What is the equation of the line that is parallel to the line x = -2 and passes through the point (-5, 4)?
x = -5
x=4
y = -5
y = 4

The simplified expression after factoring numerator and denominator is (x + 7) / x.

We can start by factoring the numerator and denominator of the first fraction:

x^2 - 49 = (x + 7)(x - 7)

The denominator can also be factored using the quadratic formula or by factoring as a product of two binomials:

x^2 - 4x - 21 = (x - 7)(x + 3)

So, the first fraction can be simplified as:

(x + 7)(x - 7)/[(x - 7)(x + 3)]

We can cancel out the (x - 7) factor in the numerator and denominator, leaving:

(x + 7)/(x + 3)

Next, we can simplify the second fraction by canceling out the common factor of (x + 3) in both the numerator and denominator:

(x + 3)/x

Putting it all together, we get:

[(x + 7)/(x + 3)] * [(x + 3)/x] = x + 7 / x

Therefore, the simplified expression is (x + 7) / x.

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____The given question is incorrect, the correct question is given below:

The numerator should be expanded and simplified. The denominator should be either expanded or factored.

Simplify (x^2-49)/(x^2-4x-21)*(x+3)/x

Answer:

slope = [tex]\frac{2}{5}[/tex]

Step-by-step explanation:

calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (0, 0) and (x₂, y₂ ) = (5, 2) ← 2 points on the line

m = [tex]\frac{2-0}{5-0}[/tex] = [tex]\frac{2}{5}[/tex]

Answer: 1583.90

In June it’s 1583.90$

the average daily balance of Elliott's account for the month of June is $902.

calculate the average daily balance for Elliott's account in June. To calculate the average daily balance, we need to determine the balance at the end of each day in June. Starting with a balance of $1223 on June 1st, we can calculate the balance at the end of each day by adding or subtracting the amount of each transaction. The table below shows the daily balances: Day of June - Transaction type - Transaction amount -Balance

1 - Starting balance - 1223 - 1223

5 - Deposit - 615 - 1838

8 - Withdrawal - -632 - 1206

9 - Withdrawal - -120- 1086

10 - 30 - No transactions - 0 1086

The sum of the daily balances is: 01086 × 30 = 32580

The average daily balance is the sum of the daily balances divided by the number of days in June:

average daily balance = 32580 / 30 = 902

Therefore, the average daily balance of Elliott's account for the month of June is $902.

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Answer:

Second string, first fret.

Step-by-step explanation:

Step-by-step explanation:

These points are in (X, Y) form. What you want to do is plug in the X coordinates into the equation and see if it equals the Y coordinate.

Equation: Y = X + 4

Point A: (-1, 3)

(-1) + 4 = 3

Point B: (2, 6)

(2) + 4 = 6

Point C: (-2, -2)

(-2) + 4 = 2

Point D: (2, 4)

(2) + 4 = 6

Only point A and point B equal their Y coordinate, making A and B the only correct answers.

Answer:

8^4

Step-by-step explanation:

8^8 divided by 8^4

Because they have the same base and it is divided, so we just need to take ^8 - ^4 and get the answer

8^4

The average value of the function f(x) = 3x2 + 4x on the interval [-1, 2] is about 4.67.

To find the average value fave of the function f(x) = 3x2 + 4x on the interval [-1, 2], solve the definite integral of f(x) over the interval and then divide by the interval length.

The definite integral of f(x) over the interval [-1, 2] can be calculated as follows:

[tex]∫[-1,2] (3x^2 + 4x) dx = [x^3 + 2x^2] between x = -1 and x = 2 = (23 + 2(22)) - ((-1)^3 + 2(-1)^2) \s= 14[/tex]

The interval length is 2 - (-1) = 3.

As a result, the average value fave of f(x) on the interval [-1, 2] is as follows:

fave =[tex](1/3) * ∫[-1,2] (3x^2 + 4x) dx \s= (1/3) * 14 \s[/tex]= 4.67 (rounded to two decimal places) (rounded to two decimal places)

As a result, the average value of the function f(x) = 3x2 + 4x on the interval [-1, 2] is about 4.67

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.

Answer:

31

Step-by-step explanation:

27.9/0.9 = 31

The point of symmetry on f⁻¹(x) is (4, 6) which is false.

The domain of f(x) is (-∞, 4) which is false.

The graphs of f(x) and f(x) are reflections across the x-axis which is also false.

The range of f⁻¹(x) is (- ∞, ∞) which is true.

Let the function f is given as

y = m(x + a) + c

Then the inverse function of the function f will be given by swapping x with y and y with x.

The function is given below.

f(x) = 5(x - 6)³ + 4

The inverse function of the function f(x) is given as,

x = 5(y - 6)³ + 4

y = ∛[(x - 4) / 5] + 6

f⁻¹(x) = ∛[(x - 4) / 5] + 6

The graph of the function and inverse function is given below.

The point of symmetry on f⁻¹(x) is (4, 6) which is false.

The domain of f(x) is (-∞, 4) which is false.

The graphs of f(x) and f(x) are reflections across the x-axis which is also false.

The range of f⁻¹(x) is (- ∞, ∞) which is true.

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The linear function modeled by the table is given as follows:

y = 2x - 5.

The slope and the intercept are given, respectively, by:

m = 2, b = -5.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

From the table, when x increases by 5, y increases by 10, hence the slope m is given as follows:

m = 10/5

m = 2.

Hence:

y = 2x + b.

When x = 3, y = 1, hence the intercept b is given as follows:

1 = 6 + b

b = -5.

Hence the function is:

y = 2x - 5.

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The quantity of gasoline that must be left in his tank if he wants to complete the trip without stopping is 8.5 gallons of gasoline.

Mathematically, the slope-intercept form of the equation of a straight line is given by this mathematical expression;

y = mx + c

Where:

In this context, an equation that models the situation is given by:

y = mx + c

340 = 28x + 102

28x = 340 - 102

28x = 238

x = 238/28

x = 8.5 gallons of gasoline.

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At the same average speed, it would take Mr Jacobs 3 hours and 12 minutes to cover a distance of 352 km.

To calculate the time it would take Mr Jacobs to cover a distance of 352 km at the same average speed, use the following formula:

Time = (Distance / Average Speed) * 60

Time = (352 km / 220 km/h) * 60

Time = (1.6) * 60

Time = 96 minutes

Time = 1 hour and 36 minutes

Therefore, it would take Mr Jacobs 3 hours and 12 minutes to cover a distance of 352 km at the same average speed.

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The rate at which lemons are being used in cups of lemonade per lemon is 0.83 cups of lemonade per lemon

To find the rate at which lemons are being used in cups of lemonade per lemon, we need to divide the number of cups of lemonade produced by the number of lemons used.

In this case, 5 cups of lemonade are produced from 6 lemons, so the rate at which lemons are being used in cups of lemonade per lemon is:

5 cups of lemonade ÷ 6 lemons = 0.83 cups of lemonade per lemon (rounded to two decimal places)

the rate at which lemons are being used in cups of lemonade per lemon is 0.83 cups of lemonade per lemon

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The appropriate response will be (A). The first equation of motion gives the link between "velocity and time."

Equation: A statement that two variable or integer expressions are equal. In essence, equations are questions, and the motivation for the development of mathematics has been the systematic search for the answers to these questions.

An equation is a mathematical representation of two equal objects, one on each side of a "equals" sign. We can solve challenges in our daily lives with the aid of equations. Most of the time, we look for help with pre algebra to resolve problems in real life. Pre-algebra concepts contain the fundamentals of mathematics.

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The percent error in a measure is given by the formula:

P = 100%*|real value - measure|/real value

Here we know that:

real value = 20.8 cm

measure = 20cm

Replacing that in the formula we will get:

P = 100%*|20.8 cm - 20cm|/20.8cm = 3.8%

That is the percent error.

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Complete question:

Jayden measured a pen to be 20 cm long the actual length of the pen is 20.8 cm, then what is the percentage error?.

The ratio of employees who work in the office to employees who work in the warehouse is 5: 7

A ratio is a comparison of two quantities, and it is expressed as a fraction.

To find the ratio of employees who work in the office to employees who work in the warehouse, we need to first determine the total number of employees. In this case, we add the number of employees in the office (20) to the number of employees in the warehouse (28), which gives us a total of 48 employees.

Next, we can express the ratio of office employees to warehouse employees as a fraction by using the following formula:

Ratio = Quantity of First Term / Quantity of Second Term

In this case, the first term is the number of employees who work in the office (20) and the second term is the number of employees who work in the warehouse (28). So, the ratio of office employees to warehouse employees is:

Ratio = 20 / 28

Simplifying this fraction, we get:

Ratio = 5 / 7

This means that for every 5 employees who work in the office, there are 7 employees who work in the warehouse.

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Answer:

Step-by-step explanation:

i have no idea sorry

Answer:

Ac = 0.833334.

Step-by-step explanation:

SINCE THE QUESTION IS PYTHAGORAS THEOREM.

THE FORMULA IS

[tex] tan = \frac{ |bc| }{ac} [/tex]

From the question tan = 18°

bc = 15

ac= ?

making ac = x

therefore

[tex] tan = \frac{ |bc| }{ |ac| } \\ tan 18 = \frac{15}{x} \\ tan18(x) = x \times \frac{15}{x} \\ tan18x = 15 \\ = \frac{tan18x}{18} = \frac{15}{18} \\ x = 0.8333334[/tex]

therefore x = 0.8333334.

Answer:aaaa

Step-by-step explanation:because

Answer:

k = -6

Step-by-step explanation:

Expand by substituting -6:

(n+5) (n-6) = n^2 + 5n - 6n (-6×5)

Thus, (n+5)(n-6) = n^2 -1n -30

(In a facotrised form for quadratics, the numbers need to add to 'bx', in this case -1, and multiply to form 'c' (-30). So -6×5 = -30 and k= -6)

Answer:

Step-by-step explanation:

Part A
First find the measure of angle C which is 52° due to it being next to angle D

Next add 52 to angle B to get 142

Subtract 142 from 180 to get 38°

Angle A is 38°

Part B

The fourth option is correct

Step-by-step explanation:

Sure, I'd be happy to help!

5 feet 7 inches is equivalent to 170.18 cm.

According to the question, it was revealed that 5% of all automobiles did not pass inspection. Of the next ten automobiles entering the inspection station

a. The probability that none will pass inspection is

P(x = 0) = [tex]^{10}C_{0}(0.05)^{0}(0.95)^{10}[/tex]

P(x = 0) = 0.5987

b. The probability that all will pass inspection is

P(x = 10) = [tex]^{10}C_{0}(0.05)^{10}(0.95)^{0}[/tex]

P(x = 10) = 0.5987

c. The probability that exactly two will not pass inspection is

P(x = 2) = [tex]^{10}C_{2}(0.05)^{2}(0.95)^{8}[/tex]

P(x = 2) = 0.0746

a. The probability that none will pass inspection is 0.001%.

b. The probability that all will pass inspection is 59.87%.

c. The probability that exactly two will not pass inspection is 0.27%.

d. The probability that more than three will not pass inspection is 0.0102.

e. The probability that fewer than two will not pass inspection is 6.48%.

In statistics, probability is the measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, where 0 means that the event is impossible, and 1 means that the event is certain.

In a particular county of our state, it was revealed that 5% of all automobiles did not pass inspection. This means that the probability of an automobile not passing inspection is 0.05, and the probability of an automobile passing inspection is 0.95.

To find the probability of none of the ten automobiles passing inspection, we need to multiply the probability of an automobile not passing inspection by itself ten times since the events are independent. Therefore, the probability of none of the ten automobiles passing inspection is 0.05¹⁰, which is approximately 0.00001 or 0.001%.

To find the probability of all ten automobiles passing inspection, we need to multiply the probability of an automobile passing inspection by itself ten times since the events are independent. Therefore, the probability of all ten automobiles passing inspection is 0.95¹⁰, which is approximately 0.5987 or 59.87%.

To find the probability of exactly two of the ten automobiles not passing inspection, we need to use the binomial distribution formula. The formula is P(X=k) = (n choose k) * p^k * (1-p)^(n-k), where n is the number of trials, k is the number of successes, p is the probability of success, and (n choose k) is the binomial coefficient. Therefore, the probability of exactly two of the ten automobiles not passing inspection is P(X=2) = (10 choose 2) * 0.05² * 0.95⁸, which is approximately 0.0027 or 0.27%.

The complement rule states that the probability of an event occurring is equal to one minus the probability of the event not occurring. Therefore, the probability of more than three of the ten automobiles not passing inspection is 1 - P(X<=3), where P(X<=3) is the probability of three or fewer automobiles not passing inspection.

To find P(X<=3), we can use the binomial distribution formula with k=0,1,2, and 3. Therefore,

P(X<=3) = P(X=0) + P(X=1) + P(X=2) + P(X=3)

=> (10 choose 0) * 0.05⁰ * 0.95¹⁰ + (10 choose 1) * 0.05¹ * 0.95⁹ + (10 choose 2) * 0.05² * 0.95⁸ + (10 choose 3) * 0.05³ * 0.95⁷, which is approximately 0.9898 or 98.98%.

Therefore, the probability of more than three of the ten automobiles not passing inspection is 1 - 0.9898, which is approximately 0.0102.

To find the probability of fewer than two of the ten automobiles not passing inspection, we need to use the complement rule again. The probability of fewer than two automobiles not passing inspection is the same as the probability of one or zero automobiles not passing inspection.

To find the probability of more than two automobiles not passing inspection, we can use the complement rule again:

=> P(X>2) = 1 - P(X<=2) = 1 - (P(X=0) + P(X=1) + P(X=2)) = 1 - [((10 choose 0) * 0.05⁰ * 0.95¹⁰ + (10 choose 1) * 0.05¹ * 0.95⁹ + (10 choose 2) * 0.05² * 0.95⁸]

which is approximately 0.0648 or 6.48%.

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Answer: A and C

Step-by-step explanation:

- Geometric sequences are sequences where there is a constant number being multiplied or divided.

- In A, we are dividing by 2 each time. In C, we are multiplying by 3

each time.

- B is not multiplication or division. Neither is D.

(っ◔◡◔)っ ♥

Hope this helps.

MM4343

The circumference of a circle with a diameter of 11 inches using  π as 22/7 is 34.86 inches.

To find the circumference of a circle, we can use the formula:

C = πd

where C is the circumference, π is a mathematical constant (approximately 22/7), and d is the diameter of the circle.

The diameter of a circle is a straight line that passes through the center of the circle and touches two points on the edge of the circle. In this problem, we are given that the diameter of the circle is 11 inches.

To find the circumference, we can substitute this value for d in the formula:

C = πd = π(11 inches)

We can simplify this by using the approximation π ≈ 3.14 (or more precisely, π ≈ 22/7), to get:

C ≈ (3.14)(11 inches) = 34.54 inches

or

C ≈ (22/7)(11 inches) = 34.86 inches

So the circumference of the circle is approximately 34.54 inches or 34.86 inches, depending on which approximation of π is used.

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Answer:

Step-by-step explanation:

You want to find the number of puzzles solved by each boy if they solved 35 puzzles together, and 1/3 of the number Andy solved is twice the number Dale solved.

Let 'a' and 'd' represent the numbers of puzzles solved by Andy and Dale, respectively. Then ...

  a + d = 35

  1/3a = 2d

Multiplying the second equation by 3, we get an expression for 'a' that can be used in the first equation:

  a = 6d

  6d +d = 35

  d = 35/7 = 5

  a = 6(5) = 30

Andy solved 30 puzzles; Dale solved 5.

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True. A piece-wise function is composed of different functions that are joined together at certain points and each of these functions will either have an x-intercept or a y-intercept.

Yes, a piece-wise function will always have at least one x-intercept or at least one y-intercept. A piece-wise function is composed of different functions that are joined together at certain points. Each of these individual functions can either be linear, quadratic, or any other type of function, and each of these functions will either have an x-intercept or a y-intercept. For example, if a piece-wise function contains two linear equations, each of them will have one x-intercept and one y-intercept. The same is true for quadratic equations, and for any other type of equation. Therefore, since a piece-wise function is composed of these individual functions, it will always have at least one x-intercept or at least one y-intercept.

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If 102 students at least plays one sport and this is 40% of the students at the school, then there 255 students at the school

Let's assume that the total number of students in the school is "x".

40 percentage  of the students at the school play at least one sport. So, the number of students who play at least one sport is 0.4x.

We also know that the number of students who play at least one sport is 102. Therefore, we can write:

0.4x = 102

Move 0.4 to the right hand side of the equation

x = 102 / 0.4

Divide the numbers

x = 255

Therefore, there are 255 students at the school.

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Using the definition of congruent triangles, the missing values are:

x = 35

y = 30°

Given that the two triangles in the image above are congruent, it implies that all its corresponding angles and corresponding side lengths have equal measure.

Therefore, we have:

2x - 10 = x + 25

Solve for x:

2x - x = 10 + 25

x = 35

Plug in the value of x to find the missing angles:

y + 90 + (2x - 10) = 180 [triangle sum theorem]

y + 90 + (2(35) - 10) = 180

y + 90 + 60 = 180

y = 30°

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The function rule for the line that passes through the origin and (-6,-12) is y = 2x.

In mathematics, a function is a rule that assigns to each element in a set a unique output value.

To find a function rule for the line that passes through the origin (0,0) and the point (-6,-12), we first need to determine the slope of the line. The slope of a line represents the rate of change between the x and y coordinates. We can find the slope using the formula:

slope = (y₂ - y₁)/(x₂ - x₁)

where (x₁, y₁) represents the coordinates of the first point, and (x₂, y₂) represents the coordinates of the second point.

Using the given points, we can substitute in the values:

slope = (-12 - 0)/(-6 - 0)

slope = -12/-6

slope = 2

Now that we have the slope, we can use the point-slope form of a linear equation to find the function rule:

y - y₁ = m(x - x₁)

where m is the slope, and (x₁, y₁) represents the coordinates of a point on the line.

Substituting in the values we have so far, we get:

y - 0 = 2(x - 0)

y = 2x

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The fraction of income spent on cleaning is 71/50.

A fraction is represented by the ratio in the form -

{x} : {y} = {x}/{y}

In terms of numbers, we can write -

2 : 3 = 2/3

Given is that 2/5 of the income of a community of neighbors they are used in fuel, 1/8 in electricity, 1/12 in garbage collection, 1/4 in maintenance of the building and the rest is used for cleaning.

Assume the fraction to be {x}. Then, we can write -

2/5 + 1/8 + 1/12 + 1/4 + x = 1

0.4 + 0.125 + 0.083 + 0.25 + x = 1

x = 0.142

x = 142/100

x = 71/50

Therefore, the fraction of income spent on cleaning is 71/50.

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{Question in english -

2/5 of the income of a community of neighbors

they are used in fuel; 1/8 in electricity, 1/12

in garbage collection, 1/4 in maintenance of the

building and the rest is used for cleaning.

What fraction of the income is spent on cleaning?}