The value of k that makes the statement true is k = 4.
What is value?Value is relative worth,merit of importance of something.if can refer to an intangible concept such as a person principal of a tangible object such as a rare coin.value vary widely across cultures, society and individual and can even vary within the same individual over time.
To show this, we can expand both sides of the equation and compare the terms. The left side of the equation becomes:
x⁴y⁸ + 7x³y¹²
The right side of the equation becomes:
2x⁴y⁸ + 7x³y¹²
Since both sides of the equation are identical, we can conclude that the value of k that makes the statement true is k = 4.
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Find the slope of a line parallel to each given line Y=-2/5x+3
Answer:
y = -2/5x + 3
Step-by-step explanation:
The slope of a line parallel to another line has the same slope. So, the slope of a line parallel to the line y = -2/5x + 3 is -2/5. To write the equation of a line with slope -2/5 that is parallel to y = -2/5x + 3, you can use the point-slope form of a line: y - y1 = m(x - x1), where m is the slope, (x1, y1) is any point on the line, and m is the slope. To use this form, you can choose any point on the line y = -2/5x + 3 and plug in the coordinates for (x1, y1). For example, if you choose (0,3), the equation for the line parallel to y = -2/5x + 3 is:
y - 3 = -2/5(x - 0)
y - 3 = -2/5x
y = -2/5x + 3.
What type of number is 80i?
Choose all answers that apply:
Real
Imaginary
Complex
Answer:
complex and imaginary.
Answer:
Imaginary/Complex. While the i means negative, it can also mean an imaginary integer. Often times, i is described as the square root of negative one, or simply an undefinable/negative integer. Since 80i can be considered both complex and imaginary, imaginary is more fitting due to the fact that i cannot be defined fully by mathematical means other than it meaning "imaginary" or "complex". In conclusion, you should pick both imaginary and complex.
Hope this helps!
find a number delta such that if |x-2| < delta then |4x-8| < epsilon, where epsilon is greater than 0.1
We can take delta as epsilon/4 to satisfy |4x - 8| < epsilon.
First of all, let us find an expression for |4x-8| in terms of |x-2|.
Since x can be either less than or greater than 2, then we'll have two cases:
Case 1: x < 2. Then 4x < 8 and |4x - 8| = 8 - 4x.
Case 2: x > 2. Then 4x > 8 and |4x - 8| = 4x - 8.
In either case, we see that |4x - 8| is proportional to |x - 2| with a constant of 4.
Therefore, we can take delta = epsilon/4 to satisfy |4x - 8| < epsilon.
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The lateral height of a cone is 4 inches and the area of the base of the cone is 49π in². It requires 2.5 minutes to paint the cone.
The area of the base is doubled.
How long will it take to paint this cone if it can be painted at the same rate? Use π≈3.14.
Enter your answer, rounded to the nearest tenth, in the box.
min
Answer:
100.2
Step-by-step explanation:if its the lateral height of 4 it has to 420
According to government data 22 percent of children in the United States under the age of 6 years live in households with incomes that are closed a pincome A simple random sample of 300 children in the United States under the age of 6 years was selected for a study of learning in early childhood if the government data are correct, which of the following best approximates the probability that at 27 percent of the children in the sample live in households that are closed at the particulo income level o represents a standard normal random variable) ole O с P D Р 0.27-0.22 (0.22)(0.78) Or pli C 0.27–0.22 (0.27)(0.73) 300 Р 0.22-0.27 10:22)(0.78) E 0.22-0.27 V (0.27)(0.73)
The problem is asking to find the probability that in a sample of 300 children under the age of 6 years in the United States, 27% of them live in households that are at or below poverty income.
The first step is to calculate the standard deviation for the proportion of children in poverty in the sample. This can be done using the formula:
σ = sqrt(p * (1-p) / n)
Where p is the proportion of children in poverty in the population (0.22) and n is the sample size (300).
Next, we can standardize the difference between the sample proportion and the population proportion using the z-score formula:
z = (p_sample - p_population) / σ
Finally, we can find the probability that the z-score is less than or equal to the z-score corresponding to a 27% sample proportion using a standard normal table or calculator. This probability can be interpreted as the probability that 27% or fewer children in the sample are living in households below poverty income.
Answer choice C, (0.27 - 0.22) * (0.73), does not seem to be related to the steps outlined above and does not provide an accurate answer for the problem.
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) suppose you have 13 tiles, each with one letter, and that the letters on these tiles spell combinatorics. how many distinct two-letter words can be made from these tiles? (note that the same tile cannot be used twice, but two tiles with the same letter can be used together.)
The number of words with two A's and the number of words with one A, which you have already counted Twice.
a). There are 3 words with 2 as well as (62) 3 words with 1 as, for a total of 8 7 6 3 6 15 6
Consider dividing 8-letter words into cases according to how many A's are present in the word:
1) You need to arrange the letters AAPRRMTT if there are two As.
2) If there are three A's, you can subdivide this based on the letter that is missing. (The examples P and M, as well as R and T, ought to have comparable counts.)
3) If there are 4 A's, then you break this into subcases based on the 2 letters omitted: RR, TT, PR, PM, PT, MR, MT.
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A researcher is planning an experiment that requires S. cerevisiae in late exponential (log) phase, whenits OD600 will be ~0.7. The researcher knows that S. cerevisiae have a doubling time of 90 minutes under the conditions that she is using. It's currently 10 AM, and her culture is in early log phase and has an OD600 of 0.2. When will her cultures be ready for the experiment?(Note: This is a real-life situation that the teaching staff deals with on a routine basis.)Early afternoon - before 3:00Late afternoon - after 3:00Tomorrow morningVery soon within the hour
Based on the doubling time and starting OD600, it can be estimated that the cultures will reach an OD600 of 0.7 in late afternoon, after 3:00 PM.
To determine the time when the S. cerevisiae culture will reach an OD600 of 0.7, we need to calculate the number of doublings that will occur.
First, we need to find the difference in OD600 between the current OD600 of 0.2 and the desired OD600 of 0.7:
0.7 - 0.2 = 0.5
Next, we can use the equation for a logarithmic growth curve to determine the number of doublings required to reach an OD600 of 0.7:
ln(0.7/0.2) / ln(2) = n
where n is the number of doublings required.
Next, we can multiply n by the doubling time of 90 minutes to determine the total time required to reach an OD600 of 0.7:
t = 90 * n
So, if it is currently 10 AM, the cultures will be ready for the experiment at
10 AM + t.
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assuming that water has a density of exactly 1 g/cm3, find the mass of 1.55 cubic meter of water in kilograms.
Answer to your question is 158kg
Solve each equation:6x + ? = 10x+5
The complete equation is 6x + 4x + 5 = 10x + 5.
What is an equation?Two algebraic expressions having same value and symbol '=' in between are called as an equation.
Given:
An equation,
6x + ? = 10x+5
To find the missing term:
Let the missing terms is n.
Then,
6x + n = 10x + 5
n = 4x + 5.
Therefore, the missing term is 4x + 5.
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Employees were asked how many times per week they exercised. The frequency table shows the results of the survey.
The answers include the following:
The total frequency is 22 + 16 + 18 + 22 + 9 + 13 + 6 + 3 + 1 = 110
We have given the frequency table
Number: 0 1 2 3 4 5 6 7 8
Frequency: 22 16 18 22 9 13 6 3 1
Probability distribution table
Number: 0 1 2 3 4 5 6 7 8
Frequency: 22/110 16/110 18/110 22/110 9/110 13/110 6/110 3/110 1/110
Probability P (x ≥ 7 ) = 3/110 + 1/110 = 4/110 = 2/55
P (x = 3 ) = 22/110 = 11/55
P (x < 4) = 22/110 + 18/110 + 16/110 + 22/110 = 78/110 = 39/55
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Blitzstein, 1.43) Let A and B be events. The symmetric difference AAB is defined to be the in A or B but not both. In logic and engineering, this event is also set of all elements that are called the XOR (exclusive or) of A and B. We will show P(AAB) P(A)+ P(B) 2P(An B) in two ways: words and a picture and (a) via an explanation of why this makes using your own sense (b) by using the definition and properties of probability.
The XOR (exclusive or) of two events A and B can be defined as the set of all elements that are in either A or B but not both.
The probability of this event, P(AAB), can be calculated by summing the probabilities of A and B and subtracting twice the probability of the intersection of A and B, as follows:
P(AAB) = P(A) + P(B) - 2P(AnB)
This can be illustrated with a Venn diagram, where A and B are represented by two overlapping circles. The intersection of A and B, AnB, is represented by the overlapping region, and the symmetric difference, AAB, is represented by the non-overlapping regions of A and B.
The probability of AAB can then be calculated by adding the area of the two non-overlapping regions and subtracting twice the area of the overlapping region.
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14y+37/5 - 8 (2y - 1)
Step-by-step explanation:
[tex]14y + \frac{37}{5} - 8(2y - 1)[/tex]
BODMAS:
We deal with the brackets first
[tex]8(2y - 1) [/tex]
we multiply everything in the brackets with 8
[tex] - 8 \times 2y = - 16y[/tex]
[tex] - 8 \times - 1 = 8[/tex]
[tex]14y + \frac{37}{5} - 16y + 8[/tex]
Let's bring the like-terms together by rearranging the question
[tex]14y - 16y + 8 + \frac{37}{5} [/tex]
[tex]14y - 16y = - 2y[/tex]
[tex]8 + \frac{37}{5} = 15.4[/tex]
Answer[tex] - 2y + 15.4[/tex]
A large equilateral triangle pyramid stands in front of the city's cultural center. Each side of the base measures 40 feet and the slant height of each lateral side of the pyramid is 50 feet.
A painter can paint 100 square feet of the pyramid in 18 minutes.
How long does it take the painter to paint 75% of the pyramid?
Enter your answer, rounded to the nearest tenth, in the box.
min
The painter takes 877.5 minutes to paint 75% of the pyramid.
What is surface Area?A 3D object's surface area is the entire area that all of its faces cover. For instance, the surface area of a cube is its surface area if we need to determine how much paint is needed to paint it. It is consistently expressed in square units.
Given:
base side= 40 feet
slant height = 50 feet.
So, the Surface area
= Base + 1/2 perimeter of the base x slant height
= (50x50) + 1/2 (50x4) (40)
= 2500 + 0.5 x 200 x 40
= 6500 ft²
Now, to paint 75% of the Pyramid
= 6500 / 100 x 75
= 4875
As, the painting rate 100 square feet
= 4875 /100 x 18
= 48.75 x 18
= 877.5 minutes
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Answer:
Step-by-step explanation:
The quotient of (x4 – 3x2 + 4x – 3) and (x2 + x – 3) is a polynomial. What is the quotient?
x4 – 2x2 + 5x – 6
x2 – x + 1
x6 + x5 – 6x4 + x3 + 10x2 – 15x + 9
x4 – 4x2 + 3x
Answer:
B
Step-by-step explanation:
Got it right on the exam
What is 3x+y=-14
-2x-y=9
Answer:
x = -5; y = 1
Step-by-step explanation:
We can solve the system of equations using the elimination method.
Because y and -y cancel out, we can eliminate this variable and solve for x:
[tex]3x+y=-14\\-2x-y=9\\\\3x-2x+y-y=-14+9\\x=-5[/tex]
Now, we can plug this x into any of the two equations to find y:
[tex]3(-5)+y=-14\\-15+y=-14\\y=1[/tex]
←
Graph: y = x-41+2
-6-4-2
6
4
2
-2
4
6
Y
2
4
9
Click or tap the graph to plot a point.
6
X
Draw
y
A graph of the absolute function y = |x - 4| + 2 with three points that fit on the axes is shown in the image attached below.
What is an absolute value function?In Mathematics, an absolute value function is a type of function that is composed of an algebraic expression, which is placed within absolute value symbols and it typically measures the distance of a point on the x-axis to the x-origin (0) of a cartesian coordinate (graph).
Next, we would use an online graphing calculator to plot the given absolute value function y = |x - 4| + 2 as shown in the graph attached below.
By observing critically the graph (see attachment), the three ordered pairs (points) that fit on its axes include the following:
Ordered pair = (2, 4).
Ordered pair = (6, 4).
Ordered pair = (4, 2).
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Find the Perimeter of the triangles.
GEOMETRY HONORS I
the perimeter of the given triangles will be 119 inches and 73.5 inches.
What is Perimeter?The perimeter of a form is the space surrounding its edge. Find the perimeter of various forms by summing the lengths of their sides.
Given a triangle that has two angles equal,
Since the isosceles triangle has both two equal sides and two equal angles.
Thus, the given triangle is an isosceles triangle
So,
7x - 13 = x + 29
6x = 42
x = 8
From the general formula of the perimeter:
The perimeter of a triangle = sum of all sides
In our case,
perimeter = 7x - 13 + x + 29+ 3x + 5
perimeter = 11x +31
Substitute the value of x
Perimeter = 11 * 8 + 31
The perimeter of the triangle = 119 in.
The same process will be followed in question number 11
and the perimeter of the triangle in question 11 will be 73.5 inches
Therefore, the perimeter of the given triangles will be 119 inches and 73.5 inches.
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true/false. the following histogram shows the distribution of house values in a certain city. the mean of the distribution is $403,000 and the standard deviation is $278,000 .
False. The histogram shows the frequency of house values, not the values themselves.
The histogram in the question does not show the actual values of house values in a certain city. It instead shows the frequency of house values. The histogram has the house values on the x-axis and the frequency of house values on the y-axis. The frequencies are shown as bars and the height of each bar represents the number of houses with that value. The mean and standard deviation mentioned in the question are statistical measures of the actual house values in the city. The mean is the average of all the house values in the city and the standard deviation is a measure of the variation in the house values. Therefore, the statement that the histogram shows the distribution of house values in a certain city with the mean of $403,000 and the standard deviation of $278,000 is false.
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Kim is in the tenth grade and takes a standardized science test. Use his test scores below to answer the question that follows. raw score 72 percentile 88 stanine 8 grade equivalent 12.1
Kim's test scores indicate that: he scored as well as or better than 72 of the test takers. 28% of the test takers scored better than he did. he would perform adequately in a twelfth grade science class. he scored as well as or better than 88% of the test takers. he answered 72% of the questions correctly.
Kim's test scores indicate that he scored as well as or better than 72% of the test takers, and 28% of the test takers scored better than him. His grade equivalent of 12.1 indicates that he would perform adequately in a twelfth grade science class.
His percentile of 88 indicates that he scored as well as or better than 88% of the test takers. His raw score of 72 does not directly indicate the percentage of questions answered correctly, but it can be assumed that he answered a majority of the questions correctly to achieve his score.
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the last digit in a measured value, whose exact value we cannot know for sure, is referred to as the . multiple choice question. rate-limiting digit certain digit uncertain digit determinant digit
The "uncertain digit" is the final digit of a measured value whose precise value we are unsure about.
Explain about the uncertain digit?The total number of certain digits in a measurement plus one estimated or uncertain digit make up the significant figures.
Specific graduations or markings on the tool that is used to record the measurement are the basis for some of the digits. A measurement with the more significant figures will be produced by a tool with much more graduations. A guess or estimate of the object's location between the closest graduations is a "uncertain digit." As a result, in a measurement that is accurately reported, the last digit is important but uncertain.Thus, the "uncertain digit" is the final digit of a measured value whose precise value we are unsure about.
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Solving equations: 12x + 5 = 4x + 37
Answer:
x = 4
Step-by-step explanation:
12x + 5 = 4x + 37
subtract 5 from both sides:
12x + 5 - 5 = 4x + 37 - 5
12x = 4x + 32
subtract 4x from both sides:
12x - 4x = 4x + 32 - 4x
8x = 32
divide both sides by 8:
8x/8 = 32/8
x = 4
the amount of garbage, g produced by a city with population p is given by . is measured in tons per week, and is measured in thousands of people. the town of tola has a population of 25,000 and produces 10 tons of garbage each week. express this information in terms of the function f
12=f is used to describe the given information in terms of the given function (40).
The equation G=f shows the relationship between the amount of garbage G produced by a city with a population of p(people in thousands) (p).
It is assumed that the town of Tola has a population of 40 000 people and that they produce 12 tonnes of trash per week. This suggests that p=40k and G=12 tonnes each week. Therefore, in the above function, change 40 to p and 12 to G.
12=f(40)
As a consequence, 12=f is used to describe the given information in terms of the given function (40).
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Imagine that a researcher conducts a study to compare rote memorization with elaborative encoding. The researcher selects 16 students at random from a class of 200 students, and then randomly assigns 8 to the rote memorization condition and 8 to the elaborative encoding condition. Just by chance, 7 of the 8 rote memorization subjects are women and 7 of the 8 elaborative encoding subjects are men. Is there something wrong with the design of this study?
A. There is a problem with the design of the study. To be valid, the researcher should make sure that men and women are equally represented in the two conditions. Otherwise the false positive rate will be greater than 5%.
B. There is a problem with the design of the study. If the subjects were being randomly assigned to the two groups, there shouldn't be such a difference in the proportion of men and women.
C. There is a problem with the design of the study. Whenever two groups are not well matched, even as a result of random sampling error, any conclusions about population means are invalid.
D. Nothing is wrong with the design of the study. By chance, two samples might differ from each other in various ways, but the likelihood of a false positive is still only 5%.
Option B is correct. When researcher conducts a study, it is important to ensure that the groups being compared are well matched.
In this case, if the subjects were truly being randomly assigned to the two conditions, it is unlikely that 7 of the 8 subjects in each condition would be either all women or all men. This suggests that there might be some issue with the randomization procedure, such as bias in the selection of subjects or unequal allocation to the two conditions. This unequal representation of men and women in the two groups could potentially affect the validity of any conclusions drawn from the study, since the two groups are not well matched. Therefore, there is a problem with the design of the study.
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1) -5y+3=2(4y+12)
2) 4 x 2 − 2 x − 2 x − 2 = − 1 2
Answer:
4x2-2x-2x-2=-12
Step-by-step explanation:
- number's
Which one of the following compound inequalities has no solution?
[A]3x + 4 < x-8 and -5x +4> 3x - 10
[B]4x-6 ≤ 5x + 6 and -3x - 2 > 2x+8
[C]-4x-3 ≤ 2x +9 and -3x+2> - 2x + 5
[D]4(x + 1) ≥ 3(x + 2) and -3(x - 1) <5(x + 2)
The compound inequality that has no solution, according to the query, is B.
What are the two inequalities' rules?Rule 1: When the same quantity is applied to or subtracted on both sides, an inequality sign does not change. Rule 2: Once both ends are duplicated or halved by a positive value, the inequality sign does not change.
[A] 3x + 4 < x - 8 and -5x + 4 > 3x - 10
Solving for x, we get:
3x + 4 < x - 8 => 2x > 12 => x > 6
-5x + 4 > 3x - 10 => 2x < 14 => x < 7
The correct solution to x is 6 < x < 7, which is the overlapping answer.
Since this two inequalities don't have any common solutions, when we solve all of the 2 inequality in [B], we find there is no solution.
In the actual number system, the equation 4x - 6 ≤ 5x + 6 can be resolved as -x ≥ 12, with no answer.
-3x - 2 > 2x + 8 can be solved as -5x > 10, which has no solution in the real number system.
[C] -4x-3 ≤ 2x +9 and -3x+2> - 2x + 5
Solving for x, we get:
-4x - 3 ≤ 2x + 9 => -6x ≤ 12 => x ≥ -2
-3x + 2 > -2x + 5 => -x > 3 => x < -3
which is an empty set and has no solution.
[D] 4(x + 1) ≥ 3(x + 2) and -3(x - 1) < 5(x + 2)
Solving for x, we get:
4(x + 1) ≥ 3(x + 2) => x ≥ -3
-3(x - 1) < 5(x + 2) => x > -2
The overlapping solution for x is x > -2 and x ≥ -3, which is a valid solution of x > -2.
Therefore, B has no solution.
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AREA The area of the rectangle in the figure is 32xy square units. Find the width of the rectangle. Write any variables in alphabetical order.
8xy
The value of the width of the rectangle is 4y² units for the area of 32xy³.
What is area?An area is just a surface that is empty. The length and breadth οf a fοrm are used tο cοmpute its area. Each shape's area is equal tο the number οf unit squares that can fit inside οf it. Many squares with sides that are οne unit by οne unit make up the grid. These squares each have an area οf οne square unit. Hence, each square is referred tο as a unit square.
Given that the area of the rectangle is 32xy³ square units.
The area of the rectangle is given as:
A = (l)(w)
Substituting the value of l = 8xy we have:
32xy³ = 8xy × (w)
w = 32xy³/ 8xy
[tex]$\Rightarrow \rm \frac{32xy^3}{8xy}[/tex]
[tex]$\Rightarrow \rm \frac{32y^3}{8y}[/tex]
[tex]$\Rightarrow \rm \frac{4y^3}{y}[/tex]
[tex]$\Rightarrow \rm \frac{4y^2}{1}[/tex]
⇒ 4y²
Hence, the value of the width of the rectangle is 4y² units.
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copy and paste the descriptive statistics for the prices variable for all 75 observations in the box to the right. make sure the output contains the n, mean, median, standard deviation, min/max, and the quartiles of the variable specified. interpret in the words of the problems the following statistics that you generated:
The shape of the distribution, is symmetric, is the best description of statistics about scores.
What is standard deviation ?
The standard deviation is the positive square root of the variance of this data set. Variance of a data set is the sum of squared differences of the data values from its mean to the total count of data values.
The given data in the problem is;
Mean = 78%
Standard deviation = 4%
Min = 64
Median = 78
Q1 = 72
Q3 = 84
Max = 99
The condition for the symmetric distribution is found as;
Q2-Q1 = Q3 - Q2
From the data we have;
Q2-Q1 = 6
Q3 - Q2= 6
So that , both are equal
Hence, the condition of symmetry is followed.
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The variables x
and y
vary directly. Use the values to find the constant of proportionality, k
. Then write an equation that relates x
and y
.
The equation that relates x and y is given by y = 24x
How to write equation that relates xand y?y = k × x
Where,
k = constant of proportionality
x = 3
y = 72
y = k × x
72 = k × 3
72 = 3k
divide both sides by 3
k = 72/3
k = 24
Hence,
The equation that relates x and y is;
y = kx
y = 24x
.
In conclusion, y = 24x is the equation that relates x and y
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y=-7x+14x-5 in vertex form
The vertex form of an equation is,
⇒ y = - 7 (x - 1)² + 2
What is Quadratic equation?An algebraic equation with the second degree of the variable is called an Quadratic equation.
We have to given that;
The equation is,
⇒ y = - 7x² + 14x - 5
Now, We can solve the equation for the vertex form as;
⇒ y = - 7x² + 14x - 5
⇒ y = - 7 (x² - 2x + 1) + 7 - 5
⇒ y = - 7 (x - 1)² + 2
Thus, The vertex form of an equation is,
⇒ y = - 7 (x - 1)² + 2
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y = 3x + 2
y = 4x-5
Please help i need to show my work
Answer: To solve for x, we need to find the value of x that makes both equations equal to each other. We can do this by setting the two equations equal to each other and solving for x:
3x + 2 = 4x - 5
Subtracting 4x from both sides:
-x - 2 = -5
Adding 2 to both sides:
-x = -3
Finally, dividing both sides by -1:
x = 3
So x = 3 is the solution that makes both y = 3x + 2 and y = 4x - 5 equal to each other.
You can substitute x = 3 into either equation to find the corresponding y value:
y = 3x + 2, when x = 3, y = 3(3) + 2 = 9 + 2 = 11
y = 4x - 5, when x = 3, y = 4(3) - 5 = 12 - 5 = 7
So the solution is (x, y) = (3, 11) or (3, 7).
Step-by-step explanation: