A transversal intersects two lines. Which condition would always make the two lines parallel?

The range of function f(x) = 4x + 5 for given input values is {-3, 1, 5, 9, 13}

The correct answer is an option (C)

In this question, we have been given a function f(x) = 4x + 5

We need to find the range of given function for input {-2, -1, 0, 1 , 2}

We know that the range of  a function is the set of all output values for given input.

for x = -2,

f(-2) = 4(-2) + 5

f(-2) = -3

for x = -1,

f(-1) = 4(-1) + 5

f(-1) = 1

for x = 0,

f(0) = 4(0) + 5

f(0) = 5

for x = 1,

f(1) = 4(1) + 5

f(1) = 9

for x = 2,

f(2) = 4(2) + 5

f(2) = 13

Therefore, the range of function f(x) = 4x + 5 for given input values is {-3, 1, 5, 9, 13}

The correct answer is an option (C)

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The required image of points (-4, 6) is (-6, -4) as per the given condition,

Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

Here,

As the image of the point (5, -1) is mapped as, (1, 5),
Which implies a function that (x, y) mapped as (-y , x)
So for (-4, 6) mapped as (-6, -4)

Thus, the required image of points (-4, 6) is (-6, -4) as per the given condition,

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Answer:

64

Step-by-step explanation:

you need to plug the number in subtract and add then multiply the number from the first pair of parenthesis into the main number and after multiply the second pair into it.

Answer:

4x4x4

Step-by-step explanation:

3x4x5= 60

4x4x4= 64

64 is a higher volume than 60

Answer:

In order to find out which box can hold more, we can find the respective volumes of the boxes.

Volume of first box

= 3 inches × 4 inches × 5 inches

= 60 inches³

Volume of second box

= 4 inches × 4 inches × 4 inches

= 64 inches³

∴Since the second box has a greater volume than the first box, the former can hence hold more than the latter.

The equation of a line perpendicular to -5x + y = 9 that passes through the point (0, -9) is [tex]y = -\frac{1}{5}x -9[/tex]

The equation of the line in slope intercept form can be represented as follows:

y = mx + b

where

Perpendicular lines follows the following rules as follows:

m₁ m₂ = -1

Let's find the slope of -5x + y = 9 .

y = 5x + 9

Hence,

slope = 5

Let's find the slope of the equation of the line that passes through (0, -9) and perpendicular to  -5x + y = 9 .

5m₂ = -1

m₂ = -1 / 5

m₂ = - 1 / 5

Therefore, let's find the y-intercept of the line using (0, -9)

-9 = - 1 / 5(0) + b

b = -9

Therefore, the equation of the line is y = - 1 / 5 x - 9

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The solution is x > -2 and x > 3

x is greater than -2 and x is greater than 3.

This can be represented by the number line Option D.

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal = ≤

Greater than and equal = ≥

We have,

(x + 2) (x - 3)² > 0

This can be written as,

x + 2 > 0 and (x - 3)² > 0

x + 2 > 0

x > -2 _____(1)

(x - 3)² > 0

Squaring both sides.

x - 3 > 0

x > 3 _____(2)

From (1) and (2) we get,

x > -2 and x > 3

Thus,

The solution is x > -2 and x > 3

x is greater than -2 and x is greater than 3.

This can be represented by the number line Option D.

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The equation for the word problem the difference of ten times a number and six is fourteen is (10x-6 = 14) and the value of x is 2.

According to the question,

We have the following information:

The difference of ten times a number and six is fourteen.

Now, let's take the number to be x.

So, we have the following expression:

10x-6 = 14

Now, moving 6 from the left hand side to the right hand side will result in the change of the sign from minus to plus:

10x = 14+6

10x = 20

x = 20/10

x = 2

Hence, the equation for the word problem the difference of ten times a number and six is fourteen is (10x-6 = 14) and the value of x is 2.

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Answer:

[tex]f(x)=-log_{3}(-x)[/tex]

Step-by-step explanation:

Based on the points given on the graph, I would say this is a Log function, reflected across both x- and y-axes.

And given the point (-3, -1), it must be [tex]-log_{3}(-x)[/tex]

Answer:

0.150985

Step-by-step explanation:

You add the two decimals together which gives you 120788.

Then, you move the decimal 4 places which is 12.0788.

Then you divide 12.0788 by 2 which gives you 6.0394.

Finally, you divide 6.0394 by 40 which gives you 0.150985.

Answer:

2x-2y=4 that is the best way u can write it

The value of pH of the coffee is 4.89

pH is a measure of hydrogen ion concentration, a measure of the acidity or alkalinity of a solution

Given:  The formula pH= -log₁₀ C,

where is the concentration of hydronium ions in the solution measured in moles per litre

The concentration(C) of Hydronium ions type of coffee is 1.3 x 10⁻⁵ moles per liter

To calculate the pH, we will substitute the value of the concentration (C) into the given formula:

pH= -log₁₀ C                     (C = 1.3 x 10⁻⁵ moles per liter)

pH = -log₁₀(1.3 x 10⁻⁵) = 4.89

Therefore, the pH of the coffee is 4.89

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Answer:

13 Remainder 44

Step-by-step explanation:

The solution after divide is, 13 and remainder = 44

We have to given that;

954 divided by 70 by using long division and with a remainder.

Now, We can divide as,

⇒ 954 divided by 70

70 ) 954 ( 13

     -70

   ----------

      254

    - 210

     ----------

         44

Therefore, The solution is, 13 and remainder = 44

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Answer:44/52

Step-by-step explanation:There are four aces in a deck of 52 cards, so the probability of not drawing an ace is 44/52 =

By using the dimensional analysis 580 lb = 263.084 kg.

What is dimensional analysis?

Dimensional analysis, which is used in both engineering and science, examines the links between various physical quantities by determining their foundational quantities and units of measurement and then following these dimensions while computations or comparisons are made.

A technique for analysis that, in the absence of sufficient data to establish accurate equations, expresses physical quantities in terms of their fundamental dimensions.

We have to convert 580 lb into kg along with the dimensional analysis.

Since, 1 pound (lb) is equal to 0.45359237 kilograms (kg).

So,

580 lb = (0.4535927) x 580

580 lb = 263.0835746

580 lb = 263.084 kg

Hence, along with the dimensional analysis 580 lb = 263.084 kg.

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The answer that best completes the visual analogy of caliper is the first option (picture attached)

Information given in the question

A polygon of 5 sides

Visual analogy refers to using the power of sight to detect of feel things

A polygon of 5 sides is called pentagon is used to describe the caliper

The movement is forecasted by:

considering these the first option become the best option

The line mark will align where the ? was positioned and the center will not be a dark spot

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The product of 17×7 using the difference of two squares is 119.

= 17×7

=(12+5)(12-5)

=12(12-5)+5(12-5)

=12×12-12×5+5×12-5×5

=12²-5²

=144-25

=119

The difference between two squares is a theorem that tells us if a quadratic equation can be written as a product of two binomials, in which one shows the sum of the square roots and the other one is the difference of the square root.

I hope this answer helps.

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Answer:

Step-by-step explanation:

The answer for this can be an inequality or an interval notation or a graph

* Subtraction of (1) in both sides of the inequality

* Let's call part A: [tex]X+1\geq 3[/tex]

* Let's call part B: [tex]\frac{4}{3} X < -8[/tex]

* Solve part A first:

Do the subtraction of (1) on both sides of the inequality.

X ≥ 3 −1

X ≥ 2

Subtract

* Solve part B now:

Multiply  for 3/4 both sides of the inequality  to eliminate the [tex]\frac{4}{3}[/tex]

[tex]\frac{4}{3} X (\frac{3}{4} < -8 (\frac{3}{4})[/tex])

X < -24/4

X < -6

Answer

Inequality Form:

x < −6 or x ≥ 2

Interval Notation:

( − ∞,−6)∪[2,∞)

In Graph:

See the attach

Considering the five number summary of the data-set, we have that:

a. None of the prices were outliers, as all the prices are within 1.5 IQR of the quartiles.

b. That is not a very low price, as it is above the first quartile, while very low prices have to be 1.5 IQR below the first quartile.

The outliers, considering the five number summary of a data-set, are the values that are more than 1.5 Interquartile Ranges from the quartiles, that is, either:

The interquartile range of a data-set is the difference between the third quartile and the first quartile, hence, for the given data-set:

IQR = Q3 - Q1 = 110 - 30 = 80.

Hence the bounds for outliers are given as follows:

Since the maximum value of 200 is less than 230, there are no outliers in the data-set.

The five number summary is given by the image at the end of the answer.

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The root of the quadratic equation is 2x² + 7x + 6 is x = -2 and x = -3 / 2.

The roots of a quadratic equation are the values of the variable that satisfy the equation. They are also known as the "solutions" or "zeros" of the quadratic equation.

The equation to find the roots, is a quadratic equation.

Hence,

2x² + 7x + 6

2x² + 3x + 4x + 6

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

Hence,

(x + 2)(2x + 3) = 0

Therefore,

x + 2 = 0    or 2x + 3 = 0

x = -2 or x = -3 / 2

The roots of the equation is x = -2 and x = -3 / 2

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The vertex is (-2, 11), then the vertex form of the quadratic is:

f(x) = 5*(x + 2)^2 - 11

A quadratic equation with a leading coefficient a and a vertex (h, k) can be written in vertex form as:

y = a*(x - h)^2 + k

And for a quadratic equation of the form:

y = a*x^2 + b*x + c

The vertex is at:

h = -b/2a

In this case, our equation is:

f(x) =5x^2 + 20x + 9

Then:

h = -20/2*5 = -2

Evaluating in x = -2 we get:

f(-2) = 5*(-2)^2 + 20*-2 + 9

f(-2) = 5*4 - 40 + 9

f(-2) = 20 - 40 + 9 = -20 + 9 = -11

The vertex is (-2, -11), and the leadin coefficient is a = 5, then the vertex form is:

f(x) = 5*(x + 2)^2 - 11

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Answer:

B(a) = a/6 - 9

Step-by-step explanation:

The equation that represents the function B(a) as the length of the side parallel to the base is B(a) = a/6 - 9, as per the area of a trapezoid.

What is the area of a trapezoid?

If the length of two parallel sides of a trapezoid is 'a', 'b' and the height of that trapezoid is 'h', then the area of a trapezoid can be represented as

= [(a + b)h]/2

Given, the base of the trapezoid is 9 and the height of the trapezoid is 12.

Therefore, 'b' is the parallel side of the base.

The given function that represents the area of the trapezoid is:

A(b) = [12(b + 9)]/2

Let, A(b) = a.

Therefore, a =  [12(b + 9)]/2

⇒ 2a = 12(b + 9)

⇒ a = 6(b + 9)

⇒ a = 6b + 54

⇒ 6b = a - 54

⇒ b = (a - 54)/6

⇒ b = a/6 - 9

If we assume the length of the side parallel to the base 'b' = B(a), therefore, the equation will be:

B(a) = a/6 - 9

The given linear equation has only one solution i.e. x = 3/4

What is a linear equation?

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."

A linear equation in one variable has

(a) Only one solution

(b) Two solutions

(c) More than two solutions

(d) No solution

Here,

On solving we have 8x - 6 = 0 or x = 3/4. The above linear equation is only true if x = 3/4 and

Hence, the given linear equation has only one solution i.e. x = 3/4.

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The budget of KT's Restaurant for newspaper advertising for the coming year is $58,533,500

Given,

The length of advertisement of KT's Restaurant in Vidalia Times in week days = 5,000

The length of advertisement of KT's Restaurant in Vidalia Times in Saturdays = 10,000

The cost of daily column = $27.55 per column inch

The cost of Saturdays = $29.35 per column inch

We have to find the budget of KT's Restaurant for newspaper advertising for the coming year;

Here,

There are approximately 53 Saturdays in a year.

So,

365 - 53 = 312

Then,

The budget of advertisement on daily column = 312 × 5000 × 27.55 = $42,978,000

The budget of advertisement on Saturday column = 53 × 10,000 × 29.35 = $1,555,500

Therefore,

The total budget for advertisement = 42,978,000 + 1,555,500 = $58,533,500

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The composition (f - g)(x) has a value of (c) (f - g)(x) = -2√x

The definitions of the functions are given as

f(x) = √4x and g(x) = √16x

Evaluate the square roots in the above equations

This gives

f(x) = 2√x and g(x) = 4√x

To find the composition (f - g)(x), we make use of

(f - g)(x) = f(x) - g(x)

Substitute the known values in the above equation So, we have the following equation

(f - g)(x) = 2√x - 4√x

Evaluate the like terms

This gives

(f - g)(x) = -2√x

Hence, the value of the composition is (c) (f - g)(x) = -2√x

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The range of market return is 15.9% and the mean of market return is 2.94%

Productive Investments Limited provided the returns for Laska stocks for 2017 to 2021.

Year         Laska return

2017         -2.2%

2018          -3.4%

2019         12.5%

2020         -0.8%

2021          8.6%

The range of market return = Highest return - lowest return

= 12.5 - (-3.4)

= 15.9%

mean market return = (-2.2 +(-3.4) + 12.5 +(-0.8) + 8.6)/5

mean market return = 2.94%

Therefore, the range of market return is 15.9% and the mean of market return is 2.94%

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The rate of spray at both times is 40 gallons/hour and it is the same.

What is the rate of change?

How quickly something changes over time is referred to as its rate of change, or ROC. Thus, it is the acceleration or deceleration of changes (i.e., the rate) rather than the magnitude of individual changes.

We have,

spray 20 gallons of water in 1/2 hour.

30 gallons and 3/4 hours (it's not 347 hours).

We simply calculate the rate for one hour:

1/2 hour = 20 gallons

3/4 hours = 30 gallons

Then for 1 hour,

1 hour = 20 * 2 = 40 gallons

1 hour = 30 * 4/3 = 40 gallons

Hence, the rate of spray at both times is 40 gallons/hour and it is the same.

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The area of the rectangle is given by the formula below:

A = 18x^2 - 27x + 7

For a rectangle of width W and length L, the area is given by the formula:

A = W*L

Here we know that the dimensions of a rectangle are 6x-7 and 3x-1, then we can define:

L = 6x - 7

W = 3x - 1

Replacing that in the area formula above we will get:

A = (6x - 7)*(3x - 1)

Now we can expand that product:

A = (6x)*(3x) + (6x)*(-1) + (-7)*(3x) + (-7)*(-1)

A = 18x^2 - 6x - 21x + 7

A = 18x^2 - 27x + 7

That is the formula for the area in terms of x.

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The length of the line segment with endpoints at (0, 3) and  (-6, -5) is 10 units

An equation shows the relationship between two or more numbers and variables.

The distance between two points A(x₁, y₁) and B(x₂, y₂) on the coordinate plane is:

[tex]AB=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}[/tex]

The line segment have endpoints at (0, 3) and  (-6, -5). Hence:

Length = √[(-5-3)² + (-6 - 0)²] = √(8² + 6²) = √100 = 10

The length of the line segment is 10 units

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Answer:

[tex]( \frac{1}{2} )^5 = \frac{1}{32}[/tex]

Step-by-step explanation:

The probability of "not a tail" is 1/2.  The five tosses are independent, so the probability of "not a tail" 5 times in succession is

[tex]\left(\frac{1}{2}\right) \cdot \left(\frac{1}{2}\right) \cdot\left(\frac{1}{2}\right) \cdot\left(\frac{1}{2}\right) \cdot\left(\frac{1}{2}\right)[/tex]