A rectangle has a length 10 more than its width. If the width is increased by 8 and the length by 4, the resulting rectangle has an area of 135 square units.
Part A Write an equation to model the above scenario. Use the model to find the length of the original rectangle?
Part B What is the perimeter of the expanded rectangle?

Answer: [tex]5x^3 - x^2 + 5x+2[/tex]

Step-by-step explanation:

[tex](f+g)(x)=(3x^2 + 5x-2)+(5x^3 - 4x^2 +4)=3x^2 + 5x-2+5x^3 - 4x^2 +4=\boxed{5x^3 - x^2 + 5x+2}[/tex]

The expressions for the number of measles are y = a(1.05)^x and y = a(1.1)^x

Let the initial number of measles in 2000 be represented as:

Initial = a

The rate of increase is given as:

Rate, r = 5.3%

The number of measles in x years after 2000 is represented as:

y = a * (1 +r)^x

Substitute r = 5.3%

y = a * (1 + 5.3%)^x

So, we have:

y = a * (1 + 0.053)^x

Evaluate the sum

y = a * (1.053)^x

To express to the nearest hundredth, we approximate to 2 decimal places

y = a(1.05)^x

To express to the nearest tenth, we approximate to 1 decimal place

y = a(1.1)^x

Hence, the expressions for the number of measles are y = a * (1.05)^x and y = a * (1.1)^x

Read more about exponential functions at:

https://brainly.com/question/2456547

#SPJ1

Answer:

Step-by-step explanation:

The ratio of the number of fiction books is 9:4

 the difference between the number of fiction and nonfictionn is 245

so if the number of fiction books = 9x

then the number of nonfiction books = 4x

then difference = 9x-4x = 5x

the difference is given 245

then 5x= 245

x=[tex]\frac{245}{5}[/tex]=49

number of fiction books =49×9=441

number of nonfiction books =49×4=196

https://brainly.com/question/27979540?answering=true&answeringSource=feedPublic%2FhomePage%2F12

#SPJ2

The depth of the sea bed is 5104 fathom and 1.986 league

The bottom of an ocean , the ocean floor is called Seabed .

It is given that

The depth of a certain part of the Earth's seabed is 36,024 feet

The depth in fathom is given by =  depth in feet / 6

The depth in fathom is = 36024 / 6

= 5104 fathom

1 league = 6046.1 * 3 feet = 18138.1 feet

The depth in League (marine) = Depth in feet / 18138.1

The depth in League (marine) = 36024/18138.1

= 1.986 league

Therefore the depth of the sea bed is 5104 fathom and 1.986 league.

To know more about Seabed

https://brainly.com/question/27133203

#SPJ1

Answer:

The cardinality Of Set A= 8, Set B = 5

Step1: Integers greater than or equal to -9 and less than or equal to -2 are

      =   -9,-8,-7,-6,-5,-4,-3,-2

Step 2: Form a set using given elements, we have

Set A = {-9,-8,-7,-6,-5,-4,-3,-2}

Step 3: Count the no. of elements

we have, no. of elements is 8.

For given Set B = {-30, -27, 20, 24, 28}

we have, no. of elements is 5.

Learn more about sets and cardinality: https://brainly.com/question/17023310

#SPJ10

Answer:

11

Step-by-step explanation:

i don't know

Answer:

Step-by-step explanation:

Jakub wants to build a new shed.

The area of the shed is 37 m².

The width of the shed is 5 m.

What is the length of the shed?

to find the side, having the area, you need to use the inverse formula Area = W * L

so

L = A: W

L = 37 : 5 = 7.4 m

If the area of the shed is 37 m²,width of the shed is 5 m as a result the length of the shed will be 7.4 m.

It is defined as two-dimensional geometry in which the angle between the adjacent sides is 90 degrees. It is a type of quadrilateral. The area occupied by the rectangle in two-dimensional planner geometry.

The area of a rectangle can be calculated using the following formula:

Rectangle area = length x width

It is given that, the area of the shed is 37 m². The width of the shed is 5 m.

Since the shed is rectangular. The length of width is found as,

Area = length × width

A = l × w

l=A/w

l=37/5

l=7.4 m

Thus, if the area of the shed is 37 m², the width of the shed is 5 m as a result the length of the shed will be 7.4 m.

Learn more about the rectangle here:

https://brainly.com/question/15019502

#SPJ2

The answer is J. [tex](x+4)(x-2)=x\cdot x[/tex]

The regression lines 3x+2y=26 and 6x+y=31 are linear regressions

The mean values are 4 and 7 and the correlation coefficient between x and y is 0.25

The standard deviation of x is 2/13

The mean value and the correlation

We have the equations to be:

3x+2y=26 and 6x+y=31

Make y the subject in the second equation

y = 31 - 6x

Substitute y = 31 - 6x in the first equation

3x+2[31 - 6x] = 26

Expand

3x+ 62 - 12x = 26

Collect like terms

3x - 12x = 26 - 62

Evaluate

-9x = -36

Divide by - 9

x = 4

Substitute x = 4 in y = 31 - 6x

y = 31 - 6 * 4

y = 7

This means that the mean values are 4 and 7

To determine the correlation coefficient, we make y the subject in 3x+2y=26 and x the subject in 6x+y=31.

So, we have:

y = 13 - 3x/2 and x = 31/6 - 1/6y

The above means that:

Bxy = -1/6 and Byx = -3/2

The correlation coefficient is then calculated as:

r^2 = Bxy * Byx

r = -1/6 * -3/2

r = 0.25

Hence, the correlation coefficient between x and y is 0.25

The standard deviation of x

We have:

Var(y) = 4

In (a), we have:

y = 13 - 3x/2

To solve further, we make use of:

Var(y) = Var(ax + b) = a^2Var(x)

This gives

Var(y) = Var(13 - 3x/2) = 13^2 * Var(x)

So, we have:

Var(y) = 13^2 * Var(x)

Substitute 4 for Var(y)

4 = 13^2 * Var(x)

Divide both sides by 13^2

4/13^2 = Var(x)

Express 4 as 2^2

(2/13)^2 = Var(x)

So, we have:

Var(x) = (2/13)^2

Take the square root of both sides

SD(x) = 2/13

Hence, the standard deviation of x is 2/13

The solution set of the inequality is:

w ∈ (-∞, -1] U [3, ∞)

The graphed parabola is f(w), and we have the inequality:

f(w) ≤ 0.

So we need to identify the intervals such that the parabola is below the horizontal axis. By looking at the graph, we can see that the two intervals are:

Left side:

(-∞, -1]

Right side:

[3, ∞)

Where the brackets are used because points x = -1 and x = 3 are solutions.

Then the solution set of the inequality is:

w ∈ (-∞, -1] U [3, ∞)

If you want to learn more about inequalities:

https://brainly.com/question/18881247

#SPJ1

Answer:

Polynomial, 6. Constant. The highest value of the exponent in the expression is known as the Degree of Polynomial. The degree of a polynomial is the largest exponent. It is also known as an order of the polynomial. While finding the degree of the polynomial, the polynomial powers of the variables should be either in ascending or descending order.

Step-by-step explanation:

A term is defined as a part of an equation separated by a +/- operation. Because there is a + operation separating two terms (-x^6 and 7x^5), the expression is a binomial, meaning the expression has two terms.

The highest exponent or degree, present in the expression is to the power of 6. Therefore, the expression is in the sixth degree.

Taken together, the expression is a sixth-degree binomial.

Considering the definition of probability:

Probability is the greater or lesser possibility that a certain event will occur.

In other words, the probability is the possibility that a phenomenon or an event will happen, given certain circumstances. It is expressed as a percentage.

The probability of any event A is defined as the quotient between the number of favorable cases (that is, the number of times that event A may or may not occur) and the total number of possible cases:

[tex]Probability=\frac{number of favorable cases}{total number of possible cases}[/tex]

The union of events, AUB, is the event formed by all the elements of A and B. That is, the event AUB is verified when one of the two, A or B, or both occurs. AUB is read as "A or B".

The probability of the union of two compatible events is calculated as the sum of their probabilities subtracting the probability of their intersection:

P(A∪B)= P(A) + P(B) -P(A∩B)

A complementary event, also called an opposite event, is made up of the inverse of the results of another event. That is, That is, given an event A, a complementary event is verified as long as the event A is not verified.

The probability of occurrence of the complementary event A' will be 1 minus the probability of occurrence of A:

P(A´)= 1- P(A)

In first place, let's define the following events:

A: The event that a student owned a laptop.

B: The event that a student owned a car.

Then you know:

In this case, considering the definition of union of events, the probability that the student owns either a car or laptop is calculated as:

P(A∪B)= P(A) + P(B) -P(A∩B)

P(A∪B)= 0.78 + 0.46 -0.38

P(A∪B)= 0.86= 86%

Then, the probability that the student owns either a car or laptop is 86%.

On the other hand, considering the definition of the complementary event and its probability, the probability that the student owns neither a car nor a laptop is calculated as:

P [(A∪B)']= 1- P(A∪B)

P [(A∪B)']= 1 - 0.86

P [(A∪B)']= 0.14= 14%

Finally, the probability that the student owns neither a car nor a laptop is 14%.

Learn more about probability:

brainly.com/question/25839839

brainly.com/question/26038361

#SPJ1

Answer:

Step-by-step explanation:

x×4=2x²(x-1)

2x³-2x²-4x=0

2x(x²-x-2)=0

x≠0

x²-x-2=0

x²-2x+x-2=0

x(x-2)+1(x-2)=0

(x-2)(x+1)=0

x=2

or

x=-1 (rejected)

Answer:

Step-by-step explanation:

Formula

The following relationship exists between the parts of each chord.

(x - 1)(2x^2) = 4*x

Solution

The easiest way to start is to divide both sides of the equation by x.

(x - 1)(2x^2)/x = 4x / x                  Divide by x    

( x-1)(2x) = 4                                 Remove the brackets

2x^2 - 2x = 4                              Subtract 4 from both sides

2x^2 - 2x - 4 = 4 - 4                    Combine

2x^2 - 2x - 4 = 0                         Pull out the common factor

2(x^2 - x - 2) = 0                         Divide by 2

x^2 - x - 2 = 0                              Factor

(x - 2)(x + 1)

Answer:

x can be 2 or x can be - 1 on paper. The x on the upper right prohibits that. A line can't have a length of - 1. So - 1 is called an extraneous solution.

The answer is x = 2

Answer:

4y +x =18

Step-by-step explanation:

y - (-5) -1

----------- = ------

x - 2 4

4y +20 = -x+2

4y +x =18

Answer:

e4fodor8rsidididi2f2

Answer:

9

Step-by-step explanation:

3:4

AB:12

cross multiply giving

3×12:4AB

36: 4AB

divide both sides by 4,thus

AB=9

Answer:

Hi! So, I'm pretty sure the answer is 1 (rounded).

However, I'm not sure if you're trying to find the answer to COS pi/10 or "the function in terms of cofunction of a complementary angle" which I'm not too sure about. I've given you the answer to the first part if this was not the right way to read the problem I deeply apologize.

Step-by-step explanation:

Using any calculator with the Cos, Sin, and Tan function, you can input

COS (pi / 10) which equals .9999849678 (which you can round as needed)

By definition of the binomial coefficient,

[tex]C(n,k) = \dfrac{n!}{k!(n-k)!}[/tex]

so we have

[tex]C(50,3) + C(50,4) = \dfrac{50!}{3!47!} + \dfrac{50!}{4!46!} \\\\ = \dfrac{50!}{3!46!} \left(\dfrac1{47} + \dfrac14\right) \\\\ = \dfrac{50!}{3!46!} \times \dfrac{51}{188} \\\\ = \dfrac{51!}{3!46!} \times \dfrac1{4\times47} \\\\ = \dfrac{51!}{4!47!} \\\\ = \dfrac{51!}{4!(51-4)!} = C(51,4)[/tex]

as required.

Answer: [tex]2\left(x-\frac{1}{4} \right)^{2}[/tex]

Step-by-step explanation:

[tex]2x^{2}-x+\frac{1}{8}\\\\=2\left(x^{2}-\frac{1}{2}x \right)+\frac{1}{8}\\\\=2\left(\left(x-\frac{1}{4} \right)^{2}-\frac{1}{16} \right)+\frac{1}{8}\\\\=2\left(x-\frac{1}{4} \right)^{2}-\frac{1}{8}+\frac{1}{8}\\\\=\boxed{2\left(x-\frac{1}{4} \right)^{2}}[/tex]

The missing equivalent forms are: a = 10%,  b = 25/100 and c = 1/2

Unit Fraction   Fraction with 100 in denominator      Percent

1/10                              10/100                                             a

1/4                                  b                                                  25%

c                                  50/100                                           50%

Complete the table by finding the missing equivalent form for each row.

From the above table, we have the following equations

a = 10/100

b = 25%

c = 50/100

The variable a must be in percentage.

So, we have:

a = 10/100

Express as percentage

a = 10%

The variable b must be a fraction with 100 in denominator

So, we have:

b = 25%

Express as fraction

b = 25/100

The variable b must be a unit fraction

So, we have:

c = 50/100

Divide the fraction by 50/50

c = 1/2

Hence, the missing equivalent forms are:

a = 10%,  b = 25/100 and c = 1/2

Read more about fraction and percentage at:

https://brainly.com/question/7244254

#SPJ1

The complete statement is divide factors of ± 8 by factors of ± 1

The polynomial is given as:

4x^3 + x^4 - 7x^2 - 8x - 8

Rewrite properly as:

x^4 + 4x^3 - 7x^2 - 8x - 8

The first term in the above equation is 1 i.e. 1x^4, while the last term is 8

To determine the possible rational roots, we divide the factors of the last term i.e. 8 by the factors of the first term i.e. 1

Hence, the complete statement is divide factors of ± 8 by factors of ± 1

Read more about rational roots at:

https://brainly.com/question/10937559

#SPJ1

The range, the mean, and standard deviation are mathematically given as

Participants ranged in age from 4 to 26.24 ( M = 26.24 , SD = 8.04 ). Option D.

Given the data presented below the given

A look at the result shows that the lowest and highest values are between 1s and 58, with a mean and standard deviation of 26.10 and 8.90, respectively.

Participants' ages varied from 18 to 58 (m-26.14, std dev = 8.01), hence option (d) is accurate.

Read more about standard deviation

https://brainly.com/question/12402189

#SPJ1

The value of the investment in 5 years is $5805.9

Interest is the amount earned over years for the amount invested.

It is given that

Principal = $5000

Rate = 3%

Compounded Quarterly

Time = 5 years

Amount = ?

The Amount is given by the formula

Amount = P( 1 + (r/n))ⁿˣ

Here n = t = time period for which the investment has been done.

Amount = 5000( 1+(3/4 * 100)⁴ˣ⁵

Amount = 5000 (1.16)

Amount = $ 5805.9

Therefore , The value of the investment in 5 years is $5805.9

To know more about Interest

https://brainly.com/question/13324776

#SPJ1

Answer:

A.

Step-by-step explanation:

The other graphs answers have a point at (3, 1) which is not on the graph.

Answer: 18, 24, 30

Step-by-step explanation:

For the segments to create a right triangle, they must satisfy the Pythagorean theorem.

The only set which satisfies the Pythagorean theorem, is 18, 24, 30, since [tex]18^{2}+24^{2}=30^{2}[/tex]

Answer:

m is not an element of real number

Answer:

A exponential equation is usually of the form f(x)=a (1±r)ˣ.

Our limitation: Initial Vale is 500.

Let's look at our options:

#1- Initial Value of 1000  --- WRONG!

#2- Initial Value of 1000  --- WRONG!

#3- Initial Value of 500 ---- Maybe

#4- Initial Value of 500 ---- Maybe

Let's look at 3 and 4:

#3- Fits Our Form of f(x)=a (1±r)ˣ ---- CORRECT!

#4- Does not fit Our Form of f(x)=a (1±r)ˣ, It's to the 2nd power, not the x power! ---- WRONG!

Hence, #3 Is correct!

Step-by-step explanation:

Well, I hope you understood, and I'd gladly explain anything that didn't make sense. A brainliest would be appreciated, thank you!

-Zylynn Jade Ardenne

Answer:

The correct answers are A B D

Step-by-step explanation:

hope this helped!