(12y2+17y-4)+9y2-13y+3)

Answers

Answer 1

Answer: $(12y^2+17y-4)+(9y^2-13y+3)=12y^2+9y^2+17y-13y-4+3=\n\n=21y^2+4y-1$

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Evaluate the factorial expression.left parenthesis 6 minus 2 right parenthesis exclamation mark

Answers

If I understood your post correctly, then this will be the equation we evaluate: (6-2)!

We can simplify this to: 4!

4! = 4 x 3 x 2 x 1 = 24

A rectangular piece of paper has a width that is 3 inches less than its length. It is cut in half along a diagonal to create two congruent right triangles with areas of 44 square inches. Which statements are true? Check all that apply.A.The area of the rectangle is 88 square inches.
B.The equation x(x – 3) = 44 can be used to solve for the dimensions of the triangle.
C.The equation x2 – 3x – 88 = 0 can be used to solve for the length of the rectangle.
D.The triangle has a base of 11 inches and a height of 8 inches.
The rectangle has a width of 4 inches.

Answers

Let

x-------> the length of the rectangle

y------> the width of the rectangle

we know that

The area of the rectangle is equal to

$A=x*y$

The area of the two congruent right triangles is equal to the area of the rectangle

$A=2*44=88\ in^(2)$

$88=x*y$ -------> equation A

$y=x-3$ -----> equation B

Substitute equation B in equation A

$x*[x-3]=88$

$x^(2) -3x-88=0$ --------> equation that can be used to solve for the length of the rectangle

Using a graph tool-------> solve the quadratic equation

see the attached figure

The solution is

$x=11\ in$ -----> the length of the rectangle

Find the value of y

$88=11*y$

$y=8\ in$ ----> the width of the rectangle

Statements

case A) The area of the rectangle is $88$ square inches

The statement is True

See the procedure

Case B) The equation $x*[x-3]=44$ can be used to solve for the dimensions of the triangle

The statement is False

Because, the equation $x*[x-3]=88$ can be used to solve for the dimensions of the triangle

case C) The equation $x^(2) -3x-88=0$ can be used to solve for the length of the rectangle

The statement is True

see the procedure

case D)The triangle has a base of $11$ inches and a height of $8$ inches

The statement is True

Because, the base of the triangle is equal to the length of the rectangle and the height of the triangle is equal to the width of the rectangle

case E) The rectangle has a width of $4$ inches

The statement is False

See the procedure

The correct statements are:

The area of the rectangle is 88 square inches.
The equation x^2 – 3x – 88 = 0 can be used to solve for the length of the rectangle.
The triangle has a base of 11 inches and a height of 8 inches.

What are the dimensions of the rectangle?

When a rectangle is split diagonally, two right triangles are formed.

The area of a triangle = 1/2 x base x height

44 = 1/2 × (x - 3) × x

Where x represents the length

In order to determine the value of x, take the following steps:

Multiply both sides of the equation by 2: 88 = x² - 3x

x² - 3x - 88 = 0

Use the factorisation method to find x: (x² + 8x) (-11x - 88x)

x(x + 8) -11(x + 8)

x + 8 = 0

x = -8

x - 11 = 0

x = 11

Width = 11 - 3 = 8

Area of the rectangle = length x width

11 x 8 = 88 square inches.

To learn more about how to determine the area of a triangle, please check: brainly.com/question/9329354

Lois is 3 years older than Oscar. The sum of their ages is no more than 20. Write an inequality that can be used to represent this situation, where x represents Oscar’s age.

Answers

Let Oscar be x years old
Lois is x+3 years old

ATQ

$\n \sf\longmapsto x+x+3\leqslant 20$

$\n \sf\longmapsto 2x+3\leqslant 20$

$\n \sf\longmapsto 2x\leqslant=17$

$\n \sf\longmapsto x\leqslant (17)/(2)$

Answer:

let Oscar's years be x

• Oscar → x

• Lois → (x+3)

${ \rm{x + (x + 3) \leqslant 20}} \n \n { \boxed{ \rm{2x + 3 \leqslant 20}} }$

Yoshi carries a balance on her credit card each month. In May, she decides she wants to use her card to buy a new dishwasher. In which part of the billing cycles charges to the minimum?

Answers

Answer:

When you do not have any past due

Step-by-step explanation:

For a minimum due, monthly payment your credit card company is willing to accept to not mark your account as “past due”. If Yoshi is paying every amount before the due date then she will be charged the least but anywhere in the cycle if the amount is paid beyond the due date, a hefty extra money will be paid.

The population of a city is modeled by the equation P(t) = 256,114e0.25t where t is measured in years. If the city continues to grow at this rate, how many years will it take for the population to reach one million?

Answers

Answer: it take 5.448 years for the population to reach one million.

Step-by-step explanation:

The population of a city is modeled by the equation

P(t) = 256,114e0.25t

where t is measured in years.

For the population to reach 1000000, it means that

1000000 = 256114e0.25t

1000000/256114 = e0.25t

3.9045 = e0.25t

Taking ln of both sides of the equation, it becomes

Ln 3.9045 = Ln e0.25t

1.362 = 0.25t

t = 1.362/0.25

t = 5.448 years

Final answer:

The city's population is modeled by an exponential function and to find when the population will reach one million, we need to solve the equation for t by setting P(t) = 1,000,000. This requires dividing by the initial population, taking the natural logarithm, and then dividing by the growth rate (0.25). The result is the time in years it takes for the city's population to reach one million.

Explanation:

Calculation of Population Growth Time

The city's population growth is modeled by an exponential function, P(t) = 256,114e0.25t. Here, P(t) is the population at time t and 'e' is Euler's number, approximately equal to 2.71828. Your goal is to find when the population reaches one million.

To do this, set P(t) = 1,000,000 and solve for t:

1,000,000 = 256,114e0.25t

You would divide both sides by 256,114 and then take the natural logarithm to isolate t:

t = ln(1,000,000 / 256,114) / 0.25

Use a calculator to solve for 't'. This gives the time in years it takes for the city's population to reach one million people. It's a clear demonstration of how exponential growth operates: as the population increases, it takes less time to add a certain number of individuals.

Learn more about Exponential Population Growth here:

brainly.com/question/39279467

#SPJ11

Given the following scenario, decide if it is a permutation or combination. Then calculate the number of possibilities. (Please write Permutation/Combination ; answer)A committee must choose 4 finalists from 15 candidates. How many ways can the committee choose the four finalists.

Answers

The right answer for the question that is being asked and shown above is that:

There are...
15 * 14 * 13 * 12 ways in order to know the four finalists.
This is equal to 32,760 ways i n order to know the four finalists.

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