The area of a rectangle is given by 3x^3+14x^2-23x+6
The width of the rectangle is given by x + 6. Find an expression for the length of the rectangle.

Answers

Answer 1

The length of the rectangle is defined by [tex](x-1)\cdot \left(x-\frac{1}{3} \right)[/tex].

Geometrically speaking, the rectangle area is equal to the product of its base and its length. According to the statement the area is represented by a third order polynomial and width by a first order polynomial and, thus, length must be a second order polynomial.

By factor the polynomial we get the following roots:

[tex]A = 3\cdot x^{3}+14\cdot x^{2}-23\cdot x + 6[/tex]

[tex]A = (x+6)\cdot (x-1)\cdot \left(x-\frac{1}{3} \right)[/tex]

Then, the length of the rectangle is defined by [tex](x-1)\cdot \left(x-\frac{1}{3} \right)[/tex].

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Related Questions

Lincoln middle school had a canned food drive. The 6th grader brought in 5.75

Answers

So the Lincoln middle school will have +5.75 pounds or ounces of ffod

Katherine Johnson is best known for her work on ________.

Answers

Answer:

Pretty sure she was best known for calculating flight paths of spacecraft.

Find the mean, median and more for the following data sets. (15, 13, 19, 17, 25, 13, 23, 18, 19, 17, 21)

Answers

Step-by-step explanation:

hope it will help you ....

4x+y=10 ( ?,-6)

Find the missing value. Show all work.

Answers

Answer:

(4 , -6) x = 4.

Step-by-step explanation:

Note that in a pair under ( X , Y) always consists of X as it's 1st element and Y as it's second element.

so now we know that ( ? , -6) has an X value which is unknown.

inorder to find X you'll simply need to use the Y value you're given which is Y = -6 from ( ? , -6)

now plot the y value into the equation

4X + Y = 10 , Y = -6

4X + (-6) = 10

4X + - 6 = 10 ...... we know that A + - B = A - B

4X - 6 = 10

now take -6 to the right side

when -6 is taken to the right side, it changes to +6

and so ..

4X = 10 + 6

4X = 16

now divide both sides by 4 to find X

4X / 4 = 16 / 4

4 the coefficient of X which is 4 cancels with out denominator which is now 4

X = 16 / 4

16 ÷ 4 = 4.

Write an integer for each situation
1. A deposit of $40
2. A loss of 20 pounds

Answers

1.) +40
2.) -20

1.) A positive increase occurs; the rise of a value.

2.) A negative decrease occurs; a loss of a value.

Triangle ABC has two known angles. Angle A measures 55 degrees. Angle B measures 30 degrees. What is the measure of angle C?​

Answers

Answer:

According to the properties of a triangle, all internal angles of a triangle must add up to 180 degrees.

Since we know A and B are 55 degrees and 30 degrees respectively, C = 180-55-30 = 95 degrees.

Thus, the measure of angle C is 95 degrees.

Which equations are true equations?


Select all correct answers.

24/2^2=50−62−8


56÷8+32=2⋅23


82−52=42−7


39−3⋅6=6⋅104+4

Answers

Answer: 24/2^2=50−62−8

Step-by-step explanation:

The equations which is true equation is 24/2² = 50−6²−8.

What is Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

1. 24/2² = 50−6²−8

LHS = 24/2² = 24/4 = 6

RHS = 50−6²−8 = 6

2. 56÷8+32=2⋅23

LHS = 56÷8+32 = 7 + 32 = 39

RHS = 2⋅23 = 46

3. 8²−5² =4²−7

LHS = 8²−5² = 39

RHS = 4²−7 = 21

4. 39−3⋅6=6⋅104+4

LHS = 39−3⋅6 = 35.4

RHS = 6⋅104+4 = 528

Hence, we can conclude that the equation 24/2² = 50 − 6² − 8 is true.

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If f(2) for f(x) = [tex]\frac{2}{x-1}[/tex]+6 is 8. then what is [tex]f^{-1} (8)[/tex]

Answers

Answer:

2

Explanation:

we get inverse functions by interchanging places of domain and range of the original fuction so rhe domain becomes a range and the range becomes a domain.

so if 2 belongs to the domain of the original fuction and its corresponding element in the range is 8, we simply interchange between 2 and 8 in order to solve the fuction without any subistitution in the original function.

What is -0.4 times -5/6?

Answers

Answer:

0.3

Step-by-step explanation:

hopes this helps

It’s 1/30 because -0.4 x -5/6 equals to -2/5 x -5/6 which leaves you with 1/30

the sum of 2 integers is 61 and their difference is 29.

Answers

Answer:

16 and 45

Step-by-step explanation:

Just use guess and check, start with a number too low like 10+39=49. Then go up until you find the number or until you go over.

which quadratic inequality does the graph below represent?
y> or equal to x^2-3.
y< or equal to x^2+3.
y< or equal to x^2-3.
y> or equal to x^2+3​

Answers

Answer:

y< or equal to x^2-3.

I hope it helps.

I got this homework packet , I did some of the questions but graphs are what I’m stuck on the most .

Answers

Answer:

For the first picture, I think it is C and the second one should be A.

Step-by-step explanation:

You use vertical lines and if it hits it multiple times it is not a function. Like if it hits two dots or something it is not a function. I hope that make sense, let me know if it doesn't.

Work out m and c for the line: 2 y + 3 x = − 5

Answers

Answer:

m is -3/2

c is -5/2

Step-by-step explanation:

The standard linear equation is given by;

[tex]{ \tt{y = mx + c}}[/tex]

» m is the slope and c is the y-intercept

Then, our slope is;

[tex] { \tt{2y + 3x = - 5 }} \\ \\ { \tt{2y = - 3x- 5}} \\ \\ { \tt{y = - \frac{3}{2}x - \frac{5}{2} }}[/tex]

Explanation of approximation, decimal place, significant figure

Answers

Answer:

im not an expert in math but i'll do my best:

1. an approximation is something that is almost, but not exactly something. for example, 5.02 is approximately 5. it's not EXACTLY 5, but it's around 5.

2. decimal place refers to the position of numbers after the decimal point. let's take the decimal number 7.89 for example. there are 2 numbers after the decimal point, which is 8 and 9. hence we say that 7.89 has 2 decimal places.

3. significant figure is kind of hard to explain, so i'll jump into the example straight away.

5.874 to 3 significant figures is 5.87. what i did was count 3 digits: starting from 5 to 7. to round to 3 significant figures, i look at the 4th digit, which is 4 in this case. if it's smaller than 5, i ignore everything past the digit 7, and leave the final answer as 5.87.

if the 4th digit is greater than or equal to 5, i add 1 to the 3rd digit THEN leave out all the numbers after the 3rd digit. (if this were the case, the answer would be 5.88)

lets take a trickier example, 0.064591

in this case i cannot start counting 3 digits starting from 0. i have to count starting from the number 6. the concept in this case is that the 1st significant figure cannot be a 0. in this case the answer to 3 significant figures would be 0.0646.

however, 0 can be a significant figure if it's after another number. for instance 0.90672

the 0 after the 9 would count as a significant figure because it's not the 1st significant figure in the number. however the 0 before the 9 would NOT count as one because 0 cannot be the 1st significant figure. the answer to 3 significant figures would be 0.907.

sorry this was so lengthy, i just hope this answers your question on what these are and how they work. good luck!

If 58 out of 100 students in a school are boys. Write decimal expressions for the part of the school that consists of boys.

(Hint: 58 is what percentage of 100?)

Answers

Answer:

58 out of 100 is

58/100

as a decmil that is

0.58

Hope That Helps!!!

A square with an area of 144cm is reduced by a factor of 1/3. How long are the new sides of the square?

Answers

Answer:

9.797. . .

Step-by-step explanation:

2/3 of 144 is 96

[tex]\sqrt{96} = 9.797...[/tex]

86,400 seconds into day.please ​

Answers

[tex]\underline\mathtt\colorbox{gold}{1 day}[/tex]

Step-by-step explanation:

1440 minutes, 24 hours or 1 day

Its easy to check - - - Divide 86400 by 60(to make into minutes) =1440 minFurther. Divide 1440 by 60 (to make into hours) =24 hrsNow who doesn't know that 24 hours is 1 day?

Triangles â–łABC and â–łDFG are similar. The lengths of the two corresponding sides are 1. 4m , and 56 cm. What is the ratio of the perimeters of these triangles ?.

Answers

Answer:

  5 : 2

Step-by-step explanation:

The ratio of perimeters of similar triangles is the same as the ratio of any pair of corresponding sides. That ratio is given as ...

  1.4 m : 56 cm = 140 cm : 56 cm = 5 : 2

The ratio of the perimeters of the triangles is 5 : 2.

_____

As a unit ratio, it is 2.5 : 1, or 2.5.

In his pocket, Hamid has $2.95 in dimes and quarters. If there are 16 coins in total, which system represents the number of dimes and quarters that Hamid has?

A. x + y = 16. 0.10 x + 0.25 y = 2.95.

B. x + y = 16. 0.05 x + 0.25 y = 2.95.

C. x + y = 2.95. 0.10 x + 0.25 y = 16.

D. x + y = 16. 0.01 x + 0.25 y = 2.95.

Answers

It’s C :)) (16-y)+0.25y = 2.95 => y=9… x+9=16
x=7

Answer:

A. x + y = 16; 0.10x + 0.25y = 2.95

Step-by-step explanation:

Given:

Dime is $0.10, number of dimes is x, total of dimes = 0.10xQuarter is $0.25, number of quarters is y, total of quarters is 0.25y

Number of coins is 16:

x + y = 16

Total amount is $2.95:

0.10x + 0.25y = 2.95

Correct choice is A

which value of the variable m satisfies the equation 20 = -2(4m - 5)

Answers

Answer:

m = - 1.25

Step-by-step explanation:

20 = - 2(4m - 5) ← divide both sides by - 2

- 10 = 4m - 5 ( add 5 to both sides )

- 5 = 4m ( divide both sides by 4 )

- [tex]\frac{5}{4}[/tex] = m , that is

m = - 1.25

ANSWER ASAP PLS

A line passes through the points (-6, 4) and (-2, 2). Which is the equation of the line?
A y=-3x+1
B x = 1/2x +7
C y=-2x-8
D y = 2x + 16

Answers

Step-by-step explanation:

m = (y2-y1)/(x2-x1)

= (2-4)/(-2+6)

= -2/4

= -1/2

now

y=mx+c

4=-1/2(-6)+c (you can take any x and y from the given two points. I took from (-6,4)

or,4= 3+c

therefore, c=1

now

y=mx+c

y= -1/2x+1

or, y = 1-x/2

Question 14
Determine if the given lines are parallel or perpendicular or neither.
3y=2-x
y=-1/3x+4

Answers

Answer:

The given lines are parallel.

Step-by-step explanation:

3y=2-x

y=-1/3x+4

-------------

y=2/3-1/3x

y=-1/3x+2/3

y=-1/3x+4

----------------

Since the two lines have exact same slopes, it follows that these two lines are parallel.

Select all the equations that have {7} as its solution set. 65−2x=6x+9 9−x=14x 3+4x=5x−4 x2+1=8x−5

Answers

Answer:

the answer is this hope it helps im not sure if its all right good luck.

Step-by-step explanation:

A. 65-2x=6x+9

B. 9-x=14x

C. 3+4x=5x-4

d is wrong

The first and third equations have {7} as their solution set.

What is an equation?

It is a mathematical statement that is made up of two expressions connected by an equal sign.

The first equation is

65−2x=6x+9

Rearranging the above equation gives

8x = 65-9 = 56

i.e x = 7

Consider the second equation,

9−x=14x

i.e x = 9 / 15 = 0.6

The third equation is:

3+4x = 5x−4

i.e x = 7

The last equation is

x^2+1 = 8x−5

Its solution is not equal to 7.

As a result of the preceding equations, we can conclude that only the first and third equations have "7" as their solution set.

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What is the value of y?

Answers

Answer : i believe 100 X is 13 Z is 12

Step-by-step explanation:

sorry if im wrong

Can someone answer number 9 for and tell me if the others are correct i have a 64% in geometry trying to raise grade up to alteast 70%

Answers

Answer:

  5, 6, 7, 8: correct

  9: the Hi.nge theorem does not apply

Step-by-step explanation:

The Hi.nge theorem says that the side opposite the angle between two pairs of congruent sides is longer if the angle is larger. This theorem is applicable to problems 5-8, and your application is correct.

__

9) The Hi.nge theorem does not apply. The marked angles are not between the congruent sides. There is no necessary relation between the marked angles and the angles that are between the congruent sides, so no conclusion can be drawn regarding the relative lengths of AB and CD.

Philip has $5,774 in a savings account. The interest rate is 13%, compounded annually.

To the nearest cent, how much interest will he earn in 5 years?

(compound interest formula)

Answers

Principal (P) = $ 5774Interest rate (r) = 13 %Number of times the amount is compounded per time period (n) = 1Time (t) = 5 years.Let the compound interest be I.Therefore,

[tex] \sf \: I = P(1 + \frac{r}{n} {)}^{nt} - P \\ \sf = 5774(1 + \frac{13}{100} ) ^{1 \times 5} - 5774 \\ \sf= 5774 \times ( \frac{113}{100} ) ^{5} - 5774 \\ \sf= 10638.22 - 5774 \\ \sf = 4864.22[/tex]

Answer:

$4864.22 (approximate value)

Hope you could get an idea from here.

Doubt clarification - use comment section.

FRUIT Lilly buys fresh fruit from a fruit stand. Apples cost $5 per pound and oranges cost $4 per pound. She has $40 to spend. The table shows the function relating the number of pounds of apples, x, and the number of pounds of oranges, y, Lilly could purchase.

Answers

Answer:

Step-by-step explanation:

8 lbs of apples on the x-intercept

10lbs of peaches on y-intercept

Suppose a normal distribution has a mean of 62 and a standard deviation of
4. What is the probability that a data value is between 56 and 64? Round your
answer to the nearest tenth of a percent.

Answers

Answer:

62.5%

Step-by-step explanation:

(56 - 62) / 4 = -1.5 z score = 0.0668

(64 - 62) / 4 = 0.5 z score = 0.6915

0.6915 - 0.0668 = 0.6247

Rounded this becomes 62.5%

The probability for the data value in between 56 and 64 is 62.5%.

What is z-score?

The z-score of a value is the count of the numbers of standard deviations between the value and the mean of set.

How to calculate z-score?

z-score can be calculated by the formula

z = (x - μ)/σ

where,

μ is the mean

σ is the standard deviation

x is the data point

What is probability?

A probability is a number that reflects the chance or likelihood that a particular event will occur.

According to the given question

Mean of a normal distribution, μ = 62

standard deviation of a normal distribution, σ = 4

Now for the data value 56, the z-score will be

z = (56 - 62) / 4 = -1.5 z score = 0.0668

So, the area under normal distribution curve z = -1.5

P(z = -1.5) = 0.0668

Similarly,

For the data value 64, the z-score will be

z-score  = (64 - 62) / 4 = 0.5

The area under normal distribution curve z = 0.5 is given by

P( z = 0.5) = 0.69

Therefore, the probability for the data value in between 56 and 64 is given by

0.6915 - 0.0668 = 0.6247 =  62.5%

Hence, the probability for the data value in between 56 and 64 is 62.5%.

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How onto add, subtract, multiply, and divide decimals

Answers

Answer:

Hope this helps. x

The triangles are congruent due to which criteria?
SAA
SAS
SSS
HL

Answers

Answer:

SAS is the answer

Step-by-step explanation:

Answer:

HL.

Step-by-step explanation:

Right triangles with the hypotenuse and one leg congruent

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