4(5x+3y) need help or get f
After factoring out, 4(5x+3y) simplifies to 20x + 12y.
What is simplification?The act of replacing a complex mathematical expression with a simpler equivalent is known as simplification (usually shorter).
An equivalent fraction is one in which the numerator and denominator are both divisible by the same non-zero number. If a fraction's numerator and denominator are both divisible by a number greater than 1, the fraction can be reduced to an equivalent fraction by reducing both its numerator and its denominator.
To simplify 4(5x+3y), we can use the distributive property of multiplication over addition:
4(5x + 3y) = 4(5x) + 4(3y)
Simplifying the multiplication:
4(5x + 3y) = 20x + 12y
Therefore, 4(5x+3y) simplifies to 20x + 12y.
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In ΔWXY, WY is extended through point Y to point Z, m∠YWX=(3x+17) , m
Angle, when two straight lines or rays intersect at a single endpoint, then an angle is created.
What is Exterior angle?The exterior angle of a triangle equals the sum of opposite interior angles. The angle between any side of a shape and a line that extends from the next side is known as the exterior angle.
∠XYZ = ∠YWX + ∠WXY
10x - 5 = 3x + 17 + 3x + 2
10x - 5 = 6x + 19
10x - 6x = 24
4x = 24
x = 6
∠WXY = 3x + 2
= 3*6 + 2
= 20°
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Write an exponential function (y=ab^x) whose graph passes through the points (2,16) and (5,128)
Answer:
Well question is not clear rewrite
can someone show me how to do this
Answer: (0, 2)
Step-by-step explanation:
The solution of a system of equations is where the lines intersect at.
We will use substitution to solve the system.
Equations:
y = 1/2x + 2
y = -1/5x + 2
Set both equations to equal each other:
1/2x + 2 = -1/5x + 2
Simplify:
7/10x = 0
x = 0
Plug 0 back in:
y = 1/2(0) + 2
y = 0 + 2
y = 2
The solution is (0, 2)
(This can also be seen by looking at the graph)
Hope this helps!
What is another way to express 63+35
Answer: 35+63
The only way to label the expression without changing our numbers is 35+63. We still get the sum of 98 and the same numbers are being used, they are just in a different order.
I hope this helped and Good Luck <3!!!
what is 2x + y = 2 in y=mx+b form?
Answer:
y=2-2x
so y=2x+2--£8;£++£
Answer: y=−2x + 2
Step-by-step explanation:
Subtract 2x from both sides of the equation.
y= 2 − 2x
Reorder 2 and −2x.
y= −2x + 2
Exam 1S22: Problem 5 Previous Problem Problem List Next Problem (8 points) Solve the following inequality. Write the answer in interval notation. x(x-7) x2 - 5x – 50 SO - Answer: Preview My Answers
In interval notation, the solution of the inequality is (25, ∞).
To solve the inequality x(x-7) < x^2 - 5x - 50, we can rearrange the terms and factor the quadratic expression:
x^2 - 7x < x^2 - 5x - 50
-2x < -50
x > 25
In interval notation, the solution is (25, ∞).
So, the answer is (25, ∞).
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What is the area of the triangle when the height is 10 and the base is 12 and the line is 13
Answer:
60
Step-by-step explanation:
Answer:
The area of the triangle is 60 unit²
Step-by-step explanation:
We know that the area of a triangle is :
[tex]A= \frac{1}{2}(Base \times Height)[/tex]
Since Base = 12 unit and Height = 10 unit
So
[tex]A= \frac{1}{2}(12\times 10)=60\\[/tex]
Hence the area of this triangle is = 60 unit²
Math part 3 question 2
[tex] \: [/tex]
[tex] \sf \: g( x ) = x - 8[/tex][tex] \: [/tex]
To find:-[tex] \sf \: ( fg ) (4) = ?[/tex][tex] \: [/tex]
Solution:-[tex] \sf \: f( x )*g( x ) = (3x²)*( x - 8)[/tex][tex] \: [/tex]
put the value of x = 4
[tex] \: [/tex]
[tex] \sf \: f( 4 )*g( 4 ) = 3(4)²*( 4 - 8 ) \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 3×16*(-4) \\ \sf \: \: \: \: \: \: \: \: \: \: \: = 48*( -4 ) \\ \: \: \: \: \underline{ \sf \red{ \: = -192 \: }}[/tex]
[tex] \: [/tex]
hope it helps! :)
A right circular cylinder has the dimensions shown below.
r = 5 cm
h = 9 cm
Find the exact surface area of the cylinder.
Include correct units.
Show all your work.
Answer:
The surface area of a right circular cylinder consists of three parts: the top and bottom circular faces, and the curved lateral surface.
The area of each circular face is given by the formula A = πr^2, where r is the radius. Therefore, the total area of the two circular faces is:
2A = 2πr^2
The lateral surface area of a cylinder is given by the formula A = 2πrh, where r is the radius and h is the height. Therefore, the lateral surface area of the cylinder is:
A = 2πrh
Substituting the given values, we get:
A = 2π(5 cm)(9 cm)
Simplifying, we get:
A = 90π cm^2
Adding the areas of the circular faces and the lateral surface, we get the total surface area:
Total surface area = 2A + A = 3A
Substituting the value of A, we get:
Total surface area = 3(90π cm^2) = 270π cm^2
Therefore, the exact surface area of the cylinder is 270π square centimeters.
Find the missing variable and indicated
angle measure.
X =
G
50°
K
H
28°
(15x-3)°
m2KHL =
J
O
The value of x is 7
What is angle on a straight line?The total sum of angles on a straight line is 180°. This means by adding all angles on a line ,it must give 180°.For example , if four angles, A, B , C ,D are align on a straight line, the sum of these angles, A+B+C +D = 180°
Therefore ;
50+28+15x-3 = 180
78-3 +15x = 180
75 +15x = 180
collect like terms
15x = 180-75
15x = 105
divide both sides by 15
x = 105/15
x = 7
therefore the value of the missing variable (x) is 7
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Joe's Plumbing Service sold 2,390 feet of 5/8-inch galvanized pipe in August. If 2,558 feet were sold in September, what is the percent increase in pipe footage sales?
7%
6.5%
14.22%
None of the above
The percent increase in pipe footage sales is approximately 7%.
To find the percent increase in pipe footage sales, use the formula:
[(New Value - Old Value)/Old Value] × 100.
In this case, the new value is the amount of pipe sold in September (2,558 feet) and the old value is the amount of pipe sold in August (2,390 feet). Plugging these values into the formula, we get:
[(2,558 - 2,390)/2,390] × 100 = [168/2,390] × 100 = 0.0703 × 100 = 7.03%
Therefore, the correct answer is 7%, which is option A. The percent increase in pipe footage sales from August to September is 7%.
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Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true? Select three options. The radius of the circle is 3 units. The center of the circle lies on the x-axis. The center of the circle lies on the y-axis. The standard form of the equation is (x – 1)² + y² = 3. The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
The radius of this circle corresponds to the radius of the circle whose answer is x2 + y2 = 9, where the circle's centre is on the x-axis.
what is circle ?In mathematics, a circle is a geometric figure made up of all the points in a sphere that are equally spaced from the circle's centre. The radius of the circle is the distance measured from any location on the circle to its centre. The width of a circle is the distance across the circle that passes through its centre, and the circumference of a circle is the distance around the circle. The equations of circles in the coordinate plane can be used to characterise them. The equation for a circle with centre (h,k) and radius r has the following conventional form:
(x - h)² + (y - k) (y - k)² = r² where (x,y) are any location on the circle's coordinates.
given
We can begin by completing the cube to rewrite the equation in standard form:
x2 - 2x + y2 = 8
(x - 1)2 + y2 = 9
We can see from this standard shape that the circle's centre is (1, 0), which is located on the x-axis. This circular has a radius of √9 units, or 3 units. Thus, the following assertions are true:
The circular has a radius of three units.
The x-axis is where the circle's middle is located.
The radius of this circle corresponds to the radius of the circle whose answer is x2 + y2 = 9, where the circle's centre is on the x-axis.
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Ms. Smith wants to buy a home theater system. which is on sale for 35% off the original price of $2299. The sales tax is 6.25%
Answer:
$948.34
Step-by-step explanation:
35% = .35
.35 x $2299
= $804.65
That is the total before the sales tax and after the sale.
6.25% = .0625
.0625 x $2299
= $143.69, and because that is 6.25% of the total, it must be added onto that as tax.
That means the total is $804.65 + $143.69
= $948.34
A helicopter spots two landing pads in opposite directions below the angle of depression to pad A to pad B is 46 and 16 degrees respectively if the straight line distance from the helicopter to pad A is 5 miles , find the distance between the landing pads.
The distance between the landing pads is approximately 12.82 miles.
What is straight line?A straight line is the shortest distance between two points in a two-dimensional space. It is a one-dimensional geometric object that extends infinitely in both directions.
Let's label the distance between the helicopter and Pad A as "x" and the distance between the helicopter and Pad B as "y". Also, let's label the distance between Pad A and Pad B as "d".
We can start by using the tangent function to find the height of the helicopter above Pad A:
tan(46) = h / x
h = x tan(46)
Similarly, we can find the height of the helicopter above Pad B:
tan(16) = h / (x + d)
h = (x + d) tan(16)
Since the helicopter is flying at a constant height, we can equate the two expressions for h and solve for d:
x tan(46) = (x + d) tan(16)
xtan(46) = xtan(16) + dtan(16)
d = x(tan(46) - tan(16)) / tan(16)
Substituting x = 5 miles and the values for the tangent functions, we get:
d = 5 (0.9851 - 0.2760) / 0.2760
d = 5 (0.7091) / 0.2760
d = 12.82 miles
Therefore, the distance between the landing pads is approximately 12.82 miles.
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What is the vertex of 2(n+9)(n-6)
Answer:
(-1.5, -112.5)
Step-by-step explanation:
f(n) = 2(n + 9)(n - 6) = 0
n = -9, n = 6
½(6 - (-9)) = ½(15) = 7.5
-9 + 7.5 = -1.5
f(-1.5) = 2(-1.5 + 9)(-1.5 - 6)
= 2(7.5)(-7.5)
= -(15 × 7.5)
= -(75 + 37.5)
= - 112.5
13 If tan(x) = 13/8 (in Quadrant-1), find 8 cos(2x) = (Please enter answer accurate to 4 decimal places.)
The value of 8 cos(2x) accurate to 4 decimal places is -3.6009.
We can start by drawing a right triangle in Quadrant 1 with an angle x, where the opposite side is 13 and the adjacent side is 8.
Using the Pythagorean theorem, we can find the hypotenuse of the triangle:
[tex]c^2 = a^2 + b^2\\ c^2 = 13^2 + 8^2\\ c^2 = 169 + 64\\ c^2 = 233\\ c = \sqrt{(233)}[/tex]
Now we can use trigonometric identities to find cos(2x):
[tex]cos(2x) = cos^2(x) - sin^2(x)[/tex]
We can find sin(x) using the triangle we drew earlier:
sin(x) = opposite / hypotenuse
sin(x) = 13 / [tex]\sqrt{(233)}[/tex]
And we can find cos(x) using the triangle as well:
cos(x) = adjacent / hypotenuse
cos(x) = 8 / [tex]\sqrt{(233)}[/tex]
Plugging these values into the identity for cos(2x):
[tex]cos(2x) = cos^2(x) - sin^2(x)\\cos(2x) = (8 / \sqrt{(233))^2} - (13 /\sqrt{(233))^2} \\cos(2x) = (64 / 233) - (169 / 233)\\cos(2x) = -105 / 233[/tex]
Finally, we can find 8 cos(2x):
8 cos(2x) = 8 * (-105 / 233)
8 cos(2x) = -3.6009 (rounded to 4 decimal places)
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In order to solve the inequality 100 - 3x>= -50, Makayla solves the equation 100 - 3x = -50 and gets x = 50. What is the solution to the inequality?
The solution to the inequality is x <= 50. This means that any value of x less than or equal to 50 will satisfy the inequality.
To solve the inequality 100 - 3x >= -50, we want to find the values of x that satisfy this inequality.
Makayla solved the equation 100 - 3x = -50 and got x = 50. This equation is not the same as the inequality we want to solve, but we can check whether Makayla's solution is a valid solution to the inequality.
Substituting x = 50 into the inequality, we get:
100 - 3x >= -50
100 - 3(50) >= -50
100 - 150 >= -50
-50 >= -50
This is a true statement, so x = 50 is a valid solution to the inequality.
However, we also need to check whether there are any other values of x that satisfy the inequality. We can do this by rearranging the inequality to isolate x:
100 - 3x >= -50
100 + 50 >= 3x
150 >= 3x
50 >= x
Therefore, the solution to the inequality is calculated to x <= 50.
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Subtract.x2+3xy−4y26x−3y−x2+xy−2y25x+3yx2+3xy−4y26x−3y−x2+xy−2y25x+3y=(Simplify your answer. Type your answer in factored form.)
The factored form is 2y(x - y) - 11x.
What is factored form?Factored form of a polynomial is when the polynomial is written as a product of its factors. Each factor is either a polynomial or a number. Factored form is useful for identifying the zeros of a polynomial and for solving polynomial equations.
To simplify the given expression, we need to combine like terms and factor if possible.
First, let's combine the like terms:
x^2 + 3xy - 4y^2 - 6x + 3y - x^2 - xy + 2y^2 - 5x - 3y
= 2xy - 2y^2 - 11x
Next, let's see if we can factor the expression:
2xy - 2y^2 - 11x
= 2y(x - y) - 11x
Since we cannot factor any further, the simplified expression in factored form is:
2y(x - y) - 11x
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Name the property illustrated.
√2+√8 is a real number
The property illustrated is
O the closure property of addition.
O the commutative property of addition.
O the associative property of addition.
O the identity property of addition.
O the inverse property of addition,
O the distributive property of multiplication over addition
O the closure property of multiplication.
O the commutative property of multiplication.
O the associative property of multiplication
O the identity property of multiplication.
O the inverse property of multiplication.
The property illustrated in "√2+√8 is a real number" is the closure property of addition,
The property illustrated in the given statement is the closure property of addition, which states that the sum of two real numbers is also a real number.
The closure property of addition states that the sum of any two real numbers is also a real number. In the given statement, √2 and √8 are both real numbers, and therefore their sum √2+√8 is also a real number.
This property applies to all real numbers, and it is an important property of the number system. which states that the sum of two real numbers is also a real number.
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If you have a 65 and you turn in a grade for 40% what would that grade turn into?
Please someone help I really need help
Answer: 26
Step-by-step explanation:
65x40%
calculate 65x0.4
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What is 10x the value of the 7/10 in 637. 739
As per the given digit value, 10 times the value of the 7 in 637.739 is 7.
To understand this problem, we need to understand the concept of place value. In our base-10 number system, each digit in a number has a specific value based on its position, or place, in the number. The rightmost digit represents the ones place, the next digit to the left represents the tens place, the next represents the hundreds place, and so on.
In the number 637.739, the digit in the tenths place is 7. This means that the 7 represents 7 tenths, or 0.7. We can see this by writing the number in expanded form:
6 hundreds + 3 tens + 7 tenths + 7 hundredths + 3 thousandths + 9 ten-thousandths
So, if we want to find 10 times the value of the digit in the tenths place (which is 7), we need to multiply 0.7 by 10:
0.7 x 10 = 7
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Find the value of x and y
.Write your answer in
simplest form.
X
45°
X =
y =
6
y
Answer:
34
Step-by-step explanation:
3dds
cylinder has a height of 16 centimeters and a radius of 4 centimeters. What is its volume? Use ≈ 3.14 and round your answer to the nearest hundredth.
By answering the above question, we may state that As a result, the cylinder cylinder's volume is around 804.23 cubic centimetres.
what is cylinder?The cylinder, which is frequently a three-dimensional solid, is one of the most fundamental curved geometric shapes. In simple geometry, it is known as a prism with a circle as its basis. The term "cylinder" is also used to refer to an infinitely curved surface in a number of modern domains of geometry and topology. A "cylinder" is a three-dimensional object made up of curved surfaces with circular tops and bottoms. A cylinder is a three-dimensional solid figure with two bases that are both identical circles connected at its height, which is defined by the separation of the bases from the centre. Cans of iced drinks and the wicks from toilet paper are examples of cylinders.
The following is the formula for a cylinder's volume:
[tex]V = \pi r^2h[/tex]
where the volume is V, the radius is r, and the height is h.
Inputting the values provided yields:
[tex]V = \pi * 4^2 * 16 = 804.24[/tex]
To the closest hundredth, we round to:
V ≈ 804.24 ≈ 804.23 (rounded to two decimal places) (rounded to two decimal places)
As a result, the cylinder's volume is around 804.23 cubic centimetres.
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At a temple to Sekhmet, there is a circular
reed bed to be planted with 4 different types
of reed, one in each of the four sections, as
shown here. The radius is 360cm and there
are two strings crossing at right angles of
lengths 560cm and 640cm.
Find out how far from the centre of the circle
the crossing point is
Therefore, the distance from the center of the circle to the crossing point of the two strings is 40sqrt(2) cm, or approximately 56.57 cm to two decimal places.
How far from the centre of the circle the crossing point is?The Pythagorean theorem can be used to calculate the distance between the circle's centre and where the two strings cross. Let A and B represent the spots where the threads converge, with O serving as the circle's centre. Next, we have:
OA2 plus OB2 equals AB2.
The circle's radius being equal to half the separation between the two strings, we get:
The equation OA = OB = sqrt((560/2)2 + (640/2)2) (156800)
And because the circle's diameter is twice its radius, we get the following equation: AB = 2 * radius = 2 * 360 = 720.
Now that we have the values, we can calculate:
2 * (156800) = AB2 => 2 * (156800) = 7202 => 313600 = 518400 - 2 * OA2 => OA2 = 102400 / 2 => OA = sqrt(51200) => OA = 40sqrt (2)
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Write an equivalent expression to m-(8-3m) without parentheses
m - (8 - 3m)
m - 8 + 3m
m + 3m - 8
4m - 8
Answer:
Step-by-step explanation:
m-(8-3m)
m-8 + 3m
=m+3m-8
=4m-8
Determine the values of a for which the system has no solutions, exactly one solution, or infinitely many solutions.x+3y−z=53x−y+2z=34x+2y+(a2−8)z=a+5Fora=there is no solution. Fora=there are infinitely many solutions. Fora=±the system has exactly one solution.
The values of a for which the system has no solutions, exactly one solution, or infinitely many solutions are a = -8, a = 8, and a ≠ ±8, respectively.
The system has no solutions when the coefficients of the variables are the same but the constants are different. In this case, the coefficients of x, y, and z are the same in the first and second equations, but the constants are different (5 and 3). Therefore, there is no solution for a = -8.
The system has infinitely many solutions when the coefficients of the variables and the constants are the same in all equations. In this case, the coefficients of x, y, and z are the same in the first and second equations, and the constants are the same (5 and 5). Therefore, there are infinitely many solutions for a = 8.
The system has exactly one solution when the coefficients of the variables are different in all equations. In this case, the coefficients of x, y, and z are different in the first and second equations, and the constants are different (5 and 3). Therefore, there is exactly one solution for a ≠ ±8.
In conclusion, the values of a for which the system has no solutions, exactly one solution, or infinitely many solutions are a = -8, a = 8, and a ≠ ±8, respectively.
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The Parks Commision hired a landscape architect to design and construct a
quadrilateral trail that connects the four sides of an isosceles trapezoid-shaped park,
with all sides of the trail the same length. The landscape architect conjectured that if
she designs the trail in the shape of a rhombus that connects the midpoint of the
adjacent sides, the trail will satisfy the Park Commission's condition for the trail's
design. Use the information on the figure below to prove the landscape architect's
conjecture.
Since the park is isosceles trapezoid-shaped, the two sides, AB and CD, that make up the parallel sides of the trapezoid are of equal length.
What is isosceles?An isosceles triangle is a type of triangle with two sides of equal length. It has two equal angles opposite of the two equal sides, and the third angle is usually different. Isosceles triangles are named after the Greek term isoskelēs, which means “equal legs”. They are very common in geometry and are used in many applications, including architecture and engineering.
We can then use the midpoints of the adjacent sides of the trapezoid, E and F, to form a rhombus. Since the rhombus is formed from the midpoints of the two parallel sides, we know that the two sides AE and CF of the rhombus are of equal length. Similarly, the two sides BE and FD of the rhombus are also equal in length. This means that the trail, if constructed in the shape of the rhombus, will have all sides of equal length, satisfying the criteria set by the Parks Commission.
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You are given that the columns of A are linearly independent. Compute the least squared error solution to \( A x=b \), \[ A=\left[\begin{array}{ll} 4 & 1 \\ 5 & 1 \\ 6 & 1 \end{array}\right], x=\left[
$$x = \frac{1}{21} \begin{bmatrix} 4b_1 + 2b_2 \\ 5b_1 - b_2 \end{bmatrix}.$$
To compute the least squared error solution to \( A x=b \), we will use the formula \(x = (A^T A)^{-1} A^T b\).
In this case, \(A = \begin{bmatrix} 4 & 1 \\ 5 & 1 \\ 6 & 1 \end{bmatrix}\), so \(A^T = \begin{bmatrix} 4 & 5 & 6 \\ 1 & 1 & 1 \end{bmatrix}\). Therefore, we have that
$$(A^T A)^{-1} A^T b = \left(\begin{bmatrix} 4 & 5 & 6 \\ 1 & 1 & 1 \end{bmatrix} \begin{bmatrix} 4 & 1 \\ 5 & 1 \\ 6 & 1 \end{bmatrix}\right)^{-1} \begin{bmatrix} 4 & 5 & 6 \\ 1 & 1 & 1 \end{bmatrix} b$$
From here, we can compute the inverse of the matrix \(A^T A\) to get
$$(A^T A)^{-1} = \frac{1}{21}\begin{bmatrix} -1 & 2 \\ 2 & -1 \end{bmatrix}$$
Substituting this into the equation above and multiplying through, we get
$$x = \frac{1}{21}\begin{bmatrix} -1 & 2 \\ 2 & -1 \end{bmatrix} \begin{bmatrix} 4 & 5 & 6 \\ 1 & 1 & 1 \end{bmatrix} b = \frac{1}{21} \begin{bmatrix} 4b_1 + 2b_2 \\ 5b_1 - b_2 \end{bmatrix}$$
Therefore, the least squared error solution to \( A x=b \) is $$x = \frac{1}{21} \begin{bmatrix} 4b_1 + 2b_2 \\ 5b_1 - b_2 \end{bmatrix}.$$
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20. Find a \( 2 \times 2 \) matrix \( A \) for which \[ \left[\begin{array}{ll} 2 & 5 \\ 1 & 3 \end{array}\right] A=\left[\begin{array}{rr} -1 & 0 \\ 4 & 2 \end{array}\right] \text {. } \]
The matrix \( A \) that satisfies the given equation is \[ A=\left[\begin{array}{rr} -1 & 0 \\ 4 & 2 \end{array}\right]. \]
To find a \( 2 \times 2 \) matrix \( A \) such that \[ \left[\begin{array}{ll} 2 & 5 \\ 1 & 3 \end{array}\right] A=\left[\begin{array}{rr} -1 & 0 \\ 4 & 2 \end{array}\right] \text {. } \], we can solve for A by multiplying both sides of the equation by the inverse of the left matrix. The inverse of \[ \left[\begin{array}{ll} 2 & 5 \\ 1 & 3 \end{array}\right] \] is \[ \left[\begin{array}{ll} -3 & 2 \\ 5 & -2 \end{array}\right]. \] Multiplying both sides of the equation by this inverse gives \[ \left[\begin{array}{ll} -3 & 2 \\ 5 & -2 \end{array}\right] \left[\begin{array}{ll} 2 & 5 \\ 1 & 3 \end{array}\right]A= \left[\begin{array}{ll} -3 & 2 \\ 5 & -2 \end{array}\right] \left[\begin{array}{rr} -1 & 0 \\ 4 & 2 \end{array}\right], \] which simplifies to \[ A=\left[\begin{array}{rr} -1 & 0 \\ 4 & 2 \end{array}\right]. \] Thus, the matrix \( A \) that satisfies the given equation is \[ A=\left[\begin{array}{rr} -1 & 0 \\ 4 & 2 \end{array}\right]. \]
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