Using function notation, write the formula for the function g(x) whose graph is obtained by
morizontally stretching the graph of f(x) by a factor of 2.
The function notation formula is given as g(x) = f(x/2)
Function notation explained.
Function notation is a way of representing a mathematical function using symbols and variables. It is a shorthand way of writing the rule or formula for a function, which specifies how the input values (usually denoted by x) are transformed into output values (usually denoted by y or f(x)).
In function notation, a function is typically represented by a letter (usually f, g, or h) followed by parentheses that enclose the input value or variable, such as f(x), g(t), or h(y). This notation indicates that the function takes an input value (x, t, or y) and produces a corresponding output value (f(x), g(t), or h(y)).
Assuming we want to horizontally stretch the graph of f(x) by a factor of 2 to obtain the graph of g(x), the function notation for g(x) can be written as:
g(x) = f(x/2)
In other words, we plug in x/2 instead of x in the formula for f(x) to get the corresponding value of g(x) that is horizontally stretched by a factor of 2. This is because when we substitute x/2 in f(x), it effectively multiplies the input (x) by 2, which horizontally stretches the graph by a factor of 2.
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21. समूह 'घ' (Group 'D') [4x5=20] रामले 3 वर्षको लागि 12% प्रतिवर्ष साधारण ब्याजदरले रु. 50000 लगानी गर्यो र श्यामले 10% प्रतिवर्ष वार्षिक चक्रीय ब्याजदरले त्यति नै समयका लागि त्यति नै रकम लगानी गर्यो भने पत्ता लगाउनुहोस् । Ram invested Rs. 50000 for 3 years at the rate of 12% simple interest per annum and Shyam invested same amount for the same time at the rate of 10% annual compound Interest, calculate. . X रामले प्राप्त गरेको ब्याज (The interest received by Ram) श्यामले प्राप्त गरेको ब्याज (The interest received by Shyam) समय र ब्याजदरलाई यथावत् राखेर बराबर ब्याज प्राप्त गर्न रामले कति बढी वा घटी रकम लगानी गर्नुपर्ला ? Without altering time and rate of interest, how much more or less amount should Ram have to invest for equal interest? (Ans: L. Rs.18000, ii, 16550, ill.
Step-by-step explanation:
रामले 3 वर्षको लागि 12% प्रतिवर्ष साधारण ब्याजदरले रु. 50000 लगानी गरेको थियो। यसको आधारमा उनले प्राप्त गरेको ब्याज हो:
Simple Interest (S.I.) = (P × R × T) / 100
यहाँ, P = रु. 50000 हो, R = 12% = 12/100 = 0.12 हो, र T = 3 वर्ष हो।
S.I. = (50000 × 0.12 × 3) / 100 = रु. 18000
त्यसैपछि, श्यामले चक्रीय ब्याजदरले रु. 50000 लगाएर 3 वर्षमा त्यति रकम लिन्छन्। चक्रीय ब्याजदरले ब्याज प्राप्त गर्नको लागि प्रत्येक वर्षको अन्तिम रकममा पूर्ववत ब्याज पनि जोडिन्छ। त्यसको आधारमा उनले प्राप्त गरेको ब्याज हो:
Compound Interest (C.I.) = P × [(1 + R/100)ᵀ - 1]
यहाँ, P = रु. 50000 हो, R = 10% = 10/100 = 0.10 हो, र T = 3 वर्ष हो।
C.I. = 50000 × [(1 + 0.10)³ - 1] = रु. 16532.10
त्यस्तै ब्याजदर र समयको आधारमा रामले पनि रकम लगाएर बराबर ब्याज प्राप्त गर्न चाहनुहुन्छ। यसलाई गणना गर्न प्रयोग गरिएको समान ब्याज तथा समय भएको सिस्टमको नाम "Compound Interest with annual installments" हो। यसक
let F=[1,0],[2,-3],then F^3
The result of the matrix multiplication for F³ is determined as [[1,0],[-2,3]].
What is matrix multiplication?
Matrix multiplication is a mathematical operation that takes two matrices and produces a new matrix.
Given two matrices A and B, the resulting matrix C is obtained by multiplying the elements of the rows of matrix A with the corresponding elements of the columns of matrix B, and summing the products.
To calculate F³, we need to multiply the matrix F by itself three times:
F² = F * F = [[1,0],[2,-3]] * [[1,0],[2,-3]] = [[11+02,10+0(-3)],[21+(-3)2,20+(-3)(-3)]] = [[1,0],[-4,9]]
F³ = F * F² = [[1,0],[2,-3]] * [[1,0],[-4,9]] = [[11+02,10+09],[21+(-3)(-4),2*0+(-3)*9]] = [[1,0],[-2,3]]
Therefore, F³ = [[1,0],[-2,3]].
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Reflect (6,-4) across the -axis. Then reflect the result across the -axis. What are the coordinates of the final point?”
The coordinates of the final point after the reflections across the x-axis twice is (6, -4)
What are the coordinates of the final point?Reflecting a point across the x-axis means that we keep the x-coordinate the same, but change the sign of the y-coordinate.
So reflecting (6,-4) across the x-axis gives us the point (6,4).
Reflecting this result again across the x-axis means that we keep the x-coordinate the same, but change the sign of the y-coordinate again.
So reflecting (6,4) across the x-axis gives us the point (6,-4).
Therefore, the final point after both reflections is (6, -4).
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Help, solve this pls
Which set has an average of 8?
A) A
B) B
C) A and B
D) none of the above
Answer:
IT IS B hope this helped
Step-by-step explanation:
Please someone help me with this question…..asap
Given the above conditions with regard to Rolle's Theorem, the answers are:
Therefore, the solution is:
F(0) = 0
f(4) = (-8) e^4
C = 1
What is the explanation for the above response?
To find F(0), we can simply substitute x=0 into the expression for f(x):
f(0) = (0^2 - 4(0)) e^0 = 0
To find f(4), we can substitute x=4:
f(4) = (4^2 - 4(4)) e^4 = (-8) e^4
Next, we need to find the critical point(s) of f(x) on the interval [0,4]. To do this, we find the derivative of f(x) and set it equal to zero:
f'(x) = (2x-4) e^x + (x^2-4x) e^x = (x^2-2x) e^x
Setting f'(x) equal to zero, we have:
(x^2-2x) e^x = 0
Since e^x is never zero, we can divide both sides by e^x to get:
x^2 - 2x = 0
Factoring out x, we have:
x(x-2) = 0
Therefore, the critical points on [0,4] are x=0 and x=2.
Since both critical points are in the open interval (0,4), Rolle's Theorem applies. This means there exists a number c in (0,4) such that f'(c) = 0. To find this value of c, we can simply take the average of the critical points:
c = (0 + 2)/2 = 1
Therefore, the solution is:
F(0) = 0
f(4) = (-8) e^4
C = 1
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When concentrations of formaldehyde in the air exceed 33 μg/ft3 1 μg=1 microgram=10−6 gram, a strong odor and irritation to the eyes often occurs. One square foot of hardwood plywood paneling can emit 3365 μg of formaldehyde per day. A 5 ft by 7 ft sheet of paneling is attached to a wall in a room having floor dimensions of 10 ft by 10 ft and height of 7 ft.
Since the limit is just 33 μg/ft³, it exceeded the given limit. Thus, with this condition, there would be strong odor and irritation of the eyes.
What do you mean by volume?A cube's volume is defined as the total number of cubic units that it takes up in its entirety. To calculate the cube's volume, we need to know how long each cube side is. In order to compute volume, use the following equation: Side x Side x Side equals volume.
33 μg/ft³ is the maximum allowed formaldehyde concentration. Our foundation should be this. It is now assumed that wood panelling generates 3,365 μg of formaldehyde per square foot. The wood panelling measures 5 feet by 6 feet; therefore the area is equal to 30 ft². As a result, the formaldehyde emission is calculated as follows: Emitted formaldehyde = (3,365 μg/ft²) (30 ft²) = 100,950 μg
The size of the room is then measured:
V = 10 ft × 10 ft × 6 ft = 600 ft³
Let's compare the ratio to our basis:
Ratio = 100,950 μg/600 ft³ = 168.25 μg/ft³
Since the limit is just 33 μg/ft³, it exceeded the given limit. Thus, with this condition, there would be strong odor and irritation of the eyes.
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If the temperature outside is 25 degrees C, what clothing would be the MOST appropriate? SHORTS OR LIGHT PANTS AND A T-SHIRT. OR LINED PANTS AND A LONG-SLEEVED JCKET,OR THERMAL UNDERWEAR,OR A SNOWSUITE?
Answer:
shorts/ and a t-shirt
Step-by-step explanation:
25° c is equal to 77° f
Standard Deviation. Find the Standard Deviation of the following set of data. You must fill out the table and show the ending calculations in order to get full credit here.
7.2, 8.9, 2.7, 11.6, 5.8, 10.2
show ALL steps
The standard deviation of the data set is 1.03.
What is the standard deviation?
The standard deviation is a measure of the amount of variation or dispersion of a set of data values. It measures how spread out the data is from the mean or average value.
To find the standard deviation, we first need to find the mean of the data set:
Mean = (7.2 + 8.9 + 2.7 + 11.6 + 5.8 + 10.2) / 6 = 7.4
Next, we calculate the deviations from the mean for each data point:
| x - mean | (x - mean)²
0.2 0.04
1.5 2.25
4.7 22.09
4.2 17.64
1.6 2.56
2.8 7.84
To find the variance, we add up the (x - mean)² values and divide by the number of data points:
Variance = (0.04 + 2.25 + 22.09 + 17.64 + 2.56 + 7.84) / 6 = 6.36/6 = 1.06
Finally, we take the square root of the variance to get the standard deviation:
Standard deviation = √(1.06) = 1.03 (rounded to two decimal places)
Therefore, the standard deviation of the data set is 1.03.
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50pts!!!!!!!!!!!!!!!!!
she has a gross income of $105500
. If she pays $26982
in income tax and $2110
for the Medicare levy, what is her net income?
Answer:
Step-by-step explanation:
Claro que sí. El ingreso neto es el ingreso que queda después de restar los impuestos y otros gastos del ingreso bruto. La fórmula del ingreso neto es:
Ingreso neto = Ingreso bruto – Impuestos – Comisiones – Intereses – Créditos – Otros Gastos
En tu caso, el ingreso bruto es $105500 y los impuestos son $26982 por el impuesto sobre la renta y $2110 por el impuesto de Medicare. No sé si tienes otros gastos que debas restar, pero si no los tienes, entonces el ingreso neto sería:
Ingreso neto = $105500 - $26982 - $2110 Ingreso neto = $77408
Espero que te haya servido de ayuda.
Could someone help answer Number 22 please
Area of the first triangle is 582.86 square units
Area of the second triangle is 694 square units
How to find the area of the trianglesThe formula for area of a triangle is solved by
= 1/2 * b * h
For the first figure, we solve for h first using trigonometry
tan 68 = 48 / h
h = 48 / tan 68
h = 19.39
The other side of the base is solved using tan 58
tan 58 = 43.22 / b
b = 43.22 / tan 58
b = 12.12
base of the triangle = 48 + 12.12 = 60.12
Area of the first triangle = 0.5 * 60.12 * 19.39 = 582.86 square units
22. Solving for h
cos 64 = h / 50
h = 50 * cos 64 = 21.92
the other part of the base
sin 64 = b / 50
b1 = 50 * sin 64 = 44.94
tan 50 = h / b2 = 21.92 / b2
b2 = 21.90 / tan 50 = 18.38
base = b1 + b2 = 44.94 + 18.38 = 63.32
Area of the second triangle = 0.5 * 21.92 * 63.32 = 693.99 square units
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The circumference of a circle is 15.25 feet. What is the diameter when 3.14 is used for pi?
Answer:
4.85423
Step-by-step explanation:
D equals C/PI
Where D=Diameter and C=Circumference and PI=PI(3.14)
All the freshmen at Hillsboro High School must sign up for one science class, and the
registration results so far have been recorded.
biology
77
physics
5
chemistry
4
earth science 46
What is the experimental probability that the next freshman will register for earth science?
Write your answer as a fraction or whole number.
P(earth science) =
After answering the provided question, we can conclude that So the experimental probability that the next freshman will register for earth science is 23/66.
What is probability?Probability is a measure of how likely an event is to occur. It is represented by a number between 0 and 1, with 0 representing an unlikely event and 1 representing an unavoidable event. Switching a fair coin and coin flips has a probability of 0.5 or 50% because there are two equally likely outcomes. (Heads or tails). Probability theory is a branch of mathematics that studies random events rather than their properties. It is applied in many fields, including statistics, finance, science, and engineering.
There are a total of 77 + 5 + 4 + 46 = 132 freshmen who have registered for a science class. Out of these, 46 have registered for earth science.
P(earth science) = number of freshmen who registered for earth science / total number of freshmen who registered for a science class
P(earth science) = 46 / 132
Simplifying the fraction, we get:
P(earth science) = 23 / 66
So the experimental probability that the next freshman will register for earth science is 23/66.
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Mel's cat eats 3/4 of a bag of cat food each month. How many
bags of cat food does Mel's cat eat in 10 months? Show your
work
Step-by-step explanation:
3/4 bag / months * 10 month = 30/ 4 bags = 7 1/2 bags
If 4x-3=5, what is the value of x
Answer: the answer is two :)
Step-by-step explanation:
4x=5+3
4x=8
x= 8/4
x=2
i need help to do spiral review 5 on lesson 9.7 pls help
Answer: wheres the page/diagram
Step-by-step explanation:
An image of a rhombus is shown.
a rhombus with a base of 20 centimeters and a height of 18.9 centimeters
What is the area of the rhombus?
378 cm2
189 cm2
126 cm2
77.8 cm2
The Area of the rhombus with base 21 cm and height 17.3 cm is 363.3 cm².
What is area of Rhombus?
To calculate the base of the rhombus, we will follow the steps below;
write the formula for calculating the area of a rhombus
area of a rhombus = b × h
where h is the height of the rhombus and b is the base of the rhombus
Given:
Base = 21 cm
Height = 17.3 cm
We know area of Rhombus = base x height
= 21 x 17.3
= 363.3 cm²
So, the area of Rhombus is 363.3 cm².
Boats from all along the Atlantic coast dock at a busy marina. Of the first boats to dock there one day, six of the boats were from Maine, while 12 were from other states. What is the experimental probability that the next boat to dock will be from Maine?
The experimental probability is0.33 or 33% to dock .
What does theoretical probability mean?The probability calculated without performing any experiments is known as theoretical probability. It can be characterised as the proportion of favourable results to all other possible outcomes. No experiment is required to determine the theoretical probability. As an alternative, we should be aware of the circumstances in order to determine the likelihood that an event will occur.
The actual outcome of an experiment is known as the experimental probability, which may differ from the theoretical probability.
In this instance, the marina 1 is home to 6 boats from Maine and 12 vessels from other states.
Hence,
6/(6+12) = 0.33 or 33%
the chance that the next boat to port comes from Maine.
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Answer:
1/3
Step-by-step explanation:
Find the volume of the solid whose base is a triangle with vertices (0,0), (0,3), and (5,0). Slices perpendicular to the x-axis are semicircles. Enter answer using exact values.
The volume of the solid whose base is a triangle with vertices (0,0), (0,3), and (5,0) is 25π/12 cubic units.
What is a triangle?
A triangle is a closed geometric shape that is formed by connecting three line segments. These line segments are called sides, and the points where they meet are called vertices. A triangle has three sides, three angles, and three vertices.
To start, let's graph the triangle to get a better understanding of the problem:
(0,3) *
|\
| \
| \
| \
| \
(0,0) *-----*-----> x
(5,0)
The height of this slice is given by the line from the point (x,0) to the point (0,3), which has equation y = 3/5 * x + 0. The radius of the semicircle is half the height of the slice, which is given by the equation r = 3/10 * x.
The area of a semicircle is πr²/2, so the volume of this slice is:
V(x) = π * (3/10 * x)² / 2 * dx
To find the total volume of the solid, we need to integrate this expression over the range of x values that covers the entire base of the solid, which is from x=0 to x=5:
V = ∫₀₅ π * (3/10 * x)² / 2 dx
V = π/20 * ∫₀₅ x² dx
V = π/20 * [x³/3] from 0 to 5
V = π/20 * (5³/3)
V = π/4 * (25/3)
V = 25π/12
Therefore, the volume of the solid is 25π/12 cubic units.
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QUESTION 5..... [1.5 marks]
The following data set represents the score distribution for the Final Exam in MATH 146:
55, 56, 57, 58, 59, 60, 60, 61, 63, 65, 69, 71, 78, 78, 79, 79, 82, 82, 83, 83
Find the 85th percentile.
Solution. Please write your detailed solution here:
answer
82
steps
put data in numerical order
55, 56, 57, 58, 59, 60, 60, 61, 63, 65, 69, 71, 78, 78, 79, 79, 82, 82, 83, 83
there are 20 numbers = 20
85 is the percentile = p
percentile rank formula
PR = (p/100) * (n + 1)
PR = (85/100) * (20 + 1) = 17.85
round up 17.85 to 18
it's the 18th number which is
82
chatgpt
How many total Sophomores were surveyed?
Answer: 22 sophomores were surveyed
Step-by-step explanation:
18 students decide they don't want to be rescued and want to continue to live in the jungle if this represents 40 of the students how many students want to be rescued. The answer is 45 right?
A, B, C and D are 4 towns
B is 30km due east of A.
C is 30km due North of A.
D is 45km due South of A.
Calculate the bearing of D to B
The bearing of D to B is approximately 33.7°, measured in a clockwise direction from the north-south axis.
We can start by drawing a diagram to represent the positions of the four towns. Let A be the origin of the coordinate system, B be located 30 km due east of A, C be located 30 km due north of A, and D be located 45 km due south of A. The diagram would look like this:
C (30 km)
|
|
|
A (0,0)---+---B (30 km)
|
|
|
|
D (45 km)
To calculate the bearing of D to B, we need to determine the angle that DB makes with the north-south axis (i.e., the y-axis) in a clockwise direction.
First, we can use the Pythagorean theorem to find the distance between B and D:
BD² = AB² + AD²
BD² = 30² + 45²
BD² = 2025
BD = √2025
BD = 45 km
Next, we can use trigonometry to find the angle that DB makes with the north-south axis. Let θ be the angle we are looking for. Then:
tan θ = (opposite / adjacent) = (AB / AD) = (30 / 45) = 2/3
Taking the arctangent of both sides, we get:
θ = tan⁻¹(2/3) ≈ 33.7°
Therefore, the bearing of D to B is approximately 33.7°, measured in a clockwise direction from the north-south axis.
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please help me on this question
Answer:
x = 30 cm
Perimeter = 72 cm
Step-by-step explanation:
By Pythagoras theorem,
x² = 18² + 24²
x² = 324 + 576
x² = 900
x² = 30²
x = 30 cm
Perimeter of a triangle is just the sum of its sides,
Perimeter = 18 + 24 + 30
Perimeter = 72 cm
Answer:
30cm, 72cm
Step-by-step explanation:
c²=a²+b²
x²=18²+24²=900
x=√900
x=30cm
p=a+b+c
p=18+24+30
p=72cm
helo I don't understand show work please
Answer:
a = 4.5 , b = 7.5
Step-by-step explanation:
using Pythagoras' identity in the two right triangle
outer right triangle
b² + 10² = (8 + a)² = 64 + 16a + a² → (1)
inner right triangle
a² + 6² = b² → (2)
substitute b² = a² + 6² = a² + 36 into (1)
a² + 36 + 100 = 64 + 16a + a² ( subtract a² from both sides )
136 = 64 + 16a ( subtract 64 from both sides )
72 = 16a ( divide both sides by 16 )
4.5 = a
----------------------------------------
substitute a = 4.5 into (2)
4.5² + 6² = b² , that is
20.25 + 36 = b²
56.25 = b² ( take square root of both sides )
[tex]\sqrt{56.25}[/tex] = b , then
b = 7.5
The mapping diagram represents a relation where x represents the independent variable and y represents the dependent variable.
(PLS HELP 100 POINTS)
We can conclude after answering the provided question that Because each element in the domain is paired with exactly one element in the range, this mapping diagram represents a function.
what is domain?The domain of a function is the range of possible values that it can accept. These numbers represent the x-values of a function such as f. (x). The domain of a function is the range of possible values that can be used with it. This set includes the value returned by the method after inserting the x value. A function with y as the dependent variable and x as the independent variable has the formula y = f. (x). When a single value of y can be produced successfully from a value of x, that value of x is said to be in the function's domain.
Each element in the domain (set of x values) is paired with exactly one element in the range (set of y values), as represented by arrows connecting the two sets in the mapping diagram. For example, the domain element 2 is paired with the range element 4, and the domain element -1 is paired with the range element 1.
Because each element in the domain is paired with exactly one element in the range, this mapping diagram represents a function. The function is not one-to-one because multiple domain elements are paired with the same range element (for example, both -2 and 3 are paired with 1).
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Find the centre and radius of 364+28y+y^2+x^2=-26x
Step-by-step explanation:
hope it will help you , and give some clue to do typical qno..
Consider the Ricardian model of international trade with two countries, China and India, and two
goods, rich (R) and automobiles (A). The table below displays unit labour requirements (how
many units of labour are required to produce one unit of output) for the two countries. China
has 1,260 labour units and India has 60 labour units.
The unit of labor required to produce one unit of output for the two countries are 2 and 1/3.
The world automobiles-to-rice relative supply curve slopes upward, indicating that as the world price ratio of rice to automobiles rises, so will the relative supply of automobiles to rice.
How to calculate supply curve?To draw the world automobiles-to-rice relative supply curve, calculate the relative supply of automobiles to rice for each country. The relative supply is the ratio of the quantity of automobiles produced to the quantity of rice produced, multiplied by the ratio of the world price of rice to the world price of automobiles. Express this mathematically as:
Relative supply of automobiles to rice = (QA/RA)/(QR/RR) x (PR/PA)
where QA and RA are the quantities of automobiles and rice produced by a country, QR and RR are the quantities of rice produced by a country, and PR and PA are the world prices of rice and automobiles, respectively.
Using the unit labor requirements given in the table, calculate the relative supply of automobiles to rice for China and India as follows:
Relative supply of automobiles to rice for China = (1/4)/(1/2) x (2/1) = 2
Relative supply of automobiles to rice for India = (1/12)/(1/2) x (2/1) = 1/3
We can then plot these points on a graph, where the x-axis represents the relative supply of automobiles to rice and the y-axis represents the world price ratio of rice to automobiles. Assume that the world price ratio of rice to automobiles is initially set at 1, which means that the price of rice is equal to the price of automobiles. We can then draw a line connecting the two points, which represents the world automobiles-to-rice relative supply curve.
The kink point of the relative supply curve occurs when the relative supply of automobiles to rice is equal to 2, which is the point where China switches from being a net exporter of automobiles to a net importer of automobiles. At this point, the world price ratio of rice to automobiles increases, which means that the price of rice increases relative to the price of automobiles. As a result, China reduces its production of automobiles and increases its production of rice, which reduces its relative supply of automobiles to rice.
The second segment of the relative supply curve occurs when the relative supply of automobiles to rice is less than 1/3, which is the point where India switches from being a net exporter of automobiles to a net importer of automobiles. At this point, the world price ratio of rice to automobiles decreases, which means that the price of automobiles increases relative to the price of rice. As a result, India reduces its production of rice and increases its production of automobiles, which increases its relative supply of automobiles to rice.
The world automobiles-to-rice relative supply curve is upward sloping, which means that as the world price ratio of rice to automobiles increases, the relative supply of automobiles to rice also increases. This reflects the fact that countries specialize in the production of goods for which they have a comparative advantage, and trade with other countries to obtain goods for which they do not have a comparative advantage.
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I have a queston can you answer it pls
Answer:
0.1 gallons per second or 6 gallons per minute
Step-by-step explanation:
Unit rate =measurement/time
Measurement=
42
gallons
Time=
7
42/7=6
Or if you want in seconds, change the mins to seconds. There are 60 seconds in a minute
7
×
60
=
420
seconds
Unit rate =
42
420
=
0.1
gallons per second
1.
2y = -2x + 6
x- 5y = -15
2.
5x + y = 2
20x + 3y = -4
please include a solution thank you.
Step-by-step explanation:
To solve the system of equations:
2y = -2x + 6 ----(1)
x - 5y = -15 ----(2)
We can use substitution method or elimination method. Here, we will use elimination method to eliminate y.
Multiplying equation (1) by -5, we get:
-10y = 10x - 30 ----(3)
Adding equations (2) and (3), we get:
-15y = -45
Dividing by -15 on both sides, we get:
y = 3
Substituting y = 3 in equation (2), we get:
x - 5(3) = -15
x - 15 = -15
Adding 15 on both sides, we get:
x = 0
Therefore, the solution of the system of equations is (x, y) = (0, 3).
To solve the system of equations:
5x + y = 2 ----(1)
20x + 3y = -4 ----(2)
We can use substitution method or elimination method. Here, we will use elimination method to eliminate y.
Multiplying equation (1) by -3, we get:
-15x - 3y = -6 ----(3)
Adding equations (2) and (3), we get:
5x = -10
Dividing by 5 on both sides, we get:
x = -2
Substituting x = -2 in equation (1), we get:
5(-2) + y = 2
-10 + y = 2
Adding 10 on both sides, we get:
y = 12
Therefore, the solution of the system of equations is (x, y) = (-2, 12).
Answer:
1) (0, 3)
2) (-2, 12)
Step-by-step explanation:
1)
2y = -2x + 6 → y = -x + 3
x - 5y = -15
Substitute the simplified first equation into the second equation and solve for x.
x - 5( -x + 3 ) = -15
x + 5x - 15 = -15
6x = 0
x = 0
Substitute into first equation to get y.
y = -(0) + 3
y = 3
The solution to the system is the coordinate (0, 3).
2)
5x + y = 2
20x + 3y = -4
Solve the first equation for y.
y = -5x + 2
Substitute this into the second equation and solve for x.
20x + 3 ( -5x + 2 ) = -4
20x - 15x + 6 = -4
5x = -10
x = -2
Substitute this value on the first equation to get y.
y = -5( -2 ) + 2
y = 10 + 2
y = 12
The solution to the system is the coordinate (-2, 12).