Simplify the following expression by expanding and collecting like terms.-(7x + 6) + 3(-5x – 3)Give your answer in the form ax + b.Provide your answer below:

The area of the circular sector is given as:

Given that, radius= 60ft and angle =40 degrees

The solution to the given inequality in interval notation is: -6 ≤ v ≤ 3

In this exercise, you're required to determine all the values of v that simultaneously satisfy given inequality. First of all, we would have to eliminate the fraction on the left-hand side of the inequality by adding using an appropriate lowest common denominator of 3 as follows:

(2 × |4v + 6|)/3 - 2/1 ≤ 10

[(2 × |4v + 6|) - (3)2]/3 ≤ 10

[(2 × |4v + 6|) - 6]/3 ≤ 10

Cross-multiplying, we have:

(2 × |4v + 6|) - 6 ≤ 10 × 3

(2 × |4v + 6|) - 6 ≤ 30

Adding 6 to both sides, we have:

(2 × |4v + 6|) - 6 + 6 ≤ 30 + 6

(2 × |4v + 6|) ≤ 36

Dividing both sides by 2, we have:

(2 × |4v + 6|)/2 ≤ 36/2

|4v + 6| ≤ 18

Evaluating the absolute value function, we have:

4v + 6 ≤ ±18

For the positive interval, we have:

4v ≤ 18 - 6

4v ≤ 12

v ≤ 12/4

v ≤ 3.

For the negative interval, we have:

4v ≥ -18 - 6

4v ≥ -24

v ≥ -24/4

v ≥ -6

Lastly, we would express the solution as an interval notation as follows:

-6 ≤ v ≤ 3

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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

:)

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

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

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.

Answer:

Step-by-step explanation:Perpendicular lines have a slope that is the negative reciprocal of the given line.

For example, if a given line has the slope 3/2, the the perpendicular line would have the slope -2/3.

For the given line: y = 4x - 7, the perpendicular line would have a slope of -1/4

There isn't enough info in the question to determine the y-intercept. Literally, any y-intercept could work and the line would still be perpendicular. Is the line supposed to pass through a certain point?

Your answer would be something like: y = -1/4 x + b

b is the y-intercept...if your question paper is multiple choice, choose the answer with the slope of -1/4. If it's supposed to pass through a certain point (x,y) replace x and y with the values in that point and solve for b to get the y-intercept.

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

Choice A

Is the answer

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:

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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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)

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.

Answer:

oiutwecldvi ufa

Step-by-step explanation:

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.

We need to factor the following polynomial:

We can see that:

And

Then, we can use the following factor rule:

We have that:

Then, we can factor the polynomial as follows:

In summary, we have:

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

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.

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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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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Answer

11 - 8 (5 -2) = -13

Explanation

11 - 8 (5 -2)

To solve this, we will first solve the one in the bracket

11 - 8 (5 -2)

= 11 - 8 (3)

= 11 - 24

= -13

Hope this Helps!!!

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

18480 feet are between her old and new house

The value of probability P(A) is 0.60

The clear tree diagram is added as an attachment

The given parameters from the tree diagram are:

The probability is calculated using the following probability formula

P(A) = P(A and D) + P(A and C)

Substitute the known values in the above equation

P(A) = 0.6 * 0.7 + 0.6 * 0.3

Evaluate the products

P(A) = 0.42 + 0.18

Evaluate the sum

P(A) = 0.60

Hence, the value is 0.60

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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.

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

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 basic knowledge of Trignometry,

We are meant to find sin S , sin R , cos S and cos R:

sin S = opposite / Hypoteuse = 18 / 26

sin R = opposite / Hypotenuse = 16 / 26

cos S = Adjacent / Hypotenuse = 16 / 26

cos R = Adjacent / Hypotenuse = 18 / 26

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