \sqrt{x} + 2) = \frac{1}{2 \sqrt{x} } [/tex]

Answer:

6/5

Step-by-step explanation:

Calculate the volume by multiplying the measured length and width of the space together, then multiply the result by the height of the room. From the example, 10 * 25 feet = 250 square feet, and 5 * 10 feet = 50 square feet.

Answer:

22

Step-by-step explanation:

3x = x+44(base angle of isosceles triangle are equal)

2x = 44

x = 22

Answer:

750 decimeters

Step-by-step explanation:

1 meter is equal to 10 decimeters.

so 75 times 10 equals your answer: 750 decimeters

Hope that helps!

x+x + y * y = 2x + y²

Answer:

[tex]2x + y^{2}[/tex]

Step-by-step explanation:

[tex]\text{If a number is being added to itself, it is basically a number being multiplied by 2. }[/tex]

[tex]\rightarrow x + x[/tex]

[tex]\rightarrow \boxed{\bold{2x}}[/tex]

[tex]\text{If a number is being multiplied by itself, it is basically the number squared.}[/tex]

[tex]\rightarrow y \times y[/tex]

[tex]\rightarrow \boxed{\bold{y^{2}}}[/tex]

Thus, the simplified expression is 2x + y².

Answer:

p(5,4)====P'(-4,5)....

C

ЖStep-by-step explanationЖ

⇒ [tex]7x^2\sqrt{2x^4}\bullet\ 6\sqrt{2x^1^2}[/tex]

[tex]=7\sqrt{2}x^4\bullet 6\sqrt{2}x^6[/tex]

[tex]=84x^1^0[/tex]

[tex]So\ choose\ C[/tex]

[tex]\{square\ root\ \}.[/tex]

I hope this helps you

:)

Answer:

8.33

Step-by-step explanation:

Answer: 8.33 minutes will it take to travel from the sun to the earth. Step-by-step explanation: Distance of the Earth from the Sun = d = 1 km = 1000 m.

Answer: 9.33

Step-by-step explanation: you divide Saturn by earth

Answer:

12

Step-by-step explanation:

x-4=2(x+8)/5

let's do my favorite strategy: distributive property!

x-4=(2x+16)/5

Now we can simplify.

x-4=(2/5)x+16/5

Let's solve for x!

Subtract 2/5 from both sides

3/5)x=36/5

Now multiply both sides by 5/3, the reciprocal.

You would get 12 as x!