Solve the following quadratic equation by completing the square. Simplify the solutions and rationalize denominators, if necessary.

3x^2−30x=−2

The value of 11 3/8 -7/8 is 10 1/2

Subtraction is the operation or process of finding the difference between two numbers or quantities . For examples, if out 100 students In a school , 40 are boys , the number of girls in the school is calculated by subtracting the number of boys from the total number of students.i.e 100 - 40 = 60

Solving 11 3/8 -7/8

= 91/8 - 7/8

= (91-7)/8

= 84/8

= 21/2

= 10 1/2

Therefore the value of 11 3/8 -7/8 is 10 1/2

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Answer:

1/4

Step-by-step explanation:

The scaled image is 1/4 of the size of the original, we can see this as one side of the original shape is 4 units, and the scaled side is 1 unit.

When a number is selected at random, the probability that a number that is not a prime number would be selected would be = 3/7.

Prime numbers are defined as those numbers that are greater than one that cannot be divided by a whole number apart from themselves without a remainder.

To calculate the probability of non prime numbers from a game of cards the formula for probability should be used. That is;

Probability = possible outcome/sample space

The possible outcome = 1,4,6 = 3

The sample space = 7

Therefore probability = 3/7

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Answer: If you are trying to find the third derivative

It would be f'''(x)=159720(11x+3y)^3

Step-by-step explanation:

The third term of the given expression [tex](11x+3y)^6[/tex] is 135[tex]x^4y^2[/tex].

The binomial theorem states that [tex](a+b)^n[/tex] can be expanded as follows:

[tex](a+b)^n[/tex] = nC0*[tex]a^n[/tex] + nC1*[tex]a^{n-1[/tex]*b + nC2*[tex]a^{n-2[/tex]*[tex]b^2[/tex] + ... + nCn*[tex]b^n[/tex]

where nCk is the binomial coefficient, which is defined as n! / k!(n-k)!.

In this case, we have [tex](11x+3y)^6[/tex], so n = 6.

The third term of the expansion is given by nC2[tex]a^{n-2[/tex][tex]b^2[/tex], which is equal to 6C211[tex]x^4[/tex]3[tex]y^2[/tex].

6C2 is equal to 6! / 2!4! = 15, so the third term is equal to 1511[tex]x^4[/tex]3[tex]y^2[/tex] = 135[tex]x^4y^2[/tex].

Therefore, the third term of [tex](11x+3y)^6[/tex] is 135[tex]x^4y^2[/tex].

Here is a breakdown of the steps:

Find the binomial coefficient nC2.

Multiply nC2 by 11[tex]x^4[/tex] and 3[tex]y^2[/tex].

Simplify the expression.

The answer is 135[tex]x^4y^2[/tex].

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The valid row-operation which needs to be performed on the given matrix to get "1" in position of row1 and column1 are "R₁ → 2R₁ + R₂" and then "R₁ → R₁/2".

The "row-operation" is a type of matrix operation that involves swapping, scaling, or adding rows in a matrix. These operations are used to transform a matrix into a more reduced form.

The Augmented matrix on which we have to perform the "row-operation" is

⇒ [tex]\left[\begin{array}{ccc}7&-4&8\\-12&7&-13\end{array}\right][/tex],

To get "1" in first row and first column,

The first row-operation is R₁ → 2R₁ + R₂

We get,

⇒ [tex]\left[\begin{array}{ccc}7\times 2-12&-4\times 2+7&8\times 2-13\\-12&7&-13\end{array}\right][/tex],

⇒ [tex]\left[\begin{array}{ccc}14-12&-8+7&16-13\\-12&7&-13\end{array}\right][/tex]

⇒ [tex]\left[\begin{array}{ccc}2&-1&3\\-12&7&-13\end{array}\right][/tex],

The second , row-operation to get a "1", is R₁ → R₁/2,

We get,

⇒ [tex]\left[\begin{array}{ccc}2/2&-1/2&3/2\\-12&7&-13\end{array}\right][/tex],

⇒ [tex]\left[\begin{array}{ccc}1&-0.5&1.5\\-12&7&-13\end{array}\right][/tex].

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Answer: 76

Step-by-step explanation:

The surface area is all of the area faces added together

The blue is 5*4  but I have 2 of those faces so I multiply by 2

(5*4*2)=40

The red is 4*2  but I have 2 of those faces so I multiply by 2

(4*2*2)=16

The green is 5*2  but I have 2 of those faces so I multiply by 2

(5*2*2)=20

Add those together

A=40+16+20=76

The distance of the point from the line is d =

Given data ,

Let the point be P ( 1 , 1 )

Let the equation of line be represented as e

where A ( -5 , 0 ) and B ( 1 , -2 ) lies on the line

So , slope m = ( 0 + 2 ) / ( -5 - 1 )

m = 2/-6

m = -1/3

So , the equation of line is

y - 0 = ( -1/3 ) ( x + 5 )

y = ( -1/3 ) ( x + 5 )

( 1/3 )x + y + 5/3 = 0

Now , the Distance of a point to line D = | Ax₀ + By₀ + C | / √ ( A² + B² )

On simplifying , we get

D = | ( 1/3 )( 1 ) + ( 1 ) ( 1 ) + ( 5/3 ) | / √[ ( 1/3 )² + ( 1 )² ]

D = | ( 6/3 ) + 1 | / √ [ ( 1/9 ) + 1 ]

D = 3 / ( 10 ) / 9

D = 27/10

D = 2.7 units

Hence , the distance is 2.7 units

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Answer:

Option C

Step-by-step explanation:

To solve this system of equations, we can use the method of elimination. Adding the two equations together eliminates the y variable, and we get:

2x = 6

Simplifying, we get:

x = 3

Substituting x = 3 into either of the original equations, we get:

3 + y = -4

Solving for y, we get:

y = -7

Therefore, the solution to the system of equations is (3, -7), which is option C.

The values of angles x in the parallelogram maze are calculated below

The question is solved by taking the shapes from left to right on each row

So, we have

x + 65 = 180 --- adjacent angles

x = 115

x + 103 = 180 --- adjacent angles

x = 77

9x = 90 --- angles in a rectangle

x = 10

x + 85 = 180 --- adjacent angles

x = 95

x + 60 = 180 --- adjacent angles

x = 120

2x = 90 --- angles in a rectangle

x = 45

x = 98 -- opposite angles in a parallelogram

3x = 81 -- opposite angles in a parallelogram

x = 27

4x + 76 = 180 --- adjacent angles

x = 26

3x = 78 -- opposite angles in a parallelogram

x = 26

8x + 68 = 180 --- adjacent angles

x = 14

4x = 72 -- opposite angles in a parallelogram

x = 18

x + 126 = 180 --- adjacent angles

x = 54

x = 90 -- opposite angles in a parallelogram

6x = 90 -- opposite angles in a parallelogram

x = 15

2x + 62 = 180 --- adjacent angles

x = 59

6x = 106 --- opposite angles in a parallelogram

x = 17.6

5x = 90 --- angles in a rectangle

x = 18

5x + 80 = 180 --- adjacent angles

x = 20

10x = 90 --- angles in a rectangle

x = 9

2x = 100 --- opposite angles in a parallelogram

x = 50

6x = 96 --- opposite angles in a parallelogram

x = 16

x + 105 = 180 --- adjacent angles

x = 75

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The other number is 156.

Let a and b be two numbers, with a = 24.

We know that the product of two numbers' HCF and LCM is equal to the product of the two numbers.

So, we have:

HCF × LCM = a × b

We are given that the reciprocal of HCF is 1/12.

So, HCF = 1 / (1/12) = 12.

We are also given that the reciprocal of LCM is 1/312.

So, LCM = 1 / (1/312) = 312.

12 × 312 = 24 × b

Simplifying, we get:

b = (12 × 312) / 24 = 156

Therefore, the other number is 156.

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Answer:

v=12

Step-by-step explanation:

9/v = 6/8

9 = 6v/8

72= 6v

v= 12

Answer:

v = 12

Step-by-step explanation:

Now we have to,

→ Find the required value of v.

Given proportion,

→ (9/v) = (6/8)

Then the value of v will be,

→ (9/v) = (6/8)

→ 9 × 8 = 6 × v

→ 72 = 6v

→ 6v = 72

→ v = 72/6

→ [ v = 12 ]

Hence, the value of v is 12.

Answer:

-45j - 9k

Step-by-step explanation:

-9(5j + k)

-9(5j) + -9(k)

-45j - 9k

Helping in the name of Jesus.

Answer

5

Solution

[5 (8^1/3 + 27^1/3)^3]^1/4

= [5 ((2^3)^1/3) + (3^3)^1/3)^3]^1/4

= [5((2+3)^3)1/4

= (5×5^3)^1/4

= (5^4)^1/4

= 5

Answer:

Answer is D.

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The cost per highlighter is approximately $1.

To find the cost per highlighter, we can use a system of equations. Let's call the cost per highlighter "h" and the cost per pen "p". Then, we can set up two equations based on the information given;

80h + 20p = 120 (day 1)

120h + 40p = 200 (day 2)

We can simplify these equations by dividing both sides by 20;

4h + p = 6 (day 1)

6h + 2p = 10 (day 2)

Now we can use the first equation to solve for p in terms of h;

p = 6 - 4h

Substitute this expression for p into second equation;

6h + 2(6 - 4h) = 10

Simplify and solve for h;

6h + 12 - 8h = 10

-2h = -2

h = 1

Therefore, the cost per highlighter is $1.

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The expression of the matrix row operation is 1/4 Row 1 ⇒ Row 1

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

[tex]\left[\begin{array}{cccc}-24&-24&12&20\\-2&3&7&5\\-7&-3&3&-5\end{array}\right][/tex] into [tex]\left[\begin{array}{cccc}-6&-6&3&5\\-2&3&7&5\\-7&-3&3&-5\end{array}\right][/tex]

From the above matrices, we understand that

This means that

row 1 = 1/4(row 1)

This in other words means that

row 1 = (row 1)/4

When these values are evaluated, we have

[tex]\left[\begin{array}{cccc}-24&-24&12&20\\-2&3&7&5\\-7&-3&3&-5\end{array}\right][/tex] into [tex]\left[\begin{array}{cccc}-6&-6&3&5\\-2&3&7&5\\-7&-3&3&-5\end{array}\right][/tex]

This means that we replace -24, -24, 12, and 20 in row 1 with -6, -6, 3 and 5

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First, we need to find the experimental probability (probability using the provided data) of landing on purple.

Experimental probability of purple = # of purple / total #

Experimental probability of purple = 2 / 26 = 1 / 13 (simplified)

Next, we need to consider the probability in the context of 13 spins, as per the question. Our experimental probability tells us that 1 out of every 13 spins will be purple. Therefore, we can expect 1 of the next 13 spins to land on purple.

Answer: 1 spin

Hope this helps!

The sum of all the pets in the list is 11.

The average number of pets that the students own is 1.375.

It should be noted that to find the sum of all the pets in the list, we simply add up all the values:

0 + 1 + 2 + 3 + 1 + 2 + 0 + 2 = 11

Therefore, the sum of all the pets in the list is 11.

Since Cameron asked eight of his classmates, we divide the sum of pets by 8 to find the mean:

11 ÷ 8 = 1.375

Therefore, the average number of pets that the students own is 1.375.

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The measures of center can be used to summarize the number of pets that students own. Cueton asked eight of his classmates how many pets they own. The results are listed below.

0  1  2  3  1  2  0  2

What is The sum of all the pets in the list

What is the average number of pets that the students own

There is a local maximum at the point (-1,6), therefore, for x = -1

option D is correct

A local maximum point on a function is  described as a point (x,y) on the graph of the function whose y coordinate is larger than all other y coordinates on the graph at points "close to'' (x,y).

We see  that the function adopts values smaller than 6 to the left of x = -1, and to the right of it:

(-3, -2), (-2, 0) to the left of x = -1 where the function's value is 6

and (0, 0), and (1, -2) to the right of x = -1

Therefore, we can say that the pints  (-1, 6) is a maximum, that is for x = -1, where the function renders a value of 6.

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1. If the expression is set equal to 10x + 5, the expression will have infinitely many solutions. 2. If the expression is set equal to 10x + 7, there would be no solution. 3. One solution.

In algebra, like terms are those in which the same variables are raised to the same powers. For instance, the fact that the variable x has been raised to the first power makes the expressions 3x, 2x, and -5x similar. Related expressions include 4y², -y², and 7y², all of which have the variable y increased to the second power. By maintaining the variable and its exponent the same, like terms can be joined by adding or removing the coefficients (the numbers placed in front of the variables).

The given expression is given as 12x - 6x + 4x + 5 = 10x + 5.

Simplifying the expression we het 10 x + 5.

1. If the expression is set equal to 10x + 5, the expression will have infinitely many solutions as it will always be true.

2. If the expression is set equal to 10x + 7, there would be no solution, as the variable is eliminated.

3. If the expression is set equal to -10x + 5, there would be only one solution.

10x + 5 = -10x + 5

20x = 0

x = 0

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Answer:

70...............................

Reason:

The left-most digit is the most significant when it comes to rounding. We bump the 6 up to 7 since 68 is closer to 70 (compared to 60). The other digits turn to 0 and become insignificant.

Do not write any of the following:

because that would mean we would have 2, 3, and 4 sig figs respectively. We simply write 70 without a decimal point.

The bank should invest $38,750 in bonds to earn an annual income of $14,650 from the investments.

(162,000 - 2x) is invested in mortgages.

The annual income earned from the bond investment is:

0.09x

The annual income earned from the CD investment is:

0.07x

The annual income earned from the mortgage investment is:

0.10(162,000 - 2x) = 16,200 - 0.20x

The total annual income earned from the investments is:

0.09x + 0.07x + 16,200 - 0.20x = 14,650

Simplifying and solving for x, we get:

-0.04x + 16,200 = 14,650

-0.04x = -1,550

x = 38,750

Therefore, the bank should invest $38,750 in bonds to earn an annual income of $14,650 from the investments.

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Answer:

The other zeros are:

1 - 2i, 1 - √5

The conditional statement is solved and you could ask for an enrollment verification notice from the school

Given data ,

Let the statement be informally proven that you are taking courses online

And , To informally prove that you are taking courses online, you can contact the professors of the courses via email and obtain informal permission from them first.

Then you can initiate the request using the new online information system of the school to obtain an enrollment verification notice

It is a legitimate document that the school has produced that may be utilized for a number of things, including debt deferments, employment, and insurance.

Hence , the conditional statement is solved

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Answer:

X = 6

Y = 17

Step-by-step explanation:

The points GHIJ for a cyclic quadrilateral.

The sum of opposite angles of a cyclic quadrilateral is 180°

So

     ∠J + ∠H = 180°

⇒   6y + 78° = 180°

⇒   6y = 180° - 78°

⇒   6y = 102°

⇒   y = 102°/6

⇒   y = 17°

Similarly for angle x

     ∠I + ∠G = 180°

⇒   16x + 14x = 180°

⇒   30x = 180°

⇒   x = 180°/30

⇒   x = 6°

Answer:

2π(10^2) + 2π(10)(16)

= 2π(100) + 2π(160)

= 200π + 320π

= 520π ft^2

Answer:

9.6

Step-by-step explanation:

sin(angle)= opposite/hypotenuse

sin(42°)=6.4/X

X*SIN(42°)=6.4

X=6.4/SIN(42)

X=9.6

Answer:

Step-by-step explanation:

sin(42°)=6.4/X

X*SIN(42°)=6.4

X=6.4/SIN(42)

sin(42°)=6.4/X

X*SIN(42°)=6.4

X=6.4/SIN(42)

X=9.6

By following trigonometry identities we get  b equals **7**

Trigonometric identities are equations involving trigonometric functions that hold for all possible values of the variables that occur and for which both sides of the equation are specified. These identities come in use if trigonometric function-based formulas need to be made simpler 1.

There are numerous distinctive trigonometric identities that involve a triangle's side length and angle 2. Only the right-angle triangle 2 is covered by the trigonometric identities. The three main trigonometric functions are sine, cosine, and tangent, while the other three are cotangent, secant, and cosecant.

Some of the most popular trigonometric identities are listed below:

sin²(x) + cos²(x) = 1

- tan(x) = sin(x)/cos(x)

- cot(x) = cos(x)/sin(x)

- sec(x) = 1/cos(x)

- csc(x) = 1/sin(x)

- sin(2x) = 2sin(x)cos(x)

- cos(2x) = cos²(x) - sin²(x)

- tan(2x) = (2tan(x))/(1 - tan²(x))

The use of these identities

.One angle in a right triangle is x°, where sin x°=4/5 . With this knowledge, we can use the inverse sine function (arcsin) to calculate the value of x, which gives us x = arcsin(4/5) = 0.9272952180016122 radians .

In addition, we are informed that NL = 22.5 and NM = 3b. We can get the value of LM, which is equal to√(NL2 + NM2), using the Pythagorean theorem. 2. When the given values are substituted, we obtain LM = √((22.5)2 + (3b)2) = sqrt(506.25 + 9b2).

LM is equivalent to b times cos(x°) since it is the polar opposite of the right angle. Consequently, we can write:

b cos(x°) = √(506.25 + 9b²)

Substituting x = arcsin(4/5), we get:

b cos(arcsin(4/5)) = √(506.25 + 9b²)

Simplifying this equation using trigonometric identities, we get:

b * (√1 - sin²(arcsin(4/5)) = sqrt(506.25 + 9b²)

b × (√(1 - (4/5)²)) = sqrt(506.25 + 9b²)

b× (√(1 - 16/25)) = sqrt(506.25 + 9b²)

b× (√(9/25)) = sqrt(506.25 + 9b²)

3b/5 = √(506.25 + 9b²)

Squaring both sides of the equation, we get:

9b²/25 = 506.25 + 9b²

Solving for b, we get:

b = 7

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Answer:

Expected number of times to roll a total of 5 = Probability of rolling a total of 5 x Total number of rolls

                                                      = (1/9) x 180

                                                      = 20

Step-by-step explanation:

The diagram is not visible in the question. However, I can provide a general method to solve the problem.

a) To find the probability of rolling a total of 5, we need to count the number of ways we can get a sum of 5 and divide it by the total number of possible outcomes. From the diagram, we can see that there are four ways to get a sum of 5: (1,4), (2,3), (3,2), and (4,1). Since each die has six equally likely outcomes, there are 6 x 6 = 36 possible outcomes in total. Therefore, the probability of rolling a total of 5 is:

Probability of rolling a total of 5 = Number of ways to get a total of 5 / Total number of possible outcomes

                                   = 4/36

                                   = 1/9 (in its simplest form)

b) If we rolled a pair of fair dice 180 times, the expected number of times we would roll a total of 5 can be calculated as follows:

Expected number of times to roll a total of 5 = Probability of rolling a total of 5 x Total number of rolls

                                                      = (1/9) x 180

                                                      = 20