In linear equation the solution set of the equations x = 1/2, y = -3.
What in mathematics is a linear equation?
A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."Multiply both sides of the equation by a
coefficient - 2(4x - 3y ) = 11 × 2
3 ( 10x + 2y ) = ( - 1 ) × 3
apply multiplicative distribution law
8x - 6y = 11 × 2
3( 10x + 2y ) = (-1) × 3
calculate the first terms
8x - 6y = 22
3( 10x + 2y ) = ( -1) × 3
remove the parentheses
8x - 6y = 22
30x + 6y = -3
add up the two equation
8x - 6y + ( 30x + 6y ) = 22 + ( -3)
remove parentheses - 8x - 6y + 30x + 6y = 22 -3
cancel the unknown variables - 8x + 30x = 22 -3
combine like terms - 38x = 22 - 3
calculate the sum or difference - 38x = 19
reduce the greatest common factor on both
sides of equation - 2x = 1
divide both sides of the equation by the coefficient of variable - x = 1/2
substitute one unknown quantity into the elimination 8 * 1/2 - 6y = 22
reduce the expression to the lowest term 4-6y = 22
reduce the greatest common factor on both sides of the equation
2 - 3y = 11
Rearrange unknown terms to the left side of the equation - 2 - 3y = 11
calculate the sum or difference -3y = 9
reduce the greatest common factor on both sides of the equation -y = 3
divide both sides of the equation by the coefficient of variable y = -3
the solution set of the equations
x = 1/2
y = -3
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Find an equation of the sphere determined by the given information. passes through the point (8, 3, -3), center (5, 6, 5)
The equation of the sphere is
[tex]x^{2} +y^{2}+z^{2}+-10x-12y-10z+4=0[/tex]
The standard form of the equation of the sphere is :
[tex](x-a)^{2}+(y-b)^{2}+(z-c^{2} )=r^{2}[/tex]
Where A (a, b , c) is the center and r is the radius.
From the question we should first find the radius
r = [tex]\sqrt{(x-a)^{2}+(y-b)^{2}+(z-c)^{2}[/tex]
Point = (x , y , z) = (8 , 3 , -3)
Center = (a, b , c)= (5 , 6 ,5)
Substituting it in the formula
r = [tex]\sqrt{(8-5)^{2}+(3-6)^{2}+(-3-5)^{2} }[/tex]
By further calculation
r = [tex]\sqrt{9+9+64}[/tex]
So, we get
r =[tex]\sqrt{82}[/tex]
Substituting it in the standard form
[tex](x-5)^{2}+(y-6)^{2}+(z-5)^{2}=\sqrt{82}^{2}[/tex]
[tex](x-5)^{2} +(y-6)^{2} +(z-5)^{2}=82[/tex]
[tex]x^{2} +y^{2}+z^{2}+25+36+25-10x-12y-10z=82[/tex]
[tex]x^{2} +y^{2}+z^{2}+-10x-12y-10z+86-82=0[/tex]
[tex]x^{2} +y^{2}+z^{2}+-10x-12y-10z+4=0[/tex]
Therefore, the equation of the sphere is
[tex]x^{2} +y^{2}+z^{2}+-10x-12y-10z+4=0[/tex]
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Why is the standard deviation of the distribution of means generally smaller than the standard deviation of the population of individuals?
The standard deviation of the distribution of means is generally smaller than the standard deviation of the population of individuals.
What is the standard deviation?The standard deviation mathematical and statistical analysis tool used to explain the diversity of treatments or values around the Mean is the standard deviation, which is also known as the square root of variance.
The population of individuals is always smaller than the entire population, therefore the possibilities for variances will be lower with the sample than with the population. The higher the population, the greater the chances for deviation from the mean.
Therefore, the standard deviation of the distribution of means is generally smaller than the standard deviation of the population of individuals.
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An inflationary gap occurs when the as curve and the ad curve intersect ________ of the potential gdp line.
An inflationary gap occurs when the SRAS curve and the AD curve intersect Right of the potential GDP line.
The SRAS curve:With the help of the short-run aggregate supply curve (SRAS), we can understand how each firm in an economy reacts to price stickiness. The SRAS curve will slope upward when prices are volatile. The SRAS curve illustrates that higher price levels lead to increased output.
AD curve:The demand for and supply of every good and service an economy produces are the main topics of discussion. As a result, the demand for all distinct goods and services is also combined and is known as aggregate demand.
What transpires throughout an inflationary gap?The price level of goods and services would then rise (naturally or as a result of government intervention) to compensate for the increased demand as well as an insufficient supply when an inflationary gap occurs. This price increase is known as demand-pull inflation.
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By paying $1500 cash and the balance is equal monthly payments, how many months would it take to pay for a car costing $12,495?
The monthly installments need to be paid is $10995.
To determine the number of months needed to pay off the remaining balance. We need to know the monthly installment.
What is installments?When you get an installment loan, you get the money you borrowed or the item you bought right away.
You pay it off in installments, which are regularly scheduled payments that may include interest. For a set number of months, or years, you generally owe the same amount on every installment. When the loan is fully repaid, the account is permanently closed.Now, as per the question;
Amount paid in cash = $1500
Remaining balance which is to be paid as monthly installments
= $12495 - $1500
=$12495 − $1500
=$10995
Thus, the monthly installments are $10995.
Now, to determine the number of months needed to pay off the remaining balance. The monthly installment is need to be known.
As a result, information on monthly installments is lacking.
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The complete question is-
What necessary piece of information is missing that prevents solving the problem? By paying $1500 cash and the balance in equal monthly payments, how many months would it take to pay for a car costing$12,495?
Check the photo and please don’t take long I need it asap
1. a bank offers a cd that pays a simple interest rate of 7.5%. how much money in dollars must you put in this cd in dollars now in order to have $5,000 in 3 years?
The money in dollars that must be put in this cd in order to have $5,000 in 3 years is $4,081.63
The formula for simple interest and procedure we will use to solve this exercise is:
A = P {1 + [(R/100) * T]}
Where:
P = principalR = rate of interest in % per annumT = timeA = amountInformation about the problem:
P = ?R = 7.5%T = 3 yearsA = $5,000Applying the simple interest formula and isolating the principal (P), we get:
A = P {1 + [(R/100) * T]}
$5,000 = P {1+[(7.5/100) * 3]}
$5,000 = P [1+(0.075*3)]
$5,000 = P (1+0.225)
$5,000 = P (1.225)
P = $5,000/ 1.225
P = $4,081.63
What is simple interest?It is the operation in which we calculate the profit produced by a capital loaned at a given percentage.
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how is solving |ax| + b = c different from solving |ax+b| = c?
Step-by-step explanation:
they are different because the first equation only ax is in absolute but in the second equation both ax and b are in absolute, so we could solve them differently.
Identify the domain and range of
the relation.
domain:
range :
Answer: domain is x and range is y
Step-by-step explanation:
Answer:
Domain: {2, 8, 30, 46}
Range: {-1, 9, 16}
Step-by-step explanation:
The domain of a function y = f(x) is the set of all values that the input values (x) that the function can accept. The range of a function is the set of all output values that the function can produce from the domain values ie the set of all values
Looking at the figure, the set of all x values that the function y can take are
{2, 8, 30, 46} and this is the domain
The output values produced from this domain are {-1, 9, 16} and that is the range
A fraction is equivalent to 2/3. The product of its numerator and denominator is 216. What is the fraction?
Does the figure below appear to have line symmetry if so how many lines of symmetry
Answer:
2
Step-by-step explanation:
You can only cut it into 2 exact equal parts <3
Answer:
It has none.
Step-by-step explanation:
If it was down the middle it wouldn’t work and if it was across it also wouldn’t work.
Find the measure of each marked angle. Assume the lines are parallel.
x+4=
9x-34=
The angles are 19; 101
What are parallel lines?Parallel lines are lines in a plane that are always the same distance apart. Parallel lines never intersect.
Given:
x+4, 9x-34
As, the lines are parallel
x+4 + 9x -34 = 180
10x + 30 = 180
10x = 150
x= 150/10
x=15
Hence, the angles are x+4 = 19; 9x-34 = 135 - 34 = 101
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Can you please help me with this ?
Answer:
the answer is 2^x-7 = 1/3x+-1/3
graph it to 1-3 and negative 1-3 figure it out i don't really good at explaining
solve the simultaneous equation
-4x+3y=1
6x-y=2
Answer:
x = 1/2, y = 1
Step-by-step explanation:
Let's change the equation,
→ 6x - y = 2
→ y = 6x - 2
Then the value of x will be,
→ -4x + 3y = 1
→ -4x + 3(6x - 2) = 1
→ -4x + 18x - 6 = 1
→ 14x = 1 + 6
→ x = 7/14
→ [ x = 1/2 ]
Hence, the value of x is 1/2 (or) 0.5.
Now the value of y will be,
→ y = 6x - 2
→ y = 6(1/2) - 2
→ y = 3 - 2
→ [ y = 1 ]
Hence, the value of y is 1.
Answer:
x = ¹/₂
y = 1
Step-by-step explanation:
Given system of equations:
[tex]\begin{cases}-4x+3y=1\\\:\:\:\:\:\:6x-y=2 \end{cases}[/tex]
Multiply the second equation by 3:
[tex]\implies 3 \cdot 6x-3 \cdot y = 3 \cdot 2[/tex]
[tex]\implies 18x-3y=6[/tex]
Add this to the first equation to eliminate the term in y:
[tex]\begin{array}{lrr}&-4x+3y & = 1\\+ & 18x-3y& = 6\\\cline{2-3} & 14x \phantom{-3x)} & = 7\end{array}[/tex]
Solve for x:
[tex]\begin{aligned}\implies 14x & = 7\\\\\dfrac{14x}{14} & = \dfrac{7}{14}\\\\\implies x & = \dfrac{1}{2}\end{aligned}[/tex]
Substitute the found value of x into the first equation and solve for y:
[tex]\begin{aligned}-4x+3y & =1\\x=\dfrac{1}{2}\implies -4\left(\dfrac{1}{2}\right)+3y & =1\\-\dfrac{4}{2}+3y & =1\\-2+3y & =1\\-2+3y+2 & =1+2\\ 3y & =3\\\dfrac{3y}{3} & =\dfrac{3}{3}\\\implies y & =1\end{aligned}[/tex]
Therefore, the solution to the given system of equations is:
x = ¹/₂ and y = 1
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Find the measure of the missing angles.
b=
93°
C=
C
b
O
*HURRY help i’m taking a test*
mario will purchase 2 rare coins each month at a cost of $50 each. how much money will mario have spent on his coin collection after 2 years if he purchases an additional 3 coins at the end of the 2 years?
a. $1200
b. $2550
c. $2400
d. $1750
c. $1250
Answer:
it should be b.
Step-by-step explanation:
2 rare coins will make them $100 each month. There are 12 months in a year.
12 × 2 = 24 months
so $100 × 24 months will give us 2400.
Then Mario purchases 3 coins making it cost $150 ($50 + $50 + $50)
2400 + 150 = 2550
Brainliest plss :,)
Vaca books has a net profit margin of 5.1 percent, a total asset turnover of 1.84, and a return on equity of 16.2 percent. what is the debt-equity ratio?
The debt-equity ratio is 0.726 : 1 or 72.64%
What is the Debt?Debt is the product of debt ratio and total equity
Debt = debt ratio × total equity
We have been given that
Asset turnover = 1.84
Profit margin = 5.1%
Return on equity of 16.2 percent
Let we have to assume that sales are $100.
Therefore net Income = 100×0.051 = 5.1
Total Assets = 100/0.84
Total Assets = 54.35
⇒ 0.162 = 5.1 / Total equity
⇒ Total Equity = 5.1 / 0.162
⇒ Total Equity = 31.48
Total assets = Total debt + Total equity
⇒ 54.35 = Total debt + 31.48
⇒ Total debt = 54.35 - 31.48
⇒ Total debt = 22.87
The debt-equity ratio = 22.87 / 31.48
The debt-equity ratio = 0.72649 : 1 or 72.649%
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What is the answer to this math problem and how do I do it? 2/5 +9 =15
The value of x from the given linear function is 15
Solving linear functionA linear function is a function hat has a leading degree of 1
Given the equation below;
2/5x +9 =15
Subtract 9 from both sides
2/5x + 9 - 9 = 15 - 9
2/5x = 15 - 9
2/5x = 6
Multiply both sides by 5
2/5x (5) = 6(5)
2x = 30
x = 15
Hence the value of x from the given linear function is 15
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Shreya took 1/2 of a cake and shweta took 1/4 of the cake. What portion of the cake is left
Step-by-step explanation:
1/2 + 1/4
2/4 + 1/4= 3/4
1 - 3/4 = 1/4 is left
Answer:
There is 1/4 left
Step-by-step explanation:
Find the amount of cake left.
The entire cake is 1
1-1/2 - 1/4
Get a common denominator of 4
1 *4/4 = 4/4
1/2 *2/2 = 2/4
Using the common denominator
4/4 - 2/4 - 1/4
2/4 - 1/4
1/4
There is 1/4 left
From midnight to 7:00 am, the temperature rose 1.1 C each hour. If the temperature at 7:00 am was -0.3 C, what was the temperature at midnight?
The temperature at midnight is -8°C.
How to calculate the temperature?Let the initial temperature be x.
It should be noted that there are 7 hours between midnight and 7am.
Therefore, the equation will be:
x + (1.1 × 7) = -0.3
x + 7.7 = - 0.3
x = -0.3 - 7.7
x = -8
The temperature at midnight is -8°C.
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need help with #3, and #4 please
The equation of the line from the given points marked on the graph is:
3. 3x+y+5=0
4. 3x+y+3=0
Given,
3.The points are:
(-1,-2) and (1,-8)
let the points be :
(-1,-2) = (x₁,y₁)
and (1,-8) = (x₂,y₂)
The equation of the line passing through the points (-1,-2) and (1,-8)
x - x₁/x₂-x₁ = y - y₁/y₂-y₁
For the given points, the equation is:
x-(-1)/1-(-1) = y-(-2)/-8-(-2)
x+1/2 = y+2/-6
-6(x+1) = 2(y+2)
-6x-6=2y+4
-6x-2y-6-4=0
-6x-2y-10=0
-2(3x+y+5)=0
3x+y+5=0 is the equation of the line.
4.The points are:
(-3,6) and (3,0)
let the points be :
(-3,6) = (x₁,y₁)
and (3,0) = (x₂,y₂)
The equation of the line passing through the points (-1,-2) and (1,-8)
x - x₁/x₂-x₁ = y - y₁/y₂-y₁
For the given points, the equation is:
x-(-3)/3-(-3) = y-6/0-6
x+3/6 = y-6/-6
-6(x+3) = 2(y-6)
-6x-18=2y-12
-6x-2y-18+12=0
-6x-2y-6=0
-2(3x+y+3)=0
3x+y+3=0 is the equation of the line
Hence we get the required equations of the line.
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what is 39/80 as a decimal
Answer:0.4875.
Step-by-step explanation:
Answer:
0.48750
explanation:
Step-by-step answer?
hi
a ( b +c) = a*b +a*c
here a = -3
b = -4x
c = +5
so :
-3 ( -4x +5) = -3*-4x + -3* 5
= -12x + (-15)
= -12x -15
as I cannot add -12x and -15 ( they are two differents sort of figures )
so it's done
Answer:
12x - 15
Step-by-step explanation:
What you need to do for this is -3 · -4x + -3 · 5 = 12x+(-15). Which simplifies to 12x - 15.
find measure of MK in the image below
Answer:
ok is the corr!ctewwwdeeecceeeeecrrr\g
Find the equation of a line that passes through the point (1, -5) and is perpendicular to a line that passes through the points (2, 4) and (3, -4). Write the equation in slope intercept
form.
The equation of a line in slope-intercept form is [tex]y = \frac{1}{8} x - \frac{41}{8}[/tex] .
What is slope intercept form?One of the most popular ways to represent a line's equation is in the slope-intercept form of a straight line.When the slope of the straight line and the y-intercept are known, the slope-intercept formula can be used to determine the equation of a line ( the y-coordinate of the point where the line intersects the y-axis).The equation of the line is given below using the slope-intercept method:
y = mx + c
where,
m = the slope of the line
c = y-intercept of the line
(x, y) represent any point on the line
To find the Slope of a line that passes through the points (2, 4) and (3, -4).
m₁ = change in y/change in x
= y₂ - y₁ / x₂ - x₁
= Δy/Δx
= [tex]\frac{-4-4}{3-2}[/tex]
= [tex]\frac{-8}{1}[/tex]
= -8
Now, we find the slope of the line perpendicular to the line with the slope -8.
m₂ = -1 / m₁
= -1 / -8
= 1/8
So, the slope of the line is 1/8.
Next, we find the equation of a line that passes through the point (1, -5) and has a slope of 1/8.
⇒ y - y₁ = m( x- x₁)
⇒ y + 5 = [tex]\frac{1}{8}[/tex] (x - 1)
Multiplying by 8 on both sides of the equation we get and then solving
⇒ 8y + 40 = x - 1
⇒ 8y = x - 41
⇒ [tex]y = \frac{1}{8} x - \frac{41}{8}[/tex]
Therefore, the equation in slope intercept form is [tex]y = \frac{1}{8} x - \frac{41}{8}[/tex] .
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Eve and her mom are volunteering at an emergency relief center. To help prepare in case of a flood, they pack emergency kits with food and water. Eve puts 5 water bottles into each kit they pack. In all, she packs 125 water bottles.
Which equation can you use to find the number of emergency kits k Eve packs?
Answer:
Step-by-step explanation:
no. of emergency kits = x
bottles per kit = 5
total no. of bottles = 5x
which means,
5x = 125
125/5 = x
x = 25
Question 1-6
Mrs. Herrera is buying one piece of candy for each of the students who have 100% attendance. The number of students in Mrs. Herrera's mach classes that have perfect attendance is
2 Square root of 196 -1. The candy costs $0.79 each, plus 7% tax. How much money does it cost for Mrs. Herrera to purchase candy for her.
$19.75
$19.82
$20.45
$21.13
The total money that will be cost for Mrs. Herrera to purchase candy for her is $10.9889
Given, Number of students that 100% attendance in the class is √196 -1 that is equal to
14-1 = 13.
So, number of students is 13.
Cost of one candy = $0.79+7%(tax)
Cost of one candy = $0.79 + (7% of 0.79)
Cost of one candy = $ 0.79 + 0.0553
Cost of one candy = $0.8453
So , total cost that Mrs. Herrera to purchase candy will be
Total cost = Number of student X Cost of one candy
Total cost = 13 X $0.8453
Total cost = $ 10.9889
Hence, The total cost for Mrs. Herrera to purchase candy for her is $10.9889
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If the mean of 9 score is 4.5 what must the 10th score be for the mean of all score to be 5
The 10th score should be 9.5 for the mean to be 5.
What is mean value ?The mean value is the average value of the given data.
According to the given question the mean of 9 score is 4.5 what must the 10th score be for the mean of all score to be 5.
The total average score for 9 games is
= ( 9 × 4.5 )
= 40.5.
The total average score for the mean to be 5 in 10 games is
= ( 10 × 5 )
= 50.
∴ The 10th score must be ( 50 - 40.5 ) which is
= 9.5.
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- The coordinate -5 has a weight of 3 and the coordinate 3 has a weight of 1. Find
the weighted average. Use the formula: WA = Sum of the Weighted Values
Sum of the Weights
Answers:
The weighted average of the given coordinates weights is; 3
What is the Weighted Average?
We are given that;
Coordinate of -5 has a weight of 3
Coordinate of 3 has a weight of 1
Now, we are given the formula to calculate the weighted average as;
WA = Sum of the Weighted Values/Sum of the Weights
Thus;
WA = ((-5 * 3) + (3 * 1))/(3 + 1)
WA = (-15 + 3)/4
WA = -12/4
WA = -3
We will take the absolute value which is; WA = 3
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Can you help me with writing a Autobiography .Please !!!
Answer:
Starting paragraphs:
My name is _______. I was born on a cloudy night on the ___ of _______, _____ in ___________ . My parents were very happy as they had been blessed with a baby boy/girl, and that girl/boy is me!
1 year passed by and my 1st birthday was celebrated with much joy and it turned out to be a super extravagant event.
I do not remember much of my early childhood but my parents said that I was a very active, curious and a communicative child. I would ask dozen of questions each minute, without waiting for the answers. I suppose that's why my parents offered me books as early as my third birthday.
Ending paragraph:
I am thankful for my parents, teachers and friends for making me the person who I am today.
Explanation:
Compose your autobiography with the help of the following points:
Past TenseParagraph for every new event occurring in your lifeChronological OrderPunctuationsAdjectives Personal Pronounsis x to the 12th power times x to the fourth power equal to x to the 8th power times x to the 8th power? Explain
The equation is simplified as [tex]x^{16}=x^{16}[/tex].
The given equation is [tex]x^{12} . \ x^{4} = x^{8} . \ x^{8}[/tex].
We need to simplify and explain the equation.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Use the exponent rule [tex]a^m . \ a^n=a^{m+n}[/tex] to simplify the given equation.
Now, [tex]x^{12} . \ x^{4} = x^{8} . \ x^{8}[/tex]
⇒ [tex]x^{12+4}=x^{8+8}[/tex]
⇒ [tex]x^{16}=x^{16}[/tex]
The exponents of both the sides of equation are the same.
Therefore, the equation is simplified as [tex]x^{16}=x^{16}[/tex].
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