Classify each pair of lines as parallel, perpendicular, or neither.
2y = x and y = -2x + 6
y + 3x = 1 and 2y = -6(x - 1)
3y + 2x = -3 and 4y = 6x + 12
y + 2 = 5x and 5y - x = -2 ​

Step-by-step explanation:

(a) The slope of the equation y = 9x + 15 is 9, and the y-intercept is 15.

(b) The rate of change or slope of the equation y = 9x + 15 is 9, which represents the constant rate at which the workers are picking oranges. For every hour of work, they pick 9 more oranges. The initial amount or y-intercept of 15 represents the number of oranges they would have picked if they had started working from the beginning of time. However, since this is not possible, it can be interpreted as the number of oranges they picked before starting to work for the period of time that is being measured.

The equation for the number of baskets is an illustration of a linear function.

The function is given as:

[tex]\bold{y=9x+15}[/tex]

(a) The slope and the y-intercept

A linear function is represented as:

[tex]\bold{y=mx+b}[/tex]

Where:

m represents the slope, and b represents the y-intercept

By comparison, the slope is 9, and the y-intercept is 15

(b) The rate of change and the initial amount

The rate of change is the slope, and the initial amount is the y-intercept

By comparison, the rate of change is 9, and the is 15

In a lab experiment, the number of bacteria on a petri dish began at 7400 and is now increasing exponentially at a rate of 13% per hour. P(t) = [tex]7400(1 + 0.13)^t[/tex] is a function that may be used to represent the population of bacteria after t hours and in which a constant can be used to calculate the rate of change each minute. The rate of change in percentage is 0.21667% per minute.

The function to represent the population of bacteria after t hours can be expressed as:

P(t) = [tex]7400(1 + 0.13)^t[/tex]

where P(t) is the population of bacteria after t hours, 7400 is the initial population, and 0.13 is the growth rate per hour expressed as a decimal.

To find the rate of change per minute, we need to convert the growth rate per hour to a growth rate per minute. There are 60 minutes in an hour, so the growth rate per minute can be found by dividing the growth rate per hour by 60:

0.13/60 = 0.0021667 (rounded to seven decimal places)

So the growth rate per minute is approximately 0.0021667 or 0.21667% (rounded to two decimal places).

Therefore, the function to represent the population of bacteria after t hours is:

P(t) = [tex]7400(1 + 0.13)^t[/tex]

and the rate of change per minute is approximately 0.21667%.

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Step-by-step explanation:

1) area= 2.4^2×3.14=18.0864

rounded=18ft^2

circumference= 4.8×3.14=15.072

rounded= 15ft

2) area= 6^2×3.14=113.04

rounded= 110ft^2

circumference= 12×3.14=37.68

rounded= 38ft

3) area= 32^2×3.14=3215.36

rounded=3220ft^2

circumference= 64×3.14=200.96

rounded=200ft

The value of such that the matrix is the augmented matrix of a linear system with The system has an infinite number of solutions if $k=-1$.

To find out the value of $k$ that results in the matrix being the augmented matrix of a linear system with infinitely many solutions, you need to reduce the matrix to row echelon form and check the conditions. If you get a row of all zeroes but the last entry in that row is not zero, then there is no solution. If you get a row of all zeroes including the last entry in that row, then there are infinitely many solutions. Therefore, the value of $k$ that leads to the augmented matrix of a linear system with infinitely many solutions is $k=-1$.

A system of linear equations has an infinite number of solutions if and only if its augmented matrix, after being transformed to row-echelon form, has at least one free variable column.

The matrix in question is given as:

[tex]$$\begin{bmatrix}2 & -2 & 4 \\ -3 & 3 & -6 \\ 1 & -1 & k\end{bmatrix}$$[/tex]

To find the value of $k$, we need to convert it to a row-echelon form.

[tex]$$ \begin{bmatrix}2 & -2 & 4 \\ -3 & 3 & -6 \\ 1 & -1 & k\end{bmatrix} \overset{R2\rightarrow R2+\frac{3}{2}R1}{\longrightarrow} \begin{bmatrix}2 & -2 & 4 \\ 0 & 0 & 0 \\ 1 & -1 & k\end{bmatrix} $$[/tex]

Notice that the second row of the matrix is all zeros, so the system either has no solution or has an infinite number of solutions. Therefore, we need to determine the value of $k$ to figure out which of the two cases apply. Since the third row is independent, we can choose to work with it only.

[tex]$$1a - 1b = c \rightarrow c = a - b$$[/tex]

We can also write it as a linear combination of $a$ and $b$:

[tex]$$\begin{aligned} c &= a - b \\ &= a(1) + b(-1) \end{aligned}$$[/tex]

Therefore, it follows that if $k$ equals -1, we can rewrite the last row as a linear combination of the first two rows.

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The value of x in the given triangle is 36.87°.

One of the six functions in mathematics is the trigonometric function (sine [sin], cosine [cos], tangent [tan], cotangent [cot], secant [sec], and cosecant [csc]) In trigοnοmetry, sin cοs and tan values are the primary functiοns we cοnsider while sοlving trigοnοmetric prοblems. These trigοnοmetry values are used tο measure the angles and sides οf a right-angle triangle. Apart frοm sine, cοsine and tangent values, the οther three majοr values are cοtangent, secant and cοsecant.

According to Trigonometric function,

Tan θ = Opposite side/Adjacent side

Therefore,

Tan θ = 6/8

θ = arctan(6/8)

θ ≈ 36.87°

This is simplest way to calculate, there is no other way to calculate.

Thus, the value of x in the given triangle is 36.87°.

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the derivative of y = sec⁻¹(1/x) with respect to x is -1/√(1 - x²). To find the derivative of y = sec⁻¹(1/x), we will use the chain rule of differentiation. Let's start by using the definition of the inverse secant function:

sec⁻¹(θ) = cos⁻¹(1/θ)

Then we can rewrite the given function as:

y = cos⁻¹(x)

Using the chain rule, the derivative of y with respect to x is:

dy/dx = d/dx [cos⁻¹(x)]

= -1/√(1 - x²) * d/dx [x]

= -1/√(1 - x²)

Therefore, the derivative of y = sec⁻¹(1/x) with respect to x is -1/√(1 - x²).

We can check this result by taking the derivative of y using the definition of the inverse secant function:

y = sec⁻¹(1/x)

sec(y) = 1/x

cos(y) = x

-sin(y) dy/dx = 1

dy/dx = -1/sin(y)

Using the Pythagorean identity sin²(y) + cos²(y) = 1, we can solve for sin(y) as:

sin(y) = √(1 - cos²(y)) = √(1 - x²)

Substituting this expression into the derivative, we get:

dy/dx = -1/√(1 - x²)

which is the same result we obtained using the chain rule. Therefore, we have confirmed that the derivative of y = sec⁻¹(1/x) with respect to x is -1/√(1 - x²).

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As a result, the probability that individuals spend between 24.7 as well as 25.5 minutes per day on average reading books is roughly 0.919, or 91.9%.

The probability that an occurrence will occur is determined by probability: P(A) = f / N. Probability and odds are linked, but probability determines what the percentages are.

Given:

Sample size (n) = 50

Sample mean (x) = 25 minutes

Standard deviation (σ) = 1.5 minutes

Range of interest: 24.7 minutes ≤ x ≤ 25.5 minutes

To find the probability that the mean time spent reading each day is between 24.7 and 25.5 minutes, we need to standardize the sample mean using the Central Limit Theorem and the z-score formula:

z = (x - μ) / (σ / √(n))

where μ is the population mean (unknown), σ is the population standard deviation (known), and √(n) is the square root of the sample size.

We can approximate the population mean with the sample mean since the sample size is large (n ≥ 30) and assume a normal distribution for the sample mean.

First, we standardize the lower bound of the range:

z1 = (24.7 - 25) / (1.5 / √(50)) = -1.76

Then, we standardize the upper bound of the range:

z2 = (25.5 - 25) / (1.5 / √(50)) = 1.76

Using a standard normal distribution table or calculator, we can find the area under the curve between z1 and z2:

P(-1.76 ≤ z ≤ 1.76) ≈ 0.919

Therefore, the probability that the mean time people spend reading books each day is between 24.7 and 25.5 minutes is approximately 0.919 or 91.9%.

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A. Investment 1: ROI = 20%, Investment 2: ROI = 18%, Investment 3: ROI = 24%. B. Select Investment 3 with the highest ROI of 24% as it generates the most return for the investment amount.

C. Investment 3 is attractive with positive residual income, but from Brown's perspective, the imputed interest charge may reduce overall profitability.

A. To calculate the ROI for each investment, we can use the following formula:

ROI = (Income / Investment) x 100%

For Investment 1: ROI = (50,000 / 250,000) x 100% = 20%

For Investment 2: ROI = (54,000 / 300,000) x 100% = 18%

For Investment 3: ROI = (96,000 / 400,000) x 100% = 24%

B. If the manager's focus is on Glengarry's divisional performance, he would select Investment 3 because it has the highest ROI of 24%. This investment generates the highest return for the amount invested, which is the primary concern for divisional performance.

C. To calculate the residual income for Investment 3, we need to subtract the imputed interest charge from its profit margin traceable to the division:

Residual Income = Profit margin traceable to the division - (Average asset investment x Imputed interest rate)

Residual Income = 96,000 - (400,000 x 22%) = 96,000 - 88,000 = 8,000

From Glengarry's perspective, Investment 3 is attractive because it generates a positive residual income of $8,000. However, from Brown's perspective, it may not be as attractive because the imputed interest charge reduces the overall profitability of the investment.

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Complete question is in the image attached below

Answer:

Step-by-step explanation:

xy=34

The area of the shaded segment of the circle will be 10.45cm².

The area of a shape simply means the total space that is taken by the shape. It simply expresses the extent of the region on a particular plane as well as a curved surface.

The area of the segment will be calculated thus:

63°/360° × πr² - (1/2 × 10 × 10 × sin 63°)

= 63/360 × 22/7 ×10² × (1/2 × 10 × 10 × sin 63°)

= 55 - 44.55

= 10.45cm²

Therefore, the area of the shaded segment of the circle will be 10.45cm².

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Answer: 6.69 dollars

Step-by-step explanation: 33.45/5 = 6.69

Answer:6.69

Step-by-step explanation:you basically divide 33.45 by 5 and the will get you 6.69 which is the unit price of pairs of socks

The solutions to the quadratic equation 4x2 = 64 are:  x= -4 and x = 4 therefore, Option (C) is correct.

The Quadratic Equation are where it is equal to zero. There are usually 2 solutions (as shown in this graph).

We can Factor the Quadratic (find what to multiply to make the Quadratic Equation) Just plug in the values of a, b and c, and do

the calculations.

Given,

4x2 = 64

We need to solve the quadratic equation.

To solve this quadratic equation,We can rewrite the equation as:

4x2 - 64 = 0

Dividing both sides by 4x2 - 16 = 0x2 = 16

Taking square root on both sides,x = ±4

Hence,The solutions to the quadratic equation 4x2 = 64 are:

x= -4 and x = 4Option (C) is correct.

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[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$3000\\ r=rate\to 2\%\to \frac{2}{100}\dotfill &0.02\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &15 \end{cases} \\\\\\ A = 3000\left(1+\frac{0.02}{12}\right)^{12\cdot 15} \implies A \approx 4048.57[/tex]

a) The maximum error in the calculated area of the disk =  23.87 cm²

b) The relative error is: 0.0211 and the percentage error is 2.11%

Let us assume that r represents the radius of the circular disk and A represents the area.

Here, the radius of a circular disk is given as 19 cm

So, r = 19 cm

and the radius has a maximum error in measurement of 0.2 cm.

So, dr = 0.2

The area of the circular disk would be,

A = πr²            ..........(1)

A = π × 19²

A = 361π cm²

Differentiating equation (1) with respect to r,

dA = 2πr × dr

dA = 2 × π × 19 × 0.2

dA = 7.6π

dA = 23.87 cm²

So, the maximum error in the calculated area is: 23.87 cm²

Now we find the relative error.

R = dA/A

R = 7.6π / 361π

R = 0.0211

And the percentage error would be:

P = relative error × 100

P = 0.0211 × 100

P = 2.11%

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This would give us the coordinates for E as (1, 4).  Similarly, we can use the same method to find the coordinates for F, G, and H.  F would be (7,2), G would be (9,-5), and H would be (3,-6).

The coordinates of E can be found by taking the average of the x and y coordinates of points A and B.  This would give us the coordinates for E as (1, 4).  Similarly, we can use the same method to find the coordinates for F, G, and H.  F would be (7,2), G would be (9,-5), and H would be (3,-6).  To find the coordinates for these points, we use the formula [tex](x1 + x2)/2, (y1 + y2)/2[/tex].  For example, to find the x coordinate for E, we would use (-2 + 4)/2 = 1, and for the y coordinate of E, we would use (3 + 5)/2 = 4.  We can then use this formula to find the coordinates for all of the midpoints.Step 1: Find coordinates of E, F, G, and H E: (1, 4) F: (7, 2) G: (9, - 5) H: (3, - 6) Step 2: Calculate the perimeter of the quadrilateral ABCD,Perimeter = |AB| + |BC| + |CD| + |DA = |(-2, 3) - (4, 5)| + |(4, 5) - (10, -1)| + |(10, -1) - (8, -9)| + |(8, -9) - (-2, 3)| = (6 + 14 + 18 + 10) = 48

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Answer:

[tex]\frac{1}{4}[/tex]

Step-by-step explanation:

To find a fraction equivalent to a percentage we have to simply put the number over 100!

For 25% this would look like [tex]\frac{25}{100}[/tex]

Now to simply this, we have to find the highest common factor in both which is 25! This means that both values (25 and 100) can divide by 25 to give a whole number!

To divide both the numerator and denominator we will get the result [tex]\frac{1}{4}[/tex]

Hope this helps, have a lovely day! :)

Sofia has a rectangle poster that is 42 inches long and 30 inches wide.  The area of the poster is 1260 square inches.

The area of ​​a rectangle depends on its sides. Basically, the area formula is equal to the product of the length and width of a rectangle. When we talk about the perimeter of a rectangle, it is equal to the sum of its four sides. Therefore, we can say that the area bounded by the perimeter of a rectangle is its area. But in the case of a square, since all sides are equal, the area of ​​the square will be equal to the square of its length.

area of ​​rectangle = length x width

We know that :

Area of rectangle = Length × Breadth

                             = 42 × 30 inches

                             = 1260 square inches.

Therefore, the area of a rectangle is 1260 square inches.

Complete Question:

Sofia has a rectangular poster that is 42 inches long and 30 inches wide. What is the area of the poster in square inches? Do not round your answer. Be sure to include the correct unit in your answer.

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The reason for step 2 is as follows:

If parallel lines are cut by a transversal, then the corresponding angles are said to be congruent to each other.

A unique sort of quadrilateral made up of parallel lines is called a parallelogram. Any angle between adjacent sides of a parallelogram is possible, but only if the sides are parallel.

If the opposite sides of a quadrilateral are parallel and congruent, it will be a parallelogram. Hence, if both sets of opposite sides are parallel and equal, a quadrilateral is referred to as a parallelogram.

Here in the question,

Its already given that AB and DC re parallel and equivalent to each other.

So, the AB and DC are cut by a transversal AC and the corresponding angles that are ∠BAC and ∠DCA are congruent to each other.

Hence, the quadrilateral is a parallelogram.

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The solution set for the stated system of linear inequalities;

y ≥ -2x + 4 and y ≥ x - 2  is the dark area below represents the intersection of a two solutions ranging upto +∞.

The collection of all solutions makes up the solution set for an inequality. Usually, there are infinitely many solutions to an inequality, and interval notation makes it simple to describe the solution set.

The group of values that fulfil a certain inequality is known as a solution set. This indicates that every single value with in solution set will fulfil the inequality, and not one other value will do so.

By utilising the equations to locate certain locations and drawing a line to reflect the point in two dimensions, you can draw the lines produced by the two equations.

y ≥ -2x + 4 and y ≥ x - 2

The coloured area thus provides the answer to this problem.

Putting together the two solutions, the intersection of both solutions, as seen in the dark zone below, reveals the answer to the system of inequality,  ranging upto +∞.

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There are 350 different lineups that can be created.

The question here is regarding the possibility of different lineups given that there are two groups of players available - guards and forwards/centers. The coach wants to choose 2 of her guards and 3 of her forwards/ centers. To avoid an unbalanced lineup, she places the names of her 5 guards in one hat and the names of her 7 forwards/centers in a second hat. Then, she will randomly select 2 guards from the first hat and 3 forwards/ centers from the second hat.

In order to get the different possibilities of lineups, we need to calculate the total number of ways we can select the guards and the forwards/centers separately.

Total number of ways to select guards =[tex]5C_2 = (5 \times 4) / (2 \times 1) = 10[/tex]

Total number of ways to select forwards/centers = [tex]7C_3 = (7 \times 6 \times 5) / (3 \times 2 \times 1) = 35[/tex]

Thus, the total number of ways the lineup can be created is 10 × 35 = 350.

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Answer:

Step-by-step explanation:

The function f(x) = 15x² is increasing over the interval x > 0.

To see why, we can look at the values of f(x) as x increases from left to right. We can see that when x is negative, f(x) is positive and increasing. When x is zero, f(x) reaches its minimum value of zero. And as x becomes positive, f(x) continues to increase without bound. Therefore, we can conclude that f(x) is increasing over the interval x > 0.

The function f(x) is decreasing over the interval x < 0.

To see why, we can again look at the values of f(x) as x increases from left to right. We can see that when x is negative, f(x) is positive and increasing. But as x approaches zero from the left, f(x) begins to decrease, reaching its minimum value of zero at x = 0. And as x becomes positive, f(x) continues to increase without bound. Therefore, we can conclude that f(x) is decreasing over the interval x < 0.

Answer: 9 weeks

i hope this helps you

Owen will have $116.60 in one year. The same principal amount is used for the calculation every period, and the interest earned each period will be the same.

Principal amount is the total amount of money borrowed or invested, excluding any interest, fees or other charges.

This can be calculated using the formula for simple interest, where

I = P x R x T, where P is the principal (the initial investment), R is the interest rate expressed as a decimal, and T is the time.

In this case, the principal (P)= $110,

the interest rate (R) = 0.056,

and the time (T)= 1 year.

Therefore, I = 110 x 0.056 x 1

= 6.16.

When this is added to the original principal of $110, we get $116.16.

This is happening because simple interest is calculated on the principal amount only.

It is not compounded, so the interest is not added to the principal and then used to calculate the interest in the next period.

Therefore, the same principal amount is used for the calculation every period, and the interest earned each period will be the same.

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Answer:

11.16

Step-by-step explanation:

there are two methods

100%+5.6%=

105.6

%

105.6%

Whole balance before interest = 100%, then add on interest

105.6% of the current balance means

105.6

100

of it.

105.6% of the current balance means  

100

105.6

​

 of it.

"Percent" literally means "out of 100."

105.6

100

=

100

105.6

​

=

1.056

1.056

To find 105.6% of the current balance, multiply by  1.056:

To find 105.6% of the current balance, multiply by 1.056:

$110

×

1.056 = $110 × 1.056 =

$116.16

$116.16

method 2

Find the interest, 5.6% of $110:

Find the interest, 5.6% of $110:

5.6

100

=

100

5.6

​

=

0.056

0.056

$

110

×

0.056

=

$110×0.056=

$

6.16

$6.16

Add the interest to the current balance:

Add the interest to the current balance:

$

110

+

$

6.16

=

$110+$6.16=

$

116.16

$116.16

​

​

The probability of a birth occurring before 245 days, which is the probability of a newborn baby being premature.

To do this, we need to calculate the area under the normal distribution curve that represents the probability of a birth occurring before 245 days.

We can use a standard normal distribution table or an appropriate applet to find this probability. Using the applet, we can enter the mean, standard deviation, and the value of 245 days to find the probability.

In mathematical terms, we can write this as:

P(birth before 245 days) = probability of a randomly selected newborn baby being premature

= P(X < 245), where X is the random variable representing pregnancy length

Using the normal distribution table or applet, we can find P(X < 245) by calculating the area under the normal distribution curve to the left of 245 days.

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The correct graph that shows the solution to x - 2y > 9 is B.

What is graph?

In mathematics, graphs can represent functions or equations, such as a line on a coordinate plane or a curve in a three-dimensional space. Graphs can also be used to represent data, such as a bar graph or a scatterplot, which can help to identify trends or correlations between different variables.

To graph the solution to the inequality x - 2y > 9, we can start by graphing the boundary line x - 2y = 9, which is the equation that results from replacing the inequality symbol with an equal sign.

The boundary line can be graphed by plotting two points on the line and connecting them with a straight line. To do this, we can choose any two values for x and y that satisfy the equation x - 2y = 9, such as:

We need to determine which side of the boundary line represents the solution to the inequality x - 2y > 9. To do this, we can choose a test point on one side of the boundary line, such as (0, 0), and substitute its coordinates into the inequality.

Substituting (0, 0) into the inequality x - 2y > 9 gives:

0 - 2(0) > 9

which simplifies to:

0 > 9

The side of the line containing (0, 0) is not the solution. Therefore, the solution to the inequality x - 2y > 9 is the side of the line that does not contain the point (0, 0).

Therefore, the correct graph that shows the solution to x - 2y > 9 is B.

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Therefore, the principal is $654.50 when rate of interest is 10% and time period is 16 months.

Percent is a way of expressing a number as a fraction of 100. It is denoted by the symbol "%". Percentages are commonly used to express ratios, proportions, and rates. They are used in many areas of everyday life, such as in finance, business, and statistics.

Here,

The Interest Formula is:

I = P * R * T

where I is the interest earned, P is the principal (initial amount of money), R is the interest rate, and T is the time period.

We can rearrange the formula to solve for P:

P = I / (R * T)

Substituting the given values, we have:

P = 1047.20 / (0.10 * 16)

= $654.50

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Answer:

ans=8.80inch

Step-by-step explanation:

given,

radius(r)=1.6 inch

height(h=2.5 inch

laternal area of cone = AL=√πrh2+r2

√3.14*2.5^2+1.6^2

8.80 inch

The approximate lateral area of the cone is,

⇒ LSA = 10.5 inches

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

To find the approximate lateral area of the cone, we need to know the height of the cone.

Since we are not given the height, we can use the Pythagorean theorem to find it:

Slant height² = h² + r²

2.5² = h² + 1.6²

6.25 = h² + 2.56

h² = 6.25 - 2.56

h² = 3.69

h = √3.69

h = 1.92 in

We know that;

The lateral surface area of a cone is calculated using the formula,

LSA =πr√(r² + h²) square units.

Substitute all the values, we get;

LSA =πr√(r² + h²) square units.

LSA = 3.14 × 1.4√(1.6² + 1.9²) square units.

LSA = 5 √2.6 + 3.6

LSA = 5 √4.2

LSA = 5 × 2.1

LSA = 10.5 inches

Thus, The approximate lateral area of the cone is,

⇒ LSA = 10.5 inches

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After solving the given equations the value of x and y are -2 and 5 respectively.

An equation is a mathematical statement consisting of two expressions joined by an equal sign.

For example, 3x – 5 = 16 is an equation.

Solving this equation gives the value of the variable x as x = 7.

So, the equations are:

7x+10y = 36 ...(1)

y = 2x +9  ...(2)

Now, insert 2x+9 in equation (1):

7x+10y = 36

7x+10(2x +9) = 36

7x+20x+90 = 36

27x = -54

x = -54/27

x = -2

Then, the value of y:

y = 2x +9

y = 2(-2) +9

y = -4+9

y = 5

Therefore, after solving the given equations the value of x and y are -2 and 5 respectively.

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