Find the correct answer & explaining why

The equation of the required line is given as y = -23x - 92.

A straight line can be written in the form of equation as, y = mx + c.

Two straight lines intersect each other only at one point.

When two straight lines are parallel to each other the angle between them is zero.

The given problem can be solved as follows,

The equation of the line is  y = −23x + 32.

Then, its slope is given by -23.

Since the parallel lines have the same slope, the slope of the line parallel to  y = −23x + 32 is -23.

Now, the equation of the line passing through (4, -7) and parallel to the given line can be written as,

(y + 7)/(x - 4) = -23

=> y + 7 = -23x - 92

=> y = -23x + -99

=> y = -23x - 92

Hence, the equation of the line passing through (4, -7) and parallel to y = −23x + 32 is  y = -23x - 92.

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Answer:

Step-by-step explanation:

12 x 3 = 36

answer is 36

Answer:

12 x 3 = 36

Step-by-step explanation:

Answer: Postulate

Step-by-step explanation:

Side-Side-Side (SSS) Postulate

If three sides of one triangle are congruent to three sides of another triangle, then the two are congruent.

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

The amount earned by 217% more from last year to this year.

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

Example:

50% = 50/100 = 1/2

25% = 25/100 = 1/4

20% = 20/100 = 1/5

10% = 10/100 = 1/10

We have,

Amount earned last year = 1,459,632,852

Amount earned this year = 4,632,859,678

The best estimate of the amount earned this year than last year.

= [ (4,632,859,678 - 1,459,632,852 ) / 1,459,632,852 ] x 100

= ( 3173226826 /1,459,632,852 ) x 100

= 217 %

Thus,

The amount earned by 217% more from last year to this year.

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Answer:

A function is a procedure or a relation that links each element of a non-empty set A, at least one element of another non-empty set B, to another element of the first non-empty set A. In mathematics, a relation f between two sets, A and B, is referred to as the function's domain and co-domain. For all values of a and b, f = (a,b)|

If every element in set A has exactly one and only one image in set B, then the relation is said to be a function.

A function is a relation from a non-empty set B such that its domain is A and it never has the same first member in two different ordered pairs.

In arithmetic, a function can be represented as:

a set of ordered pairs

an arrow diagram

a table form

a graphical form

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The required slopes of the line are as follows,
(a) y = 12, the slope is m = 0,
(b) x = -13, the slope is not defined.
(c) -6y = -2x + 30, the slope is positive, m = 1 / 3.
(d) 3x + 5y =15, the slope is negative, m=  -3/5.

The slope of the line is a tangent angle made by line with horizontal. i.e. m =tanx where x in degrees.

here,
(a)
y = 12

Comparing the above expression with the standard equation of line y = mx + c,
From comparison,
mx = 0
m = 0

(b)
x = -13,
x + 13 = 0
Comparing the above expression with the standard equation of line y = mx + c,
From comparison,
mx = 1 / 0     (because the equation does not contain the term y)
m =  not defined.

Similarly,
(c) -6y = -2x + 30, the slope is positive, m = 1 / 3.
(d) 3x + 5y =15, the slope is negative, m=  -3/5.

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Answer:

Q14    x = 3

Q15    No unique solution

Step-by-step explanation:

Q14

The value of x where the line crosses the x axis is the solution for x

Here we see the line crosses the x axis at x = 3 so solution is x =3

Mathematically,

2x - 3 = 3

2x = 3 + 3  adding 3 to both sides

2x = 6

x = 6/2 = 3

Q15

This is a horizontal line which crosses the y-axis at y = 1

Since this does not cross the x axis but is parallel to it, there is no unique solution for x

Mathematically,
-4x + 2 = -4x + 1

Adding 4x to both sides we get the absurdity that 2 = 1 and that indicates no unique solution for x. Alternatively we can say that x has an infinite number of solutions

The mass of the boy removed is 54.

What is the linear equation?

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are present. The variables in the above equation are y and x, and it is occasionally referred to as a "linear equation of two variables."

let's take the weight of five boys is x

so,

x/5 = 62

x = 310

and let's take the weight of four boys is y.

so,

y/4 = 64

y = 256

let's take the weight of a boy which is removed from them is z

so,

x - z = y

x - y = z

310 - 256 = z

z = 54

Hence, the mass of the boy removed is 54.

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answer:the answer for digital index of 23475 is 3

answer: 3

explanation: the digital index is 3 because 23475 is divisible by 3

Answer:

10 and 8

Step-by-step explanation:

must be in the ratio 5:4, 5 x 4 =20, so if you multiply by 2 the ratio is 10:8 (same thing). The least common multiple of 10 and 8 is 40 because you can do 10 x 4 = 40 and 8 x 5 = 40.

Step-by-step explanation:

here is your answer to your question

Answer: 20x^4 + 2x³ - 19x² - 28x + 6

Step-by-step explanation:

Single bookcase units with two sides, top and bottom should be no wider than 36 inches without a center support.

Each shelf can hold 33 books

There are 1221 mystery books

Therefore the number of shelves he will need to build can be calculated as follows

= 1221/33

= 37

Hence Landon will need to build 37 shelves,

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Your answer will be letter C [-4, ∞)

The kind of sequence is a prime number if Norma cuts 3, 5, 8, 13 roses from the four bushes.

A prime number is a natural number higher than 1 that is not the sum of two lesser natural numbers. A composite number is any natural number that is more than 1 but not a prime. As an illustration, the number 5 is prime since there are no other ways to write it either a product than as 1 5 or 5 1. The basic arithmetic theorem states that every natural number greater than 1 is either a prime itself or can be factored as a product of primes that is unique up to their order, making primes a prominent concept in number theory.

Given,

The number of roses cut by Norma from the first rose bush are 3 roses.

And from the second rose bush are 5 roses and from the third rose bush are 8 roses.

And from the fourth rose bush are 13 roses.

1     2     3     4

3     5     8      13

Here, the roses are 3, 5, 8, 13

Therefore, the kind of sequence is a prime number.

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Answer:

98-5 = 93

Step-by-step explanation:

Answer: 6.3x + 2.885

Step-by-step explanation:

Since there is only one factor of x, we cannot simplify x.

We can simplify the constants though.

6.3x + (-7.015 + 9.9)

= 6.3x + 2.885

The segments that could be the image of segment AB after a sequence of reflections, rotations, and/or translations include:

A. Line segment GH

D. Line segment NP

F. Line segment CD

From the information, the coordinates of the point A is (1, 2), the coordinates of the point B is (5, 2)

Therefore, the length of the line AB = 5 - 1 = 4 units

In this case, the transformations are, reflections, rotations, and/or translations which are rigid transformations, such that the length of the image of AB will be the same as the length of AB

Therefore, the possible images of AB are;

PN with coordinates P(5, -2) and N(9, -2) and length 9 - 5 = 4 units

HG with coordinates H(-4, -4) and G(-4, -8) and length -4 - (-8) = -4 + 8 = 4 units

CD with coordinates C(-4, 6) and D(-4, 2) and length 6 - 2 = 4 units

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Answer:

Step-by-step explanation:

Answer:   -4608

========================================================

Explanation:

a = 9 = first term

r = -2 = common ratio

We multiply each term by -2 to generate the next term

The nth term for this geometric sequence is a*(r)^(n-1) which becomes 9(-2)^(n-1)

If you tried plugging in say n = 2, you should find that,

9(-2)^(n-1)

9(-2)^(2-1)

9(-2)^1

9(-2)

-18

So that confirms the second term. I'll let you try the other values of n to confirm it further.

----------------------

From here, you plug in n = 10 to find the tenth term

9(-2)^(n-1)

9(-2)^(10-1)

9(-2)^9

9(-512)

-4608

The value of x that will make L || M is x/2

As a parallel line part of the qualities include that the slopes of the lines  are equal  

The equation of line is L = 2x + 5 and M = x - 5

The slope intercept form of the form as

y = mx + c

where

m = slope

c = intercept

x = input variables

y = output variables

to make line L parallel to line M

2x ⇔ x

hence x in line L will be equal to x/2

L = 2x + 5

L = 2(x/2) + 5

L = x + 5

L = x + 5 is parallel with M = x - 5

L = 2x + 5 is parallel with M = 2x - 5

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Answer:

  (b)  g(x) = 6√x +7

Step-by-step explanation:

You want the equation of the square root function after it has been vertically stretched by a factor of 6 and translated up 7 units.

A vertical stretch is accomplished by multiplying the function value by 'a', where 'a' is the vertical stretch factor. That means the stretched square root function will be ...

  f(x) = √x . . . . original square root function

  h(x) = 6·f(x) = 6√x . . . . . vertically stretched by a factor of 6

A translation upward is accomplished by adding the translation amount to the function value. The translated function will be ...

  h(x) . . . . . original function

  g(x) = h(x) +7 . . . . . translation upward by 7 units

Our stretched and translated function is ...

  g(x) = 6√x +7

x² - 8x + 5 can be expressed as (x - 4)² - 11 in the form (x - a)² - b, where a = 4 and b = 11.

Let y = x² - 8x + 5 ..................( 1 )

Expanding (x - a)² - b we get,

x² - 2ax + a² - b ......................( 2 )

Equating ( 1 ) and (2), we get

x² - 8x + 5 = x² - 2ax + a² - b

Comparing the coefficient of x,

- 8  =  - 2a

a = 4

Comparing constants,

a² - b =  5

since we know a = 4

4² - b =  5

16 - b =  5

b = 11

Hence x² - 8x + 5  = (x - 4)² - 11

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The ratio of the radii of smaller circle to that of larger circle is 1/√2.

Let the Radius of smaller circle is "r".

So the area of the smaller circle will be π(radius)²=πr²

Let the Radius of the larger circle is "R".

So the area of the larger circle will be π(radius)²=πR².

In question it is given that, the area of the smaller circle is half of the area of larger circle.

That means,

area of smaller circle=1/2 area of larger circle

area of smaller circle=1/2 area of larger circleπr²=1/2 πR²

area of smaller circle=1/2 area of larger circleπr²=1/2 πR²r²=1/2 R²

area of smaller circle=1/2 area of larger circleπr²=1/2 πR²r²=1/2 R²r²/R²=1/2

area of smaller circle=1/2 area of larger circleπr²=1/2 πR²r²=1/2 R²r²/R²=1/2r/R=√1/2

area of smaller circle=1/2 area of larger circleπr²=1/2 πR²r²=1/2 R²r²/R²=1/2r/R=√1/2r/R=1/√2

Ratio of smaller circle to that of larger circle is 1/√2 .

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The values of sin2x, cos2x and tan2x is -3/5, -4/5 and 3/4 respectively.

What is sine function?

The ratio of the opposite side's length to the hypotenuse of a right-angled triangle is known as the sine function in trigonometry. A right triangle's unknown sides or angles can be determined using the sine function. The ratio of the side opposite the angle (also known as the perpendicular) and the hypotenuse is known as the sine of an angle in a right-angled triangle.

The ratio of the perpendicular of a right-angled triangle to the hypotenuse is known as the sine of the angle. The following is the sin formula: sin = Perpendicular / Hypotenuse.

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Answer:

125 in^2

Step-by-step explanation:

Assuming that s is the length of a side in the base.

For the above system of equations, 4x-4y=12 and 16x-6y=-12, the values of x and y are 4.5 and -10 respectively.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

Here,

4x-4y=12

16x-6y=-12

multiply equation 1 by 4,

16x-16y=48

-16x+6y=12

-10y=60

y=-10

-16x-60=12

-16x=72

x=72/16

x=4.5

The value of x is 4.5 and y is -10 for the given system of equation as 4x-4y=12 and 16x-6y=-12.

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The value of the variable 'y' will be 3. Then the correct option is A.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

The system of the linear equation is given below.

2x - 5y = 1                ...1

-3x + 2y = - 18         ...2

Multiply equation 1 by 2 and equation 2 by 5, then we have

4x - 10y = 2

-15x + 10y = - 90

Add both equations, then we have

4x - 15x = 2 - 90

11x = 88

x = 8

Then the value of the variable 'y' is calculated as,

-3 (8) + 2y = - 18

- 24 + 2y = - 18

2y = 24 - 18

2y = 6

y = 3

The worth of the variable 'y' will be 3. Then the right choice is A.

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Answer: The value of x is 0.625

Step-by-step explanation:

x=5/0.8

since figure A is scaled to 5 by 0.8, we divide 5 by 0.8 to find x.

x=0.625