Write the equation of the line in slope-intercept form. m=−2 , passes through the point (1,8)

Answer:

9 and -i

Step-by-step explanation:

12-3 + 5i-4i

9 + -i

9-i

Answer:

A) [tex]x=\frac{C-By}{A}[/tex]

Step-by-step explanation:

[tex]Ax+By=C\\Ax=C-By\\x=\frac{C-By}{A}[/tex]

The Inverse of ƒ(x) is given by y = 21x + 7 For the given function, the inverse is y = 21x + 7.

Given,ƒ(x) = 1/3 - 1/21x

To find the inverse of ƒ(x)

We can use the following steps,

Replace ƒ(x) with y, y = 1/3 - 1/21x

Swap x and y, then we get x = 1/3 - 1/21y

Solve for y

We have to isolate y on one side and other terms on the other side,

Add 1/21 y to both sides + 1/21 y = 1/3

Now, Multiply both sides by 21 to get rid of the denominator.21x + y = 7

Then the inverse of ƒ(x) is given by y = 21x + 7 For the given function, the inverse is y = 21x + 7.

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The height of the rectangular recycling bin is 7 ft.

To find the height of the rectangular recycling bin, we can use the formula for the surface area of a rectangular box:

Surface Area = 2lw + 2lh + 2wh

Given:

Length (l) = 16 ft

Width (w) = 9 ft

Surface Area = 638 ft²

Substituting these values into the surface area formula, we have:

638 = 2(16)(9) + 2(16)h + 2(9)h

638 = 288 + 32h + 18h

638 = 288 + 50h

350 = 50h

h = 350 / 50

h = 7

Therefore, the height of the rectangular recycling bin is 7 ft.

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a). Probability (3 balls are all white) = 220/1771 = 0.124

b). Probability of drawing one ball of each color = 336/1771 = 0.19

c). Probability of drawing 3 balls of the same color = 259/1771 = 0.146

(a) Probability of drawing 3 white balls:

Total number of balls = 7 red + 12 white + 4 green = 23 balls

Number of favorable outcomes = selecting 3 white balls = 12C3 = (12!)/(3!(12-3)!) = 220

Total number of possible outcomes = selecting 3 balls from 23 = 23C3 = (23!)/(3!(23-3)!) = 1771

So, Probability of drawing 3 white balls = Number of favorable outcomes / Total number of possible outcomes

P(3 white balls) = 220/1771 = 0.124

b). Probability of drawing one ball of each color:

Number of favorable outcomes = selecting 1 ball of each color = 7C1 × 12C1 × 4C1 = 7 × 12 × 4 = 336

Total number of possible outcomes (as calculated above) = 1771

Probability of drawing one ball of each color = Number of favorable outcomes / Total number of possible outcomes

P(1 ball of each color) = 336/1771 ≈ 0.19

C. Total number of favorable outcomes = 35 + 220 + 4 = 259

Total number of possible outcomes (as calculated above) = 1771

Probability of drawing 3 balls of the same color = Number of favorable outcomes / Total number of possible outcomes

P(3 balls of the same color) = 259/1771 = 0.146

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Answer:  (x² - 5)(x - 7)

Step-by-step explanation:

Grouping the terms, we have:

(x^3 - 7x^2) + (-5x + 35)

Now, let's factor out the common factors from each pair:

x^2(x - 7) - 5(x - 7)

Notice that we have a common factor of (x - 7) in both terms. We can factor it out:

(x^2 - 5)(x - 7)

Therefore, the resulting expression after factoring by grouping is (x^2 - 5)(x - 7).

There exists two solutions to the absolute value function |0.5x + 1| = 5.

The absolute value function in this problem is defined as follows:

|0.5x + 1| = 5.

The first solution is obtained as follows:

0.5x + 1 = -5

0.5x = -6

x = -6/0.5

x = -12.

The second solution is obtained as follows:

0.5x + 1 = 5

0.5x = 4

x = 4/0.5

x = 8.

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Amount received by B can be calculated by solving the equation, Amount received by B = $2750So, the amount B gets is $2750.

The correct option for the given question is B. 2750.Divide $5000 along A, B and C so that A may receive 1/4th much as B and C together and B gets 1/3rd of what A and C received together.

The amount that B gets.

Let's suppose the amount B gets is x.

Now, we can proceed as given below:

Given that the total amount = $5000

Amount received by A = (1/4) * (Amount received by B and C)

Amount received by B = (1/3) * (Amount received by A and C)

Amount received by C = (Amount received by B and A) - (Amount received by B)

Now, we have,Amount received by B + Amount received by C = 3 * Amount received by B/3 + Amount received by A/3

Amount received by A = (1/4) * [Amount received by B + Amount received by C]

Amount received by B = (1/3) * [Amount received by A + Amount received by C]

Amount received by C = [Amount received by B + Amount received by A] - [Amount received by B]

Let's solve this problem in detail: Amount received by A = (1/4) * (Amount received by B + Amount received by C)

Now, Amount received by A = (1/4) * ($5000 - Amount received by A)

By solving the above equation,

Amount received by A = $1000Amount received by B = (1/3) * (Amount received by A + Amount received by C)

Also, Amount received by B + Amount received by C = 3 * Amount received by B/3 + Amount received by A/3

Again, $5000 - Amount received by A = 2 * (Amount received by B + Amount received by C)

By substituting the value of Amount received by A in the above equation,Amount received by B + Amount received by C = $3000

Amount received by B = (1/3) * [Amount received by A + Amount received by C]

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The probability of obtaining exactly 2 frozen rains after defeating 20 Frigid Elements in the video game is approximately 0.2713 or 27.13%.

q = 1 - p

q = 1 - 0.019

q = 0.981

X: The number of successful outcomes.

In this scenario, we can model the situation using a binomial distribution. Let's determine the values of n, p, q, and X:

n: The number of trials or attempts.

In this case, the number of trials is the number of Frigid Elements defeated, which is given as 20.

n = 20

p: The probability of success on a single trial.

The probability of a frozen rain item dropping after defeating a Frigid Element is given as 1.9%, which can be expressed as 0.019.

p = 0.019

q: The probability of failure on a single trial.

The probability of failure is the complement of the probability of success. Therefore:

q = 1 - p

q = 1 - 0.019

q = 0.981

X: The number of successful outcomes.

We want to find the probability of 2 frozen rains dropping, so X is 2.

X = 2

Now that we have determined the values, we can calculate the probability using the binomial distribution formula. The formula for the probability mass function of the binomial distribution is:

P(X = x) = [tex](nCx) * (p^x) * (q^(n-x))[/tex]

where nCx represents the binomial coefficient, which is the number of ways to choose x successes out of n trials.

Using this formula, we can substitute the values into the equation:

P(X = 2) = [tex](20C2) * (0.019^2) * (0.981^(20-2))[/tex]

Calculating the binomial coefficient:

(20C2) = (20!)/(2!(20-2)!)

= (20 * 19 * 18!)/(2 * 18!)

= (20 * 19)/(2 * 1)

= 190

Now substituting the values:

P(X = 2) = [tex]190 * (0.019^2) * (0.981^18)[/tex]

Now we can calculate the probability:

P(X = 2) ≈ 0.2713 or 27.13% (rounded to two decimal places)

Therefore, the probability of obtaining exactly 2 frozen rains after defeating 20 Frigid Elements in the video game is approximately 0.2713 or 27.13%.

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The given sequence does not follow a simple arithmetic or geometric pattern, making it challenging to determine an explicit rule based on the given terms.

To identify the type of sequence and write the explicit rule, we need to examine the pattern of the given sequence: -39, -45, 51, 57, ...

By observing the differences between consecutive terms, we can determine if it follows an arithmetic or geometric pattern.

Arithmetic sequences have a common difference between each term, meaning that by adding (or subtracting) the same value repeatedly, we can generate the sequence. Geometric sequences, on the other hand, have a common ratio between each term, meaning that by multiplying (or dividing) by the same value repeatedly, we can generate the sequence.

Let's calculate the differences between consecutive terms:

-45 - (-39) = -6

51 - (-45) = 96

57 - 51 = 6

From the differences, we can see that the sequence is not arithmetic since the differences are not constant. However, the differences alternate between -6 and 6, indicating a possible geometric pattern.

Let's calculate the ratios between consecutive terms:

-45 / (-39) ≈ 1.1538

51 / (-45) ≈ -1.1333

57 / 51 ≈ 1.1176

The ratios are not constant, indicating that the sequence is neither geometric nor arithmetic.

Therefore, the given sequence does not follow a simple arithmetic or geometric pattern, and it is difficult to determine the explicit rule based on the given terms. It is possible that the sequence follows a more complex pattern or rule that is not apparent from the given terms.

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The values for x and y derived using trigonometric ratios are:

3). x = 3 and y = 3+ √3

4). x = 6 and y = 12

The trigonometric ratios is concerned with the relationship of an angle of a right-angled triangle to ratios of two side lengths.

The basic trigonometric ratios includes;

sine, cosine and tangent.

3). Considering right triangle ADB:

sin45 = x/3√2 {opposite/hypotenuse}

√2/2 = x/3√2

x = (3√2 × √2)/2 {cross multiplication}

x = 3

cos45 = BD/3√2

√2/2 = BD/3√2

BD = 3

Considering that triangle ADC:

tan60 = 3/DC

√3 = 3/DC

DC = √3

y = BD + DC = 3 + √3

y = 15 × tan23 {cross multiplication}

y = 6.3671

cos23 = 15/x {adjacent/hypotenuse}

x = 15/cos23

x = 16.2954

4). Considering right triangle ADB:

sin60 = 3√3/x

√3/2 = 3√3/x

x = 6

cos60 = BD/6

1/2 = BD/6

BD = 3

considering right triangle ADC:

tan30 = 3√3/DC

√3/3 = 3√3/DC

DC = 9

y = 3 + 9 = 12

Therefore, the values for x and y derived using trigonometric ratios are:

3). x = 3 and y = 3+ √3

4). x = 6 and y = 12

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The length of the path is 130 yards

To determine the value of the path, c, we need to know the Pythagorean theorem

Using the Pythagorean theorem which states that the square of the longest leg of a triangle is equal to the sum of the squares of the other two sides of the triangle.

In this case, we have that;

c² = length² + width²

Substitute the values from the information given, we have that;

c² = 50²+ 120²

Find the squares, we get;

c² = 2500 + 14, 400

add the values, we get;

c² = 16900

c = 130 yards

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Answer:

x=7

Step-by-step explanation:

Assuming the angles to be congruent, then 7 and x are both congruent sides, which makes the figure an isosceles triangle. Therefore, x=7 as well.

Slope = 4

y-intercept = -1

Slope-intercept form is one of the most common ways to write a linear equation when graphing.

Slope-intercept Form

Slope-intercept form is written as y = mx + b. In this equation, m is the slope. Slope represents the rate of change of the equation. The slope can also be described as the change in y over the change in x.

Additionally, the b represents the y-intercept. The y-intercept is the y-value where the graph intersects with the y-axis.

Finding Slope and Y-intercept

The equation we are given is y = 4x - 1. This means that the slope is 4. So, the rate of change for the equation is 4 units up per 1 unit right. Additionally, the y-intercept is -1. This means that the function will intersect the y-axis when y = -1. Using this information, we could graph the function if we wanted.

To convert 14 cm² to in² using dimensional analysis, we can use the following conversion factors:

1 cm = 0.393701 in (exact conversion factor)

1 in = 2.54 cm (exact conversion factor)

We want to convert cm² to in², so we need to use the conversion factor that relates cm² to in². This is:

1 cm² = (0.393701 in)² = 0.15500031 in² (approximate conversion factor)

To set up the dimensional analysis, we start with the given quantity and multiply it by the appropriate conversion factors so that the units cancel out and we are left with the desired units. We can set it up as follows:

14 cm² * (0.15500031 in² / 1 cm²) = 2.17000434 in² (approximate answer)

Therefore, 14 cm² is approximately equal to 2.17000434 in².

The values of `a, b,` and `c` correctly complete the division of [tex]$$\frac{1}{5}\div \frac{5}{6}[/tex] = [tex]\frac{6}{25}$$[/tex] is `a-1, b-5, c-8`. The correct option is $\boxed{\textbf{(C)}\ a-1,b-5,c-8}$.

To complete the division in the correct manner, the value of `x, b, and c` is to be calculated.

The given fraction is:

[tex]\frac{1}{5}\div \frac{5}{6}[/tex]

= [tex]\frac{1}{5}\cdot \frac{6}{5}[/tex]

= [tex]\frac{6}{25}$$[/tex]

Therefore, the value of `x` is `6`.

Now, we have the equation `5/6 = 6/bc` that is to be solved for `b` and `c`.

Multiplying both sides of the above equation with `bc`,

we get:

[tex]\frac{5bc}{6} = 6$$[/tex]

Multiplying both sides of the equation by `6/5`, we get:

[tex]bc = \frac{36}{5}$$[/tex]

Therefore, the values of `a, b,` and `c` correctly complete the division of [tex]$$\frac{1}{5}\div \frac{5}{6}[/tex] = [tex]\frac{6}{25}$$[/tex] is `a-1, b-5, c-8`.

Hence, the correct option is $\boxed{\textbf{(C)}\ a-1,b-5,c-8}$.

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The values of a, b and c in the expression are a = 1, b = 1 and c = 6

From the question, we have the following parameters that can be used in our computation:

1/5 * 5/6 = a * b/c

From the above, we have

1/5 * 5/6 = a * b/c

Evaluate the products

1/6 = a * b/c

Rewrite the expression as

1 * 1/6 = a * b/c

By comparison, we have

a = 1, b = 1 and c = 6

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The population to the nearest whole number, the population of bacteria in the culture after 7 hours is approximately 816.

Based on the given formula P = Po *  2[tex]^{(t/d)}[/tex], we can calculate the population of bacteria in the culture after 7 hours.

The initial population (Po) is 350 bacteria, and the doubling time (d) is 6 hours.

Let's substitute the values into the formula and calculate:

P = Po * 2[tex]^{(t/d)}[/tex]

P = 350 * 2[tex]^{(7/6)}[/tex]

Using a calculator or simplifying the exponent manually, we have:

P ≈ 350 * 2[tex]^{(1.1667)}[/tex]

Calculating 2^(1.1667), we get approximately 2.3323.

P ≈ 350 * 2.3323

P ≈ 816.31

Rounding the population to the nearest whole number, the population of bacteria in the culture after 7 hours is approximately 816.

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Answer:

These are two linear equations with two unknowns, P (price of pants) and S (price of socks). You can solve them by using either substitution or elimination methods.

Let's use the elimination method.

First, let's subtract the second equation from the first:

1P + 2S - (1P + 3S) = 60 - 75

After simplifying this, we get:

-1S = -15

Dividing both sides by -1, we find:

S = 15

Now, we can substitute S = 15 into the first equation to find the price of pants (P):

1P + 2(15) = 60

1P + 30 = 60

Subtract 30 from both sides to get:

1P = 60 - 30

1P = 30

So, the price of one pair of pants (P) is $30.

The derivative of f(x) = 6x + 1 at x = 2 is 6, obtained through the limit definition of the derivative.

To find the derivative of f(x) = 6x + 1 at x = 2, we can use the formula for the derivative of a function: f'(x) = lim(h → 0) [f(x + h) - f(x)]/h

We substitute x = 2 into the formula to get: f'(2) = lim(h → 0) [f(2 + h) - f(2)]/h

We plug in f(x) = 6x + 1: f'(2) = lim(h → 0) [(6(2 + h) + 1) - (6(2) + 1)]/h

Simplifying the expression:

f'(2) = lim(h → 0) [(12 + 6h + 1) - (12 + 1)]/h

      = lim(h → 0) (6h)/h = lim(h → 0) 6

The limit of 6 as h approaches 0 is simply 6. Therefore, the derivative of f(x) = 6x + 1 at x = 2 is f'(2) = 6.

The derivative of f(x) = 6x + 1 at x = 2 is 6.

In mathematics, a derivative is the rate at which a function changes in relation to a variable. Calculus and differential equations issues must be solved using derivatives.

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Answer:

x=4

Step-by-step explanation:

angles on a straight line always add up to 180°

so...

25x+20+15x=180°

simplify the left side of the equation

40x+20=180°

take away 20

40x=160°

divide by 40

x=4

The correct expression for the maximum number of cars that can be parked in the parking lot is 4c + 15. Option C

Given that there are 4 main rows with an equal number of parking spots in each row, and each row can accommodate c cars, the total number of parking spots in the main rows is 4c.

Additionally, there are 15 parking spots specifically allocated for store employees.

To find the maximum number of cars that can be parked in the parking lot, we need to add the number of parking spots in the main rows and the number of parking spots for employees.

Expression:

Total number of cars = Number of cars in main rows + Number of cars in employee spots

Number of cars in main rows = 4c

Number of cars in employee spots = 15

Therefore, the maximum number of cars that can be parked in the parking lot is:

Total number of cars = 4c + 15

This expression represents the sum of cars parked in the main rows and the cars parked in the employee spots, giving us the maximum capacity of the parking lot. Option C.

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The functions f and g are:

a. f(x) = 1/x

b. g(x) = x + 2

a) To find two functions f and g such that (fog)(x) = 1/(x + 2), we need to determine how the composition of the two functions f and g produces the given expression.

Let's start by assuming g(x) = x + a, where a is a constant. This means that g(x) adds the constant a to the input x.

Next, let's determine the function f(x) such that (fog)(x) results in the desired expression. We have:

(fog)(x) = f(g(x)) = f(x + a)

b) To simplify the expression 1/(x + 2) and make it match f(g(x)), we can consider f(x) = 1/x.

Substituting the expressions for f(x) and g(x) into (fog)(x), we have:

(fog)(x) = f(g(x)) = f(x + a) = 1/(x + a)

Comparing this with the desired expression 1/(x + 2), we see that a = 2. Therefore, the functions f and g are:

a. f(x) = 1/x

b. g(x) = x + 2

Using these functions, we can verify the composition (fog)(x):

(fog)(x) = f(g(x)) = f(x + 2) = 1/(x + 2)

Thus, (fog)(x) = 1/(x + 2), which matches the desired expression.

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Answer:

45.

Step-by-step explanation:

so every 1/9 lightbulbs are defective, so make that L/400, (L for amount of defective bulbs).

Take the total, 400, and divide it by 9, which equals 44.4444444444. Evaluate 44.4444444444/400 and you get 0.11111111111. Evaluate 1/9, and you get 0.11111111111. So they are equivalent. But you cant have 44.4444444444 lightbulbs defective, because you can't have a lightbulb 40% defective, it either works, or doesn't work. So, round your answer up, and you get 45 total defective lightbulbs if they make 400.

Answer:

Vertical Stretch

Step-by-step explanation:

The parent function [tex]f(x)=|x|[/tex] when multiplied by 2.5 is a vertical stretch of the absolute value equation. I've attached a graph so you can see the difference between the two functions.

a. The relative frequency of landing on the number 4 is 0.24

b. The relative frequency of landing on a prime number is 0.20

Relative frequency is the ratio of the frequency of a particular event in a statistical experiment to the total frequency.

This means to find the relative frequency of a particular outcome of an event, we divide the frequency of the event with the total frequency.

Here, the total frequency is

= 14+9+6+12+4+5

= 50

a. The frequency of 4 is 12

therefore the relative frequency of landing on 4 =

12/50 = 0.24

b. A prime number is a number that can only be divided by itself. Therefore 3 and 5 are the prime numbers in the outcome.

landing on 3 = 6/50 = 0.12

landing on 5 = 4/50 = 0.08

On a prime number = 0.12 + 0.08

= 0.20

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The 8th term of the given Sequence is 26.

A sequence is a list of numbers arranged in a particular order. It can be finite or infinite. The nth term of a sequence is represented by Tn.

It can be found using the formula: Tn = a + (n-1)d, where a is the first term, d is the common difference and n is the number of terms being considered.

If we know any three of the terms, we can use the formula to find the fourth term. Let's consider an example to understand this concept better. Example: Find the 8th term of the sequence 5, 8, 11, 14,...Solution:

We can see that the first term of the sequence is 5. Also, the common difference between the terms is 3. Using the formula Tn = a + (n-1)d, we get:T8 = 5 + (8-1)3T8 = 5 + 21T8 = 26

Therefore, the 8th term of the given sequence is 26.

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Answer: D

Step-by-step explanation: X is being subtracted by 1 so it will now add 1 in the inverse

The terms that do not apply to a rhombus are:

Right angle: A rhombus does not have any right angles. Its angles are typically acute or obtuse, but never right angles.

Perpendicular sides: In a rhombus, the opposite sides are parallel to each other, but they are not perpendicular. Perpendicular sides are characteristic of rectangles and squares.

The terms that do not apply to a rhombus are:

Right angle: A rhombus does not have any right angles. Its angles are typically acute or obtuse, but never right angles.

Perpendicular sides: In a rhombus, the opposite sides are parallel to each other, but they are not perpendicular. Perpendicular sides are characteristic of rectangles and squares.

Congruent angles: While the opposite angles in a rhombus are equal to each other, the adjacent angles are not necessarily congruent. Congruent angles are a characteristic of rectangles and squares.

Right triangle: A rhombus does not contain any right angles, so it cannot be classified as a right triangle. A right triangle is a triangle that has one right angle.

Equilateral: A rhombus is not an equilateral polygon. An equilateral polygon has all sides of equal length, while a rhombus has all sides equal in length but does not require all angles to be equal.

It's important to note that a rhombus is a quadrilateral with opposite sides that are parallel and equal in length, but it does not possess the characteristics mentioned above.

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The statements that are true about the rational equations are options A and C.

[tex]\frac{4}{x + 6} + \frac{1}{x^{2} } = \frac{x+10}{x^{3} +6x^{2} }[/tex]

Note that x ≠ 0, and x ≠ -6

The left side of the equation is equal to

[tex]\frac{4}{x + 6} + \frac{1}{x^{2} } = \frac{4*x^{2} + (x+6)}{(x+6)x^{2} } = \frac{4x^{2} + x + 6 }{x^{3} + 6x^{2} }[/tex]

Since the left side of the equation have the same denominators, their numerators are equal. Hence

4x² + x + 6 = x + 10

then

4x² = 10-6
4x² = 4
x² = 1,

x₁ = 1, and x₂ = -1

Thus, both numbers are the solution of the given problem.

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Full Question:

Although part of your question is missing, you might be referring to this full question:

Which of the following statements are true about the given rational equation?

4/x+6 +1/x²=x+10/x³+6x²

Check all of the boxes that apply.

A. x = 1 is a solution.

B. x = 0 is an extraneous solution.=

C. x = –1 is a solution.

D. x = –6 is an extraneous solution.