Cynthia Besch wants to buy a rug for a room that is 25 ft wide and 31 ft long. She wants to leave a uniform strip
of floor around the rug. She can afford to buy 567 square feet of carpeting. What dimensions should the rug
have?

The solution for the given system of equations, y = [tex]\frac{-1}{2}[/tex]x + 5 and y = 3x - 2 is (2,4) and the graph is attached below

The system of equations is a set of equations consist the same variables. If the given equation are all linear then, it is the system of linear equation.

To solve such system, it is required to figure out the variable values that can solve all the equations involved in the system.

For the given system of equation the variable value is x.

So,  [tex]\frac{-1}{2}[/tex]x + 5  = 3x - 2

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

7 = x ([tex]\frac{6+1}{2}[/tex]) = [tex]\frac{7x}{2}[/tex]

x = 2

Now apply the obtained value of x in either of the equations:

y = 3x - 2

y = 6 - 2

y = 4

To know more about linear equations visit:

https://brainly.com/question/11897796

#SPJ9

ANSWER

x = 38

EXPLANATION

To solve this equation, first, we have to apply the distributive property of multiplication over addition to eliminate the parenthesis,

Subtract 3x from both sides of the equation,

And add 8 to both sides,

Hence, the solution is x = 38.

The point (4,2) is not in the solution set as it do not satisfy the first inequality 4x+y<2.

To be in the solution set of the system of inequalities the point (4.2) must satisfy both the given linear inequalities.

So, 4x + y < 2

when x = 4, y = 2

4(4) + 2 = 18 which is not less than 2

So, point do not satisfies this linear inequality

Now, for y>-2,

y = 2 which satisfies the inequality

Therefore, we say that the point (4,2) is not in the solution set of the system of inequalities.

Learn more about system of inequalities here https://brainly.com/question/19526736

#SPJ1

Solving an Equation

We are given the equation:

The first step is to multiply the constants by the binomials in parentheses:

This step was correctly done by Jose.

The second step is to 'pass' the 4x from the right side of the equation to the left by adding 4x on both sides:

This step was also correct.

Now we must 'pass' 15 to the right by subtracting 15:

And here we find the first error. Jose subtracted 15-20 instead of 20-15 and erroneously got -5.

Answer: First error in step 3

Part a: The people can arrive in 5040 ways

Part b: In 120 ways, Jim can arrive first and Kim last

Part c: The probability that Jim will arrive first and Kim last is 1/42

People invited to the party: Jim, Eduardo, Larry, Simone, Ian, Dawn, Tyrone, and Kim

Part a:

Since there are 7 people, the number of ways they can arrive is 7*6*5*4*3*2*1 =.5040 ways

Part b:

For Jim to arrive first and Kim last:

The remaining 5 people can arrive in any order so, the number of ways in which they can arrive is 5*4*3*2*1 = 120 ways

Part c:

The probability that Jim will arrive first and Kim last is given by:

Number of ways Jim can arrive first and Kim last/ Total number of ways in which all the people can arrive at the party

= 120/5040 = 1/42

Learn more about probability:

https://brainly.com/question/11234923

#SPJ1

Critical points are the points where the slope of the function is zero thus at θ = 0,π/22,π11,3π/22 ... will be the critical points of function g(θ) = sin²(11θ).

A slope is a tangent or angle at a point and a slope is the intensity of inclination of any geometrical lines.

Slope = Tanx where x will be the angle from the positive x-axis at that point.

As per the given function,g(θ) = sin²(11θ).

The critical points are the points where the slope of the tangent of the function is zero.

The slope of the tangent of a function is the first derivative thus,

g'(θ) = 0 ⇒ 2× 11 sin(11θ)cos(11θ) = 0

Sin(11θ) = 0 ⇒ θ = 0

Cos(11θ) = 0 ⇒ 11θ = π/2

θ = π/22

Since, sinusoidal functions are repeating thus,

Next critical point = π/22 + π/22 = π/11 and so on.

Hence "Critical points are the points where the slope of the function is zero thus at θ = 0,π/22,π11,3π/22 ... will be the critical points of function g(θ) = sin²(11θ)".

To learn more about slopes,

https://brainly.com/question/3605446

#SPJ1

K (5 * 3)

K * 15

15K

The answer is 15K based on the information available. I asked the student twice if he has more details about this exercise but he become unresponsive.

Hope that this is the answer to the actual exercise.

Closing the session.

Answer:

2

Step-by-step explanation:

If you have 1 cookie and someone gives you another cookie you now have 2.

Slope-intercept format is represented by the following expression:

Then to rewrite it, we need to isolate the variable y, using inverse operations to solve equations:

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

18.5

Answer:

18.5

Step-by-step explanation:

PEMDAS (parenthesis, exponents, multiplication, division, addition, subtraction)

(8+7)+(3.5)

(15)+(3.5)

18.5

(b) To determine the year the population will reach 1,200,000, substitute p(t) = 1,200,000 into p(t) above and calculate the value of t

The year when t= 8, given that t=0 in 2014 is the year 2022

(c) the rate of change of the population in the year 2019

Firstly, differentiate p(t) with respect to t

In the year 2019, t = 5

Substitute t=5 into the rate of change above

Answer:

f(x) = x^4

Step-by-step explanation:

h(x) = f(g(x)) = (x - 2)^4

g(x) = x - 2

h(x) = f(g(x)) = (g(x))^4

f(x) = x^4

The order of the numbers from lowest to highest is 4.68 × 10⁻⁶,  8.34 × 10⁻², 1.2  × 10⁷, 3.24 × 10⁹ and  5.48  × 10⁹

The given numbers are expressed in standard form. Standard form is a way of writing numbers as a power 10 e.g 100 = 1 × 10² and 0.01 = 1 × 10⁻².

So converting the numbers back to ordinary numbers will be useful.

To do this, we will multiply or divide the powers of 10 with the decimal numbers.

We will multiply if the power is positive e.g 2.4 x 10² = 2.4 x 100 = 240 and divide if the power is negative  2.4 x 10⁻² = 2.4/100 = 0.024

3.24 × 10⁹  = 3.24 x 1000,000,000 =  3240000000

4.68 × 10⁻⁶ = 4.68 / 1000000 = 0.00000468

5.48  × 10⁹ = 5480000000

8.34 × 10⁻² = 8.34/100 = 0.0834

1.2  × 10⁷ = 12000000

Therefore, arranging from lowest to highest. We have:

4.68 × 10⁻⁶,   8.34 × 10⁻², 1.2  × 10⁷, 3.24 × 10⁹ and  5.48  × 10⁹

To learn more about standard form:

https://brainly.com/question/13517742

#SPJ1

The zeros of the function are x = 3 and x = -3

The equation of the function is given as

f(x) = x(squared) - 9

Rewrite the equation properly

So, we have the following equation

f(x) = x^2 - 9

Express the equation as a difference of two squares

So, we have the following equation

f(x) = (x - 3)(x + 3)

Set the equation to 0

(x - 3)(x + 3) = 0

Split

x - 3 = 0 and x + 3 = 0

Solve for x

x = 3 and x = -3

Hence, the solutions are -3 and 3

Read more about equation zeros at

https://brainly.com/question/14625910

#SPJ1

We want to find the diagonal length of the square given in the question.

Since this shape is a square, all four sides are of equal length. Therefore, each side of the square must be [tex]1[/tex] unit.

Next, we will use the Pythagorean Theorem to find the length of the hypotenuse of a right triangle. This value is also equal to the length of our diagonal. We can find the length of the diagonal using the formula below;

Therefore, the correct answer to our question is the following equality;

Second option should be the answer.

Answer:

11.34 m³

Explanation:

The volume of a right rectangular prism can be calculated as:

So, replacing the height by 3.6 m, the length by 2.1 m, and the width by 1.5m, we get:

Therefore, the volume of the prism is 11.34 m³

If the full-time year-round median salary for U.S. men in 2010 was $42,600. The​ full-time year-round median salary for U.S. men in 2010 was 121% of the​ full-time year-round median salary for U.S. women in 2010.

Using this formula

Median salary percentage = 2010 Median salary in US men / 2010 Median salary in US women

Let plug in the formula

Median salary percentage = $42,500 / $35,000

Median salary percentage = 1.2143 × 100

Median salary percentage = 121.43%

Median salary percentage = 121% (Approximately)

Therefore median salary for men in 2010 was 121% of  median salary for  women in 2010.

Learn more about median salary here:https://brainly.com/question/17429430

#SPJ1

The correct answer is:

Mei statement that the inequality is -9 < -3 is True.

Mei is correct because -9 is to the left of -3 on the number line. ( first option in the picture).

Step 1

There are 18,652 geese on a lake

Required: To round this off to the ten thousand place

Step 2

Hence, we will approximate the thousands and add its value to the ten thousand.

Step 3

The mechanic rounds the weight of the car to the nearest thousand and gets 4000 lb.

Using the rule below;

Therefore,

Therefore,

Solution

Step 1

Two lines are perpendicular if the product of their slope = -1

Step 2

Step 2

Answer:

ez

Step-by-step explanation:

ezz

57 items are correct.

What is an item?

Items are a fundamental component of an OracleAS Portal page. Item types are used to categorize items. Item types determine the contents of an item as well as the information kept about it. Users with the necessary permissions can add an item or create an item type. The properties of an object type define the information stored about it. The item types that you can add to a page differ depending on whatever item types the page group administrator has included in the page group. If the built-in item types are insufficiently flexible, users with proper access can develop new custom item kinds to fulfill their needs.

1/5 of 60 items = 60/5 = 12 items

3/4 of 12 items = 12x3/4 = 9 items

Total no. of correct items = 60 - 12 + 9 = 57 items

To know more about items, click on the link

https://brainly.com/question/11408596

#SPJ9

The value of height (h) will be 1.35 inches.

What is Surface area?

The space occupied by a plat surface is called Surface area.

Given that;

Surface area (S) = 2πr² + 2πrh

Where, r is the base radius and h is the height.

Now, When Surface area = 175 square inches

Radius (r) = 6 inches.

Then, We can calculate height as;

Since,

Surface area (S) = 2πr² + 2πrh

175 = 2 × 3.14 × (6)² + 2 × 3.14 × 6 h

175 = 226.08 + 37.68h

175 - 226.08 = 37.68 h

- 51.08 = 37.68 h

h = - 51.08 / 37.68

h = - 1.35

Thus, The value of height (h) will be 1.35 inches.

Learn more about the surface area visit:

https://brainly.com/question/20771646

#SPJ1

The volume of the silo with given height and diameter is 4374π ft or 13734.36 ft. (approximately).

What is volume?

Volume is a measurement of 3-D space that is occupied. Numerous imperial units or SI-derived units, such as the cubic meter and liter, are frequently used to quantify it numerically (such as the gallon, quart, cubic inch). Volume and length (cubed) have a symbiotic relationship. The volume of a container is typically thought of as its capacity, not as the amount of space it takes up.

Given in the question,

The diameter of the cylindrical silo is 18 ft,

and its height is 54 ft.

Volume of a cylinder can be calculated using the formula:

[tex]V = \pi r^2 h[/tex]

Here, V = volume, r = radius, h = height,

We know that, radius is half of diameter. So, radius = 18/2 = 9 ft

Putting the given value in the formula:

[tex]V = \pi 9^2 \times 54[/tex]

[tex]V = \pi \times 81 \times 54[/tex]

V = 4374π ft.

Putting the value of π as 3.14 (approximately)

So, volume of the silo becomes 13734.36 ft.

To know more about volume, go to link

https://brainly.com/question/9554871

#SPJ9

In any equation in math, the most basic thing is the the fact that both expressions on either side of the equality sign are of the same value. This means -35 and 5b (in number 1) are of the same value. Therefore, whatever you do to the one on the left, you must likewise do to the one on the right. That is, if you have to add 10 to the one on the left, you must simultaneously add 10 to the one on the right. Hence, number 1 is solved as follows;

(1) -35 = 5b

To eliminate the 5 and isolate the b variable, divide both sides by 5

-35/5 = 5b/5

- 7 = b

(2) x - 6 = - 26

Add 6 to both sides of the equation;

x - 6 + 6 = - 26 + 6

x = - 20

(3) 130 = 13b

Divide both sides of the equation by 13

130/13 = 13b/13

10 = b

(4) 19 = 16 + m

Subtract 16 from both sides of the equation

19 - 16 = 16 - 16 + m

3 = m

(5) a + 15 = 11

Subtract 15 from both sides of the equation

a + 15 - 15 = 11 - 15

a = - 4

(6) p - 8 = - 8

Add 8 to both sides of the equation

p - 8 + 8 = - 8 + 8

p = 0

(7) - 17 + x = - 24

Add 17 to both sides of the equation

- 17 + 17 + x = - 24 + 17

x = - 7

(8) 4 + n = 13

Subtract 4 from both sides of the equation

4 - 4 + n = 13 - 4

n = 9

(9) - 3x = 0

Divide both sides of the equation by - 3

- 3x/-3 = 0/-3

x = 0

(10) 0.6 = m - 0.8

Add 0.8 to both sides of the equation

0.6 + 0.8 = m - 0.8 + 0.8

1.4 = m

(11) x - 5.3 = 1.27

Add 5.3 to both sides of the equation

x - 5.3 + 5.3 = 1.27 + 5.3

x = 6.57

To determine if a function is even or odd, we start from its definition.

While for an EVEN FUNCTION we have: F(x) = F(-X), for an ODD FUNCTION we have F(-X) = -F(X)

Now, from this, we can check that all the values the function achiever for any X value, the -X has same height. The function presents a symmetry over the Y-axis, and this implies in a function to be an EVEN FUNCTION.

And from the solution developed above, the only statement that is true is the

C) The function is an even function.

Answer: i believe its 0.46 im not for sure though

Step-by-step explanation:

Inequalities

Solve:

For a better understanding, we first multiply the inequality by -1. Recall by doing so, the sign must be flipped:

Factor the binomial:

We have a product of two variable expressions and it must be positive or zero. That can only be possible if:

* Both factors are positive or zero

* Both factors are negative or zero

The answer can come from any of the conditions stated above, so the solution is the OR combination of the individual solutions.

The first condition states:

x - 4 ≥ 0 AND x + 4 ≥ 0

This leads to the solution:

x ≥ 4 AND x ≥ -4

If x must be greater or equal to 4 and greater or equal to -4, then the AND combination gives the solution: x ≥ 4

The second condition states:

x - 4 ≤ 0 AND x + 4 ≤ 0

This leads to:

x ≤ 4 AND x ≤ -4

The AND combination gives the second solution x ≤ -4

The final solution is the first solution OR the second solution, that is:

x ≤ -4 or x ≥ 4

Representing the solution in the number line, we get the graph below:

Expressed in interval form: (-∞ , -4] U [4, +∞)

Given

To find the interval.

Explanation:

It is given that,

That implies,

a) The interval notation is, (-7,-5).

b) The interval notation is, [-6,6].

c) The interval notation is, (-7,-1).

d) The interval notation is, [5,7].

e) The interval notation is, [-2,-1).