I have a calculus question about limit functions. Pic included.

We need to estimate the sum:

In order to do so, we first round each term to the nearest integer. Then we add them.

We have:

Then, we can estimate the sum to be:

Therefore, option C is correct.

Solve the system of equations:

step 1: Substitute the value of 2y-3 for x in equation (2) and solve for y

step 2: Solve for x by substituting 4 for y in equation (1)

Therefore, the solution to the system of equations in ordered pair is

The area of the larger triangle will be equal to 36 square units.

Triangle may be defined as a closed figure of three sides and three interior angles. Scaling of image may be defined as a ratio that can be used to represent the relationship between the shape and size of a figure and the corresponding dimensions of the actual figure or object. Dilation may be defined as the process for creating similar figures by changing the size. A graph can be defined as a pictorial representation or a diagram that represents data or values. According to question the area of smaller triangle is given as 9 square units. After scaling the length of scale copies become double and the area becomes four times. So, the area of bigger triangle is 4×9 = 36.

Learn more about the Scale images here:

brainly.com/question/13194929

#SPJ9

Complete Question:

These two triangles are scaled copies of one another. The area of the smaller triangle is 9 square units. What is the area of the larger triangle? Explain or show how you know.

Answer:

Explanation:

Here, we want to get the amount of money it costs each of the friends to bowl

Let us call this cost x

For the 9, the cost will be:

To rent a bowling shoe, it costs $3, the cost for all will be :

The sum of the bowling cost and the shoe rental cost is a total $162

Mathematically, we have it that:

It costs each of the friends $15 to bowl excluding the shoe rental cost

Answer:84

Step-by-step explanation:

200 - 2x = 32-2x = -168x = 84

Answer:

His age is 84

The function is one-one can be dtermined by using horizontal line test. If horizontal line on the graph of function intersect the function more than once then such function is not one-one. The graph of function is,

Since horizontal lines intersect the curve of function only once so function is one-one.

Determine the inverse of the function.

Interchange x with y and y with x and simplify the obtain equation for x.

Substitute y by x for the inverse of function.

So inverse of the function is -2x/(3x - 2).

So functions f and g are inverse of each other if,

Check the obtained inverse function by composition.

The mass of isotope 239-Pu left after 4000 years is approximately 3.3g

Radioactivity is the phenomenon of the spontaneous disintegration of unstable atomic nuclei to atomic nuclei to form more energetically stable atomic nuclei. Radioactive decay is a highly exoergic, statistically random, first-order process that occurs with a small amount of mass being converted to energy.

In solving the disintegration constant, we can use the half-life formula.

The half-life of a sample is given as;

[tex]T_\frac{1}{2} = \frac{ln2}{\lambda}[/tex]

Substituting the values into the equation;

[tex]T_\frac{1}{2} = \frac{ln2}{\lambda}\\24100 = \frac{ln2}{\lambda} \\\lambda = \frac{ln2}{24100} \\\lambda = 0.00002876years^-^1[/tex]

The formula of radioactivity is given as

[tex]N = N_oe^(^-^\lambda ^t)[/tex]

We can plug in the values and solve.

[tex]N = N_oe^(^-^\lambda ^t)\\N = 3.7e^-^(^0^.^0^0^0^0^2^8^7^6 ^*^4^0^0^0^)\\N = 3.297g\\N = 3.3g[/tex]

The amount left after 4000 years is 3.3g.

Learn more on radioactivity here;

https://brainly.com/question/26626062

#SPJ1

Let there are x pets in the store. So 90% of all pets means that 0.9x.

The equation for the dogs anf total pets in the store is,

Simplify the equation to obtain the value of x.

So there are 60 pets in the pet store.

Given,

The function of the graph is,

Answer:

ramila ate four ninth of orange before lunch and two-ninths of orange after lunch.how much of the orange did she eat at All?

Answer

Event 3, Event 2, Event 4, Event 1.

Explanation

Given data:

Box A has 6 purple pens and 2 blue pens.

Box B has 12 purple pens and 8 blue pens.

Let X represents purple, Y represents blue, and Z represents red.

Box A: n(X) = 6, n(Y) = 2, and n(Z) = 0. Hence, n(S) = 6 + 2 + 0 = 8

Box B: n(X) = 12, n(Y) = 8, and n(Z) = 0. Hence, n(S) = 12 + 8 + 0 = 20

So if a pen is randomly chosen from each box, the probability of:

Event 1: choosing a purple or blue pen from Box B. will be:

Event 2: choosing a blue pen from Box B will be:

Event 3: choosing a red pen from Box A will be:

Event 4: choosing a purple pen from Box A wil be:

If a pen is randomly chosen from each box, the list of the events from least likely to most likely are:

Event 3, Event 2, Event 4, Event 1.

Using it's concept, the average rate of change for each function on the interval [1,5] is given as follows:

The average rate of change of a function is given by the change in the output divided by the change in the input. Hence, over an interval [a,b], the average rate of change is given according to the following rule:

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

For the each function, we have that the numeric values are given as follows:

Hence the rate is given by:

r = (2 - 4)/(5 - 1) = -0.5.

Even though they have different formats, they have the same average rate of change, as the only values mattering to calculate the rate of change are the values at x = 1 and x = 4, which are the same for each graph.

More can be learned about the average rate of change of a function at https://brainly.com/question/13930624

#SPJ1

SOLUTION

The end behavior of a polynomial function is the behavior of the graph of f(x) as x approaches positive infinity or negative infinity. The degree and the leading coefficient of a polynomial function determine the end behavior of the graph.

The first option is the correct answer.

ANSWER

B. Andy did not graph 3 3/4

EXPLANATION

That measure, 3 3/4 in, is not graphed on the plot line.

Shape area of timber measured in millimeters is 10.8 m2.

Given:

Rectangle 1's length is 4000 mm, or 4 meters.

Rectangle 1's width is 1200 mm, or 1.2 meters.

Rectangle 2's length is [6200-1200] mm, or 5 meters.

Rectangle width 2 = 1200 mm = 1.2 m

Area of the form,

Shape's area is equal to the sum of its two rectangles.

Shape area equals [(4)(1.2)] plus [(5)(1.2)].

Shape's area equals 4.8 + 6.

Length area of the shape is 10.8 m2.

Learn more about area at

https://brainly.com/question/22684014

#SPJ9

Answer:

$389,200

$21,200

Since,

We are to find PV when the PMT is $35000. Since the PVA is 11.12,

Hence, Austin would need to deposit $389,200.

For the last part, we first need to solve the PV at 4% in 20 years.

The PVIF would be:

Then, solving for the PV:

Now, to know how much more should Austin deposit, we need to subtract the original PV from the PV that we got from part B.

That would be,

Austin would need to deposit $21,200 more to achieve his withdrawal goal.

To solve the exercise, we can use the following property of logarithms:

Then, we can solve the equation like this:

Therefore, the solution of the equation rounded to two decimal places is -0.01.

The value of

which can be written as:

is

Given that:

- A race car game takes 6 points each time the player hits a cone.

- You must find the integer that represents the change in total points if the player hits 10 cones.

It is important to remember that the Set of Integers contains the negative numbers, the positive numbers, and zero.

Then, by analyzing the data given in the exercise, you can identify two integers that must be multiplied, in order to calculate the total points if the player hits 10 cones. These are:

Since the game takes 6 points from the player each time this hits a cone, the integer that represents the points taken from the player must be negative.

In order to multiply the integers, you need to remember the Sign Rules for Multiplication:

Therefore, you get this result:

Hence, the answer is:

x + y = 150

5x + 8y = 930

y = -x + 150

5x + 8(-x + 150) = 930

5x - 8x + 1200 = 930

-3x = -270

x = 90

90 + y = 150

y = 60

90 boletas para estudiantes y 60 a los invitados vendieron

30,60,90,

Step-by-step explanation:

Answer:

See my photo bro. hope it can help

Norman, this is the solution to the exercise:

According to the information provided, we have:

• Highest interest rate = 8.81%

• Second highest interest rate = 8 4/5 % = 8.8%

• Middle interest rate = 8 1/2 % = 8.5%

• Second lowest interest rate = 8.313%

• Lowest interest rate = 8.3%

Given functions are:

So:

The value of x in part (a) is [-3+√21]/6 and [-3-√21]/6, the value of t in part (b) is (1/5+√11/5) and (1/5-√11/10), the value of t in part (c) is 1/5 and the value of t in part (d) is 1/5-3/5i and 1/5+3/5i.

Part a. Solving for x,

1/x - 1/(x+1) = 3

(1-x+x)/x(x+1) = 3

1/(x²+x) = 3

1 = 3x²+3x

3x²+3x-1=0

Solving the quadratic by using quadratic formula,

x = [-b±√(b²-4ac)]/2a

Here,

a = 3

b = 3

c = -1

Putting all the values,

x= [-3±√(3²-4(3)(-1)]/6

x = [-3±√21]/6

We get,

x = [-3+√21]/6 and

x = [-3-√21]/6

Part b. Solving for t;

2 =√[(1+t)²+(1-2t)²]

Squaring both sides,

4 = (1+t)²+(1-2t)²

4 = 1+t²+2t+1+4t²-4t

2 = 5t²-2t

5t²-2t-2=0

Solving the equation by using quadratic formula,

t= [-b±√(b²-4ac)]/2a

Here,

a = 5

b = -2

c = -2

Putting all the values,

t = [2±√(4-4(5)(-2))]/10

t = [2±√44]/10

We get

t = (1/5+√11/5) and (1/5-√11/10)

Part c. Solving for t;

3/√5 = √[(1 + t)² + (1 − 2t)²]

Squaring both sides,

9/5 = (1+t)²+(1-2t)²

9/5 = 1+t²+2t+1+4t²-4t

9 = 5+5t²+10t+5+20t²-20t

25t²-10t+1=0

t = [-b±√(b²-4ac)]/2a

Here,

a = 25

b = -10

c = 1

Putting all the values,

t = [10±√(100-4(25))]/50

t= [10±0]/50

t= 1/5

Part d. Solving for t;

0 = √[(1 + t)²+(1 − 2t)²]

Squaring both sides,

(1+t)² =-(1-2t)²

1+t²+2t = -(1+4t²-4t)

1+t²+2t = -1-4t²+4t

5t²-2t+2=0

Solving the equation by using quadratic formula,

t = [-b±√(b²-4ac)]/2a

Here,

a = 5

b = -2

c = 2

Putting all the values,

t = [2±√(4-4(5)(-2)]/10

t = [2±√(-36)]/10

t = [2±6√(-1)]/10

√-1 is 'iota' or i.

t = (2±6i)/10

We get,

t = 1/5-3/5i and 1/5+3/5i

To know more about Quadratic formula, visit,

https://brainly.com/question/1214333

#SPJ1

The elements in the first 3 columns are the coefficients of system of equations.

The 4th column are the constants of the system of equations.

This is a system of 3 equations.

Let's write the system using the variables x, y, and z. Shown below:

Let's simplify and write the equations:

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data

7, 7, 3, 2, 7, 16, 12, 16, 12 ​

mode = ?

Step 02:

7, 7, 3, 2, 7, 16, 12, 16, 12 ​

n = 9

2, 3, 7, 7, 7, 12, 12, 16, 16

The mode is the value that appears most frequently in a serie of data.

mode = 7

The answer is:

The mode is 7.

Answer:

There are 45 packets of biscuits

Step-by-step explanation:

Ratio    Actual

5                           Sweets

3                           Biscuits

8           120           Total

Make a proportion:

[tex]\frac{Bicuit}{total}[/tex] = [tex]\frac{biscuits}{total}[/tex]  ratio on the left and actual on the right

[tex]\frac{3}{8}[/tex] = [tex]\frac{x}{120}[/tex]       x equals the unknown actual biscuit count.

8 x 15 =120, so solve for x by multiplying 3 by 15

x = 45

Answer:

15

Step-by-step explanation:

equation=

[tex]5x+3x=120\\equals..\\8x=120\\x= 15[/tex]

There are 15 packets each of both sweets and biscuits.

Check!

[tex]5(15)=75[/tex] sweets

[tex]3(15)=45[/tex] biscuits

[tex]75+45=120[/tex] sweets and biscuits altogether

Hence, there are 15 packets of biscuits.