Find the length of the midsegment of the trapezoid with the vertices 0,3 2,5 6,4 2,0

Answer:

see explanation

Step-by-step explanation:

let length be l and width be w , then perimeter P is

P = 2(l + w)

given P = 20 , then

2(l + w) = 20 ( divide both sides by 2 )

l + w = 10 ( subtract w from both sides )

l = 10 - w → (1)

area (A) is calculated as

A = lw

given A = 24 , then

lw = 24

substitute l = 10 - w into this equation

(10 - w)w = 24

10w - w² = 24 ( subtract 24 from both sides )

10w - w² - 24 = 0 ( multiply through by - 1 and rearrange )

w² - 10w + 24 = 0 ← in standard form

(w - 4)(w - 6) = 0 ← in factored form

equate each factor to zero and solve for w

w - 4 = 0 ⇒ w = 4

w - 6 = 0 ⇒ w = 6

substitute these values into (1)

w = 4 : l = 10 - 4 = 6

w = 6 : l = 10 - 6 = 4

Then

length = 6 cm , width = 4 cm

or

length = 4 cm , width = 6 cm

The correct statement is the area of the two inner squares on the left must be the same as the area of the inner square on the right.

A square is a geometric shape with four equal sides and four right angles. It is a type of rectangle, and also a type of parallelogram. In a square, all interior angles measure 90 degrees, and the diagonals bisect each other at 90-degree angles.

there are two identical squares, each with an area of 52 square units (since each side measures 7 units). The two squares are arranged in such a way that they form a larger square with sides measuring 14 units. The area of this larger square is 142 square units.

there is also a square with sides measuring 13 units. This square has an area of 132 square units.

If we subtract the area of the two inner squares from the area of the larger square in the left figure, we get:

142 - 2(52) = 38

This means that the four triangles in the right figure must have a total area of 38 square units, which is the difference between the area of the large square (132 square units) and the area of the inner square (94 square units). Since the four triangles are congruent, each triangle must have an area of 9.5 square units.

Therefore, the area of the two inner squares on the left must be the same as the area of the inner square on the right, since they all have an area of 94 square units (which is the area of the large square minus the area of the four triangles). This leads to the relationship:

52 + 122 = 132

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Robert Wadlow's height is more extreme than Chandra Bahadur Dangi's height.

Robert Wadlow is more extreme than Chandra Bahadur Dangi. To calculate this, we need to use the formula for standard deviation:

Standard Deviation (SD) = (Individual measurement - Mean) / SD

For Robert Wadlow, his height of 272 cm is 97.88 cm higher than the mean of 174.12 cm. Using the formula, this translates to a standard deviation of 13.77:

SD = (272 - 174.12) / 7.10 = 13.77

For Chandra Bahadur Dangi, his height of 54.6 cm is 119.52 cm lower than the mean of 174.12 cm. Using the same formula, this translates to a standard deviation of 16.87:

SD = (54.6 - 174.12) / 7.10 = -16.87

Since Robert Wadlow has a larger standard deviation than Chandra Bahadur Dangi, his height is more extreme.

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The original price of the goods was RM 39.13

Suppose that the original price is P, if we have an increase of x (where x is the decimal form of a percentage) the new price will be given by:

P' = P*(1 + x)

In this case the percentage is 15%, then x = 15%/100% = 0.15

Now we know that the final price is RM 45, then we can write the equation:

45 = P*(1 + 0.15)

45 = P*1.15

Solving this for P:

P = 45/1.15 = 39.13

The original price was RM 39.13

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The approximate probability of acceptance if the true proportion of non conformances in the lot is 10% is 0.964

To find the approximate probability of acceptance, we can use the binomial distribution. Let's define the following variables

n = 50 (sample size)

p = 0.1 (true proportion of nonconformances in the lot)

q = 1 - p = 0.9 (true proportion of conformances in the lot)

k = 0, 1, 2, ..., 5 (number of nonconformances allowed)

The probability of accepting the lot is the probability of observing k or fewer nonconformances in a sample of size n

P(X ≤ k) = Σ [n choose i] p^i q^(n-i), i=0 to k

Using a binomial calculator or software, we can find the probability of acceptance to be

P(X ≤ 5) ≈ 0.964

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The probability that exactly two couples state incompatibility as the reason is equal to the probability of two couples citing incompatibility and two couples not citing it.

HTML formatted answer: Given: 65% of all divorce cases cite incompatibility as the underlying reason. To find: Probability that exactly two will state incompatibility as the reason. Solution: As per the given data, The probability of citing incompatibility as the underlying reason for divorce is 65%.

Then, the probability of citing any other reason is (100% - 65%) = 35%.Let the probability of citing incompatibility by any couple as A, and the probability of not citing incompatibility by any couple as B. Here, the total couples filing for divorce = 4. Probability of two couples citing incompatibility and two couples not citing it.P(2C, incompatibility and 2C, not incompatibility)= \[\left( \begin{matrix}
  4  \\
  2  \\
\end{matrix} \right)\] × 0.65² × 0.35²The probability of choosing any 2 out of 4 couples = \[\left( \begin{matrix}
  4  \\
  2  \\
\end{matrix} \right)\] = 6The probability of 2 couples citing incompatibility = 0.65²The probability of 2 couples not citing incompatibility = 0.35²Hence,The probability that exactly two couples state incompatibility as the reason isP(2C, incompatibility) = \[\left( \begin{matrix}
  4  \\
  2  \\
\end{matrix} \right)\] × 0.65² × 0.35² = 6 × 0.4225 × 0.1225 = 0.3218Therefore, the required probability is 0.3218.

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Answer: x = 27

Step-by-step explanation:

we know that vertical angles are equal to each other, so

4x + 7 = [ 5 (x - 4) ]

distribute

4x + 7 = 5x - 20

subtract 4x from each side to combine variables

4x - 4x + 7 = 5x - 4x - 20

simplify

7 = x - 20

add 20 to both sides to solve for x

7 + 20 = x -20 + 20

simplify

27 = x

check your work, substitute value of x into equation

4x + 7 = 5x - 20

4(27) + 7 = 5(27) - 20

108 + 7 = 135 - 20

115 = 115

solution equals and is true, problem solved!

The area of the composite figure is 47 cm².

The perimeter of the composite figure is 36 cm.

The figure above is a composite figure because it's compose of two shapes.

Therefore, we have to find the area of the individual shape and sum it  to get the area of the composite figure.

Hence,

area of the composite figure = area of the rectangle1 + area of the rectangle2

55 mm = 5.5 cm

area of the rectangle1  = 2 × 5.5 = 11 cm²

60mm = 6 cm

l = 2 + 6 = 8cm

w = 10 - 5.5 = 4.5 cm

area of the rectangle2 = 8 × 4.5

area of the rectangle2 = 36 cm²

Therefore,

area of the composite figure = 36 + 11 = 47 cm²

perimeter of the composite figure = 2 + 10 + 8 + 4.5 + 6 + 5.5

perimeter of the composite figure =  36 cm

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[tex]\textit{internal division of a line segment using ratios} \\\\\\ P(1,-2)\qquad Q(4,10)\qquad \qquad \stackrel{\textit{ratio from P to Q}}{2:1} \\\\\\ \cfrac{P\underline{T}}{\underline{T} Q} = \cfrac{2}{1}\implies \cfrac{P}{Q} = \cfrac{2}{1}\implies 1P=2Q\implies 1(1,-2)=2(4,10)[/tex]

[tex](\stackrel{x}{1}~~,~~ \stackrel{y}{-2})=(\stackrel{x}{8}~~,~~ \stackrel{y}{20}) \implies T=\underset{\textit{sum of the ratios}}{\left( \cfrac{\stackrel{\textit{sum of x's}}{1 +8}}{2+1}~~,~~\cfrac{\stackrel{\textit{sum of y's}}{-2 +20}}{2+1} \right)} \\\\\\ T=\left( \cfrac{ 9 }{ 3 }~~,~~\cfrac{ 18}{ 3 } \right)\implies T=(3~~,~~6)[/tex]

Answer:

3.5

Step-by-step explanation:

3x -(y / 2+ 5)                     x = 3.5 and y = 4

= 3(3.5) -(4/2 + 5)

= 3(3.5) -(2 + 5)

= 10.5 -(2 + 5)

= 10.5 -(7)

= 10.5 - 7

= 3.5

Explanation:

There are 12 makes and 16 total free throws.

The ratio of makes to total is 12:16. The order is important. We list the makes first, then the total second.

Divide both parts of that ratio by the GCF 4

12:16 reduces to 3:4

It means for every 3 free throws made, the basketball player has attempted 4 free throws total.

Sean and his six companions will each receive 1/7 of the original action figures.

Let's assume Sean originally had x action figures. After donating some, he has 1/3 of them left, which is (1/3)x.

To find out how many action figures Sean has left, we can use the equation:

(1/3)x = x - y

where y is the number of action figures Sean donated.

Simplifying this equation, we get:

y = (2/3)x

Now, Sean wants to share his remaining action figures with 6 friends, so they will split the total number of action figures into 7 equal parts (Sean + 6 friends).

Therefore, each person will get 1/7th of the total number of action figures.

To find out what fraction of the original action figures each person will get, we need to divide the number of action figures each person will get by the original number of action figures (x):

1/7 = [tex]\frac{[(\frac{1}{3} )x - y]}{x}[/tex]

Substituting y = (2/3)x, we get:

1/7 = [tex]\frac{[(\frac{1}{3} )x - (\frac{2}{3} )x]}{x}[/tex]

1/7 = (1/3)

Therefore, each person will get 1/7th of the original number of action figures.

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Answer:

(k+4)(k-6)

(2k+1)(2k-1)

(x+7)(x+4)=0

The probability that at any given time, all three users are transmitting simultaneously is option (b) 0.001

Probability is a measure of the likelihood or chance of an event occurring. It is a number between 0 and 1, where 0 indicates that the event is impossible and 1 indicates that the event is certain to occur.

The question asks about the probability of all three users transmitting simultaneously on a shared 4Mbps link, given that each user transmits only 10% of the time.

Assuming that the transmission of each user is independent of the others, the probability of all three users transmitting simultaneously can be calculated using the binomial distribution as follows

P(all three transmitting) = (0.1)^3 = 0.001

Therefore, the correct option is (b) 0.001

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Answer:

Proofs attached to answer

Step-by-step explanation:

Proofs attached to answer

The graph of [tex]y=x^2+10x+21[/tex] includes a vertex at (-5, 17) and two roots at (-6, 0) and (-4, 0).

To graph the equation [tex]y=x^2+10x+21[/tex], we can complete the square to find the vertex and use the quadratic formula to find the roots.

First, we'll find the vertex. We can do this by adding and subtracting [tex](10/2)^2 = 25[/tex] inside the parentheses:

[tex]y = x^2 + 10x + 21[/tex]

[tex]y = (x^2 + 10x + 25) - 4 + 21[/tex]

[tex]y = (x + 5)^2 + 17[/tex]

So the vertex is (-5, 17).

Next, we'll find the roots using the quadratic formula:

x = (-b ± sqrt([tex]b^2 - 4ac[/tex]))/(2a)

where a = 1, b = 10, and c = 21.

x = (-10 ± sqrt([tex]10^2 - 4[/tex](1)(21)))/(2(1))

x = (-10 ± sqrt(4))/(2)

x = -5 ± 1

So the roots are x = -6 and x = -4.

Now we can plot the vertex at (-5, 17) and the roots at (-6, 0) and (-4, 0) on the accompanying set of axes.

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Tο make a wοοden lid fοr a decοrative bοx with the given dimensiοns, yοu will need tο cut a rectangular piece οf wοοd with dimensiοns 10 1/2 inches by 12 1/2 inches. This will allοw fοr the 2 inch deep sides tο be added tο the lid.

In a twο-dimensiοnal space, area is a unit used tο describe hοw big a surface οr regiοn is. It is measured in terms οf square measurements like square inches (in2), square metres (m2), οr square feet (ft2). A shape's area can be calculated using a variety οf fοrmulas, including multiplying the shape's length by its breadth.

The area οf a rectangle, fοr instance, can be calculated using the fοrmula A = l w, where A denοtes the area and l, w, and w are the length and breadth respectively. Geοmetry, physics, architecture, and building are just a few οf the fields in which the cοncept οf area is applied.

Tο calculate the dimensiοns οf the rectangular piece οf wοοd needed fοr the lid, yοu need tο add twice the depth οf the sides (2 inches) tο each οf the width and length οf the lid:

Width οf wοοden lid = 6 1/2 inches + 2 inches + 2 inches = 10 1/2 inches

Length οf wοοden lid = 8 1/2 inches + 2 inches + 2 inches = 12 1/2 inches

Therefοre, the rectangular piece οf wοοd needed fοr the lid shοuld be 10 1/2 inches by 12 1/2 inches.

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Complete Question:

Wendell wants to make a wooden lid for a decorative box.

The lid needs to be 6 1/2inches wide and 8 1/2inches long with sides 2 inches deep.

Part A

Find the area of wood that Wendell will need to make the lid.

Drag numbers to complete the measurements.

Each tile may be used once or not at all.

Answer:

1256 in.3

Step-by-step explanation:

V = pi x r^2 x h
V = 3.14 x 20/2 x 4
V = 3.14 x 10 x 4

V = 1256in^3

Answer:

1256 in³

Step-by-step explanation:

To calculate volume of a cylinder the formula is: π · r2 · h

Since Pi is already given to us as 3.14, we now have to find the radius

The radius is always the diameter cut in half meaning it will be 20/2 which gives us 10 (radius is figured)

The height is given to us as 4 meaning the equation will be

3.14 x 10 x 10(seeing as it's radius squared) x 4

10x10 = 100

100 x 4 = 400

400 x 3.14 = 1256

The answer is in cubed(³) because it is volume

Considering a six-sided spinner, it is found that the probability of spinning a 1 and tossing a head is of [tex]\dfrac{1}{12}[/tex].

A probability is given by the number of desired outcomes divided by the number of total outcomes.

In this problem:

Since the events are independent, the probability of spinning a 1 and tossing a head is given by:

[tex]\text{p}=\dfrac{1}{6} \times\dfrac{1}{2} =\dfrac{1}{12}[/tex]

The ratio of the area of circle A to the area of circle B is 100 : 64.

What is ratio?

A ratio is a mathematical expression that compares the magnitude or size of two or more quantities.

The circumference of a circle is directly proportional to its radius. Therefore, if the circumference of circle B is 80% of the circumference of circle A, then the ratio of their radii is also 80%.

Let's assume that the radius of circle A is r. Then, the radius of circle B is 0.8r.

The area of a circle is proportional to the square of its radius. Therefore, the ratio of the areas of circle A to circle B is:

[tex](Area of circle A) : (Area of circle B) = r^2 : (0.8r)^2\\\\= r^2 : 0.64r^2\\\\= 100 : 64[/tex]

Therefore, the ratio of the area of circle A to the area of circle B is 100 : 64.

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Answer:

width = 44

Step-by-step explanation:

let l be length then width = 4l

the perimeter (P)  of a rectangle is calculated as

P = 2(l + w)

given P = 110 , then

2(l + 4l) = 110 ( divide both sides by 2 )

l + 4l = 55

5l = 55 ( divide both sides by 5 )

l = 11

then

width = 4l = 4 × 11 = 44

Answer:

with = 44

Step-by-step explanation:

let the lenght l, = x

b or width = 4x

Perimeter of rectangle = 2(l + b)

110 = 2( x + 4x )

110 = 2( 5x )

110 = 10x

10x = 110

x = 110/10

x = 11

Therefore width = 4x

width = 4 (11)

with = 44

Therefore, approximately 65.9 square feet of paint will be needed to cover all visible surfaces of the rocket ship float.

Surface area is the measure of the total area that the surface of an object occupies. It is the sum of all the areas of the individual faces or surfaces of the object. For example, if you have a cube, the surface area would be the sum of the areas of all six faces of the cube. The surface area is usually measured in square units, such as square meters, square centimeters, or square feet, depending on the system of measurement used. Surface area is an important concept in many fields of study, including mathematics, physics, chemistry, and engineering.

by the question.

To calculate the total surface area that needs to be painted, we need to find the surface area of the cylinder and the surface area of the cone, and then add them together.

Surface area of the cylinder:

The cylinder has a radius of 1.5 feet and a height of 4 feet. The formula for the surface area of a cylinder is:

[tex]SA_cylinder = 2πrh + 2πr^2[/tex]

where r is the radius and h is the height of the cylinder.

Plugging in the values, we get:

[tex]SA_cylinder = 2π(1.5)(4) + 2π(1.5)^2\\SA_cylinder = 12π + 4.5π\\SA_cylinder = 16.5π[/tex]

[tex]SA_cylinder = 51.8 ft²[/tex] (rounded to the nearest tenth)

Surface area of the cone:

The cone also has a radius of 1.5 feet, and a height of 2 feet. The formula for the surface area of a cone is:

[tex]SA_cone = πr√(r^2 + h^2)[/tex]

Plugging in the values, we get:

[tex]SA_cone = π(1.5)√(1.5^2 + 2^2)\\SA_cone = π(1.5)√(2.25 + 4)\\SA_cone = π(1.5)√6.25[/tex]

[tex]SA_cone = π(1.5)√(1.5^2 + 2^2)\\SA_cone = π(1.5)√(2.25 + 4)\\SA_cone = π(1.5)√6.25[/tex] (rounded to the nearest tenth)

Total surface area:

Adding the surface area of the cylinder and the surface area of the cone, we get:

[tex]Total SA = SA_cylinder + SA_cone[/tex]

Total SA ≈ 65.9 ft² (rounded to the nearest tenth)

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Rounded to the nearest tenth of a square foot, the area that needs to be painted is 76.9 square feet.

What exactly is a cylinder?

In geοmetry, a cylinder is οne οf the fundamental 3d fοrms with twο parallel circular bases at a distance.

The first step is to calculate the lateral surface area of the cylinder and cone. The lateral surface area of the cylinder is the product of the height and the circumference of the base, which is:

4 feet x 2π(1.5 feet) = 12π square feet

The lateral surface area of the cone is half the product of the slant height and the circumference of the base, which is:

1/2 x 2π(1.5 feet) x √(2^2 + 1.5^2) = 7.5π square feet

The total area to be painted is the sum of the lateral surface areas of the cylinder and cone, plus the area of the base of the cone, which is congruent to the base of the cylinder. The base has a radius of 1.5 feet, so the area of each base is:

π(1.5 feet)^2 = 2.25π square feet

The total area to be painted is:

12π + 7.5π + 2(2.25π) = 24.5π square feet

Using a calculator, this is approximately equal to 76.95 square feet.

Therefore, Rounded to the nearest tenth of a square foot, the area that needs to be painted is 76.9 square feet.

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Answer:

7

Step-by-step explanation:

f(x) = 6 + 3 - 2

= 7

f(x) = 13 + 3 - 2

= 14

According to the given information, option (b) is the correct answer.

What is an algebraic expression?

An algebraic expression is a mathematical phrase that can contain numbers, variables, and mathematical operations such as addition, subtraction, multiplication, and division. Algebraic expressions are used to represent quantities or values that can vary, depending on the values assigned to the variables in the expression. Algebraic expressions can be simple or complex, and they can have one or more variables.

b) 2/11d¹² is the equivalent expression for 4d⁻³ /22d⁹.

To simplify the expression, we can use the rule of negative exponents: d⁻ⁿ = 1/dⁿ

So, 4d⁻³ /22d⁹ = 4/22d¹² = 2/11d¹²

Therefore, option (b) is the correct answer.

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a. We get that it will take approximately 108 months, or 9 years, to double the value of the tithe. b. annual interest rate of approximately 5.84% c. approximately $27,714.28.

In finance, interest refers to the cost of borrowing money or the return on invested money. It is the compensation paid by a borrower to a lender for the use of their money or the compensation paid by an institution to an individual or organization for depositing money with them.

a. Using the TVM Solver with the given information, we get:

Present value (PV) = -$35,000 (since it is a tithe, we are starting with a negative value)

Future value (FV) = $70,000 (since we want the tithe to double in value)

Interest rate (I/Y) = 7.75/12 (since the APR is compounded monthly)

Number of periods (N) = ? (this is what we want to find)

Solving for N, we get that it will take approximately 108 months, or 9 years, to double the value of the tithe.

b. Using the compound interest formula, we have:

A = P(1 + r/n)ⁿˣ

where A is the future value, P is the present value, r is the annual interest rate, n is the number of times per year the interest is compounded, and x is the number of years.

Plugging in the given values, we get:

$50,000 = $22,500(1 + r/2)²*¹⁴

Solving for r, we get that an annual interest rate of approximately 5.84% (compounded semi-annually) is required for the $22,500 to accumulate to $50,000 in 14 years.

c. Using the TVM Solver with the given information, we want to solve for the present value (PV):

Future value (FV) = $40,000

Interest rate (I/Y) = 4.25/4 (since the APR is compounded quarterly)

Number of periods (N) = 9

Payment (PMT) = 0 (since there are no regular payments)

Solving for PV, we get that the present value required to return $40,000 in 9 years at 4.25% APR compounded quarterly is approximately $27,714.28.

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According to the question the area of the smaller rectangle is 0.04 times the area of the larger rectangle.

The surface area of an object is the sum of all the shapes that make up its surface. This kind of rectangle's area is calculated by multiplying its length and breadth.

Given,

To solve this problem, we first need to find the length of the larger rectangle, which we can do using the fact that the two rectangles are similar, meaning their corresponding sides are in proportion.

We can set up a proportion using the widths of the two rectangles:

12 cm / 15 cm = 6000 mm / x

where x is the length of the larger rectangle in millimeters.

We could cross-multiply and simplify to find x's value:

12 cm * x = 15 cm * 6000 mm

x = (15 cm * 6000 mm) / 12 cm

x = 7500 mm

So the length of the larger rectangle is 7500 mm.

To determine the scale factor used to enlarge the smaller rectangle, we can divide the corresponding sides of the two rectangles. Since we know the width of the smaller rectangle is 12 cm and the width of the larger rectangle is 6000 mm (which is equivalent to 60 cm), we can set up the proportion:

12 cm / 60 cm = 1/5

So the scale factor used to enlarge the smaller rectangle is 1/5 or 0.2.

Finally, we can find the relationship between the areas of the two rectangles by using the fact that the ratio of the areas of two similar shapes is equal to the square of the scale factor. In this case, the scale factor is 0.2, so:

Area of smaller rectangle / Area of larger rectangle = (0.2)^2

Area of smaller rectangle / Area of larger rectangle = 0.04

Therefore, the area of the smaller rectangle is 0.04 times the area of the larger rectangle.

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In the word problem, Johnson set aside $80 for food party.

What is percentage?

Divide the A value or ratio that may be stated as a fraction of 100 is referred to in mathematics as a number by the total and multiply by 100 to find the percent of a given number. Therefore, the percentage refers to a portion per hundred. Per 100 is what the word percentage signifies. The letter "%" stands for it.

Here Total money  that Johnson has is 100%.

In 100% of money he spent $320 and set aside 25%.

Then Money he spent = 100%-25% = 75%.

Then,

100% = 320

25% = x

=> x = [tex]\frac{320\times25\%}{100\%}[/tex]  = $80.

Hence Johnson set aside $80 for food party.

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Answer:

yes this is because to find similarity of triangles two interior angles must be the same which automatically means that the lat angle would be the same

Neither of the two points is a solution of the linear equation.

Here we have the linear equation.

2x - y = 1

And we have the graph of this line.

We want to check if the points (0, 1/2) and (-7, -3) are solutions.

You can do this in two ways, one is finding the points on the coordinate axis and check if the points lie on the line, the other is replace the values in the eequation and see if it becomes true.

Because the graph is really small in the image, I will do the second one.

For (0, 1/2) we have:

2*0 - 1/2 = 1

0 - 1/2 = 1

-1/2 = 1

This is false.

For the second (-7, -3) we have:

2*-7 - (-3) = 1

-14 + 3 = 1

-11 = 1

This is false.

Neither of the points is on the line.

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Answer:

The amount for loss would be RM 600 and the amount for profit would be RM 600.

Step-by-step explanation:

Loss percent

25=loss/CP *100

25/100=L/CP *100

25/100=100L/240,000

10000L/10000=240,000*25/10000

L=24*25

L=RM 600

Profit percent

25/100=P/240,000 *100

25/100= 100P/240000

10000P/10000=240000*25/10000

P=RM 600

Answer:

Step-by-step explanation:

RM (⁠≧⁠▽⁠≦⁠)