MATHEMATICS COLLEGE

50 points!!What are the factors of the following polynomial: x^2−x−56
Do not include any spaces in your answer. Use parentheses to separate your factors. A sample answer might be (x+1)(x-4).

Answers

Answer 1
Answer:

Answer:

(x-8) (x+7)

Step-by-step explanation:

x^2 -x-56

We want to factor this problem.

What two numbers multiply to negative 56 and add to -1

-8 *7 = -56

-8+7 = -1

We can use -8 and 7

(x-8) (x+7)

Check:

FOIL

first: x*x =x^2

outer: 7x

inner:-8x

last: -8*7 = -56

Add this together

x^2 +7x-8x -56 = x^2 -x-56

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A study was conducted to estimate the mean amount spent on Christmas gifts for a typical family having two children. A sample of size of 101 was taken and the mean amount spent was $225 with astandard deviation equal to $50. Find a 95% confidence interval for the mean for all such families. Round to the nearest whole dollar.The confidence interval is from(Do not enter dollar signs.)

(9c^2 + 3c + 9) - (9c^2 + 2c + 7)

Answers

Answer:

c+2

Step-by-step explanation:

Distribute the Negative Sign:

=9c2+3c+9+−1(9c2+2c+7)

=9c2+3c+9+−1(9c2)+−1(2c)+(−1)(7)

=9c2+3c+9+−9c2+−2c+−7

Combine Like Terms:

=9c2+3c+9+−9c2+−2c+−7

=(9c2+−9c2)+(3c+−2c)+(9+−7)

Answer:

c + 2

Step-by-step explanation:

(9c² + 3c + 9) - (9c² + 2c + 7)

9c² + 3c + 9 - 9c² - 2c - 7

9c² + 3c + 9 - 9c² - 2c - 7

c + 2

At the end of 2019, Mark owes $250,000 on the mortgage related to the 2016 purchase of his residence. When his daughter went to college in the fall of 2019, he borrowed $20,000 through a home equity loan on his house to help pay for her education. The interest expense on the main mortgage is $15,000, and the interest expense on the home equity loan is $1,500. How much of the interest is deductible as an itemized deduction?

Answers

Answer:

  $15,000

Step-by-step explanation:

The $1500 interest on a home equity loan used for purposes other than home improvement is not deductible with other home loan interest as an itemized deduction.

However, the interest on a loan for qualified educational expenses may be considered an adjustment to income, within limits.

Only the $15,000 main mortgage interest can be an itemized deduction.

Final answer:

The total possible mortgage interest deduction for Mark in this scenario is $16,500. However, the actual amount he can deduct depends on his adjusted gross income and whether his itemized deductions exceed the standard deduction.

Explanation:

Under US tax law, taxpayers can deduct the interest on home mortgages and home equity loans, subject to some limitations. The interest expense on the main mortgage ($15,000) and the interest expense on the home equity loan ($1,500) can be combined for a total interest deduction of $16,500. However, the deduction may not be the full amount if there are other factors that would limit the amount of itemized deductions that Mark can claim. This can depend on his adjusted gross income and whether the total of his itemized deductions exceeds the standard deduction. It's also worth noting that the tax benefits of home ownership, such as the mortgage interest deduction, is a key reason why many people choose to buy rather than rent, as it can lead to significant financial savings.

Learn more about Mortgage Interest Deduction here:

brainly.com/question/30516273

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An ice cube tray holds 12 ice cubes. Each cube is 5 cm. what is the volume of all 12 cubes?

Answers

Cube is length of one side cubed (or to the third power)
This one side is 5 cm which means it's volume is 125cm^3 or cubic centimeters.
Multiply 125 * 12 to get the volume of all 12 cubes combined. 
(1500 cubic centimeters)
Hello!

To find the volume of one ice cube, you'll need to find the length, width, and height. In the question, it states that each cube is 5cm. So, 5cm will be the length, width, and height. So you'll need to multiply 5 three times (5*5*5) ---> (25*5) ---> (125).

The volume, V, of one ice cube is 125cm³

Now to find the total volume of all of the cubes, you'll need to multiply 125 by 12. After doing so, you'll get a volume of...

V=1500cm³

I hope this helps!

What is the solution of the equation (x - 5)2 +3(x-5)+9 = 0? Use u substitution and the quadratic formula to solve.​

Answers

Answer:

x= (7+3i√(3) )/(2) and (7-3i√(3) )/(2)

Step-by-step explanation:

(x - 5)^(2) +3(x-5)+9

(x - 5)^(2)= x2−10x+25

3(x-5)= 3x-15

x^2-10x+25+3x-15+9

x^2-7x+19=0

a=1 b=-7 c=19

use quadratic formula

\frac{-b+\sqrt{b^(2) -4ac} }{2a}

\frac{-(-7)+\sqrt{-7^(2)-4(1)(19) } }{2}

\frac{7+\sqrt{49{}-4(19) } }{2}

\frac{7+\sqrt{49{}-76 } }{2}

\frac{7+\sqrt{-27{} } }{2}

√(-27) =3i√(3)

(7+3i√(3) )/(2)

The length of a rectangle is four times its width. If the perimeter of the rectangle is 50 cm, find its area.

Answers

Answer:

width=25/3

Length=75/3

Step-by-step explanation:

Given

Perimeter=50

Let width=x

Length=4x

So perimeter =2(length+width)

2(length+width)=50

2(X+2x)=50

3x=25

X=25/3

So width=25/3

Length=75/3

The volume V of an ideal gas varies directly with the temperature T and inversely with thepressure P. A cylinder contains oxygen at a temperature of 320 degrees Kelvin and a pressure of


25 atmospheres in a volume of 120 liters. Find the pressure if the volume is decreased to 110


liters and the temperature is increased to 335 degrees Kelvin.


Hint: Look at the equation V = k* Then use the initial values to solve for k. Then plug in the


values you know for the second set of values and solve for your unknown.

Answers

Answer:

Pressure=22.55 atmospheres

Step-by-step explanation:

Let

V=volume of the ideal gas

P=pressure

T=temperature

Volume varies directly with temperature and inversely with pressure

V=kT/P

t=320°K

P=25 atmospheres

V=120 liters

V=kT/P

120=k*320/25

120=320k/25

120×25=320k

3000=320k

k=300/320

=9.375

k=9.375

V=110 liters

p=?

t=335°K

V=kT/P

110=9.375*335/p

110=3,140.625/p

110p=3,140.625

P=3,140.625/110

=28.55

P=22.55 atmospheres
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