Answers
Answer:
(p o q) = 54
(q o p) = 68
Step-by-step explanation:
Another way to write is (p o q)(3) is p(q(3)). As you can see, you start with the inner function and 3 is an input in the q(x) function. Then, the output of this becomes the input of p(x) (the outer function), which yields a final output and the answer:
[tex]p(x) = 4x + 2\\q(x)=5x-2\\\\p(q(3))\\\\q(3)=5(3)-2=13\\p(13)=4(13)+2=54[/tex]
You do the same process for (q o p)(3), which can be written as q(p(3)), where you start with p(3) and then plug in this result as the input for q(x):
[tex]p(x)=4x+2\\q(x)=5x-2\\\\q(p(3))\\\\p(3)=4(3)+2=14\\q(14)=5(14)-2=68[/tex]
Related Questions
Greta’s family drinks 3. 1/4 quarts of milk and 1 5/6 quarts of juice in one week. About how much more milk than juice does Greta’s family drink in one week?
Answers
Answer:1 5/12 or written the other way 17/12
Step-by-step explanation:
The nutrition information on the cereal box says that a 1/2-cup serving provides 210 calories and 9 grams of dietary fiber. At that rate, find how many calories and grams of fiber are in a 2/3-cup serving.
Answers
Answer:
280 calories and 12 grams of dietary fiber
Step-by-step explanation:
because 210(2/3) = 140
= 140 ÷ 1/2 = 280
we do the same steps with grams
9(2/3) = 6
= 6 ÷ 1/2 = 12
Solve for A.
W=A/6.
Help please.
Thank you! TIA
Answers
Answer:
A = w*6
Step-by-step explanation:
W = A/6
Multiply both sides by 6 using the multiplication property of equality.
A = W*6
or
A = W x 6
Hope this helps!
How to show steps upon problem to get answer
Answers
The simplified form of the expression xy( x³y⁵ - x⁷ ) is x⁴y⁶ - x⁸y.
What is the simplified form of the expression?Given the expression in the question;
xy( x³y⁵ - x⁷ )
To simplify the expression, apply distributive property.
xy( x³y⁵ - x⁷ )
xy( x³y⁵ ) - xy( x⁷ )
xy( x³y⁵ ) - xy( x⁷ )
Multiply xy and ( x³y⁵ )
x⁴y⁶ - xy( x⁷ )
Multiply xy and ( x⁷ )
x⁴y⁶ - x⁸y
Therefore, the simplified form is x⁴y⁶ - x⁸y.
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Find an equation for the perpendicular bisector of the line segment whose endpoints are (−2 ,− 9) and (−6,7). PLSLLSLS
Answers
The equation of the perpendicular bisector of the line segment joining (-2, -9) and (-6, 7) is y = (-1/4)x - 2
What is the slope of the line?The slope of the line is a tangent angle made by line with horizontal. i.e. m =tanx where x in degrees.
Here,
The midpoint of the line segment joining (-2, -9) and (-6, 7) can be found using the midpoint formula:
Midpoint = ( (x₁+x₁)/2 , (y₁+y₁)/2 )
Midpoint = ( (-2-6)/2 , (-9+7)/2 )
Midpoint = (-4,-1)
Next, we need to find the slope of the line joining the two points (-2, -9) and (-6, 7). We can do this using the slope formula:
Slope = (y₂ - y₁) / (x₂ - x₁)
Slope = (7 - (-9)) / (-6 - (-2))
Slope = 4
The slope of the line perpendicular to the line segment is the negative reciprocal of the slope of the line joining the two points. So the slope of the perpendicular line is -1/4.
Using the point-slope form of a line, the equation of the perpendicular bisector can be written as:
y - y₁ = m(x - x₁), where (x₁, y₁) is the midpoint and m is the slope of the line.
Plugging in the values we found, we get:
y - (-1) = (-1/4)(x - (-4))
y + 1 = (-1/4)(x + 4)
y + 1 = (-1/4)x - 1
y = (-1/4)x - 2
Therefore, the equation of the perpendicular bisector of the line segment joining (-2, -9) and (-6, 7) is y = (-1/4)x - 2.
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Which expression is equivalent to
Answers
The expression equivalent to 5x +10y -15 by taking the common factor is 5(x + 2y - 3).
What is taking out common factors?
The takeout of the common factor is the procedure, ab + ac = a(b + c). Think about how the expression 5x + 10 gets factored. The common factor 5, which was previously in front of the brackets, has been removed.
Figuring out what to multiply to create an expression. It is comparable to "splitting" an expression into numerous smaller expressions.
Given, the expression is 5x + 10y -15
So, 5x +10y -15 = 5x + 5*2y - 5*3
= 5(x + 2y - 3)
Hence, the required answer is 5(x + 2y - 3).
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The ratio of the number of model cars that Jim owns to the number of model cars Terrence owns is 8 : 6. Terrence owns 36 models cars. How many model cars does Jim own?
Answers
The provided statement indicates that Jim and Terrence each possess eight model automobiles, whereas Terrence owns six, making an 8:6 ratio. Jim is the owner of the 48 model card, then.
What does a ratio mean mathematically?If b is really not equal to 0, then an arrangement of the numbers a and b expressed as a/b is a ratio. An equation known as a percent establishes two ratios with the identical value. You might, for instance, write the ration as described in the following: 1: 3 in the case of 1 male and 3 girls.
You are aware that Jim and Terrence own an 8:6 ratio in terms of the total number of model automobiles they own.
Accordingly, you can answer the task as follows: Let's say Jim owns x model automobiles.
8/6 = x/36
x = 36*8/6
x = 288/6
x = 48
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if 30% of a number is 7, then what is 10% of the number ?
Answers
Answer:
70.0000
Step-by-step explanation:
aka 70%
Yasmin is participating in a 5-day cross-country biking challenge. She biked for 45,60,68 and 52 kilometers on the first four days. How many kilometers does she need to bike on the last day so that her average (mean) is 58 kilometers per day?
Answers
Step-by-step explanation:
The total distance biked by Yasmin on the first four days can be calculated as follows:
45 + 60 + 68 + 52 = 225 km
To find out how many kilometers she needs to bike on the last day to achieve an average of 58 km per day over the 5 days, we can set up an equation based on the formula for the mean:
(45 + 60 + 68 + 52 + x) / 5 = 58
Where x is the number of kilometers Yasmin needs to bike on the last day. Expanding the equation:
225 + x = 5 * 58
225 + x = 290
Subtracting 225 from both sides:
x = 65
So Yasmin needs to bike 65 kilometers on the last day to achieve an average of 58 kilometers per day over the 5 days
Graph the line with slope 2 passing through the point (-3, -4).
Answers
The solution is, the equation is y=2/3x.
What is meant by graph?In math, a graph can be defined as a pictorial representation or a diagram that represents data or values in an organized manner. The points on the graph often represent the relationship between two or more things.
A diagram representing a system of connections or interrelations among two or more things by a number of distinctive dots, lines, bars, etc.
here, we have,
so the line is in slope intercept form
y=mx+b, m=slope and b=y intercept
we know the slope so just solve for b
y=2/3x+b
subsitute
3 for x and 2 for y
2=2/3(3)+b
2=2+b
subtract 2 from both sdies
0=b
so the equaiton is
y=2/3x+0 or just simply
y=2/3x
here is the graph
just input values for x and get y values exg
x=3 y=2
x=6 y=4
x=0 y=0
x=-3 y=-2
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As part of a larger experiment, Dale (1992) looked at six samples of a wetland soil undergoing a simulated snowmelt. Three were randomly selected for treatment with a neutral pH snowmelt; the other three got a reduced pH snowmelt. The observed response was the number of Copepoda removed from each microcosm during the first 14 days of snowmelt Reduced pH Neutral pH 256 159 149 54 123 248 (a) [3 points Write two simple models: one model for the number of Copepoda in a neutral pH snowmelt and one model for the number of Copepoda in a reduced pH snowmel. Use mathematical notations. (b) 2 points We want to test whether the two treatments have equal average numbers of Copepoda. Write the n and the alternative hypotheses using the notations defined in the previous question (c) 5 points We want to perform a t-test. What assumptions are you making? Compute the corresponding test statistic. Give the critical value for a level of significance v = 0.05. What do you conclude? (d) 5 points) Using a randomization-based analysis, test the nul hypothesis that the two treatments have equal average numbers of Copepoda versus a two-sided alternative. Use a level of significance v = 0.05.
Answers
(a) The mathematical notations is (xₙ, yₙ)
(b) The alternative hypotheses using the notations defined in the previous question is t = (Xₙ - Yₙ) / SE
(c) The assumptions making is variances of the two populations are equal.
A hypothesis is a tentative explanation or prediction of a phenomenon, and it is essential in scientific research. In this study, we have two hypotheses:
Null Hypothesis: There is no significant difference in the average number of Copepod between the reduced pH and neutral pH snowmelt treatments.
Alternative Hypothesis: There is a significant difference in the average number of Copepod between the reduced pH and neutral pH snowmelt treatments.
Model:
A model is a mathematical representation of a phenomenon, and it is used to make predictions or explanations. In this experiment, we can create two simple models:
Model for Neutral pH Snowmelt:
Let Yₙ be the number of Copepod in a microcosm treated with neutral pH snowmelt. Then, Yₙ follows a normal distribution with mean µn and standard deviation σn.
Model for Reduced pH Snowmelt:
Let Yₙ be the number of Copepod in a microcosm treated with reduced pH snowmelt. Then, Yₙ follows a normal distribution with mean µr and standard deviation σr.
Assumptions:
Before conducting a t-test, we must ensure that the data satisfies the following assumptions:
The sample is a random and representative sample of the population.
The data is normally distributed.
The variances of the two populations are equal.
The test statistic for the t-test is:
t = (Xₙ - Yₙ) / SE
where Xₙ is the sample mean of neutral pH snowmelt, Yₙ is the sample mean of reduced pH snowmelt, and SE is the standard error.
Assuming a level of significance v = 0.05, we have a critical value of t = 2.306 for a two-tailed test with 4 degrees of freedom. If our calculated t-value is greater than 2.306 or less than -2.306, we reject the null hypothesis.
We can perform a randomization test as follows:
If the p-value is less than 0.05, we reject the null hypothesis and conclude that there is a significant difference in the average number of Cope pod between the reduced pH and neutral pH snowmelt treatments. If the p-value is greater than 0.05, we fail to reject the null hypothesis.
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st other people Suppose there are no implicit premises: this is the whole argument. Which of the following is true about this argument? o A The premise entails the conclusion because, if the premise is true, the conclusion has to be true B The premise does not entail the conclusion because, if the premise is true, the conclusion could still be false (setting aside facts not supplied by the premise) O с The premise entails the conclusion because, setting aside facts not supplied by the premise, there is no way the premise could be true and the conclusion false. D The premise does not entail the conclusion because it has no suppositional strength.
Answers
The true argument is option B) The premise does not entail the conclusion because, if the premise is true, the conclusion could still be false
The argument presented lacks logical reasoning and does not provide enough information to support the conclusion. The premise that "Bob is 13 feet tall" is a factual statement, but it is not sufficient to conclude that "Bob is taller than most other people." Without further information about the height distribution of people.
It is impossible to make such a conclusion based solely on Bob's height. Additionally, the argument does not provide any logical reasoning to connect the premise to the conclusion, so it is not a valid deductive argument.
Therefore, the correct option is (B)
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The given question is incomplete, the complete question is :
Bob is 13 feet tall So, Bob is taller than most other people Suppose there are no implicit premises: this is the whole argument. Which of the following is true about this argument?
A The premise entails the conclusion because, if the premise is true, the conclusion has to be true
B The premise does not entail the conclusion because, if the premise is true, the conclusion could still be false (setting aside facts not supplied by the premise)
C The premise entails the conclusion because, setting aside facts not supplied by the premise, there is no way the premise could be true and the conclusion false.
D The premise does not entail the conclusion because it has no suppositional strength
3x + 3xy + 4x +2xy combine like term
Answers
Answer:
the final answer is 7x + 5xy.
Step-by-step explanation:
3x + 4x = 7x
3xy + 2xy = 5xy
So, the final answer is 7x + 5xy.
Answer:
5xy+7x
Step-by-step explanation:
You see which ones have the same exact variables (x or xy)
Then you add the ones with the same variables together.
3x+4x=7x
3xy+2xy = 5xy
5xy+7x
(Depending on your teacher, they may not have to be in this order)
Write the inequality shown by the shaded region in the graph with the boundary line −5x+2y=−2
Answers
Answer:
Step-by-step explanation:
The boundary line of the shaded region in the graph, which is represented by the equation -5x + 2y = -2, can be used to write the inequality that represents the shaded region. To do this, we first need to determine which side of the boundary line the shaded region is on.
If the shaded region is on the same side of the line as the open half-plane that contains the y-axis, then the inequality is given by:
-5x + 2y > -2
If the shaded region is on the same side of the line as the closed half-plane that does not contain the y-axis, then the inequality is given by:
-5x + 2y ≥ -2
So, the inequality that represents the shaded region depends on the specific context and requirements of the problem, as well as the interpretation of the graph.
A set of data has a mean of 10 and a standard deviation of 3.
(a) Each value in the data set has 6 added to it. Write down the value of
(i) the new mean;
(ii) the new standard deviation.
(b) Each value in the original data set is multiplied by 6.
(i) Write down the value of the new mean.
(ii) Find the value of the new variance.
Answers
Answer:
Step-by-step explanation:
(a) (i) The mean of the original data set is denoted as μ and the constant value being added to each data point is denoted as c.
The formula for the new mean is simply μ + c, so the new mean is μ + 6 = 10 + 6 = 16.
(a) (ii) The standard deviation of the original data set is denoted as σ. Adding a constant value to each data point does not change the spread of the data set, so the new standard deviation is still σ = 3.
(b) (i) The mean of the original data set is denoted as μ and the constant value being multiplied to each data point is denoted as k.
The formula for the new mean is μ * k, so the new mean is μ * 6 = 10 * 6 = 60.
(b) (ii) The variance of the original data set is denoted as V. To find the new variance after multiplying each data point by k, we can use the formula: k^2 * V.
So, the new variance is 6^2 * V = 36 * V.
--------
Here is a definition of each variable:
μ: The mean of a set of data is the sum of all the values divided by the number of values. It represents the average value of the data set.
σ: The standard deviation of a set of data is a measure of the spread of the data set about the mean. It is the square root of the variance.
V: The variance of a set of data is the sum of the squares of the deviations of each value from the mean, divided by the number of values. It is a measure of the spread of the data set about the mean, but it is measured in squared units.
c: A constant value added to each data point.
k: A constant value multiplied to each data point.
A. 30.28 square feet
B. 24.28 square feet
C. 36.56 square feet
D. 30.56 square feet
Answers
Answer:
B. 24.28 square feet
Step-by-step explanation:
You want the area of a figure composed of a rectangle, triangle, and semicircle.
Area formulasThe formulas for the areas of the parts of the figure are ...
A = LW . . . . rectangle of length L and width W
A = 1/2bh . . . . triangle with base b and height h
A = π/2r² . . . . . . semicircle of radius r
RectangleThe area of the rectangle is ...
A = (4 ft)(3 ft) = 12 ft²
TriangleThe area of the triangle is ...
A = 1/2(4 ft)(3 ft) = 6 ft²
SemicircleThe semicircle has a radius that is half the diameter. The diameter is shown as 4 ft so the radius is 2 ft. The area of the semicircle is ...
A = π/2(2 ft)² = 4(3.14)/2 ft² = 6.28 ft²
Composite figure areaThe area of the composite figure is the sum of the areas of its parts:
Area = 12 ft² +6 ft² +6.28 ft² = 24.28 ft²
The area of the composite figure is about 24.28 ft².
A function is given.
g(t) = t4 − t3 + t2; t = −6, t = 6
(a) Determine the net change between the given values of the variable.
(b) Determine the average rate of change between the given values of the variable.
Answers
On solving the provided question we can say that the net change will be 17 and average rate of change = 17/1 = 17.
What is function?The subject οf mathematics includes quantities and their variatiοns, equations and related structures, shapes and their locations, and places where they can be fοund.
The term "functiοn" refers to the relationship between a set of inputs, each of which has an associated output. A cοnnection between inputs and outputs in which each input leads to a single, distinct result is known as a functiοn.
Each function is given a dοmain and a codomain, or scope. Usually, f is used to denote functiοns (x). input is an x. There are fοur main types of functions accessible. based οn the following factors: οn functions, one-to-one functions, many-tο-one functions, inside functiοns, and on functions.
The functiοn will be
h(4)=2(4²)-4
=32-4
=28
h(5)=2(5²)-5
=50-5
=45
Net change is 45-28 = 17
average rate of change = 17/1 = 17
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Rewrite the equation in Ax+By=C form
y=(1/3)x+3
Answers
To rewrite the equation in Ax + By = C form, we need to rearrange it so that the x and y terms are on the same side of the equation and the constant is on the other side and the equation become x + 3y = 9.
What is Equation?
An equation is a mathematical statement that shows the equality of two expressions or values. It typically contains one or more variables and an equal sign, which indicates that the expressions on either side of the equal sign have the same value. Equations can be used to represent various relationships between different mathematical objects and are used extensively in many fields of mathematics, science, engineering, and other disciplines. Equations can be solved to find the values of the variables that make the equation true, which is often the goal of many mathematical problems.
To rewrite the equation in Ax + By = C form, we need to rearrange it so that the x and y terms are on the same side of the equation and the constant is on the other side.
Starting with:
y = (1/3)x + 3
We can multiply both sides by 3 to eliminate the fraction:
3y = x + 9
Now we can rearrange to get the x and y terms on the left side:
-x + 3y = 9
So the equation in Ax + By = C form is:
x + 3y = 9
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You randomly survey middle school students and high school students about whether they prefer spring or winter. The results
are shown in the two-way table. Find the percent of middle school students that prefer each season and the percent of high school students that prefer each season
Answers
The percentage of middle school students that prefer each season and the percentage of high school students that prefer each season is 57.93% and 42.07% respectively.
What is the percentage?The percentage is the ratio of the composition of value to the overall composition of value multiplied by 100.
Here,
Total number of students = 93 + 31 + 36 + 54 = 214
The percentage of students in middle school prefer spring,
= number of students in middle school prefer spring / total student × 100%
= 93/214 × 100%
= 43.45%
Similarly,
The percentage of students in middle school prefer winter,
= number of students in middle school who prefer winter/ total students × 100%
= 31/214 × 100%
= 14.48%
Thus, the percentage of middle school students that prefer each season and the percentage of high school students that prefer each season are 43.45 + 14.48 = 57.93% and 100-57.93% = 42.07%.
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What is the answer? Provide steps please.
Answers
The given expression is proved.
What is trigonometry?
Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
here, we have.
tan∅/(1+ sec∅)
=(sin∅/cos∅)/(1+ sec∅) [tan∅=(sin∅/cos∅)]
=(sin∅/cos∅)/(1+1/cos∅)
=sin∅/1+cos∅
multiplying both numerator & denominator by 1-cos∅, we get,
=sin∅(1-cos∅)/ sin^2∅
=(1-cos∅)/sin∅
=cosec∅ - cot∅
Hence, The given expression is proved.
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PLEASE HELP WILL GIVE BRAINIEST!!
At what point does the graph of a function of this form start?
Answers
The start point the graph of a function of this form is (h, k)
How to determine the start of the functionFrom the question, we have the following parameters that can be used in our computation:
f(x) = a√(x - h) + k
The domain is given as
x ≥ h
This means that the initial x value is h
From the question, we have the following parameters that can be used in our computation:
f(h) = a√(h - h) + k
Evaluate
f(h) = k
Hence, teh initial point is (h, k)
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Solve for x, each figure is a trapezoid
Answers
By calculating , The value of x we get is 5 as a final resultant.
What is trapezoid ?
A trapezoid is a quadrilateral with two parallel sides, called the "bases," and two non-parallel sides, called the "legs." The parallel sides can have different lengths, and the trapezoid can be either right-angled or oblique. In other words, a trapezoid is a geometric shape that has two parallel sides, two non-parallel sides and four angles.
Since a Trapezoid has 360 Degrees total and since the sides are equal we can say that
180=110+17x-15
70=17x-15
85=17x
x=5
Therefore, By calculating , The value of x we get is 5 as a final resultant.
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Draw the following triangle after a 90 degrees counterclockwise rotation about the origin.
Answers
A graph of the triangle after a 90 degrees counterclockwise rotation about the origin is shown in the image attached below.
What is a rotation?In Geometry, the rotation of a point 90° about the center (origin) in a counterclockwise (anticlockwise) direction would produce a point that has these coordinates (-y, x).
By applying a rotation of 90° counterclockwise to the vertices for D, the coordinates of the vertices of the image point D' are as follows:
(x, y) → (-y, x)
Ordered pair A = (-3, 4) → Ordered pair A' = (-4, -3)
Ordered pair B = (-5, -1) → Ordered pair B' = (1, -5).
Ordered pair C = (-1, 2) → Ordered pair C' = (-2, -1).
In this exercise, we would use an online graphing calculator to plot the vertices of triangle A'B'C' as shown in the graph attached below.
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1.2. Identify and explain TWO types of goals in line with Anelisa 'story. 1.3. Discuss the benefits of goal setting on your career choice. 1.4. Discuss any THREE challenges Anelisa experienced that could have been been obstacles in achieving his goals. 1.5. Analyse how Anelisa's personal values contributed to his success. 1.6. Critically discuss how relationships can impact negatively on the achievement of goals TOTAL ACTIVITY 1: [30] Gauteng Department of Education (2+2) (4) (2x2) (4) (3x2) (6) (4x2) (8) (2x3) (6) 2023 Grade 11 Life Orientation Task
Answers
Types of Goals in line with Anelisa's story:
Personal Growth Goals: These goals are related to Anelisa's personal development and could include things like increasing her knowledge, learning new skills, and expanding her experiences.Career Goals: These goals are related to Anelisa's professional development and could include things like advancing in her career, increasing her income, or improving her job performance.Benefits of goal setting on your career choiceGoal setting helps individuals focus their efforts, prioritize their time and resources, and measure their progress towards achieving their goals. In the context of career choice, goal setting can help individuals:
Clarify their career aspirations and identify their strengths, weaknesses, opportunities, and threats.Develop a roadmap for their career journey and align their actions with their career vision.Stay motivated and engaged in their work and avoid feeling overwhelmed or discouraged by the challenges they face.Improve their performance and productivity, and increase their chances of achieving their desired outcomes.Challenges Anelisa experienced:
Lack of resources: Anelisa may have lacked the resources needed to achieve her goals, such as financial support, access to training programs, or sufficient time to complete her tasks.Resistance from others: Anelisa may have encountered resistance from others who opposed her goals, either because they disagreed with her vision or because they felt threatened by her ambition.Self-doubt and fear of failure: Anelisa may have struggled with self-doubt and fear of failure, which could have held her back from pursuing her goals and taking calculated risks to achieve them.Anelisa's personal values, such as determination, resilience, and a strong work ethic, likely played a significant role in her success. These values likely gave her the motivation and drive to pursue her goals, despite the challenges she faced. Additionally, her values may have helped her stay focused on her goals, maintain her sense of purpose, and make decisions that aligned with her vision for her life.
Relationships can impact the achievement of goals in both positive and negative ways. On the positive side, supportive relationships can provide individuals with emotional support, encouragement, and practical resources that can help them achieve their goals. On the negative side, relationships can also be a source of conflict and distraction, especially if they are not aligned with the individual's goals or values.
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Answer:
Step-by-step explanation:
lack of financial stability Nd resoouces
Sears is having a 35% off sale on all tires. Michelin tires sells for $125, find the Sales Price.
Answers
Answer:
You will pay 81.25
Step-by-step explanation:
If the cost is 35% off, you will need to pay 100% - 35% = 65%
125 * 65 %
125 *.65
81.25
You will pay 81.25
petra jogs 60 miles in 110 minutes, at this rate how long would her take to jog per one minutes
Answers
The speed of Petra will be 0.55 mile/minute.
What exactly is speed?
The definition of speed is:
The pace at which an object's location changes in any direction.
Speed is defined as the ratio of distance travelled to time spent travelling. Because it has just one direction and no magnitude, speed is a scalar number.
Formula for Speed
The speed formula is shown below:
s=d/t
Where,
s is the speed in metres per second, d is the distance travelled in metres, and t is the duration in seconds.
Now,
As given petra jogs 60 miles in 110 minutes
then in one minute she will jog =60/110 mile
=0.5454 mile/min
Hence,
The speed of Petra will be 0.55 mile/minute.
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Which of the following equations listed below are linear equations?
Answers
Only Equation I is a linear equation. A linear equation is defined as an equation where the highest power of the variable is 1, and the relationship between the variables is a straight line.
What is Straight line?
A straight line is a type of geometric shape that is defined as a line with no curvature, extending infinitely in both directions. In other words, it is a one-dimensional object that extends indefinitely without bending or curving. Straight lines are often represented mathematically as y = mx + b, where m is the slope (or gradient) of the line and b is the y-intercept.The slope determines the steepness of the line, and the y-intercept determines where the line crosses the y-axis. Straight lines play a crucial role in mathematics, especially in geometry and linear algebra.
Only Equation I is a linear equation.
A linear equation is defined as an equation where the highest power of the variable is 1, and the relationship between the variables is a straight line. In Equation I, P is equal to 4 times s, so the highest power of the variable (s) is 1, making this a linear equation.
In Equation II, the right-hand side of the equation contains a single constant ($3), not a variable, and therefore it is not a linear equation.
Equation III is not a linear equation because it is just a constant equal to 2 and does not contain a variable.
So the answer is: 1. Equation I, only.
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equation or inequality best
75x + 0.55y = 125
Answers
The solution set for the given equation is (0, 227), (1, 91) and (2, -45.45)
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
The given equation is 75x + 0.55y = 125.
The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.
Substitute x=0, 1, 2, 3, 4, 5,....
When x=0
75(0)+0.55y=125
0.55y=125
y=125/0.55
y=227
When x=1
75(1)+0.55y=125
0.55y=50
y=50/0.55
y=91
When x=2
75(2)+0.55y=125
0.55y=-25
y=-25/0.55
y=-45.45
Therefore, the solution set for the given equation is (0, 227), (1, 91) and (2, -45.45)
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please hel me.
i need help i don't know how to do this
Answers
The tables with their equations are
Table (a): y = 1/xTable (b): y = √xTable (c): y = x³Table (d): y = xHow to match the tables with their equationsFrom the question, we have the following parameters that can be used in our computation:
Tables and equations
Table (a)
Here, we notice that:
The output is the reciprocal of the input
This is represented as
y = 1/x
Table (b)
Here, we notice that:
The output is the square root of the input
This is represented as
y = √x
Table (c)
Here, we notice that:
The output is the cube of the input
This is represented as
y = x³
Table (d)
Here, we notice that:
The output is the same as the input
This is represented as
y = x
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new later
A scatter plot is shown below.
10
8
6
A
N
02 4
6
8 10 12 14 16
Which statement best explains why these data can or cannot be modeled using a line of best fit?
a. A line would not be appropriate because there is a negative association.
b. A line would not be appropriate because the points follow a nonlinear pattern.
c. A line would be appropriate because there is a positive association.
d. A line would be appropriate because the points follow a nonlinear pattern.
Answers
The points are scattered in the scatterplot and thus, a line would not be appropriate because the points follow a nonlinear pattern.
Hence, option b is the correct answer.
How can scatterplot identify relationships?Numerous different kinds of associations between two variables can be found using a scatterplot.
When there is no pattern visible in the points on a scatterplot, a relationship has no correlation.
When the points on a scatterplot exhibit a pattern rather than a straight line, a relationship is non-linear.
When the points on a scatterplot exhibit a largely straight line pattern, a relationship is linear. We shall look at this relationship in detail.
From the given graph we observe that the points do not follow a linear pattern.
The points are scattered and thus, a line would not be appropriate because the points follow a nonlinear pattern.
Hence, option b is the correct answer.
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The correct question is:
