Which graph represents a linear function

If after the second hour, the increase in ticket sales every hour was 20 more than the increase of the previous hour, it will take 12 hours to sell 10,000 tickets for the Boulders concert.

To solve this problem, we need to find the number of hours it will take to sell 10,000 tickets for the concert. We are given the number of tickets sold in the first three hours and the rate at which ticket sales increase each hour after the second hour.

Let's denote the number of tickets sold in the fourth hour by "x". Then, the number of tickets sold in the fifth hour will be "x + 20", and the number of tickets sold in the sixth hour will be "x + 40", and so on.

Using this information, we can set up an equation to find "x":

500 + 560 + x + (x + 20) + (x + 40) + ... = 10,000

Simplifying the equation, we get:

3x + 1020 + 20n = 9500

where "n" is the number of hours after the third hour.

Solving for "n", we get:

n = (10,000 - 1020 - 3x) / 20

Now, we need to find the value of "x" that satisfies this equation. We can do this by testing different values of "x" until we find the one that gives an integer value for "n".

Let's start by trying "x = 640 + 20 = 660". Plugging this value into the equation, we get:

n = (10,000 - 1020 - 3(660)) / 20 = 9

We arrived at this solution by using the given information about the rate of increase in ticket sales and setting up an equation to solve for the number of hours it will take to sell 10,000 tickets. We then tested different values of "x" until we found the one that satisfied the equation and gave an integer value for "n".

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Answer:

Step-by-step explanation:

To calculate the final account balance for a savings account with an initial deposit of $5,460.75, compounded semiannually with an interest rate of 3.92%, for 51 months, we need to use the formula:

A = P * (1 + r/n)^(nt)

where A is the final account balance, P is the initial deposit, r is the interest rate (as a decimal), n is the number of times the interest is compounded in a year, t is the number of years, and nt is the number of compounding periods.

In this case, n = 2 (since the interest is compounded semiannually), r = 3.92%/100 = 0.0392, t = 51 months / 12 months/year = 4.25 years, and nt = 2 * 4.25 = 8.5.

Substituting the values into the formula, we get:

A = $5,460.75 * (1 + 0.0392/2) ^ (8.5)

A = $5,460.75 * 1.0196^8.5

A = $5,460.75 * 1.2408

A = $6790.32

So, the final account balance if the initial deposit is invested with interest compounded semiannually is $6790.32.

B) Comparing the final account balance of the simple interest account and the compound interest account, we can see that the compound interest account yields a higher balance ($6790.32) than the simple interest account ($6370.51). This is because compounding interest allows for the interest earned in one period to be reinvested, so the interest earns interest in future periods, which increases the overall amount of interest earned over time. In contrast, simple interest is calculated only on the initial deposit, so the amount of interest earned remains constant over time.

Using the value of principal, annual rate and time, the simple interest is $375

Simple interest is a method of calculating the interest charge on a loan or deposit. It is based on the principle of earning interest only on the initial amount (principal) that was borrowed or deposited.

The formula for simple interest is:

I = P * r * t

where:

I is the interest amount

P is the principal amount

r is the interest rate (expressed as a decimal)

t is the time period (in years)

In the given problem, we can calculate the simple interest by substituting the values into the formula

A = P(1 + rt)

A = 250(1 + 0.05(10))

A = 375

The simple interest is $375

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Given parallelogram points are (4,3),(-4 3), and (2, -3).

Let's say A= (4,3) , B=(-4 3) ,C=(2, -3) and D=(x, y)

Parallelogram defined as opposite sides are equal and parallel to each other.

From the properties of parallelogram :

We can say diagonals bisect each other.

From this we can easily find 4th point of parallelogram by using mid point concept.

Mid point formula

 (X,Y)=[tex](\frac{x_{1} +x_{2}}{2},\frac{y_{1} +y_{2}}{2})[/tex]

Find mid point between AC line

midpoint (X,Y)= [tex](\frac{4 +2}{2},\frac{3-3}{2})[/tex]

                (X,Y)=[tex](\frac{6}{2},\frac{0}{2})[/tex]

                 (X,Y)=(3,0)

Find mid point between BD Line

Mid point (X,Y)= [tex](\frac{-4 +x}{2},\frac{3+y}{2})[/tex]

Mid point of AC and BD are equal to each other

(3,0)=[tex](\frac{-4 +x}{2},\frac{3+y}{2})[/tex]

Equate x-coordinate and y-coordinate.

[tex]3=(\frac{-4 +x}{2})[/tex]        and      [tex]0=(\frac{3+y}{2})[/tex]

6=-4+x             and       0=3+y

x=10                 and        y=-3

Therefore ,the coordinates of the 4th point is D(x, y)=(10,-3)

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The coordinates of the fourth point that would complete the parallelogram are (10, -3).

A parallelogram is defined as a special type of quadrilateral that has both pairs of opposite sides parallel and equal.

We know A, B, and C, where A = (4, 3), B = (-4, 3), and C = (2, -3).

To determine the fourth point, which represents D.

First, we need to find the vector representing side AB.

Subtracting the coordinates of point B from the coordinates of point A. So:

AB = A - B = (4, 3) - (-4, 3) = (8, 0)

Next, we need to find a point that is on the line that is parallel to AB and passes through point C.

The vector CD (where D is the point) is equal to AB. So:

CD = AB = (8, 0)

We know that C = (2, -3),

We can start by adding CD to C to get D:

D = C + CD = (2, -3) + (8, 0) = (10, -3)

Therefore, the coordinates of the fourth point are (10, -3).

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The value of function f(5) is 8.

A function is defined as a relation between a set of inputs having one output each. A function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range. A function is generally denoted by f(x) where x is the input.

The general representation of a function is y = f(x).

Injective function or One to one function: When there is mapping for a range for each domain between two sets.

Surjective Function or Onto function: When there is more than one element mapped from domain to range.

Polynomial function: The function which consists of polynomials

Inverse function: The function which can invert another function.

Given:

x with entries -4, -1, 3 and 5.

f(-4) = 2

f(-1) = 5

f(3) = 4

f(5) = 8

The value of f(5) is 8.

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Answer: f(5) is -8

Step-by-step explanation:

took the quiz

Answer:

Step-by-step explanation:

Method 1: Counting the number of committees with exactly one engineer:

There are 2 ways to choose the engineer, and 10 ways to choose the remaining 9 computer scientists. Hence, there are 2 * 10 = 20 different committees with exactly one engineer.

Method 2: Using the combinations formula:

There are 12 people in total, and we need to choose 10 of them for the committee. We can use the combinations formula to calculate the number of different ways to choose 10 people from 12: C(12, 10) = (12!) / (10! * (12-10)!) = (12!) / (10! * 2!) = 66.

So, there are 66 different ways to create a committee of 10 people with at least one engineer represented.

Answer:

The common factor of all the terms of the polynomial 16x² - 14x is:

2x

Step-by-step explanation:

We are given a polynomial:

16x²-14x

We have to find the common factor of all terms.

First we factorize each term separately and then see the common factor.

16x²=2×2×2×2×x×x

14x=2×7×x

We observe that the common factor is:

2x

Hence,  the common factor of all the terms of the polynomial 16x² - 14x is:

2x

Answer:

2x

Step-by-step explanation:

16 = 2^4

14 = 2 × 7

Common factor of 16 and 14 is 2.

x² = x × x

x = x

Common factor of x² and x is x

The common factor of the two terms is 2x.

The conclusion that can be drawn about the number of trials and the probability is A. The experimental probability is closer to the theoretical probability for group Y than X.

The theoretical probability for picking a heads or tails is 50 % as there are only two outcomes of heads and tails.

The experimental probability for heads is 53 % in Group Y and 47 % for tails. This is close enough to the 50 % theoretical probability.

For group X, the experimental probability for heads for Group x is :

= 33 / 50

= 66 %

This is too far from the theoretical probability.

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Answer:

Step-by-step explanation:

Find common denominator.

1/x + x-1/9x = 1  => 9/9x + x-1/9x = 1  (The common denominator is 9x.)

Combine like terms.

9 + x - 1 / 9x = 1  =>  x + 8/ 9x = 1

Cancel out 9x from denominator. What you do to one side, you do to the other.

(9x)(x + 8/9x) = 1(9x)  =>  x + 8 = 9x

Solve for x.

8 = 8x  =>  x = 1  (subtract x from both sides at the beginning and then simplify.)

The Area of Rhombus is 97.5 cm².

The area of a rhombus is equal to half the product of the lengths of the diagonals. The formula to calculate the area of a rhombus using diagonals is given as, Area = (a × b )/2 where, a and b are the diagonals of the rhombus.

Given:

As, diagonals of rhombus bisect perpendicularly.

so, In triangle OAD using Pythagoras theorem

AD² = OD² + OA²

10² = 7.8² + OD²

OD= 6.25 cm

So, length of BD = 2 x 6.25 = 12.5 cm

Now, area of Rhombus = 1/2 x a x b

                                       = 1/2 x 15.6 x 12.5

                                       = 97.5 cm².

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The expression simplifies to 1, which means that 100,000 • 1/100,000 is equal to 1.

The exponential expression that is equivalent to 100,000 • 1/100,000 is:

[tex](10^5) * (10^-5)[/tex]

To simplify this expression using addition or multiplication on the powers, we can use the property of exponents that states:

[tex]a^m *a^n = a^{(m+n)[/tex]

This means that when we multiply two numbers with the same base, we can add their exponents to simplify the expression. However, this property does not work for division, as we need to subtract the exponents instead.

Using this property, we can simplify the expression as follows:

[tex](10^5) * (10^-5) = 10^{(5-5)} = 10^0 = 1[/tex]

Therefore, the expression simplifies to 1, which means that 100,000 • 1/100,000 is equal to 1. We can see that in this case, addition and multiplication do not help us simplify the expression, but we can use the exponent property to do so.

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If number of pencils are triple the number of pens, then the number of pens is 30

Total number of pens and pencils = 120

Number of pencil is triple the number of pens

Consider the number of pens as x

Number of pencils = 3x

Sum of the pens and pencils = 120

Then the equation will be

Number of pens +  Number of pencils = Sum of number of pens and pencils

Substitute the values in the equation

x + 3x = 120

Add the like terms

(1 + 3)x = 120

4x = 120

Move 4 to the right hand side of the equation

x = 120 / 4

x = 30

Therefore, the number of pens is 30

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Answer:

Both have the same median but set A has a larger mean.

Step-by-step explanation:

You're welcome.

The statement must be true are A, B and D.

Two triangles are said to be congruent if the length of the sides is equal, a measure of the angles are equal and they can be superimposed.

We are Given that Triangle DKL is congruent to Triangle PVX

We know that when two triangles are congruent then Acc. to CPCT [ Corresponding Parts of Congruent Triangle]

the corresponding parts are also congruent keeping in mind the vertices and the segments are in same comparison as given in the congruent triangles.

(a) Triangle LKD is congruent to Triangle XVP.

(b) Triangle VPX is congruent to Triangle KDL.

(c) Triangle VPX is not congruent to Triangle DLK as according to CPCT, V vertex is not congruent to D, P vertex is not congruent to L and X vertex is not congruent to K.

(d) Angle D is congruent to angle P.

(e) Thus Segment DL is not congruent to Segment PV ( as according to CPCT, Segment DL is congruent to PX and not PV.)

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The solution is, Option A. Line X

A straight line is an endless one-dimensional figure that has no width. It is a combination of endless points joined both sides of a point and has no curve.

here, we have,

We have to identify the line which represents the function f(x) = 3x - 5

The given equation is y = 3x -5, in which slope of the line should be 3 and y- intercept is -5.

In these lines line x is having y-intercept as -5.

Line x passes through (1, 2) and (0, -5)

So slope of the given line will be = y2 - y1/ x2 - x1

= -5-2/ 0-1

= 3

Therefore, option A : Line X is the answer.

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Two paintings in an art display have shapes that are similar figures. the similarity ratio is 9:7 and the perimeter of the smaller painting is 6 meters therefore the perimeter of the larger painting to the nearest tenth is 7.7 meters.

This is referred to as the total distance around a two-dimensional shape.

Perimeter of the smaller painting is 6 meters and similarity ratio is 9:7

9 = x

7 = 6

7x = 54

x = 54/7 = 7.7 meters.

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Answer:

350 calories

Step-by-step explanation:

see the attachment.

Calories in one cheeseburgers = 135

And, Calories in one medium fries = 583

We have to given that,

At McDonald's four cheeseburgers and three medium fries have a total of 2290 calories.

And, Six cheeseburgers and two medium fries have 2560 calories.

Let us assume that,

Calories in one cheeseburgers = x

And, Calories in one medium fries = y

Hence, We get;

4x + 3y = 2290  . (i)

6x + 3y = 2560 .. (ii)

From (i);

3y = 2290 - 4x

Substitute above value in (ii);

6x + (2290 - 4x) = 2560

6x - 4x + 2290 = 2560

2x = 2560 - 2290

2x = 270

x = 270 / 2

x = 135

From (ii);

6 x 135 + 3y = 2560

810 + 3y = 2560

3y = 2560 - 810

3y = 1750

y = 1750/3

y = 583

Therefore, Calories in one cheeseburgers = 135

And, Calories in one medium fries = 583

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Answer:

j≥19

hope this helpss :))

The required measure of x is given in each triangle are given as,
2. x = 74.01     3.   25.09      4.  x = 23.78
5. x = 26.64    6. x = 21.03°  7. x = 39.55°

If you know the lengths of two sides of a right triangle, you can use trigonometric ratios to calculate the measures of one (or both) of the acute angles.

Here,
2.
For the given triangle
Apply the trigonometric ratios,

Tan 62 = x/25
x = 25 tan62
x = 74.01

Similarly,
3. x = 11/sin26  = 25.09
4. x = 32sin48 = 23.78
5. x = 29/cos12 = 29.64
6. cosx = 14/15 = 21.03°
7. tanx = 19/23 = 39.55°

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Answer: 49.5 dollars

Step-by-step explanation: the original price is 330, but the sale takes 15 percent off

so we turn 15% into a decimal so we can multiply 330 and 15%

we get 0.15 × 330 = 49.5

Answer:

I don't understand French

Step-by-step explanation:

Answer: X=2

Step-by-step explanation:

X times 2

1 x 2 = 2

3 x 2 = 6

6 x 2 =12

9 x 2 = 18

The graph of the linear inequality  [tex]y\geq -3x+4[/tex] is given below.

What is linear inequality?

The expressions that compare two linear expressions using inequality symbols are referred to as linear inequalities. A linear inequality, which is an inequality including at least one linear algebraic expression, is when a polynomial of degree 1 is compared to another algebraic expression of a degree less than or equal to 1. There are numerous ways to depict various kinds of linear inequalities.

Given linear inequality is [tex]y\geq -3x+4[/tex] for which y region will be in the positive range.

Hence, the graph of the given linear inequality is given below.

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5.4%   is the percent error .

What is the formula for errors?

The difference between the estimated value and the actual value in relation to the actual value is given as a percentage and is known as the percent error.

                             The relative error is multiplied by 100 to calculate the % error, in other words. The absolute value of the difference between the measured value and the actual value is divided by the actual value, then multiplied by 100 to get the percent error. 

 = 500 - 473/500  * 100

 =   27/500 * 100

 =   5.4%

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The measure of angle D is 90 degrees

The sum of the interior angle of a parallelogram is equivalent to 360 degrees

From the information given, the measure of the angles are;

17x + 5, 13x + 7 + 118 and 80

Equate the angles to the sum of interior angles

17x + 5 + 13x + 7 + 118 + 80 = 360

collect the like terms, we get;

30x = 360 - 210

substract the like terms

30x = 150

Make x the subject

x = 5

Hence, the angle is 90 degrees

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The measure for the angle m∠D of the quadrilateral CDEF is equal to 90°

For any quadrilateral, the sum of its four interior angles is equal to 360°, hence we shall calculate for the angle m∠D by first finding the value of x as follows:

17x + 5 + 13x + 7 + 118° + 80° = 360°

30x + 210° = 360°

30x = 360° - 210° {subtract 210° from both sides}

30x = 150°

x = 150°/30

x = 5

m∠D = 17(5) + 5 = 90°

Therefore, the measure for the angle m∠D of the quadrilateral CDEF is equal to 90°.

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Answer:

  (b)  area = 29 units²

Step-by-step explanation:

You want the area of the irregular shape shown in the figure.

The area of a rectangular shape is the product of its length and width:

  A = LW

The given shape can be considered to be a 6 unit square with some pieces removed. The area of the remaining shape is the area of that square less the areas of the removed pieces.

The piece removed from the upper left corner is a 2-unit square. Its area is ...

  A = (2 units)(2 units) = 4 units²

The piece removed from the lower right side is 3 units by 1 unit, so its area is ...

  A = (3 units)(1 units) = 3 units²

The area of the square before those pieces were removed was ...

  A = (6 units)(6 units) = 36 units²

Then the area of the remaining shape after the pieces are removed is ...

  Area = 36 units² -4 units² -3 units² = (36 -7) units² = 29 units²

The area of the figure is 29 units².

__

Additional comment

Quite often, the area of an irregular shape is more easily found by subtracting missing areas than by dividing up the existing shape into pieces whose area formulas you know.

The second attachment shows division of the area into smaller rectangles. Working clockwise from upper left, their areas are 1×2, 3×4, 3×1, 3×4, for a total of 2+12+3+12 = 29 square units.

Rachel's Coffee Shop used 33 pounds of type A coffee at a cost of $4.20 per pound, and four times as many pounds of type B coffee at a cost of $5.50 per pound, to create a blend costing a total of $864.60.

Let's use the variable "x" to represent the number of pounds of type A coffee used in the blend.

The amount of type B coffee used in the mix was four times that of type A, therefore we can write:

number of pounds of type B coffee = 4x

The total cost of the blend is given as $864.60, so we can write an equation based on the cost:

[tex]4.2x + 5.5(4x) = 864.60[/tex]

Simplifying and solving for x, we get:

[tex]4.2x + 22x = 864.60[/tex]

[tex]26.2x = 864.60[/tex]

[tex]x = 33[/tex]

As a result, the mix contained 33 pounds of type A coffee.

To check our answer, we can substitute x = 33 into the equation we used to solve for it and verify that the total cost is indeed $864.60.

[tex]4.2(33) + 5.5(4*33)[/tex]

= [tex]138.6 + 726.0[/tex]

= [tex]864.6[/tex]

The total cost matches, so our answer is correct.

Therefore, Rachel's Coffee Shop used 33 pounds of type A coffee in the blend.

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The complete question is:

A blend made by Rachel's Coffee Shop combines two different kinds of coffee. Rachel pays $4.20 per pound for type A coffee and $5.50 for type B coffee. This month's blend cost $864.60 and included four pounds more of type B coffee than type A. How many pounds of coffee of type A were consumed?

The slope-intercept equation of this linear function is y = -3x + 5.

Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

Where:

Based on the information provided, we can logically deduce the following data points on the line:

At point (0, 5), a linear equation of this line can be calculated in slope-intercept form as follows:

y - 5 = (2 - 5)/(1 - 0)(x - 0)

y - 5 = -3(x - 0)

y = -3x + 5

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Answer:

x < -5

Step-by-step explanation:

- 3x > 15 is equal to x < -5