Answer:
then what's the question???..
If K = (AB)/(A+B) , then B = ?
(a) (A)/(1−A)
(b) (AK)/(A−K)
(c) (AK)/(K−A)
(d) (A+K)/(A)
(e) (A−K)/(AK)
Lets do
[tex]\\ \sf\longmapsto K=\dfrac{AB}{A+B}[/tex]
[tex]\\ \sf\longmapsto \dfrac{1}{K}=\dfrac{A+B}{AB}[/tex]
[tex]\\ \sf\longmapsto \dfrac{1}{K}=\dfrac{1}{A}+\dfrac{1}{B}[/tex]
[tex]\\ \sf\longmapsto \dfrac{1}{B}=\dfrac{1}{K}-\dfrac{1}{A}[/tex]
[tex]\\ \sf\longmapsto \dfrac{1}{B}=\dfrac{K-A}{AK}[/tex]
[tex]\\ \sf\longmapsto B=\dfrac{AK}{K-A}[/tex]
CALC 1: Spud's mom is going to make him a round birthday cake, and has asked for your help. Spud is a bit weird, and has already
announced that when he slices the cake, your slice will have a perimeter of 16 inches, because you're his favorite friend, and
that's his favorite number. Since you're helping his mom with the baking, what diameter cake will you recommend she makes
so that you end up with the most possible cake at weird Spud's party? (Hint: you can ignore the thickness df the cake, since
this will be the same, regardless of its diameter.)
10.1
in
Answer:
15.7 in
Step-by-step explanation:
A slice of a round pie is a sector of a circle.
The perimeter of a slice is the arc length s plus twice the radius r.
P = s + 2r
s = rθ = r(16/360) = r/22.5. So,
16 = (r/22.5) + 2r = (r + 45r)/22.5 = 46r/22.5
16 × 22.5 = 46r
360 = 46r
r = 7.826
D = 2r = 2 × 7.826 = 15.7 in
The diameter of the cake should be 15.7 in.
Check:
[tex]\begin{array}{rcl}P & = & s + 2r\\& = & \dfrac{r}{22.5} + 2r\\\\16 & = & \dfrac{7.826}{22.5} + 2 \times 7.826\\\\16 & = & 0.35 + 15.65\\16 & = & 16.00\\\end{array}[/tex]
It checks.
nick cut a circular cookie into 5 equal slices. what is the angle measure of each slice?
Using concepts of circles, it is found that the angle measure of each slice is of 72º.
--------------------------------------------
The cookies have circular formats.A complete circle, which is the format of a cookie, has an angular measure of 360º.If it is divided into a number n of equal slices, the angles will be 360 divided by n.--------------------------------------------
5 equal slices, thus:
[tex]\frac{360}{5} = 72[/tex]
The angle measure of each slice is of 72º.
A similar problem is given at https://brainly.com/question/16746988
Find mABC.
A. 102°
B. 54°
C. 14°
D. 78°
By the supplementary angles theorem, we know that both of the angles add up to equal 180°, so:
(4x + 22) + (8x - 10) = 180
12x + 12 = 180
12x = 168
x = 14
Now you just have to plug in x into the value for ∠ABC:
∠ABC = 4x + 22
∠ABC = 4(14) + 22
∠ABC = 46 + 22
∠ABC = 68°
Answer:
D = 78
Step-by-step explanation:
The two angles form a straight line so they add to 180
4x+22 + 8x-10 = 180
Combine like terms
12x +12 =180
Subtract 12 from each side
12x+12-12 = 180-12
12x = 168
Divide by 12
12x/12 =168/12
x=14
We want to find ABC
4x+22 = 4*14+22 = 56+22 = 78
What is meant by the term "90% confident" when constructing a confidence interval for a mean? Group of answer choices
Answer:
The question is not complete, below is the complete question:
What is meant by the term 90% confident? when constructing a confidence interval for a mean?
a. If we took repeated samples, approximately 90% of the samples would produce the same confidence interval.
b. If we took repeated samples, approximately 90% of the confidence intervals calculated from those samples would contain the sample mean.
c. If we took repeated samples, approximately 90% of the confidence intervals calculated from those samples would contain the true value of the population mean.
d. If we took repeated samples, the sample mean would equal the population mean in approximately 90% of the samples.
Answer:
The correct answer is:
If we took repeated samples, approximately 90% of the confidence intervals calculated from those samples would contain the true value of the population mean. (c)
Step-by-step explanation:
a 90% confidence level means that if repeated samples were taken, 9 out of 10 times, the confidence intervals of the sample chosen will be close to the mean (true value), which is a true representation of the population parameter. when using confidence intervals, there are always margins of allowable accuracy, and this is suggested by using standard diviations snd variances.
I attached a simple document to this answer that will give you more insight into confidence intervals used in statistics.
The fraction model below shows the steps that a student performed to find a quotient. Which statement best interprets the quotient? A: There are 5 1/5 five-sixths in 4 1/3. B: There 6 1/6 five sixths-in 4 1/3. C: There are 5 1/5 four and one-thirds in 5/6. D: There are 6 1/6 four and one-thirds in 5/6.
Answer:
The answer is D
Step-by-step explanation:
there are 8 1/6 five and one sixth in 2/3
-8=8(-3+a) plz help me and show work simply
Answer:
[tex] - 8 = 8( - 3 + a) \\ - 8 = - 24 + 8a \\ 8a = 16 \\ a = 2[/tex]
Answer:
2
Step-by-step explanation:
-8 = 8a - 24
16 = 8a
a =2
I hope this helps! :)determine if the following side lengths create an acute,obtuse,or right triangle. a) 20, 21, 28 b) 3, 6, 4 c) 8, 12, 15
Answer:
a) 20, 21, 28 : acute
b) 3, 6, 4 : obtuse
c) 8, 12, 15 : obtuse
Step-by-step explanation:
You can see if a triangle is acute, obtuse, or right using the Pythagorean theorem as follows:
If [tex]a^2+b^2=c^2[/tex] , then the triangle is right.
If [tex]a^2+b^2>c^2[/tex] , then the triangle is acute.
If [tex]a^2+b^2<c^2[/tex] , then the triangle is obtuse.
Solve each to find if the given lengths form an acute, obtuse, or right triangle ( The biggest number is the hypotenuse length, since the hypotenuse is always the longest side in a triangle. This is represented by c):
a) 20, 21, 28
Insert numbers, using 28 as c:
[tex]20^2+21^2[/tex]_[tex]28^2[/tex]
Simplify exponents ([tex]x^2=x*x[/tex]):
[tex]400+441[/tex]_[tex]784[/tex]
Simplify addition:
[tex]841[/tex]_[tex]784[/tex]
Identify relationship:
[tex]841>784[/tex]
The sum of the squares of a and b is greater than the square of c. This triangle is acute.
b) 3, 6, 4
Insert numbers, using 6 as c:
[tex]3^2+4^2[/tex]_[tex]6^2[/tex]
Simplify exponents:
[tex]9+16[/tex]_[tex]36[/tex]
Simplify addition:
[tex]25[/tex]_[tex]36[/tex]
Identify relationship:
[tex]25<36[/tex]
The sum of the squares of a and b is less than the square of c. This triangle is obtuse.
c) 8, 12, 15
Insert numbers, using 15 as c:
[tex]8^2+12^2[/tex]_[tex]15^2[/tex]
Simplify exponents:
[tex]64+144[/tex]_[tex]225[/tex]
Simplify addition:
[tex]208[/tex]_[tex]225[/tex]
Identify relationship:
[tex]208<225[/tex]
The sum of the squares of a and b is less than the square of c. This triangle is obtuse.
:Done.
The correct values are,
a) 20, 21, 28 = Acute
b) 3, 6, 4 = Obtuse
c) 8, 12, 15 = Obtuse
What is mean by Triangle?A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that;
The sides are,
a) 20, 21, 28
b) 3, 6, 4
c) 8, 12, 15
Now,
We know that;
If three sides of a triangle are a, b and c.
Then, We get;
If a² + b² = c², then the triangle is right triangle.
If a² + b² > c², then the triangle is acute triangle.
If a² + b² < c², then the triangle is obtuse triangle.
Here, For option a;
⇒ 20, 21, 28
Clearly, a² + b² = 20² + 21²
= 400 + 441
= 841
And, c² = 28² = 784
Thus, a² + b² > c²
Hence, It shows the acute angle.
For option b;
⇒ 3, 6, 4
Clearly, a² + b² = 3² + 4²
= 9 + 16
= 25
And, c² = 6² = 36
Thus, a² + b² < c²
Hence, It shows the obtuse angle.
For option c;
⇒ 8, 12, 15
Clearly, a² + b² = 8² + 12²
= 64 + 144
= 208
And, c² = 15² = 225
Thus, a² + b² < c²
Hence, It shows the obtuse angle.
Learn more about the triangle visit:
https://brainly.com/question/17335144
#SPJ5
Drag each factor to the correct location on the image.
If p(1) = 3, p(-4) = 8, p(5) = 0, p(7) = 9, p(-10) = 1, and p(-12) = 0,
P(x).
Answer:
(x-7) and (x+12) are the factors and the rest are non factors...
Help me with this please.
Answer:
the answer should be B
Step-by-step explanation:
take the total of people who got the flu(63) and the amount of them who were vaccinated(35) and write it as a fraction. 35/63 in its simplest form is 5/9
Evaluate the function f(x)=x^2-2x+2. a.f(2)
Answer:
f(2) = 2
Step-by-step explanation:
f(x)=x^2-2x+2
Let x=2
f(2)=2^2-2*2+2
= 4 -4 +2
= 2
Find the standard form of the equation of the ellipse with the given characteristics. center: (0, 0) focus: (3, 0) vertex: (4, 0)
Answer:
[tex]\frac{x^2}{4^2}+\frac{y^2}{\sqrt{7} ^2}=1[/tex]
Step-by-step explanation:
Since the vertex of the parabola is at (4,0), it has the vertex on the x axis (horizontal axis). The standard equation of an ellipse with horizontal major axis is given by:
[tex]\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1[/tex]
Where (h,k) is the center of the ellipse, a is the vertex and ±√(a²- b²) is the focus (c).
Since the ellipse center is at (0, 0), h = 0 and k = 0. Also the vertex is at (4, 0) therefore a = 0
To find b we use the equation of the focus which is:
[tex]c=\sqrt{a^2-b^2}\\ \\Substituing:\\\\3=\sqrt{4^2-b^2} \\4^2-b^2=3^2\\b^2=4^2-3^2\\b^2=16-9\\b^2=7\\b=\sqrt{7}[/tex]
Substituting the values of a, b, h and k:
[tex]\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1\\\\\frac{(x-0)^2}{4^2}+\frac{(y-0)^2}{\sqrt{7} ^2}=1\\\\\frac{x^2}{4^2}+\frac{y^2}{\sqrt{7} ^2}=1[/tex]
give 12 consecutive integers, in how many ways can three of these integers be selected to give a sum which divides by 4?
Answer:
55 waysStep-by-step explanation:
Out of 12 consecutive integers:
3 - divide by 4, so the remainder is 03- give remainder of 13- give remainder of 23 - give remainder of 3Sum of 3 integers will be divisible by 4 if the remainders are:
0 - 0 - 0 ⇒ 1 combination0 - 1 - 3 ⇒ 3*3 = 9 combinations0 - 3 - 1 ⇒ 3*3 = 9 combinations1 - 1 - 2 ⇒ 2*3 = 6 combinations1 - 2 - 1 ⇒ 2*3 = 6 combinations2 - 1 - 1 ⇒ 2*3 = 6 combinations3 - 0 - 1 ⇒ 3*3 = 9 combinations3 - 1 - 0 ⇒ 3*3 = 9 combinationsSo total number of combinations is:
1 + 4*9 + 3*6 = 55Mandy has $25 and she plans to save $2 each week. Her brother
Thomas has no money now, but he plans to save $3 each week.
Make a table that shows the amount of money Mandy and
Thomas have every week for 10 weeks. Let m be the
amount of money Mandy has and let y be the amount of
money Thomas has.
Write two different algebraic expressions to describe each
person's savings.
Given the formula A = 5h (B + b); solve for B.
2
Answer:
B = A/5h - b; You could use
B = (A - 5hb)/5h This just puts everything over a common denominator.
Step-by-step explanation:
A = 5h (B + b) Divide both sides by 5h
A/5h = B + b Subtract b from both sides.
A/5h - b = B
Find a • b. a = 5i + 7j, b = -4i + 3j (5 points)
<1, 10>
<-20, 21>
1
41
Answer:
[tex]a\cdot b[/tex] = 1
Step-by-step explanation:
Given that,
Vector [tex]a=5i+7j[/tex]
Vector [tex]b=-4i+3j[/tex]
We need to find [tex]a{\cdot} b[/tex] means the dot product of a and b. So,
[tex]a{\cdot} b=(5i+7j){\cdot} (-4i+3j)[/tex]
We know that,
[tex]i{\cdot}i, j{\cdot}j,k{\cdot}k=1\ \text{and}\ i{\cdot}j= j\cdot i=0[/tex]
So,
[tex]a{\cdot} b=(5i+7j){\cdot} (-4i+3j)\\\\=5i{\cdot}(-4i)+5i{\cdot} 3j+7j\cdot(-4i)+7j\cdot 3j\\\\=-20+21\\\\=1[/tex]
So, the value of [tex]a\cdot b[/tex] is 1.
Answer:
1
Step-by-step explanation:
What value of x makes this equation true?
17 5 - 7 = -4
x=
y Su
What value of x makes this equation true? X/6-7=-4
Answer:
x=18
Step-by-step explanation:
x/6 - 7 = -4
x/6 = 3
(x/ 6) * 6 = 3*6
x = 18
4. Tony bought a computer, a cell
phone, and a television. The
computer costs 2.5 times as much
as the television. The television cost 5 times as much as the cell phone. If Tony spent a total of $925, how much did the cell phone
cost?
Answer:
$50
Step-by-step explanation:
Let x represent the cost of the cell phone.
Since the TV cost 5 times as much as the cell phone, its cost can be represented by 5x.
Since the computer cost 2.5 times as much as the TV, its cost can be represented by 12.5x.
Create an equation to represent the situation, and solve for x:
x + 5x + 12.5x = 925
18.5x = 925
x = 50
So, the cell phone cost $50
Answer:
$50
Step-by-step explanation:
Let x represent the cost of the cell phone.
Since the TV cost 5 times as much as the cell phone, its cost can be represented by 5x.
Since the computer cost 2.5 times as much as the TV, its cost can be represented by 12.5x.
Create an equation to represent the situation, and solve for x:
x + 5x + 12.5x = 925
18.5x = 925
x = 50
So, the cell phone cost $50
Please help!! find the circumference of a circle with a diameter of 13 meters
Answer:
C = 2pie(r)
r= d/2= 13/2= 6.5
C = 2*3.14*6.5
C= 41
Step-by-step explanation:
What is the answer to 11.24 divided by 9
Answer:
1.24
Step-by-step explanation:
oahsofhasdf0as0dfadera
Find the vector and parametric equations for the line through the point P(0, 0, 5) and orthogonal to the plane −1x+3y−3z=1. Vector Form: r
Answer:
Note that orthogonal to the plane means perpendicular to the plane.
Step-by-step explanation:
-1x+3y-3z=1 can also be written as -1x+3y-3z=0
The direction vector of the plane -1x+3y-3z-1=0 is (-1,3,-3).
Let us find a point on this line for which the vector from this point to (0,0,5) is perpendicular to the given line. The point is x-0,y-0 and z-0 respectively
Therefore, the vector equation is given as:
-1(x-0) + 3(y-0) + -3(z-5) = 0
-x + 3y + (-3z+15) = 0
-x + 3y -3z + 15 = 0
Multiply through by - to get a positive x coordinate to give
x - 3y + 3z - 15 = 0
Does anyone have the solution to this
Step-by-step explanation:
There is 1 root at x = 1, where the function crosses the x-axis.
There are 2 roots at x = -2, where the function touches the x-axis but does not cross.
So there are 3 real roots total.
The function is:
y = (x − 1) (x − (-2))²
y = (x − 1) (x + 2)²
Choose the situation that represents a function.
A) The number of raisins in an oatmeal raisin cookie is a function of the diameter of the cookie.
B) The inches of rainfall is a function of the day’s average temperature.
C) The time it takes to cook a turkey is a function of the turkey’s weight.
D) The number of sit-ups a student can do in a minute is a function of the student’s age.
Answer:c
Step-by-step explanation:
Answer: The answer is C.
Hope this helps you!
How do you complete the square of x2+8x+26?
Answer:
see below
Step-by-step explanation:
x^2+8x+26
Take the coefficient of the x term
8
Divide by 2
8/2 = 4
square it
4^2 =16
we need to add 16 to 26 = 16+10
x^2 + 8x+16 +10
(x+4)^2 +10
The answer you are looking for is (x+4)²+10.
Solution/Explanation:
Selecting the "x" term's coefficient,
It would be 8.
Now, dividing it by 2,
8/2=4.
Squaring 4,
4²=16.
So, now, since (x+4)²=x²+8x+16, you must solve for 26-16, which equals 10, which you would supplement into the equation.
So, therefore, (x+4)²+10.
I hope this has helped you. Enjoy your day.
Consider the following. x = t2 − 2t, y = t5, 1 ≤ t ≤ 4 Set up an integral that represents the length of the curve. 4 1 dt Use your calculator to find the length correct to four decimal places.
Answer:
L ≈ 1023.0562
Step-by-step explanation:
We are given;
x = t² - 2t
dx/dt = 2t - 2
Also, y = t^(5)
dy/dt = 5t⁴
The arc length formula is;
L = (α,β)∫√[(dx/dt)² + (dy/dt)²]dt
Where α and β are the boundary points. Thus, applying this to our question, we have;
L = (1,4)∫√[(2t - 2)² + (5t⁴)²]dt
L = (1,4)∫√[4t² - 8t + 4 + 25t^(8)]dt
L = (1,4)∫√[25t^(8) + 4t² - 8t + 4]dt
Using online integral calculator, we have;
L ≈ 1023.0562
The length of the curve is 1023.0562 and this can be determined by doing the integration using the calculator.
Given :
[tex]\rm x = t^2-2t[/tex][tex]\rm y=t^5[/tex][tex]\rm 1\leq t\leq 4[/tex]First, differentiate x and y with respect to 't'.
[tex]\rm \dfrac{dx}{dt}=2t-2[/tex]
[tex]\rm \dfrac{dy}{dt}=5t^4[/tex]
Now, determine the length of the curve using the below formula:
[tex]\rm L = \int^b_a\sqrt{\left(\dfrac{dx}{dt}\right)^2+\left(\dfrac{dy}{dt}\right)^2} dt[/tex]
Now, substitute the value of the known terms in the above formula and then integrate it.
[tex]\rm L = \int^4_1\sqrt{(2t-2)^2+(5t^4)^2} dt[/tex]
[tex]\rm L = \int^4_1\sqrt{25t^8+4t^2-8t+4} \;dt[/tex]
Now, simplify the above integration using the calculator.
L = 1023.0562
For more information, refer to the link given below:
https://brainly.com/question/18651211
If the nth term is , then the (n+1)st is: Please make sure you check the image :)
Answer:
( n+1) /2 *( 3n+2)
Step-by-step explanation:
n/2 * ( 3n-1)
We want the n+1 term
Replace n with n+1
( n+1) /2 *( 3( n+1) -1)
Distribute
( n+1) /2 *( 3n+3 -1)
( n+1) /2 *( 3n+2)
Answer:
[tex]\large \boxed{\sf C. \ \frac{n+1}{2} (3n+2)}[/tex]
Step-by-step explanation:
[tex]\displaystyle \frac{n}{2} (3n-1)[/tex]
To find the (n+1)st term, replace the n variable with n+1.
[tex]\displaystyle \frac{n+1}{2} (3(n+1)-1)[/tex]
Expand brackets.
[tex]\displaystyle \frac{n+1}{2} (3n+3-1)[/tex]
Subtract like terms in brackets.
[tex]\displaystyle \frac{n+1}{2} (3n+2)[/tex]
Find the Taylor series for f(x) centered at the given value of a. [Assume that f has a power series expansion. Do not show that Rn(x) → 0.] f(x) = 4 cos(x), a = 7π
Answer:
The Taylor series of f(x) around the point a, can be written as:
[tex]f(x) = f(a) + \frac{df}{dx}(a)*(x -a) + (1/2!)\frac{d^2f}{dx^2}(a)*(x - a)^2 + .....[/tex]
Here we have:
f(x) = 4*cos(x)
a = 7*pi
then, let's calculate each part:
f(a) = 4*cos(7*pi) = -4
df/dx = -4*sin(x)
(df/dx)(a) = -4*sin(7*pi) = 0
(d^2f)/(dx^2) = -4*cos(x)
(d^2f)/(dx^2)(a) = -4*cos(7*pi) = 4
Here we already can see two things:
the odd derivatives will have a sin(x) function that is zero when evaluated in x = 7*pi, and we also can see that the sign will alternate between consecutive terms.
so we only will work with the even powers of the series:
f(x) = -4 + (1/2!)*4*(x - 7*pi)^2 - (1/4!)*4*(x - 7*pi)^4 + ....
So we can write it as:
f(x) = ∑fₙ
Such that the n-th term can written as:
[tex]fn = (-1)^{2n + 1}*4*(x - 7*pi)^{2n}[/tex]
In this exercise we must calculate the Taylor series for the given function in this way;
[tex]f_n= (-1)^{2n+1}(4)(x-7\pi)^{2n}[/tex]
The Taylor series of f(x) around the point a, can be written as:
[tex]f(x) = f(a) + f'(a)(x-a)+\frac{1}{2!} f''(a)(x-a)^2+....[/tex]
Here we have:
[tex]f(x) = 4cos(x)\\a = 7\pi[/tex]
Then, let's calculate each part:
[tex]f(a) = 4cos(7\pi) = -4\\df/dx = -4sin(x)\\(df/dx)(a) = -4sin(7\pi) = 0\\(d^2f)/(dx^2) = -4cos(x)\\(d^2f)/(dx^2)(a) = -4cos(7\pi) = 4[/tex]
Here we already can see two things:
1) The odd derivatives will have a sin(x) function that is zero when evaluated in [tex]x=7\pi[/tex].
2) We also can see that the sign will alternate between consecutive terms.
So we only will work with the even powers of the series:
[tex]f(x) = -4 + (1/2!)*4*(x - 7\pi)^2 - (1/4!)*4*(x - 7\pi)^4 + ....[/tex]
So we can write it as:
[tex]f(x)=\sum f_n[/tex]
Such that the n-th term can written as:
[tex]f_n= (-1)^{2n+1}(4)(x-7\pi)^{2n}[/tex]
See more abour Taylor series at: brainly.com/question/6953942
3. Using the identity (a + b)² = (a² + 2ab + b²), evaluate 122²
.....
plz it's request to do answer fast and I will make him or her brainlist
[tex]\\ \sf\longmapsto 122^2[/tex]
[tex]\\ \sf\longmapsto (100+22)^2[/tex]
[tex]\\ \sf\longmapsto 100^2+2(100)(22)+22^2[/tex]
[tex]\\ \sf\longmapsto 10000+4400+484[/tex]
[tex]\\ \sf\longmapsto 14400+484[/tex]
[tex]\\ \sf\longmapsto 14884[/tex]
112²
Using Identity(a + b)² = (a² + 2ab + b²)
Solution⇛122²
⇛(100 + 22)²
⇛(100)² + 2 × 100 × 22 + (22)²
⇛10000 + 4400 + 484
⇛14400 + 484
⇛14884
Determine the maturity value of a 45-day note for $1,250 dated May 23 and bearing interest 8%.
The maturity value of a 45-day note for $1,250 dated May 23 and bearing interest 8% is $1,262.5
Using this formula
Maturity value=Principal amount+ Interest
Let plug in the formula
Maturity value=$1,250+($1,250*8%*45 days/360 days)
Maturity value=$1,250+$12.5
Maturity value=$1,262.5
Inconclusion the maturity value is $1,262.5
Learn more about maturity value here:
https://brainly.com/question/2496341
solve the following system of equations
1/2x+1/4y=-2
-2/3x+1/2y=6
x=
y=
Answer:
x = -6
y = 4
Step-by-step explanation:
Rewriting the equations :
2x + y = -84x - 3y = -36Now, solving the two equations using substitution method, we get :
x = -6
y = 4
Answer:
y = 4
x = -6
Step-by-step explanation:
1/2 x + 1/4 y= -2 first equation
-2/3 x + 1/2 y = 6 second equation
solution:
from the first equation:
8(1/2 x + 1/4 y) = -2*8
8x*1/2 + 8y*1/4 = -16
8x/2 + 8y/4 = -16
4x + 2y = -16 third equation
from the second equation
6(-2/3 x + 1/2 y) = 6*6
6x*-2/3 + 6y*1/2 = 36
-12x/3 + 6y/2 = 36
-4x + 3y = 36 fourth equation
from the third & fourth equation:
4x + 2y = -16
-4x + 3y = 36
0 + 5y = 20
5y = 20
y = 20/5
y = 4
from the fourth equation:
-4x + 3y = 36
-4x + 3*4 = 36
-4x + 12 = 36
-4x = 36 - 12
-4x = 24
x = 24/-4
x = -6
Check:
from the first equation:
1/2 x + 1/4 y = -2
1/2 *-6 + 1/4 * 4 = -2
-3 + 1 0 -2
from the second equation:
-2/3 x + 1/2 y = 6
-2/3 * -6 + 1/2 * 4 = 6
4 + 2 = 6