What is the ANWSER to the question ? Thank you

What Is The ANWSER To The Question ? Thank You

Answers

Answer 1
Each salary pattern can be described with an expression that looks like:

starting salary + (annual increase) x (number of years)

Company A:  [tex]24000+3000n[/tex]
Company B:  [tex]30000+2400n[/tex]

You want to know when those two expressions will be equal.

[tex]2400+3000n=30000+2400n \\ 24000+600n=30000 \\ 600n=6000 \\ n=10[/tex]

The salaries from Company A and Company B will be equal after 10 years.

Related Questions

A graph is shown below:

A graph is shown. The values on the x axis are 0, 3, 6, 9, 12, and 15. The values on the y axis are 0, 9, 18, 27, 36, and 45. Points are shown on ordered pairs 0, 36 and 3, 27 and 6, 18 and 9, 9 and 12, 0. These points are connected by a line

What is the equation of the line in slope-intercept form?

y = 36x − 3
y = −3x + 36
y = −3x + 12
y = −12x + 3

Answers

Answer:

Yeah its B

(y = -3x = 36)

Step-by-step explanation:

The equation of the line in slope-intercept form is y = −3x + 36.

What is slope- intercept form?

The equation of a straight line in the form y = mx + b where m is the slope of the line and b is its y-intercept.

Given:

x axis are 0, 3, 6, 9, 12, and 15.

y axis are 0, 9, 18, 27, 36, and 45.

slope= 27-36/ 3-0= -3

Slope intercept form

y - y1 = m(x- x1)

y- 36 = -3 ( x- 0)

y - 36 = -3x

y + 3x = 36

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The volume of a cube is 27n^27 cubic units. What is the length of one side of the cube?

A. 3n^3
B. 3n^9
C. 27n^3
D. 27n^9

Answers

The answer is B.
(3n^9)^3=27n^27
[tex]V=a^3\\\\ a^3=27n^{27}\\\\ a^3=3^3 \cdot n^{9\cdot 3}\\\\ a^3=3^3 \cdot (n^9)^3\\\\ a^3=(3n^9)^3\\\\ a=3n^3[/tex]

Answer B

John needs to make a scale drawing of his school building for art class. If the building is 256.25 meters long, and John scales it down using a ratio of 25 meters to 1 inch, how long will the building be in the sketch?

Answers

If the ratio is already determined to be 25 meters, this makes the problem.

We would do 256.25/25 = 10.25

The building will be 10.25 inches long in the sketch.

Answer:

10.25 inches

Step-by-step explanation:

John needs to make a scale drawing of his school building for art class.

The building is 256.25 meters long.

John scales it down using a ratio of 25 meters to 1 inch.

Therefore, 256.25 meters = [tex]\frac{256.25}{25}[/tex] = 10.25 inches

The sketch of the building would be 10.25 inches long.

a right triangle has a base that measures 39 inches and a height that measures 80 inches what is the length of the hypotense

Answers

A right triangle has three sides: the two sides that share a vertex are known as the legs, and the other side is known as the hypotenuse.  The legs are known as a and b, while the hypotenuse is c.
The Pythagorean Theorem states the a^2 + b^2 = c^2.  If we plug the numbers into this equation, we will find the length of the hypotenuse.
39^2 + 80^2 = c^2
1521 + 6400 = c^2
7921 = c^2
We have c squared now, but we want to know how much c is equal to.  The square root of c^2 will be our answer.
89 = c
The length of the hypotenuse of a right triangle with legs that measure 39 and 80 inches is 89 inches.


American car makers produce 5,650,000 cars each year. In a report, Ben wrote that Americans made 6,550,000 cars. What mistake did Ben make? How can he fix it? Find the error.

Answers

Ben wrote the number for the hundred thousands place in the millions place

Write words to match expression 3+(4x12)

Answers

3+(4x12)'s word expression could be:

Jeffy bought 4 rows and 12 columns of soup cans in a package. The cook, Chef PeePee gave him 3 more soup cans. How many soup cans does Jeffy have now. if u want de answer it is 51

The character names are from SML

Please help. This is summer homework that's due in 2 days!

Answers

Split the surface area into geometric shapes as shown in the figure below.

Top part
The area of one triangle is
A₁ = (1/2)*(10 cm)*(4 cm) = 20 cm²
There are 3 of these triangles.

Vertical sides..
The area of one vertical side is
A₂ = (10 cm)*(6 cm) = 60 cm²
There 3 of them.

Bottom part
The triangle is equilateral with each side  = 10 cm, and each angle = 60 deg.
The area is (from the Law of Sines)  equal to
A₃ = (1/2)(10 cm)*(10 cm)*sin(60) = 43.3 cm²

The total surface area is
3A₁ + 3A₂ + A₃
= 3*20 + 3*60 + 4.3
= 283.3 cm²

Answer: The surface area is  283.3 cm²

Boundary Peak in Nevada is 13,000 feet high. Guadalupe Peak in Texas is 8,749.75 feet high. How much higher than Guadalupe Peak is Boundary Peak? Round your answer to match the less precise measurement.

Answers

4250.25
this is the correct answer all you need to do is round it. Hope this helps!

Answer:

The Boundary peak is 48.58% higher than Guadalupe peak.

Step-by-step explanation:

Givens:

Boundary Peak is 13,000 ft high.Guadalupe Peak is 8,749.75 high.

To know how much higher is Boundary Peak than Guadalupe peak, we only need to subtract:

Boundary Peak - Guadalupe peak = 13,000 - 8,749.75 = 4250.25 m.

However, the best way to represent this is to express it in percentage. To do that, we need to use the rule of three. If 100% is 8749.75, what percentage would be 13000:

[tex]13000m\frac{100\%}{8749.75m}=148.58 \%[/tex]

Therefore, the Boundary peak is 48.58% higher than Guadalupe peak.

1). The $70 selling price of a bicycle is the cost increased by 4 times the cost. Find the cost?
2). Three pounds less than twice mikes weight is 215 pounds. What is his weight?
3). If mr Washingtons saving were increased by 5 times his savings. He would then save $36,000. How much has he saved ?


PLEASE SHOW YOUR WORK !!!!

Answers

70 = x + 4x
70 = 5x
70/5 = x
14 = x <== the cost
=================
2m - 3 = 215
2m = 215 + 3
2m = 218
m = 218/2
m = 109 <== Mike's weight
==================
x + 5x = 36,000
6x = 36,000
x = 36,000/6
x = 6000 <== what he saved

1.  The cost of the bicycle is $14.

2. Mike's weight is 109 pounds.

3. Mr. Washington has saved $6,000.

Let's solve each problem step by step:

1. The $70 selling price of a bicycle is the cost increased by 4 times the cost.

Let's assume the cost of the bicycle is C dollars.

According to the given information, the selling price of the bicycle is $70, and it is equal to the cost increased by 4 times the cost:

70 = C + 4C

Combine like terms:

70 = 5C

Now, divide both sides by 5 to solve for C:

C = 70 / 5

C = 14

So, the cost of the bicycle is $14.

2. Three pounds less than twice Mike's weight is 215 pounds.

Let's assume Mike's weight is W pounds.

According to the given information, three pounds less than twice Mike's weight is 215 pounds:

2W - 3 = 215

Add 3 to both sides to isolate 2W:

2W = 215 + 3

2W = 218

Now, divide both sides by 2 to solve for W:

W = 218 / 2

W = 109

So, Mike's weight is 109 pounds.

3. If Mr. Washington's savings were increased by 5 times his savings, he would then save $36,000.

Let's assume Mr. Washington's initial savings is S dollars.

According to the given information, if his savings were increased by 5 times, he would save $36,000:

S + 5S = 36000

Combine like terms:

6S = 36000

Now, divide both sides by 6 to solve for S:

S = 36000 / 6

S = 6000

So, Mr. Washington has saved $6,000.

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What is the area of a trapezoid that has bases of 1 1/4 feet and 14 inches and a height of 3 inches? 43.5 in. 2 87 in. 2 22.9 in. 2 3.6 in. 2

Answers

The area of a trapezoid is the average of the bases times the height, mathematically:

A=h(b1+b2)/2, in this case:

A=3(1.25ft(12in/ft)+14)/2

A=3(29)/2

A=43.5 in^2


Answer:

13.5 in^2 is the answer

Step-by-step explanation:

The price of an item has been reduced by 85%. The original price was $77.

Answers

Multiply the original price by the decimal form of the percent and subtract that from the original price.
77*0.85=65.45
77-65.45=11.55
Answer: New price is $11.55
Made percent in a decimal form - 0.85 then multiply 0.85 and 77
.85*77= 65.45
Then 77.00 subtract by 65.45
77.00-65.45= 11.55

4a to the fourth power -2b to the second power +40 when a =2 and b =7

Answers

Hi!

Let's set up the equation.

[tex]4^{a} - 2^{b} + 40 [/tex]

Put in the values...

[tex]4^{2} - 2^{7} + 40 [/tex]

Now solve using PEMDAS

Exponents
[tex]16 - 128 + 40 [/tex]

Subtract
[tex]-112 + 40 [/tex]

Add
[tex]-72[/tex]

The answer is -72

Hope this helps! :)
4a to the fourth power -2b to the second power +40 means that
4a^4-2b^2+40 when a=2 and b=7, so
4a^4-2b^2+40
Substitute a with 2 and b with 7
4(2)^4-2(7)^2+40
=4(16)-2(49)+40
=64-98+40
=-34+40
=6. As a result, the correct answer is 6. Hope it help!

An Internet, telephone,and cable TV package plan costs 85$ each month. The Internet part of the bill is $20. The telephone part bill is $12

Answers

cable is 53 dollas ,20 plus 12 equals 32, 85 minus 32  equals 53 

About 400,000 people visited an art museum in December. What could be the exact number of people who visited the art museum?

Answers

The exact number of people who visited the art museum is; C) 352,483

How to approximate numbers?

We are told that about 400,000 people visited an art museum in December.

Now, the given statement makes it clear that the 400000 people is an approximate value. This means that it has been rounded up to the nearest 100000.

Now among the options, the only that when rounded up to the nearest hundred thousand will give 400000 will be Option C which is 353,483.

Read more about Approximation of numbers at; https://brainly.com/question/1689499

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Complete question is;

About 400,000 people visited an art museum in December. What could be the exact number of people who visited the art museum?

A) 478,051

B) 452,223

C) 352,483

D) 348,998

The relationship between the base and rate a plumber charges and his hourly fee is modeled by the linear function f (x) = 25x + 100 where x is the number of hours he works. What is the total bill if the plumber works for 6 hours ?

Answers

f(6)=25(6)+100
f(6)=150+100
f(6)=250
Final answer: $250

Identify the equation that translates y=ln(x) five units down.
A) y= ln(x-5)
B) y=ln(x)+5
C) y=ln(x+5)
D) y=ln(x)-5

Answers

The equation that translates (y = ln(x)) five units down is (y = ln(x) - 5) and this can be determined by using the transformation.

Given :

Logarithmic equation  --  (y = lnx)

The following steps can be used in order to identify the equation that translates (y = ln(x)) five units down:

Step 1 - The graph of the logarithmic function (y = ln(x)) intersect x-axis at (x = 1).

Step 2 - According to the given data, the graph of (y = ln(x)) is translated down by five units. So, to translate the given function five units down subtract the given function y by 5 unis.

Step 3 - So, the resulting logarithmic equation after transformation is given by:

y = ln(x) - 5

Therefore, the correct option is D).

For more information, refer to the link given below:

https://brainly.com/question/17267403

hope this helps you out >_>



PLZ Help
The tables show the cost of different numbers of t-shirts ordered at two different stores, Store A and Store B:

Store A

Number
of T-shirts Cost (in $)
2 $6
4 $12
8 $24


Store B

Number
of T-shirts Cost (in $)
3 $12
6 $24
9 $36


Which of these explains which store has a better buy?

Store A, because the ratio of the number to the cost is 3:1 in Store A and 4:1 in Store B

Store B, because the ratio of the number to the cost is 2:8 in Store A and 3:15 in Store B

Store B, because the ratio of the number to the cost is 8:2 in Store A and 15:3 in Store B

Store A, because the ratio of the number to the cost is 1:3 in Store A and 1:4 in Store B

Answers

Store A, because the ratio of the number to the cost is 1:3 in Store A and 1:4 in Store B

Answer:

The last one.

Step-by-step explanation:

I tried it and got it right. Bye. If it helped please let me know. Also if u need anymore help try reaching out to me.

I need help with this math problem _:5=72:30
i need to fill in the blank

Answers

30/5 = 6

72/6 = 12

your blank is 12

12:5 = 72:30

hope this helps

how to do this problem -9=x-14

Answers

Hello there!

To solve for this problem, you need to solve for x. To do that, you must isolate the variable (x) on one side of the equation.

We have the following equation:
-9 = x - 14

To isolate x, we need to get rid of -14.
So, to get rid of -14, we need to cancel it out by implementing a number of equal but opposite value. The opposite of -14 and is of equal value is 14.
Add 14 to both sides.

-9 + 14 = 5
-14 + 14 = 0

We are now left with the following solution:
x = 5

I hope this helps!

Earth is approximately 9.3 × 107 miles from the sun. Saturn is approximately 8.87 × 108 miles from the sun. About how much farther is Saturn from the sun than Earth is?

Answers

Both distances are in the scientific notation:
Earth - Sun = 9.3 * 10^7 miles
Saturn - Sun = 8.87 * 10^8 miles
8.87 * 10^8 - 9.3 * 10^7 =
= 88.7 *10^7 - 9.3 * 10^7 =
= 79.4 * 10^7 = 7.94 * 10 ^8 = 794,000,000 miles
Answer: Saturn is  7.94 * 10^8 miles farther from Sun than Earth is.

Answer:

B. 7.94 * 10^8 miles

Step-by-step explanation:

is the correct answer

Which of the following is not a Pythagorean triple? A. 28,45,53 B. 16,63,65 C. 13,84,85 D. 11,61,62

Answers

the answer would be D. hope this helps
The answer would be choice D because if you follow the steps of the Pythagorean theorem then you would get this.
A)28^2 + 45^2 = 53^2
784 + 2025 = 28092809 = 2809
B)16^2 + 63^2 = 65^2265 + 3969 = 42254225 = 4225
C)13^2 + 84^2 = 85^2169 + 7056 = 72257225 = 7225
D) (Your Answer!!!)11^2 + 61^2 = 62^2121 + 3721 = 38443842 does not equal 3842
I hope that helped!

mMelissa is making clothes for her dolls. She has 7/8 yard of fabric. Each doll shirt requires 2/7 of a yard of fabric. How many shirts can she make for her dolls?

Answers

need to divide 7/8 by 2/7

7/8 / 2/7 = 7/8 x 7/2 =49/16 = 3 1/16

she will be able to make 3 shirts

A line has a slope of 3/5. It passes through (3,5) and (x,9). What is the value of x?

Answers

Final answer:

The value of x for the line with a slope of 3/5 that passes through (3,5) and (x,9) is 9 2/3 or 9.67 when expressed as a decimal.

Explanation:

To find the value of x for the point (x, 9) on a line with a slope of 3/5, we can use the slope formula which is (change in y) / (change in x) = slope. We know two points on this line, (3, 5) and (x, 9).

First, calculate the change in y which is 9 - 5 = 4. Then, use the slope of 3/5 and set it equal to the change in y (which is 4) over the change in x (which is x - 3):

3/5 = 4 / (x - 3)

To find x, we cross-multiply:

3 x (x - 3) = 5 x 4

3x - 9 = 20

Add 9 to both sides: 3x = 29

Divide both sides by 3: x = 29/3

Therefore, x = 9 2/3 or 9.67 when expressed as a decimal.

This calculation shows the x-coordinate for the point where the line passes through y-coordinate 9.

Two pounds of peaches cost $4.20. How much will five pounds cost?

Answers

Set up multiplication of ratios so that they cancel out units that you do not need in your final answer...

5lb($4.20/2lb)=$10.50
2 pounds of peaches cost $4.20
5 pounds of peaches cost $??

5 x 4.20 / 2 = 10.5

answer

five pounds will cost  $10.50

100 AAA batteries were tested on a particular MP3 player. Suppose the battery has a mean lifetime of 31.7 hours, with a standard deviation of 2.9 hours. How long do we expect the majority of batteries to last?A. Between 2.9 and 31.7 hours
B. Between 28.8 and 31.7 hours
C. Between 31.7 and 34.6 hours
D. Between 28.8 and 34.6 hours

Answers

31.7 -2.9 = 28.8

31.7 + 2.9 = 34.6

 between 28.8 & 34.6 hours

D is the correct answer

Simplify (5ab^4c)(-abc^2)

Answers

That's the answer I'm sure

This is the answer that u seek

-5a^2b^5c^3

A regular octagon has side lengths of 11 centimeters. Determine the perimeter of the octagon. 66 cm 77 cm 88 cm 99 cm

Answers

an octagon has 8 sides

 the perimeter would be 8 x length of side

8x11 = 88 cm

Answer:

8*11 = 88 cm

Step-by-step explanation:

simple

Tentukan hasil dari (tanpa menghitung satu persatu)
a. 1+3+5+7+9+.....+99
b. 1-2+3-4+5-6+7-8+.....-100
c. -100-99-98-..........-2-1-0+1+2+.....+48+49+50

Answers

a . 1 + 3 + 5 + 7 + 9 + ... + 99 = 2500

b. 1 - 2 + 3 - 4 + 5 - 6 + 7 - 8 + ... - 100 = -50

c. -100 - 99 - 98 - .... -2 - 1 - 0 + 1 + 2 + ... + 48 + 49 + 50 = -3775

Further explanation

Let us learn about Arithmetic Progression.

Arithmetic Progression is a sequence of numbers in which each of adjacent numbers have a constant difference.

[tex]\large {\boxed {T_n = a + (n-1)d } }[/tex]

[tex]\large {\boxed {S_n = \frac{1}{2}n ( 2a + (n-1)d ) } }[/tex]

Tn = n-th term of the sequence

Sn = sum of the first n numbers of the sequence

a = the initial term of the sequence

d = common difference between adjacent numbers

Let us now tackle the problem!

Question a :

1 + 3 + 5 + 7 + 9 + ... + 99

initial term = a = 1

common difference = d = ( 3 - 1 ) = 2

Firstly , we will find how many numbers ( n ) in this series.

[tex]T_n = a + (n-1)d[/tex]

[tex]99 = 1 + (n-1)2[/tex]

[tex]99-1 = (n-1)2[/tex]

[tex]98 = (n-1)2[/tex]

[tex]\frac{98}{2} = (n-1)[/tex]

[tex]49 = (n-1)[/tex]

[tex]n = 50[/tex]

At last , we could find the sum of the numbers in the series using the above formula.

[tex]S_n = \frac{1}{2}n ( 2a + (n-1)d )[/tex]

[tex]S_{50} = \frac{1}{2}(50) ( 2 \times 1 + (50-1) \times 2 )[/tex]

[tex]S_{50} = 25 ( 2 + 49 \times 2 )[/tex]

[tex]S_{50} = 25 ( 2 + 98 )[/tex]

[tex]S_{50} = 25 ( 100 )[/tex]

[tex]\large { \boxed { S_{50} = 2500 } }[/tex]

Question b :

In this question let us find the series of even numbers first ,  such as :

2 + 4 + 6 + 8 + ... + 100

initial term = a = 2

common difference = d = ( 4 - 2 ) = 2

Firstly , we will find how many numbers ( n ) in this series.

[tex]T_n = a + (n-1)d[/tex]

[tex]100 = 2 + (n-1)2[/tex]

[tex]100-2 = (n-1)2[/tex]

[tex]98 = (n-1)2[/tex]

[tex]\frac{98}{2} = (n-1)[/tex]

[tex]49 = (n-1)[/tex]

[tex]n = 50[/tex]

We could find the sum of the numbers in the series using the above formula.

[tex]S_n = \frac{1}{2}n ( 2a + (n-1)d )[/tex]

[tex]S_{50} = \frac{1}{2}(50) ( 2 \times 2 + (50-1) \times 2 )[/tex]

[tex]S_{50} = 25 ( 4 + 49 \times 2 )[/tex]

[tex]S_{50} = 25 ( 4 + 98 )[/tex]

[tex]S_{50} = 25 ( 102 )[/tex]

[tex]\large { \boxed { S_{50} = 2550 } }[/tex]

At last , we could find the result of the series.

1 - 2 + 3 - 4 + 5 - 6 + 7 - 8 + ... - 100

= ( 1 + 3 + 5 + 7 + ... + 99 ) - ( 2 + 4 + 6 + 8 + ... + 100 )

= 2500 - 2550

= -50

1 - 2 + 3 - 4 + 5 - 6 + 7 - 8 + ... - 100 = -50

Question c :

-100 - 99 - 98 - .... -2 - 1 - 0 + 1 + 2 + ... + 48 + 49 + 50

initial term = a = -100

common difference = d = ( -99 - (-100) ) = 1

Firstly , we will find how many numbers ( n ) in this series.

[tex]T_n = a + (n-1)d[/tex]

[tex]50 = -100 + (n-1)1[/tex]

[tex]50+100 = (n-1)[/tex]

[tex]150 = (n-1)[/tex]

[tex]n = 151[/tex]

We could find the sum of the numbers in the series using the above formula.

[tex]S_n = \frac{1}{2}n ( 2a + (n-1)d )[/tex]

[tex]S_{151} = \frac{1}{2}(151) ( 2 \times (-100) + (151-1) \times 1 )[/tex]

[tex]S_{151} = 75.5 ( -200 + 150 )[/tex]

[tex]S_{151} = 75.5 ( -50 )[/tex]

[tex]\large { \boxed { S_{151} = -3775 } }[/tex]

Learn moreGeometric Series : https://brainly.com/question/4520950Arithmetic Progression : https://brainly.com/question/2966265Geometric Sequence : https://brainly.com/question/2166405

Answer details

Grade: Middle School

Subject: Mathematics

Chapter: Arithmetic and Geometric Series

Keywords: Arithmetic , Geometric , Series , Sequence , Difference , Term

The sum of the series are:

Part(a): [tex]\fbox{\begin\\\ \math S=2500\\\end{minispace}}[/tex]

Part(b): [tex]\fbox{\begin\\\ \math S=-50\\\end{minispace}}[/tex]

Part(c): [tex]\fbox{\begin\\\ \math S=-3775\\\end{minispace}}[/tex]

Further explanation:

A series is defined as a sum of different numbers in which each term is obtained from a specific rule or pattern.

In this question we need to determine the sum of the series given in the part (a), part (b) and part (c).

Part(a):

The series given in part (a) is as follows:

[tex]1+3+5+7+9+...+99[/tex]

All the terms in the given series are odd numbers.

From the given series in part(a) it is observed that the series is an arithmetic series with the common difference of [tex]2[/tex].

An arithmetic series is a series in which each successive member of the series differs from its previous term by a constant quantity.

From the above series it is observed that the first term is [tex]1[/tex], second term is [tex]3[/tex], third term is [tex]5[/tex], fourth term is [tex]7[/tex], fifth term is [tex]9[/tex] and the last term is [tex]99[/tex].

The nth term in a arithmetic series is given as follows:

[tex]a_{n}=a+(n-1)d[/tex]           (1)

In the above equation a represents the first term, [tex]n[/tex] represents the total terms and [tex]d[/tex] represents the common difference.

Substitute [tex]99[/tex] for [tex]a_{n}[/tex], [tex]1[/tex] for [tex]a[/tex] and [tex]2[/tex] for [tex]d[/tex] in equation (1).

[tex]\begin{aligned}99&=1+2(n-1)\\2(n-1)&=98\\n-1&=49\\n&=50\end{aligned}[/tex]

Therefore, total number of terms in the series is [tex]50[/tex]. This implies that [tex]a_{50}=99[/tex].

The sum of an arithmetic series is calculated as follows:

[tex]S_{n}=\dfrac{n}{2}(a+a_{n})[/tex]          (2)

Substitute [tex]50[/tex] for [tex]n[/tex] in equation (2).

[tex]\begin{aligned}S_{50}&=\dfrac{50}{2}(a+a_{50})\\&=25\times (1+99)\\&=25\times 100\\&=2500\end{aligned}[/tex]

Therefore, the sum of the series for part(a) is [tex]\bf 2500[/tex].

Part(b):

The series given in part (b) is as follows:

[tex]1-2+3-4+5-6+7-8+….-100[/tex]

Express the given series as follows:

[tex]S=(1+3+5+7+...+99)-(2+4+6+8+...+100)\\S=S^{'}-S^{''}[/tex]

The series [tex]S^{'}[/tex] is as follows:

[tex]S^{'}=1+3+5+7+...+99[/tex]

It is observed that the above series [tex]S^{'}[/tex] is exactly same as the series given in the part(a) and the sum of the series of part(a) as calculated above is [tex]2500[/tex].

Therefore, sum of the series [tex]S^{'}[/tex] is [tex]2500[/tex] i.e., [tex]S^{'}=2500[/tex].

The series [tex]S^{"}[/tex] is as follows:

[tex]S^{"}=2+4+6+8+...+100[/tex]

From the above series it is observed that the series [tex]S^{"}[/tex] is an arithmetic series as the difference between each consecutive member is [tex]2[/tex] and the last term is [tex]100[/tex].

Substitute [tex]2[/tex] for [tex]a[/tex], [tex]2[/tex] for [tex]d[/tex] and [tex]100[/tex] for [tex]a_{n}[/tex] in equation (1).

[tex]\begin{aligned}100&=2+(n-1)2\\(n-1)2&=98\\n-1&=49\\n&=50\end{aligned}[/tex]

This implies that [tex]a_{50}=100[/tex].

To calculate the sum of  substitute [tex]50[/tex] for [tex]n[/tex] in equation (2).

[tex]\begin{aligned}S_{50}&=\dfrac{50}{2}(a+a_{50})\\&=(25)(2+102})\\ &=25\times 102\\&=2550\end{aligned}[/tex]

Therefore, sum of the series [tex]S^{"}[/tex] is [tex]2550[/tex].

Substitute [tex]2550[/tex] for [tex]S^{"}[/tex] and [tex]2500[/tex] for  in equation (3).

[tex]\begin{aligned}S&=S^{'}+S^{"}\\&=2500-2550\\&=-50\end{aligned}[/tex]

Therefore, the sum of the series for part(b) is [tex]\bf -50[/tex].

Part(c):

The series given in part(c) is as follows:

[tex]-100-99-9-...-2-1-0+1+2+...+48+49+50[/tex]

From the above series it is observed that it is an arithmetic series with common difference as [tex]1[/tex], first term as [tex]-100[/tex] and the last term as [tex]50[/tex].

Substitute [tex]-100[/tex] for [tex]a[/tex], [tex]1[/tex] for [tex]d[/tex] and [tex]50[/tex] for [tex]a_{n}[/tex] in equation (1).

[tex]\begin{aligned}50&=-100+(n-1)1\\n-1&=150\\n&=151\end{aligned}[/tex]

Substitute [tex]151[/tex] for [tex]n[/tex] in equation (2).

[tex]\begin{aligned}S_{151}&=\dfrac{151}{2}(a+a_{151})\\&=\dfrac{151}{2}(-100+50)\\&=-25\times 151\\&=-3775\end{aligned}[/tex]

Therefore, the sum of the series for part(c) is [tex]\bf -3775[/tex].

Learn more:

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Answer details:

Grade: High school

Subject: Mathematics

Chapter: Series

Keywords: Series, sequence, arithmetic sequence, arithmetic series, 1+3+5+7+9+….+99, 1-2+3-4+5-6+7-8+….-100, -100-99-98-….-2-1-0+1+2+…..+48+49+50, sum of series, first term, common difference.

A map of square piece of property is drawn at a scale of 1 : 500. If a side of the property on the map is 16 cm, what is the property's actual area?

Answers

can I get dimensions?

Answer:

[tex]\text{Actual area of property}}=6400\text{ m}^2[/tex]

Step-by-step explanation:

Let x represent the actual side of square property.

We have been given that a map of square piece of property is drawn at a scale of 1 : 500.

We will use proportions to solve for our given problem.

[tex]\frac{\text{Actual length}}{\text{Map length}}=\frac{500}{1}[/tex]

[tex]\frac{x}{16\text{ cm}}=\frac{500}{1}[/tex]

[tex]\frac{x}{16\text{ cm}}*16\text{ cm}=500*16\text{ cm}}[/tex]

[tex]x=8000\text{ cm}[/tex]

[tex]x=80\text{ m}[/tex]

We know that area of a square is square of its side length.

[tex]\text{Actual area of property}}=(80\text{ m})^2[/tex]

[tex]\text{Actual area of property}}=6400\text{ m}^2[/tex]

Therefore, the actual area of property is 6400 square meters.

How to factor a polynomial when the leading coefficient isn't 1

Answers

You cant... The leading coefficient has to be a whole number, bigger than one

Final answer:

To factor a polynomial with a leading coefficient that isn't 1, use the ac method or factoring by grouping, identify common factors, and check your work by expanding the factors.

Explanation:

When factoring a polynomial with a leading coefficient that isn't 1, you should consider each term, and factor out any common factors first. If the polynomial is a quadratic, for instance, with a leading coefficient greater than 1, you can use techniques such as the ac method or factoring by grouping. The ac method involves finding two numbers which multiply to give you the product of the leading coefficient and the constant term, and add up to the middle term's coefficient. Once you have these numbers, you can rewrite the middle term and then factor by grouping.

Step-by-Step Explanation

Identify the leading coefficient, the constant term, and the middle term's coefficient.Find two numbers that multiply to the product of the leading coefficient and the constant term, and add to the middle term's coefficient.Rewrite the middle term using the two numbers found in step 2, splitting it into two terms.Factor by grouping, which involves pairing off the terms in such a way that they have a common factor, and then factoring out the greatest common factor from each pair.If you have factored correctly, you should be able to factor out an additional term from the resulting expression, resulting in a factored polynomial.Simplify further if possible, and check your answer by expanding the factors to ensure you get the original polynomial.
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