we are given
system of equations
First equation is
[tex]3x-2y=31[/tex]
Second equation is
[tex]3x+2y=-1[/tex]
now, we can find augmented matrix
[tex]A=\begin{pmatrix}3&-2&31\\ 3&2&-1\end{pmatrix}[/tex]
now, we can change it into reduced row echelon form
step-1: multiply the 1st row by 1/3
[tex]A=\begin{pmatrix}1&-2/3&31/3\\ 3&2&-1\end{pmatrix}[/tex]
step-2:add -3 times the 1st row to the 2nd row
[tex]A=\begin{pmatrix}1&-2/3&31/3\\ 0&4&-32\end{pmatrix}[/tex]
step-3:multiply the 2nd row by 1/4
[tex]A=\begin{pmatrix}1&-2/3&31/3\\ 0&1&-8\end{pmatrix}[/tex]
step-4: add 2/3 times the 2nd row to the 1st row
[tex]A=\begin{pmatrix}1&0&5\\ 0&1&-8\end{pmatrix}[/tex]
so, we get
[tex]x=5,y=-8[/tex]
Answer is (5,-8)
Solution is (5,-8)
3x – 2y = 31
3x + 2y = -1
first we write it in matrix form
3 -2 | 31 -------------> Row 1
3 2 | -1 -------------> Row 2
We use row operations and get matrix in 1 0 and 0 1 form
Subtract Row 2 by row 1. R2 -> R2 - R1. So R1 remains the same
3 -2 | 31 -------------> Row 1
0 4 | -32 -------------> Row 2
Divide row 1 by 3, R1-> R1/3. So R2 remains the same
1 [tex]\frac{-2}{3}[/tex] | [tex]\frac{31}{3}[/tex] -------------> Row 1
0 4 | -32 -------------> Row 2
Divide row 2 by 4. R2 -> R2/4
1 [tex]\frac{-2}{3}[/tex] | [tex]\frac{31}{3}[/tex] -------------> Row 1
0 1 | -8 -------------> Row 2
Now we need to get 0 in the place of -2/3
Multiply Row 2 by 2/3 and add it with Row 1. R1 --> 2/3 times R2 + R1
1 [tex]1*\frac{2}{3}+\frac{-2}{3}[/tex] | [tex]-8*\frac{-2}{3}\frac{31}{3}[/tex] -------------> Row 1
0 1 | -8 -------------> Row 2
Now simplify the fraction
1 0 | 5 -------------> Row 1
0 1 | -8 -------------> Row 2
So from this we can see that x=5 and y = -8
Solution is (5,-8)
$.87 per day is equal to how many dollars per year
Hi can you help?
Find the missing x- and y-values and Pythagorean triples using the identity given
[tex](x^{2}-y^{2})^{2}+(2xy)^{2}+(x^{2}+y^{2})^{2}[/tex]
X Value: 4
Y Value: 3
Pythagorean Triples: ?
X Value: 5
Y Value: ?
Pythagorean Triples: (9,40,41)
X Value: ?
Y Value: 3
Pythagorean Triples: (27,36,45)
X Value: 7
Y Value: 5
Pythagorean Triples: ?
(x²-y²)² + (2xy)² = (x²+y²)²
Find the missing x- and y-values and Pythagorean triples using the identity given
A Pythagorean triple consists of three positive integers a, b, and c, that satisfy the equation from the Pythagorean theorem, thus, a² + b² = c², such triple is commonly written (a,b,c).
We are given the equation : (x²-y²)² + (2xy)² = (x²+y²)² since this, we have :
a = (x²-y²)
b = (2xy)
c = (x²+y²)
Question 1)
X Value = 4
Y Value = 3
Pythagorean triples: ?
We can replace the values of x and y, to determine a, b and c.
a = (x²-y²) = (4²-3²) = 16-9 = 7
b = (2xy) = (2*4*3) = 24
c = (x²+y²) = (4²+3²) = 16+9 = 25
Answer 1 : Pythagorean triples : (7,24,25)
Question 2)
X Value = 5
Y Value = ?
Pythagorean Triples: (9,40,41)
Now we have a, b, and c, to determine Y
b = (2xy) = 40
Y = 40/2x = 40/2*5 = 40/10 = 4
Answer 2 : Y = 4
Question 3)
X Value = ?
Y Value = 3
Pythagorean Triples: (27,36,45)
Now we have a, b, and c, to determine X
b = (2xy) = 36
X = 36/2y = 36/2*3 = 36/6 = 6
Answer 3 : X = 6
Question 4)
X Value = 7
Y Value = 5
Pythagorean Triples: ?
We can replace the values of x and y, to determine a, b and c.
a = (x²-y²) = (7²-5²) = 49-25 = 24
b = (2xy) = (2*7*5) = 70
c = (x²+y²) = (7²+5²) = 49+25 = 74
Answer 4 : Pythagorean triples : (24,70,74)
Hope this helps!
[tex]\textit{\textbf{Spymore}}[/tex]
By using the given identity and substituting known values of x and y, we can find missing x or y values and compute the Pythagorean triples. For instance, when x=4 and y=3, the Pythagorean triple is (7,24,25). Similarly, we can find missing triples or variables for other sets.
Explanation:This question pertains to the topic of Pythagorean triples and their relationship with a given identity. A Pythagorean triple consists of three positive integers (a, b, c), such that a2 + b2 = c2. Inserting known values of x and y into the identity provided can help us find the Pythagorean triples.
For x=4 and y=3: (42 - 32)2 = 72, (2*4*3)2 = 242, (42 + 32)2 = 252. Therefore Pythagorean triple is (7,24,25).For x=5, the Pythagorean triple is (9,40,41), therefore by reversing the process we find y=4.For y=3, the Pythagorean triple is (27,36,45), therefore by inserting values and solving the equation we find x=6.Finally, for x=7 and y=5, the process yields the Pythagorean triple (12,35,37).Learn more about Pythagorean triples here:https://brainly.com/question/31900595
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A circle has been drawn in the center of a square. A dot will be randomly placed inside the square. What is the probability that the dot will be placed in the purple section?
A) 11%
B) 20%
C) 38%
D) 40%
Answer: D) 40%
==========================================================
Work Shown:
Area of purple rectangle (ignore circular cutout for now) = base*height = 6*12 = 72
I'm assuming the center of the circle is located on the right edge of the purple rectangle. If so, then we can subtract off half the circle's area from the purple rectangle area
Semicircle Area = (pi*r^2)/2 = (pi*3^2)/2 = 14.1371669
Area of purple region = (Rectangle Area) - (Semicircle Area)
Area of purple region = 72-14.1371669
Area of purple region = 57.8628331
-------
Now divide this area by 144 as this is the total area of the entire largest square (12 by 12 square) to get 57.8628331/144 = 0.401825 which is approximate. This rounds to 0.40 and converts to 40% which explains how I got choice D as the answer
Answer:
That probability is approx. 40%. See below.
Step-by-step explanation:
That probability is the area of the purple section divided by the total area of the square before coloring purple.
This area of the square is (12 cm)^2, or 144 cm^2.
Half the area of the circle is pi*(3 cm)^2, or 9*pi cm^2.
Thus, the purple area is (144 cm^2) / 2 - (9/2)*pi cm^2, or (72 - 9*pi/2) cm^2. This is approx. 57.86.
The ratio of this purple area to the full area of the square is:
57.86 cm^2
--------------------------------- = 0.4 (approximately)
144 cm^2
Graph the image of the given triangle after the transformation that has the rule (x, y)→(−x, −y) .
Select the Polygon tool. Then, click the points of the triangle vertices to create the triangle by connecting the sides.
Please answer fast, need the help : ))
Answer:
It is given that Graph the image of the given triangle after the transformation that has the rule (x, y)→(−x, −y) .
From the given figure it is noticed that the vertices of the triangle are (6,7), (7,4), (-2,5).
From the given rule (x, y)→(−x, −y) the vertices of the image are (-6,-7), (-7,-4) and (2,-5).
Plot these points on the coordinate plane.
In the below graph, the image of the given triangle is represented by green lines.
Study shows that 26% of car owners parallel park regularly and 74% do not. Does the Grafton picked the data fairly
It's not possible to determine if Grafton's data collection was fair or not based on the provided information, as the question lacks details like the size of the sample used and where the sample was taken from. Accurate and representative data collection is a critical part of conducting a study.
Explanation:Based on the data provided in the question, it's not possible to say whether Grafton picked the data fairly or not. The principles of statistics tell us that for data to be considered fair, it must be representative of the population being studied. In the context of the question, this means that for the data to be considered fair, it must accurately represent the car owning population. The question, however, does not provide enough information for us to make this determination.
For example, we don't know the sample size that Grafton used, where the sample was taken from, or any information about the population the data is supposed to represent. Without this additional data, we cannot determine if the data collection was biased or not. Remember, data collection is a crucial part of conducting a valid study and it's important to ensure that the sample used is unbiased and representative of the whole population.
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Carol has only 20p and 10p coins in her purse she has three times as many 20p coins and 10p coins if Carol has ?4.20 altogether, how many 20p coins does she have
Suppose that Carol has x 10p coins in her purse. Since she has three times as many 20p coins as 10p coins, then she has 3x 20p coins in her purse.
x coins of 10p value $0.10x and 3x coins of 20p value $0.60x.
In total this amount of money is $(0.10x+0.60x)=$0.70x that is exactly $4.20. Thus, you get the equation
0.70x=4.20.
Solve it:
[tex]x=\dfrac{4.20}{0.70}=6.[/tex]
Carol has 6 coins of 10p and 3·6=18 coins of 20p.
Answer:
I'm not sure how euros work but I'm almost certain there are 18 20p coins
Step-by-step explanation:
A cube shaped packing box can hold 729 cubic inches of packing material. Solve 729= s ^3 to find the length of one side of the box
729 = s^3
9^3 = s^3
s = 9 in.
Which steps transform the graph of y = x2 to y = –2(x – 2)2 + 2? (1 point)
A. translate 2 units to the left, translate down 2 units, stretch by the factor 2
B. translate 2 units to the right, translate up 2 units, stretch by the factor 2
C. reflect across the x-axis, translate 2 units to the left, translate down 2 units, stretch by the factor 2
D. reflect across the x-axis, translate 2 units to the right, translate up 2 units, stretch by the factor 2
y = x^2 to Green
y = –2(x – 2)^2 + 2 Blue
The correct answer is D.
Answer:
The correct option is D.
Step-by-step explanation:
The parent function is
[tex]y=x^2[/tex]
The transformed function is
[tex]y=-2(x-2)^2+2[/tex] .... (1)
The translation is defined as
[tex]f(x)=k(x+a)^2+b[/tex] .... (2)
Where, k is stretch factor, a is horizontal shift and b is vertical shift.
If a>0, then the graph shifts a units left and if a<0, then the graph shifts a units right.
If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.
From (1) and (2) it is clear that
[tex]a=-2,b=2,k=-2[/tex]
It means,
a=-2<0 the graph shifts 2 units right.
b=2>0 the graph shifts 2 units up.
k=-2, the graph reflect across the x-axis and stretch by the factor 2.
The graph reflect across the x-axis, translate 2 units to the right, translate up 2 units, stretch by the factor 2. Therefore the correct option is D.
Solve for d. Show each step: d(e-f)=g
Hey there!!
Given equation :
d(e-f) = g
Solve for d :
Dividing by ( e - f ) on both sides :
d = g / e - f which is [tex]d=\frac{g}{e-f}[/tex]
Hope my answer helps!
A researcher determined the amount of ducks that were in a pond over a four-year time span. The results are shown in the table below.
Year Ducks
1 64
2 78
3 92
4 106
Select an equation that best models the amount of ducks (d) that will be in the pond during the nth year.
Every year there are 14 more ducks. The starting point would be 50 and the equation is:
d = 14*year+50
What is the probability the person is a clown, given they are a boy? (30 pts)
Answer: Answer would be 23
Step-by-step explanation:
Jason spent half of his allowance going to the movies. he washed the family car and earned 8 dollars. What is his weekly allowance if he ended up with 11 dollars.
$6 dollars because 11-8 = 3, 3x2 =6
He starts with $6.00
It says he spends 1/2 of his allowance on the movies. 6/2=3
He has $3. Then it says He gained $8.00 for washing the "family" car.
$6.00+$8.00
=$11
Answer=$6.00
What is 8 times 8 plus for and add 1,600
Answer:
1668
Step-by-step explanation:
8(8)= 64
64+4=68
1,600+68= 1,668
Antonio's father bought tickets for the planetairium.He bought 6 tickets each ticket cost 16 what is the total cost of the 6 tickets?
Answer:
$96
Step-by-step explanation:
Multiply The Number Of Tickets By Amount Of People Going
16 * 6
Help please!!
Celine observed that 80% of patrons at the local library liked reading sci-fi novels. If 35 patrons did not like reading sci-fi novels, how many patrons did enjoy sci-fi novels?
Part A: Write an equation in one variable that can be used to find the total number of patrons at the library? Define the variable used in the equation.
Part B: How many patrons enjoy reading sci-fi novels? Show your work.
Answer: Part A = (100% - 80%)P = 35, Part B = 140
Step-by-step explanation:
Percentage: Like + Don't like = 100%
80% + Don't like = 100%
-80% -80%
Don't like = 20%
People: 20% of Patrons = Don't Like
0.20 x Patrons = 35
÷ 0.20 ÷ 0.20
Patrons = 175
Now, let's write the equation we used to get that answer:
Let P represent the total number of patrons, then the equation is:
(100% - 80%)P = 35
= (1.00 - 0.80)P = 35
= 0.20P = 35
= P = 175
Part B:
80% of Patrons = Like
0.80 x 175 = Like
140 = Like
Extended Response
6. The coordinates of the vertices of parallelogram RSTU are R(0, 0), S(2, 3), T(6, 3), and U(4, 0). What are the coordinates of the vertices of Ry=x(RSTU)?
Answer:
The Coordinate of the vertices of Parallelogram RSTU are R(0,0), S(2,3),T(6,3) and U (4,0).
we have to find the vertices of a point which cuts the side of parallelogram ST .It is given that line y = x passes through R.
Suppose that it cuts the side ST at M (p,q).
Equation of line passing through T(6,3)and S (2,3) is
[tex]\frac{y-3}{x-2}= \frac{3-3}{6-3}\\\frac{y-3}{x-2} = 0\\y- 3=0[/tex]
it passes through (p,q)∴
∴ q -3 =0 ...........(1)
Line y=x passes through (p,q).
p -q=0
p=q
Equation (1) becomes
p= q=3
So the line y =x cuts TU at M (3,3).
There a sixteen friends sharing four cup cakes if they divide the cupcakes evenly so that they can each get four pieces of a cupcake how many pieces do they need to cut each cupcake into
Which package has the lowest ratio of cost to number of lessons? $90 for 10 lessons $160 for 20 lessons $80 for 10 lessons $120 for 20 lessons
$90/10 = 9
$160/20 = 8
$80/10 = 10
$120/20 = 6
The package that has the lowest ratio cost to number of lessons is $120 for 20 lessons.
Hope this Helps!!
The package with the lowest ratio of cost to number of lessons is the $120 for 20 lessons option, calculating to a cost of $6 per lesson, which is the most cost-effective option.
To find this, we calculate the cost per lesson for each package by dividing the total cost by the number of lessons.
For $90 for 10 lessons: $90 / 10 = $9 per lessonFor $160 for 20 lessons: $160 / 20 = $8 per lessonFor $80 for 10 lessons: $80 / 10 = $8 per lessonFor $120 for 20 lessons: $120 / 20 = $6 per lessonTherefore, the package with the lowest ratio of cost to number of lessons is $120 for 20 lessons, with a cost of $6 per lesson.
Please help with geometry homework
Area = Base x height:
area = 3 1/2 x 3/4 = 2 5/8 sq. ft.
The answer is the 2nd one.
The answer would be the second one or 2 5/8 sq ft hope that helps
Which basic geometric figure is labeled as CD? A. Plane B. Segment C. Line D. Angle
Answer:
B
Step-by-step explanation:
In mathematics, we usually label a segment using two letters, one at the beginning of the segment and the second one at the end. On the other hand, in mathematics, angles are labeled using 3 letters (∠ABC).Lines are labeled using just one capital letter (where the line starts)And finally a plane is generally labeled using 3 letters (Plane ABC)Therefore a geometric figure labeled CD would be a segment and the correct answer is B)
During 4 days, the price of the stock of PEV Corporation went up 1/4 of a point, down 1/3 of a point, down 3/4 of a point, and up 7/10 of a point. What was the net charge?
The price of the stock of PEV Corporation varies as shown. we have to determine the net charge. Net change is just how much it changed overall, so we will look for all the ups minus all the downs.
Here, "went up" goes with a + sign, and "went down" goes with a - sign.
So, Net charge = [tex]\frac{1}{4} - \frac{1}{3}-\frac{3}{4} + \frac{7}{10}[/tex]
= [tex]\frac{1}{4}-\frac{3}{4}- \frac{1}{3} + \frac{7}{10}[/tex]
= [tex]-\frac{2}{4}- \frac{1}{3} + \frac{7}{10}[/tex]
= [tex]-\frac{1}{2}- \frac{1}{3} + \frac{7}{10}[/tex]
LCM of 2,3 and 10 is 30
= [tex]\frac{-15-10+21}{30}[/tex]
= [tex]\frac{-4}{30}[/tex]
= [tex]\frac{-2}{15}[/tex]
So, the net charge is [tex]\frac{-2}{15}[/tex]
1. Simplify by collecting like terms. Show your work when more than one step is required.
A and B for #1 are done I just need C
c. ?
2. Evaluate each expression for the given value of the variable. Show your work.
I need both A and B
a. ?
b. ?
3. The freshman class will be selling carnations as a class project. What is the class's income after it pays the florist a flat fee of $200 and sells c carnations for $2 each? Write an algebraic expression that models the situation.
I need this one as well
Hello,
Please, see the attached files.
Thanks.
Elect two binomials that are factors of this trinomial. X^2-x-30
Answer:
so what’s the answer
Step-by-step explanation:
The figure below is a parallelogram. Find the value of X and Y
The values of x and y is 2 and 17 respectively.
We need to find the value of x and y.
What is parallelogram?A parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure.
Now, x+2=4
⇒x=2
y-5=12
⇒y=17
Therefore, the values of x and y is 2 and 17 respectively.
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HELP ASAP PLSSSSSSS
Select the correct answer.
What is the rhyme scheme in this excerpt from Robert Frost’s "The Road Not Taken"?
Two roads diverged in a yellow wood,
And sorry I could not travel both
And be one traveler, long I stood
And looked down one as far as I could
To where it bent in the undergrowth;
A.
abacb
B.
abaab
C.
ababa
D.
babab
Answer:
B because eaxh section either repeats itself or is close to repeating its previous part
Step-by-step explanation:
solve the quadratic equation y^2-2y-35=0
Hello,
To solve we need to factor y^2-2y-35:
(y-7)(y+5)=0
Now solve for :
(When will (y-7)(y+5)equal zero?)
When y-7=0 or y+5=0
Solve for the 2 equations above and;
y= 7,-5
Hope this helps, have a great day!
Please help asap 25 pts
Step 1. Subtract 3 from both sides
2|7x - 4| = 51 - 3
Step 2. Simplify 51 - 3 to 48
2|7x - 4| = 48
Step 3. Divide both sides by 2
|7x - 4| = 48/2
Step 4. Simplify 48/2 to 24
|7x - 4| = 24
Step 5 Break down the problem into these 2 equations
7x - 4 = 24
-(7x - 4) = 24
Step 6. Solve the 1st equation: 7x - 4 = 24
x = 4
Step 7. Solve the 2nd equation: -(7x - 4) = 24
x = -20/7
Step 8. Collect all solutions
x = -20/7,4
The answer is C.
Samuel has 20$ in his savings account before he makes a deposit of $160. After 2 weeks, he withdraws $160. How did samuels savings account balance change?
There was no change in Samuel's savings account balance. He made a deposit of $160 but after two weeks, he withdrew the same sum. He still had $20 in his account as a result.
Explanation:This math query relates to fundamental financial operations. Samuel has $20 in his savings account at the start of the story. His total now stands at $180 after his subsequent $160 deposit. He withdraws $160, though, after two weeks. He now has $20 in his account after that. Finally, there was no change in Samuel's savings account balance. His account was $20 from beginning to end.
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Using the slope formula, find the slope of the line through the given points. (4,9) and (6,1)
The slope formula:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have the points (4, 9) and (6, 1).
Substitute
[tex]m=\dfrac{1-9}{6-4}=\dfrac{-8}{2}=-4[/tex]
Factor the expression completely over the complex numbers.
x^4−625
Factor the expression completely over the complex numbers.
x^4+10x^2+25
[tex]x^4-625=(x^2-25)(x^2+25)=(x-5)(x+5)(x-5i)(x+5i)\\\\x^4+10x^2+25=(x^2+5)^2=((x-\sqrt5i)(x+\sqrt5i))^2=(x-\sqrt5i)^2(x+\sqrt5i)^2[/tex]
Answer:
1) [tex]x^4-625=(x+5i)(x-5i)(x+5)(x-5)[/tex]
2) [tex]x^4+10x^2+25=(x+\sqrt{5}i)^2(x-\sqrt5 i)^2[/tex]
Step-by-step explanation:
1) Given : Expression [tex]x^4-625[/tex]
To find : Factor the expression completely over the complex numbers ?
Solution :
We can re-write the expression as,
[tex]x^4-625=(x^2)^2-(25)^2[/tex]
Applying identity, [tex]a^2-b^2 = (a+b)(a-b)[/tex]
[tex]x^4-625=(x^2+25)(x^2-25)[/tex]
[tex]x^4-625=(x^2+25)(x^2-5^2)[/tex]
Again apply same identity,
[tex]x^4-625=(x^2+25)(x+5)(x-5) [/tex]
The factor of [tex]x^2+25=(x+5i)(x-5i)[/tex]
Factor form is [tex]x^4-625=(x+5i)(x-5i)(x+5)(x-5)[/tex]
2) Given : Expression [tex]x^4+10x^2+25[/tex]
To find : Factor the expression completely over the complex numbers ?
Solution :
Expression [tex]x^4+10x^2+25[/tex]
Let [tex]x^2=y[/tex]
[tex]y^2+10y+25[/tex]
To factor we equate it to zero.
[tex]y^2+10y+25=0[/tex]
Apply middle term split,
[tex]y^2+5y+5y+25=0[/tex]
[tex]y(y+5)+5(y+5)=0[/tex]
[tex](y+5)(y+5)=0[/tex]
Substitute back,
[tex](x^2+5)(x^2+5)=0[/tex]
[tex](x^2+5)^2=0[/tex]
[tex]x^2+5=0[/tex]
[tex]x^2=-5[/tex]
Taking root both side,
[tex]x=\sqrt{-5}[/tex]
[tex]x=\pm \sqrt{5}i[/tex]
So, The factors are [tex](x+\sqrt{5}i)(x-\sqrt5 i)[/tex]
Factor form is [tex]x^4+10x^2+25=(x+\sqrt{5}i)^2(x-\sqrt5 i)^2[/tex]