With the Application of probability The expression is [ x^r] = C ( r - 1, r - 8 ).
What is probability?
There are four primary categories of probability: axiomatic, axiomatic, classical, and empirical. Probability is the area of mathematics that deals with the possibility of a random event. It is possible to claim that probability is the likelihood that a specific event will occur as the two words are equivalent.
solution:
G(x) = ( x^1 + x^2 + x^3 .....)^8
G(x) = (x( x^1 + x^2 + x^3 .....) )^8
Then using infinite geometric series,
= x^8 ( 1 / ( 1 - x )) ^8
Then using negative binomial series:
So [ x^r] = 0 if r = 0, 1, 2, 3...7 and [ x^r] = C ( r - 1, r - 8 ) if r > 7
Therefore, The expression is [ x^r] = C ( r - 1, r - 8 )
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What is the rule that describes the translation ABC → A' B' C' ?
The rule that describes the translation will be as T<-3, 2>
Given,
Translation;-
Translation is the act of moving a shape or a figure from one location to another. A figure can move in translation up, down, right, left, or anywhere else in the coordinate system. Only the object's position changes during translation; its size stays the same.
Here,
In order to move from A = (-3,3) to A' = (-6, 5), we must first move 3 units to the left and 2 units up.
Step 1's change causes x to become x-3.
Step 2's change causes y to become y+2.
When you combine these, (x, y) becomes (x-3, y+2).
That is equivalent to writing T<-3, 2>.
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find the equation for the line containing the points (-4,-2) and (-3,5)
Answer:
Step-by-step explanation:
Given the points
(4, 2)
(3, 5)
We know that the slope-intercept form of the line equation is
where m is the slope and b is the y-intercept
substituting m=-3 and the point (4, 2) to get the y-intercept i.e. b
2=(-3)4 + b
2 = -12 + b
b = 2+12
b = 14
Now, substituting b=14 and m=-3 in the slope-intercept form to determine the equation of a line in the slope-intercept.
y=(-3)x+(14)
y=-3x+14
Thus, the equation of the line containing (4,2) and (3,5) in the slope-intercept form will be:
y=-3x+14
Compute the orthogonal projection of [-2 2] onto the line through [ -1 5] and the origin. The orthogonal projection is [ __ __ ]
the orthogonal projection of [-2 2] onto the line through [-1 5] and the origin is [-1.25 3.75] using unit vector.
First, we need to calculate the unit vector of the line. This can be done by subtracting the two given points and dividing the result by the magnitude of the vector:
[-1 5] - [0 0]
= [-1 5]
|[-1 5]| = sqrt(1^2 + 5^2) = sqrt(26) = 5.1
Unit vector = [-1/5.1 5/5.1] = [-0.196 0.980]
Next, we need to calculate the dot product of the vector [-2 2] and the unit vector [-0.196 0.980]. This will give us the scalar projection.
(-2)(-0.196) + (2)(0.980) = -0.392 + 1.960 = 1.568
Finally, we can calculate the orthogonal projection by multiplying the scalar projection by the unit vector.
[-0.196 0.980] (1.568) = [-0.301 1.527]
Rounding to two decimal places, the orthogonal projection of [-2 2] onto the line through [-1 5] and the origin is [-1.25 3.75].
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At the West Texas Balloon Festival in El Paso, a hot air balloon started its descent from an altitude of 800 feet. After 1 minute, it is at a height of 700 feet and continues at this rate till it reaches the ground.
A. Write a linear equation to find the height, h of the balloon after m minutes.
B. What is the rate of change. What does it represent in this situation?
C. What is the y-intercept and what does it represent?
D. What is the x-intercept and what does it represent?
The linear equation and the definition of the parts of the equation of the motion of the balloon are as follows;
A. The equation is; h = 800 - 100·m
B. The rate of change is 100 ft/min. The rate of change represents the height the balloon descends in one minute
C. The y-intercept is 800 (feet). The y-intercept represents the initial height of the balloon
D. The x-intercept is 8 (minutes). The x-intercept represents the time it takes the balloon to reach the ground
What is a linear equation?A linear equation is one that has a straight line graph.
The initial height of the balloon = 800 feet
Height of the balloon after 1 minute = 700 feet
A. The change in height of the balloon in one minute = 100 feet
The rate of change of the height of the balloon = -100 feet per minute (the height reduces by 100 feet after each minute)
The linear equation for the balloon, can therefore be obtained from the following details;
The initial height of the balloon = The y-intercept of the linear equation, c = 800 feet
The rate of change of the height of the balloon = The slope of the linear equation, m = -100 ft/min
The linear equation in the form, y = m·x + c, that can be used to find the height of the balloon is therefore;
h = -100·m + 800
h = 800 - 100·mB. The rate of change is the rate at which the height of the balloon changes, which is 100 feet per minute
The rate of change represents the slope of the linear equation and the rate at which the height of the balloon reduces.C. The y-intercept is the point at which the linear equation intersects the y-axis which is the point at which the input variable, m, is zero, indicating the height at which the balloon started its descent.
Therefore, the y-intercept represents the initial height of the balloonD. The x-intercept is the point at which the graph intersects the x-axis, and at which the y-value (value of the output variable) is zero, and the x-intercept can be specified by the x-value at the point of the intersection.
At the x-intercept, therefore, h is zero, which is the ground level, and m is the time it takes the balloon to reach the ground.
At the x-intercept, therefore, we het;
h = 0 = 800 - 100·m
100·m = 800
m = 800 ÷ 100 = 8
The x-intercept is m = 8 minutes
The x-intercept therefore, represents the time (8 minutes) it takes the balloon to reach the ground.Learn more about graphs of linear equations here:
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The sides of AUVW are UV = 8x-19,
VW = 5x-5, and UW = 9x -22. If the
perimeter of AUVW is 86, list the angles in order from largest to smallest.
i need help asap!!! please help me i don’t know how to do this!!
If loan Amy is 89000 monthly payment is 479.66 rate is 4.2 what is the interest principal and balance for month 1 and month2
The amount of money an account with simple interest at an annual rate of 4.2% would be $3738 after 1 month and 7476 dollar after 2 month.
What is simple interest?Simple interest is a method of calculating the interest charge. Simple interest can be calculated as the product of principal amount, rate and time peroid.
Simple Interest = (Principal × Rate × Time) / 100
Given that loan Amy is 89000 monthly payment is 479.66 rate is 4.2
Amount = $89000
Rate = 4.2 %
Time = 1 month
Therefore, Simple Interest = (Principal × Rate × Time) / 100
Simple Interest = 89000 × 4.2% × 1
Simple Interest = 3738
Also,
Simple Interest = 89000 × 4.2% × 2
Simple Interest = 7476
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A football match consists of two 45 minute halves and a 30 minute break in between. How many minutes does the whole match last for?
The whole match lasts for 45 minutes + 45 minutes + 30 minutes = 120 minutes. Answer: 120 min.
Write this set using interval notation.
Please help me!!!
Answer:
Step-by-step explanation:
The set {x | x < 0 or x > 3 } can be written in interval notation as (-∞, 0) ∪ (3, ∞).
The set {x | x < 0 or x > 3 } consists of all real numbers that are either less than 0 or greater than 3. This set can be represented as the union of the set of all numbers less than 0, which can be written as (-∞, 0), and the set of all numbers greater than 3, which can be written as (3, ∞).
Therefore, the set {x | x < 0 or x > 3 } can be written in interval notation as (-∞, 0) ∪ (3, ∞).
Harry and Sally both invest $2500 for their
school tuition in 3 years. Harry chooses to
invest his money at bank A at 2.5%/a
compounded monthly while Sally chooses
to invest her money at bank B at 2.75%/a
compounded quarterly. How much money
will Harry and Sally have in their bank
account after 3 years? Who made the best
investment? Explain your answer.
The amount Harry has in his account is $2,694.50
The amount Sally has in his account is $2,714.23.
Sally made the best investment.
What is compound interest?It is the interest we earned on the interest.
The formula for the amount earned with compound interest after n years is given as:
A = P [tex](1 + r/n)^{nt}[/tex]
P = principal
R = rate
t = time in years
n = number of times compounded in a year.
We have,
Harry:
P = $2500
T = 3 years
r = 2.5%
n = 12
A = 2500 [tex](1 + 0.208)^{36}[/tex]
A = 2500 x [tex]1.208^{36}[/tex]
A = $2,694.50
Sally:
P = $2500
T = 3 years
r = 2.75%
n = 4
A = 2500 [tex](1 + 0.69)^{12}[/tex]
A = 2500 x [tex]1.69^{12}[/tex]
A = $2,714.23
Thus,
Harry has $2,694.50 in his account.
Sally has $2,714.23 in his account.
Sally made the best investment.
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you are managing a portfolio of $1 million. your target duration is 10 years, and you can invest in two bonds, a zero-coupon bond with maturity of five years and a perpetuity, each currently yielding 7.8%.
40% percentage of your portfolio in the zero-coupon bond with a maturity of 5 years and 60% of your portfolio in the perpetuity. This would result in an overall duration of 10 years.
To achieve your target duration of 10 years, you would need to allocate your investments in a way that has an overall duration of 10 years. You could do this by investing 40% of your portfolio in the zero-coupon bond with a maturity of 5 years and 60% percentage of your portfolio in the perpetuity. This would result in an overall duration of 10 years.
Duration of zero-coupon bond = 5 years
Duration of perpetuity = infinity
Weighted duration of portfolio = (0.4 x 5) + (0.6 x infinity) = 10 years.
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To find a value that is in an unordered array of 100 items, how many values must linear search examine on average?
a) 101
b) 100
c) 7
d) 50
e) 10
Answer: D its 50
Step-by-step explanation:
How do I solve this problem and if u could explain it from step by step?
2/3 (2 - 6 ) =
The value of the equation A = ( 2/3 ) ( 2 - 6 ) is A = -8/3
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
A = ( 2/3 ) ( 2 - 6 ) be equation (1)
On simplifying the equation , we get
A = ( 2/3 ) ( 2 - 6 )
A = ( 2/3 ) ( -4 )
Multiply by -4 on the numerator , we get
A = ( 2 x -4 ) / 3
A = -8 / 3
Therefore , the value of A is -8/3
Hence , the value of the equation is -8/3
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Please help! (Attached image) remainder Theorem
Answer:
First is option B)
Second is option B)
I hope my answer helps you.
a line that includes the point (17,2) and has a slope of 1. what is its equation in slope-intercept form?
Answer:
y = x - 15
Step-by-step explanation:
y-2 = 1(x-17)
y-2 = x - 17
y = x -17 + 2
y = x - 15
Triangle Congruence: Question 3
In the proof, what is the reason for (5) ?
Given: V W║Z Y
W X=Y X
Prove: ΔVWX ΔXYZ
Select one:
SSA
H
SAS
ASA
SSS
In the proof, The reason for (5) ΔVWX ≅ ΔXYZ is ASA
Two triangles are congruent when their three angles and three sides are equal to each other. The two triangles need to be of the same size and shape to be congruent. Both the triangles under consideration should superimpose on each other.
There are 4 property we use to congruent two triangles ( ASA , RHS , SSS and SAS)
According to the question,
Given = V W║Z Y
W X=Y X
We have to prove : ΔVWX ≅ ΔXYZ
Proof =>
It is given that V W║Z Y ,
Using parallel line property ,
(1) ∠W = ∠Y (interior alternate angles )
(2) ∠V = ∠Z ( Interior angle property)
(3) W X=Y X (given)
Therefore , By using ASA property
ΔVWX ≅ ΔXYZ
Hence , In the proof, the reason for (5) is ASA
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Solve the equation.
9(z + 3) = 45
Answer:
Step-by-step explanation:
9z + 27 = 45
9z= 18
z= 18/9
z = 2
Answer:
[tex]z=2[/tex]
Step-by-step explanation:
[tex]9(z+3)=45\\9z+27=45\\9z=45-27\\9z=18\\z=\frac{18}{9}\\ z=2[/tex]
Hope it helps you
Round 3.122 to the nearest hundredth
Answer:
3.12
Step-by-step explanation:
1 number after the decimal - tenths place.
2 numbers after the decimal - hundredths place.
3 numbers after the decimal - thousandths place.
4 numbers after the decimal - ten thousandths place.
5 numbers after the decimal - hundred thousandths place.
Answer:
3.12
Step-by-step explanation:
3.122 rounds up to 3.12 because 2 is less than 5, so the number rounds down.
Repeat Exercise 8.9 for the following repeating sequence of lw addresses (given in hexadecimal) and cache configurations. The cache capacity is still 16 words. 74 A0 78 38C AC 84 88 8C 7C 34 38 13C 388 18C (a) direct mapped cache, b = 1 word(b) fully associative cache, b = 2 words(c) two-way set associative cache, b = 2 words(d) direct mapped cache, b = 4 words
The direct framed(mapped) cache in the given hexadecimal has all the miss.
Given cache parameters
b block size( given no. of words)
Cache capacity 16 words
( a) Direct mapped cache with b = 1 word
Address mapping = Total = 8 bits
Index = 4 bits
Offset = 0 bit
Tag(Label) = remaining bits = 4 bits
illustration of mapping = 74---> 01110100
where 0111 is the label and the rest is the index
Sequencing of law addressing = 0 * 74 to binary = 01110100
Then, word offset = log₂( b) = log₂( 1) = 0 bit
Line offset = log₂(16/1) = 4
Label(tag) is the remaining bit
b) completely associative cache with b = 2 words
# of lines = 16/2 W = 8
Address mapping Offset = log ₂( 2) = 1 bit
Remaining bit = 01110100
where 0 is offset and the rest is a label
In this cache design, line no. isn't needed to map the data as we directly compare CPU- generated markers with existing markers in the cache controller.
Still, apply the LRU algorithm, if the cache is full.
c) Two- way set associative cache with b = 2 words
#sets = #lines/ p- way = (16/2)/ 2 = 4
Address mapping
Set offset = log₂( 4) = 2
Word offset = log₂( 2) = 1
Tag(label) = remaining bits
ADDRESS INDEX OFFSET HIT/MISS
74 10 0 MISS
A0 00 0 MISS
78 00 0 MISS
38C 10 0 MISS
AC 10 0 MISS
84 10 0 MISS
88 00 0 MISS
8C 00 0 MISS
7C 00 0 MISS
34 00 0 MISS
38 00 0 MISS
13C 00 0 MISS
388 00 0 MISS
18C 00 0 MISS
Replacement policy(which is default) LRU
( d) Direct planned or mapped cache with b = 4 words( each instruction size = AW)
Line offset = log₂( 4) = 2 bit
Word offset = log₂( 4) = 2 bit
Tag(Label) = remaining bits
# lines = 16/ W = 4
0 * 74-----> 01110100
where,
01 is the line offset
00 is the word offset
0111 is the tag(label).
Therefore, the tag, line offset and line offset of the hexadecimal is given to be in a binary number.
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Given that events A and B are independent with
P(A) = 0.42 and P(B) = 0.05, determine the value
of P(AN B), rounding to the nearest thousandth, if
necessary.
Answer
P(A∩B) = 0.021
Step-by-step explanation:
For independent events P(A∩B) is the same as P(A)*P(B) so for this 0.42*0.05 = 0.021
The efficiency for a steel specimen immersed in a phosphating tank is the weight of the phosphate coating divided by the metal loss (both in mg/ft2). An article gave the accompanying data on tank temperature (x) and efficiency ratio (y).
Temp 170 172 173 174 174 175 176 177 Ratio 0.76 1.27 1.48 0.99 0.99 1.02 1.12 1.70 Temp. 180 180 180 180 180 181 181 182 Ratio 1.43 1.50 1.57 2.15 2.11 0.88 1.33 0.84 Temp. 182 182 182 184 184 185 186 188 Ratio 1.73 2.04 2.70 1.59 2.62 3.10 1.89 3.18 (a) Determine the equation of the estimated regression line. (Round all numerical values to five decimal places.) y = . 1017x-16.592 レ 19174x (b) Calculate a point estimate for true average efficiency ratio when tank temperature is 182. (Round your answer to four decimal places.) 1.9174 (c) Calculate the values of the residuals from the least squares line for the four observations for which temperature is 182. (Round your answers to four decimal places.) (182, 0.84) 1581 (182, 1.73) (182, 2.04) (182, 2.70)
The efficiency for a steel specimen immersed in a phosphating tank is the weight of the phosphate.
a) The equation of the estimated regression line is ŷ = - 16.592 + 0.1017x.
b) A point estimate is 1.9174 for true average efficiency ratio when tank temperature is 182.
c) The values of the residuals from the least squares line for the four observations for which temperature is 182 are -1.0774, -0.1874, 0.1226, 0.7826..
We have given the accompanying data on tank temperature (x) and efficiency ratio (y).
a) We have to find out the equation of the estimated regression line. Consider the calculations shown in the above table:
ΣΧ= 4308 ; ΣΥ= 39.99 ; ΣΧΥ = 7229.47 ;
ΣX² = 773790
Determine the slope and intercepts using the following formulas,
Slope b₁ = (n ΣΧΥ - ΣX ΣΥ)/(nΣΧ² - (ΣX)²)
=> b₁ = [24 (7229.47) - (4308) (39.99)]/(24(773790)-(4308)²)
=> b₁ = 1230.36/12096 = 0.10171626984
=> b₁ ≈ 0.1017
Intercept, b₀ = ΣY /n - b₁ΣΧ /n
=> b₀ = 39.99/24 - 0.1017×4308/24
= -16.592
Thus, the estimated regression equation of the form, ŷ = b₀ + b₁ x
ŷ = - 16.592 + 0.1017x
b) Calculate the point estimate for true average efficiency ratio when tank temperature is 182.
y = -16.592 + 0.1017x
=> y= -16.592 +0.1017 (182)
=> y= 1.9174
Therefore, the point estimate for true average efficiency ratio when tank temperature is 182 is 1.9174..
c)We have to find out the values of the residuals from the least squares line for the four observations for which temperature is 182.
From part (b), the value of ŷ is 1.9174.
The table below shows the residuals.
Vi ŷ e = y₁ - y
0.84 1.9174 -1.0774
1.73 1.9174 -0.1874
2.04 1.9174 0.1226
2.70 1.9174. 0.7826
Hence, we got all the required values.
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A certain skin cream is 80 percent effective in curing a common rash. A random sample of 100 people with the rash will use the cream. Which of the following is the best description of the shape of the sampling distribution of the sample proportion of those who will be cured? А Bimodal B Uniform SO с Approximately normal D Strongly skewed to the left E) Strongly skewed to the right 11 8 GA N TALK ESTU MacBook Pro esc O F3 090 F FS FO aa E7 DI TO DO F9 F10 ! 1 $ % A 12. 2 3 4 C 5 & 7 6 3 0 * 8 9 ВЫ В ㅉ ㅈ CC C 77 u i Q W E R E T Y U HHHH 0 Р L o
The best description of the shape of the sampling distribution is C. Approximately normal.
The sampling distribution of the sample proportion of those who will be cured with the skin cream is approximately normal.
A sampling distribution is the distribution of a statistic calculated from a random sample of data. In this case, the statistic is the sample proportion of those who will be cured with the skin cream.
The Central Limit Theorem states that the sampling distribution of a statistic will be approximately normal if the sample size is large enough, regardless of the shape of the underlying distribution.
Since the sample size of 100 people is large enough, the sampling distribution of the sample proportion of those who will be cured with the skin cream is approximately normal.
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The question is -
Certain skin cream is 80 percent effective in curing a common rash. A random sample of 100 people with the rash will use the cream. Which of the following is the best description of the shape of the sampling distribution of the sample proportion of those who will be cured? А. Bimodal B. Uniform C. Approximately normal D. Strongly skewed to the left E. Strongly skewed to the right.
Can someone help please? Picture is already attached. If its wrong please correct it. This isn’t mine by the way, I’m posting it for someone else to double check if it’s right
The value of the other points in the number line for each case are;
a) M = -2¹/₂
N = -1
R = 4
b) M = -1
P = 1
R = 1.6
c) M = -125
P = 125
N = -50
d) N = -6
P = 15
R = 24
How to interpret Number Lines?a) We are given that P = 2¹/₂
From the point 0 of the number line to point P is 5 units and as such;
Each unit = 2¹/₂/5 = ¹/₂
Thus;
M = -2¹/₂
N = -1
R = 4
b) We are given that N = -0.4
From the point 0 of the number line to point N is 2 units and as such;
Each unit = 0.4/2 = 0.2
Thus;
M = -1
P = 1
R = 1.6
C) We are given that R = 200
From the point 0 of the number line to point R is 8 units and as such;
Each unit = 200/8 = 25
Thus;
M = -125
P = 125
N = -50
D) We are given that M = -15
From the point 0 of the number line to point N is 5 units and as such;
Each unit = 15/5 = 3
Thus;
N = -6
P = 15
R = 24
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Please help will mark Brainly
The range of the function will be 0 ≤ y ≤ 960
Range of a FunctionThe range of a function is the set of all its outputs. Example: Let us consider the function f: A→ B, where f(x) = 16x and each of A and B = {set of natural numbers}. Here we say A is the domain and B is the co-domain. Then the output of this function becomes the range. The range = {set of even natural numbers}.
Generally, the range of a function is the possible values of y in the that function and can be from -negative infinity to positive infinity.
In the given question, the function y = 16x models the situation and the capacity of the the container is 960 ounces
The range will fall between 0 ≤ y ≤ 960
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Which ordered pair is NOT a point on the graph of f(x)=1/2. x-7
(1,-61/2)
(2,8)
(-2,-8)
(0,-7)
The ordered pair that is NOT a point on the graph of f(x) = (1/2)*x - 7 is (2,8) , the correct option is (b) .
In the question ,
it is given that ,
the function is given as ;
f(x) = (1/2)*x - 7 ,
Option(a) ,
the ordered pair is (1 , [tex]-6\frac{1}{2}[/tex] )
To satisfy the function f(x) , on putting x = 1 , we should get y = [tex]-6\frac{1}{2}[/tex] .
f(1) = (1/2) - 7 = (1 - 14)/2 = -13/2 .
So , this point lies on graph of f(x) .
Option(b) ,
the ordered pair is (2,8) ,
f(2) = (1/2)*2 - 7 = 1 - 7 = -6 ≠ 8 .
So , this point does not lie on graph of f(x) .
Option(c) ,
the ordered pair is (-2,-8) ,
f(-2) = (1/2)*(-2) - 7 = -1 - 7 = -8 = -8 .
So , this point lies on graph of f(x) .
Option(d) ,
the ordered pair is (0,-7) ,
f(2) = (1/2)*0 - 7 = - 7 = -7 .
So , this point lies on graph of f(x) .
Therefore , the ordered pair (2,8) is not on the graph .
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Solve the system of linear equations
Answer:
Below
Step-by-step explanation:
I'll do the first one....you can then do the second one
-4x-2y = -12
4x+8y = -24 add these two equations together ( this will eliminate 'x')
6y = -36
y = - 6 use this value in either equation to compute x = 6
HINT: On the next one....multiply either equation by -1 then add together
The sum of the first 15 terms of the sequences 7, -14, 28, -56, 112,...
The sum of the first 15 terms of the geometric sequences will be 76,456.33.
What is the sum of a geometric sequence?The aggregate to boundless GP implies, the number of terms in a limitless GP.
Let a₁ be the first term, n be the total number term, and r be a common ratio.
Then the sum of the geometric sequence will be
Sₙ = [a₁ (1 - rⁿ)] / (1 - r)
The geometric sequence is given below.
7, -14, 28, -56, 112,...
The first term of the geometric sequence is 7 and the common ratio of the geometric sequence is given as,
r = - 14 / 7
r = - 2
Then the sum of the first 15 terms of the sequences will be given as,
S₁₅ = [7 (1 - (-2)¹⁵)] / (1 - (-2))
S₁₅ = [7(1 + 32,768)] / 3
S₁₅ = -229,369 / 3
S₁₅ = 76,456.33
The sum of the first 15 terms of the geometric sequences will be 76,456.33.
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Linear function k has a zero at 3 and a y-intercept of 9 . Which graph best represents k ?
In the graph B we can see that y intercept is 9 and zero is 3. So the graph b is the correct answer.
In the given question, linear function k has a zero at 3 and a y-intercept of 9.
We have to choose which graph best represents k.
As we know that;
A linear equation represent the relationship between the two unknown variable. The equation of linear equation is of one degree.
The simplest linear equation shows the correlation between (x,y), which may then be used to make a table or a graph on the coordinate plane or to assess at a specific x or y value.
We represent linear function in the form of y=mx+c.
where m is the slope of the line, c is the y intercept of the line, x is independent variable and y is the dependent variable.
As we see the y intercept in the graph crosses the y axis.
Here y intercept is 9.
The zeros of the linear function is that where y value is zero.
As in the graph B we can see that y intercept is 9 and zero is 3. So the graph b is the correct answer.
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A set of 3 consecutive even integers adds up to 6. What are the integers?
-3x+2y=9 X-3y=4 solve this system of equations by using the scientific method, the ordered pair of solutions is written in the format (x,y)
The ordered pairs of the solution to the system of equation are (-5, -3).
How to solve system of equation?System of equation can be solved using methods like substitution method, elimination method and graphical method.
Let's solve the system of equation by substitution method.
Therefore,
-3x + 2y = 9
x - 3y = 4
Hence,
x = 3y + 4
Substitute the value of x in equation(i)
-3x + 2y = 9
-3(3y + 4) + 2y = 9
-9y - 12 + 2y = 9
-7y = 9 + 12
-7y = 21
y = 21 / -7
y = -3
Let's find x using equation(ii)
x = 4 + 3y
x = 4 + 3(-3)
x = 4 - 9
x = -5
Hence, x = -5 and y = -3
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