The function f(x)=2×5x can be used to represent the curve through the points (1,10), (2,50) , and (3,250) what is the multplicative rate of change of the function?

(0, 5), (1, 1 ), ( - 1, 9 )

to test the points substitute the x-coordinate into the equation and if the value is equal to the y- coordinate then it is an ordered pair

(0, 5 ) → y = 0 + 5 = 5 ← ordered pair

(1, 1 ) → y = - 4 + 5 = 1 ← ordered pair

(- 1, 9 ) → y = 4 + 5 = 9 ← ordered pair

( - 1, - 1 ) → y = 4 + 5 = 9 ← not an ordered pair

( - 1, - 9 ) → y = 4 + 5 = 9 ← not an ordered pair

(1, - 1 ) → y = - 4 + 5 = 1 ← not an ordered pair

(- 1, 1 ) → y = 4 + 5 = 9 ← not an ordered pair

Answer:

Can you attach a picture of the diagram?

Step-by-step explanation:

Answer:

9.42 Square Units

How:

You need to use the sector area formula.

Sector Area = Measure of Arc / 360° × π r²

So then you just plug in the numbers:

Sector Area = 45° / 360° × π 5²

Sector Area = 1/8 × 25π

Sector Area = 9.817477

Sector Area = 45° / 360° × π 7²

Sector Area = 1/8 × 49π

Sector Area = 19.242255

Then all you have to do is subtract them both to find the area.

19.242255 - 9.817477 = 9.42 Square Units

I Hope this helped!

Answer:

It's 3.14x10^1

Step-by-step explanation:

(x + 7)² = 20

subtract 34 from both sides

x² + 14x = - 29

add (half the coefficient of the x- term )² to both sides

x² + 2(7)x + 49 = - 29 + 49

(x + 7)² = 20

You need to know the 30-60-90 triangles rules for lengths. (b, b√3, 2b)

the given side length of corresponds to the 30° angle.  So, b = 8

side y corresponds to the 60° angle so it is b√3. Since we determined that b = 8, then b√3 is 8√3.

side x corresponds to the 90° angle so it is 2b.  Since we determined that b = 8, then 2b = 2(8) = 16

Answer: x = 16, y = 8√3

(28 mph) x (5,280 ft/mi) / (60 min/hr) / (60 sec/min) = 41 feet per second

Solution is attached below

Here in the given equation, 3x + 8 the term 8 represents the weight of the empty bucket.

Its given that the number of marbles is x, and the weight of each marble is same which is 3. So, total weight of marbles is 3x.

Now, if 3x + 8 is the weight of the bucket and marbles, then 8 represents the weight of the empty bucket.

90

divide 45 cookies by 15 to obtain cookies per student then multiply this amount by 30 to obtain cookies for 30 students

15 students → 45 cookies

30 students → 45 × [tex]\frac{30}{15}[/tex] = 90 cookies

[tex]x^2 + 10x + 24 = 0\\\\x^2+2x+12x+24=0\\\\x(x+2)+12(x+2)=0\\\\(x+12)(x+2)=0\\\\x=-12 \vee x=-2\Rightarrow \text{A}[/tex]

How to get answer:

[tex]\mathrm{Group\:like\:terms}\\4x+8=2x+2x+7-20\\\mathrm{Add\:similar\:elements:}\:2x+2x=4x\\4x+8=4x+7-20\\\mathrm{Add/Subtract\:the\:numbers:}\:7-20=-13\\4x+8=4x-13\\\mathrm{Subtract\:}8\mathrm{\:from\:both\:sides}\\4x+8-8=4x-13-8\\\mathrm{Simplify}\\4x=4x-21\\\mathrm{Subtract\:}4x\mathrm{\:from\:both\:sides}\\4x-4x=4x-21-4x\\Simplify\\0=-21\\The\:sides\:are\:not\:equal\\[/tex]

Steps:

4x + 8 = 2x + 7 + 2x - 20

Group like terms:

4x + 8 = 2x + 2x + 7 - 20

Add similar elements: 2x + 2x = 4x

4x + 8 =4x + 7 - 20

Add/Subtract the numbers: 7 - 20 = -13

4x + 8 = 4x - 13

Subtract 8 from both sides

4x + 8 - 8 = 4x - 13 - 8

Simplify:

4x = 4x - 21

Subtract 4x from both sides:

4x - 4x = 4x - 21 - 4x

Simplify

0 = -21

Hope this helps! :) and Happy Halloween! ~Zane

Subtract the cost from the revenue:

(-0.32x^2+270x) - (70x+52)

270x - 70x = 200x

The answer would be -0.32x^2 + 200x + - 52

Answer:

P(x) = -0.32x² + 200x + (-52)

Step-by-step explanation:

A company sells lab equipment. Daily revenue and costs are modeled by the function as given in the question.

Revenue:             R(x) = -0.32x² + 270x

Cost :                   C(x) = 70x + 52

Here x = Number of units sold.

Now we have to determine the function P(x) for daily profit.

Since Profit = Revenue - Cost

            P(x) = R(x) - C(x)

            P(x) = (-0.32x² + 270x) - (70x + 52)

                   = -0.32x² + 270x - 70x - 52

            P(x) = -0.32x² + 200x - 52

Therefore, answer will be P(x) = -0.32x² + 200x + (-52)

Answer:

[tex]x^{2}-16x+64[/tex]

Step-by-step explanation:

To solve this problem you must apply the proccedure shown below:

1. You have the following perfect square trinomial given in the problem:

[tex]x^{2}-16+[/tex]

2. To fill the missing term, you must divide the coefficient -16 by 2 and then you must square it, as following:

[tex](\frac{-16}{2})^{2}=(-8)^{2}=64[/tex]

Answer:

24 spark plugs

Step-by-step explanation:

To find smallest quantity that could accommodate every order we will find LCM of 4,6 and 8.

Multiples of 4 are: 4,8,12,16,20, 24,28,..

Multiples of 6 are: 6,12,18,24,30,36,42,..

Multiples of 8 are: 8,16,24,32,40,..    

We can see that LCM of 4, 6 and 8 is 24. Therefore, order of 24 spark plugs will accommodate every order.

Parabola A: directrix is at x = -1 and focus is at (2,2) so the vertex is the midpoint between those.  Vertex = (0.5, 2)

Parabola B: directrix is at x = 5 and focus is at (2,2) so the vertex is the midpoint between those.  Vertex = (3.5, 2)

Distance between Vertex A and Vertex B is the distance between (0.5, 2) and (3.5, 2) = 3

Answer: B

*(The Answer)*= [tex]y = \frac{2}{3} x-2[/tex]

*(Equation)*= The equation for slope-intercept form is [tex]y=mx+b[/tex]

*(Additional Information)*=                                                                                                   m = slope, and b = y-intercept

Hope this helps

Person who answered: BangtanBoyScouts

Answer:  The correct option is

(C) [tex]y=\dfrac{2}{3}x-2.[/tex]

Step-by-step explanation:  We are given to select the equation of a line in slope-intercept form with slope [tex]\dfrac{2}{3}[/tex] and y-intercept at (0, -2).

We know that

the slope-intercept form of the equation of a line with slope m and y -intercept at the point (0, c) is given by

[tex]y=mx+c.[/tex]

For the given line, we have

[tex]\textup{slope, }m=\dfrac{2}{3},\\\\\\\textup{y-intercept},~(0,c)=(0,-2)\\\\\Rightarrow c=-2.[/tex]

Therefore, the equation of the line in slope-intercept form is

[tex]y=mx+c\\\\\Rightarrow y=\dfrac{2}{3}x+(-2)\\\\\\\Rightarrow y=\dfrac{2}{3}x-2.[/tex]

Thus, the required equation of the line in slope-intercept form is [tex]y=\dfrac{2}{3}x-2.[/tex]

Option (C) is CORRECT.

Final answer:

To find the dimensions of the field with a perimeter of 600 feet where the length is three times the width, solve the equation derived from the perimeter formula. The width comes out to be 75 feet and the length 225 feet.

Explanation:

The question is about finding the dimensions of a rectangular field that is three times as long as it is wide, with a total perimeter of 600 feet. First, let's denote the width of the field as W and the length as 3W since the length is three times the width. The formula for the perimeter of a rectangle is 2(length + width), which in this case is 2(3W + W) = 8W. Given that the perimeter is 600 feet, we can set up the equation 8W = 600. Solving this for W gives us W = 75 feet. Therefore, the length, being three times the width, is 225 feet.

So, the dimensions of the field are 75 feet in width and 225 feet in length.

Answer:

The statement is true.

Step-by-step explanation:

Given the statement we have to tell the statement is true or false.

The statement is

"The circumcenter of a triangle is the center of the only circle that can be circumscribed about it"

The circumcenter of triangle is the point in the triangle where the perpendicular bisectors of sides intersect.

The center of the circumscribed circle is the the point where the perpendicular bisectors of the sides meet.

Hence,

The circumcenter is also center of the triangle's circumcircle - the circle that pass through all three of the triangle's vertices.

Therefore, the given statement is true.

Answer:

True

Step-by-step explanation:

Circumcircle: A circle drawn outside a circle is called circumcircle and its center is called circum-center.

Circum-center of triangle:It is the point where the perpendicular bisectors of a  triangle intersect.

The circumcenter of triangle is also the center of triangle's circumcircle.

The circumcenter is equidistant from each vertex of the triangle.

The circumcenter of right triangle falls on the side opposite the right triangle.

Hence, the circumcenter of a triangle is the center of the only circle that can be circumscribed about it.

Answer :True

65X60/45=260/3km/hr=86.66km/hr

Answer:

1. You divide by 3 then multiply by 1 and multiply by 3 again

2. Slope of -3

3. Slope of 0

Step-by-step explanation:

Hello!

Given the function, [tex]f(x) = 2(\frac{1}{2})^{x}[/tex], notice that the function f(x) is an exponential function.

All exponential functions have a horizontal asymptote at y = 0, and this means that the graph never goes over the line y = 0. Therefore, the range is less than zero, but never equal to zero.

Also, this means that the domain of the function f(x) is all real numbers because as we substitute positive x-values into the function, the graph goes closer to zero, but never across zero. But, if we substitute negative x-values into the equation, it goes to infinity.

Therefore, the answer is choice C. The domain of f(x) is all real numbers, and the range is y > 0.

We want to find the domain and range of the given equation.

We will see that the correct option is C:

Domain: all real numbers;

Range: y > 0

First, we need to define what these are.

For a given function y = f(x), the domain is the set of all the possible x-values we can input on the function, and the range is the set of the possible outcomes.

We have the exponential equation:

f(x) = 2*(1/2)^x

To get the domain we start by assuming that the domain is the set of all real numbers, and then we see if the equation has a problem for a given value of x, then we remove that from the domain.

But here we have x on the exponent, so there are no value of x that causes problems, thus the domain is the set of all real numbers.

To get the range we can look at the graph, we can see that the range goes from near 0 to infinity, so we can say that:

range = y > 0.

(note that the function tends asymptotically to zero, meaning that it never becomes equal to zero).

Then the correct option is C:

Domain: all real numbers;

Range: y > 0

If you want to learn more, you can read:

https://brainly.com/question/21853810

Answer:

the answer is no

Step-by-step explanation:

8²+12²≠16²

Joseph made no error.

The answer is F) no error

Answer:

Option: F is the correct answer.

F) No error.

Step-by-step explanation:

We are given the steps that Joseph used while solving as:

Step 1: 85 – 30 = 55

Step 2: 80 – 55 = 25

Step 3: 140 – 80 = 60

Step 4: 60 – 30 = 30

Step 5: 25 + 30 = 55

Clearly the steps involves simple addition as well as subtraction of the mathematical numbers.

Hence all his steps are correct as he has not committed any wrong operation.He evaluated the expressions in the right manner.

          Hence, the answer is:

                    Option: F

Hello there!

[tex]1-f=\frac{9}{10}[/tex]

Explanation:

↓↓↓↓↓↓↓↓↓↓↓↓↓

First you had to subtract by 1 from both sides of the equation.

[tex]1-f-1=\frac{9}{10}-1[/tex]

Simplify

[tex]-f=-\frac{1}{10}[/tex]

Then you divide by -1 from both sides of the equation.

[tex]\frac{-f}{-1}=-\frac{1}{10}/-1[/tex]

Simplify it should the correct answer.

[tex]f=\frac{1}{10}[/tex]

Answer⇒⇒⇒f=1/10

Hope this helps!

Thank you for posting your question at here on Brainly.

Have a great day!

-Charlie

[tex]14-4y\geq38\qquad|\text{subtract 14 from both sides}\\\\-4y\geq24\qquad|\text{change the signs}\\\\4y\leq-24\qquad|\text{divide both sides by 4}\\\\y\leq-6\\\\Answer:\ \boxed{d.\ y\leq-6}[/tex]