A rectangular garden has a length of 57 m and a width of 42 m. How many m2 will decrease the area of a garden, if the ornamental fence with a width of 60 cm will be planted inside its perimeter?

This is about slope intercept form of equation. y = 3x + 66

We are told that the equation of the straight line L is x + 3y = 18

Now, from the attached image, we can see that the line crosses the x axis at point B and the y axis at point E. These points are known as intercepts.

The x-intercept is when y = 0 while the y intercept is when x = 0. Thus;

x-intercept;

x + 3(0) = 18

x = 18

y-intercept;

0 + 3y = 18

3y = 18

y = 18/3

y = 6

This means we have two coordinates now which are;

B(18, 0) and E(0, 6)

We are told that AE = EB

From midpoint formula between two points, we can say that coordinate of point E is; (x + 18)/2 , (y + 0)/2

where x and y are coordinates of point A.

Thus; (x + 18)/2 = 0

x + 18 = 0

x = -18

Also, (y + 0)/2 = 6

y + 0 = 6 × 2

y = 12

The coordinates of point A are (-18, 6)

The equation of a line in slope intercept form is; y = mx + c

Thus; x + 3y = 18 gives; y = -(1/3)x + 18

where -1/3 is the slope

Line M passes through A and perpendicular to line L. Thus slope of line M = -1/(-1/3) = 3

Equation of Line M is; y - 12 = 3(x - (-18))

⇒ y - 12 = 3x + 54

⇒ y = 3x + 66

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Correct question:

ABCD is a rectangle. A, E and B are points on the straight line L with equation x + 3y = 18. A and D are points on the straight line M. AE = EB. Find the equation for M in the form y = ax + b where a and b are integers

For exponential function g(x)=10ˣ, the table is given below.

An exponential function is a Mathematical function in the form f (x) = aˣ, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0. The most commonly used exponential function base is the transcendental number e, which is approximately equal to 2.71828.

Exponential Growth

In Exponential Growth, the quantity increases very slowly at first, and then rapidly. The rate of change increases over time. The rate of growth becomes faster as time passes. The rapid growth is meant to be an “exponential increase”. The formula to define the exponential growth is:

y = a ( 1+ r )ˣ

Where r is the growth percentage.

Exponential Decay

In Exponential Decay, the quantity decreases very rapidly at first, and then slowly. The rate of change decreases over time. The rate of change becomes slower as time passes. The rapid growth meant to be an “exponential decrease”. The formula to define the exponential growth is:

y = a ( 1- r )ˣ

Where r is the decay percentage.

Now given function

g(x)=10ˣ

then function g(x-1)=10^(x-1)ˣ⁻¹

So, g(x)/g(x-1)=10*10ˣ⁻¹=10ˣ⁻¹=10

Therefore, the table will be as

 x             g(x)              g(x)/g(x-1)

 2             100                 10

 3               1000              10

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Answer:
the answer should be A

Step-by-step explanation:

Answer:

y = 2 [tex](3)^{x}[/tex]

Step-by-step explanation:

the standard form of an exponential function is

y = a [tex]b^{x}[/tex]

to find a and b use ordered pairs from the table

using (1, 6 )

6 = a[tex]b^{1}[/tex] , that is

6 = ab → (1)

using (3, 54 )

54 = ab³ → (2)

divide (2) by (1) on both sides

[tex]\frac{54}{6}[/tex] = [tex]\frac{ab^3}{ab}[/tex] , that is

b² = 9 ( take square root of both sides )

b = [tex]\sqrt{9}[/tex] = 3

substitute b = 3 into (1) and solve for a

6 = 3a ( divide both sides b 3 )

2 = a

then the exponential function for the table is

y = 2 [tex](3)^{x}[/tex]

Answer:

wassup my mf jsbhdhdbsidhdbududbdbdishdbjdudhdbd

Answer:

below

Step-by-step explanation:

First find the area ( pi r^2) of the endcaps...then multiply by the height

pi r^2 h =  3.14 (5^2)(5) = 392.50 cm^3

After using the deductive reasoning the procedure always produces the number 8.

Procedure:

Let the number be x.

We have to add 5 to the number x.

So the expression is x + 5.

We have to multiply the sum by 3.

Now the expression is 3(x + 5).

Now we have to subtract 7.

Now the expression is 3(x + 5) - 7.

Then we have to decrease this difference by the triple of the original number.

The triple of original number is 3x.

Now the expression is {3(x + 5) - 7} - 3x.

Now solving this expression

= {3(x + 5) - 7} - 3x.

First simplify the bracket

= 3x + 15 - 7 - 3x.

= 8

Now we can se that the after following the whole procedure the answer is 8.

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1. The area of triangle ABC = 10 units²

2. The area of triangle DEC = 2.5 units²

3. No

4. Scale factor = 2

A right triangle is defined as a triangle in which one angle is a right angle or two sides are perpendicular.

The figure is given in the question, as shown

As per the question, the required solution would be as:

1. the area of triangle ABC = 1/2 x 5 x 4  = 20/2 = 10 units²

2. the area of triangle DEC = 1/2 x (5/2) x (4/2)  = 20/8 = 2.5 units²

3. No

4. scale factor = 5/(5/2) = 2

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The question seems to be incomplete the missing part has been attached below

The solution to the algebraic expression (ab²)³/b⁵ using laws of exponents is; ab

The algebraic expression we are trying to solve is;

(ab²)³/b⁵

Now, according to laws of exponents, we have that;

1) Product Law of exponents: To multiply two expressions with the same base, add the exponents while keeping the base the same

2) Quotient Law of Exponents: To divide two expressions with the same base, subtract the exponents while keeping the base same

3) Zero Law of exponents: Any number (other than 0) raised to 0 is 1

4) Power of a power law of exponents: It states that when we have a single base with two exponents, just multiply the exponents.

We will first apply the power of a power law to get;

(ab²)³/b⁵ = ab⁶/b⁵

= ab

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The exact values of the six trigonometric functions of the angle:

sin θ =  -3/ [tex]\sqrt{13}[/tex]

cos θ =  2/ [tex]\sqrt{13}[/tex]

tan θ =  -3/2

csc θ =  - [tex]\sqrt{13}[/tex] /3

sec θ =  [tex]\sqrt{13}[/tex] / 2

cot θ = -2/3

Let us assume that θ be an angle formed with postive x-axis.

Let (x, y) = (4, -6)

This point is on the terminal side of an angle in standard position.

r = [tex]\sqrt{x^2+y^2}[/tex]

r = [tex]\sqrt{4^2+(-6)^2}[/tex]

r = [tex]2\sqrt{13}[/tex]

Now we find the value of trigonometric functions.

We know that 1) sin θ = y/r

sin θ = (-6) /  [tex]2\sqrt{13}[/tex]

sin θ = -3/ [tex]\sqrt{13}[/tex]

2) cos θ = x/r

cos θ = 4 /  [tex]2\sqrt{13}[/tex]

cos θ = 2/ [tex]\sqrt{13}[/tex]

3) tan θ = y/x

tan θ = (-6) / 4

tan θ = -3/ 2

4) csc θ = 1/( sin θ)

csc θ =1/(-3/ [tex]\sqrt{13}[/tex])

csc θ = -[tex]\sqrt{13}[/tex] / 3

5) sec θ = 1/( cos θ)

sec θ =1/(2/ [tex]\sqrt{13}[/tex])

sec θ = [tex]\sqrt{13}[/tex] / 2

6)  cot θ = 1/( tan θ)

cot θ =1/(-3/2)

cot θ = -2 / 3

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Answer:

12q=1200

12q/12=1200/12

q=100

1 quintal has 100 kg. The equation above was to show how to solve it with a variable. Hope this helps!

Step-by-step explanation:

The probability of a single value greater than 134 is given as follows:

P(X > 134) = 0.6844 = 68.44%.

The probability of the sample mean greater than 134 is given as follows:

P(M > 134) = 0.9641 = 96.41%.

The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation for this problem are given as follows:

[tex]\mu = 155, \sigma = 43.7[/tex]

The probability of a single value above 134 is one subtracted by the p-value of Z when X = 134, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Z = (134 - 155)/43.7

Z = -0.48

Z = -0.48 has a p-value of 0.3156.

Hence:

1 - 0.3156 = 0.6844 = 68.44%.

For the sample of 14, the standard error is given as follows:

[tex]s = \frac{43.7}{\sqrt{14}} = 11.68[/tex]

Hence:

Z = (134 - 155)/11.68

Z = -1.8

Z = -1.8 has a p-value of 0.0359.

Hence:

1 - 0.0359 = 0.9641 = 96.41%.

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The journal entry for the transaction will be:

Debit Cash $617,500

Credit Preferred stock   $475,000

Credit Paid up Capital in excess of Par  142,500

(Issued Preferred Stock in Cash)

A journal entry is the act of recording any transaction, whether one that is economic or not. An accounting diary that displays the debit and credit balances of a corporation lists transactions.

4,750 Preferred Stock issued at 100 Par Value at $ 130

Means $ 30($ 130-$ 100) Paid up Capital in excess of Par

Total amount Received :

Preferred Stock Par Value           = 4,750 Shares at 100       = $475,000

Paid up Capital in excess of Par  = 4,750 Shares at 30    = $ 142,500

Total Received = $ 617,500

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To solve for the value of x that would make KM ∥ JN, we can use the converse of the side-splitter theorem.

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Answer:

15 - 3 ?

Step-by-step explanation:

We will start by doing the equation on the left:

5(x-3)

Since we will substitute X for 6 the updated equation will be:

5(6-3)

We will now solve it using bodmas so it will be 6-3 which is 3. Then 3 multiplied by 5 is 15.

We will start by doing the equation on the right:

x + 13

Since we will substitute X for 6 the updated equation will be:

6 + 13

So now to simplify it all it will be:

15x = 6 + 13

The difference in length between the two rows is 3 units.

Fraction strips are rectangular pieces (electronic or paper) that represent distinct sections of the same whole. They may be taken apart and manipulated to demonstrate how different portions can be combined to produce the whole or to compare different fractional quantities for equivalence.

Let's assume that each fraction strip has a length of 1 unit. If Kendall puts four 1-unit fraction strips in one row, then the total length of that row would be 4 units. If Kendall puts one 1-unit fraction strip in the row below it, then the total length of that row would be 1 unit.

The difference in length between these two rows would be the length of the top row minus the length of the bottom row. Substituting the values we found, we get:

4 units - 1 unit = 3 units

Therefore, the difference in length between the two rows is 3 units.

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y = 45x is the equations can be used to find the number of test tubes, y , in x boxes.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

Given, There are 135 test tubes in 3 boxes.

Since, Each box has an equal number of test tubes.

Thus,

Test tubes in each box = 135/3

Test tubes in each box = 45

For expression  the number of test tubes, y , in x boxes,

Thus,

In x boxes number of test tubes = 45*x

So,

y = 45x

Therefore, equations can be used to find the number of test tubes, y , in x boxes is y = 45x.

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The required simplified value of the given root is given as x√7.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

here,
Given expression,
= √7x²
= √7 × (x²)¹/²
= x√7

Thus, the required simplified value of the given root is given as x√7.

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Answer:

69 ways.

Step-by-step explanation:

The average slope of the line is 0.5 and the slope represent the steepness of rocket.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The formula to find the slope of a line is slope = (y₂-y₁)/(x₂-x₁).

Given that, a graph of the altitude in kilometers versus the time after launch in seconds.

From the given table we have (190, 150) and (192, 151).

Slope (m) = (151-150)/(192-190)

= 1/2

= 0.5

Hence, the average slope of the line is 0.5 and the slope represent the steepness of rocket.

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Answer:

The large box contains 18.5 kg of fruit.

The small box contains 6.75 kg of fruit.

Step-by-step explanation:

We know that 3L + 2S = 69 and 5L + 6S = 133.

In order to solve for one variable, we can multiply the first equation by 3 so we can eliminate S.

The new equations are 9L + 6S = 207 and 5L + 6S = 133.

Now, we can subtract the equations from each other to solve for one variable, L.

We now get 4L = 74, and when we divide 4 from both sides, we get L = 18.5. This means that a large box has 18.5 kg of fruit.

Now that we know what the large box contains, we can plug the answer into one of the original equations to solve for S.

We now get 3(18.5) + 2S = 69, which we can solve by distributing to get 55.5 + 2S = 69, subtracting 55.5 from both sides to get 2S = 13.5, and then dividing 2 from both sides to get S = 6.75.

We now know both boxes, with the large containing 18.5 kg and the small containing 6.75 kg.

Answer:

56cm

Step-by-step explanation:

Ratio = 3 : 5 : 7

Perimeter = 120 cm

Process

# of parts = 3 + 5 +7 = 15

Divide 120 by 15 = 120 / 15

Number of parts  = 8

First side = 3 x 8 = 24 cm

Second side = 5 x 8 = 40 cm

Third side = 7 x 8 = 56 cm

Perimeter = 24 + 40 + 56 = 120 cm

The factor by which g(x) grows over the interval from 14 to 16 is 64/56 = 1.1429.

An interval is a specific range of values within a set of data. It is the difference between the maximum and minimum values of the data set, and is used to measure the spread of the data. Intervals can be used in a variety of ways, from measuring the distribution of data over time to help identify trends in the data. Intervals can also be used to find outliers or unusually high or low values in a data set. Interval data is often used in statistics to measure the variability of data.

The factor by which g(x) grows over the interval from 14 to 16 can be determined by dividing the value of g(16) by the value of g(14).
The value of g(14) is 56, and the value of g(16) is 64.
Therefore, the factor by which g(x) grows over the interval from 14 to 16 is 64/56 = 1.1429.

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As a range of values that are bound above and below the statistic's mean, a confidence interval is likely to contain an unidentified population parameter. So the statement is true.

The mean of your estimate plus and minus the range of that estimate constitutes a confidence interval. Within a specific level of confidence, this is the range of values you anticipate your estimate to fall within if you repeat the test.

In statistics, confidence is another word for probability. For many different statistical estimates, such as proportions, population means, differences between population means or proportions, and estimates of variation among groups, confidence intervals can be calculated.

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The time is spent on modern dance and hip-hop is, 17/24 hours.

A fraction is a part of whole number, and a way to split up a number into equal parts. Or, A number which is expressed as a quotient is called fraction. It can be written as the form of p : q, which is equivalent to p / q.

We have to given that;

There are 24 hours of dance lessons during the dance convention.

And, 1/3 of the time is spent on modern dance, 3/8 of the time is spent on hip hop.

Hence, The time is spent on modern dance and hip-hop is,

⇒ 1/3 + 3/8

⇒ 8/24 + 9/24

⇒ 17/24 hours

Thus, The time is spent on modern dance and hip-hop is, 17/24 hours

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Yes, there always exists a perfect match with no weak instability.

For part (a), an example of a set of men and women with preference lists for which every perfect matching has a strong instability would be if all members of one gender ranked all members of the opposite gender equally.

This would mean that no matter which pairing was chosen, one member of the pairing would prefer to be with another member.

As for part (b), an example of a set of men and women with preference lists for which every perfect matching has a weak instability would be if some members of one gender ranked all members of the opposite gender equally, while others had a strict preference.

In this case, the members with strict preferences would always have an alternative that was preferred by one or both members of the pairing, leading to weak instability.

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In a Isosceles triangle, DEF , ∆DFB is congruent to ∆DEC by SAS Congruence criteria, i.e., ∆DFB ≅ ∆DEC.

SAS congruance Criteria : If two sides and the angle between these two sides of one triangle are congruent to the corresponding sides and angle of another triangle, then the two triangles are congruent. We have a triangle DFE with base FE, see in above figure. The EC congruent to FB, i.e., FB ≅ EC. We have to prove ∆DFB ≅ ∆DEC.

Proof : It is known that ∆DEF is isocles triangle with base FE. So, two sides of triangle are equal.

In ∆DFB and ∆DEC,

=> DF = D E ( by definition of Isoceles triangle)

Also, base FB≅ EC ( since, we have)

Now, ∠DFE = ∠DEF => ∠DFB = ∠DEC ( because DE = DF in ∆DEF , corresponding angles of equal sides are equal) .

So, Two sides and the angle between the sides of one triangle, ∆DFB is congruent to the corresponding sides and angle of another triangle, ∆DEC. Therefore, by SAS Congruence criteria, Triangle DFB is congruent to triangle DEC, i.e., ∆DFB≅ ∆DEC. Hence proved..

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Complete question:

Given: ΔDFE is isosceles with base FE; FB ≅ EC. Prove: ∆DFB ≅ ∆DEC.Complete the missing parts of the paragraph proof. We know that triangle DFE is isosceles with base FE and that segment FB is congruent to segment EC because . Segment DF is congruent segment by the definition of isosceles triangle. Since these segments are congruent, the base angles, angles , are congruent by the isosceles triangle theorem. Therefore, triangles are congruent by SAS

Answer:

$490.36

Step-by-step explanation:

We can start solving the problem by using the formula for compound interest:

A = [tex]P(1+\frac{R}{n})^{nt}[/tex]

Where A is the final amount, P is the initial principal, R is the interest rate, n is the number of times the interest is compounded in a year, and t is the number of years.

First, we need to calculate the outstanding amount after 60 payments. Since the interest is 12.5% convertible semi-annually, we can use the following formula:

A = [tex]P(1+\frac{R}{2})^{2t}[/tex]

Where P = $50,000 (initial principal), R = 12.5/100 = 0.125, n = 2 (convertible semi-annually), t = 60/12 = 5 years.

A =$ [tex]$50,000(1+\frac{0.125}{2*5})[/tex]

= $ [tex]$50,000(1.0625)^{10}[/tex]

= $50,000(1.7440312)

= $87,201.56

So, the outstanding amount after 60 payments is $87,201.56

Next, we need to calculate the remaining balance after paying $10,000 as a lump sum, which is $87,201.56 - $10,000 = $77,201.56

Now, we need to calculate the monthly payments for 10 years at 11% interest convertible semi-annually. Using the formula above:

A =[tex]P(1+\frac{R}{n})^{nt}[/tex]

Where P = $77,201.56, R = 11/100 = 0.11, n = 2 (convertible semi-annually), t = 10 years.

To find the value of x, we can set up the equation:

$77,201.56 = [tex]x*(1+\frac{0.11}{2})^{2*120}[/tex] - $10,000

Solving for x gives:

x ≈ $490.36 is the monthly instalment for 10 years at 11% interest convertible semi-annually.

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