What is the standard form of the linear function that passes
through the points (4, 1) and (2, -2)?
Answers
standard form for a linear equation means
• all coefficients must be integers, no fractions
• only the constant on the right-hand-side
• all variables on the left-hand-side, sorted
• "x" must not have a negative coefficient
\((\stackrel{x_1}{4}~,~\stackrel{y_1}{1})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{-2}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-2}-\stackrel{y1}{1}}}{\underset{run} {\underset{x_2}{2}-\underset{x_1}{4}}}\implies \cfrac{-3}{-2}\implies \cfrac{3}{2} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{1}=\stackrel{m}{\cfrac{3}{2}}(x-\stackrel{x_1}{4})\)
\(\stackrel{\textit{multiplying both sides by }\stackrel{LCD}{2}}{2(y-1)=2\left( \cfrac{3}{2}(x-4) \right)}\implies 2y-2 = 3(x-4)\implies 2y-2=3x-12 \\\\\\ -3x+2y-2=-12\implies -3x+2y=-10\implies \stackrel{\times -1\textit{ to both sides}}{3x-2y=10}\)
Related Questions
Emilio's Publishing prints and sells cookbooks to stores for $4.50 each. Their weekly profits can be modeled by the quadratic function P(x) = −0.1x2 + 15x + 120, where P(x) is profit and x is the number of $0.05 price increases. Use the graph to answer the question.
Graph of function p of x equals negative 0.1 x squared plus 15 x plus 120. The graph has the x-axis labeled as number of price increases, and the y-axis labeled as profit. The curve begins at (0, 120), increases to (75, 682.5), and decreases through (157.614, 0).
Approximately what amount should the company sell each cookbook for to maximize profit? (1 point)
$8.25
$9.50
$10.20
$17.00
Answers
Using the vertex of the quadratic equation, it is found that the profit will be maximized when each cookbook is sold for $8.25.
What is the vertex of a quadratic equation?A quadratic equation is modeled by:
\(y = ax^2 + bx + c\)
The vertex is given by:
\((x_v, y_v)\)
In which:
\(x_v = -\frac{b}{2a}\)
\(y_v = -\frac{b^2 - 4ac}{4a}\)
Considering the coefficient a, we have that:
If a < 0, the vertex is a maximum point.If a > 0, the vertex is a minimum point.In this problem, the function is modeled as follows, considering x as the price divided by $0.05.
P(x) = -0.1x² + 15x + 120.
The coefficients are a = -0.1 < 0, b = 15, c = 120, hence the x-value of the vertex is given by:
\(x_v = -\frac{15}{2(-0.1)} = \frac{15}{0.2} = 75\)
75 increases of $0.05, hence the price will be of:
4.5 + 75 x 0.05 = $8.25.
Hence, the profit will be maximized when each cookbook is sold for $8.25.
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with a reserve requirement of 5% and an initial deposit of $400, what is the maximum total amount of money that will be in the money supply? assume that all currency is deposited in a bank 7 banks hold no excess reserves (rr=.05)
Answers
The maximum money supply with a 5% reserve requirement and a $400 initial deposit is $8,000.
How to find maximum money?To calculate the maximum total amount of money that will be in the money supply, we need to consider the money multiplier effect based on the reserve requirement.
The money multiplier is given by the formula: MM = 1 / reserve requirement.
Given that the reserve requirement is 5% (rr = 0.05), the money multiplier is MM = 1 / 0.05 = 20.
The initial deposit is $400.
To calculate the maximum total amount of money in the money supply, we multiply the initial deposit by the money multiplier:
Maximum Money Supply = Initial Deposit * Money Multiplier
= $400 * 20
= $8,000.
Therefore, the maximum total amount of money that will be in the money supply is $8,000 when the reserve requirement is 5% and all currency is deposited in banks with no excess reserves.
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What is the measure of angle 3 in degrees?
27 degrees
33 degrees
60 degrees
153 degrees
Answers
Find the length of BC. *
Answers
Please help please please please please please please!!!!
Answers
Answer:
Angle YXZ
Step-by-step explanation:
The smaller the side the smaller is opposite angle
(ii) 4xz? [- xyz + 3yz?]
Answers
Answer: -4x²z²y + 12xz²y
Step-by-step explanation:-------------
Most engaged couples expect or at least hope that they will have high levels of marital satisfaction. However, because 54% of first marriages end in divorce, social scientists have begun investigating influences on marital satisfaction. (Data Source: These data were obtained from the National Center for Health Statistics. ) Suppose a counseling psychologist sets out to look at the role of having children in relationship longevity. A sample of 78 couples with children score an average of 51. 1 with a sample standard deviation of 4. 7 on the Marital Satisfaction Inventory. A sample of 94 childless couples score an average of 45. 2 with a sample standard deviation of 12. 1. Higher scores on the Marital Satisfaction Inventory indicate greater satisfaction.
Suppose you intend to conduct a hypothesis test on the difference in population means. In preparation, you identify the sample of couples with children as sample 1 and the sample of childless couples as sample 2. Organize the provided data by completing the following table:
Answers
To organize the provided data, we can create a table comparing the samples of couples with children (sample 1) and childless couples (sample 2) as follows:
Sample Sample Size Sample Mean Sample Standard Deviation
1 78 51.1 4.7
2 94 45.2 12.1
In this table, we have listed the sample number (1 and 2), the sample size (number of couples in each group), the sample mean (average Marital Satisfaction Inventory score), and the sample standard deviation (measure of variability in the scores) for each group. This organization allows us to compare the data and proceed with hypothesis testing on the difference in population means between the two groups.
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What is the volume of a square pyramid with a base length of 5 cm and a height of 6 cm?
Enter your answer in the box
Answers
Answer:
Step-by-step explanation:
The volume is \(V = \frac{1}{3} b^{2} h\)
Known facts:
length of base: 5cmheight of pyramid: 6cmLet us plug in the known value into the pyramid
\(v=\frac{1}{3} * 5^{2} *6 = 50\) cubic centimeters
The volume of a square pyramid is 50 cubic centimeters!
Hope that helps!
WHATS THE SLOPE? I need this ASAP!!
Answers
Answer:
4/3
Step-by-step explanation:
Lets begin by moving the negative 1 to the right. We are now at 4x = 3y + 6. If we move the 3y to the left and 4x to the right, we then get to -3y = -4x +6. We now need to divide by -3. This simplifies to y = 4/3x + 6. Therefore, the slope would be 4/3.
What is the slope of a line perpendicular to the line y = 1/5x - 3
Answers
Answer:
-5
Step-by-step explanation:
Perpendicular lines have negative reciprocal slopes.
find an equation of the tangent line to the given curve at the specified point. y = x 2 − 1 x 2 x 1 , ( 1 , 0 )
Answers
The equation of the tangent line to the curve \(y = \frac {(x^2 - 1)}{ (x^2 + x + 1)}\) at the point (1, 0) is y = (2/3)x - 2/3.
To find the equation of the tangent line to the curve at the point (1, 0), we need to find the slope of the tangent line and then use the point-slope form of a linear equation.
Let's differentiate \(y = \frac {(x^2 - 1)}{ (x^2 + x + 1)}\) using the quotient rule:
\(y' = [(2x)(x^2 + x + 1) - (x^2 - 1)(2x + 1)] / (x^2 + x + 1)^2\)
Substituting x = 1 into the derivative expression:
\(y'(1) = [(2(1))(1^2 + 1 + 1) - (1^2 - 1)(2(1) + 1)] / (1^2 + 1 + 1)^2\)
\(= [2(3) - (0)(3)] / (3)^2\)
= 6/9
= 2/3
Using the point-slope form y - y₁ = m(x - x₁), where (x₁, y₁) = (1, 0) and m = 2/3 we get,
y - 0 = (2/3)(x - 1)
y = (2/3)x - 2/3
The point-slope form of a linear equation is given by y - y₁ = m(x - x₁) where (x₁, y₁) is a point on the line, and m is the slope of the line.
Therefore, the equation of the tangent line to the curve y = (x^2 - 1) / (x^2 + x + 1) at the point (1, 0) is y = (2/3)x - 2/3.
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The complete question is:
Find an equation of the tangent line to the given curve at the specified point, \(y = \frac {(x^2 - 1)}{ (x^2 + x + 1)}\) at (1,0).
a restaurant offers a choice of 4 salads, 5 main courses, and 3 desserts. how many possible 3-course meals are there?
Answers
Using the Fundamental Counting Theorem, it is found that there are 60 possible 3-course meals.
Given,
In the question:
A restaurant offers a choice of 4 salads, 5 main courses, and 3 desserts.
To find the how many possible 3-course meals are there?
Now, According to the question:
Let's know:
What is the Fundamental Counting Theorem?
It is a theorem that states that if there are n things, each with ways to be done, each thing independent of the other, the number of ways they can be done is:
\(N=n_1\) × \(n_2\) × \(n_3\)... ×\(n_n\)
In this problem, considering the number of salads, main courses and desserts, we have that:
\(n_1=4 , n_2=5,n_3=3\)
The total number of options is given by:
N = 4 × 5 × 3
N = 60
Hence, Using the Fundamental Counting Theorem, it is found that there are 60 possible 3-course meals.
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a​ _______ variable is a variable that has a single numerical​ value, determined by​ chance, for each outcome of a procedure.
Answers
A random variable is a variable that has a single numerical value, determined by chance, for each outcome of a procedure.
A random variable is defined as a variable that has posses a single numerical value, and determined for each outcome of an event. That is a variable whose value is either unknown or a function that assigns values to each of an experiment's outcomes. It can be either discrete (having specific values) or continuous (any value in a continuous range). Generally, random variables are represented by capital letters for example, X and Y. For example consider the tossing of coin event, then the values Heads = 0 and Tails= 1 and we have a Random Variable "X". Hence, required answer is random variable.
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Complete question:
a _______ variable is a variable that has a single numerical value, determined bychance, for each outcome of a procedure.
what’s the equation for this graph pls help me :)
Answers
Answer:
y=-1/8x
Step-by-step explanation:
John left school with $8.43. He found a quarter on his way home and then stopped to buy an apple for $0.89. How much money did he have when he got home?
Answers
Answer:
He had $7.79.
Step-by-step explanation:
8.43 + 0.25 = 8.68
8.68 - 0.89 = 7.79
Quadrilateral FGHI is similar to quadrilateral JKLM. Find the measure of side KL. Round your answer to the nearest tenth.
Answers
Answer:
The answer is "31.888".
Step-by-step explanation:
When their respective angles were congruent or their side lengths have a constant relation, they know that two quadrilaterals are similar
FGHI is similar to JKLM because of quadrilateral
\(\to \frac{FG}{JK} =\frac{GH}{KL}=\frac{HI}{LM}=\frac{FI}{JM}\\\\\to \frac{GH}{KL} =\frac{HI}{LM}\\\\\to \frac{7}{KL}= \frac{9}{41}\\\\\to KL=\frac{7 \times 41}{9}=31.888\\\\\)
Answer:
12.3
Step-by-step explanation:
Trust me I got it wrong
Find the measure of each angle
Answers
Answer:
m∠QRT = 47°
m∠TRS = 133°
Step-by-step explanation:
Because points Q, R, and S are collinear, ∠QRT and ∠TRS are supplementary. This means that:
m∠QRT + m∠TRS = 180°
Plug-in the known values and simplify:
3x + 5 + 10x - 7 = 180
13x - 2 = 180
13x = 182
x = 14
Now that you have the value of x, plug them into the values of the angles:
m∠QRT = 3x+ 5
= 3(14) + 5
= 42 + 5
= 47°
m∠TRS = 10x - 7
= 10(14) - 7
= 140 - 7
= 133°
To double-check:
133° + 47° = 180° ☺
Need help for this question pleaseeee
Answers
9514 1404 393
Answer:
y = 27·x² or (a, n) = (27, 2)
Step-by-step explanation:
Taking the log (base 3) of the given equation, we have ...
\(\log_3(y)=n\cdot\log_3(x)+\log_3(a)\)
Using the points given on the graph, we have 2 equations in n and 'a'.
3 = n·0 +log₃(a) . . . . . log₃(y) = 3, log₃(x) = 0
a = 3³ = 27
and
7 = n·2 +3 . . . . . log₃(y) = 7, log₃(x) = 2
4 = 2n
2 = n
The values of a and n are 27 and 2, respectively.
Graph the equation using the slope and y-intercept? y= -3x+5
Answers
Answer:
Step-by-step explanation:
You need to graph 2 points then you have to draw a line through it.
The 2 points I used were (0,5) and (1,2). Then just draw a line.
The following system of linear equations is shown in the graph.
y=1/4x+5
x-4y=4
How many solutions does the system of linear equations have?
A. No solution
B. Infinitely many solutions
C. One solution at (4,0)
D. One solution at (0,-1)
Answers
Answer:
Step-by-step explanation:
The slopes of both those lines are the same so there is no solution. Use slope triangles to find out the slope. They are both 1/4.
A. No solution
y = 1/4x+5
x - 4y = 4
You can simplify the second equation into y = 1/4x - 1
Since these equations both have the same slope, they are parallel. When two lines are parallel, they have no solutions.
The perimeter of a rectangle is 54 meter. The difference of the length and the width is 11 meters. Find the demensions of the rectangle. Can you please just show the equation thanks.
Answers
Answer:
1246tfghbn ,jgytdzfdcbnmlkjiuytfrcgvgbn
Step-by-step explanation:
jjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjbbbbbbbbbbbbbbbbbbbyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyffffffffffffffffffffffffffffffffffff ttttttt
\(\frac{2x^{2} -50}{x^{2} +7x+10}\)
Answers
Step-by-step explanation:
\( \frac{2 {x}^{2} - 50}{ {x}^{2} + 7x + 10 } \)
\( \frac{2( {x}^{2} - 25) }{(x + 5)(x + 2} \)
\( \frac{2(x + 5)(x - 5)}{(x + 5)(x + 2)} \)
\( \frac{2(x - 5)}{x + 2} \)
a^2 b^2 c^2 for a =2, b and c=4
Answers
Answer:
1,024
Step-by-step explanation:
2*2*4*4*4*4=1024
Which of the sequences is an arithmetic sequence?
O A. 1, 8, 16, 24, 32, ...
OB. 3, 6, 9, 15, 24, ...
O C. 1, -2, 3, 4, 5, ...
OD. -3, -10,-17, -24, -31,...
Answers
The sequence which shows arithmetic sequence is -3, -10, -17, -24, -31, ....... so the correct option is Option D.
What is Arithmetic Sequence?
An arithmetic progression (AP) is a sequence where the differences between every two consecutive terms are the same.
Here, out of the given option option D follows the definition.
Difference between two consecutive term is equal.
-10 - (-3) = -10 + 3 = -7
-17 - (-10) = -17 + 10 = -7
-24 - (-17) = -24 + 17 = -7
-31 - (-24) = -31 + 24 = -7
Thus, the sequence which shows arithmetic sequence is -3, -10, -17, -24, -31, ....... so the correct option is Option D.
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Tammy and Jay go out to dinner. Their total bill, including tax, comes out to $46.14. Once they add tip, they end up spending $53.98. What percent tip did they give? (Round to the nearest percent).
Answers
A 96 in. board will be cut into pieces to add a decorative trim to a rectangular table. The length of the table is twice the width. All of the board will be used to add the trim, and the board will be cut into only four pieces to match the four sides of the table. Find the location of the cut marks on the board...
Answers
Answer:
16, 16, 32, 32
Step-by-step explanation: If you take 92 and divide it by 4 you get 24 but you need one side to be longer than the other, subtract 6 and you get 16, and 16x2 is 32, if you add 16+16+32+32 you get 96.
Answer:
Hello...
Step-by-step explanation:
based on the 2010 census ,the population of gorgia was 9.6 x 10^6 people wihch state has a higher population
Answers
New York had the larger population with 1.9 x 10⁷ people. The correct option is B.
To compare the populations of the states, we need to convert all the populations to the same unit of measurement. In this case, all the populations are given in terms of millions (10⁶).
We can see that New York's population is 1.9 x 10⁷, which means 19 million people. Georgia's population is given as 9.6 x 10⁶, which is 9.6 million people. Comparing these two values, it is evident that New York has a larger population than Georgia.
Check the populations of the other states:
Alaska: 7.1 x 10⁵ = 0.71 million people
Wyoming: 5.6 x 10⁵ = 0.56 million people
Idaho: 1.5 x 10⁶ = 1.5 million people
New York's population of 19 million is much larger than any of the other states listed, making it the state with the largest population among the options provided. The correct option is B.
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Complete question:
Based on the 2010 census, the population of Georgia was 9.6 x 10^6 people. Which state had a larger population? A. Alaska: 7.1 x 10^5 B. New York: 1.9 x 10^7 C. Wyoming: 5.6 x 10^5 D. Idaho: 1.5 x 10^6
"In the formula, P3 = Dx/(R − g), the dividend is for period:
a. four.
b. two.
c. one.
d. five.
e. three."
Answers
The dividend in the formula P3 = Dx/(R - g) is for period e. three.
In the given formula P3 = Dx/(R - g), the dividend, Dx, refers to the cash flow or payment made during a specific period. The subscript "3" in P3 indicates the period of time for which the dividend is associated.
In the given formula, P3 = Dx/(R - g), the subscript 3 represents the period of time for which we are calculating the dividend.
The dividend, Dx, represents the cashflow or payment made during a specific period. In this case, the dividend is associated with period 3.
Therefore, the dividend in the formula corresponds to period e. three.
The dividend in the formula P3 = Dx/(R - g) is for period e. three
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.............................................................................................
Answers
Answer:.............................................................................................
Step-by-step explanation:
.............................................................................................
The lines shown below are perpendicular.
5
(-2,4)
4
(2.1)
5
(0,-2)
(-4,-2)
A. True
B. False
Answers
Answer:
False. The two lines in this diagram are not perpendicular with one another.
Step-by-step explanation:
Two lines in a plane are perpendicular if and only the product of their slopes is \((-1)\).
If a non-vertical line in a plane goes through two points, \((x_{0},\, y_{0})\) and \((x_{1},\, y_{1})\) (\(x_{0} \ne y_{0}\),) the slope of this line would be:
\(\begin{aligned}m &= \frac{y_{0} - y_{1}}{x_{0} - x_{1}}\end{aligned}\).
Find the slope of the two lines given the coordinates of the points.
Slope of the line sloping downwards:
\(\begin{aligned}m_{a} &= \frac{4 - (-2)}{(-2) - 0} \\ &= \frac{6}{(-2)} \\ &= (-3)\end{aligned}\).
Slope of the line sloping upwards:
\(\begin{aligned}m_{b} &= \frac{1 - (-2)}{2 - (-4)} \\ &= \frac{3}{6} \\ &= \frac{1}{2}\end{aligned}\).
The product of the slopes of the two lines is:
\(\begin{aligned}m_{a}\, m_{b} &= (-3) \times \frac{1}{2} \\ &= \left(-\frac{3}{2}\right)\end{aligned}\).
Therefore, these two lines are not perpendicular to one another since the product of their slopes isn't \((-1)\).