If a graphical solution to a linear equation
results in the point of intersection (8. 13), then
the solution to the equation is _____​

Answer:

Step-by-step explanation:

20$

Answer:

b

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

The correct value of Z for the solution to true system is -2

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

2x + 3y - z = 4

x - 3y + 2z = -3

3x + y - z = 5

Transform the third equation

So we have

2x + 3y - z = 4

x - 3y + 2z = -3

9x + 3y - 3z = 15

Eliminate y in the equations by subtraction

So we have

x - 3z = 7

10x - z = 12

Multiply x - 3z = 7 by 10

10x - 30z = 70

10x - z = 12

Subtract the equations

-29z = 58

So, we have

z = -2

Hence, the correct value of Z  is -2

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Answer:

C- 4/5 cups

Step-by-step explanation:

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data:

275,000 x 0.00019

Step 02:

scientific notation:

275,000 = 2.75 x 10 ^ 5

0.00019 = 1.9 x 10 ^ (- 4)

2.75 x 10 ^ 5 X 1.9 x 10 ^ (- 4) = 5.225 x 10 ^ 1

The answer is:

5.225 x 10 ^ 1

Answer:

I think n=4 hope this helps :)

Step-by-step explanation:

Answer:

N = 4

Step-by-step explanation:

Approximately 34.658 Hispanic females out of 26,000 to have this particular disease.

A woman or girl who identifies as Hispanic or Latino, which usually refers to persons of Spanish-speaking origin or lineage from Latin America or Spain, is referred to as a "Hispanic female."

The proportion of Hispanic females with the disease is 1 in 750, which can be expressed as:

1 / 750 = 0.001333

This means that for every 750 Hispanic females, one is expected to have the disease.

To calculate the expected number of Hispanic females with the disease in a group of 26,000, we can multiply the proportion by the total number of Hispanic females:

0.001333 * 26,000 = 34.658

So we would expect approximately 34.658 Hispanic females out of 26,000 to have this particular disease.

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The values of x and y are 8 and 10, respectively

The list of the numbers is given as:

4, 7, x, y, 11

The mean and median of the five numbers are the same.

The median is the middle number.

So, we have

Median = x

This means that

Mean = Median = x

The mean is calculated as:

Mean = Sum/Count

This gives

(4+ 7+ x+ y+ 11)/5 = x

Evaluate the sum

(22 + x + y)/5 = x

This gives

22 + x + y = 5x

Evaluate the like terms

4x = 22 + y

Based on the order of the list, we have:

7 < x < y < 11

Assume y = 10

4x = 22 + 10

This gives

x = 32/4

x = 8

Recall that:

7 < x < y < 11

This means that

7 < 8 < 10 < 11

The above is true

Hence, the values of x and y are 8 and 10, respectively

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Answer:

The answer is 21

Step-by-step explanation:

Person 3's payment exceeded person 2's payment by $20.

To find out how much more person 3 paid than person 2, we need to calculate the amounts each person paid based on the given ratio and then compare their payments.

The ratio given is 1:2:3, which means that person 1 gets 1 part, person 2 gets 2 parts, and person 3 gets 3 parts of the total amount.

Step 1: Calculate the total number of parts in the ratio.

1 + 2 + 3 = 6

Step 2: Determine the value of one part.

$120 (total amount) divided by 6 (total number of parts) = $20

Step 3: Calculate the payments for each person based on the ratio.

Person 1: 1 part * $20 = $20

Person 2: 2 parts * $20 = $40

Person 3: 3 parts * $20 = $60

Therefore, person 3 paid $60, while person 2 paid $40. To find out how much more person 3 paid than person 2, we subtract the amount person 2 paid from the amount person 3 paid:

$60 - $40 = $20

Hence, person 3 paid $20 more than person 2.

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Answer:

9² and 10²

Step-by-step explanation:

9² = 81

10² = 100

100 - 81 =19

Answer

P= 2L+2W

P=2(12) +2(7) =38

Step-by-step explanation:

The width of a rectangle is 5 meters less than its length. The area is 84 square meters. Find the dimensions of the rectangle and the perimeter of the rectangle.

First it helps to draw a picture so draw a rectangle

Remember that area of a rectangle =Length times width and the perimeter is P= 2 times the length plus 2 times the width

So A=LW and P=2L+2W

84= area

L=length

W= length -5

L(L-5)=84 distribute the L and you have L2 -5L=84 now subtract 84 from both sides and get L2 �5L-84 next factor to get (L+7)(L-12) next set both to =0 (L+7)=0 (L+12)=0 solve for L

L=-7 and L=12 you can�t have a negative length so -7 is out. So L=12 now plug in to the original area equation

84=LW 84= 12w now divide both sides by 12 to isolate W, this gives you W=7

L=12 and W= 7

For perimeter use 12 for the length and 7 for width Remember that P= 2L+2W

P=2(12) +2(7) =38

The graph which represents the polar curve r = -4 sin ( 3θ ) is plotted

Polar coordinates describe the position of a point P in the plane by its separation from the origin, r, and the angle formed between the positive x-axis and the line segment leading to P.

To graph the polar curve, we make use of the following representations:

r represents the y-axis

θ represents the x-axis

Polar coordinates can also be extended into three dimensions using the coordinates (ρ, φ, θ), where ρ is the distance from the pole, φ is the angle from the z-axis ( called the co-latitude or zenith and measured from 0 to 180° ) and θ is the angle from the x-axis ( as in the polar coordinates ).

Given data ,

Let the polar curve be represented as A

Now , the polar coordinates is given as

r = -4 sin ( 3θ )

And , To graph the polar curve, we make use of the following representations:

r represents the y-axis

θ represents the x-axis

So , on simplifying , we get

The graph which represents the polar curve r = -4 sin ( 3θ ) is plotted

Hence , the polar curve is r = -4 sin ( 3θ )

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Answer:

D

Step-by-step explanation:

We can conclude that the hypotheses of the Existence and Uniqueness Theorem are satisfied in any rectangular region in the ty-plane that does not contain the curve t² + y² = -1.

The Existence and Uniqueness Theorem for first-order ordinary differential equations states that if a differential equation of the form y' = f(t, y) satisfies the following conditions in some rectangular region in the ty-plane:

1. f(t, y) is continuous in the region.

2. f(t, y) satisfies a Lipschitz condition in y in the region, i.e., there exists a constant L > 0 such that |f(t, y₁) - f(t, y₂)| ≤ L|y₁ - y₂| for all t and y₁, y₂ in the region.

then there exists a unique solution to the differential equation that passes through any point in the region.

In the case of the differential equation y' = (y cot(2t)) / (t² + y² + 1), we have:

f(t, y) = (y cot(2t)) / (t² + y² + 1)

This function is continuous everywhere except at the points where t² + y² + 1 = 0, which is the curve t² + y² = -1 in the ty-plane. Since this curve is not included in any rectangular region, we can say that f(t, y) is continuous in any rectangular region in the ty-plane.

To check if f(t, y) satisfies a Lipschitz condition in y, we can take the partial derivative of f with respect to y and check if it is bounded in any rectangular region. We have:

∂f/∂y = cot(2t) / (t² + y² + 1) - (2y² cot(2t)) / (t² + y² + 1)²

Taking the absolute value and simplifying, we get:

|∂f/∂y| = |cot(2t) / (t² + y² + 1) - (2y² cot(2t)) / (t² + y² + 1)²|

= |cot(2t) / (t² + y² + 1)| * |1 - (2y² / (t² + y² + 1)))|

Since 0 ≤ (2y² / (t² + y² + 1)) ≤ 1 for all t and y, we have:

1/2 ≤ |1 - (2y² / (t² + y² + 1)))| ≤ 1

Also, cot(2t) is bounded in any rectangular region that does not contain the points where cot(2t) is undefined (i.e., where t = (k + 1/2)π for some integer k). Therefore, we can find a constant L > 0 such that |∂f/∂y| ≤ L for all t and y in any rectangular region that does not contain the curve t² + y² = -1.

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Answer:

The highest you could reach with this ladder is 30 feet or 9.14 meters.

Step-by-step explanation: To solve for x in this literal equation, I would first distribute the C through the parentheses to get y = cx + cb.

Now subtract cb from both sides to get y - cb = cx.

Finally, divide both sides by c to get y - cb / c = x.

Option B: Lin can make 2 batches of blueberry muffins. Option C:Lin needs to make 2/3 of a batch of blueberry muffins to use all of the blueberries.

A number that combines a whole number and a fraction is referred to as a mixed number. The entire number is written first, followed by the fraction, with a space or + sign between them. As an illustration, the mixed number 2 1/4 depicts the addition of the numbers 2 and 1/4. Mixed numbers are frequently used to represent things that aren't whole numbers but are near to them, like length or time measures. In mathematics, mixed numbers can be transformed into improper fractions, which are easier to compare and manipulate since the numerator is more than or equal to the denominator, or into decimals and mixed fractions.

The total number of blueberries are: 4.

The amount of blueberries used per batch.

4 cups ÷ (3/2) cups = 8/3 batches = 2.6

Thus, Lin can make 2 batches of blueberry muffins.

C. For the fraction of batch we have:

4 cups − 2 batches × (3/2 cups) = 1 cup

1 cup ÷ (3/2 cups) = 2/3 of a batch.

Hence, Lin needs to make 2/3 of a batch of blueberry muffins to use all of the blueberries.

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x=1

combine like terms and simplify

Answer:

-2

Step-by-step explanation:

just had to answer it :)

Using graphical method to find the solution to the system of linear equation, x = -7/2, y = 1/2

The system of linear equations is the set of two or more linear equations involving the same variables. Here, linear equations can be defined as the equations of the first order, i.e., the highest power of the variable is 1.

The equations given are

Using graphical method, the solution to the system of linear equation is the point of intersection between the two lines.

Using a graphing calculator;

The point of intersection (x, y) are ( - 3.54, 0.494) which can be estimated as x = -7/2, y = 1/2

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The the coefficient of variation for set a is 15.7% and the coefficient of variation for set b is 22.3%.

The formula for calculating the coefficient of variation is:

CV = (standard deviation / mean) x 100%

where standard deviation is a measure of the spread of the data around the mean. The CV expresses the standard deviation as a percentage of the mean.

To calculate the CV for set a, we first need to find the mean and standard deviation of the data set. The mean can be calculated by adding all the values and dividing by the number of values.

Mean = (3.97 + 3.47 + 3.99 + 4.30 + 3.16 + 3.07 + 4.24 + 2.94 + 3.56 + 3.43 + 3.06 + 3.34 + 4.35 + 3.57) / 14 = 3.65

The standard deviation can be calculated using a calculator or a spreadsheet software such as Microsoft Excel. For this set, the standard deviation is 0.574.

CV = (0.574 / 3.65) x 100% = 15.7%

To calculate the CV for set b, we need to first remove the dollar sign from each value and then find the mean and standard deviation.

Mean = ($24,800 + $30,000 + $22,300 + $20,400 + $19,000 + $32,200 + $23,000 + $23,000 + $24,000 + $27,200 + $34,900) / 11 = $25,727.27

The standard deviation can be calculated using a calculator or spreadsheet software. For this set, the standard deviation is $5,746.38.

CV = ($5,746.38 / $25,727.27) x 100% = 22.3%

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Answer: a) To find out how many dollars Mr Anil got with Rs 540,000, we'll divide the amount in Nepali rupees by the exchange rate.

Therefore, Mr Anil got 4,500 dollars with Rs 540,000.

b) After the devaluation of the Nepali rupee by 5%, the new exchange rate would be 5% less than the previous rate.

New exchange rate = Previous exchange rate - (Previous exchange rate * 5%)

The new exchange rate after the devaluation is 1$ = Rs 114.

c) To calculate how much Mr Anil gained or lost, we need to compare the initial exchange rate with the new exchange rate.

Gained or lost = Number of dollars * (New exchange rate - Initial exchange rate)

Mr Anil lost 27,000 rupees due to the devaluation of the Nepali rupee.

d) If the bank took a 2% commission on the transaction, we need to calculate the commission amount and adjust the gain or loss accordingly.

After the devaluation of the Nepali rupee and considering the 2% commission, Mr Anil would lose 27,090 rupees.

Answer:

⅞.

Step-by-step explanation:

- multiplied by - makes +

Thereof, 5/8+2/8 sums up to ⅞.

Answer:

3 2/25 = 3.08

Step-by-step explanation:

The minimum length of pipe required to deliver water to points A and B is approximately 20.375 miles.

We are given that a water pumping station is to be built on a river at point P in order to deliver water to points A and B. The design requires that LAPD = /BPC so that the total length of piping that will be needed is a minimum. We need to find this minimum length of pipe.

The given figure is shown below: \(AB = 10 \ miles\)\(BC = 6 \ miles\)\(CP = 12 \ miles\). We are given that \(LAPD = LCPB\).

Now, we need to find the minimum length of pipe required for delivering the water to points A and B.The total length of the pipe, \(L_{total} = LA + AB + BP\)Since \(LAPD = LCPB\), we can say that\(AP^2 + PD^2 = BP^2 + PC^2\).

From the triangle ACP, we can say that\(AC^2 = AP^2 + PC^2\). So, we can substitute AP^2 + PC^2 with AC^2 to get\(AP^2 + PD^2 = BP^2 + AC^2\)Now, we can substitute AP = AC - PC and BP = BC + PC in the above equation to get\((AC - PC)^2 + PD^2 = (BC + PC)^2 + AC^2\).

After solving this equation, we get\(AC = \frac {37}{8}\) and \(PC = \frac {27}{8}\)Now, we can calculate the length of pipe required as follows: \(L_{total} = LA + AB + BP = 10 + 6 + \frac {27}{8} = \boxed{20.375 \ miles}\). Therefore, the minimum length of pipe required to deliver water to points A and B is approximately 20.375 miles.

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The dimensions of the garden that create the maximum area are 5 meters by 15 meters, and the maximum possible area is 75 square meters

What is measurement?

Measurement is the process of assigning numerical values to physical quantities, such as length, mass, time, temperature, and volume, in order to describe and quantify the properties of objects and phenomena.

Let's assume that the rock wall is the width of the garden and the wire fencing is used for the length and the other two sides. Let's denote the length of the garden as L and the width as W.

Since we have 30 meters of fencing available, the total length of wire fencing used is:

L + 2W = 30 - W

Simplifying this equation, we get:

L = 30 - 3W

The area of the garden is:

A = LW

Substituting the expression for L from the previous equation, we get:

A = W(30 - 3W)

Expanding the expression, we get:

A = 30W - 3W²

To find the maximum area, we need to take the derivative of A with respect to W and set it equal to zero:

dA/dW = 30 - 6W = 0

Solving for W, we get:

W = 5

Substituting this value back into the expression for L, we get:

L = 15

Therefore, the dimensions of the garden that create the maximum area are 5 meters by 15 meters, and the maximum possible area is:

A = 5(15) = 75 square meters

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Answer:  The correct answer is (#3) this is a ssa situation, only one triangle is possible.

Step-by-step explanation:

This is an obtuse scalene triangle.

Sides:

a = 9   b = 12   c = 20.233

Area: T = 28.135

Perimeter: p = 41.233

Semiperimeter: s = 20.616

The three angles:

Angle ∠ A = α = 13.401°

Angle ∠ B = β = 18°

Angle ∠ C = γ = 148.599°

The calculation of this triangle has two phases; calculate all three sides of the triangle from the input parameters, then calculate other triangle characteristics, such as angles, area, perimeter, heights, etc.

Using the Law of Cosines, you can find all three side lengths.

a = 9 , b = 12 , β = 18 degree

b^2 = a^2 + c^2 - 2ac \cos β

12^2 = 9^2 + c^2 -2

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The equation that represents x, the side length of the greater square is this:  x² + (x-2)²= 100.

The equation that represents x, the greater side length is  x² + (x-2)²= 100. According to the instruction from the teacher, one of the squares should have a side that is two units greater than the first side.

So, if the first side was x, then the new side will be x2 and the same will be true of side, x -2 which now becomes (x-2)². Of course, multiplying a side 10 by 10 will also give 100. So, the correct equation will be C.

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Answer:

C

Step-by-step explanation:

The rotation of 90 degree anti clockwise makes more sense as the reflection is across the x axis shows us a line of symmetry above after the rotation of 90 degree anticlockwise at x axis (0) so that the rectangle is reflected ito (-8,-3)) (-3,-3) (-8,-6) (-3,-6)

Proving that the rectangle is 5cm long and 3cm high after 90 degree rotation and reflection from y axis to the x axis position in the far left corner.