Find the equation of the linear function represented by the table
below in slope-intercept form.
X 0,1,2,3,4 y 6,8,10,12,14
Answers
to get the equation of any straight line, we simply need two points off of it, let's use those two in red in the picture below
[tex](\stackrel{x_1}{1}~,~\stackrel{y_1}{6})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{12}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{12}-\stackrel{y1}{6}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{1}}} \implies \cfrac{ 6 }{ 2 } \implies 3[/tex]
[tex]\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}{6}=\stackrel{m}{ 3}(x-\stackrel{x_1}{1}) \\\\\\ y-6=3x-3\implies {\Large \begin{array}{llll} y=3x+3 \end{array}}[/tex]
Related Questions
given that M > N, determine whether the inequality M/N > N/M is always sometimes or never true
Answers
Answer:
An equation is a proposition of two expressions that are equal.
Step-by-step explanation:
30 POINTS AND BRAINLIEST!! PLEASE HURRY I HAVE 20 MIN LEFT. <3 tysm (:
Answers
25. doubled
26. doubled
27. increases 4 times
28. remains unchanged
29. increases 6 times
A poster measuring 150cm by 180cm is enlarged in the ratio 8:5. Find the length and breadth of the enlarged poster
Answers
Answer:
240 cm by 288 cm
Step-by-step explanation:
You want the dimensions of a 150 cm by 180 cm poster enlarged by the ratio 8:5.
SolutionThe enlargement ratio, expressed as a fraction, multiplies each of the original dimensions to get the new dimensions. The new dimensions are ...
(8/5)·150 cm by (8/5)·180 cm = 240 cm by 288 cm
78 children attended a trip to the fair. 60 of them were girls. Find the ratio of the number of girls to boys.
Do not put in simplest form.
Answers
Answer:
First, find the number of boys: [tex]78-60=18[/tex]
The ratio of the number of girls to boys would be 60 : 18.
A neighborhood planner uses a coordinate plane to design a new neighborhood. The coordinates A(1,−1) , B(1,−2) , and C(2,−1) represent House A, House B, and House C. The planner decides to place a playground centered at the origin, and moves the houses to make space. House A is now located at A′(3,−4) . What are the new coordinates of House B and House C when each house is moved using the same translation?
Answers
The new coordinates of House B and House C are
B' ( 3 , -5 ) and C' ( 4 , -4 ) respectively
What is Translation?
A translation moves a shape up, down, or from side to side, but it has no effect on its appearance. A transformation is an example of translation. A transformation is a method of changing a shape's size or position. Every point in the shape is translated in the same direction by the same amount.
Given data ,
Let the 3 houses be A , B ,C
The coordinate of House A = A ( 1 , -1 )
The coordinate of House B = B ( 1 , -2 )
The coordinate of House C = C ( 2 , -1 )
Now , the houses are relocated to new coordinates with
The new coordinate of House A = A' ( 3 , -4 )
The translation of Point A can be expressed in the form of x and y coordinate as there is a translation occurred with a scale factor
So ,
A ( x₁ , y₁ ) to A' ( x₂ , y₂ )
A ( 1 , -1 ) to A' ( 3 , -4 )
x₂ = x₁ + 2
y₂ = y₁ - 3
From the figure , we can clearly see that the coordinates of the houses A , B and C are translated by a scale factor and the new coordinates are
x₂ = x₁ + 2
y₂ = y₁ - 3
Therefore ,
B ( x₁ , y₁ ) to B' ( x₂ , y₂ )
B' ( x₂ , y₂ ) = B' ( 3 , -5 )
C ( x₁ , y₁ ) to C' ( x₂ , y₂ )
C' ( x₂ , y₂ ) = C' ( 4 , -4 )
Hence , the new coordinates of House B and House C are B' ( 3 , -5 ) and C' ( 4 , -4 ) respectively
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can someone pls help me i don’t ll get this
Answers
Answer: 6
Step-by-step explanation:
Angles opposite congruent sides in a triangle are congruent, so both angles are equal to [tex](13x-6)^{\circ}[/tex].
Since angles in a triangle add to [tex]180^{\circ}[/tex], so:
[tex]36+2(13x-6)=180\\\\2(13x-6)=144\\\\13x-6=72\\\\13x=78\\\\x=6[/tex]
Un taxi en Myrtle Beach cobra $2 por milla y $1 por cada persona. Si un viaje en taxi para dos personas cuesta $12.
¿Cuánto viajó el taxi?
Answers
Respuesta:
5 millas
Explicación paso a paso:
Si hay 2 personas y cuesta 12 dólares primero restarás 2 dolars por cada persona dejándote con 10 dólares. Después de eso, dividirá 10 por 2 para las millas porque cada milla cuesta 2 dólares. que te llevará a 5 millas
GRACIAS
A nursing administrator went through a sample of hospital records and found that, out of 500 randomly selected records, 217 of the patients had been admitted for heart issues. What is the sample statistic?
Answers
The sample statistic when the nursing administrator went through a sample of hospital records is 217.
What is statistic?A statistic is a metric used to describe a sample. Estimation or hypothesis testing can be used to determine how likely it is that a sample statistic differs from the population parameter.
A sample is an analytic subset of a larger population in statistics. The use of samples enables researchers to conduct studies with more manageable data and more quickly. Randomly drawn samples have little bias if they are large enough, but obtaining such a sample can be costly and time-consuming.
A sample statistic is a piece of statistical data derived from a small number of items. A sample is merely a subset of a population. Therefore, the 217 of the patients had been admitted for heart issues is the sample.
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One year consumers spent an average of $23 on a meal at a restaurant. Assume that the amount spent on a restaurant meal is normally distributed and that the standard deviation is $5.
A) What is the probability that a randomly selected person spent more than $25?
B) What is the probability that a randomly selected person spent between $12 and $21?
C) Between what two values, symmetrically distributed around the mean, will the middle 95% of the amounts of cash spent fall?
Answers
Using the normal distribution, it is found that:
a) The probability that a randomly selected person spent more than $25 is of 0.3446 = 34.46%.
b) The probability that a randomly selected person spent between $12 and $21 is of 0.3307 = 33.07%.
c) The middle 95% of the amounts are between $13.2 and $32.8.
How to obtain probabilities using the normal distribution?The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.The mean and the standard deviation for the costs of the meal are given as follows:
[tex]\mu = 23, \sigma = 5[/tex]
The probability that a randomly selected person spent more than $25 is one subtracted by the p-value of Z when X = 25, hence:
Z = (25 - 23)/5
Z = 0.4
Z = 0.4 has a p-value of 0.6554.
1 - 0.6554 = 0.3446 = 34.46%.
The probability that a randomly selected person spent between $12 and $21 is the p-value of Z when X = 21 subtracted by the p-value of Z when X = 12, hence:
X = 21:
Z = (21 - 23)/5
Z = -0.4
Z = -0.4 has a p-value of 0.3446.
X = 12:
Z = (12 - 23)/5
Z = -2.2
Z = -2.2 has a p-value of 0.0139.
0.3446 - 0.0139 = 0.3307 = 33.07%.
The normal distribution is symmetric, meaning that the bounds of the middle 95% of values are given as follows:
2.5th percentile: X when Z = -1.96.97.5th percentile: X when Z = 1.96.-1.96 = (X - 23)/5
X - 23 = -1.96 x 5
X = $13.2
1.96 = (X - 23)/5
X - 23 = 1.96 x 5
X = $32.8
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There are 1400 students in a school. Out of these 350 students wear glasses. What percentage of students wear glasses
Answers
Answer:
25%
Step-by-step explanation:
divide the number by the total then multiply by 100 and add a percent sign
350/1400*100=25%
someone help pls due soon
Answers
Answer:
snap to solve
Step-by-step explanation:
u can use snap to solve to get ur answers
Answer:
Step-by-step explanation:
cost price = $640
sell price = $940
percentage = ?
Rate * Base = Amount
Percent * Sell Price = Cost Price
P * 940 = 640
P940 = 640
P940/940 = 640/ 940
P = 0.66666667
Percent = (0.66666667 × 100)/100 = 66.666667
Correct Answer is 66 2/3%
#11 i
PROBLEM SOLVING The table shows the heights y of a competitive water-skier x seconds after jumping off a ramp.
Time (seconds), x 0 0.25 0.75 1 1.1
Height (feet), y
22 22.5 17.5 12 9.24
Write a function that models the height of the water-skier over time.
The function y =
Interpret the y-intercept.
B
22
I U
models the height.
T' T₂
When is the water-skier 5 feet above the water? Round your answer to the nearest hundredth.
70°F
Cloudy
The skier is 5 feet above the water after about
second(s).
O Search the web
J
O
L
D
(
1/10000 Word L
Answers
The function modelled for the given condition is [tex]y = -16x^{2} + 6x +22[/tex] and the time after which the skier is 5 feet above the water is 1.23 seconds.
A competitive water skier's heights y, x seconds after soaring off a ramp.
For x = 0, y = 22
for x = 0.25, y = 22.5
For x = 0.75, y = 17.5
For x = 1, y = 12
For x = 1.1, y = 9.24
The general equation of a quadratic equation is y = [tex]ax^{2} + bx +c[/tex]
Putting x = 0 and y = 22 in the equation, we get :
[tex]y = ax^{2} +bx +c[/tex]
c = 22
Now, putting x = 1 and y =12, we get,
12 = a*1 + b*1 + 22
a +b = 12 - 22 = -10 equation (1)
Putting x = 0.25, y = 22.5,
22.5 = a* [tex]22.5^{2}[/tex] +b*22.5 +22
506.25 a +22.5b = 0.5 equation(2)
Solving equation (1) and equation(2), we get :
a = -16 and b = 6 and c = 22
So, the quadratic equation becomes,
[tex]y = -16x^{2} + 6x +22[/tex]
Now, Time when the skier is 5 feet above the water,
[tex]x = \frac{3 +\sqrt{281} }{16} = 1.23 seconds[/tex]
Hence, the function modelled for the given condition is [tex]y = -16x^{2} + 6x +22[/tex] and the time after which the skier is 5 feet above the water is 1.23 seconds.
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Solve the following expression when
t = 6 and d = 8
t + d/8-6
Answers
Answer:
1
Step-by-step explanation:
Replace the variable letter with the number.
t + d / 8 - 6
6 + 8 / 8 - 6
6 + 1 - 6
7 - 6
1
Consider the following linear equation.
y=2+34x
Step 1 of 2 : Determine the slope and the y-intercept (entered as an ordered pair) of the equation above. Reduce all fractions to lowest terms.
Answers
The slope of the function y = 2 + 34x is 34 and the y-intercept of the function y = 2 + 34x is 2.
First, let us understand the slope intercept form;
The slope intercept form is simply a way of writing a line's equation so that the slope (steepness) and y-intercept (where the line crosses the vertical y-axis) are obvious.
We know that the slope intercept form of a line is y = mx + c where m is the slope of the line and b is the y-intercept of the line.
We are given:
y = 2 + 34x
y = 34x + 2
Compare with y = mx + c, we will get;
m = 34
b = 2
So, the slope is 34 and the y-intercept is 2.
Thus, the slope of the function y = 2 + 34x is 34 and the y-intercept of the function y = 2 + 34x is 2.
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Prizes in a raffle are determined by taking a ball from a bag. There are 15 balls in the bag, 12 of them are green, two of them with black stars. There are two silver balls, one with a black star, and one gold ball. If you draw the green ball, without the black star, you win a small prize. If you get a green ball with the black star, you get a medium prize. If you get the silver ball without the star, you get a large prize. If you get the silver ball with the black star, you get the extra-large prize. If you get the gold ball, you get the super deluxe prize.
If you get a ball, what is the probability of getting the green with the black star?
The probability of getting the green ball with the star is
a.) 0.1333
b.) 0.1133
c.) 0.0123
d.) 0.0333
This is an example of:
a.) a joint event
b.) an elementary event
The probability of winning the small prize is:
a. 0.7666
b. 0.6666
c. 0.6667
d. 0.6777
This is an example of:
a.) a joint event
b.) an elementary event
What is the probability of winning the super deluxe prize?
The probability of winning the super deluxe prize is:
a.) 6.6677
b.) 0.6667
c.) 0.7667
d.) 0.0667
This is an example of:
a.) a joint event
b.) an elementary event
Answers
Answer:
a. )
Step-by-step explanation:
There are 15 balls ...... two are green with a star
2 out of 15 = 2/15 = .1333
What is the solution to the system of equations
Answers
The solution of the given system of equations is (-1, -2).
Explain the method of substitution?Three steps make up the substitution technique: For each of the variables, solve one equation. Put this expression (or plug it in) into the other equation, then solve it. To identify the corresponding variable, rewrite the value's original equation.We are aware that a linear system of equations can be solved using a substitution method.
The intersection of the two lines represents the system's solution.
The given equations are-
y = 3x+1 ...eq 1
y = -2x-4 ...eq 2
Put the value of eq 1 in eq2 .
3x+1 = -2x-4
3x + 2x = -4 - 1
5x = -5
x = -5/5
x = -1
Put the x in eq 1.
y = 3(-1)+1
y = -2
Thus, the solution of the given system of equations is (-1, -2).
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The complete question is-
What is the solution to the system of equations-
y=3x+1 ;
y=-2x-4
The functions r and s are defined as follows.
r(x) = 2x+1
s(x) = -x²
Find the value of r (s (4)).
r(s(4))=
Answers
Answer:
[tex]33[/tex]
Step-by-step explanation:
Define functions:
[tex]r(x) = 2x+1\\s(x) = -x^2[/tex]
Substitute [tex]s(x)[/tex] into [tex]r(x)[/tex]:
[tex]2(-x^2) + 1[/tex]
Solve for value:
[tex]= 2((-4)^2)+1\\= 2(16) + 1\\= 32 + 1\\= 33[/tex]
** assuming that the function of [tex]s(x)[/tex] the x value is squared with the negative sign.
Help on number 1 please!! Thanks.
Answers
Answer:
I believe the answer is c
Can some one please help me do these work sheets before I fail my class♀️
Answers
Answer of the given question are respectively,
[tex]-x^2y , 2w ,\\\\h^6 , -14a^5b^2\\x^6 , 4m^8\\9x^4/14 , y^2\\-5/x^2 , 1/2k\\7 , 1[/tex]
Exponent:
A quantity representing the power to which a given number or expression is to be raised, usually expressed as a raised symbol beside the number or expression.
Example:
[tex]2^3[/tex] = 2 × 2 × 2
Combine like term:
1. [tex]9x^2y -10x^2y[/tex] = [tex]-x^2y[/tex]
2. Subtract 6w from 8w
8w -6w = 2w
Rule:
[tex]x^{a} * x^{b} = x^{a+b} \\\\[/tex]
1.
[tex]h^2 * h^4 = h^{2+4} \\ \\\\= h^6[/tex]
2.
[tex](-2a^2b).(7a^3b)\\\\-14 a^{2+3} b^{1+1} \\\\= -14 a^5 b^2[/tex]
Rule:
[tex](x^a)^b = x^{ab}[/tex]
1. [tex](x^2)^3 = x^6[/tex]
2.
[tex](-2m^3)^2 * m^2 \\\\4m^6*m^2\\\\4m^8[/tex]
Rule:
[tex]x^a/x^b = x^{a-b}[/tex]
1.
[tex]27x^5/42x\\\\= 9x^4 /14[/tex]
2.
[tex](y^3)^2/y^4\\\\y^6/y^4\\\\y^2\\[/tex]
Rule:
[tex]x^{-a}= 1/x^a[/tex]
1.
[tex]-5x^{-2} \\\\= -5/x^2[/tex]
2.
[tex]4k^2/8k^3\\\\= k^{-1} /2\\\\= 1/2k[/tex]
Rule:
[tex]x^0 =1[/tex]
1.
[tex]7x^0\\\\= 7[/tex]
2.
[tex](w^4)^2/w^8\\\\w^8/w^8\\\\w^0\\\\=1[/tex]
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What is the image point of (-6, -4) after the transformation T4.-1 ° ry=-x?
Answers
(16, 36) is the image point .
What is image point?
The provided point P is "reflected" in the mirror, appearing on the other side of the line at a distance equal to that from it. To see this, move the point P. Conventionally known as P' (pronounced "P prime"), the point P's reflection over the line is also referred to as the point P's "image."Reflecting (-6, -4) in the line y= - x yields the point (4, 6).
Dilating (4, 6) by a factor of 4 gives the point (16, 36).
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A student 6ft tall is standing 20ft away from a 35ft tall flagpole.
The flagpole is 60ft away from a building.
From the students point of view, the flagpole is lined up perfectly with the top of the building.
What's the height of the building?
PLEASE HELP MEEEE!!!!!
Answers
A student 6ft tall is standing 20ft away from a 35ft tall flagpole.
The flagpole is 60ft away from a building.
From the students point of view, the flagpole is lined up perfectly with the top of the building.
What's the height of the building?
the area of a square photo frame is 250 cm2 .find the perimeter of photo frame
Answers
Answer:
63.2 cm
Step-by-step explanation:
Perimeter formula from Area =
4√Area units.
4√250 =
4 × 15.8 =
63.2 cm
The graphs of f(x) and g(x) are shown below. On a coordinate plane, a straight line with negative a slope represents f (x) = negative x. The line goes through points (0, 0), (negative 6, 6) and (6, negative 6). On a coordinate plane, a straight line with a positive slope represents g (x) = 2 x. The line goes through points (negative 3, negative 6), (0, 0) and (3, 6). Which of the following is the graph of (g – f)(x)? On a coordinate plane, a straight line with a negative slope goes through points (negative 2, 6), (0, 0), and (2, negative 6) On a coordinate plane, a straight line with a negative slope goes through points (negative 6, 6), (0, 0), and (6, negative 6). On a coordinate plane, a straight line with a positive slope goes through points (negative 2, negative 6), (0, 0), and (2, 6).
Answers
The option that is the graph of (g – f)(x) is; On a coordinate plane, a straight line with a positive slope goes through points (negative 2, negative 6), (0, 0), and (2, 6).
How to Interpret Inequality Graphs?We are given the function as;
f(x) = -x
Now, the line passes through the points (0,0),(-6,6) and (6,-6) is;
The function given as; g(x) = 2x
This line passes through the points (-3,-6),(0,0) and (3,6).
Before we graph (g - f)(x), we have to first simplify it to get;
The graph of of (g - f)(x)
(g - f)(x) = g(x) - f(x)
= 2x - (-x)
= 3x
At x = 0, we have;
(g - f)(0) = 3(0) = 0
At x = 2, we have;
(g - f)(2) = 3(2) = 6
At x = -2, we have;
(g - f)(-2) = 3(-2) = -6
At x = -6, we have;
(g - f)(-6) = 3(-6) = -18
Looking at the options, option C is true
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I need to know what NM is
Answers
The length of NM is 10 units
What are similar triangles?
If two triangles' corresponding angles and sides are identical and their corresponding sides are proportional, or if the ratios between the lengths of the corresponding sides are comparable, then two triangles are said to be similar.
Similar triangles are triangles with the same shape but different sizes. Examples of related objects are all equilateral triangles and squares with any side length.
The triangles ONP and LNM are similar triangles.
So, the following is true.
(ON/LN)=(NP)/(NM)
(3.6/6)=(6)/(NM) ( LN=LO+ON=2.4+3.6=6 )
3.6 NM=6*6 =36
NM=36/3.6 = 10
So, the length of NM is 10 units
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Atudent mark tardy 5 different times in 40 days what percentage was he tardy
Answers
The percentage is the indicating hundredth is 12.5%.
What is the percentage?A specific number in every hundred is what is meant by the percentage. It is a fraction with 100 as the denominator, and one percent is used to symbolize it.
Using the percentage formula, a number between 0 and 1 can be expressed. A number that is expressed as a fraction of 100 is what it is. It is mostly used to compare and determine ratios and is represented by the symbol %.
Given:
A student was marked tardy five different times in a 40-day period.
Percentage of 5 among 40
= (5/40) x 100
= 12.5%
Hence, The percentage of times the students marked will be 12.5%".
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Write the sentence as an equation.
191 is the same as 266 added to the product of 109 and
Answers
Answer:
191=266+109x
Step-by-step explanation:
It says 191 is the same as 266 added to the product of 109 and _____. i am guessing you meant to say a variable.
At a time t seconds after an object is tossed vertically upward, it reaches a height s in feet given by the equation:
s=64t-16t^2
In how many seconds does the object reach its maximum height?
Answers
The time it takes the object to attain maximum height is 2 seconds
Time to Attain Maximum HeightTo find the time it takes the object to attain maximum height, we have to use the quadratic equation to do so. The formula can be given as
t = -b/2a
But let's write and define our quadratic equation with it's variables.
S = 64t - 16t²
To attain maximum height;
t = -b/2a
a = -16, b = 64,c = 0
Substituting the values
t = -64/2(-16)
t = 2
The time is 2 seconds
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10] Salim walked 1 1/2 miles to school and then 2 1/2 miles to work after school. How far did he walk in all?
Answers
Answer:
4
Step-by-step explanation:
Solution by separating parts
Rewriting our equation with parts separated
=1 + 1/2 + 2 + 1/2
Solving the whole number parts
1 + 2 = 3
Solving the fraction parts
1/2 +1/2 = 2/2
Reducing the fraction part, 2/2,
2/2 = 1/1
Simplifying the fraction part, 1/1,
1/1 = 1
Combining the whole and fraction parts
3 + 1 = 4
Answer:
4 miles
Step-by-step explanation:
1 1/2 = 1.5
2 1/2 = 2.5
1.5 + 2.5 = 4 miles
A firm makes circular drink mats , of radius 4.5cm , that are 3mm thick . They want to produce a rectangular box to hold a pile of 12 mats. What are the minimum dimensions of the box.
Please answer with working out
Thank you
Answers
Answer:
13.5
Step-by-step explanation: that's the minimum of dimensions for the box
The Bloomington Times had 8,050 subscribers last year. This year, after the paper was bought out, it had 70% more. How many subscribers were there this year?
plwease help due tommrow
Answers
Answer:
13685
Step-by-step explanation:
8050 + .7(8050)
8050 + 5635
13685