Answer:
1/4 of the brownies were eaten
there were 1 - 1/4 = 3/4 of brownies left
2/3 of the 3/4 were eat or: (2/3)(3/4) = 1/2 of the whole pan of brownies were eaten
the total of brownies eaten is: 1/4 + 1/2 = (1*1 + 2*1)/4 = 3/4 of the whole pan of brownies were eaten.Step-by-step explanation:
John ate half or 50% of the original whole pan of brownies. This is calculated by multiplying 3/4 (the remaining brownies after 1/4 had been eaten) by 2/3 (the fraction John ate of the remaining amount).
Explanation:Firstly, the question pertains to the proportion of brownies that were consumed. Initially 1/4 of the brownies were eaten, implying that 3/4 of the brownies were left on the counter. John ate 2/3 of the remaining brownies, so we will calculate 2/3 of 3/4 to determine how much of the whole pan of brownies John ate:
Step 1: Convert 3/4 and 2/3 to decimal points (0.75 and 0.67 respectively).
Step 2: Multiply 0.75 (the remaining brownies) by 0.67 (the fraction that John consumed). This equals approximately 0.50.
Step 3: The result 0.50 implies that John consumed 50% or half of the original brownies amount.
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Write a quadratic function to model the graph to the right
Answer:
y = x² + 2x + 5
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
Here the vertex = (- 1, 4), thus
y = a(x + 1)² + 4
To find a substitute (0, 5) a point on the graph into the equation
5 = a(0 + 1)² + 4
5 = a + 4 ( subtract 4 from both sides )
a = 1, thus
y = (x + 1)² + 4 ← expand and simplify
= x² + 2x + 1 + 4
= x² + 2x + 5
The quadratic function to model the graph to the right is f(x) = x² + 2x + 5.
What is a quadratic equation?Any equation of the form [tex]\rm ax^2+bx+c=0[/tex] where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.
As we know, the formula for the roots of the quadratic equation is given by:
[tex]\rm x = \dfrac{-b \pm\sqrt{b^2-4ac}}{2a}[/tex]
The graph of the quadratic function is given in the picture.
As we know,
(y - h)² = 4a(x - k)
(h, k) is the vertex of the parabola:
Or
y = a(x - h)² + k
From the graph:
Here the vertex = (- 1, 4)
y = a(x + 1)² + 4
Plug x = 0, and y = 5 to find the value of a
5 = a(0 + 1)² + 4
a = 1
y = (x + 1)² + 4
f(x) = x² + 2x + 5
Thus, the quadratic function to model the graph to the right is f(x) = x² + 2x + 5.
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If 3 apples and 1 orange costs $5 and I apple and I
orange costs $3. how much does each apple and orange cost?
Equation 1:
Equation 2:
Solution:
Answer:
Step-by-step explanation:
Equation 1: 3a + 1o =5 3(1) + 1(2) = 5
Equation 2: 1a + 1o =3 2(1) + 1(2) = 3
Solution: apples are $1.00 each and oranges are $2.00 each
The taxi ride costs 18.00 (mop). Now convert this to US Dollars. Here's the convertion fact: 1 US Dollar=7.98 MOP.
18.00 MOP equals to 2.26 US Dollars.
Step-by-step explanation:
Cost of taxi ride = 18.00 MOP
It is given that;
1 US Dollar = 7.98 MOP
It can also be written as,
7.98 MOP = 1 US Dollar
Therefore,
1 MOP = [tex]\frac{1}{7.98}\ US\ Dollars[/tex]
Now,
18.00 MOP = [tex]\frac{1}{7.98}*18.00\ US\ Dollars[/tex]
[tex]18.00\ MOP=\frac{18.00}{7.98}\ US\ Dollars\\18.00\ MOP= 2.26\ US\ Dollars[/tex]
18.00 MOP equals to 2.26 US Dollars.
Keywords: conversion, division
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Which set of rational numbers is arranged from least to greatest? 1 over 5, −1.4, negative 1 over 2, 3 3, negative 1 over 2, −1.4, 1 over 5 3, 1 over 5, −1.4, negative 1 over 2 −1.4, negative 1 over 2, 1 over 5, 3
Answer:
Option 4 - [tex]-1.4,\ -\frac{1}{2},\ \frac{1}{5},\ 3[/tex]
Step-by-step explanation:
To find : Which set of rational numbers is arranged from least to greatest?
Solution :
The set of rational numbers are
[tex]3,\ \frac{1}{5},\ -1.4,\ -\frac{1}{2}[/tex]
Writing all number in one form,
[tex]\frac{1}{5}=0.2[/tex]
[tex]-\frac{1}{2}=-0.5[/tex]
Now, -1.4<-0.5<0.2<3
From least to greatest the set of natural numbers are
[tex]-1.4<\ -\frac{1}{2}<\frac{1}{5}<\ 3[/tex]
So, [tex]-1.4,\ -\frac{1}{2},\ \frac{1}{5},\ 3[/tex]
Therefore, option 4 is correct.
Answer:
Option 4
Step-by-step explanation:
Domestic bees make their honeycomb by starting with a single hexagonal cell, then forming ring after ring of hexagonal cells around the initial cell, as shown. The number of cells in successive rings forms an arithmetic sequence..
A-Write a rule for the number of cells in the
ring.
b. How many cells are in the honeycomb after the ninth ring is formed?
Answer:
Part B is 271!!!
Step-by-step explanation:
a9=54
S9=9/2(6+54)=270
270+1
=271
By plugging in the ring number, 9, in the equation for the number of
cells in a ring, gives 54.
Response:
A. The rule for the number of cells in the ring is, aₙ = 6 + (n - 1) × 6
B. The number of cells in the ninth ring are 54 cells
How can the number of cells be expressed as an arithmetic sequence?Given;
The type of sequence = Arithmetic sequence
From the possible drawing of the question obtained from a similar question, we have;
Number of cells in the first ring that goes around the first cell = 6
Number of cells that go around the second ring = 12
A. The common difference of the arithmetic sequence = 12 - 6 = 6
We have that the nth term of an arithmetic sequence is; aₙ = a + (n - 1)·d
Taking the first ring as the first term, we have;
a = 6
Which gives;
The rule for the number of cells in the ring is, aₙ = 6 + (n - 1) × 6
Where;
n = The ring number
B. In the ninth ring, we have;
a₉ = 6 + (9 - 1) × 6 = 54
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use the properties of inequalities to isolate the variable W. 600-25w greater than or equal to 200
Answer:
w<=16
Step-by-step explanation:
600-25w>=200
25w>=600-200
25w>=400
w>=400/25
w>=16
w<=16
what is c
5c+16.5=13.5+10
Isolate the variable by dividing each side by factors that don't contain the variable.
Exact Form:
c = 7/5
Decimal Form:
c = 1.4
Mixed Number Form:
c = 1/2/5
Edit: I answered this on Jan 7th, 2021.
At a sale this week, a sofa is being sold for $244.80. This is a 64% Discount from the original price. What is the original price?
Answer:
680$
Step-by-step explanation:
If this is a 64% discount, the price 244.80 is 36% of the original price
244.8 = 36% -Divide by 36 on both sides
6.8 = 1% - Times by a hundred
680 = 100%
The original price is 680$
To find the original price of the sofa given a 64% discount, divide the sale price by the discount percentage and subtract it from 100%.
Explanation:To find the original price, we need to determine what the discount percentage represents in terms of the original price. Since the sale price is 64% of the original price, the discount is 100% - 64% = 36%. Let's represent the original price as x:
36% of x = $ 244.80
To solve this equation, we can convert 36% to the decimal form by dividing it by 100: 36/100 = 0.36. Now we can solve for x:
0.36x = $ 244.80
Dividing both sides of the equation by 0.36, we get:
x = $ 244.80 / 0.36 = $ 680
Therefore, the original price of the sofa was $ 680.
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Which of the following is 4.15 * 106 in standard notation?
A. 41.5000000
B. 415,000
C. 4,150,000
D. 4.15000000
The average amount of money spent by a person who attended a local sporting event in 2000 was $8.00, of which 75% was the ticket price. In 2005, the average amount of money spent by a person who attended a local sporting event increased by 50%, but the ticket price did not increase. By how many dollars did the non-ticket costs of 2000 increase to become the non-ticket costs of 2005?
Answer:
4$
Step-by-step explanation:
in 2000, ticket price is 75% of 8$ that is 6$. in 2005, money spent is increased by 50% of 8$ that is 12$ with same ticket price(6$). so non ticket price is increased from 2$(in 2000) to 6$(in 2005).
Answer:
4
Step-by-step explanation:
6(2005) - 2(2000) = 4
Easier to read then the one above, like its addition
Which of the following expressions is equivalent to the one above? 42x + 21.
Please help ASAP
Answer:
21(2x+1)
Step-by-step explanation:
42x+21=21(2x+1)
1/9(-9x+18)-1/5(10+15x)
Answer:
-4x
Step-by-step explanation:
A square sticky note has sides that are 15 centimeters long. What is the area of the sticky note?
Answer:
The answer is 225 cm
Step-by-step explanation:
15×15=225
Answer:
5 or 3
Step-by-step explanation:
The height of Jake's window is 5x - 3 inches and the width is 3x + 2 inches. What is the perimeter of Jake's window ?
The perimeter of Jake window is 16x - 2 inches
Solution:Given that height of Jake window is 5x - 3 inches
Also given that width is 3x + 2 inches
To find: perimeter of Jake window
We know that, in general a window is of rectangular shape
The perimeter of rectangle is given as:
Perimeter of rectangle = 2(length + width)
Substituting the values we get,
Perimeter of rectangle = 2(5x - 3 + 3x + 2)
Perimeter of rectangle = 2(8x - 1) = 16x - 2
Hence, the perimeter of the window is 16x – 2 inches
Evaluate each expression for g = -7 and h = 3 and match it to its value.
1. -4 g + h
2. 10 g - h
3. -10 h - g
4. -21 gh
5. 2 g + h2
6. 46 g2 - h
So you got to match the ones on the left to the right
The given expressions are solved and matched
Solution:To match the given expressions we need to solve the expressions with the given values of g and h and find their value.
Given that g = -7 and h = 3
[tex]\begin{array}{l}{\text { 1) } g+h=-7+3=-4} \\\\ {\text { 2) } g-h=-7-3=-10} \\\\ {\text { 3) } h-g=3+7=10} \\\\ {\text { 4) } g h=-7 \times 3=-21} \\\\ {\text { 5) } g+h^{2}=-7+3^{2}=-7+9=2} \\\\ {\text { 6) } g^{2}-h=(-7)^{2}-3=49-3=46}\end{array}[/tex]
The expressions are evaluated by substituting g = -7 and h = 3 into each one. After calculation, the matching values are found for each expression.
Explanation:To evaluate each expression for g = -7 and h = 3, we'll substitute these values into the equations and perform the operations step by step.
-4g + h : -4(-7) + 3 = 28 + 3 = 3110g - h : 10(-7) - 3 = -70 - 3 = -73-10h - g : -10(3) - (-7) = -30 + 7 = -23-21gh : -21(-7)(3) = -21 * 21 = -4412g + h^2 : 2(-7) + 3^2 = -14 + 9 = -546g^2 - h : 46(-7)^2 - 3 = 46 * 49 - 3 = 2254 - 3 = 2251Then, you can match each expression to its corresponding value that has been calculated:
Expression 1 matches with 31Expression 2 matches with -73Expression 3 matches with -23Expression 4 matches with -441Expression 5 matches with -5Expression 6 matches with 2251And exercise 17th pause grapes cost 2.35 per pound oranges cause 0.99 per pound and apples cost 1.65 per pound. Running to the nearest whole number about how much did Adrian pay for all the fruit
Answer:
Adrian needs to pay $5 for all the fruit.
Step-by-step explanation:
Consider the provided information.
Grapes cost $2.35 per pound, oranges cost $0.99 per pound, and apples cost $1.65 per pound.
In order to find how much Adrian needs to pay we need to add $2.35, $0.99 and $1.65.
[tex]\$2.35 + \$0.99 + \$1.65=\$4.99[/tex]
Now round $4.99 to the nearest whole number.
[tex]\$4.99\approx\$5[/tex]
Hence, Adrian needs to pay $5 for all the fruit.
The graph shows the height,h, in inches, of a plant after d days. The plant had a height of 4 inches after 6 days. Which equation can you use to represent the situation?
Answer:
2/3d=h
Step-by-step explanation:
2/3 is the amount it grows (in inches)
d represtenst the days
h represents height
2/3*6 = 4
Answer: 2/3
Step-by-step explanation: 2/3 is the amount it grows (in inches)
D= THE DAYS
H= THE HEIGHT
So... 2/3x6= 4
= 2/3
7 mm = _____ cm
0.7
7,000
700
70
Answer:
0.7
Step-by-step explanation:
7 millimiters equals 0.7 centimeters
Answer:
0.7 cm
Step-by-step explanation:
1 mm=0.1 cm
7 mm=0.1*7=0.7 cm
Kelsey is writing a thank-you note to a friend. She has 9 kinds of cards and 7 kinds of envelopes that fit the cards. She has 3 designs of first-class stamps, although she only needs to use one. Finally, Kelsey has to pick a color of pen with which to write the note, and she has 2 to choose from. How many different ways can the thank-you note look?
Answer:
378
Step-by-step explanation:
Work 1:She has 9 kinds of cards out of which she has to chose only 1.
The number of ways of doing this is 9 (she can pick any one of them).
Work 2:She has 7 kinds of cards out of which she has to chose only 1.
The number of ways of doing this is 7 (she can pick any one of them).
Work 3:She has 3 designs of first-class stamps out of which she has to chose only 1.
The number of ways of doing this is 3 (she can pick any one of them).
Work 4:She has to pick the color of pen and she has 2 to choose from.
The number of ways of doing this is 2 (she can choose any one of them).
She has to do Work 1 and Work 2 and Work 3 and Work 4.
∴By the fundamental counting principle, the total number of different ways in which the thank-you note can look is 9×7×3×2 = 378
3.78 divided by 0.9
The division of 3.78 by 0.9 equals 4.2 after rounding to the nearest tenth. The given problem is an arithmetic division question typically encountered in mathematics. The keyword 3.78 is the number being divided by 0.9.
Explanation:The division question posed: 3.78 divided by 0.9, is a simple arithmetic problem. To solve, we will perform the division calculation directly. First, we divide 3.78 (the dividend) by 0.9 (the divisor). This yields a quotient of approximately 4.2. Thus, 3.78 divided by 0.9 equals 4.2 when rounded to the nearest tenth. This division problem would be typically encountered in arithmetic, a branch of mathematics that deals with numbers and numerical computation.
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2x+4=8 what would the equation be and what does x equal
Answer:
x=2
Step-by-step explanation:
2x+4=8
2x=8-4
2x=4
x=4/2
x=2
Answer:
x = 2
Step-by-step explanation:
The equation shown is a perfectly good equation.
___
Look at what is being done to the variable. It is multiplied by 2, and 4 is added to the product.
To find the value of the variable, we reverse these operations, in reverse order. We undo the addition by adding the opposite of 4 (to both sides of the equation).
2x +4 -4 = 8 -4
2x = 4 . . . . . simplify
We undo the multiplication by multiplying by the inverse value, 1/2 (to both sides of the equation).
(1/2)(2x) = (1/2)(4)
x = 2 . . . . . simplify
_____
The rules of equations are pretty simple: whatever you do to one side, you must also do to the other side.
_____
Comment on this equation
You may notice that all of the numbers in this equation are divisible by 2. Another way to solve it is to start by dividing (both sides!) by 2:
x + 2 = 4
Now, you have a 2nd-grade problem in addition facts: what added to 2 gives 4? Since you know your addition facts, you know the answer is 2. In algebra, we solve this by subtracting 2 (from both sides!).
x = 2
The formula for converting Celsius temperatures to Fahrenheit temperatures is a linear equation. Water freezes at 0°C, or 32°F and it boils at 100°C, or 212°F. Find the slope and y-intercept for a graph that gives degrees Celsius on the horizontal axis and degrees Fahrenheit on the vertical axis. Then write an equation in slope-intercept form that converts degrees Celsius into degrees Fahrenheit
Answer:
1.8=100x+b
Step-by-step explanation:
The formula y = mx + b sometimes appears with
different symbols.
For example, instead of x, we could use the
letter C. Instead of y, we could use the letter F.
Then the equation becomes
F = mC + b.
All temperature scales are related by linear
equations. For example, the temperature in
degrees Fahrenheit is a linear function of degrees Celsius.
Water freezes at: 0°C, 32°F
Water Boils at: 100°C, 212°F
Antony and Lily started moving in opposite directions from the same point at the same time. If Antony was biking with average 12 mph speed and Lily was walking by 4 mph, how soon the distance between them will be 76 miles?
4 hours and 45 minutes
The number of miles increasing each hour is 16, 16 times 4 is 64, and to get to 76, you add an extra 3/4 of an hour, which is 45 minutes.
The distance between Antony and Lily will be 76 miles after 4.75 hours.
What is Speed?Speed is the unit rate in terms of distance travelled by an object and the time taken to travel the distance.
Speed is a scalar quantity as it only has magnitude and no direction.
Given that,
Antony and Lily started moving in opposite directions from the same point at the same time.
Speed of Antony = 12 mph
Speed of Lily = 4 mph
Let x be the distance traveled by Antony.
Then the distance traveled by Lily = 76 - x
Time will be the same, let it be t.
t = x /12 and t = (76 - x) / 4
x/12 = (76 - x) / 4
4x = 12 (76 - x)
4x + 12x = 912
16x = 912
x = 57
t = 57/12 = 4.75 hours
Hence the time is 4.75 hours.
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Given that ABCD is a rhombus, what is the value of x?
(3x + 12
Answer:
19.5
is the correct answer
Answer:
The answer is 19.5
Step-by-step explanation
Have an amazing day :)
The school that Stefan goes to is selling tickets to a choral performance. On the first day of ticket sales the school sold 3 senior citizen and 1 child ticket for a total of $38. The school took in $52 on the second day by selling 3 senior tickets and 2 child tickets. Find the price of a senior citizen ticket and the price of a child ticket.
The price of senior citizen ticket is $8 and that of children ticket is $14
Solution:Let the price of ticket for senior citizen be ‘s’ and for child be ‘c’
Given that on the first day of ticket sales the school sold 3 senior citizen and 1 child ticket for a total of $38
So, an equation can formed which is as follows:
3s + c = 38 ---- eqn 1
On the Second day of ticket sales the school sold 3 senior citizen and 2 child ticket for a total of $52
3s + 2c = 52 ---- eqn 2
Multiply eqn 1 by 2
6s + 2c = 76 ---- eqn 3
Now subtract eqn 2 from eqn 2
6s + 2c = 76
(-) 3s + 2c = 52
---------------------
3s = 24
s = 8
Plug in s = 8 in eqn 2,
24 + 2c = 52
2c = 28
c = 14
Hence, the price of senior citizen ticket is $8 and that of children ticket is $14
In triangle abc , side BC is 3 inches long and side AB is 16 inches long. Angle A measures 20 °. Given that angle C is an obtuse angle, find the measure of angle C. Round to the nearest tenth of a degree
Answer:
Angle C is 101 degrees
Step-by-step explanation:
Given triangle ABC,
Side BC =3
Side AB =16
Angle A=20
Also, Angle C is an obtuse angle.
To find Angle C:
As shown in figure,
By using basic trigonometry,
Angle A =20 and AB=13
BD =13sin20 and AD = 13cos20
Now, AD=AC+CD
CD=13cos20-3
CD=2.30506
And BD =13sin20=11.86828
In triangle BDC,
Tan(BCD) = [tex]\frac{BD}{CD}[/tex]
Tan(BCD) = [tex]\frac{11.86828}{2.30506}[/tex]
Tan(BCD) = [tex]\frac{11.86828}{2.30506}[/tex]=5.1487
Angle BCD = 79.00
Therefore, Angle BCA =180-Angle BCD=180-79=101.
Angle C is 101 degrees
The measure of angle C in triangle ABC is approximately 150.8° when rounded to the nearest tenth of a degree.
To find the measure of angle C, we can use the fact that the sum of the angles in any triangle is 180°. Given that angle A is 20° and angle C is obtuse, we can set up the following equation:
[tex]\[ \angle A + \angle B + \angle C = 180 \][/tex]
Since angle A is 20°, we can substitute this value into the equation:
[tex]\[ 20 + \angle B + \angle C = 180 \][/tex]
To find the measure of angle B, we can use the Law of Sines, which states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all three sides of the triangle:
[tex]\[ \frac{a}{\sin(\angle A)} = \frac{b}{\sin(\angle B)} = \frac{c}{\sin(\angle C)} \][/tex]
We can use the sides AB and BC to find angle B:
[tex]\[ \frac{16}{\sin(20)} = \frac{3}{\sin(\angle B)} \][/tex]
Solving for[tex]\(\sin(\angle B)\)[/tex]:
[tex]\[ \sin(\angle B) = \frac{3}{16} \cdot \sin(20) \][/tex]
Now, we calculate the value of [tex]\(\sin(\angle B)\)[/tex]:
[tex]\[ \sin(\angle B) = \frac{3}{16} \cdot \sin(20) \approx \frac{3}{16} \cdot 0.3420 \approx 0.0649 \][/tex]
Taking the inverse sine [tex](sine) of \(\sin(\angle B)\)[/tex] gives us the measure of angle B :
[tex]\[ \angle B = \sin(0.0649) \approx 3.7 \][/tex]
Now we have the measures of angles A and B, so we can find angle C :
[tex]\[ 20 + 3.7 + \angle C = 180 \] \\[/tex]
[tex]\[ \angle C = 180 - 20 - 3.7\] \\[/tex]
[tex]\[ \angle C = 180 - 23.7 \] \\[/tex]
[tex]\[ \angle C = 156.3 \][/tex]
Since angle C is obtuse, we do not need to consider any other solutions for angle B that might be less than 90°. Therefore, the measure of angle C is approximately 156.3°, which rounds to the nearest tenth of a degree as 150.8°.
Which of these is the net of a cube?
Answer:
B
Step-by-step explanation:
A triangular courtyard has a perimeter of 120 meters. The lengths of two sides are 30 meters and 50 meters. How long is the third side?
Answer:
the third side is 40 m long
Step-by-step explanation:
The perimeter of the triangle is the sum of its three sides, and they give you what that value in meters is (120 m)
Your are given the length of two of them: 30 m and 50 m, and need to find the third one (let's call it "x" for this unknown side)
Now set the following equation:
Perimeter = side 1 + side 2 + side 3 --> replace these with the info you know
120 m = 30 m + 50 m + x --> add 30 m and 50 m obtaining 80 m
120 m = 80 m + x --> now solve for x (isolate the x on one side) by subtracting 80 m from both sides
120 m - 80 m = x --> perform the subtraction 120 m - 80 m = 40 m
40 m = x
Which tells us that the third unknown side has a length of 40 m
Answer:
The third side is 40 meters long
Step-by-step explanation:
From the question, we were told that a triangular courtyard has a perimeter of 120 meters, we are to find the length of the third side if the other two sides are 30 and 50 meters.
First, we need to know that perimeter is the distance around a polygon.
Let the third side = side c, let the two sides be side A and side B
Perimeter = side A + side B + side c
side A = 30 meters
side B = 50 meters
side C = ?
Perimeter = 120 meters
We can now proceed to insert the values in the equation above
Perimeter = side A + side B + side c
120 = 30 + 50 + side c
120 = 80 + side c
Subtract 80 from both-side of the equation
120 - 80 = 80 - 80 + side c
40 = side c
side c = 40 meters
Therefore, the third side is 40 meters long
2. Which of the following (a,b) pairs is
ollowing (a,b) pairs is the solution
the system of equations 2a + b = 3 and
a - 3b = 5?
F. (-2, 7)
G. (0, 3)
J. (2,-1)
K. (3,-3)
The pair (2, -1) is the solution the system of equations.
The given system equations are 2a+b = 3 and a - 3b = 5.
What is a linear system of equations?A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.
Here,
2a+b = 3 --------(1) and a - 3b = 5 --------(2)
Multiply equation (1) by 3
6a+3b=9 --------(3)
Add equation (2) and (3), we get
a - 3b+6a+3b = 5+9
⇒ 7a = 14
⇒ a = 2
Put a=2 in the equation (1), that is
2(2)+b=3
⇒ b=-1
Therefore, the pair (2, -1) is the solution the system of equations.
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Final answer:
The correct pair (a,b) that solves the given system of equations 2a + b = 3 and a - 3b = 5 is (2, -1), which is option J.
Explanation:
To find which pair (a,b) is the solution to the system of equations 2a + b = 3 and a - 3b = 5, we can use substitution or elimination. Here's a step-by-step explanation using the elimination method:
Multiply the second equation by 2 to align the coefficients of a: 2(a - 3b) = 2(5) gives us 2a - 6b = 10.Add this new equation to the first equation: (2a + b) + (2a - 6b) = 3 + 10, simplifying to 4a - 5b = 13.Now we solve this new equation for a: a = (13 + 5b) / 4.Substitute this expression for a in one of the original equations: 2((13 + 5b) / 4) + b = 3.Simplify and solve for b: (13 + 5b)/2 + b = 3, which gives b = -1.Now that we have b, we can find a: 2a - 1 = 3 which gives a = 2.Therefore, the correct solution to the system of equations is (2, -1), which corresponds to option J.
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