find the twelfth term in the geometric sequence, given the first term and the common ratio. a1=2 and r=-1

Answer:

284.96

Step-by-step explanation:

Hope it helps:)

According to the computation, each ticket is $37.5 is t = ($175 - $25)/4.

An equation is a formula that uses the equals symbol (=) to denote the equality of two expressions. Multiple languages may have somewhat distinct meanings for the term equation and its cognates.  For instance, in English, an equation is any properly constructed formula that consists of two expressions joined by the equals sign, whereas in French, an equation is any well-formed formula that contains one or more

variables 5.

Given the overall cost of parking and four tickets for a baseball game = $175.00

cost of parking = $25

The price of 4 tickets = $175 - $25

let cost of each ticket is t

t =($175 - $25)/4

cost of each ticket is $37.5

Therefore, the formula for a ticket is

t = ($175 -$25)/4, cost of ticket is $37.5.

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The answer of the given question based on the quadratic expression is Vertex: (3, -1) ,  Axis of symmetry: x = 3 , y-intercept: (0, 8) , x-intercepts: (2, 0) and (4, 0) , Shape: upward-opening parabola.

A quadratic expression is a mathematical expression that can be written in the form ax² + bx + c, where a, b, and c are constants (numbers) and x is a variable. The term "quadratic" comes from the Latin word "quadratus," which means "square."

To graph the quadratic function f(x) = x² - 6x + 8, we can first find the vertex of the parabola by using the formula x = -b/2a. In this case, a = 1 and b = -6, so the x-coordinate of the vertex is x = -(-6)/(2*1) = 3.

To find the y-coordinate of the vertex, we can substitute x = 3 into the expression for f(x):

f(3) = (3)² - 6(3) + 8 = -1

Therefore, the vertex of the parabola is (3, -1).

we can find y-intercept by setting x = 0:

f(0) = (0)² - 6(0) + 8 = 8

So the y-intercept is (0, 8).

To find the x-intercepts, we can set f(x) = 0 and solve for x:

x² - 6x + 8 = 0

(x - 4)(x - 2) = 0

x = 2 or x = 4

So the x-intercepts are (2, 0) and (4, 0).

Finally, we can see that the leading coefficient of the quadratic expression is positive (a = 1), so the parabola opens upward.

Therefore, the key features of the graph of f(x) = x² - 6x + 8 are:

Vertex: (3, -1)

Axis of symmetry: x = 3

y-intercept: (0, 8)

x-intercepts: (2, 0) and (4, 0)

Shape: upward-opening parabola.

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Each game should cost us roughly 8 cents.This game's expected value is negative, thus playing it is not a good idea because you will most likely lose money in the long run.

Given problem describes that there can be 4 unique ball colour combinations as :

Provided that each colour contains two balls in the respective boxes, each combination has a probability of happening of 2/4 * 1/3 = 1/6. The likelihood that the payoff will be zero is thus 4 * 1/6 = 2/3.

Red balls make two different combinations as: (red, red) in left box and (red, red) in  right box. Due to the fact that each box contains just one red ball, each combination has a probability of happening of 1/4 * 1/3 = 1/12. The likelihood that the dividend will be $0.50 is thus 2 * 1/12, or 1/6

Blue balls makes two different combinations as: blue and blue in the left box and (blue, blue) in the right box. Due to the fact that each box contains just one blue ball, each combination has a probability of happening of 1/4 * 1/3 = 1/12. Hence, the likelihood that the payoff will be $1 is 2 * 1/12, or 1/6.

In the left box, there is only one conceivable pair of balls that are both green: (green, green). Given that there is only one green ball in the left box, this combination has a probability of happening of 1/4 * 1/3, or 1/12. Hence, there is a 1/12 chance that the payment will be $16.

[tex]Payout\; |\;Probability\\ \ $0 \qquad \qquad 2/3\\$0.50 \quad \qquad 1/6\\$1 \qquad \qquad 1/6\\$16 \qquad \qquad 1/12[/tex]

By multiplying each payout by the associated probability and adding them together, the anticipated value is determined. The predicted outcome in this situation is:

[tex]\$ 0 * 2/3 + \$0.50 * 1/6 + \$1 * 1/6 + \$16 * 1/12 - \$1 = -\$0.0833[/tex]

The anticipated value of playing this game, according to the revised figures above, is [tex]-\$0.0833[/tex], which indicates that you should anticipate losing on average roughly $0.08 every game. Thus, it is unprofitable game to play if played on regular basis.

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Hence by using Pythagoras the height of tree before it break is 47.02m

Describe Pythagoras.

The Ionian Greek philosopher and mathematician Pythagoras is credited with creating Pythagoreanism. He was born in 570 BCE in Samos, Ionia (Greece), and passed away at Metapontum, Lucania, between 500 and 490 BCE. (Italy). The three sides of a right-angled triangle are the subject of Pythagoras' most famous theorem, which is now referred as as Pythagoras' theorem.

Let A'CB represent the tree before it broke at point C, and let A' be the point at which the tree's top contacts the earth after it broke. Then, at B, ABC is a right triangle.

AB=20 m and BC=15 m

Using Pythagoras theorem,   H²  = P²+ B²

In ΔABC

(AC) ²

=(AB)² +(BC) ²

(AC) ²

=(20) ²+15)²

(AC) ² =400+625

(AC) ²=1025

AC=  32.02

​Hence total height is 32.02+15 =47.02m

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Answer:

48 units squared

Step-by-step explanation:

The area of a trapezoid is 1/2(base1+base2)*height. By counting,  Base 1 is 4 units, base 2 is 8 units, and the height is 8 units. (Just count the squares each side takes and multiply by 2). So we can plug in these values into the formula above, to get 1/2(4+8)*8. Solving this , we get 1/2(12)*8=6*8=48.

Answer:

48 sq units

Your mistake was probably thinking each square unit on the graph was 1 unit, but if you look closely each one is 2, this is proven by the 6 covering 3 boxes.

Step-by-step explanation:

This is the formula for the area of a trap:

A = (a + b)/2 * h

A is the area

a is one of the bases

b is the other base

h is the height

A = (4+8)/2 * 8

A = (12)/2 * 8

A = 6 * 8

A = 48 sq units

Therefore, a point c satisfying the conclusion of the Mean Value Theorem for f(x) = x⁻³ on the interval [1, 8] is approximately x = 2.3608.

In mathematics, a function is a relation between a set of inputs and a set of possible outputs with the property that each input is related to exactly one output. A function is often represented as an equation or a graph. It is a fundamental concept in mathematics and plays a crucial role in many areas, including calculus, algebra, and geometry. Functions are used to model real-world phenomena and solve problems in various fields, such as physics, engineering, economics, and more.

Here,

By the Mean Value Theorem, there exists a point c in the open interval (1, 8) such that:

f'(c) = [f(8) - f(1)] / (8 - 1)

where f'(x) is the derivative of f(x).

First, let's find the derivative of f(x):

f(x) = x⁻³

f'(x) = -3x⁻⁴

Now, substitute the values into the Mean Value Theorem equation:

-3c⁻⁴ = [8⁻³ - 1⁻³] / (8 - 1)

Simplify the right-hand side:

-3c⁻⁴ = (1/512) - (1/1)

-3c⁻⁴ = -511/512

Solve for c:

c⁻⁴ = (511/512) / 3

c⁻⁴ = 511/1536

c = [tex](511/1536)^{\frac{1}{4} }[/tex]

c ≈ 2.3608

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Answer:

  9

Step-by-step explanation:

You want the radius of a circle that has a tangent of length 12 meeting an external segment of length 6.

The given triangle is a right triangle with legs x and 12, and hypotenuse (x+6). The Pythagorean theorem tells you the relationship is ...

  (x+6)² = x² +12²

  x² +12x +36 = x² +144

  12x = 108 . . . . . . . . . . . . subtract (x²+36)

  x = 9 . . . . . . . . . . . . . divide by 12

The value of x in the figure is 9.

__

Additional comment

You can also consider what you know about Pythagorean triples. Two that might be applicable to a side length of 12 are {3, 4, 5} and {5, 12, 13}.

If the triple used here were {5, 12, 13}, that would make x=5 and the external segment 13-5=8 instead of 6.

If the triple used here were {3, 4, 5}, it would have a scale factor of 3 to become {9, 12, 15}. Then x=9 and the external segment is 15-9 = 6. This is the solution.

Another way to solve this is using the secant/tangent relation. For this, you need to extend the line 6+x across the circle. Then the relation is ...

  12² = 6(6+2x) . . . . tangent² = (segment to near)·(segment to far)

  12 = 3 +x . . . . . divide by 12

  x = 9

Therefore, Kyle's score at the tennis event is 0.74, or 74%.

Percent, denoted by the symbol %, is a way of expressing a number as a fraction of 100. Percentages can be used to compare two or more values or to express a change in a quantity over time. Percentages are commonly used to represent proportions, rates, or changes over time, and they are widely used in many fields, such as finance, statistics, and science. To calculate a percentage, we can multiply the given value by the percentage as a decimal or fraction.

Here,

To calculate Kyle's score at the tennis event, we need to use the given percentages for each category and apply them to the weight of each category. First, let's calculate Kyle's score for serves:

Kyle's serves score = 10% of 85%

= 0.1 * 0.85

= 0.085

Next, let's calculate Kyle's score for return balls:

Kyle's return balls score = 40% of 70%

= 0.4 * 0.7

= 0.28

Finally, let's calculate Kyle's score for wins:

Kyle's wins score = 50% of 75%

= 0.5 * 0.75

= 0.375

Now, we can add up all of Kyle's scores to get his overall score:

Kyle's score = Kyle's serves score + Kyle's return balls score + Kyle's wins score

= 0.085 + 0.28 + 0.375

= 0.74

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The retirement account is worth $424647.577  after 29 years. Rounded to two decimal places, the answer is  $424647.577

Capital is the amount you owe at any one time. This is exactly your loan amount if you  just took the loan. As you pay EMIs, the principal is reduced and when it reaches zero, your loan is closed.

 To calculate the future value of a pension account, we can use the formula:

FV =[tex]FV = P(1 + r/n)^(nt)[/tex]

where:

FV = Future Value

P = capital (initial amount)

r = annual interest  (as a decimal)

n = number of times the interest rate is increased per year

t = time (in years)

In this case, the principal is $100,509, the annual interest  is 5%, and the interest is compounded quarterly (4 times a year). The  period is 29 years.

So we can plug these values ​​into the formula and get:

FV =[tex]100509(1 + 0.05/4)^(4*29)[/tex]

FV = 100509(1.0125)^116

FV = 100509 (4.22497)

FV = $424647.577

Therefore, the value of the retirement account  after 29 years is $ $424647.577 Rounded to two decimal places, the answer is  $424647.577

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The surface area of a rectangular prism is 490 in² by the area of each face and then add them up.

We refer to the prism as a rectangular prism since each face is shaped like a rectangle. A cuboid, which has six rectangular faces, and each opposite rectangular face is equal to and parallel to another rectangular face is known to have a similar shape.

To find the surface area of the right rectangular prism, we need to find the area of each face and then add them up.

Looking at the net, we can see that there are 6 faces, each with its own dimensions:

The top and bottom faces are both rectangles with dimensions 10 in by 13 in, so each has an area of 10 in × 13 in = 130 in².

The front and back faces are both rectangles with dimensions 10 in by 5 in, so each has an area of 10 in × 5 in = 50 in².

The left and right faces are both rectangles with dimensions 13 in by 5 in, so each has an area of 13 in × 5 in = 65 in².

Therefore, the total surface area of the right rectangular prism is:

2(130 in²) + 2(50 in²) + 2(65 in²) = 260 in² + 100 in² + 130 in² = 490 in²

So, the surface area of the right rectangular prism is 490 square inches.

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The income elasticity and types of goods, based on the change in demand as a result of a rise in income is:

Clubs are most likely to be classified as a luxury good.

To compute the income elasticity of demand for each good, we use the formula:

Income Elasticity of Demand (E) = (% Change in Quantity Demanded) / (% Change in Income)

Tokens:

E = (15% increase in quantity demanded) / (13% increase in income)

E = 15 / 13

E = 1.15

Hearts:

E = (5% decrease in quantity demanded) / (13% increase in income)

E = -5 / 13

E = -0.38

Clubs:

E = (34% increase in quantity demanded) / (13% increase in income)

E = 34 / 13

E = 2.62

A luxury good is a type of normal good with a high income elasticity of demand (E > 1). In this case, clubs have the highest income elasticity of demand (E = 2.62). Therefore, clubs are most likely to be classified as a luxury good.

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The antiderivative of cos(sin x) is 1/2 (sin⁻¹(sin x) + 1/2 sin(2 sin⁻¹(sin x))) + C.

Integration is a mathematical technique that involves finding the integral of a function. The integral of a function is the area under the curve of the function, and it is represented by a symbol ∫. Integration is the inverse of differentiation, which is a technique for finding the derivative of a function.

There are two main types of integrals: definite integrals and indefinite integrals. A definite integral is the integral of a function over a specific interval, while an indefinite integral is the integral of a function without specifying the interval. Definite integrals are used to find the area under the curve of a function between two points, while indefinite integrals are used to find a family of functions that differ by a constant.

Let u = sin x, then du/dx = cos x and dx = du/cos x. Substituting these expressions into the integral, we get:

∫ cos(sin x) dx = ∫ cos(u) du/cos x

= ∫ cos(u) du / √(1 - u²)

We can now use a trigonometric substitution to evaluate this integral. Let u = sin θ, then du/dθ = cos θ and:

cos² θ + sin² θ = 1

cos² θ = 1 - sin² θ = 1 - u²

Substituting these expressions into the integral, we get:

∫ cos(u) du / √(1 - u²) = ∫ cos(θ) cos θ dθ

= ∫ cos² θ dθ

= ∫ (1 + cos(2θ))/2 dθ

= 1/2 ∫ dθ + 1/2 ∫ cos(2θ) dθ

= 1/2 (θ + 1/2 sin(2θ)) + C

Substituting back u = sin x and θ = sin⁻¹(u), we get:

∫ cos(sin x) dx = 1/2 (sin⁻¹(sin x) + 1/2 sin(2 sin⁻¹(sin x))) + C

Therefore, this is the antiderivative of cos(sin x).

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The scale of the map is that 4 inches on the drawing represents 1 mile in real life

We can use the scale formula:

scale = distance on map / actual distance

In this case, the distance on the map is 8 inches, and the actual distance is 2 miles.

Now we can plug in the values:

scale = 8 inches / 2 miles

scale = 4 inches /1 mile

Therefore, the scale of the map is 4 inches represents 1 mile

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From the given statement, g(-13) = 0 is the the statement that could be true for g.

A function, g, has the following properties: g(0) = -2, g(-9) = 6, and its domain and range are -20 ≤ x ≤ 5, and -5 ≤ g(x) ≤ 45, respectively.

Let's examine each choice to see if it falls within the defined domain and range.

g(7) = -1

7 is not within our purview. G(7) cannot thus be true.

g(-13) = 20

Our range includes 20 and our domain includes x=-13. This holds true for g, so.

g(0) = 2

This is untrue because g(0)=-2 is a given.

g(-4) = -11

11 is outside of the acceptable range. Therefore, this claim is untrue.

From the given statement, g(-13) = 0 is true.

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The complete question is,

Answer:

64.8

Step-by-step explanation:

take 77.2 + 54 = 139.7 then 21.6 x 3 = 64.8

During summer vacation, Alexa read, on average, 10 pages per night. The number of pages per night Alexa averaging now is 2 pages.

A % is a quantity or ratio that, in mathematics, represents a portion of one hundred. A dimensionless relationship between two numbers can be represented in a variety of ways, such as through ratios, fractions, and decimals.

By calculating the percentage of the original Wesley is now reading, we can make the inquiry a little simpler. He is reading 20% of what he used to read rather than 80% less, for example.

Now we need to set up a proportion to solve the problem.

20% of the 10

20/100 = x/10

Cross multiply

20 x 10 = 200

200/100 = 2

He is currently reading 2 pages per night

Thus, the number of pages is 2.

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The mean number of manufacturing processes that need to be performed before a commercially successful one is 8.

Probability is a way to gauge how likely something is to happen. It is a mathematical concept that measures the probability or likelihood of an event occurring. It is stated as a number between 0 and 1, with 0 denoting impossibility and 1 denoting certainty.

The probability of a single manufacturing process producing a commercially successful result is 12.5%, which can be expressed as a probability of success (p) of:

p = 0.125

The probability of the first commercially successful process occurring on the first attempt is p, and the probability of it occurring on the second attempt is (1-p)p (i.e. the probability of failure on the first attempt times the probability of success on the second attempt). Similarly, the probability of it occurring on the third attempt is (1-p)²p, and so on.

The mean, or expected value, of the number of processes required to achieve a single success can be calculated using the geometric distribution, which describes the number of independent Bernoulli trials required to achieve the first success. The formula for the mean of the geometric distribution is:

mean = 1/p

Substituting the value of p, we get:

mean = 1/0.125

mean = 8

Therefore, the mean number of manufacturing processes that need to be performed before a commercially successful one is 8.

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The probability that both Brian and Leo are both assigned window seats on the way to their grandmother's house is the product of the probabilities of each event occurring independently.

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.

The probability of an event can be determined by dividing the number of favorable outcomes by the total number of possible outcomes. For example, if a coin is tossed, there are two possible outcomes: heads or tails.

In the given question,

The probability that Brian is assigned a window seat on any one flight is 50/150, which simplifies to 1/3. Since there are two flights involved (one to his grandmother's house and one back), we can think of this as two independent events.

The probability that both Brian and Leo are both assigned window seats on the way to their grandmother's house is the product of the probabilities of each event occurring independently.

P(both assigned window seats on the way there) = P(Brian gets window seat) x P(Leo gets window seat) = (1/3) x (1/3) = 1/9.

The probability that Brian is assigned a window seat on the flight to his grandmother's house and the flight home from his grandmother's house is the probability of the intersection of two events: Brian getting a window seat on the flight there and Brian getting a window seat on the flight back.

Since these are two independent events, we can multiply their probabilities:

P(Brian gets window seat on flight there and back) = P(Brian gets window seat on flight there) x P(Brian gets window seat on flight back) = (1/3) x (1/3) = 1/9.

Comparing the two probabilities, we can see that they are the same:

P(both assigned window seats on the way there) = P(Brian gets window seat on flight there and back) = 1/9.

Therefore, the answer to the second part of the question is "the same as".The probability that both Brian and Leo are both assigned window seats on the way to their grandmother's house is the product of the probabilities of each event occurring independently.

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Answer: Use the steps that are easiest to draw a parabola!

Step-by-step explanation:

I used Desmos, here are the key points.

Vertex: (-5,-2)

Extra points to graph:

Hope this helps!

The expression "2[tex]m^{3}[/tex]- 11" represents the difference of twice the cube of a number (2[tex]m^{3}[/tex]) and 11, which is option C.

What is Algebraic expression ?

An algebraic expression is a mathematical phrase that can contain numbers, variables, and operations such as addition, subtraction, multiplication, and division. It represents a quantity or a relationship between quantities, and it can be simplified or evaluated by performing the indicated operations.

The expression "2[tex]m^{3}[/tex]- 11" can be broken down into two parts: "2[tex]m^{3}[/tex]" and "-11". The first part, "2[tex]m^{3}[/tex]", represents twice the cube of a number (in this case, the number is "m"). To obtain the cube of a number, you multiply the number by itself three times, so "[tex]m^{3}[/tex]" means "m x m x m". Multiplying this by 2 gives "2m x m x m" which can be written as "2[tex]m^{3}[/tex]".

The second part, "-11", simply represents the number 11 decreased by 11. Therefore, the difference between "2[tex]m^{3}[/tex]" ad "-11" is "2[tex]m^{3}[/tex] - 11".

Therefore, the expression "2[tex]m^{3}[/tex] - 11" represents the difference of twice the cube of a number (2[tex]m^{3}[/tex]) and 11, which is option C.

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Under the HL criteria, the triangles are congruent. The proof is so finished.

Since M is the midpoint of BC, we have BM = CM.

Therefore, by Hypotenuse-Leg (HL) congruence criterion, we have:

Therefore, ∆ABM ≅ ∆DCM; the triangles are congruent by HL criterion.

Hence, the proof is complete.

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The quadratic function in factored form can be written as:

f(x) = a(x + 5)(x - 9)

The value of a is -1/3, and the equation of f(x) in factored form is -(1/3)(x + 5)(x - 9).

What is quadratic equation?

it's a second-degree quadratic equation which is an algebraic equation in x. Ax2 + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term, is the quadratic equation in its standard form.

The -intercepts of a quadratic function correspond to the zeros of the function, which means that the roots of the quadratic equation are -5 and 9.

Therefore, the quadratic function in factored form can be written as:

f(x) = a(x + 5)(x - 9)

where a is a constant. We can find the value of a by using the point (-2,11) that lies on f(x). Substituting x=-2 and y=11 into the function, we get:

11 = a(-2 + 5)(-2 - 9)

11 = a(3)(-11)

11 = -33a

Solving for a, we get:

a = -1/3

Therefore, the equation of f(x) in factored form is:

f(x) = -(1/3)(x + 5)(x - 9)

Completing the statements:

The value of a is -1/3, and the equation of f(x) in factored form is -(1/3)(x + 5)(x - 9).

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Answer:

u = -1

Step-by-step explanation:

5(u + 6) - 8u = 33

5u + 30 - 8u = 33

5u - 8u + 30 = 33

-3u + 30 = 33

      -30  = -30

-3u         = 3

u = -1

Based on the results of this test, there is not enough evidence to conclude that children with antisocial tendencies have greater difficulty recognizing surprise than do children without antisocial tendencies.

The null hypothesis stated using symbols is: H0: μ ≤ 11.80 (where μ represents the population mean score on the emotion recognition scale for 12-year-old children with antisocial tendencies)

The alternative hypothesis stated using symbols is: H1: μ > 11.80

This is a one-tailed test, as the alternative hypothesis is only looking for an increase in the population mean score for recognizing the emotion of surprise among children with antisocial tendencies.

Using the Distributions tool with a one-tailed test and α = 0.05, the critical region is in the right tail of the distribution and the critical value of t is 1.684.

The degrees of freedom (df) for α = 0.05 and n = 40-1 = 39 is 39.

The estimated standard error is the standard deviation of the sample divided by the square root of the sample size, which is 3.28/√40 = 0.518. The t statistic is (12.55 - 11.80) / 0.518 = 1.45 (rounded to four decimal places), which is not greater than the critical value of t. Therefore, we fail to reject the null hypothesis.

Based on the results of this test, there is not enough evidence to conclude that children with antisocial tendencies have greater difficulty recognizing surprise than do children without antisocial tendencies.

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The slope of the line is -3, which means that Scott's delivery time decreased by 3 minutes per day on average.

(a) To find the equation of the line, we can use the point-slope form of the equation, which is:

where m is the slope of the line, and (x₁, y₁) is a point on the line. We can use the two intercepts given in the question as two points on the line.

The y-intercept is (0, 30), and the x-intercept is (10, 0). So, we have:

y - 30 = m(x - 0)

and

y - 0 = m(x - 10)

Simplifying the first equation, we get:

y - 30 = mx

Simplifying the second equation, we get:

y = mx + 0.

We can see that both equations are equivalent and represent the same line.

Therefore, the equation of the line in slope-intercept form is:

y = mx + 30

To find the value of m, we can use the formula:

where (x₁, y₁) and (x₂, y₂) are any two points on the line. We can use the intercepts given in the question:

m = (0 - 30) / (10 - 0)

m = -3

Therefore, the equation of the line in point-slope form is:

y - 30 = -3(x - 0)

Simplifying, we get:

y - 30 = -3x

(b) The y-intercept of the line is 30, which represents the delivery time on day 0. So, initially, it took Scott 30 minutes to deliver his packages.

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Answer

its scale factor is ​4/3 and 0.75

Step-by-step explanation: