The cost of producing x units of a certain commodity is C(x) = 1000 +5.70x + .7x^2
What is the instantaneous rate of change of C with respect to x when x =
100?

Answer:

x= 14.1

y= 19.4

(to the nearest tenth)

Step-by-step explanation:

Please see attached picture for full solution.

Answer:

[tex]\frac{13}{3}[/tex] ÷ [tex](-\frac{5}{6})[/tex]

Step-by-step explanation:

[tex]4\frac{1}{3}/(-\frac{5}{6})=\\\\\frac{13}{3}/(-\frac{5}{6})[/tex]

Answer:

53 sweets.

Step-by-step explanation:

The mean out of 10 bags of sweets is 42. That means that all the numbers of sweets added up would be 420.

39 + 40(2) + 41(5) + 43 + x = 420

39 + 80 + 205 + 43 + x = 420

367 + x = 420

x = 53.

So, in the 10th bag, there are 53 sweets and a sugar high for whoever eats that many sweets.

Hope this helps!

Answer:

X=53 sweets

Step-by-step explanation:

Answer & Step-by-step explanation:

For this problem, we will be using the tangent trig ratio because we are dealing with the opposite side and the adjacent side of the triangle. Although cosine may be a good ratio to use as well, it is not the best ratio to use because if you were to use the cosine ratio, you will have more steps to complete in order to solve the problem. Plus, we are not dealing with the hypotenuse side of the triangle. Therefore, it is best to use the tangent ratio because it is more efficient and it corresponds to the side lengths we are using.

On the next page, we are given a Venn Diagram. We are asked to tell the difference between finding the angle and finding the side. Then, we are asked to find the similarity between them.

When solving for the unknown side, you have to flip the equation because one of the sides will be known as a variable.

When solving for the unknown angle, you have to use the inverse of the trig ratio that you are using for that problem.

The similarity between the two is that they will always use one of the trig ratios.

Answer:

Step-by-step explanation:

One solution would be (1, -4), and the other would be (4, -7).

The ordered pairs which are the solutions of the system of equations shown in the graph below are (1,-4) and (4,-7).

The ordered pair is the pair of two numbers which represented in a manner that it provides a particular order.

In a order pair the first term indicates the x-coordinate, while the second term indicate the y-coordinates. The ordered pair are written in close bracket in the following way.

[tex](x,y)[/tex]

System of equation-

In the given graph, one linear line and one parabola is shown. In this graph the parabola intersect with the line at point (1,-4) and (4,-7).

Thus, the ordered pairs which are the solutions of the system of equations shown in the graph below are (1,-4) and (4,-7).

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Answer:

Step-by-step explanation:

Given,

Radius ( r ) = 1 m

Height (h) = 10 m

Surface area of cylinder= ?

Now,

Surface area of cylinder :

[tex]2\pi \: {r}^{2} + 2\pi \: r \: h[/tex]

[tex] = 2\pi \: r \: (r + h)[/tex]

[tex] = 2\pi \: \times 1(1 + 10)[/tex]

[tex] = 2\pi \: \times 1 \: \times 11[/tex]

[tex] = 22\pi[/tex]

[tex] = 22 \: \times 3.14[/tex]

[tex] = 69.08 \: {m}^{2} [/tex]

Hope this helps...

Good luck on your assignment..

Answer:

B. 30 in

Step-by-step explanation:

The circumference is pi d.

30 pi = pi d

30 pi / pi = d

30 = d

Answer:

x< 2 2/3

Step-by-step explanation:

5/8 X -1/3 < 1 1/3

Add 1/3 to each side

5/8 X -1/3+1/3 < 1 1/3+1/3

5/8x < 1 2/3

Change to an improper fraction

5/8 x < 5/3

Multiply each side by 8/5 to isolate x

8/5 * 5/8x  < 5/3 * 8/5

x < 8/3

Changing back to a mixed number

x< 2 2/3

Answer:

Step-by-step explanation:

an equation perpendicular to the equation given will have a slope of -1, because a perpendicular slope is opposite and reciprical. if it goes through the point 4,-1 and has a slope of -1, the y intercept has to be 3. y = -x + 3

parallel lines have to have the same slope of 3.

Answer:

The answer is A oon EDG

Step-by-step explanation:

Answer:

mRP = 125°

mQS = 125°

mPQR = 235°

mRPQ = 305°

Step-by-step explanation:

Given that

Then:

Given that

Then:

Given that

Then:

Given that

Then:

mQOS + mROP + mQOR + mSOP = 360°

250° + 2mQOR = 360°

mQOR = (360°- 250°)/2

mQOR = mSOP = 55°

And (QOR and SOP are central angles):

Finally:

measure of arc PQR, mPQR = mQOR + mSOP + mQOS = 55° + 55° + 125° = 235°

measure of arc RPQ, mRPQ = mROP + mSOP + mQOS = 125° + 55° + 125° = 305°

Answers:

minor arc RP = 125 degrees

minor arc QS = 125 degrees

============================================================

Explanation

Definition: A minor arc is a piece of a circle such that it is smaller than a semi-circle with the same radius. In other words, it's measure is always less than 180 degrees.

Based on this definition, a minor arc is where we take the shortest path between any two points on a circle. For minor arc RP, we start at R then go to the right and take the shortest path to P. We do not go left when we start at R because that's the longer path and it is the major arc.

Minor arc RP is subtended by central angle ROP = 120 degrees. This central angle is equal to the arc measure in question. This isn't really a theorem, but more a definition if anything.

Central angle QOS is equal to angle ROP through the vertical angles theorem. Any pair of vertical angles are always congruent. Since QOS is 125 degrees, so is minor arc QS.

Answer:

Arc RP is 125, Arc QS is 125, Arc QR is 55, and arc SP is 55

Step-by-step explanation:

We know Arc QS is 125 degrees because angle QOS is a vertical angle with Angle ROS, so Arc QS is 125, and ARC RP is 125. We can figure out the other two arcs using the knowledge that ARC QR is equal to arc PS because angle QOR an SOP are vertical angles and all the degrees have to add up to 360. From this we get 2x + 125 + 125 = 360. From here we simplify and get 2x + 250 = 360; 2x = 110; x = 55, so arc QR and ARC SP are both 55.

Hope this helps :)

Answer:

The answer is -6p +1/7.

hope it helps...

Hope this helps!

Stay safe and have a great day :D

The properties of exponents, which mathematical operation changes 2 1/3 to 2 is 2^(1/3) * 2^(2/3) = 2

The steps are as follow:

a^m * a^n = a^(m + n)

2^1 = 2^(1/3) * 2^n

2^1 = 2^(1/3)+n

1 = (1/3) + n

n = 2/3

So the properties of exponents, which mathematical operation changes 2 1/3 to 2 is 2^(1/3) * 2^(2/3) = 2

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Graph of function is attached below.

Option D is correct.

To understand more, check below explanation.

We have to draw the graph of function,

                    [tex]f(x)=\left \{ {x, {x < 1} \atop {1, x\geq 1}} \right.[/tex]

The graph of above function is attached below,

For domain [tex]x > 1, f(x)=x[/tex]

For domain, [tex]x\geq 1, f(x)=1[/tex]

After observing attached graph, option D is correct.

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The function is plotted and is attached , Option D is the correct graph similar to one in the image.

It is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (dependent).

It is given in the question that

f(x) =

x if x <1

1 if x>_ 1

The graph of above function is attached below,

For domain x > 1, f(x)=x

For domain, x≥ 1, f(x)=1

When we see the graph that have been plotted on the basis of domain, Option D is the correct graph similar to one in the image attached.

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Answer:

A

Step-by-step explanation:

Let me know If you want me to explain it.

Answer:

A. h = V/(pi * r^2)

Step-by-step explanation:

V = pi r^2 h

Divide both sides by pi r^2.

V/(pi r^2) = h

The h variable is isolated now.

Answer:

x=1

x=-5

Step-by-step explanation:

we know that

The solution of the system of equations is the intersection point both graphs

In this problem there are two intersection points

so

The system has two solutions

we have

one solution is the point (-4.9, 5.4) and the other (0.92, -0.42)

see the attached figure

therefore

x=1

x=-5

Step-by-step explanation:

Answer:

The answer is D.

Step-by-step explanation:

Answer:

f(1) = -11

f(n) = f(n-1) +3  n=2,3,4,5

Step-by-step explanation:

-11,-8,-5,-2,1,....

We are adding 3 each time

-11 +3 = -8

-8+3 = -5

f(1) = -11

Take the previous term and add 3

f(n) = f(n-1) +3  n=2,3,4,5

Answer :

Answer:

Step-by-step explanation:

I = PRT

P = 1000

R = 2.5% or 0.025

T = 4

I = (1000)(.025)(4)

I=100

1000+100=1100

but the answer choices???

Answer:

25

Step-by-step explanation:

u stink

Explanation:

Focus on one point, such as A = (1,2). Note how it moves to point A ' = (-1, -2). Both x and y coordinates have been flipped from positive to negative. The rule therefore is [tex](x,y) \to (-x,-y)[/tex]. This describes a 180 degree rotation (either clockwise or counterclockwise, it doesn't matter). Points B and C follow the same idea.

Side note: Lines AA', BB' and CC' all go through the origin (0,0).

Answer:

[tex] \boxed{ \sf Rose's \ height = 1.5 \ m \ \ \ OR \ \ \ 150 \ cm} [/tex]

Given:

Cole's height = 1.7 m

Rose's height = 20 centimetres shorter than Cole

To Find:

Rose's height

Step-by-step explanation:

[tex]\sf 1 \ m = 100 \ cm \\ \\ \sf So, \\ \sf 1.7 \ m = 1.7 \times 100 \ cm \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 170 \ cm[/tex]

[tex]\therefore \ \sf Cole's \ height = 170 \ cm \\ \\ \sf \implies Rose's \ height = Cole's \ height - 20 \\ \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 170 - 20 \\ \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 150 \: cm[/tex]

[tex]\sf 1 \ cm = \frac{1}{100} \ m \\ \\ \sf So, \\ \sf 150 \ cm = 150 \times \frac{1}{100} \ m \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf = \frac{150}{100} \:m \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf = 1.5 \: m[/tex]

[tex]\therefore \ \sf Rose's \ height = 1.5 \ m[/tex]

Using algebra, Rose's height in centimeters is calculated as: 150 centimeters.

Let's use algebra to find Rose's height in centimeters based on the given information.

Let's assume Rose's height in centimeters is represented by "R".

We know that Cole is 1.7 meters tall, which is equivalent to 170 centimeters.

According to the given information, Rose is 20 centimeters shorter than Cole. So, we can set up the equation:

R = 170 - 20

Simplifying the equation:

R = 150

Therefore, Rose's height in centimeters is 150 centimeters.

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Answer:

its wht u r searching for...

Answer:

Solution,

Principal=$1200

Rate=3%=3/100=0.03

Interest=$108

Time=?

Now,

[tex]t = \frac{i}{p \times r} [/tex]

[tex] = \frac{108}{1200 \times 0.03} \\ = \frac{108}{36} \\ = 3 \: years[/tex]

Hope this helps...

Good luck on your assignment..

Answer: A

Slope = -6

Step-by-step explanation:

Given that the column of the table are:

Column X (-2,-1,0,1,2) and

Column Y (8,2,-4,-10,-16) 

Since the table represent a linear function, the equation of the function will obey the general linear equation

Y = MX + C

Where M = slope

M = ( Y2 - Y1 ) / ( X2 - X1 )

Let Y1 = 8, Y2 = 2 and X1 = -2 and X2 = -1

Substitutes all the parameters into the formula

M = ( 2 - 8 )/( -1 - - 2 )

M = ( 2 - 8 ) / ( -1 + 2 )

M = -6/1

M = -6

Therefore, the slope of the function is -6

Answer:

40°

Step-by-step explanation:

The triangle is a right triangle, so one measure of one of the angles is 90 degrees.

One acute angle measures 50 degrees.

Angles in a triangle add up to 180 degrees.

180 - 90 - 50

⇒ 40

The measure of the other acute angle is 40 degrees.

Acute angles measure less than 90 degrees. 40 degrees is less than 90 degrees, so it is an acute angle.

The measure of the other acute angle is 40°.

Given that, in a right triangle, one acute angle measures 50°.

A right angled triangle is a triangle with one of the angles as 90 degrees. A 90-degree angle is called a right angle, and hence the triangle with a right angle is called a right triangle.

Let the measure of other acute angle be x.

Using angle sum property of a triangle, we get

90°+50°+x=180°

⇒ x=180-140

⇒ x=40°

Therefore, the measure of the other acute angle is 40°.

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Answer:

second option

Step-by-step explanation:

Under a rotation about the origin of 90°

a point (x, y ) → (- y, x )

The solution is, :A triangle is rotated 90° about the origin, then, (x, y) - (y, -x), this rule describes the transformation.

A transformation is a dramatic change in form or appearance. An important event like getting your driver's license, going to college, or getting married can cause a transformation in your life. A transformation is an extreme, radical change.

here, we have,

Rotation is a process in which the orientation of a given figure is changed by turning it about a point called origin.  The rotation can be done either clock-wisely or counterclockwise about the origin.

If the given triangle is rotated 90° clockwise, the rule that describe the transformation is; (x, y) - (y, -x)

If the given triangle is rotated 90° counterclockwise, the rule that describe the transformation is; (x, y) - (-y, x)

In the given question, the required rule is; (x, y) - (y, -x). This shows a clockwise rotation of 90° about the origin.

Hence, The solution is, :A triangle is rotated 90° about the origin, then, (x, y) - (y, -x), this rule describes the transformation.

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Answer:

- Inverse Variation

- Equation: [tex]XY = 12[/tex]

Step-by-step explanation:

Given

X-> 2 | 4 | 8 | 12

Y-> 6 | 3 | 3/2 | 1

Required

- State the type of variation the table represents

- Determine the equation to model the data

To check for type of variation; we'll make use of trial by error method.

To start with; We'll check for direct variation.

This is done using the following expression;

[tex]Y = kX[/tex]where k is the constant of variation

Make k the subject of formula

[tex]k = \frac{Y}{X}[/tex]

When Y = 6, X= 2

[tex]K = \frac{6}{2} = 3[/tex]

When Y = 3, X = 4

[tex]K = \frac{3}{4}[/tex]

There's no need to check further as both values of k are not equal

To check for inverse variation;

[tex]Y = \frac{k}{X}[/tex]

Make k the subject of formula

[tex]k = YX[/tex]

When Y = 6, X= 2

[tex]K = 6 * 2 = 12[/tex]

When Y = 3, X = 4

[tex]K = 3 * 4 = 12[/tex]

When Y = 3/2; X = 8

[tex]K = \frac{3}{2} * 8 = \frac{24}{2} = 12[/tex]

When Y = 1, X = 12

[tex]K = !2 * 1 = 12[/tex]

Note that for all values of X and Y, K remains constant;

Hence, the table represents an inverse direction

To determine the equation;

We make use of  [tex]k = YX[/tex]

Substitute 12 for k

So, the equation becomes

[tex]12 = XY[/tex]

Reorder

[tex]XY = 12[/tex]

Hence, the equation is [tex]XY = 12[/tex]