Answer:
Step-by-step explanation:
So the first step is to simply set up the problem based on what we are given. So here have two numbers, we are going to call the first number x and the second one y. With that now addressed, we can now proceed with the setup.
So the difference between the squares of the numbers is 24. So we have:
[tex]x^{2} -y^{2} = 24[/tex]
Then it says that three times the square of the first number (which we said was x) increased by the square of the second number is 76. So:
[tex]3x^{2} + y^{2} = 76[/tex]
Now we can see that this is simply a system of equations and we can use elimination to solve this! We even have the setup already as the coefficients in front of our y are opposite in sign and are equal. So:
[tex]x^{2} -y^{2} = 24\\3x^{2} +y^{2} = 76[/tex]
We can cancel our y squared terms out and that leaves, when we add the equations together:
[tex]4x^{2} = 100[/tex]
We can then solve for x by diving by four and taking the square root of the result.
[tex]x^{2} = 25\\[/tex]
Therefore, x = ±5
We have both negative and positive answers because if we squared -5 or +5 they would both give us 25. So we cant rule a negative answer out yet.
So now we can plug in x = -5 or +5 to either equation to solve for y as so:
[tex]5^{2} - y^{2} = 24\\25 - y^{2} = 24\\-y^{2} = -1 \\y^{2} = 1[/tex]
So y = ±1
In this case both negative and positive versions of our answer work (you can also double check), so we are left with:
x = ±5 and y = ±1
We can solve the problem by expressing one variable through another from one equation and substituting it into the second equation. Then solve for the first variable and substitute the found value in one of the equations to find the corresponding other variable.
Explanation:The subject of this question is algebra, specifically equations involving squares of numbers and systems of equations. Let's denote the unknown numbers as 'x' and 'y'. From the problem, we know two equations:
x² - y² = 24 3x² + y² = 76
One possible approach to finding the values of x and y would be to use the substitution method. From equation (1), we can express y² as x² - 24 and substitute this into equation (2):
3x² + (x² - 24) = 76
If we simplify and solve for x, we find that x = 4, -4.
Then, substituting 'x' into the first equation will yield corresponding 'y' values. That's how you can solve this kind of problems by using squares of numbers and method of substitution.
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Look at the system of equations below.
4x-5y=3
3x+5y=13
A student makes this argument: Elimination is the best method for solving this system because the y-coefficient in the first equation is the opposite of the y-coefficient in the second equation.
Complete the student’s argument by explaining why substitution and graphing are less efficient methods than elimination for this system.
Answer:
Substitution and graphing are less efficient methods than elimination for this system as there is extra amount of steps we have to take to solve the same system of equations - hence time consuming and a margin or error may happen. Therefore, elimination is the suitable method for solving this system.
Step-by-step explanation:
Let us consider the system of equation below.
[tex]4x-5y=3[/tex]
[tex]3x+5y=13[/tex]
Elimination method sounds the most appropriate option to solve the given system of equations as we can easily sort out an equation in one variable x in minimal steps by just adding the both equations as the y-coefficient in the first equation is the opposite of the y-coefficient in the second equation, and we can determine an equation in one variable x.
Adding both equations will eliminate the y-variable and we can easily sort out the value of x from the resulting equation.
As the given system of equation
[tex]4x-5y=3[/tex][tex]......[1][/tex]
[tex]3x+5y=13[/tex][tex]......[2][/tex]
Adding Equation 1 and Equation 2
[tex]4x-5y+3x+5y=3+13[/tex]
[tex]7x=16[/tex]
[tex]x=[/tex][tex]\frac{16}{7}[/tex]
Putting [tex]x=[/tex][tex]\frac{16}{7}[/tex] in Equation [1]
[tex]4x-5y=3[/tex][tex]......[1][/tex]
[tex]y=[/tex][tex]\frac{43}{35}[/tex]
Although substitution or graphing methods can also be used to bring the solution of the given system of equations, but using substitution or graphing method can be sometimes cumbersome or time-consuming as it would have to take some additional steps to solve the system.
For example, if we would have to use the substitution methods to solve the given system of equations, first we would have to solve one of the equations by choosing one of the equation for one of the chosen variables and then putting this back into the other equation, and solve for the other, and then back-solving for the first variable.
As the given system of equation
[tex]4x-5y=3[/tex][tex]......[1][/tex]
[tex]3x+5y=13[/tex][tex]......[2][/tex]
Solving the equation 2 for x variable
[tex]3x=13-5y[/tex]
[tex]x=\frac{13-5y}{3}[/tex]
Plugging [tex]x=\frac{13-5y}{3}[/tex] in equation [1]
[tex]4(\frac{13-5y}{3}) -5y=3[/tex]
[tex]y = \frac{43}{35}[/tex]
Putting [tex]y = \frac{43}{35}[/tex] in Equation 2
[tex]3x+5y=13[/tex][tex]......[2][/tex]
[tex]x = \frac{16}{7}[/tex]
So, you can figure out, we have to make additional steps when we use substitution method to solve this system of equations.
Similarly, using graphing method, it would take a certain time before we identify the solution of the system.
Hence, from all the discussion and analysis we did, we can safely say that substitution and graphing are less efficient methods than elimination for this system as there is extra amount of steps we have to take to solve the same system of equations - hence time consuming and a margin or error may happen.
Therefore, we agree with the student argument that Elimination is the best method for solving this system because the y-coefficient in the first equation is the opposite of the y-coefficient in the second equation.
Keywords: substitution method, system of equations, elimination method
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The substitution and graphing methods are less efficient methods than elimination method for this system as there is extra amount of steps we have to take to solve the same system of equations 4x-5y=3 , 3x+5y=13
We have equations
4x-5y=3 ... (1)
3x+5y=13 ...(2)
Solving by substitution methodSubstituting the value of 5y = 13-3x from equation (2) into equation(1)
4x-(13-3x)=3
4x-13+3x=3
7x= 3+13
7x= 16
x = [tex]\frac{16}{7}[/tex]
Substitute the value of x = [tex]\frac{16}{7}[/tex] in y value, we get
[tex]5y=13-3(\frac{16}{7} )\\y=\frac{43}{35}[/tex]
By graphing methods it can take a lot of time as first we have to make the table for both the equations and then need a graph to plot the values.By elimination method :4x-5y=3
3x+5y=13
Adding both the equations, we get
[tex]7x=16\\x=\frac{16}{7}[/tex]
Put the value of x in any one of the above equation, we get
[tex]3\frac{16}{7} +5y=13\\y=\frac{43}{35}[/tex]
So, the Elimination method is the best method for solving this system because the y-coefficient in the first equation is the opposite of the y-coefficient in the second equation and it is less time consuming.
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Please answer the 3 questions above and SHOW YOUR WORK!
If you reply me with something like “amdblwdbkw” or “I don’t know the answer” I’m going to report account.
Question # 1 Solution:
As the expression [tex]13v + 8f +6b+3m[/tex] represents her cost, in dollars for the arrangements when she buys
v vases, f stems of flowers, b stems of wood bark, and m packages of marbles for the bottom of the vasesWhich statement is true?
A.The term 13v represents the cost of 13 vases.
B.The coefficient 6 represents the cost of b stems of wood bark.
C.The term 8f represents the cost of f stems of flowers at $8 per stem.
D.The coefficient 3 represents the number of packages of marbles she buys.
Choosing the correct statement:
As the formula for cost of any item can be calculated by multiplying the cost of one item with the total number of items.
So, if f represents the stems of flowers, and the cost of f stems of flowers at $8 per stem. Then according to the formula for cost of any item, the statement C is true i.e. "The term 8f represents the cost of f stems of flowers at $8 per stem" is the correct statement.
Question # 2 Solution
As the inequality is given as:
12x + 9x - 3 ≤ 3(2x + 14)
and we have to find the value of x.
So,
12x + 9x - 3 ≤ 3(2x + 14)
Step 1: Simplify both sides of the inequality
21x - 3 ≤ 6x + 42
Step 2: Subtract 6x from both sides.
21x - 3 - 6x ≤ 6x + 42 - 6x
15x - 3 ≤ 42
Step 3: Add 3 to both sides.
15x - 3 + 3 ≤ 42 + 3
15x ≤ 45
Step 4: Divide both sides by 5
15x/5 ≤ 45/5
3x ≤ 9
x ≤ 9/3
So, x ≤ 9/3 is the right answer. Please note that x ≤ 9/3 can also be written as x ≤ 3.
Hence, option A i.e. x ≤ 9/3 is correct. The solution graph is also attached in figure a.
Question # 3 Solution
As we have to find the correct statements from the given graph that represents John's weight (in pounds) as a function of time t, measured in days since January 1, 2017.
So, here are the correct statements that validate the graph:
The statement 'The independent variable is t, the number of days since January 1, 2017' is correct as t represents the independent variable because John's weight (in pounds) being the function of time t depends on the time t. Hence, time t is independent variable. The statement 'f(t) = 160 means that John weighed 160 lbs. on day 12, 120, and 172 after January 1, 2017' is correct because the output value i.e. f(t) of graph is showing John's weight weighed 160 lbs. i.e. f(t)=160 on the input values of day 12, 120, and 172 i.e. t = 12,120 and 172 after January 1, 2017. The statement 'f(0) = 140 means that John weighed 140 lbs. on January 1, 2017' is correct because the output value i.e f(0) of graph is showing John's weight weighed 140 lbs. i.e. f(0)=140 right on the day January 1, 2017 because t = 0 on January 1, 2017. And the value of t increases after January 1, 2017. The statement 'f(40) = 180 means that John gained 40 lbs. since January 1, 2017' is correct because on t = 40, the graph reaches to 180 i.e. the output value i.e. f(40) = 180 on t = 40. As on January 1, 2017, John was already weighed 140 i.e. f(0) = 140 on t = 0. So, f(40) = 180 means that John gained 40 lbs. since January 1, 2017.The statement 'f(200) - f(160) = 30 means that John gained 30 lbs. from day 160 after January 1, 2017 to day 200' is correct because the difference of f(200) and f(160) is 30 lbs. So, it specifies that on days' intervals from 160 to 200, the constitute gain of John's weight was 30 lbs.The statement 'The most appropriate domain for this function is all integers' is incorrect because when we talk about all integers it means it must have consisted negative integers too. But, as we cannot have negative time or days, and his weight also cannot be negative. So, to say that 'The most appropriate domain for this function is all integers' is not correct.
Keywords: inequality, equation, graph, rate of change, function
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7/8÷2/8 equal gfffghgddth
Answer:
3.5
Step-by-step explanation:
You missed a monthly payment on your mortgage. Your monthly payment is $1,278. Your mortgage holder places a 5%
penalty on all late monthly payments. What is your total penalty cost?
Answer: $63.90
Step by Step explanation:
$1,278 + 5% = 63.90
Find the slope of the line that passes through the following points. (6 points, 2 points each)
A (10,4) and B(-2,-5)
C(-7.1) and D(7,8)
E(1, 1) and F/2.3)
Answer:
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(-5-4)/(-2-10)
m=-9/-12
m=9/12
m=3/4
------------------------
m=(y2-y1)/(x2-x1)
m=(8-1)/(7-(-7))
m=7/(7+7)
m=7/14
m=1/2
-------------------------
m=(y2-y1)/(x2-x1)
m=(3-1)/(2-1)
m=2/1
m=2
Final answer:
The slope of a line between two points is found using the formula slope (m) = (y2 - y1) / (x2 - x1), with an example given for points A (10,4) and B (-2,-5), resulting in a slope of 3/4.
Explanation:
The slope of a line passing through two points (A and B) can be determined using the formula slope
(m) = (y2 - y1) / (x2 - x1).
This formula calculates the rate of change in the y-values with respect to the x-values, resulting in a description of the steepness of the line.
For example, let's find the slope for points A (10,4) and B (-2,-5). Applying the formula, we have:
m = (y2 - y1) / (x2 - x1) = (-5 - 4) / (-2 - 10) = (-9) / (-12) = 3/4
The slope between points A and B is 3/4. This process can be repeated for other pairs of points to find the respective slopes.
The ages of three siblings combined is 27. The oldest is twice the age of the youngest. The middle child is 3 years older than the youngest. Write and solve an equation to find the ages of each sibling
Answer:
Youngest Age = 6
Middle Age = 9
Oldest Age = 12
Step-by-step explanation:
Let youngest age be x
Middle one age be y
Oldest age be z
So,
x < y < z
Now lets come up with the equations using the statements.
Three age combined is 27, so we can write:
x + y + z = 27
Oldest is TWICE youngest, so we can write:
z = 2x
Middle is 3 YEARS OLDER than youngest, so we can write:
y = x + 3
Now we replace first equation with 2nd and 3rd, to get:
x + y + z = 27
x + x + 3 + 2x = 27
We can solve this for x:
x + x + 3 + 2x = 27
4x + 3 = 27
4x = 24
x = 24/4
x = 6
Now finding y:
y = x + 3
y = 6 + 3
y = 9
Now finding z:
z = 2x
z = 2(6)
z = 12
Thus,
Youngest Age = 6
Middle Age = 9
Oldest Age = 12
Solve for a.
a-15=4a-3
Answer:-4
Step-by-step explanation:
a-15=4a-3
a-4a=-3+15
-3a=12
a=-4
evaluate
5/6 f for f=4/9
10/27
1 7/8
8/15
Answer:
The answer is 10/27
Step-by-step explanation:
5/6 times 4/9 is equal to 10/27
A discount store normally sells DVDs for $14.44. If the DVDs go on sale for $13.72, which of the following is closest to the percent of decrease in the price?
Answer:
4.9%
Step-by-step explanation:
To find the percentage you first find the decrease in price, divide it by the original price then multiply it by 100.
(14. 44-13. 72)
= -------------------- ×100
14. 44
0. 72
= -------- × 100
14. 44
= 0. 72× 6. 925207759
= 4. 986149584
~ 4. 9
Which graph shows the system of equations 4x+y=3 and 2x-3y=3?
Answer:
The graph in the attached figure
Step-by-step explanation:
we have
[tex]4x+y=3[/tex] ----> Red line
[tex]2x-3y=3[/tex] ---> blue line
Solve the system by graphing
Remember that the solution is the intersection point both graphs
using a graphing tool
The solution is the point (0.857,-0.429)
The graph in the attached figure
What is the value of x in the equation 3/4x+2=5/4x-6
Solving for x...
3/4x+2=5/4x-6
8=2/4x
8=1/2x
x=16
To find the value of x in the given equation, we can eliminate the fractions, combine like terms, and solve for x. The value of x is 16.
Explanation:To find the value of x in the equation 3/4x+2=5/4x-6, we need to isolate x on one side of the equation. We can do this by first getting rid of the fractions. Multiplying each term in the equation by the LCD (Least Common Denominator) of 4 will help us eliminate the fractions. Then, we can combine like terms and solve for x.
Multiplying both sides of the equation by 4, we get: 4(3/4x+2) = 4(5/4x-6), which simplifies to: 3x + 8 = 5x - 24.Next, we can subtract 3x from both sides to isolate the x terms: 3x + 8 - 3x = 5x - 24 - 3x, giving us: 8 = 2x - 24.Then, we can add 24 to both sides of the equation to further isolate x: 8 + 24 = 2x - 24 + 24, which simplifies to: 32 = 2x.
Finally, we can divide both sides by 2 to solve for x: (32/2) = 2x/2, resulting in x = 16.
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Which of the following is a tangent to the circle?
Answer:
Step-by-step explanation:
line l
Find the value of x that makes ABCD a parallelogram.
Answer:
x=70
Step-by-step explanation:
I'm pretty sure the sum of all angles has to be 360°
and 70+70+40+40=220
so 220+x=360
we figure this out by taking 360-220 which equals 140
and then we divide 140 by 2 which is 70.
To double check, if you add 70+70+40+40+70+70, it equals 360.
The value of x from the given parallelogram is 70°. Therefore, option B is the correct answer.
What is parallelogram?A parallelogram is a special kind of quadrilateral that is formed by parallel lines. The angle between the adjacent sides of a parallelogram may vary but the opposite sides need to be parallel for it to be a parallelogram. A quadrilateral will be a parallelogram if its opposite sides are parallel and congruent.
Given that, ABCD is a parallelogram.
Here, ∠A+∠B+∠C+∠D=360°
70°+x+40°+70°+x+40°=360°
220°+2x=360°
2x=360°-220°
2x=140°
x=70°
Therefore, option B is the correct answer.
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If James borrows $4,200 to pay his college tuition. He signs a 5 year simple interest loan. If monthly payments are $78.40, what is the interest rate on the loan?
0.024 /yr
Step-by-step explanation:
Without interest, the monthly repayment would be;
5 yrs = 12 months * 5 = 60 months
$4200 / 60
= $70
James, however, pays $78.40 monthly. The interest therefore is;
Jmaes pays a total of $78 * 60 = $4704 at the end of the 5 years. The formula for finding simple interest is;
A = P(1 + rt)
Where:
A = Total Accrued Amount (principal + interest)
P = Principal Amount
I = Interest Amount
r = Rate of Interest per year in decimal; r = R/100
R = Rate of Interest per year as a percent; R = r * 100
t = Time Period involved in months or years
4704 = 4200 (1 + 5r )
4704 = 4200 + 21000r
504 = 21000r
r = 504/21000
r = 0.024
Interest rate = 0.024 /yr
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The circumference of a circle is 8.97cm.
Find the length of the diameter.
Give your answer rounded to 2 DP
The length of the diameter is 2.86 cm rounded to 2 DP
Step-by-step explanation:
The formula of the circumference of a circle is
C = 2πr, where r is the radius of the circleC = πd, where d is the diameter of the circle∵ The circumference of a circle is 8.97 cm
- We need to find the diameter of the circle, then we will use
the 2nd formula of circumference above
∵ The circumference = πd
- Substitute the value of the circumference in the formula
∴ 8.97 = πd
- Subtract both sides by π
∴ 2.855 = d
- Round it to 2 decimal places (to the nearest hundredth)
∴ d = 2.86 cm
The length of the diameter is 2.86 cm rounded to 2 DP
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English muffins are on sale for $1.99 per package, but only if you buy five packages. This is a $1.00 discount per package. What percent do you save off the regular price when buying the English muffins on sale? Round the answer to the nearest tenth.
Answer:
50.3% of profit.
Step-by-step explanation:
English muffins are on sale for $1.99 per package, but only if you buy five packages.
Therefore, the price of five packages of muffins on sale is $(1.99 × 5) = $9.95.
There is a $1.00 discount per package on sale.
So, the ordinary price per package of muffins is $(1.99 + 1) = $2.99.
Therefore, the ordinary price of five packages of muffins is $(2.99 × 5) = $14.95.
Hence, the percentage of profit that I will make when I purchase the package of muffins in the sale is [tex]\frac{14.95 - 9.95}{9.95} \times 100\% = 50.25\%[/tex] ≈ 50.3 % (Answer)
5x – 4y=8
-x + 2y = -4
1.
2.
44 - by = -6
4x – 4y = -8
-x + 2y = -4
-x = -2y - 4
x = 2y + 4
5(2y + 4) - 4y = 8
10y + 20 - 4y = 8
6y + 20 = 8
6y = -18
y = -3
-x + 2y = -4
-x + 2(-3) = -4
-x - 6 = -4
-x = 2
x = -2
The coordinate pair is (-2, -3) (x = -2, y = -3.)
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the concept and full method
Answer:
Step-by-step explanation:
This kinda looks like the limiting definition of a derivative.
Anyway, what we are doing with the f(2 + h) is evaluating f(x) with 2+h in place for x. That looks like this:
f(2 + h) = 2(2 + h) - 3 which simplifies to
f(2 + h) = 4 + 2h - 3 which simplifies to
2h + 1
From that we are subtracting f(2). What we are doing with that is evaluating f(x) with 2 in place for x. That looks like this:
f(2) = 2(2) - 3 which simplifies to
f(2) = 4 - 3 which simplifies to
f(2) = 1. Now put those together over h to get:
[tex]\frac{f(2+h)-f(2)}{h}=\frac{2h+1-1}{h}=\frac{2h}{h}=2[/tex]
what is
7/4 times 10
Answer: 17.5 hope this helps
the answer is 17.5
:D
consider the linear system of equations Y = 2/5x - 1 and 2x -3y + 1 = 0
Answer:
The solution is the point (-5,-3)
Step-by-step explanation:
The complete question is
Consider the linear system of equations y = 2/5x - 1 and 2x -3y + 1 = 0
The solution of the system of equations is?
we have
[tex]y=\frac{2}{5}x-1[/tex] ----> equation A
[tex]2x-3y+1=0[/tex] ----> equation B
Solve by substitution
substitute the equation A in equation B
[tex]2x-3(\frac{2}{5}x-1)+1=0[/tex]
solve for x
[tex]2x-\frac{6}{5}x+3+1=0[/tex]
[tex]2x-\frac{6}{5}x+4=0[/tex]
Multiply by 5 both sides to remove the fraction
[tex]10x-6x+20=0[/tex]
[tex]4x+20=0[/tex]
subtract 20 both sides
[tex]4x=-20[/tex]
divide by 4 both sides
[tex]x=-5[/tex]
Find the value of y
[tex]y=\frac{2}{5}(-5)-1[/tex]
[tex]y=-3[/tex]
The solution is the point (-5,-3)
The question involves solving a system of linear equations from high school algebra. Substituting Y from the first equation into the second and solving for x, we find that x = -5 and Y = -3.
Explanation:The student is asking about solving a system of linear equations, which is a concept in algebra that falls under high school mathematics. To find the solution to the given linear system, we can use either substitution or elimination methods. Let's use substitution since the first equation has Y isolated.
From the first equation Y = 2/5x - 1, we substitute for Y in the second equation, which gives us 2x - 3(2/5x - 1) + 1 = 0. Simplifying, we get 2x - 6/5x + 3 + 1 = 0, which further simplifies to 4/5x + 4 = 0. Solving for x gives x = -5. Substituting x back into the first equation to find Y yields Y = 2/5(-5) - 1, so Y = -3. Therefore, the solution to the system of equations is x = -5 and Y = -3, which is the point where the two lines intersect.
if the number 9,899,399 is increased by 2,082 the result will be
Answer:
Step-by-step explanation:
9,899,399+2082
=9901481
Final answer:
To find out what 9,899,399 increased by 2,082 is, add the two numbers together, resulting in 9,901,481.
Explanation:
The question asks what the result will be if the number 9,899,399 is increased by 2,082. To find the result, we simply need to add the two numbers together. This type of problem involves basic arithmetic operations and is fundamental in understanding how to manipulate and work with numbers.
To calculate the result:
Start with the original number: 9,899,399.
Add the increase: 2,082.
Perform the addition: 9,899,399 + 2,082 = 9,901,481.
Therefore, when the number 9,899,399 is increased by 2,082, the result is 9,901,481.
Jamie has 1/10 yard of blue felt and 5/6 yard yard of green felt.
Which answer is the most accurate estimate for how much more green felt Jamie has than blue felt?
Answer:
Jamie has 11/15 yards of Green Felt more than Blue Felt
Step-by-step explanation:
Green felt- Blue felt
= 5/6- 1/10
= 25/30- 3/30 ( taking LCM)
= 25 - 3/30
=22/30
=11/15 yards
LCM= 2*3*5= 30
Factors of 6= 2*3
Factors of 10= 2*5
What would be the answer to this? Would it be a rotation of 90 degrees counterclockwise followed by reflection over x- axis???help
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Jessica's hamster cage is shaped like a rectangular prism. The cage has a height of 24 inches and a volume of 6,480 cubic inches. Jessica puts a piece of paper on the bottom of the cage. The paper fits the bottom of the cage perfectly.
What is the area of the paper on the bottom of the cage?
Enter your answer in the box.
in²
Answer:
270
Step-by-step explanation:
I am not sure if i am correct but i think you should divide 6,480 by 24 which is 270
Answer:
270 in2
Step-by-step explanation:
Divide 6480 . by 24
Servey says!?: 270 is the awnser!
Can someone help me with these problems? I'm in k12 and this assignment was in classkick, so if anyone already completed this and can help, please do. I also am going to be asking some more questions, if you can help with those too. Thanks! (Will give brainliest.)
PLEASE HELP ME!
SOLVING QUESTIONS FROM 1ST PAGE
Given the point B(-5, 0)y = -3x - 5
Putting x = -5, and y = 0 in y = -3x - 5
0 = -3(-5) - 5
0 = 15 - 5
0 = 10 ∵Putting B(-5, 0) in y = -3x - 5 does not equate the equation.
As L.H.S ≠ R.H.S
So,
Does this check?
Answer: no ∵ L.H.S ≠ R.H.S
Given the point C(-2, 1)y = -3x - 5
Putting x = -2, and y = 1 in y = -3x - 5
1 = -3(-2) - 5
1 = 6 - 5
1 = 1 ∵Putting C(-2, 1) in y = -3x - 5 rightly equates the equation.
As L.H.S = R.H.S
So,
Does this check?
Answer: yes ∵ L.H.S = R.H.S
Given the point D(-1, -2)y = -3x - 5
Putting x = -1, and y = -2 in y = -3x - 5
-2 = -3(-1) - 5
-2 = 3 - 5
-2 = -2 ∵Putting D(-1, -2) in y = -3x - 5 rightly equates the equation.
As L.H.S = R.H.S
So,
Does this check?
Answer: yes ∵ L.H.S = R.H.S
SOLVING QUESTIONS FROM 2ND PAGE
Given the point B(6, 18)y = -2x + 18
Putting x = 6, and y = 18 in y = -2x + 18
18 = -2(6) + 18
18 = -12 + 18
18 = 6 ∵Putting B(6, 18) in y = -2x + 18 does not equate the equation.
As L.H.S ≠ R.H.S
So,
Does this check?
Answer: no ∵ L.H.S ≠ R.H.S
Given the point C(9, 24)y = 2x + 6
Putting x = 9, and y = 24 in y = 2x + 6
24 = 2(9) + 6
24 = 18 + 6
24 = 24 ∵Putting C(9, 24) in y = 2x + 6 rightly equates the equation.
As L.H.S = R.H.S
So,
Does this check?
Answer: yes ∵ L.H.S = R.H.S
SOLVING QUESTIONS FROM 3RD PAGE
Given the point D(2, 7)y = 3x + 4
Putting x = 2, and y = 7 in y = 3x + 4
7 = 3(2) + 4
7 = 6 + 4
7 = 10 ∵Putting D(2, 7) in y = 3x + 4 does not equate the equation.
As L.H.S ≠ R.H.S
So,
Does this check?
Answer: no ∵ L.H.S ≠ R.H.S
SOLVING QUESTIONS FROM 4th PAGE
b. Which function could have produced the values in the table.
A. y = 3x + 4
B. y = -2x + 18
C. y = 2x + 6
D. y = x + 9
The Table:
x y
3 12
6 18
9 24
Checking A) y = 3x + 4
Putting (3, 12), (6, 18) and (9, 24) in y = 3x + 4
For (3, 12)
y = 3x + 4
12 = 3(3) + 4
12 = 13 ∵ L.H.S ≠ R.H.S
Does this check?
Answer: no ∵ L.H.S ≠ R.H.S
For (6, 18)
18 = 3(6) + 4
18 = 18 + 4
18 = 22 ∵ L.H.S ≠ R.H.S
Does this check?
Answer: no ∵ L.H.S ≠ R.H.S
For (9, 24)
24 = 3(9) + 4
24 = 27 + 4
24 = 31 ∵ L.H.S ≠ R.H.S
Does this check?
Answer: no ∵ L.H.S ≠ R.H.S
So, the equation y = 3x + 4 could have not produced the all values in the table as the the ordered pairs in table do not satisfy(equate) the equation.
Checking B) y = -2x + 18
Putting (3, 12), (6, 18) and (9, 24) in y = -2x + 18
For (3, 12) ⇒ y = -2x + 18 ⇒ 12 = -2(3) + 18 ⇒ 12 = 12 ⇒ L.H.S = R.HSFor (6, 18) ⇒ y = -2x + 18 ⇒ 18 = -2(6) + 18 ⇒ 18 = 6 ⇒ L.H.S ≠ R.HSFor (9, 24) ⇒ y = -2x + 18 ⇒ 24 = -2(9) + 18 ⇒ 18 = 0 ⇒ L.H.S ≠ R.HSSo, y = -2x + 18 could have not produced all the values in the table, as (6, 18) does not equate the equation.
Checking C) y = 2x + 6
Putting (3, 12), (6, 18) and (9, 24) in y = 2x + 6
For (3, 12) ⇒ y = 2x + 6 ⇒ 12 = 2(3) + 6 ⇒ 12 = 12 ⇒ L.H.S = R.HSFor (6, 18) ⇒ y = 2x + 6 ⇒ 18 = 2(6) + 6 ⇒ 18 = 18 ⇒ L.H.S = R.HSFor (9, 24) ⇒ y = 2x + 6 ⇒ 24 = 2(9) + 6 ⇒ 24 = 24 ⇒ L.H.S = R.HSSo, y = 2x + 6 could have produced the values of in the table as all the orders pairs in the table satisfy/equate the equation.
Checking D) y = x + 9
Putting (3, 12), (6, 18) and (9, 24) in y = x + 9
For (3, 12) ⇒ y = x + 9 ⇒ 12 = 3 + 9 ⇒ 12 = 12 ⇒ L.H.S = R.HSFor (6, 18) ⇒ y = x + 9 ⇒ 18 = 6 + 9 ⇒ 18 = 15 ⇒ L.H.S ≠ R.HSFor (9, 24) ⇒ y = x + 9 ⇒ 24 = 9 + 9 ⇒ 24 = 18 ⇒ L.H.S ≠ R.HSSo, y = x + 9 could have also not produced all the values in the table, as (6, 18) and (9, 24) do not satisfy/equate the equation.
So, from all the verification we conclude that:
HENCE, ONLY y = 2x + 6 COULD HAVE PRODUCED THE VALUES IN THE TABLE AS ALL THE ORDERED PAIRS OF THE TABLE SATISFY/EQUATE THE EQUATION.
SOLVING QUESTIONS FROM 5th PAGE
What is the domain and range of the relation?
{(-3, 7), (6, 2), (5, 1), (-9, -6)}
Domain: Domain is the set of all the x-coordinates of the ordered pairs of the relation, meaning the all first elements of the ordered pairs in a relation include in the domain of the relation. Range: Range is the set of all the y-coordinate of the ordered pairs of the relation, meaning the all second elements of the ordered pairs in a relation include in the range of the relation.As the given relation is {(-3, 7), (6, 2), (5, 1), (-9, -6)}
The domain is: {-3, 6, 5, -9}
Note: generally, we write the numbers in ascending order for both the domain and range.
The domain could also be written in order as: {-9, -3, 5, 6}
The range is: {7, 2, 1, -6}
The range could also be written in order as: {-6, 1, 2, 7}
Keywords: equation, point, ordered pair, domain, range
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How do u solve
1×-2y=4
-1×+10y=8
Answer: x = -8 ; y = -6
Step-by-step explanation:
1*x-2*y=4
1*x = 4 + 2*y
x = 4 + 2*y
Now you replace the value of x on the following equation:
-1*x+10*y=8
-1*(4 + 2*y) = 8
-4 - 2*y = 8
-2*y = 8+4
-2*y = 12
y = -12/2
y = -6
You replace the value of y in the previous equation:
x = 4 + 2*y
x = 4 + 2*(-6)
x = 4 - 12
x = -8
write 1/5 as a terminating decimal
Answer: The answer is 0.2
Step-by-step explanation:
1 divided by 5 is 0.2 because 1 goes into 5 0.2 times.
Hope this helps!
What is the line through the points (2,3) and (19,17)
Answer:
y-3=14/17(x-2)
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(17-3)/(19-2)
m=14/17
y-y1=m(x-x1)
y-3=14/17(x-2)
Write the expression that represents the phrase,
"two times the difference of a number and 17."
Use x as the variable.
Answer:
2x + 17
Step-by-step explanation:
Answer:
2(x-17).
Step-by-step explanation:
The given phrase is "two times the difference of a number and 17."
We need to find the expression for given phrase.
Let x be the unknown variable.
Difference is denoted by "-" symbol.
Time is denoted by "×" symbol.
Difference of a number and 17 = x-17
Two times the difference of a number and 17 = 2×(x-17) = 2(x-17)
Therefore, the required expression is 2(x-17).
Simplify completely quantity 12 x plus 36 over quantity x squared minus 4 x minus 21 and find the restrictions on the variable.
a.) 12 over quantity x minus 7, x ≠ 7
b.) 12 over quantity x minus 7, x ≠ 7, x ≠ −3
c.) quantity x plus 3 over quantity x minus 7, x ≠ 7
d.)quantity x plus 3 over quantity x minus 7, x ≠ 7, x ≠ −3
Option B
12 over quantity x minus 7, x ≠ 7, x ≠ −3
Solution:
Given that we have to simplify quantity 12 x plus 36 over quantity x squared minus 4 x minus 21
So we have to simplify,
[tex]\frac{12x + 36}{ {x}^{2} - 4x - 21 }[/tex]
We have to find the restrictions on the variable
The above given Rational function is defined, for
[tex]{x}^{2} - 4x - 21\ne0\\\\(x+3)(x-7)\ne0\\\\x\ne -3,x\ne7[/tex]
In order to simplify the above expression, we need to factor both the numerator and the denominator
[tex]\rightarrow \frac{12x + 36}{ {x}^{2} - 4x - 21 } = \frac{12(x + 3)}{ {x}^{2} - 4x - 21}[/tex]
For the denominator, we need to split the middle term of the quadratic to get factored form,
[tex]\rightarrow \frac{12x + 36}{ {x}^{2} - 4x - 21 } = \frac{12(x + 3)}{ {x}^{2} - 7x + 3x- 21}[/tex]
[tex]\frac{12x + 36}{ {x}^{2} - 4x - 21 } = \frac{12(x + 3)}{ x(x - 7) + 3(x- 7)}[/tex]
Fcatoring the denominator part,
[tex]\frac{12x + 36}{ {x}^{2} - 4x - 21 } = \frac{12(x + 3)}{ (x + 3)(x - 7)}[/tex]
Cancel out common factors to get,
[tex]\frac{12x + 36}{ {x}^{2} - 4x - 21 } = \frac{12}{x - 7} \\\\where\\\\x\ne -3,x\ne7[/tex]
Thus option B is correct. 12 over quantity x minus 7, x ≠ 7, x ≠ −3
The simplified expression is 12 / (x - 7) with restrictions x ≠ 7, x ≠ -3. The correct answer is option b.) 12 over quantity x minus 7, x ≠ 7, x ≠ −3.
The expression((12x + 36) / (x² - 4x - 21)) and finding the restrictions on the variable.
First, we factor both the numerator and the denominator.
The numerator can be factored as 12(x + 3).
The denominator can be factored by finding two numbers that multiply to -21 and add to -4, which are -7 and 3.
Thus, the denominator factors to (x - 7)(x + 3). Our expression then simplifies to (12 / (x - 7)), after cancelling out the (x + 3) terms.
To find the restrictions on the variable, we note that the original denominator, (x² - 4x - 21), cannot be zero, as division by zero is undefined.
Setting (x - 7)(x + 3) to zero gives us the restrictions x ≠ 7 and x ≠ -3, to ensure the denominator is not zero.
Therefore, the simplified expression is 12 / (x - 7), with the restrictions x ≠ 7, x ≠ -3.