Use Taylor's Inequality to determine the number of terms of the Maclaurin series for e^x that should be used to estimate e^0.1 to within 0.0000001.

Answer:

--------------------------------

Rocket is in the air until it hits the ground.

Therefore we need to find the value of t when h = 0.

The rocket is in the air for 6 seconds.

Answer:

6 seconds

Step-by-step explanation:

Given function:

[tex]h(t)=-16t^2+72t+144[/tex]

where:

To find how long the rocket is in the air, find the positive value of t when h(t)=0.

[tex]\implies -16t^2+72t+144=0[/tex]

[tex]\implies -8(2t^2-9t-18)=0[/tex]

[tex]\implies 2t^2-9t-18=0[/tex]

[tex]\implies 2t^2+3t-12t-18=0[/tex]

[tex]\implies t(2t+3)-6(2t+3)=0[/tex]

[tex]\implies (t-6)(2t+3)=0[/tex]

Apply the zero-product property:

[tex]t-6=0 \implies t=6[/tex]

[tex]2t+3=0 \implies t=-\dfrac{3}{2}[/tex]

Therefore, as t > 0, the rocket is in the air for 6 seconds.

The number of lattice points in the first quadrant of the graph is equal to five (5).

In Mathematics, an ordered pair can be defined as a pair of two (2) elements or points that are commonly written in a fixed order within parentheses as (x, y), which represents the x-coordinate or x-axis (abscissa) and the y-coordinate or y-axis (ordinate) on the coordinate plane of any graph.

In Mathematics, a lattice point can be defined as a point on a graph whose ordered pair (x and y coordinates) are both positive and whole numbers.

By critically observing the graph of the function 3x + 4y = 59, we can reasonably infer and logically deduce that the number of lattice points in the first quadrant (where the ordered pair are both positive) are five (5).

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Based on the null hypotheses, the type of error is Decrease the significance level to decrease the probability of Type I error.

What does null hypotheses means?

In math, null hypotheses refers a type of statistical hypothesis that proposes that no statistical significance exists in a set of given observations.

Here we have give that researchers are testing a new diagnostic tool designed to identify a certain condition. the null hypothesis of the significance test is that the diagnostic tool is not effective in detecting the condition. for the researchers, the more consequential error would be that the diagnostic tool is not effective, but the significance test indicated that it is effective.

And we need to find in which of the following should the researchers do to avoid the more consequential error.

According to the given question, the null hypothesis is that the new diagnostic tool is not effective in detecting the condition.

Here the more consequential error described is that the diagnostic tool is not effective, but the significance test indicated that it is effective. This is a type I error.

And in Hypothesis testing, a type I error involves rejecting the null hypothesis and accepting the alternative hypothesis when in reality, the null hypothesis is true.

Therefore, it involves saying there is significant evidence to show that the new diagnostic tool is effective in detecting the condition when in reality, it isn't.

When the level of significance (α) of a hypothesis test directly gives the probability of a type I error. So, by setting it lower, we reduce the chances of a type I error.

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Answer:

To create a chocolate blend using 61% cocoa and 51% cocoa, 18 ounces of the 61% chocolate and an appropriate amount of the 51% cocoa are combined together. The exact amount of 51% cocoa required will depend on the desired concentration of the final blend.

Step-by-step explanation:

The given expression can be written in scientific notation as 1.729 x 10⁹.

Scientific notation is a way of expressing numbers that are too large or too small to be conveniently written in decimal form.

Given is to express the given expression in scientific notation.

The given expression is -

(1.33) (13 × 10⁸)

Solving further -

1.33 x 13 x 10⁸

17.29 x 10⁸

1.729 x 10⁹

Therefore, the given expression can be written in scientific notation as 1.729 x 10⁹.

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The ΔPQR and ΔCBA are congruent using ( SAS , AAA , ASA) properties

If the three angles and the three sides of a triangle are equal to the corresponding angles and the corresponding sides of another triangle, then both the triangles are said to be congruent.

The two triangles need to be of the same size and shape to be congruent. Both the triangles under consideration should superimpose on each other.

According to the question,

We have to identify all the pairs of congruent

In ΔPQR and ΔCBA,

If we look the figure

(1) ∠Q ≅ ∠B

(2) ∠R ≅ ∠A

(3) ∠P ≅ ∠C

(4) PQ ≅ CB

(5) QR ≅BA

Therefore , All three angles are equal and all three sides

hence , ΔPQR ≅ ΔCBA by using AAA or ASA or SAS properties

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a brokerage firm keeps track of the total money spent on tesla stocks by their clients each day of the week is C(T) = $730 + $25T

R(T) = $35T

T = 193 transact

C = cost ; R = revenue ; T = number of transactions

Amount paid per transaction = $25

Cost keeping office open = $730

Amount collected on each transaction = $35

(a) Find a formula that gives C as a function of T.

C(T) = Cost of keeping office open + (cost per transaction × number of transactions)

C(T) = $730 + $25T

(b) Find a formula that gives R as a function of T.

R(T) = (Amount collected per transaction * number of transactions)

R(T) = $35T

(c) Find the number of daily transactions that are needed to make the revenue $1200 more than the cost.

R = C + 1200

Substitute the value of R and C into the equation:

35T = 730 + 25T + 1200

35T - 25T = 730 + 1200

10T = 1930

T = 1930 / 10

T = 193 transactions

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The probability that fewer than 2 rolls result in snake eyes is approximately equal to 0.492.

To calculate the probability that fewer than 2 rolls result in snake eyes, we need to calculate the probability that exactly 0 rolls and the probability that exactly 1 roll result in snake eyes, and then sum these probabilities.

The probability that exactly 0 rolls result in snake eyes is given by the binomial probability formula:

P(exactly 0 rolls) = (n choose k) * p^k * (1-p)^(n-k)

Where:

n = the number of rolls

k = the number of successful rolls (in this case, 0)

p = the probability of success on a single roll (in this case, 1/6, since there is a 1/6 probability of rolling snake eyes on a single roll)

Plugging in the values, we get:

P(exactly 0 rolls) = (5 choose 0) * (1/6)^0 * (5/6)^5 = 0.164

The probability that exactly 1 roll results in snake eyes can be calculated in a similar manner:

P(exactly 1 roll) = (5 choose 1) * (1/6)^1 * (5/6)^4 = 0.328

To get the probability that fewer than 2 rolls result in snake eyes, we sum these probabilities:

P(fewer than 2 rolls) = P(exactly 0 rolls) + P(exactly 1 roll) = 0.164 + 0.328 = 0.492

Therefore, it would not be surprising if fewer than 2 rolls result in snake eyes.

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Complete Question:

Question 2 (25 points) Calculating a binomial probability PROBLEM: When rolling two fair six-sided dice, getting a pair of ls is called "snake eyes." The probability of getting "snake eyes" on any roll is 1/36. Suppose that a game player rolls the two dice 80 times. Let X = the number of rolls that result in "snake cyes." Find P(X = 2). Interpret this value in context If two dice are rolled 80 times, then there is a 27.089% chance that we get a pair of snake eyes. Question 3 (25 points) Calculating a binomial probability PROBLEM: See the preceding alternate example. Should the player be surprised if fewer than 2 of the rolls result in snake eyes? Calculate an appropriate probability to support your answer.

Answer:

x = 1

Step-by-step explanation:

2x + 8 = 10 ( isolate the x- term by subtracting 8 from both sides )

2x = 2 ( isolate x by dividing both sides by 2 )

x = 1

The value of x that will make the two given solids similar is: d. x = 31.

Similar solids are solids that are scale copy of each other, that is, either of the solids can produce the other when enlarged by a scale factor to get the dimension of the other solid.

Therefore, if two solids are similar, their corresponding linear dimensions would have an equal ratio, or they would be proportional.

Applying the definition of similar solids, the equation below would be created in order to determine the value of x:

x/15.5 = 29/14.5

Cross multiply:

14.5x = 15.5 × 29

14.5x = 449.5

14.5x/14.5 = 449.5/14.5

x = 31

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The factors that  you need to consider when preparing to move gondolas are:

Height

width

length

color.

A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity

In choosing gondola one need to look at some  factor in decisions such as height.

Know that it is good to  consider the construction material and also the center wall configuration for its building also.

The factors that  you need to consider when preparing to move gondolas are:

Height

width

length

color.

Hence, Height, width, length and color are the other factors we need to consider while moving Gondola.

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The expressions that represents Carissa's distance to the right of the center of the skitrail, i.e, h in terms of the number of times Carissa has traveled since she started skiing,d is h = 1.3 cos( d/1.3). So, correct answer is option (c).

We have, Carissa skis along a circular ski trail. Radius of circle , r = 1.3 km

Carissa starts at the 3-o'clock position of the trail travels in the counter clockwise direction. let "d" km be total distance that Carissa has traveled since she started skiing and "h" km be Carissa's distance to the right of the center of the skitrail in km.

We have to wright an expressions for "h" in terms of d . Here, we see an sector is formed with one side length is r and arc's distance is d km . Let θ be angle formed by this sector . Using the sector formula,

θ = arc length /radius of circle

=> θ = d/r = d/1.3 --(1)

Also, ∆ formed here , h = r cos θ

=> h = 1.3 cos( d/1.3)

Hence, the required expression is h=1.3 cos( d/1.3).

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Complete question:

Carissa skis along a circular ski trail with a radius 1.3 km long. Carissa starts at the 3-o'clock position of the trail (the East-side) and travels in the CCW direction. Which of the following expressions represents Carissa's distance to the right of the center of the skitrail in km, h, in terms of the number of km that Carissa has traveled since she started skiing.d?

a)h 1.3 cos(d+ 1.3)

b) h = 1.3 cos(1.3/d)

c)h = 1.3 cos (d /1.3 )

d)h = 1.3 cos(d)

e) h = COS( 1.3 )

Submit Question 16. Points possible:

To determine that an item is not in an unordered array of 100 items, total numbers of values which have to linear search examine on average is 100. The correct answer is C.

Linear Search is described as a sequential search algorithm which starts at one end and goes through each element of a list until the needed element is found, otherwise the search continues till the end of the data set. This is the simplest searching algorithm.

Starting at the beginning of the data set, each item of data is examined until a match is made. Once the item is found, the search ends.

Hence, in this case, since there are 100 items, then there will be 100 numbers of values.

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The market research can increase the precision of the result of the study by  using a randomized block design RBD.

The best design the market research company should use for the study is d. A randomized block design Use packaging as a block. Randomly assign the nine combinations of three price levels and three packaging types so that three stores use each combination

Reason:

The given parameters are;

The study = The effect of price and type of packaging

Number of stores in the study = 27 stores

Characteristics of the shoppers in the stores = Similar

Number of packaging type = 3 (three)

Number of price levels = 3 (three)

The number of pair combinations = ⁶₂C - (3, pairs of the same packaging +

3, pairs of the same prices) = 9

Required:

The best design to use for the study

Solution:

Given that the shoppers at each store are similar, in order to differentiate and show the effect of the price and package combination, it is possible to group the treatment into groups having a particular characteristics, while ensuring that the other available treatments are assigned to each member within a group at least once.

The above design of the study is known as a randomized block design,

Therefore the correct option is d. A randomized block design Use packaging as a block. Randomly assign the nine combinations of three price levels and three packaging types so that three stores use each combinations.

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It is based on a sample and provides information about the sample based on a survey of 35 samples, this four cell phone is a statistic, so the response is a statistic.

When looking at populations, the term "median" is a significant and frequently used statistic. Most of the time, it's used to represent a set of numbers.

We sort the population numbers to find the one in the middle to find the median. It differs from the mean and can sometimes be more useful than the mean, such as when there are outliers that could have an excessive impact on the mean. We should take the average of the two values in the middle if the number of values is even.

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If the parent function f(x) = x² is horizontally shrunk by factor of 1/3 ad vertically stretch by factor of 4 then g(c) will be g(x) = 4(1/3x)² , the correct option is (c)  .

In the question ,

it is given that ,

the parent function is ⇒ f(x) = x² ;

the graph is horizontally shrunk by a factor of 1/3 that means

the function will become (1/3x)² .

next the function is then vertically stretch by a factor of 4 ,that means

then the function becomes g(x) = 4(1/3x)².

Therefore , the correct option is g(x) = 4(1/3x)²  .

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The interquartile range (IQR) of the salaries = 20

In descriptive statistics, the interquartile range is a measure of statistical dispersion, or the spread of the data. The middle 50%, fourth spread, or H-spread are further names for the IQR. It is described as the discrepancy between the data's 75th and 25th percentiles.

According to the given information

We are given that

Q1=50  and  Q3=70

Inter quartile range =IQR

                                = Q3 -Q1

                                = 70 - 50

                               = 20

The interquartile range (IQR) of the salaries = 20

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Based on probability, three of the four selected calculators will contain no defective.

Probability refers to the likelihood or chance that an expected outcome occurs in the midst of many possible outcomes or events.

Probability is zero when uncertain and one when 100% certain.  Otherwise, probability lies between zero and one, which yields a fractional value denoted by decimals, percentages, or fractions.

The number of shipped graphing calculators = 30

The number of defective calculators = 7

The probability of defective calculators = 0.233 (7/30)

The probability of no defective calculators = 0.767 (1- 0.233)

The number of calculators to be sent to a high school = 4

The number of these that will contain no defective calculators = 3.068 (4 x 0.767)

= 3

Thus, the local high school will probably receive 3 non-defective units.

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The percentage of sugar in the drink is 64%

A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100. It is represented by the symbol “%”.

The data given are;

The percentage of sugar in the carbohydrate can be calculated as;

Percentage = (16 / 25) * 100

Percentage = 0.64 * 100

Percentage = 64%

The percentage of sugar is 64%

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The two possible variables design are; "COHORT STUDY" and "CROSS-SECTIONAL STUDY".

Cohort study design is an observational study in which people who receives a particular treatment or are under a particular condition, are been observed and studied. This type of research model also allows a researcher to compare people affected by a condition to people unaffected by the same conditions.

The investigator is likely to use the cohort design because it will help in studying the children that are always exposed to smoke, and to observe the affected and unaffected children.

The CROSS-SECTIONAL design is an observational study in which a specific population are studied at a particular time. This type of research allows the researcher to study the difference in that population at a time interval.

This study design is likely to be used by the investigator, because it will help the investigator to determine the amount of secondhand smoke each child inhale at a particular time. It will also help the investigator to know the outcome of each child after 5years

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Answer:

8584946569585889594934u

At the end of her daughter's 10th birthday, the woman has deposited a total of 310 eur. On her first birthday, a woman transfers 100 euros into her daughter's bank account. every birthday after that.

On the daughter's 1st birthday:

100 eur deposit

On the daughter's 2nd birthday:

100 eur (previous year) + 10 eur (increase) = 110 eur deposit

On the daughter's 3rd birthday:

110 eur (previous year) + 10 eur (increase) = 120 eur deposit

On the daughter's 4th birthday:

120 eur (previous year) + 10 eur (increase) = 130 eur deposit

On the daughter's 5th birthday:

130 eur (previous year) + 10 eur (increase) = 140 eur deposit

On the daughter's 6th birthday:

140 eur (previous year) + 10 eur (increase) = 150 eur deposit

On the daughter's 7th birthday:

150 eur (previous year) + 10 eur (increase) = 160 eur deposit

On the daughter's 8th birthday:

160 eur (previous year) + 10 eur (increase) = 170 eur deposit

On the daughter's 9th birthday:

170 eur (previous year) + 10 eur (increase) = 180 eur deposit

On the daughter's 10th birthday:

180 eur (previous year) + 10 eur (increase) = 190 eur deposit

Total deposited over 10 years:

100 eur (1st birthday) + 110 eur (2nd birthday) + 120 eur (3rd birthday) + 130 eur (4th birthday) + 140 eur (5th birthday) + 150 eur (6th birthday) + 160 eur (7th birthday) + 170 eur (8th birthday) + 180 eur (9th birthday) + 190 eur (10th birthday) = 1,100 eur

Total deposited over 10 years: 1,100 eur - 100 eur (1st birthday deposit) = 1,000 eur

Total deposited over 10 years: 1,000 eur / 10 years = 100 eur per year

Total deposited over 10 years: 100 eur x 10 years = 1,000 eur

Total deposited over 10 years: 1,000 eur + 100 eur (1st birthday deposit) = 1,100 eur

Total deposited over 10

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The probability of rainfall actually occurring tomorrow is 0.3465. The correct answer is therefore 0.3465.

To solve this problem, you can use Bayes' Theorem. Bayes' Theorem is a way to calculate the probability of an event occurring based on prior knowledge of conditions that might be related to the event.

In this case, we are trying to find the probability of rainfall occurring tomorrow, given that it has been predicted. Let's call this probability P(R|P), where R is the event of rainfall occurring and P is the event of rain being predicted.

According to the problem statement, the probability of rain occurring on any given day during the summer is 2/10, or P(R) = 0.2.

The probability of rain not occurring is 1 - P(R) = 0.8.

The probability of rain being predicted, given that it does rain, is 0.7, or P(P|R). The probability of rain being predicted, given that it does not rain, is 0.33, or P(P|¬R).

Using Bayes' Theorem, we can calculate the probability of rain occurring tomorrow as follows:

P(R|P) = [P(P|R) * P(R)] / [P(P|R) * P(R) + P(P|¬R) * P(¬R)]

Substituting in the values from the problem statement, we get:

P(R|P) = [0.7 * 0.2] / [0.7 * 0.2 + 0.33 * 0.8]

Simplifying this expression gives us:

P(R|P) = 0.3465

So the probability of rainfall actually occurring tomorrow is 0.3465.

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An SRS of size 26 is drawn from a population that has a Normal distribution, the standard error of the mean is 0.7844..

The standard error of the mean, or simply standard error, indicates how much the population mean can differ from the sample mean. It indicates how much the sample mean would change if the survey were repeated with new samples from a single population. It is calculated by dividing the standard deviation by the square root of the sample size.

We have given that,

SRS size , n = 26

The distribution is normal distribution,

Mean, u = 143.5

Standard deviations, sd = 4

standard error of the mean = sd/√n

= 4√26 = 0.7844

Hence, the standard error of mean is 0.7844..

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The objective function is -x1 + x2. Also, the multiplier associated with the x1 + x3 - 2x1 = 0 constraint is 0,  satisfies the KKT condition.

To find the optimal solution graphically, first plot the points (-1,0), (0,1), (1,0), and (0,-1) on the coordinate plane. These points form a square. The objective function for this problem is to minimize -x1 + x2. So we need to find the point on the square that is as low as possible on the y-axis (because the y-axis represents x2).

The constraint in question is x1 + x3 - 2x1 = 0, which can be rewritten as x3 = 2x1. Since x1 and x3 are variables, this represents a line on the coordinate plane. You can draw this line by selecting two points on this line and connecting them with a line. For example, you can select points (-1, -2) and (1, 2). These points lie on the line x3 = 2x1 and the connecting lines are plotted in the coordinate plane.

We can find the best solution by finding the point on the square that is the lowest possible on the straight line of y-axis and x3 = 2x1. The point that satisfies both of these conditions is the point (0,-1). This is the best solution for your problem.

To answer the second part of the question we need to determine whether the Fritz-John condition or the KKT condition is the optimal solution. The Fritz-John condition is an optimality requirement involving an objective function and problem constraints. A KKT condition is a necessary and sufficient condition for optimality that includes an objective function, a constraint, and a multiplier associated with the constraint.

The Fritz-John condition is not considered optimal for this problem. This is because the optimal solution does not satisfy the condition x1 + x3 – 2x1 = 0. The point (0,-1) does not satisfy the condition because it is not on the line x3 = 2x1.

KKT conditions are considered to be the best solution. This is because the point (0,-1) is a legal point (it lies on the square representing the legal region) and the global minimum of the objective function is -x1 + x2. Also, the multiplier associated with the x1 + x3 - 2x1 = 0 constraint is 0, which satisfies the KKT condition.

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The interval of time after solving the inequality -16[tex]t^{2}[/tex] + 40t + 2 > 18 is 0.5 < t < 2

Inequalities are of two types, > and <. The > sign means that left hand side is greater than the right hand side, while the < sign means that the left hand side is less than than the right hand side.

We can solve the inequality by assuming the inequality sign as the = sign, except that when we divide or multiply one side by (-1), the inequality sign will reverse (for eg it will change from > to <).

-16[tex]t^{2}[/tex] + 40t -16 > 0

Dividing the equation by 8,

-2[tex]t^{2}[/tex] + 5t - 2 > 0

Rearrange gives,

2[tex]t^{2}[/tex]  - 5t + 2 < 0

Using middle term breaking,

(2t-1)(t-2) < 0

Hence, the interval is 0.5 < t < 2

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The Fibonacci sequence is the sequence in which the numbers are written such that each succeeding number is sum of two preceding numbers.

The Fibonacci sequence is defined recursively as follows:

F0 = 0

F1 = 1

For n > 1, Fn = Fn-1 + Fn-2

(b) The sequence of partial sums is:

S0 = 0

S1 = 0 + 1 = 1

S2 = 0 + 1 + 1 = 2

S3 = 0 + 1 + 1 + 2 = 4

S4 = 0 + 1 + 1 + 2 + 3 = 7

S5 = 0 + 1 + 1 + 2 + 3 + 5 = 12

(c) A closed formula for the sequence of partial sums in terms of Fn is not possible, since the sequence of partial sums depends on the values of all previous terms in the Fibonacci sequence. However, it is possible to express the nth term of the sequence of partial sums, Sn, in terms of the nth term of the Fibonacci sequence, Fn, using the following formula:

Sn = F0 + F1 + ... + Fn = (F0 + F1) + (F1 + F2) + ... + (Fn-1 + Fn) = F1 + F2 + ... + Fn + F0 + F1 + ... + Fn-1 = 2Sn-1 - Fn + F0

This formula can be derived by considering the previous term in the sequence of partial sums and adding the current term of the Fibonacci sequence to it.

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Answer:

Step-by-step explanation:

You have a particle whose acceleration is a(t) = 3t²/160 -t³/800 and whose velocity at t=20 is 0. You want to show the initial speed is 0, find the maximum speed, and the distance traveled in 20 seconds.

The speed is the sum of the initial speed and that due to acceleration. The speed due to acceleration is the integral of acceleration:

  [tex]\displaystyle s(20)=s_0+\int_0^{20}{\dfrac{1}{800}(15t^2-t^3)\,dt}}=s_0+\left(\dfrac{t^3}{3200}(20-t)\right)_0^{20}=s_0=0[/tex]

The change in speed over 20 seconds is zero, so the final speed is the initial speed. The final speed is zero, so the initial speed is 0.

The maximum speed is where the acceleration is zero.

  a(t) = 0 = (t²/800)(15 -t)

The acceleration is zero at t=0 and at t=15.

From the above integral, the maximum speed is ...

  s(15) = 15³(20 -15)/3200 = 5.2734375 m/s ≈ 5.27 m/s

The distance traveled is the integral of the speed.

  [tex]\displaystyle d=\dfrac{1}{3200}\int_0^{20}{(20t^3-t^4)}\,dt=\left.\dfrac{t^4(25-t)}{16000}\right|_0^{20}}=50[/tex]

The particle traveled 50 meters from A to B.

Aaron has 32 dimes and 8 quarters

From the question, we have the following parameters that can be used in our computation:

Worth of coins = 520 cents

Type of coins = Dimes and quarters

Four times as many dimes as quarters

Represent the dimes with d and the quarters with q

So, we have the following representation

d = 4q

When the dimes and quarters are converted to dollars, we have the following representations

Dimes = $0.10

Quarters = $0.25

So, we have the following representation

0.10d + 0.25q = 5.20

Recall that

d = 4q

So, we have

0.10 * 4q + 0.25q = 5.20

Evaluate the products

0.65q = 5.20

Divide both sides by 0.65

q = 8

Recall that

d = 4q

So, we have

d = 4 * 8

Evaluate

d = 32

Hence, the number of dimes is 32

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The equation of the graphed on the coordinate grid parallel to line M y = x and passing through the point P(4, -7) is equal to y = x - 11.

As given in the question,

Equation of the line M is given by :

y = x

Slope of the line M by comparing it with standard equation of the line with slope m is given by :

y = mx + c

Equation of the line M is y = x

Here m = 1

Slope of the required line is m₁ = 1 as it is parallel to line M

Equation of the required line which passes through ( x₁ , y₁) = ( 4, -7) with slope m₁ = 1 is given by:

y - y₁ = m₁( x - x₁)

⇒ y + 7 = 1( x - 4)

⇒ y= x - 4 -7

⇒ y= x - 11

Therefore, the equation of the required line which is parallel to line M and passing through point P is equal to y = x - 11.

Line M is graphed on the coordinate grid. y = x. Which equation can be used to represent a line parallel to M passing through the point P(4, -7)?

A.  x = 4          B. x = -7             C. y = -7              D. y = 4

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