Given the equation 3x + y = 6, write a second equation that, together with the first,
will create a system of equations that
(a) has one solution;
(b) has an infinite number of solutions;
(c) has no solution;
(d) has the ordered pair (4, -6) as its only solution.

Answer:

Step-by-step explanation:

I gotchu.

sinS = 2/9

S = sin^-1(2/9)

S = 12.84 = 321/25 or 12 21/25

The area of the lateral surfaces will be 192.55 square centimetres.

The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the prism in a two-dimensional plane is called as the area of the prism.

Given that there is a triangular prism having sides the height of the triangular side is 4.3 cm and its base is 5 cm.

The lateral surface area will be calculated as:-

SA = 2 x ( 5 x W ) + 10 x 50 + ( 1 / 2 ) x 5 x 4.3

W = √ ( 5² + 4.3²)

W = √43.49

W = 6.59 cm

SA = 2 x ( 10 x W ) + 10 x 50 + ( 1 / 2 ) x 5 x 4.3

SA = 2 x ( 10 x 6.59 ) + 10 x 5 + ( 1 / 2 ) x 5 x 4.3

SA = 131.8 + 50 + 10.75

SA = 192.55 square centimetres

Therefore, the area of the prism will be 192.55 square centimetres.

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The sides n and s of the given similar triangles are 12 and 10 respectively.

What are similar triangles?

If two triangles have an equal number of corresponding sides and an equal number of corresponding angles, then they are similar. Similar figures are described as items with the same shape but varying sizes, such as two or more figures.

The polygon with three sides is a triangle. The prerequisites for a triangle's similarity are that the corresponding angles on both triangles must be equal, and the corresponding sides must be proportional to one another.

In the given figure both triangles are similar triangles.

So according to the properties of similar triangles,

[tex]\frac{15}{s} = \frac{9}{6}=\frac{n}{8}[/tex]

Solving the above equations,

15/s = 9/6

s = 10

n/8 = 9/6

n = 12

Therefore the sides n and s of the given similar triangles are 12 and 10 respectively.

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For the triangle ABC the interior angles measures ∠A = 80°, ∠B = 58°, and ∠C = 42°.

What are triangles?

Triangles are a particular sort of polygon in geometry that have three sides and three vertices. Three straight sides make up the two-dimensional figure shown here. An example of a 3-sided polygon is a triangle. The total of a triangle's three angles equals 180 degrees. One plane completely encloses the triangle.

According to the angles of a triangle theorem, the sum of angles of a triangle is 180°.

The measure of ∠A = 80°.

The measure of ∠B = 8x + 2.

The measure of ∠C = 6x.

The equation is -

∠A + ∠B + ∠C = 180°

Substitute the values into the equation -

80° + 8x + 2 + 6x = 180

Collect the like terms -

8x + 6x = 180 - 80 - 2

14x = 98

x = 98/14

x = 7°

So, the measure of ∠B = 8(7) + 2 = 58°

The measure of ∠C = 6(7) = 42°

The interior angles of the triangle are 80°, 58° and 42°.

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The coordinates of R are (2,3) which represents an intersecting point of the given lines.

The equation is defined as a mathematical statement that has a minimum of two terms containing variables or numbers that are equal.

The lines are given in the question, as follows:

y = x+1 ...(i)

x+2y = 8  ...(ii)

Since both lines intersect at R.

Substitute the value of equation (i), in (ii), and we get

x+2(x+1) = 8

x + 2x + 2 = 8

3x = 8 - 2

3x = 6

x = 2

Substitute the value of x = 2 in equation (i),

y = 2 + 1

y = 3

Thus, the coordinates of R are (2,3).

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The question seems incomplete, the correct question would be as:

If the lines y=x+1 and x+2y=8 intersect at R, find the coordinates of R. Show this the coordinate plan.

It is important to check that the number of successes and number of failures in each sample is at least 10 because this helps ensure that the normal approximation of the binomial distribution is accurate.

When constructing a confidence interval for the difference between two population proportions, it is important to check that the number of successes and the number of failures in each sample is at least 10 because this helps ensure that the normal approximation of the binomial distribution is accurate. The normal approximation is often used in constructing confidence intervals for proportions because it simplifies the calculations, but it is only accurate if the sample size is large enough.

A common rule of thumb is that each sample should have at least 10 successes and 10 failures in order to ensure that the normal approximation is reasonable. This is because the Central Limit Theorem states that the sum of many independent and identically distributed random variables will approximately follow a normal distribution. When the sample size is large enough, the distribution of the sample proportions will be approximately normal, even if the individual observations are not.

If the number of successes and failures in each sample is less.

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The number of distinct 10-letter arrangements that can be formed from the letters in the word "statistics" is 40320, which can be calculated by finding the permutation of 8 objects taken 8 at a time

Permutation is a mathematical concept that deals with counting the number of ways to arrange a set of objects in a particular order.

The number of permutations of a set of n objects taken r at a time can be calculated using the formula:

=> n! / (n - r)!.

Where "n!" represents n factorial, which is the product of all positive integers less than or equal to n.

In this case, we are going to find out the number of distinct 10-letter arrangements that can be formed from the letters in the word "statistics".

In our case, the number of objects is 8 (the letters in the word "statistics") and we are taking 10 at a time, so the formula becomes:

=> 8! / (8 - 10)! = 8! / (-2)!.

The factorial of a negative number is undefined, so this case is not possible.

Since we cannot take more objects than the number of available objects, we have to find the number of permutations of 8 objects taken 8 at a time. The formula becomes:

=> 8! / (8 - 8)! = 8! / 0! = 8!.

Finally, 8! = 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 40320,

which means that there are 40320 distinct 10-letter arrangements that can be formed from the letters in the word "statistics".

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Only matrices of the same size can be added or subtracted.

A matrix is a rectangular array of numbers and is composed of rows and columns. In order to add or subtract matrices, the matrices must have the same number of rows and columns. If the matrices do not have the same size, they cannot be added or subtracted.

For example, if one matrix is a 2x3 matrix, the other matrix must also be a 2x3 matrix. Similarly, if one matrix is a 3x2 matrix, the other matrix must also be a 3x2 matrix. The numbers in each matrix may vary, but the size of the matrices must be the same for the operation to be valid.

When adding or subtracting matrices, the numbers in the same position (row and column) are added or subtracted. For example, if one matrix is [[1,2,3], [4,5,6], [7,8,9]] and the other matrix is [[2,4,6], [8,10,12], [14,16,18]], the resulting matrix would be [[3,6,9], [12,15,18], [21,24,27]].

Adding and subtracting matrices is a useful tool in mathematics and is often used to solve equations and simplify complex problems. It is important to remember that only matrices of the same size can be added or subtracted.

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The actual length of the dragonfly if the drawing is 8. 5 cm, can be found to be 6. 375 mm

The scale on the science textbook is such that every 4 cm of the drawing of an insect is the same as 3 mm of the actual insect.

If a drawing is 8. 5 cm therefore, the actual length of the dragonfly would be :

= ( Drawing length of dragonfly x Scale of insect ) / Drawing scale of insect

The actual length is therefore :

= ( 8. 5 x 3 ) / 4

= 6. 375 mm

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By understanding stratified random sampling concept, it can be concluded that the problem is a type of stratified random sampling.

Stratified random sampling is a structured random sampling technique that is carried out by dividing members of the population into several strata (levels), then a sample is selected from each level.

Population elements are divided into several levels based on the characters attached to them.

With this method, it is expected that the sampling will be evenly distributed at all levels and the sample represents the character of all heterogeneous population elements.

By understanding this concept, it can be concluded that the problem is stratified random sampling.

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A negative number that have a value greater then 8 does not exist

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

negative number that have a value greater then 8

The number 8 is a positive number

As a general rule:

No negative number is greater than a positive number

Hence, the negative number does not exist (DNE)

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In the Fixed deposit account, you will not be able to withdraw your money before time without a penalty fee from the bank and you will receive a fixed amount of interest on your original deposit.

In a Fixed-Term Deposit account, an account is opened with a bank wherein, the bank pays a guaranteed interest rate on the sums deposited for a fixed period or tenure.

This type of account allows you to earn higher returns (interest) on funds lying idle in your Savings Account.

Banks are free to charge their own penalty fee in the case of premature withdrawal of Fixed Deposit.

At the end of the stipulated period, the deposit will automatically be renewed unless you update your maturity instructions.

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Answer:

The general form of a quadratic equation is ax^2 + bx + c = y.  From the equation for c, our a is -2, our b is -7 and our c is 5.  

When a < 0, the function opens downward and has a maximum for its vertex.

When a quadratic function has maximum, its x values will always be increasing from negative infinity to the x-coordinate of the maximum (You can also simply write x < x coordinate of the maximum as you've already done).

We can find the x-coordinate of the maximum using the equation

[tex]-b/2a[/tex]

Thus, since b is -7 and a is -2, we have

[tex]-(-7)/2(-2)\\7/-4\\-7/4=-1.75[/tex]

This is how you get that the function is increasing from x < -1.75.

The green line in the attached picture also highlights the same idea.

For the trigonometric function -0.575 = cos c the value is obtained as c = 2.18340 + 2πn and c = 2.18340 - 2πn.

What is trigonometric function?

Simply put, trigonometric functions also referred to as circular functions are the functions of a triangle's angle. This means that these trig functions provide the relationship between the angles and sides of a triangle.

The trigonometric function is -

-0.575 = cos c

The value for c is -

cos c = -0.575

c = arccos (-0.575)

c = 2.18340 + 2πn

In radians the value of c is -

c = 2.18340 + 2πn and c = 2.18340 - 2πn

In degrees the value of c is -

c = 125.1° + 360° and c = 125.1° - 360°

Therefore, the value of c is c = 2.18340 + 2πn.

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Answer:

  3.  · (times)

Step-by-step explanation:

You want to know the operation that will give a binomial result from the expressions (3y^6 +4) and (9y^12 -12y^6 +16).

The like terms in the two expressions are 3y^6 and -12y^6, or +4 and +16. Combining these terms by addition or subtraction will not result in the elimination of either the y^6 term or the constant term. Hence addition or subtraction cannot result in a binomial.

We know that the sum of cubes is factored into the product of a binomial and a trinomial:

  a³ +b³ = (a +b)(a² -ab +b²)

Comparing this form to the given binomial and trinomial, we see that we can choose ...

  a = 3y^6

  b = 4

to make the given factors match exactly. That tells us their product will be a binomial sum:

  (3y^6 +4) × (9y^12 -12y^6 +16) = (3y^6)^3 +(4)^3 = 27y^18 +64

The operation "times" (·) will result in a binomial.

Answer:

1. -23

2. -20

3. 20

4. 23

Step-by-step explanation:

The measure of {x} in the figure is 14.

In Euclidean geometry, a parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure.

Given is a parallelogram as shown in the image.

Opposite angles of a parallelogram are equal. So, we can write -

x + 50 = y

y - x = 50                                                                  .... Eq { 1 }

Sum of the angles of a quadrilateral are 360°. We can write -

2(x - 30) + (x + 50) + y = 360                                          .... Eq { 2 }

2x - 60 + x + 50 + y = 360

3x + y = 370

3x + 50 + x = 370

4x = 320

x = 80

y = 130

Therefore, the measure of {x} and {y} are 80 and 130 respectively.

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{Question in english -

Help please, I need to find the values, well, I'll settle for one...}

Match each quotient of the complex numbers accordingly as shown below.

A complex number is a number that can be expressed in the form a + bi, where a and b are real numbers and i is the imaginary unit, which is defined as the square root of -1. The real part of a complex number is represented by a, while the imaginary part is represented by bi.

No. 1

Multiply the numerator and denominator by 3-4i:

1/(3 + 4i) = 1/(3 + 4i)  * (3 - 4i)/(3 - 4i)  

             =  (3 - 4i)/(9 + 16)

             =  (3 - 4i)/25

             =  3/25 - 4/25 i

No. 2

Multiply the numerator and denominator by 3+4i:

1/(3 - 4i) = 1/(3 - 4i)  * (3 + 4i)/(3 + 4i)  

             =  (3 + 4i)/(9 + 16)

             =  (3 + 4i)/25

             =  3/25 + 4/25 i

No. 3

i/i = 1

   = 1 + 0i

No. 4

Multiply the numerator and denominator by 3-4i:

(3 - 4i)/(3 + 4i) = (3 - 4i)/(3 + 4i) * (3 - 4i)/(3 - 4i)

                       = (9 - 24i -16) / (9 + 16)

                       = (-7 - 24i) / 25

                       = -7/25 - 24i/25

No. 5

(3 - 4i)/ 1 = 3 - 4i

No. 6

Multiply the numerator and denominator by 3+4i:

(3 + 4i)/(3 - 4i) = (3 + 4i)/(3 - 4i) * (3 + 4i)/(3 + 4i)

                       = (9 + 24i -16) / (9 + 16)

                       = (-7 + 24i) / 25

                       = -7/25 + 24i/25

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The probability that the doctor makes an incorrect diagnosis and the patient sues is 0.27.

The probability that a doctor correctly diagnoses a particular illness is 0.7.

P(A) = 0.7

Therefore, the probability that a doctor incorrectly diagnose illness is,

P(A)' = 1-0.7 = 0.3

IF the doctor made a  incorrect diagnosis, the probability that the patient files a lawsuit is 0.9.

P(B) = 0.9

The probability of doctor makes an incorrect diagnosis and the patient sues,

P(C) = 0.3 * 0.9 = 0.27

The probability that the doctor makes an incorrect diagnosis and the patient sues is 0.27.

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Show A is 90 minutes long, and Show B is 45 minutes long.

Let's say Show A is x minutes long. Then Show B is x/2 minutes long since Show A is twice as long as Show B. The total duration of Show A and Show B is 2 hours and 15 minutes, or 135 minutes.

So, x + x/2 = 135

Multiplying both sides by 2, we get 2x + x = 270

Combining like terms, we get 3x = 270

Dividing both sides by 3, we get x = 90

So Show A is 90 minutes long, and Show B is 45 minutes long.

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Answer:

Step-by-step explanation:

Given, the sides of triangle ABC are 12, 16 and 20, which form a right triangle (as 20 is the hypotenuse).

Let us assume that the sides of triangle XYZ are x, y and 24 (XZ=24).

Since ABC ~ XYZ, we can use ratios of corresponding sides to find the lengths of the sides of triangle XYZ:

x/12 = y/16 = 24/20

Solving for x and y, we get:

x = 9 and y = 12

So, the perimeter of triangle AXYZ = 9 + 12 + 12 + 24 = 57.

Answer:

D. 12x = -8

Step-by-step explanation:

D. 12(-2/3) = -8

-24/3 = -8

-8 = -8

The completed table is given below

Sr. No. Mortgage Amount Interest Rate First Monthly Payment Amount of Interest Amount of Principal New Principal

a b c d e f

(given) (a*b/12) (c-d) (a-e)

1 86,000 8.00% 663.92 573.33 90.59 85,909.41

2 1,65,000 5.00% 886.05 687.50 198.55 1,64,801.45

3 42,500 6.50% 286.88 230.21 56.67 42,443.33

Answer to Question 4

Investment in house 96,400.00

Down Payment 25% 24,100.00 (96,400*25%)

Mortgage Amount 72,300.00 (96,400-24,100)

Mortgage Amount Interest Rate First Monthly Payment Amount of Interest Amount of Principal New Principal

a b c d e f

(given) (a*b/12) (c-d) (a-e)

72,300 5.50% 410.66 331.38 79.29 72,220.72

Thus First Monthly Payment used to reduce Principal is $79.29

5.

Investment in house 1,37,400.00

Down Payment 17,400.00

Mortgage Amount 1,20,000.00 (1,37,400-17,400)

Mortgage Amount Interest Rate First Monthly Payment Amount of Interest Amount of Principal New Principal

a b c d e f

(given) (a*b/12) (c-d) (a-e)

1,20,000 6.00% 772.80 600.00 172.80 1,19,827.20

New Principal will be $119,827.20.

6. Investment in house 2,87,000.00

Down Payment 31,000.00

Mortgage Amount 2,56,000.00 (287,000-31,000)

Mortgage Amount Interest Rate First Monthly Payment Amount of Interest Amount of Principal New Principal

a b c d e f

(given) (a*b/12) (c-d) (a-e)

2,56,000 6.00% 1,536.00 1,280.00 256.00 2,55,744.00

The first Monthly Payment used to reduce the Principal is $256 and New Principal after first monthly payment is $255,744.

7 Investment in house 87,500.00

Down Payment 17,500.00

Mortgage Amount 70,000.00 87,500-17,500)

Month Mortgage Amount Interest Rate Monthly Payment Amount of Interest Amount of Principal New Principal

a b c d e f

(given) (a*b/12) (c-d) (a-e)

1 70,000 6.00% 409.50 350.00 59.50 69,940.50

2 69,941 6.00% 409.50 349.70 59.80 69,880.70

3 69,881 6.00% 409.50 349.40 60.10 69,820.61

4 69,821 6.00% 409.50 349.10 60.40 69,760.21

5 69,760 6.00% 409.50 348.80 60.70 69,699.51

6 69,700 6.00% 409.50 348.50 61.00 69,638.51

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Answer:

12 houses

Step-by-step explanation:

First you need to figure out how many were sold the first month. You need to figure out how much 1/3 of 48 is, so you need to divide 48 by 3, equaling 16. You then multiply 16 by two, because they didnt sell 1/3, but 2/3. 16 times 2 is 32, so 32 houses were sold in the first month, by doing 48-32, you can say that there were 16 houses left to sell. Then if 1/4 of those houses were sold the next month, then you need to figure out what 1/4 of 16 is. In the same way as before, you divide 16 by 4, which equals 4. If they sold 4 of 16 the next month, you then need to subtract 16 by 4, equaling 12. This means there are 12 houses remaining to be sold.

Answer:

735/420 + 2 = 735/420 + 420/420 = 1155/420

Step-by-step explanation:

To add the three fractions, we need to find a common denominator. A common denominator for all three fractions is 420:

30/15 = 2

25/40 = 25/40 * 3/3 = 75/120

30/35 = 30/35 * 12/12 = 360/420

Adding the three fractions with the common denominator:

2 + 75/120 + 360/420 = 2 + 375/420 + 360/420

Combining like terms:

2 + 735/420 = 2 + 735/420

The answer is 735/420 + 2 = 735/420 + 420/420 = 1155/420.

Answer:

$141.30

Step-by-step explanation:

180 - 38.70 = 141.30

The correct way to solve for the answer is to divide the quantity of potatoes the store bought by the quantity of each bag of potatoes.

Quantity of potatoes the store bought = 250 kilograms

Quantity of each bag of potatoes= 10 pounds

Convert kilograms to pounds:

1 kilogram = 2.20462 pounds

25 kilograms= 551.156 pounds

Number of bags of potatoes= Quantity of potatoes the store bought / Quantity of each bag of potatoes

= 551.156 pounds ÷ 10 pounds

= 55.1156 bags

Approximately,

55 bags

Therefore, the store will pack an approximate number of 55 bags of potatoes.

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