If f(x) =5x2 - 3x + 1, calculate the following

The equation of the line that is parallel to k and passes through (-1, 3) is

- x + 2y = 7

The equation of a line can be represented in different form such as point slope form, slope intercept form and standard form.

Therefore, the equation of the line is parallel to k.

Parallel line shave the same slope.

Therefore, let's find the slope of k to find the slope of the equation of the line.

Hence, using (7, 2)(1, -1)

m = -1  - 2 / 1 - 7

m = - 3 / -6

m = 1/ 2

Therefore, the slope of the line is 1 / 2. Let's find the y-intercept using the point (-1, 3)

3 = 1 / 2(-1) + b

3 = - 1 / 2 + b

b = 3 + 1 / 2

b = 7 / 2

Hence, the equation is as follows;

y = 1  /2x + 7 / 2

2y = x + 7

2y - x = 7

- x + 2y = 7

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By solving matrices  we get,

[tex]A+B= \left[\begin{array}{ccc}13&10\\4&7\\7&5\end{array}\right] , C-B=\left[\begin{array}{ccc}-8&1\\-7&4\\3&-5\end{array}\right] \\\\\\\\A+B+C = \left[\begin{array}{ccc}13&14\\2&12\\14&-6\end{array}\right][/tex]

A matrix is a rectangular array or table that contains numbers, symbols, or expressions that are arranged in rows and columns to represent a mathematical object or a characteristic of such an entity. As an illustration, consider a matrix with two rows and three columns.

Adding matrices, subtracting matrices, and multiplying matrices are the three algebraic operations that make up the majority of matrix operations. Array of numbers or expressions arranged in rows and columns is called a matrix. The field of mathematics has several useful uses for matrices.

Here the matrices A, B and C are given in the question, so we use matrix addition and matrix subraction operations to solve the question.  

When solving by using the matrices solving method we get

[tex]A+B=\left[\begin{array}{ccc}5&7\\-1&6\\3&-9\end{array}\right] +\left[\begin{array}{ccc}8&3\\5&1\\4&4\end{array}\right]= \left[\begin{array}{ccc}5+8&7+3\\-1+5&6+1\\3+4&-9+4\end{array}\right]=\left[\begin{array}{ccc}13&10\\4&7\\7&5\end{array}\right] \\[/tex]

[tex]C-B = \left[\begin{array}{ccc}0-8&4-3\\-2-5&5-1\\7-4&-1-4\end{array}\right] =\left[\begin{array}{ccc}-8&1\\-7&4\\3&-5\end{array}\right][/tex]

[tex]A+B+C= \left[\begin{array}{ccc}5+8+0&7+3+4\\-1+5+-2&6+1+5\\3+4+7&-9+4+-1\end{array}\right] = \left[\begin{array}{ccc}13&14\\2&12\\14&-6\end{array}\right][/tex]

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Answer:

C' (6, 9 )

Step-by-step explanation:

under a reflection in the y- axis

a point (x, y ) → (- x, y ) , then

C (- 6, 9 ) → C' (6, 9 )

Answer:29

Step-by-step explanation:

9+4 spots times five days

The number of copies that can be made would be: 35 copies

We would have to solve this problem through the use of cross multiplication

such that we have 20 copies = 8 dollars

unknown copies ? = 14 dollars

This can be re written to be arranged in the form

20 = 8 dollars

? = 14 dollars

we would have to cross multiply

14 x 20 = 8 x ?

280 = 8?

divide through by 14

? = 280 / 14

= 20

Hence the copies that would be made is 35 copies for 14 dollars at the local print shop

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The parallel between 2 highlights is called eduidistand

The powers of the imaginary number i have four possible values: 1, i, -1, and -i. Let's see some examples:

i⁰ = 1 (any number with the exponent 0 equals 1)

i¹ = i (any number with the exponent 1 is the number itself)

i² = -1 (this follows from the definition of the imaginary number, the square root of -1)

i³ = i² * i = -1 * i = -i

Now, the results start to repeat from 1 to -i:

i⁴= i² * i² = (-1) * (-1) = 1

i⁵ = i⁴ * i = 1 * i = i

i⁶ = i * i⁵ = i * i = i² = -1

i⁷ = i⁶ * i = -1 * i = -i

From that, we can follow the steps below to find the value of a power of i:

• divide the exponent by 4;

• if the rest of the division is 0, then the power equals ,i⁰ = 1,;

• if the rest of the division is 1, then the power equals ,i¹ = i,;

• if the rest of the division is 2, then the power equals ,i² = -1,;

• if the rest of the division is 3, then the power equals ,i³ = -i,.

So, for the power i⁶⁴⁹, the exponent is 649. Following the steps above, we find:

• 649/4, has a quotient of 162 and the, rest 1,. Therefore:

i⁶⁴⁹ = i¹ = i

Thus, i⁶⁴⁹ equals i.

Answer:5760

Step-by-step explanation:

48 beats per min and its 120 min in 2 hours so multiply 120×48=5760

If the point M (4,3) is translated using the rules (x, y) ⇒ (x, y-2),  then the coordinates of the M' = (4,1)

The point is M(4,3)

The translation rules is

(x, y) ⇒ (x, y-2)

The translation states that the movement of the graph either horizontally  or vertically. When we translate the graph, the shape and size will not change, only the coordinates of the graph changes.

We know the values of

x = 4

y = 3

Substitute the values in the equation

The coordinates of the M' = (x, y-2)

= (4, 3-2)

= (4,1)

Hence, if the point M (4,3) is translated using the rules (x, y) ⇒ (x, y-2),  then the coordinates of the M' = (4,1)

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Answer: so there for the answer is 498

Step-by-step explanation:

The expressions that gives x in terms of y from the given expression 7 y = 2 x − 5 is x = (7y +5)/2.

The concept that will be used in this question is solving of linear equation, because the equation is linear, then we perform the simplification.

The given expression is  is 7 y = 2 x − 5

Then from the expression we can make 2x the subject of the formula by rearranging it as 2x = 7y +5

Then this can be further expressed by dividing the both sides by the factor of 2, which can be expressed as ;

x = (7y +5)/2

Therefore, option A is correct because it is the expression that gives the x in terms of y.

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Check the missing options:

A. x = (7y +5)/2

B. y = (7x +5)/2

C. x=(7y +5)/3

pls provide the picture below, because of that its an incomplete answer

The equations of the lines are:

7. y = 3/2x - 3/2

8. y = -1/3x - 8/3

The equation that represents a line, in slope-intercept form is, y = mx + b.

7. Find the slope (m) between (5, 6) and (1, 0):

Slope (m) = (6 - 0)/(5 - 1) = 6/4

Slope (m) = 3/2

Find the y-intercept of the line, b, by substituting m = 3/2 and (x, y) = (1, 0) into y = mx + b:

0 = 3/2(1) + b

-3/2 = b

b = -3/2

To write the equation, substitute m = 3/2 and b = -3/2 into y = mx + b:

y = 3/2x - 3/2

8. Find the slope (m) between (-5, -1) and (1, -3):

Slope (m) = (-1 -(-3))/(-5 - 1) = 2/-6

Slope (m) = -1/3

Find the y-intercept of the line, b, by substituting m = -1/3 and (x, y) = (1, -3) into y = mx + b:

-3 = -1/3(1) + b

-3 = -1/3 + b

-3 + 1/3 = b

-8/3 = b

b = -8/3

To write the equation, substitute m = -1/3 and b = -8/3 into y = mx + b:

y = -1/3x - 8/3

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the correct answer is a so write it

[tex]\frac{2(x-8)}{5}[/tex] = y

To Solve: value of y

Given: 2x-5y=16

Solution: The solution to this problem involves the following steps:

2x-5y-16=0

2x-16=5y

[tex]\frac{2x-16}{5}[/tex] = y

[tex]\frac{2(x-8)}{5}[/tex] = y

Answer: The final answer is : [tex]\frac{2(x-8)}{5}[/tex] = y

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If the function f(3) has a value of 6, then the value of f⁻¹(6) is 3

From the question, the definition of the function is given as

f(x)

Such that

The value of f(3) is 6

This is represented as

f(3) = 6

Also, the function can be represented as

y = f(x)

In f(3) = 6, we have

x = 3 and y = 6

When the inverse function is calculated, we have

f⁻¹(y) = x

This means that

f⁻¹(6) = 3

Express as an inverse function

f⁻¹(6) = 3

Hence, the inverse function f⁻¹(6) has a value of 3

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They will next meet again after 1386 seconds or 23.1 minutes from the starting point.

Given that Robert, John, and Paul begin running in the same direction from the same starting point around a circular track If they take 126 seconds, 154 seconds, and 198 seconds respectively to complete one round of the track.

The highest common factor is defined as the set of numbers with the highest common multiple. The highest positive integer with more than one factor in the set is HCF.

To determine whether they will next meet again at the starting point.

We have to calculate the LCM of the numbers 126, 154, and 198

⇒ Prime factors of 126 = 2 × 2 × 3 ×7

⇒ Prime factors of 154 = 2 × 11 ×7

⇒ Prime factors of 198 = 2 × 3 × 3 ×11

So the LCM of the numbers 126, 154, and 198 will be as:

⇒ 2 × 3 × 3 × 7 × 11 = 1386

Therefore, they will meet after 1386 seconds or 23.1 minutes.

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Probability that selected chip is white: 1/2

Probability that the other chip in the bowl is red given if the selected chip is white: 1/3

Let A be the event that bowl A is randomly selected; let B be the event that bowl B is randomly selected; and let C be the event that bowl C is randomly selected. All these three bowls are equally likely to be selected:

P(A) = P(B) = P(C) = 1/3

The probability of selecting a white chip from a bowl depends on from which bowl the chip is selected.

Let W be the event that a white chip is randomly selected.

Attached is the picture solution.

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Given a block play problem, the minimum number of blocks Agnes can use to build a tower is 3 or 1.

To calculate the average (mean) of a set of values, first divide by the number of values in the set. Therefore, the sum of the values in the set is equal to their average multiplied by the number of values in the set. The average number of blocks in each tower was 25, and since there were 5 towers, the total number of blocks used was 5 × 25 = 125. Yuri's Tower used 32 blocks, so the remaining towers used a total of 125 minus 32 = 93 blocks.

To find the minimum possible number of blocks for Agne's tower, let the other three towers use as many blocks as possible. Now we know that Yuri's tower used the most blocks and each tower used a different number of blocks. So the other 3 towers can use up to 31, 30 and 29 blocks respectively. The result was an absolute minimum number of blocks that Agnes could use, 93 - 31 - 30 - 29 = 3

By the way, the minimum number of blocks Agnes can use is not 93 - 32 - 32 - 32 = - 3 , but negative value is not possible. so, if everyone could use the same number of blocks. Agnes must have used at least one block, as it is possible to use a negative number of blocks.

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Given:

yearly salary=28,800

Required:

To calculate adjusted monthly income

Explanation:

student loan

250 dollar

SOLUTION.

AC and BD will intersect at the mid-point between points A and C.

So let's find the mid-point between points A and C

Point A(-2, 4) and point C(-6, 0)

This becomes

Therefore, the correct answer is option C.

This is a geometric sequence since there is a common ratio between each term. In this case, multiplying the previous term in the sequence by

1

3

gives the next term. In other words,

a

n

=

a

1

r

n

−

1

.

Geometric Sequence:

r

=

1

3

This is the form of a geometric sequence.

a

n

=

a

1

r

n

−

1

Substitute in the values of

a

1

=

486

and

r

=

1

3

.

a

n

=

486

(

1

3

)

n

−

1

Apply the product rule to

1

3

.

a

n

=

486

1

n

−

1

3

n

−

1

One to any power is one.

a

n

=

486

1

3

n

−

1

Combine

486

and

1

3

n

−

1

.

a

n

=

486

3

n

−

1

Substitute in the value of

n

to find the

n

th term.

a

5

=

486

3

(

5

)

−

1

Simplify the denominator.

Tap for more steps...

a

5

=

486

81

Divide

486

by

81

.

a

5

=

6

The greatest number of cards that April can place in a row , so that the two families have same number of cards in each row is  14.

In the question ;

it is given that

number of card that Bride's family has = 154

number of cards that Groom's family has = 140 cards.

So , to find the greatest number of cards that April can place in a row we need to find the GCF(154,140) ,

to find the GCF (154,140)

prime factorization of 154 = 2*7*11

prime factorization of 140 = 2*2*5*7

common factors = 2*7

Hence the GCF(154,140) = 14

Therefore , the greatest number of cards that April can place in a row , so that the two families have same number of cards in each row is  14.

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Answer:

I think it's 4 on the left and 5 on the right side

Step-by-step explanation:

4*4*4=64

and

5*5*5=125

Answer:

126

Step-by-step explanation:

90 ÷ 10 = 9

9 × 4 = 36

90 + 36 = 126

First, we can start input small whole numbers in the function to see if we get a whole number. Let's try with 0, 1 and 2:

None of those values worked. Let's try negative integers, such as -1 and -2:

We get integer coordinates if we use negative integers. Then, we need at least 5 points. Let's use x = -1, -2, -3, -4, -5

We have the points:

(-1, -8), (-2, -7), (-3, -5), (-4, -1) and (-5, 7)

If we locate them in the cartesian plane:

And now, we can estimate the graph. An exponential function where the base is smaller than 1, describes an exponential decay, and the term "-9" is applying a shift 9 units down, and also y = -9 is a horizontal asymptote. With all this and the points we just found:

The solution to the given expression is 7,677.6.

This is a question of multiplication.

Multiplication

In mathematics, multiplication is used as a method of finding the product of two or more numbers. It is one of the arithmetic operations,  like addition, subtraction and division that we use in everyday life. The major application we can see in multiplication tables.

In arithmetic, the multiplication of two numbers is represented by  the repeated addition of one number with respect to another.

Given expression:-

[−3*914]*[(−0.1)*(−28)]

We have to find the solution of the given expression.

We have,

-3*914 = -2742

(-0.1)*(-28) = 2.8

Hence, we can write,

[−3*914]*[(−0.1)*(−28)] = (-2742)*(2.8)

(-2742)*(2.8) = 7,677.6

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