What is x, y and z? show your work
x - y + 9z = -27
2x - 4y - z = -1
3x + 6y - 3z = 27
Answers
Answer: z = -3 , y = 2 , x = 2
The solution to the system of equations is: x - y + 9z = -27 , 2x - 4y - z = -1 , 3x + 6y - 3z = 27 is
x = 2
y = 2
z = -3
Given the system of equations:
1. x - y + 9z = -27
2. 2x - 4y - z = -1
3. 3x + 6y - 3z = 27
We'll use the method of elimination to solve this system.
Step 1: Eliminate y from equations (1) and (2):
Adding equations (1) and (2):
(x - y + 9z) + (2x - 4y - z) = -27 + (-1)
x + 2x - y - 4y + 9z - z = -27 - 1
3x - 5y + 8z = -28
Step 2: Eliminate y from equations (2) and (3):
Multiplying equation (2) by (3) and equation (3) by (2):
6x - 12y - 3z = -3 (from equation 2)
6x + 12y - 6z = 54 (from equation 3, after multiplying by 2)
Adding these two equations:
(6x - 12y - 3z) + (6x + 12y - 6z) = -3 + 54
6x + 6x - 12y + 12y - 3z - 6z = 51
12x - 9z = 51
Now, we have two equations:
1. 3x - 5y + 8z = -28
2. 12x - 9z = 51
From equation (2), let's solve for (x):
12x - 9z = 51
12x = 51 + 9z
x = (51 + 9z) ÷ 12
Now, we'll substitute this expression for (x) into equation (1) to solve for (z):
3x - 5y + 8z = -28
[tex]\[ 3\left(\frac{51 + 9z}{12}\right) - 5y + 8z = -28 \][/tex]
[tex]\[ \frac{153 + 27z}{12} - 5y + 8z = -28 \][/tex]
Next, we'll isolate (z):
153 + 27z - 60y + 96z = -336
249z - 60y = -489
Now, let's solve for (z):
249z = -489 + 60y
z = (-489 + 60y) ÷ 249
Now, we'll substitute the expression for (z) back into equation (2) to solve for (y):
[tex]\[ 12x - 9\left(\frac{-489 + 60y}{249}\right) = 51 \][/tex]
[tex]\[ 12x - \frac{-489 + 60y}{27} = 51 \][/tex]
[tex]\[ 12x = 51 + \frac{-489 + 60y}{27} \][/tex]
[tex]\[ x = \frac{51 + \frac{-489 + 60y}{27}}{12} \][/tex]
[tex]\[ x = \frac{51\times27 + -489 + 60y}{12\times27} \][/tex]
[tex]\[ x = \frac{1377 - 489 + 60y}{324} \][/tex]
[tex]\[ x = \frac{888 + 60y}{324} \][/tex]
[tex]\[ x = \frac{148 + 10y}{54} \][/tex]
Now, we'll substitute the expressions for (x) and (z) into equation (1) to solve for (y):
x - y + 9z = -27
[tex]\[ \frac{148 + 10y}{54} - y + 9\left(\frac{-489 + 60y}{249}\right) = -27 \][/tex]
The least common multiple of (54) and (249) is (54 × 249).
⇒ (148 + 10y) × 249 - 54 × 249 × y + 9 × 54 × (-489 + 60y) = -27 × 54 × 249
⇒ 36752 + 2490y - 133146y - 233640 + 29160y = -1458 × 249
⇒ 2490y - 133146y + 29160y + 36752 - 233640 = -1458 × 249
⇒ -106496y - 197888 = -362682
⇒ -106496y = -164794
⇒ y = (-164794) ÷ (-106496)
y ≈ 1.547
y ≈ 2
Now that we have found (y = 2), we can substitute this value back into the expressions for (x) and (z) to find their values.
For (x):
[tex]\[ x = \frac{148 + 10(2)}{54} = \frac{168}{54} = 2 \][/tex]
For (z):
[tex]\[ z = \frac{-489 + 60(2)}{249} = \frac{-369}{249} = -\frac{3}{1} = -3 \][/tex]
So, the solution to the system of equations is:
x = 2
y = 2
z = -3
Related Questions
LOOK AT THE PICTURE I NEED THIS DONE ASAP PLEASE HELP ME!!!
Answers
I got 224. 7(4)^2 = 112 •2 =224
can someone help me please ? :(
Answers
Answer:
last one
Step-by-step explanation:
Answer:
The second graph.
Step-by-step explanation:
The graph is the only possible answer. In the table, both values are shown to be rising, the second graph is the only one with both increasing values.
In the first one, only D is rising
In the third, only C is increasing
In the last, d is decreasing while C is increasing.
Which only leaves the second option.
what is the mass in slugs of a body weighing 500 ib?
Answers
W=500lb
m=?
W=mg(m=W÷g)
500=m×10
500÷10=m
50=m
In the English Engineering system, the unit slug is used to measure mass. The mass of an object in slugs can be calculated by dividing its weight in pounds (lb) by the acceleration due to gravity (32.2 [tex]ft/s^2[/tex]). Therefore, a body weighing 500 lb would have a mass of about 15.53 slugs.
Explanation:In physics, the unit slug is used in the English Engineering system where force is expressed in pounds (lb). The relationship between slug and lb is tied to the acceleration due to gravity on Earth which is approximately 32.2 [tex]ft/s^2[/tex]. To convert the weight of an object in lb to its mass in slugs you divide the weight by the acceleration due to gravity.
Thus, if an object weighs 500 lb, its mass in slugs can be found by dividing 500 lb by 32.2 [tex]ft/s^2[/tex]. So, the equation is:
Mass = 500 lb / 32.2 [tex]ft/s^2[/tex] = 15.53 slugs
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Please explain your answer as well. THX!!
Answers
Answer: Third option
[tex]P = 0.354[/tex]
Step-by-step explanation:
We have an elevator with 5 men and 7 women. We want to find the probability that 3 women and one man will come down from the elevator.
To calculate this probability we can use combinations.
The formula of combinations is:
[tex]nCr = \frac{n!}{r!(n-r)!}[/tex]
Where you can choose between n people and choose r from them.
First we calculate all the possible results of the experiment.
That is, the amount of ways to select 4 people from a group of 12 people.
[tex]12C4 = \frac{12!}{4!(12-4)!} = 495[/tex]
There are 495 results.
Now we calculate the possible number of ways to obtain the desired result, that is 3 women and one man.
The possible combinations of selecting 3 women from a group of 7 is.
[tex]7C3 = \frac{7!}{3!(7-3)!} = 35[/tex].
The possible combinations of selecting 1 a man from a group of 5 is
[tex]5C1 = \frac{5!}{1!(5-1)!} = 5[/tex]
Then the number of ways in which 3 women and one man can be obtained is:
[tex]7C3 * 5C1 = 35 * 5 = 175[/tex]
Finally the probability is:
P = Number of ways to obtain the desired result ÷ possible number of results
[tex]P = \frac{7C3 * 5C1}{12C4}\\\\P = \frac{175}{495}[/tex]
[tex]P = 0.354[/tex]
How much interest is earned on $2,700 in one year if it is invested at 3%?
$8.10
$81.00
$810.00
Answers
Answer:
The correct option is b $81.00
Step-by-step explanation:
Interest earned can be found simply by multiplying the interest rate into the principal amount.
Our Interest rate is = 3%
and principal amount = $2,700
Interest earned = $2700 * 3/100
Interest earned =$ 81
So, the correct option is b $81.00.
Answer:
$ 81.00.
Step-by-step explanation:
What is the area of parallelogram ABCD
Answers
Answer:
B
Step-by-step explanation:
The area (A) of a parallelogram is calculated using the formula
A = base × perpendicular height
base = DC = 4 and height = DB = 5, thus
A = 4 × 5 = 20 units² → B
The area of the parallelogram is 20 square units.
What is a parallelogram?A basic quadrilateral with two sets of parallel sides is known as a parallelogram.
In a parallelogram, the opposing or confronting sides are of equal length, and the opposing angles are of equal size.
The area of a parallelogram is base multiples by height as two triangles form a parallelogram.
We know, The area of a parallelogram is 2×(1/2)×base×height, As a parallelogram can be divided into two congruent triangles.
From the given information, If we draw an altitude to it will of 5 units and the base of the parallelogram is 4 units.
Therefore, The area of the parallelogram is, (5×4) = 20 square units.
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P(A1) = 0.60, P(A2) = 0.40, P(B | A1) = 0.05, and P(B | A2) = 0.10. Use Bayes’ theorem to determine P(A1 | B).
Answers
The result follows from manipulating the conditional probability. By definition,
[tex]P(A_1\mid B)=\dfrac{P(A_1\cap B)}{P(B)}=\dfrac{P(B\mid A_1)P(A_1)}{P(B)}[/tex]
[tex]P(A_1\mid B)=\dfrac{0.05\cdot0.60}{P(B)}[/tex]
By the law of total probability,
[tex]P(B)=P(B\cap A_1)+P(B\cap A_2)=P(B\mid A_1)P(A_1)+P(B\mid A_2)P(A_2)[/tex]
So we have
[tex]P(A_1\mid B)=\dfrac{0.05\cdot0.60}{0.05\cdot0.60+0.10\cdot0.40}\approx0.4286[/tex]
the probability P(A1 | B) is approximately 0.42857
Bayes’ theorem formula is:
[tex]P(A1 | B) = \frac{[P(B | A1) \times P(A1)]}{P(B)}[/tex]
We first need to calculate P(B):
[tex]P(B) = P(B | A1) \times P(A1) + P(B | A2) \times P(A2)[/tex]
Substitute the given values:
[tex]P(B) = 0.05 \times 0.60 + 0.10 \times 0.40\\\\P(B) = 0.03 + 0.04\\\\P(B) = 0.07[/tex]
Next we use Bayes' theorem to find P(A1 | B):
[tex]P(A1 | B) = \frac{[0.05 \times 0.60]}{0.07}\\\\P(A1 | B) = \frac{0.03}{0.07}\\\\P(A1 | B) \approx 0.42857[/tex]
Therefore, the probability P(A1 | B) is approximately 0.42857.
which linear equation approximates the best fit to the data?
A) y=-2x+65
B)y=-5x+100
C)y=-x+68
D) y=-0.5x+55
Answers
Answer:
I believe A
Hope This Helps! Have A Nice Day!!
Answer:
A.
Step-by-step explanation:
In my opinion the best one is A cause it just fits the best if you draw the line.
hope this halps :D
In a group of students, 18 read marketing, 19 read economics, 16read finance, 6 read marketing only, 9 read economics only, 5 read marketing and economics only, and 2 read economic and finance only... find out
1) how many read all three subjects?
2) how many read finance only?
3) how many read marketing and finance only?
4) how many students are there altogether?
Answer:1)3
2)7
3)4
4)36
Answers
Final answer:
1. The number of students reading all three subjects is 3.
2. Those reading finance only is 7.
3. Those who read marketing and finance only is 4.
4. In total, there are 36 students.
Explanation:
To solve this Venn diagram problem involving students reading different subjects, let's take a methodical approach.
First, we know that 6 students read only marketing, and 9 read only economics.5 read both marketing and economics but not finance. This is found by subtracting those who read both from the total only marketing and economics readers.Next, 2 read economics and finance, but not marketing.The number of students that read all three subjects is found by taking the intersection of all three subjects and subtracting the sum of the intersections of two, which is given as 18 (for marketing) + 19 (for economics) + 16 (for finance) - 6 (marketing only) - 9 (economics only) - 2 (economics and finance only) - 5 (marketing and economics only), subtracting the students counted twice. The total number of students reading only one subject is 17 (6 marketing only + 9 economics only + 2 finance only).For the students reading all three, we have the total number of students minus the number of students reading only one or two subjects giving us 3 students reading all three.Those who read finance only can be calculated by taking the total number of finance readers (16) and subtracting those who read finance with other subjects (5 marketing and economics, 2 economics and finance, 3 all subjects), which gives us 16 - 3 - 2 - 5 = 7.The number of students who read marketing and finance only is found by subtracting those who read all three (3) from those who read both marketing and finance (8), this is, 8 (from finance total) - 3 (all subjects) - 1 (finance and economics only) = 4.To find out how many students there are altogether, we sum all the distinct category readers including those who read all three subjects once. This gives us 6 (marketing only) + 9 (economics only) + 2 (finance only) + 5 (marketing and economics) + 2 (economics and finance) + 4 (marketing and finance) + 3 (all three subjects) = 31. However, since there are 36 students, we conclude that there are 5 more students who do not fit into our calculated categories.Help me please?????????????
Answers
Please give brainliest!
Answer: The answer to the first one is 99m. The answer to the second one is 62cm.
Step-by-step explanation: You would multiply 63 by 2 to get 126. You would subtract 126 from 324 to get 198. Then you would divide 198 by 2 which would equal 99 which is your answer.
You would divide 5828 by 94 to get 62 wich would be your answer.
Hope this helps!
Have a blessed day :)
5(2c - 3) = 3(3c - 5)
Answers
The answer to this equation would be:
C=0
Answer:c=0
Step-by-step explanation:
The following equation is a proportion.10\18=25\45 = TrueFalse please help asap
Answers
Answer:
true
Step-by-step explanation:
What type of angle is
Answers
Answer:
I'm really sorry I can't tell you the answer because you have to measure the angle by yourself using a protractor. But I gave you information about types of angles if you got the degree of angles ( e.g 90 degrees). Hope it helped.
Step-by-step explanation:
acute angle-an angle between 0 and 90 degrees
right angle-an 90 degree angle
obtuse angle-an angle between 90 and 180 degrees
straight angle-a 180 degree angle
For this case we have that by definition:
Sharp angle: It is less than 90 degrees.
Flat angle: Measures 180 degrees.
Obtuse angle: Measures more than 90 degrees
The figure shows a pair of angles, each measuring 77 degrees. Now they enter the definition of acute angles.
To find the angle CEB we subtract:
[tex]180-77 = 103[/tex] degrees
This is the same measure of angle AED.
These would be obtuse angles.
Answer:
Sharp angles (77 degrees)
Obtuse angles (103 degrees)
200 cocoa beans make 1 lb. chocolate. How many cocoa beans are needs to make 3 pounds of chocolate
Answers
Answer:
600
Step-by-step explanation:
200*3=600
Answer:
600 cocoa beans
Step-by-step explanation:
1×3=3, 200×3= 600
what is the answer to -5+9>44
Answers
Simplify -5 + 9 to 4
4 > 44
Since 4 > 44 is false, there is no solution.
= No solution
what is the measure of angle c
Answers
Answer:
Angle C=35 degrees
Step-by-step explanation:
Angle C is an external angle. So, we can use the external angle theorem and get the equation
Angle C= 1/2(100-30)
Angle C=1/2(70)
Angle C=35 degrees
Answer:
35
Step-by-step explanation:
<C = 1/2 (large arc - small arc)
<C = 1/2 (100-30)
=1/2(70)
= 35
Match each injury with a long-term consequence.
Spinal cord injury
Headaches
B. Traumatic brain injury
Quadriplegia
C. Knee injury
Limited ability to walk and run
Answers
Answer:
I think
"Quadriplegia" would go with a "spinal cord injury".
Quadriplegia is a spinal cord injury that causes you to lose feelings in all four limbs.
A "knee injury" would go with "Limited ability to walk and run."
"Headaches" with "traumatic brain injury."
Hope this helps!
Answer:
Quadriplegia-Spinal cord injury
Headaches-Traumatic brain injury
Limited ability to walk and run-Knee injury
Step-by-step explanation:
Quadriplegia is the state in which a person can´t move any of its extremities, this is often cause by an accident to the spinal cord and it causes the nerves that connect the brain and the muscles in the bosy to stop functioning properly.
Headaches can be the consequence of a traumatic brain injury that didn´t healed well.
A knee injury often has as result the limited ability to walk and run.
plz help
Bernie's Bikes rents bicycles for $10 plus $4 per hour. You have $26 to spend. Write an equation that will give you eh number of hours that you could rent the bike and solve your equation algebraically.
Answers
Answer:
10+4x=26
Step-by-step explanation:
Answer:
Step-by-step explanation:
26-10 ÷ 4 = X
∨
16 ÷ 4 = X
x= 4
you can only rent the bike for 4 hours.
your down payment is $10 so you subtract it form the money you have now you are left with $16 dollars you divide it by four becuase 4 x 4 is 16 there for you know you can only go for 4 hours
What is the value of x?
A.34
B.56
C.68
D.79
Answers
Answer:
A complementary angle is two angles whose sum add up to 90°
Step-by-step explanation:
To find x you have to add both angles.
x + 22° + x° = 90°
(x + x) + 22 = 90
Combine like terms.
2x + 22 = 90
Subtract 22 from both sides
2x = 68
Divide both sides by 2
x = 34
The value of x is 34°
Reducing the fraction to the lowest terms
Answers
Which one? The fractions to the right?
Hannah rode her bike 1 hour and 15 minutes until she got a flat tire at 2:30 P.M.What time did hannah start riding her bike
Answers
Answer:1:15 P.M
Step-by-step explanation:just substract it 230-115 and you get your time
If she rode for 1.5 hours and caught a flat @ 2:30 pm she had to have started at 1:15
for the graphed exponential equation calculate the average rate of change from x=-4 to x=1
-1/3
-5/8
-4/5
-7/8
Answers
Answer:
- [tex]\frac{4}{5}[/tex]
Step-by-step explanation:
The average rate of change of f(x) in the closed interval [ a, b ] is
[tex]\frac{f(b)-f(a)}{b-a}[/tex]
here [ a, b ] = [ - 4, 1 ]
f(b) = f(1) = - 4 ← value from graph
f(a) = f(- 4) = 0 ← value from graph
Hence
average rate of change = [tex]\frac{-4-0}{1-(-4)}[/tex] = - [tex]\frac{4}{5}[/tex]
The average rate of change of a function is -4/5 from x=-4 to x=1 function is decreasing.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have a graph of a function shown in the picture.
f(-4) = 0
f(1) = -4
Average rate of change of a function = (-4-0)/(1-(-4))
= -4/5
Thus, the average rate of change of a function is -4/5 from x=-4 to x=1 function is decreasing.
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Which expression can be used to find the area of triangle RTS?
Answers
answer is 13 but I can't understand the question
I think there is no correct answer in this question!
you can solve this by analytic geometry rules easily!!
what’s the explicit formula for the sequence 27, 18, 12, 8
Answers
Answer:
a(n) = 27*(2/3)^(n - 1)
Step-by-step explanation:
The first four terms are 27, 18, 12, 8.
Find the common ratio:
To do this, let that ratio = r, and write and solve 27r = 18. Thus, r = 2/3.
The general explicit formula for this sequence is
a(n) = a(1)*(2/3)^(n - 1), or, since a(1) = 27, a(n) = 27*(2/3)^(n - 1)
Answer:
The sequence is A(n) = 27*(1.5)^(n-1)
Step-by-step explanation:
First, we need to see which type of sequence we have:
Differences:
27 - 18 = 9
18 - 12 = 6
the differences are different, let's try with the ratios.
27/18 = 1.5
18/12 = 1.5
12/8 = 1.5
So we have that this ratio is constant, then the sequence can be:
A(n) = 27*(1.5)^(n-1)
For n an integger number
where:
A(0) = 27*1.5^0 = 27
A(1) = 27*1.5^1 = 18
A(2) = 27*1.5^2 = 12
A(3) = 27*1.5^3 = 8
lisa says that 43 is a 2 digit odd number that is composite. Is she correct.
Answers
No, even though 43 is a 2 digit odd number it’s not a composite.
[tex]\text{Hey there!}[/tex]
[tex]\text{Odd numbers are basically numbers that isn't evenly divided by 2}[/tex]
[tex]\text{Even numbers counts by 2 because you could find half of those numbers, you}[/tex] [tex]\text{can't find half of 43 which means that it is an odd number}[/tex]
[tex]\text{Yes, 43 is a(n) odd number but it is not a composite number}[/tex]
[tex]\boxed{\boxed{\text{Thus, Lisa is incorrect}}}\checkmark[/tex]
[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{LoveYourselfFirst:)}[/tex]
A can of tomatoes has a 4 in. diameter and is 4.5 in. high. What is the area of the paper label that goes around the can
A) 14.1 in2
B) 28.2 in2
C) 56.5 in2
D) 81.6 in2
Answers
Answer:
56.5
Step-by-step explanation:
The length of the paper around the can is equal the circumference of the base.
Circumference = πd
Circumference = 3.14 * 4
Circumference = 12.56
And since the height is 4.5 (which is also the width of the paper if you unwrap it), Multiply the circumference by 4.5.
12.56 * 4.5
= 56.52
Jane needs $20 to buy her radio. She has saved $15. What percent of the cost of radio has she saved?
Answers
Answer:
75%
Step-by-step explanation:
Because if 10 is half and 5 is half of 10 its 75%
Jane has saved 75% of the radio cost
Percentage can be described as a fraction out of an amount that is usually expressed as a number out of hundred. Percentage is a measure of frequency.
The radio Jane wants to purchase costs $20 but she has saved only $15. The fraction of the amount Jane has saved to the total cost of the radio is [tex]\frac{15}{20}[/tex]. This fraction would have to multiplied by 100 to convert it to a percentage.
Percentage of the radio cost she has saved = (amount Jane has saved / cost of the radio) x 100
[tex]\frac{15}{20}[/tex] x 100 = 75%
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Match each exponential function to the description of its percent rate of change. 22% growth 12% decay 2% decay 20% growth 20% decay 22% decay 2% growth 12% growth. f(x) = 44(0.88)^x, f(x) = 124(1.22)^x, f(x) = 22(0.8)^x, f(x) = 42(1.12)^x
Answers
The exponential function is defined as y = a(1+r)^x, where "a" represents the original account and "r" the rate of growth or decay.
Then we have the following:
1) 22% grow
y = a( 1 + 22%/100 )^x = a(1.22)^x
So the solution is: 124(1.22)^x
2) 12% decay
y = a( 1 - 12%/100 )^x = a(0.88)^x
So the solution is: y = f(x) = 44(0.88)^x
3) 20% decay
y = a( 1 - 20%/100 )^x = a(0.8)^x
So the solution is: f(x) = 22(0.8)
4) 12% Groth
y = a( 1 + 12%/100 )^x = a(1.12)^x
So the solution is: f(x) = 42(1.12)^x
Final answer:
Each exponential function is matched to its percent rate of change by the base of the exponent; a base greater than 1 indicates growth, while a base less than 1 indicates decay.
Explanation:
The question involves matching each exponential function to its corresponding percent rate of change, which indicates whether there is exponential growth or decay. The base of the exponent in the function represents the rate of change: a base greater than 1 indicates growth, while a base less than 1 indicates decay. Here's how we match the given functions:
f(x) = 44[tex](0.88)^x[/tex] corresponds to 12% decay because 0.88 represents a decay rate of 12%.
f(x) = 124[tex](1.22)^x[/tex] corresponds to 22% growth because 1.22 represents a growth rate of 22%.
f(x) = 22[tex](0.8)^x[/tex] corresponds to 20% decay because 0.8 represents a decay rate of 20%.
f(x) = 42[tex](1.12)^x[/tex] corresponds to 12% growth because 1.12 represents a growth rate of 12%.
By recognizing the base of the exponential function, we can determine the percentage rate of change and appropriately classify each function as either exponential growth or decay.
25 points
Select all that apply.
The bar graph below represents the following table, but the graph has at least one mistake. Choose the statements that describe what is wrong with the graph.
There is a missing label.
The labels are switched.
The "sunny" bar is the wrong length.
The "partly cloudy" bar is the wrong length.
The "cloudy" bar is the wrong length.
The key is missing.
Answers
Answer:
1.The labels are switched.
2.The "partly cloudy" bar is the wrong length.
3.The "cloudy" bar is the wrong length
Step-by-step explanation:
In the bar graph, the labels are switched.The lable for the horizontal axis should read -----number of days------ and the label for the vertaical axis should read----type of weather----
The scale of the bar graph is good, where a unit distance in the x-axis represent a single day.However, the length for party cloudy is indicated as 7 instead of 8. This is wrong length. Similar mistake is observed in the length for cloudy which is indicated as 6 in the graph instead of 5 as shown in the table.
Answer:
1.The labels are switched.
2.The "partly cloudy" bar is the wrong length.
3.The "cloudy" bar is the wrong length
Step-by-step explanation:
The graph of the equation x – 2y = 5 has an x-intercept of 5 and a slope of1/2 . Which shows the graph of this equation?
Answers
This is the graph of x-2y=5 start by writing it into y=mx+b format then plug in numbers for x then graph!