an expression for the area of a rectangular piece of sheet metal is X^2+8x+12.
An expression for the length of the same piece of sheet metal is x+6.
Determine an expression for the width.

Answers

Answer 1

[tex]\text{Area of rectangle} = \text{Length} \times \text{Width}\\\\\\\implies \text{Width} = \dfrac{\text{Area of reactangle}}{\text{Length}} = \dfrac{x^2 +8x +12}{x+6} = \dfrac{x^2 + 6x +2x +12}{x+6}\\\\\\\\ = \dfrac{x(x+6) +2(x+6)}{x+6}=\dfrac{(x+6)(x+2)}{x+6} = x+2[/tex]


Related Questions

What are the solutions to this quadratic equation? x2+6x-5 A. B. C. D.

Answers

Factoring x2-6x+5

The first term is, x2 its coefficient is 1 .
The middle term is, -6x its coefficient is -6 .
The last term, "the constant", is +5

Step-1 : Multiply the coefficient of the first term by the constant 1 • 5 = 5

Step-2 : Find two factors of 5 whose sum equals the coefficient of the middle term, which is -6 .

-5 + -1 = -6 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -5 and -1
x2 - 5x - 1x - 5

Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x-5)
Add up the last 2 terms, pulling out common factors :
1 • (x-5)
Step-5 : Add up the four terms of step 4 :
(x-1) • (x-5)
Which is the desired factorization

Equation at the end of step
1
:

(x - 1) • (x - 5) = 0
STEP
2
:
Theory - Roots of a product

2.1 A product of several terms equals zero.

When a product of two or more terms equals zero, then at least one of the terms must be zero.

We shall now solve each term = 0 separately

In other words, we are going to solve as many equations as there are terms in the product

Any solution of term = 0 solves product = 0 as well.

Solving a Single Variable Equation:

2.2 Solve : x-1 = 0

Add 1 to both sides of the equation :
x = 1

Solving a Single Variable Equation:

2.3 Solve : x-5 = 0

Add 5 to both sides of the equation :
x = 5

Supplement : Solving Quadratic Equation Directly

Solving x2-6x+5 = 0 directly
Earlier we factored this polynomial by splitting the middle term. let us now solve the equation by Completing The Square and by using the Quadratic Formula

Parabola, Finding the Vertex:

3.1 Find the Vertex of y = x2-6x+5

Parabolas have a highest or a lowest point called the Vertex . Our parabola opens up and accordingly has a lowest point (AKA absolute minimum) . We know this even before plotting "y" because the coefficient of the first term, 1 , is positive (greater than zero).

Each parabola has a vertical line of symmetry that passes through its vertex. Because of this symmetry, the line of symmetry would, for example, pass through the midpoint of the two x -intercepts (roots or solutions) of the parabola. That is, if the parabola has indeed two real solutions.

Parabolas can model many real life situations, such as the height above ground, of an object thrown upward, after some period of time. The vertex of the parabola can provide us with information, such as the maximum height that object, thrown upwards, can reach. For this reason we want to be able to find the coordinates of the vertex.

For any parabola,Ax2+Bx+C,the x -coordinate of the vertex is given by -B/(2A) . In our case the x coordinate is 3.0000

Plugging into the parabola formula 3.0000 for x we can calculate the y -coordinate :
y = 1.0 * 3.00 * 3.00 - 6.0 * 3.00 + 5.0
or y = -4.000

Parabola, Graphing Vertex and X-Intercepts :

Root plot for : y = x2-6x+5
Axis of Symmetry (dashed) {x}={ 3.00}
Vertex at {x,y} = { 3.00,-4.00}
x -Intercepts (Roots) :
Root 1 at {x,y} = { 1.00, 0.00}
Root 2 at {x,y} = { 5.00, 0.00}

The owner of a bookstore buys used books from customers for one dollar and 50 Cent each owner then resells the used books for 400% of the amount he paid for them what is the price of a used book in the bookstore?

Answers

seeing as $1.50 would be 100% of the price a 400% mark up would cause you to multiply 100% of the cost($1.50) by 4 giving you $6
1.50 x 4 = 6

please help me with -6 - (1 - 2 x) in Distributive Property this question

Answers

Answer:

-7 + 2x

Step-by-step explanation:










y=−2x−5
y=2x−2

Answers

Answer:

This doesn't make since.

Step-by-step explanation:


Emily is on a Ferris wheel and her height is modeled by the equation
27
y = 30.48 cos2pi/4.25 (x - 2) + 34.27 where x = the number of minutes since the
ride began and y = the height in feet of Emily.
a) What is the radius of the Ferris wheel?
b) How long does it take Emily to make one rotation?
The radius is______
feet and it takes Emily_____
minutes for one rotation.

Answers

The given function for the height of the Ferris wheel is a sinusoidal equation.

a) The radius is 30.48 feet and it takes Emily 4.25 minutes for one rotation

Reasons:

The function that gives the height of the Ferris wheel is presented as follows;

[tex]\displaystyle y = 30.48 \cdot cos \frac{2\cdot \pi }{4.25} \cdot \left(x - 2 \right) + 34.27[/tex]

Where;

x = The number of minutes since the ride began

y = The height in feet of Emily

a) Required:

The radius of the Ferris wheel

Solution:

Comparing the given equation with the general equation of a Ferris wheel, we have;

[tex]\displaystyle f(t) = \mathbf{A \cdot trig\left(B \cdot \left(t + C\right) \right) + D}[/tex]

The amplitude of the Ferris wheel = A = 30.48

The amplitude, A = The largest distance from the center = The radius, r

A = r

Therefore;

The radius of the Ferris wheel, r = A = 30.48 feet

b) The time it takes the Emily to make one rotation is given by the period, T, of the motion of the Ferris wheel as follows;

[tex]\displaystyle T = \mathbf{\frac{2 \cdot \pi}{B}}[/tex]

By comparison, we have;

[tex]\displaystyle B = \frac{2 \cdot \pi}{4.25}[/tex]

Therefore;

[tex]\displaystyle The \ period, \, T = \frac{2 \cdot \pi}{\left(\frac{2 \cdot \pi}{4.25} \right)} = 4.25[/tex]

The time it takes Emily to make one rotation, T = 4.25 minutes

Learn more here:

https://brainly.com/question/21165143

see image above ^^^^​

Answers

Triangle ABC was rotated 90 degrees counter clockwise to become triangle STU

quick mafs ill mark brainliest​

Answers

Answer:

LJ< JK<LK

Step-by-step explanation:

for a theorem, the order of the side of the triangle is the same as the order of the opposite angles since for the angles it's K<L<J, you replace each with the opposite side (quick trick, it's the one not containing the letter!)

Ln(x)+ln(x+7)=1
solve this log equation

Answers

7n-1/1+n this should be it

is this linear or not and why

Answers

Answer:

Yes

Step-by-step explanation:

Both equations of this system are of degree one.

They are both linear as the graph of both is a line.

Answer:

yes

Step-by-step explanation:

The highest power of variable is 1 . So it is a linear equation of two variables .

6=4x^3-10x^2 please hurry it's a test

Answers

Answer:

x = about 2.705

Step-by-step explanation:

Does this help? Are you supposed to find x? That's what I did but you don't state what exactly you need.... So.....?

tammy has soccer practice every 12 days, basketball 18 days, band practice 20 days, and music class every 24 days. If she has all these practices on the same day today, then how many days will it be until she has all four practices.

Answers

Answer:

360 days

Step-by-step explanation:

It would be a whole year until the classes line up on the same day again, because it would only be the exact same date of the next year that they line up.

Hope this helps!

Find positive numbers x and y satisfying the equation xy=20 such that the sum 4x+y is as small as possible.

Answers

The answer is 4 and 5.

They are 2 positive numbers that satisfy the equation, (5)(4)=20.

If that doesn’t work try 2 and 10.

Hope this works!! :)

Robert earns $498.00 for 40 hours of work. How much does he earn if works 30 hours at the same pay rate? Do not round your answer.

Answers

Answer:$373.50

Step-by-step explanation:

$498.00 divided by 40 is 12.45

12.45 times 30 is $373.50

You need to divide 498 on 40 hours so you could know how much he earn every hour

Can someone put an answer for each box plzzzz.

Answers

we need the drop down options..

NEED ASAP

in a company, 65% of workers are men. if 1,995 people work for the company who aren’t men, how many worker are their in all.

Answers

Answer:

5700

Step-by-step explanation:

Assume that the total number of people working for the company is x. Since 65% of workers are men and 1,995 people working for the working are not men, then that means that 35% of the total number of people working for the company is equal 1,995.

Set up an equation: 0.35x = 1,995 and find x.

x = 5700

Alyssa is baking a cake the recipe calls for 8 cups of flour she already put in 2 cups how many more cups does she need to add

Answers

You need 6 cups hope that helps

if in a game of glass stepping stones. there are 18 tiles of glass. two in each row. one is tempered and will be fine if you jump on it. and the other will break. if 1 player was to play what are his/her chances of getting across?
(NO links)​

Answers

There chance for just getting across each row would be 50% but there chance of getting across completely is 1 in 18

Students are running in a relay race. Each team will run a total of 3 miles. Each member of a team will run 1/3 mile
How many students will a team need to complete the race? Circle the correct number below

Answers

Answer:

9 students

Step-by-step explanation:

If 1 student runs a 3rd we need 3 students to run 1 mile.

Since we need 3 times that amount of miles we multiply the amount of students it takes to run 1 mile so that we find out how many we need to run 3 miles.

3 x 3 = 9

They will need 9 students I hope this helps have a great day :)

How much is f(x) = 3(4)x

Answers

Answer:

f ( x ) = 12 x

Step-by-step explanation: 3x4=12 so that makes it f(x)=12x

What do you measure the amount of water in a vase

Answers

Liquid volumeis the amount of liquid in a container.

What is 34÷18? Explain or show your reasoning.

Answers

Answer:

1.8889

Step-by-step explanation:

HELP ME PLEASE ASAP ASAP

Answers

The answer to this question is £155

I will give Brainliesttttt :D!

A car's gas mileage is the distance it can go using 1 gallon of gas (measured in miles per gallon).

Based on the graph, what is this car's gas mileage? Explain.​

Answers

Answer:

20 mpg

Step-by-step explanation:

Answer:

The car is traveling 20 miles per gallon.

Step-by-step explanation:

There are two ways you can solve this.

1) Since this is a graph of the car's gas mileage, all you have to do is look to find the miles for one gallon, which is plotted in this case. As you can see, for one, it is plotted halfway between 0 and 40, so that means the mile number would be 20. Looking at this, the car travels 20 miles per gallon.

2) You can also look at the point at the top that is clearly defined, and the point is (12, 240), 12 gallons used for 240 miles. To get the exact number of miles for one mile, you would divide 12 and 240 both by 12, which results in (1, 20). Since it is miles per gallon, the car gas mileage is 20 miles per gallon.

Hope this helped and have a great day!

what has a fraction in numerator, denominator or both???

Answers

a fraction that has a numerator and a denominator, is called a Complex fraction, i’m not sure if this is what you were asking for though.

Abcd is a parallelogram determine the length of BE
A)51 units
B)102 units
C)96 units
D) -11 units

Answers

Answer:

  B)  102 units

Step-by-step explanation:

The diagonals of a parallelogram bisect each other. This means ...

  BE = ED

  3 -9x = -8x +14

  -11 = x . . . . . . . . . . . . add 9x -14

  BE = 3 -9x = 3 -9(-11) = 3 +99

  BE = 102 units

I need help on this
Here it is

Answers

Solution:

2. Barlow School: (4 / 9) * 873 = 388 of the students are boys.

873-388 = 485 of the students are girls.

The b(boy) to g(girl) ratio at Barlow School is 388b:485g


1. Willow School: (2 / 3) * 630 = 420 of the students are girls.

630-420 = 210 of the students are boys.

The b(boy) to g(girl) ratio at Willow School is 420g:210b

3. 388 - 210 = 178


Answer: Barlow School has the greater number of boys by 178 students.

2(x + 1) - 3x
howwwwwww

Answers

Answer:

a = -x + 2

Step-by-step explanation:

First, you must distribute to get 2x + 2 and adding in the -3x it equals 2x + 2 - 3x = a

Combine the like terms to get -x + 2 = a

Since there is 2 variables then the answer will stay a = -x + 2 because x or a must be substituted in order to find the other variable

Ze answer is -x + 2 my dude

Dan received 64 dollars for his birthday. He went to a sporting goods store
and bought a baseball glove, baseball, and bat. He had 31 dollars left over,
how much did he spent on the baseball gear?

Answers

Answer:

the answer is 33 bucks because you have subtract the 64 -31 =33

He started with a total of $64 and $31 remained after his expenses.

We can create an Algebraic equation to represent the scenario. The variable “x” is equal to how much of his birthday money he spent.

64-x=31 [Equation]

64-64-x=31-64 [Subtract 64 from both sides to cancel it out and isolate x]

-x=-33 [Simplification after subtraction]

-x/-1=-33/-1 [Divide by -1 on both sides to cancel it out and solve for x]

x=33 [Defined Variable]

*Recall that “x” is equal to his expenses.

Therefore, Dan spent $33 of his $64.

We can check this because 64-33=31.

Please give Brainliest

Please lots of points I wasn’t at school when this was taught

Answers

Answer:

4x+2=4x+4, no solution

Step-by-step explanation:

first, i'm assuming the flower bed is a square so that all 4 sides are x+1. next, to find the perimeter you have to add up the side lengths of each shape.

vegetables: x + x+1 + x + x+1 = 4x+2 so the perimeter of the vegetables must be 4x+2

flowers: x+1 + x+1 + x+1 + x+1 = 4x+4

since the two must be equal, we have 4x+2=4x+4, this is the equation Trent can use

next, to solve the equation, subtract 4x from both sides to get 2=4. this obviously isn't true so there is no solution

Scores on a recent exam followed a normal distribution and letter grades will be assigned with 15% A, 35% B, 30% C, 15% D, and 5% F. Suppose that Sue took the exam and had a standardized score of 0.85. What letter grade will Sue get?

Answers

Using the normal distribution, it is found that Sue will get a letter grade of B.

In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

It measures how many standard deviations the measure is from the mean.  After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.

In this problem, Sue got a grade of 0.85, hence [tex]z = 0.85[/tex].

Looking at the z-table, z = 0.85 has a p-value of 0.8023, hence she is approximately in the top 20%, which is below the top 15% but above the top 50%, hence she got a letter grade of B.

A similar problem is given at https://brainly.com/question/25745464

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