A rectangular room is 4 meters longer than it is wide, and its perimeter is 24 meters. Find the dimension of the room.The length is : meters and the width is meters.

The values of k for the different quadratic equation solutions are as follows

a  the equation 2x² - x + 3k = 0 has two distinct real roots

b. the equation 5x² - 2x + (2k − 1) = 0 has equal roots

ci the equation -x² + 3x + (k + 1) = 0 has real roots

d the equation 3kx² - 3x + 2 = 0 has no real solutions

Quadratic equations of the form ax² + bx + c = 0 is solved using the formula

[tex]-b+\frac{\sqrt{b^{2}-4ac } }{2a}[/tex]     OR     [tex]-b-\frac{\sqrt{b^{2}-4ac } }{2a}[/tex]

The equation b² - 4ac is called the discriminant and it is used as follows

To solve the equation and get two real roots: 2x² - x + 3k = 0

substituting the values gives

(-1)² - 4 * 2 * 3k > 0

1 - 24k > 0

1 > 24k

divide through by coefficient of k

k < 1/24

To solve the equation and get equal roots: 5x² - 2x + (2k − 1) = 0

substituting the values gives

(-2)² - 4 * 5 * (2k - 1) = 0

4 - 40k + 20 = 0

-40k = -24

divide through by coefficient of k

k = 3/5

To solve the equation and get real roots  -x² + 3x + (k + 1) = 0

substituting the values gives  

(3)² - 4 * -1 * (k+1) > 0

9 + 4k + 4> 0

4k > -13

divide through by coefficient of k

k > -3.25

To solve the equation and get  no real solutions  3kx² - 3x + 2 = 0

substituting the values gives  

(-3)² - 4 * 3k * 2 < 0

9 - 24k² > 0

9 > 24k²

divide through by coefficient of k²

k² < 24/9

k < ± 1.633

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Answer:

ax² + bx + c = 0 is solved using the formula

Step-by-step explanation:

Recall that:

Since the business has a total revenue of $55,000 and total expenses of $63,000, therefore the net income is:

Answer: Option D.

18480 feet are between her old and new house

Solution

Step 1

Let the number of adult tickets = 3m

The number of child tickets = m

Step 2

Step 3:

Total sales = $706.20

Number of child tickets that were sold that day = 22

In the given equation:

f(x) = 30x+ 10, where x is the number of days

We can see that at the beggining, when x = 0, then f (0) = 30 · 0+ 10 = 10

Then, renting a car costs at least $10, so $10 is the fixed fee

Each day that passes $30 is being multiplicated, then it cost $300 per day.

Then, the equation is expressed by

f(x)= daily rate · x + fixed fee

If the agency doubles the fixed fee, it would be that 2 · $10 = $20

If the agency increases the daily rate by $5, in addition, then $30 + $5 = $35 woul be the cost each day.

Then, with these new costs we reaplce our equation

f(x)= daily rate · x + fixed fee

f(x)= 35 · x + 20

Using the Factor Theorem, the polynomial function with the desired characteristics is given by:

f(x) = -x(x² + 9)(x - 1)(x - 2).

The Factor Theorem states that a polynomial function with roots(also called zeros) [tex]x_1, x_2, \codts, x_n[/tex] is given by the rule presented as follows.

[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]

In which a is the leading coefficient of the polynomial, determining if it is positive(a positive) or negative(a negative), determining the end behavior of the function.

For this function, we have:

The two other roots are free, hence I am going to attribute x = 1 and x = 2, hence the equation is:

f(x) = ax(x² + 9)(x - 1)(x - 2).

The end behavior is that the function increases to the left and decays to the right, meaning that the leading coefficient is negative, hence a possible function is given by:

f(x) = -x(x² + 9)(x - 1)(x - 2).

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The resultant of the subtraction of the equation 8x³ + 2x² - 5x -6 from the equation 9x³ + 3x² - 6x + 4 is x³ + x² - x + 10.

To subtract in mathematics is to take something away from a group or a number of objects.

The group's total number of items decreases or becomes lower when we subtract from it.

As per the given equations,

9x³ + 3x² - 6x + 4 and 8x³ + 2x² - 5x -6

The subtraction of  both equations will be,

⇒ [9x³ + 3x² - 6x + 4] - [8x³ + 2x² - 5x -6 ]

⇒  9x³ + 3x² - 6x + 4 - 8x³ - 2x² + 5x + 6

⇒ 9x³ - 8x³ + 3x² - 2x² - 6x + 5x + 4 + 6

⇒ x³ + x² - x + 10.

Hence "The resultant of the subtraction of the equation 8x³ + 2x² - 5x -6 from the equation 9x³ + 3x² - 6x + 4 is x³ + x² - x + 10".

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Probability that a plant had each type of flower. 0.36 and 0.64

What is Probability?

Probability is a branch of mathematics that quantifies the Probability of an event occurring or the Probability of a statement being true. The probability of an event is a number between 0 and 1, with approximately 0 indicating the improbability of the event and 1 indicating certainty.

Number of white flower plants = 660

Number of purple flower plants = 368

To discover the empirical Probability that a plant had each sort of flower.

Formula

empirical Probability is found by rehashing an test and watching the outcomes.

P(event) = (the number of time the occasion happens) ÷ (add up to number of trial)

Here, Total number of plants = (660+368) = 1028

Now, Probability of white flower plant = = 0.64

And,

Probability of purple flower plant = = 0.36

Hence, The empirical Probability of white flower is 0.64 and the empirical Probability of purple flower is 0.36

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Answer: 5

Step-by-step explanation: add up the numbers to get 30 then divide by 6 (the amount of numbers) to get 5

Answer: 5

Step-by-step explanation:

the mean is the average. add the numbers together then divide by how many addends you have.

2 + 4 + 5 + 6 + 6 + 7 =  30

30/6 = 5

:)

Tracy's Termite Control has a net worth of $750,000.

The assets total $980,235.

Recall that the assets are the sum of liabilities and equity.

For the given case,

Assets = $980,235

Equity = $750,000

Let us substitute these values into the above formula and solve for liabilities

Therefore, the amount of the liabilities is $230,235

The 4th option is the correct answer.

Where the coordinates of a points pedepend on the distance to the origin of the coordinate system and also depend on the angle, the coordinate system is a POLAR coordinate system.

Data:

• p1 = ,the proportion of Republican voters in the first state

• p2 =, the proportion of Republican voters in the second state

• P1 = ,the proportion of Republican voters in the sample from the first state

• P1 = ,the proportion of Republican voters in the sample from the second state

• n = ,sample

Procedure

0. Finding the mean proportions

2. Finding the standard deviation of the difference

To have a greater percentage of republicans in the second state than in the first, the difference should be less than zero. Thus, the value of the difference of the proportion corresponds to zero.

Using the Standard Normal Table, the value of Z previously calculated corresponds to 0.2394.

Therefore, the probability that the survey will show a greater percentage of Republican voters in the second state than in the first state is 0.24.

Answer: C) 0.24

Answer:

XY ≈ 14.32

Step-by-step explanation:

XY² = XZ² + ZY²

XY² = 6² +13²

XY² = 36 + 169

XY² = 205

XY = [tex]\sqrt{205\\[/tex]

XY ≈ 14.32

The equation given is a quadratic equation that has roots -1 and 5.

To solve this problem, we have to find the roots of the quadratic equation and we can simply multiply through and then calculate the roots.

[tex](x+1)(x-5) = x^2 -5x + x - 5\\f(n) = x^2 -4x - 5[/tex]

Let's solve this quadratic equation above.

Using factorization method, we can find the factors of the quadratic equation and simplify.

[tex]x^2 - 4x -5 = 0\\(x+1)(x-5) = 0\\x + 1 = 0\\or \\x - 5 = 0\\x = -1 or x = 5[/tex]

The roots to the equation (x + 1)(x - 5) = 0 are - 1 and 5.

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Answer:

£22

Step-by-step explanation:

x+1/2x=33

1.5x=33

33/1.5=22

The weekly allowance for Yasir last year is £22.

The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.

Given that Yasir received a 50% increase in his allowance this year. He now receives £33 a week.

The weekly allowance for last year will be calculated as,

1.5 x (X) = £33

X = £33 / 1.5

X = £330 / 15

X = £22

Therefore, Yasir's weekly allowance for last year is £22.

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Solution

Problem

A ladder is leaning on a wall that is 6 feet tall. The distance from the bottom of the ladder to the wall is 8 feet wide.

Solution

Therefore, using the Pythagorean Theorem, 6^2 + 8^2 = 36 + 64 = 100. The square root of 100 is 10. The triangle's hypotenuse or the ladder's length is 5 feet.

Answer: 12 minutes

Step-by-step explanation:

Julie needs 6 minutes, when she completes one, she will be at the bgining, Malcolm at half, and Tony with her, therefore you will need to double it.

In order to evaluate this expression, let's calculate the operations in the left side and compare the final value with the value in the right side:

Since the values don't match, so the expression is FALSE.

hello

we're required to write an equation to represent the sequence

-2, 8, -32

first of all, let's identify the first term

first term = -2

common ratio = ?

c

125.625 kilometers per hour

Note:

60 minutes = 1 hour

32 minutes = 32/60 hours

The speed is the distance traveled in 1 hour

Distance = 67 km

Time = 32/60 hours

Speed = Distance / time

From the graph, we can't see any clear asymptote. Also, the arrow at the right tip of the graph tells us that it continues indefinitely, i.e., both the number of years and the population increases indefinitely.

Now, notice that the population increases as the number of years increases.

Therefore, the only true statement is:

As the number of years increases without bound, the population increases without bound.

To begin solving this question, let us represent the unknown number by x.

First

We are told that twice a number is increased by one-third the same number

so, we can represent this as

Next, we are told that the result is 28, thus

The final step will be to simplify the expression

Cross multiply to get x

Hence, the number is 12

FIrst calculate the speed, as follow:

speed = distance/time

distance = 2 1/4 mi = 2.25 mi

time = 3/4 h = 0.75 h

speed = 2.25 mi/0.75 h = 3 mi/h

next, for the distance traveled in 2 1/2 hours, use:

distance = speed x time

time = 21/2 h = 2.5 h

distance = (3 mi/h) x (2.5 h)

distance = 7.5 mi =7 1/2 mi

Hence, you can walk 7 1/2 miles in 2 1/2 hours

there are infintely many solutions. The solution set is {(x, y)| x = 7y - 9} or {(x, y)| 2x - 14y = -18 (option B)

Given:

x = 7y - 9 . . .(1)

2x - 14y = -18 . . . (2)

To find:

the solution of the system of equations

To determine the value of x and y, we will apply the substitution method:

we will substitute for x in equation (2):

2(7y - 9) - 14y = -18

2(7y) + 2(-9) - 14y = -18

14y - 18 - 14y = -18

14y - 14y - 18 = -18

0 - 18 = -18

-18 = -18

The left-hand side of the equation is equal to the right side of the equation.

when this happens, it is called infinitely many solutions.

Hence, there are infintely many solutions. The solution set is {(x, y)| x = 7y - 9} or {(x, y)| 2x - 14y = -18 (option B)

Percent change of people living with the disease = 72.1%

Percent change of number of death = 5.2%

The Number of people living with the disease increased from 22.6 million in 2005 to 38.9 million in 2015

To get the percentage, we will apply the formula:

The number of death increased from 1.9 million to 2 million from 2005 to 2015:

Conclusion:

The number of people living with the disease increased drastically within 10 years.

But the percent change in the number of death isn't as high as the number of people living with the disease. It means the disease is highly infectious but has a low death rate

Answer:

oiutwecldvi ufa

Step-by-step explanation:

Answer:

distance = rate x time

Step-by-step explanation:

distance = ?

rate = 24 m/s

time = (35 x 60) = 2100 s

thus,

distance = 24 x 2100 = 50400 m

Answer:

6x²+17x+12

Step-by-step explanation:

open the bracket

3x(2x+3) 4(2x+3)

6x²+9x+8x+12

6x²+17x+12

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Answer:

6x^2 + 17x + 12

Step-by-step explanation:

first (distribute):

(3x+4)(2x+3)

3x(2x+3) + 4(2x + 3)

then (distribute) again:

3x(2x+3) = 6x^2 + 9x

4(2x + 3) = 8x + 12

then (combine terms):

6x^2 + 9x + 8x + 12

6x^2 + 17x + 12

m²+5mn+5n²

To factor the above, we need two factors of 5n², such the sum gives 5n and the product gives 5n²

No such factors exists, hence the polynomial is prime.