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

Answers

Answer 1

Answer:

y = -2x+10

Step-by-step explanation:

Slope-intercept form of the equation for a line is

y = mx+b  where m is the slope and b is the y intercept

We know the slope is -2

y = -2x+b

Substituting the point in for x and y and solving for b.

8 = -2(1) + b

8 = -2+b

10 =b

Now

y = -2x+10

Answer 2

Answer:

y = - 2x + 10

Step-by-step explanation:

The equation of a line in slope-intercept form is given by:

y = m x + c

Here,

m → slope of the line

c →  y-intercept

In this case, the slope (m) is given as -2, and the line passes through the point (1, 8). We can substitute these values into the equation to find the y-intercept (c)

Using the point-slope form of a line, we have:

( y - y₁ ) = m ( x - x₁ )

Substituting the coordinates ( x₁, y₁ ) = ( 1, 8 ), and the slope m = -2:

( y - 8 ) = - 2 ( x - 1 )

Expanding and rearranging the equation:

y - 8 = - 2x + 2

Adding 8 to both sides:

y = - 2x + 10


Related Questions

Select the correct answer.
A department store's customer parking lot has 4 rows with an equal number of parking spots in each row. The lot also has 15 parking spots for store
employees. If c cars can be parked in each of the 4 main rows of the parking lot, what is the expression for the maximum number of cars that can be
parked in the parking lot?
O A. 150-4
OB. 15-4)
OC. 40+15
OD.
4(0+15)

Answers

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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Use the table, along with dimensional analysis to convert the given square unit indicated.
14cm^2 to in^2

Answers

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.

Sara and Steve each bought a pair of pants and some socks .The pants that they purchased cost the exact same amount and the pair of socks are also the same amount.

Sara paid $60 for one pair of pants and two pairs of socks

Steve paid $75 for one pair of pants and three pairs of socks

What was the cost of 1 pair of pants?

Equations

1P+2S=60

1P+3S=75

Answers

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.

46. 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. Find how much B
gets?
A. 1000
C. 1250
B. 2750
D. 2500

Answers

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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State the expression for finding Tn the n th term in the sequence what is the Tn

Answers

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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please, answer! 50 pts!

Answers

Answer:

Slope = 4

y-intercept = -1

Step-by-step explanation:

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.

X intercept (1/4 0)
Y intercept (0,-1)

A garden is designed in the shape of a rhombus formed from 4 identical 30°-60°-90° triangles. The shorter distance across the middle of the garden measures 30 feet.

What is the distance around the perimeter of the garden?

Answers

Answer: 120 ft

Explanation: The length of 30 feet consists of two shorter sides of the triangles. Since we know that the triangles are the same size then one side must be half of the total.

Short side in 30-60-90: 15ft

The outer edges of the rhombus are the hypotenuses of the triangles. In all 30-60-90 the hypotenuse is twice as long as the shortest side.

One edge of rhombus: 30ft

30 x 4 = 120

please help with the questions on the photo

Answers

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

What is relative frequency?

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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What terms do not apply to a rhombus

Answers

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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Instructions: Identify the type of sequence and write the explicit rule. write Explicit Rule Sequence: -39, -45, 51, 57,... Type: Arithmetic e Explicit Rule: ​

Answers

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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What type of transformation takes the graph of f(x)=|x| to the graph of g(x)=2.5|x|?

Answers

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.

Which of the following statements are true about the given rational equation? Check all of the boxes that
apply.
4
1 x+10
+1=
x+622³+62²
Ox=1is a solution.
Ox=0 is a solution.
O x=-1 is a solution.
Ox=-6 is a solution.
DONE

Answers

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

How   is this so?

[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.

A culture of bacteria has an initial population of 350 bacteria and doubles every 6
hours. Using the formula P = Po 22, where Pt is the population after t hours, Po
is the initial population, t is the time in hours and d is the doubling time, what is the
population of bacteria in the culture after 7 hours, to the nearest whole number?
.

Answers

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

How to determine the the population of bacteria in the culture after 7 hours

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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Given the diagram below, find the value for x. Enter a number only.

Answers

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

What is the sum of 12-5i and -3+4i?

Answers

Answer:

9 and -i

Step-by-step explanation:

12-3 + 5i-4i

9 + -i

9-i

Find x and y for the figure below

Answers

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

3). x = 3 and y = 3+ √3

4). x = 6 and y = 12

What is trigonometric ratios?

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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a factory makes lightbulbs. the probability that a bulb is defective is 1/9. if 400 lightbulbs are tested, about how many are expected to be defective

Answers

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.

A recycling bin is in the shape of a rectangular box. Find the height of the box if its length is 16 ​ft, its width is ​9 ft, and its surface area is 638ft^2 ​(In the​ figure h=height, Assume that the given surface area includes that of the top lid of the​ box.)

Answers

The height of the rectangular recycling bin is 7 ft.

How to calculate the height of the box

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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Use the scenario below to determine the correct values of n, p, q and x of the binomial distribution.
Suppose that in a certain video game there is a 1.9% item drop rate of frozen rain after defeating a Frigid Element.
What is the probability that 2 frozen rains will drop if 20 Frigid Elements are defeated?
n=
p=
q=
X =

Answers

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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Solve the formula Ax+ By= C for x.
Solve for x

Answers

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]

How many solutions exist for the absolute value of 1/2x+1=5

Answers

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

How to solve the absolute value function?

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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A bag contains 7 red, 12 white and 4 green balls. Three balls are drawn randomly. What probability that (a) 3 balls are all white (b) 3 balls are one of each color (c) 3 balls are same color​

Answers

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

Therefore:

(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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A new city park will have a path from the southeast corner to the northwest corner. The shape of the park is rectangular. With the information given, determine how many yards long the path will be. The rectangles length is 50 yd and the width is 120 yd

Answers

The length of the path is 130 yards

How to determine the value

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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Which values of a, b, and c correctly complete the division?
1/5 5/6= x b/c

O a-4,b-5,c-8
○a-1,b-8,c-5
O a-1,b-5,c-8
O a-4,b-8,c-5

Answers

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

How to determine the values of a, b and c

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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find two functions f and g

a. f(x) =
b. f(x) =

Answers

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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Factor x3 – 7x2 – 5x + 35 by grouping. What is the resulting expression?

Answers

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).

f(x)=x-1. Find the inverse of f(x).

Answers

Answer: D

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

Find the value of x.

Answers

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.

The answer is 7 because it is an isosceles triangle so the other side is equal.

Find the derivative of f(x) = 6x + 1 at x = 2

Answers

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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Find the inverse of function f.
ƒ(x) = 1/3 - 1/21 x

Answers

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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