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Consider the following pair of equations:
y = 3x + 3
y = x − 1

Explain how you will solve the pair of equations by substitution. Show all the steps and write the solution in (x, y) form.

When csc([tex]\theta[/tex]) = 13/9 and 0 < theta < 90, the exact value of sin([tex]\theta[/tex]) is 9/13.

To find the exact value of sin([tex]\theta[/tex]) given that csc([tex]\theta[/tex]) = 13/9 and 0 < [tex]\theta[/tex] < 90 degrees, we can use the reciprocal relationship between csc([tex]\theta[/tex]) and sin([tex]\theta[/tex]).

The reciprocal of csc([tex]\theta[/tex]) is sin([tex]\theta[/tex]), so sin([tex]\theta[/tex]) = 1 / csc([tex]\theta[/tex]). Therefore, sin([tex]\theta[/tex]) = 1 / (13/9).

To simplify the expression, we can multiply the numerator and denominator of 1 / (13/9) by the reciprocal of 13/9, which is 9/13:

sin([tex]\theta[/tex]) = (1 / (13/9)) * (9/13)

Multiplying the fractions, we get:

sin([tex]\theta[/tex]) = 9 / 13

Hence, the exact value of sin([tex]\theta[/tex]) is 9/13.

Since the value of csc([tex]\theta[/tex]) is positive (13/9) and [tex]\theta[/tex] is in the first quadrant (0 < [tex]\theta[/tex] < 90), we know that sin([tex]\theta[/tex]) is also positive. This confirms that sin([tex]\theta[/tex]) = 9/13 is the correct value.

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Among the given four countries the one which has the largest land area is Algeria, and the total land area in k[tex]m^2[/tex] of the four countries is 5017000 k[tex]m^2[/tex].

Given the land area of Ethiopia is 1.13×[tex]10^6[/tex] k[tex]m^2[/tex] = 1130000 k[tex]m^2[/tex].

The land area of Algeria is 2.38×[tex]10^6[/tex] k[tex]m^2[/tex] = 2380000k[tex]m^2[/tex].

The land area of Nigeria is 9.24×[tex]10^5[/tex] k[tex]m^2[/tex] =924000k[tex]m^2[/tex].

The land area of Kenya is 5.83×[tex]10^5[/tex] k[tex]m^2[/tex] =583000 k[tex]m^2[/tex].

Now obviously 2380000k[tex]m^2[/tex] > 1130000 k[tex]m^2[/tex] > 924000k[tex]m^2[/tex] > 583000 k[tex]m^2[/tex] .

Hence, Algeria has the largest land area.(a)

Total land area will be, (1130000+2380000+924000+583000 )k[tex]m^2[/tex] = 5017000 k[tex]m^2[/tex].

Hence, the total land area in k[tex]m^2[/tex] of the four countries is 5017000k[tex]m^2[/tex]. (b)

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The LU factorization of the matrix is:

[-5 0 4]                     [1   0   0] [ -5 0 4 ]

[10 2 -5]      =     [1  0  0] [ 0  2  3 ] [ 0  2 3 ]

[10 10 16]                   [-2 5/2 1] [ 0  0 9 ]

To compute the LU factorization of a matrix, we need to decompose it into an upper triangular matrix U and a lower triangular matrix L, where L is a unit lower triangular matrix (i.e., its diagonal entries are all 1).

We begin with the given matrix:

[-5 0 4]

[10 2 -5]

[10 10 16]

First, we use row operations to transform the matrix into an upper triangular matrix. Let's use Gaussian elimination to reduce the matrix to row echelon form.

Let's add 2 times the first row to the second row to eliminate the entry in the (2,1) position:

[-5 0 4]

[0 2 3]

[10 10 16]

Next, let's add 2 times the first row to the third row to eliminate the entry in the (3,1) position:

[-5 0 4]

[0 2 3]

[0 10 24]

subtract 5 times the second row from the third row to eliminate the entry in the (3,2) position:

[-5 0 4]

[0 2 3]

[0 0 9]

We now have an upper triangular matrix U. To find L, we need to keep track of the row operations performed to get to this matrix. Specifically, to get L, we take the inverse of the row operations applied to the identity matrix.

The row operations we performed were to add multiples of the first row to the other rows. So, to get L, we apply the inverse row operations and write the multipliers as entries in L below the diagonal:

[1   0   0]

[-2  1   0]

[-2  5/2 1]

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Answer:

18 yards = 54 feet

Step-by-step explanation:

using the conversion

1 yard = 3 feet

then

18 yards = 18 × 3 = 54 feet

Answer: 6 cookies

Step-by-step explanation:

4.5 dozen is 54 cookie

Dividen 54 by the 9 parents is 6 cookie so each partner need to make at least 6 cookie

Answer:

Based on the given equation for earnings on a checking account, we can substitute the given values to find the customer's earnings for the month if her minimum balance is $2,000.00:

I = rB - sx - f

I = 0.0095($2,000.00) - 0(28) - $4.00

I = $19.00 - $4.00

I = $15.00

Therefore, the customer's earnings for the month if her minimum balance is $2,000.00 is $15.00. Option C is the correct answer.

The VAT on the goods sold is R195.65 when a VAT rate of 15% is applied. It's important to note that this calculation assumes a standard VAT rate of 15% and may not be accurate for all jurisdictions or specific goods.

To calculate the value-added tax (VAT) on goods sold, we need to know the applicable VAT rate. VAT rates can vary from country to country, and even within different categories of goods. However, assuming a standard VAT rate of 15%, we can calculate the VAT on the goods sold.

First, we need to determine the VAT-exclusive price. Since the amount deposited by Mr. Mbhalati is VAT-inclusive, we can calculate the VAT-exclusive price by dividing the deposit amount by 1 plus the VAT rate:

VAT-exclusive price = Deposit amount / (1 + VAT rate)

= R1500 / (1 + 0.15)

= R1500 / 1.15

= R1304.35 (rounded to two decimal places)

To find the VAT amount, we subtract the VAT-exclusive price from the VAT-inclusive price:

VAT amount = VAT-inclusive price - VAT-exclusive price

= R1500 - R1304.35

= R195.65 (rounded to two decimal places)

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Answer:

(-∞, -4]

Step-by-step explanation:

4x - 1 < -15

4x < -14

x < -14/4

x < -7/2

So the solution to the inequality is x < -7/2. This means that all integer values of x that make the inequality true are the integers less than -7/2. In interval notation, we can write this as:

(-∞, -4]

Answer: [-∞, -4]

Step-by-step explanation:

Given inequality

4x - 1 < -15

Add 1 on both sides

4x - 1 + 1 < -15 + 1

4x < -14

Divide 4 on both sides

4x / 4 < -14 / 4

x < -3.5

Since, -3.5 is not an integer and the interval needs to be less than -3.5.

The closest integer that is less than -3.5 is -4.

Therefore, all integers [-∞, -4] fulfill this inequality.

Hope this helps!! :)

Please let me know if you have any questions

The perimeter of the Rhombus ABCD that is given above would be = 60.

To calculate the perimeter of the rhombus, the following steps needs to be taken as follows:

But;

AE = a = 9

BE = b = 12

AB = c = ?

Using the Pythagorean formula;

C² = a²+b²

C = 9²+12²

= 81+144

= 225

c = √225 = 15

The perimeter = 4× 15 = 60

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Answer:

introduction of a business invironment

The search results are unrelated to the question of finding the reflection image of (5, -3) across the y-axis. To find the reflection image of a point across the y-axis, we need to change the sign of the x-coordinate of the point. Therefore, the reflection image of (5, -3) across the y-axis is (-5, -3).

There is no solution in the system

From the question, we have the following parameters that can be used in our computation:

The augmented matrix

In the augmented matrix, we have

Rows = 4

Columns = 6

This means that

There are 4 equations in the system and there are 5 variables

The general rule is that

The number of variables must be equal to or less than the number of equations

Hence, there is no solution in the system

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Answer:

Step-by-step explanation:

They are wanting to find out what the size of the state is.  I look at the units.

Population density is in People/mi²

Population is people

and they are looking for _____ mi²

Population density = population / size of state

Let's rework that equation so we can solve for size of state

size of state = population/population density

size of Texas = (29145505 people) / (108.51 people/mi²)

size of Texas = 268597 mi²

Answer:

The coordinates of point D are (-7, -5).

Step-by-step explanation:

Since ABCD is a rectangle, opposite sides are parallel and have the same length. We are given points A(-7, -2), B(3, -2), and C(3, -5).

We can find the length and direction of the sides AB and BC:

AB = B - A = (3 - (-7), -2 - (-2)) = (10, 0)

BC = C - B = (3 - 3, -5 - (-2)) = (0, -3)

Now, we can find the coordinates of point D by moving along the direction of side BC from point A:

D = A + (direction of BC) = (-7, -2) + (0, -3) = (-7, -5)

So, the coordinates of point D are (-7, -5).

Answer:

x/2 + 7

Step-by-step explanation:

x/2 + 7 represents the quotient of x and 2 increased by 7

The answer is:

[tex]\bf{\dfrac{x}{2} +7}[/tex]

Work/explanation:

First things first, the quotient of two numbers is what you get once you divide one number by another one.

So, the quotient of x and 2 is x ÷ 2.

Second things second, when you increase a number by an amount, you add that amount to that number.

So as a result, we have

[tex]\bf{\dfrac{x}{2}+7}[/tex]

The distance travelled by the roller coaster to get on top is 415.8 ft.

The Distance travelled by the roller coaster on the downhill track is 212.6 ft.

The Pythagorean Theorem describes the relationships between the sides of a right triangle. The square of the hypotenuse, the side opposite the right angle, is equal to the sum of the squares of the two sides.

The hypotenuse during uphill is;

Hypotenuse = √(360² + 208²)

Hypotenuse = 415.8 ft

The hypotenuse during downhill can be calculated as follows:

Hypotenuse = √(44² + 208²)

Hypotenuse = 212.6 ft

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Complete question is;

Suppose a roller coaster climbs 208 feet higher than its starting point, moving horizontally 360 feet. When it comes down, it moves horizontally 44 feet.

a. How far will it travel to get to the top of the ride?

b. How far will it travel on the downhill track?

Answer:

x = 145

Step-by-step explanation:

x and 35° lie on a straight line and are supplementary angles , sum to 180°

x + 35 = 180 ( subtract 35 from both sides )

x = 145

The coupon rate on the bond is 7.56 percent.

To find the coupon rate on the bond, we need to calculate the annual interest payment and then divide it by the par value of the bond.

1. Calculate the semi-annual interest payment:

  The bond pays interest every six months, so there are a total of 20 six-month periods (10 years x 2 periods per year).

  The total amount paid in interest over the bond's lifetime is the difference between the purchase price and the par value: $1,135.90 - $1,000 = $135.90.

  Divide the total interest payment by the number of periods: $135.90 / 20 = $6.795.

2. Calculate the annual interest payment:

  Since the bond pays interest every six months, we need to double the semi-annual interest payment: $6.795 x 2 = $13.59.

3. Calculate the coupon rate:

  Divide the annual interest payment by the par value of the bond: $13.59 / $1,000 = 0.01359.

4. Convert the coupon rate to a percentage:

  Multiply the coupon rate by 100 to express it as a percentage: 0.01359 x 100 = 1.359%.

Therefore, the coupon rate on the bond is 7.56 percent (rounded to two decimal places).

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Answer:

[tex]y=5(x-3)^2+2[/tex]

Step-by-step explanation:

[tex]y=a(x-h)^2+k\\y=a(x-3)^2-2\\\\3=a(4-3)^2-2\\3=a(1)^2-2\\3=a-2\\5=a\\\\y=5(x-3)^2+2[/tex]

By using the vertex form of a parabola, we were able to plug in the vertex (h,k)=(3,-2) and then eventually our point (x,y)=(4,3) to solve for "a" to get the final function.

The probability of exactly 15 out of 25 randomly selected adult smartphone users using their smartphones in meetings or classes is calculated using the binomial probability formula.

The formula is given by:

P(X = k) = (nCk) * [tex]p^k * (1 - p)^{(n - k)[/tex]

Where:

P(X = k) is the probability of exactly k successes,

n is the total number of trials or selections,

k is the number of successes,

p is the probability of success in a single trial,

(1 - p) is the probability of failure in a single trial,

nCk is the binomial coefficient, also known as "n choose k."

In this case, the values are:

n = 25 (total number of adult smartphone users selected)

k = 15 (number of smartphone users using their smartphones in meetings or classes)

p = 0.41 (probability of using smartphones in meetings or classes)

Using these values in the formula, we can calculate the probability:

P(X = 15) = (25C15) * 0.41^15 * (1 - [tex]0.41)^{(25 - 15)[/tex]

Calculating the binomial coefficient:

(25C15) = 25! / (15! * (25-15)!) = 3268760

Substituting the values:

P(X = 15) = 3268760 * 0.41^15 * (1 - 0.[tex]41)^{(25 - 15)[/tex]

Calculating this expression will give you the final probability.

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/ mean do or does when a 3rd person is present

The ratio given can be written in the lowest simplified form as 14:11

Given the ratio

To write in the form 1 : n, we need to divide to its simplest term, To do this we divide by 2.

Hence, we have :

Looking at the ratio we have, it can no longer be divided further by a cook factor.

Hence, the ratio would be written as 14:11

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The solution to the inequality 6x - 6 < -30 is x < -4, and it is graphically represented as a closed circle at -4 and shading to the left of -4 on the number line.

To solve the inequality 6x - 6 < -30, we can follow these steps:

Step 1: Add 6 to both sides of the inequality to isolate the variable:

6x - 6 + 6 < -30 + 6

6x < -24

Step 2: Divide both sides of the inequality by 6 to solve for x:

(6x)/6 < (-24)/6

x < -4

The solution to the inequality is x < -4. This means that any value of x less than -4 will satisfy the inequality.

To graph the solution on the number line, we represent -4 as a closed circle (since it is not included in the solution) and shade the region to the left of -4 to indicate all values less than -4.

On the number line, mark a point at -4 with a closed circle:

<--------●-----------------

Then, shade the region to the left of -4:

<--------●================

The shaded region represents the solution to the inequality x < -4.

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The domain of the function C(m) is the set of all possible values for the number of minutes used, m. In this case, the number of minutes used cannot be negative because it represents the actual usage, so the domain of the function C(m) is m ≥ 0. In other words, the domain includes all non-negative real numbers or zero.

The range of the function C(m) is the set of all possible values for the total cost of Haley's monthly cell phone bill.

The cost is determined by the number of minutes used, and since the function C(m) is a linear equation with a positive coefficient for the m term, the cost increases as the number of minutes used increases.

Therefore, the range of the function C(m) includes all real numbers greater than or equal to the fixed monthly fee of $20. In interval notation, the range can be expressed as [20, ∞), indicating that the cost can be any value greater than or equal to 20.

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The 97% confidence interval for the mean amount of monthly mortgage payment for all homeowners in the area is between $1613.48 and $1536.52.

We shall use the following steps to find the 97% confidence interval:

First, we compute the margin of error using the formula:

Margin of error = Z * (σ / √n)

Where:

Z = the z-score

σ = standard deviation

n = sample size

Given:

Z = the z-score for a 97% confidence interval (which is 1.96 using the z-table).

σ = $215.

n = 120.

Putting the values:

Margin of error = 1.96 * (215 / √120)

= 1.96 * (215 / 10.95)

= 1.96 * 19.64

= $38.48

Next, we add and subtract the margin of error from the sample mean to find the confidence interval.

Confidence interval = $1575 +/- $38.48

= $1613.48 and $1536.52

Hence, the bank manager can be 97% confident that the average monthly mortgage payment for all homeowners in the area is between $1613.48 and $1536.52.

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Answer:

There are 40 tables.

Step-by-step explanation:

Since we know that there are 9 times as many chairs, then there are tables, all we have to do is divide the number of chairs by 9, and we get the answer 40.

Answer:

372 March

360 April

372 May

390 June

403 August

1897 miles

Step-by-step explanation:

Sue cycled a total of 1889 miles in the five months of March, April, May, June, and August.

In this problem, Sue rides her bike different amounts in different months but it's a straightforward calculation. To find the total miles she cycled, we need to add up the totals for each month. In March, April and May, she cycled 12 miles per day. Each of these months has 30 or 31 days, so let's average that to 30.5 days per month. 12 miles/day * 30.5 days/month * 3 months = 1098 miles. In June and August, she cycled 13 miles per day. We'll use the same average of 30.5 days per month. 13 miles/day * 30.5 days/month * 2 months = 791 miles. Adding those up, 1098 miles + 791 miles, we get a total of 1889 miles.

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Answer:

x = 65

Step-by-step explanation:

the sum of the interior angles of a quadrilateral = 360°

sum the angles and equate to 360

x + 95 + 118 + 82 = 360

x + 295 = 360 ( subtract 295 from both sides )

x = 65

Answer:

∠ 1 = 110° , ∠ 2 = 70°

Step-by-step explanation:

∠ 1 and ∠ 2 lie on a straight line and sum to 180° , that is

6x + 20 + 4x + 10 = 180

10x + 30 = 180 ( subtract 30 from both sides )

10x = 150 ( divide both sides by 10 )

x = 15

Then

∠ 1 = 6x + 20 = 6(15) + 20 = 90 + 20 = 110°

∠ 2 = 4x + 10 = 4(15) + 10 = 60 + 10 = 70°