you are vacationing in jamaica from the united states and have 50 u.s. dollars to spend on souvenirs. how many souvenirs can you buy if each one costs 500 jamaican dollars? (1 u.s. dollar

The function g(X) will be of the form g(x) = |x/6| ,when stretched by a factor of 6.

The function is f(x)=|x| .

We know that for transformation of a function of the form horizontal stretch by a factor of 'a' is given by the g(x)= f(x/a)

So in this given function the horizontal stretch is by a factor of 6.

Therefore g(x) = f(x/6)

or, g(x) = |x/6|

In the graph attached the green represents the function f(x) while the red represents the function g(x).

A function transformation either "moves," "resizes," or "reflects" the graph of anything similar to the parent function. The following are the three main types of function transformations:

Dilation is the only one of these changes that modifies the size of the original shape; the other two just change its location.

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The value for the given expression  [tex]\alpha ^{2} + \beta ^{2}[/tex] will be [tex](\alpha +\beta )^{2}-2\alpha \beta[/tex].

What are Algebraic Identities?

Algebraic identities are algebraic equations that hold true for any value of each of their variables. In factoring polynomials, they are also used.

As we know, [tex](a+b)^{2} = a^{2} +2ab + b^{2}[/tex]  then,

For the given question, [tex](\alpha +\beta )^{2} = \alpha ^{2} +2\alpha \beta + \beta ^{2}[/tex]

Now, subtracting [tex]2\alpha \beta[/tex] on both sides then, we get

or, [tex](\alpha +\beta )^{2}-2\alpha \beta = \alpha ^{2} +2\alpha \beta + \beta ^{2}-2\alpha \beta[/tex]

or, [tex](\alpha +\beta )^{2}-2\alpha \beta = \alpha ^{2} + \beta ^{2}\\[/tex]

or, [tex]\alpha ^{2} + \beta ^{2}=(\alpha +\beta )^{2}-2\alpha \beta[/tex]

That's how the value  [tex]-2\alpha \beta[/tex] comes.

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Answer:

x = 41.5

Step-by-step explanation:

the sum of the 3 angles in a triangle = 180°

sum the 3 angles and equate to 180

2x + 9 + x + 13 + x - 8 = 180 , that is

4x + 14 = 180 ( subtract 14 from both sides )

4x = 166 ( divide both sides by 4 )

x = 41.5

⇒The sum of the interior angles of a triangle is 180°

⇒Meaning (2x+9)°+(x-8)°+(x+13)°=180°

⇒Simplify the above equation to find the value of x.

⇒[tex]2x+x+x+9-8+13=180\\4x+14=180\\4x=180-14\\4x=166\\\frac{4x}{4} =\frac{166}{4} \\x=41.5[/tex]

∴ x=41.5

From the given figure, m∠AEB = (3x + 54)° and m∠DEC = (7x -30)°, then the measure of angle AEB is equal to 117°.

As given in the question,

For the given figure,

Two lines AC and BD intersect each other at point E.

Measure of angles in the form of x is given as :

m∠AEB = (3x + 54)°

m∠DEC = (7x -30)°

∠AEB and  ∠DEC are vertically opposite angles.

⇒m∠AEB = m∠DEC

⇒ (3x + 54)°= (7x -30)°

⇒ 7x - 3x = ( 54 + 30 )°

⇒ 4x = 84°

⇒ x = 21°

Hence,

m∠AEB = (3x + 54)°

⇒m∠AEB = (3(21) + 54)°

⇒m∠AEB = 117°

Therefore, from the given figure m∠AEB = (3x + 54)° and

m∠DEC = (7x -30)°, then the measure of angle AEB is equal to 117°.

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Answer:

[tex]\sf s =\dfrac{-q}{pr}[/tex]

Step-by-step explanation:

               q = -spr

            -spr = q

     Isolate 's' by dividing both sides by (-pr).

           [tex]\sf \dfrac{-spr}{-pr}=\dfrac{q}{-pr}\\\\\\ s = \dfrac{-q}{pr}[/tex]

Each text will cost Hassan $0.09

A rate is a special ratio in which the two terms are in different units. It can also be defined as the amount of money that is charged for goods or services. For example, if a 12 malt can of costs 69¢, the rate is 69¢ for 12 malt. Then 1 malt will cost ¢69/12.

Similarly $5.31 is the cost of 59 text messages

Therefore a text message will cost $5.31/12=$0.09

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Line 1  4x³ + 2x² − 6x +3 is having error.

Line 1.

4x³ + 2x² − 6x +3

Line 2.

= 2x²(2x + 1) − 3(2x + 1)

= 4x³ + 2x² - 6x - 3

Line 3.

= 2x²(2x + 1) + ( − 3)(2x + 1)

= 4x³ + 2x² - 6x - 3

Line 4.

= (2x² − 3)(2x + 1)

= 4x³ + 2x² - 6x - 3

expect line 1 remaining all three are equal.

Therefore Line 1  4x³ + 2x² − 6x +3 is having error.

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Answer:

∠T

Step-by-step explanation:

∠T is the common angle found in both triangles.

In ΔPTS, ∠PTS represents ∠T.

In ΔQTR, ∠T is represented by ∠QTR.

Answer:

The angle T is common side.

Step-by-step explanation:

Given triangles,

→ ∆PTS & ∆QTR

Now we have to,

→ fInd common angle of both triangles.

The common angle is,

→ <T (angle T)

→ As it is present in both triangles.

Hence, the common part is angle T.

Answer:

2 minutes for a whole song.

Step-by-step explanation:

Given that,

→ (1/6) song = (1/3) minutes

Parts of whole song is,

→ (1/6) × 6 = 1

Then the required minutes taken to play whole song will be,

→ x/6 = 1/3

→ x = (1/3) × 6

→ x = 6/3

→ [ x = 2 min ]

Hence, 2 minutes for a whole song.

Answer:

Step-by-step explanation:

Arithmetic Sequence

Answer:

  (a)  Arithmetic Sequence

Step-by-step explanation:

You want to know if the graph of a straight line represent an arithmetic, geometric, or neither sequence.

An arithmetic sequence is characterized by a common difference between terms that are 1 unit apart. A graph of an arithmetic sequence is points that lie on a straight line.

The graph shows an Arithmetic Sequence.

__

Additional comment

A graph of a geometric sequence would show points that lie on an exponential curve.

The line that has a slope of -2 and a y-intercept of -1 is shown in the graph below.

An equation of a line in slope-intercept form that is expressed as y = mx + b, can be graphed if we know the value of the slope (m), and the value of the y-intercept (b).

We are given the following:

To write the equation of the line in slope-intercept form, substitute m = -2 and b = -1 into y = mx + b:

y = -2x - 1

This means that the rise/run of the line, which is the slope, to be graphed would be equal to -2 while the line will intercept the y-axis at point -1, because the y-intercept given is -1.

The line with the stated features are shown in the graph below.

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The possible dimension of the triangular garden assuming it to be a right-angle triangle is (12,2),(8,3), and (4,6).

A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are three sides and three angles in every triangle, some of which may be the same.

The area of a triangle is given as (1/2) × base × height.

The given area of the triangle = 12 feet².

Thus,

12 =  (1/2) × base × height

Base × height = 12 × 2

Base × height = 24

The combination of two quantities gives 24 by multiplying will be (12,2),(8,3), and (4,6).

For example, the triangle with dimensions (4,6) is attached below.

Hence "The possible dimension of the triangular garden assuming it to be a right-angle triangle is (12,2),(8,3), and (4,6)".

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Answer:

212 feet fallen after 7 seconds

Step-by-step explanation:

You visit the Grand Canyon and drop a penny off the edge of the cliff. The distance the penny will fall is 32ft for the first second, 62ft the next second, 92ft the third second, and so on. How far will the penny have traveled after 7 seconds?

if 32 ft for 1 second

if 62 ft for 2 second

if 92 ft for 3 second

We see that the penny from second 1, falls an addition 30 ft/s.

equation: 32 + 30 (t - 1)

when t = 7 seconds:

32 + 30 (7 - 1)

32 + 30 (6)

32 + 180

= 212 feet fallen after 7 seconds

The measure of ∠ YXR is 55 degrees.

Given that:-

m∠ XOY = 110 degrees

XR is a tangent to circle O at X.

We have to find the measure of ∠ YXR.

Draw the radii XO and OY to form the isosceles triangle XOY.

We know that the radius of the circle is perpendicular to the tangent.

Hence,  ∠OXR = 90 degrees.

Consider the triangle XOR, we know that XO and OY are the radii of the triangle and hence equal.

Let, ∠ OXY = OYX = x

Hence,

110 + x + x = 180 degrees

2x = 70 degrees

x = 35 degrees

Now, we know that,

∠ OXR = ∠ OXY + ∠ YXR

90 = 35 + ∠ YXR

∠ YXR = 90 - 35 = 55 degrees.

∠ YXR = 55 degrees.

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The quadratic expression can be factorized to:

x*(x - 6)

Here we have the expression:

x^2 - 6x

To factorize this, first, we need to find the roots, which are the solutions of:

x^2 - 6x = 0

Notice that one of the solutions is trivial, and it is x = 0.

If now we assume that x ≠ 0 and divide both sides by x, we get:

x - 6 = 0

x = 6

That is the other solution.

Now, for a square polynomial with the roots a and b, the factorized form is:

(x - a)*(x - b)

In this case, the roots are 0 and 6, then:

x^2 - 6x = (x - 0)*(x - 6) = x*(x - 6)

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Equation of the given data y = 1750x -20,000 and graph of the equation is attached.

As given in the question,

Data of the table :

Year :               1                 2                   3              4                5

Investment : $20,000      $21,750      $23,500    $25,250      $27,000

(x₁, y₁) = ( 1, 20,000)

(x₂, y₂) = ( 2, 21,750)

Equation of the given graph is :

( y - 20,000)/ (x -1) = (21,750 - 20,000)/ (2 -1)

⇒ ( y - 20,000)/ (x -1) = 1750

⇒ y = 1,750x -18,250

Graph of the equation  y = 1,750x -18,250 s represented by the graph.

Graph is attached.

Therefore, equation of the given data y = 1750x -20,000 and graph of the equation is attached.

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Answer:

Step-by-step explanation:

Yahweh’s

The number of cans that are recycled is approximately 1 billion cans in 1 week.

Multiplication is the mathematical operation that is used to determine the product of two or more numbers. If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.

Given that  51.9 billion aluminum cans were recycled.

Therefore, the rate of recycled the can is;

51.9 billion / 1 year

We know that 1 year has 52 weeks

Then

51.9 billion / 1 year  x  1 year / 52 weeks

= 51.9 (1) billion / 1 (52 ) weeks

= 51.9 billion/ 52 weeks

= 1 billion/ 1 week

Hence, the number of cans that are recycled is approximately 1 billion cans in 1 week.

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Answer:

15 coaches

Step-by-step explanation:

750 people go on a coach trip each coach can hold 50 people How many coaches are needed?

750/50 = 15 coaches

Answer:

750÷50 = 15

The answer is 15.

Because 750 people are going in a coach trip and each coaches can hold 50 people.

Using remainder theorem, Quotient = x-9 and Remainder = x² - x.

P(x) = −x³ – 2x² −9

P(-1) = −(-1)³ – (-1)x² −9

P(-1) = −(-1) – 2(1) −9

= 1 -2 -9

= -10

Remainder of  P(-1) = −(-1)³ – (-1)x² −9 is -10.

Remainder of P(x+1)

= −x³ – 2x² −9 / x+1

Quotient = x-9 and Remainder = x² - x

Hence, using remainder theorem, Quotient = x-9 and Remainder = x² - x.

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The probability that you select a black card and a red card is 26/51 as per the condition mentioned "choosing two cards (without replacement )".

The area of mathematics known as probability studies potential outcomes of events as well as their relative probabilities and distributions. Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of various outcomes. Statistics is the study of events that follow a probability distribution.

Here,

Since we have not mentioned the order,

so it can black-red or red-black,

=26/52*26/51+26/52*26/51

=2*26/52*26/51

=26/51

Assuming you choose two cards (without replacement), there is a 26/51 chance that you will choose a black card and a red card.

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We see BC is in the middle of the lines AB and BD, therefore mABC + mCBD = mABD.

We're given mABD = 75, mABC = 40.

Therefore, mCBD = mABD - mABC = 75 - 40 = 35.

Answer:

∠CBD = 35°

Step-by-step explanation:

We are told in the question that m∠ABD = 75° and m∠ABC = 40°. We are then asked what the value of m∠CBD is.

As we can see from the diagram, ∠ABD is made up of the angles ABC and CBD. Therefore:

∠ABD = ∠ABC + ∠CBD

⇒ 75° = 40° + ∠CBD

⇒ 75° - 40° = 40° + ∠CBD - 40°       [

⇒ 35° = ∠CBD

∴ ∠CBD = 35°

Most researcher fix level of significance at 5% i.e. they conclude a significant relationship when nothing is going on in 5% of cases. Hence,

Option A is correct which is 1.5%

Given that,

The majority of social scientists are willing to claim that a link is statistically significant if the likelihood of observing the relationship in the sample when nothing is happening in the population is greater than a certain threshold.

To find:

Less than what percentage of the population truly experiences nothing at all (i.e., random chance)

The majority of researchers set the level of significance at 5%, which means they draw conclusions about a meaningful association even when nothing is happening in 5% of cases.

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The equation of the parabola with the vertex (3,5) in the form of f(x)=a(x-h)^2+k is f(x)=7(x-3)^2+5.

In the given question we have to find the equation of parabola in the form of f(x)=a(x-h)^2+k

The given function is f(x)=7x^2.

The given vertex = (3,5)

The equation of the parabola with the vertex of (h,k) is

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

On comparing we get; a=7, h=3, k=5

Now putting the value

f(x)=7(x-3)^2+5

Hence, the equation of the parabola with the vertex (3,5) in the form of f(x)=a(x-h)^2+k is f(x)=7(x-3)^2+5.

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The exponential equation represents an exponential growth because the rate of decay is 1.02 which is greater than 1.

y = 90(1.02)^x

The general form equation is:

y(x)= a(1+r)^x such that r is the decay percent.

on comparing,

1 + r = 1.02

r = 1.02 - 1

r = 0.02

converting into percent

r = 0.02 * 100

r = 2%.

Hence the exponential growth is 2%.

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Answer:

a) 1

b) 0.5

c)0

The amount a container would take to spray 1 entire lawn is 7 litres.

Given that a container with 3½ liters of weed killer can spray 1/2 of a lawn.

We want to find the amount of liters to take a spray 1 entire lawn.

3½ liters of weed killer can spray 1/2,

liters take to spray 1 lawn is 3½/1/2=7 liters

Hence, the amount of liters it would take to spray 1 entire lawn when a container with 3½ liters of weed killer can spray of a lawn is 7 liters.

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When Niecy combines the fruit she will have a total of Start Fraction 12 over 14 End Fraction

information form the question

Niecy has Nine-fourteenths of a cup of pears

Three-fourteenths of a cup of mangos

The problem is faced with addition of fractions

writing out the fractions in figures gives

Niecy has Nine-fourteenths of a cup of pears = 9 / 14

Three-fourteenths of a cup of mangos = 3 / 14

Addition of the fraction is done as follows

= 9 / 14 + 3 / 14

=  (9 + 3) / 14

= 12 / 14

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