Which of the following best describes the slope of the line below?
A. Positive
B. Zero
C. Negative
D. Undefined

The partial fraction decomposition in terms of x for the given equation is:

3x + 9 = (a(x-5) + b(x+1))

To solve for a and b, we need to multiply both sides by (x+1)(x-5). This will give us:

3x² + 4x - 45 = ax - 5a + ax + b

Now we can move all the terms with an x to one side and all the terms without an x to the other side. This will give us:

3x² + 4x - ax + b = 45 - 5a - b

We can rearrange this equation to get the following:

3x² - ax + (4 + b) = (45 - 5a - b)

Now we can use the quadratic formula to solve for a and b:

a = (4 + b) + √(4²- 4×3×(45 - 5a - b))/ (2×3)

b = (45 - 5a - (3x² - ax)) / (4 + b)

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Answer:

It's C

Step-by-step explanation:

StartFraction 3 x + 9 Over (x + 1) (x minus 5) EndFraction = StartFraction negative 1 Over x + 1 EndFraction + StartFraction 4 Over x minus 5 EndFraction

No, not all quadratic equations can be solved by factoring. This is because not all quadratic expressions, ax2 + bx + c, are factorable.

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The length of each of Rosie's jumps, given that she overshoots the 120 - step mark by 6 steps, is 21 steps.

Rosie is involved in the 120 - step contest and when she took 6 jumps, she overshot the 120 - step mark by 6 steps. This simply meant that she took 6 more steps over the 120 mark, thanks to her jump length.

The number of steps she took in total is therefore :

= 120 + 6

= 126 steps

This then means that the length of each jump was :

= Number of steps in total / Number of jumps

= 126 / 6

= 21 steps

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The solution is

a) The number of solutions to the equation is 1

b) Diego finishes the milkshake in 30 seconds and Lin finishes the milkshake in 36 seconds

c) Diego finishes the milkshake first

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the time to finish the milkshake by Lin and Diego be represented as A and B respectively

Now , the equation will be

The amount of milkshake with Lin = 12 ounce

The rate at which Lin finishes her milkshake = 1/3 milkshake per second

The time for Lin to finishes her milkshake A = amount of milkshake with Lin / rate at which Lin finishes her milkshake

Substituting the values in the equation , we get

The time for Lin to finishes her milkshake A = 12/ ( 1/3 )

The time for Lin to finishes her milkshake A = 36 seconds

Now ,

The amount of milkshake with Diego = 20 ounces

The rate at which Diego finishes his milkshake = 2/3

The time for Diego finishes his milkshake B = 20 / ( 2/3 )

The time for Diego finishes his milkshake B = 30 seconds

Hence , Diego finishes his milkshake faster

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a) The system of equations to find Fred and Natalie's ages are:

b) Solving the system of equations shows that their respective ages are:

A system of equations is two or more equations simultaneously or concurrently solved.

We call this a system of equations or simultaneous equations because they are solved at the same time.

Let Natalie's age = x

Let Fred's age = y

The total ages of Natalie and Fred = 38

x + y = 38

Let Natalie's age = 3x

Let Fred's age = y

The total ages of Natalie and Fred = 66

3x + y = 66

Subtract Equation 1 from Equation 2:

3x + y = 66

-

x + y = 38

2x = 28

x = 14

y = 38 - 14

y = 24

Thus, Fred is 24 years old while Natalie is 14 years.

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The triangle's third side will measure 6.71 units in length.

According to the Pythagorean theorem, two squares added together equal the square of the longest side.

The Pythagoras theorem's equation is as follows:

H² = P² + B²

The triangle's third side will be the following length:

Let x represent the triangle's third side's length. Next, we have

9² = 6² + x²

81 = 36 + x²

x² = 45

x = 6.708

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So, on solving the provided question, we cans ay that new slope interest equation is y = 3x +c

In mathematics, the intersection point is the place on the y-axis where the slope of the line crosses. a place where the y-axis crosses on a line or curve. Y = mx+c, where m stands for the slope and c for the y-intercept, is used as the equation for the straight line to show this. The slope (m) of the line and its y-intercept (b) are emphasised in the equation's intercept form. When an equation has the intercept form (y=mx+b), the slope is m and the y-intercept is b. Some equations can also be rewritten such that they seem to be slope intercepts. If y=x is rewritten as y=1x+0, for instance, the slope and y-intercept are both changed to 1.

given, x = 5, that is lope

coordinates = (1,0)

new slope interest equation is

y = 3x +c

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The correct question is -

Draw a line parallel to the line x=5 that intersects the x-axis at (1,0). What is the equation of this line?

The range of the relation on the graph is:

R: {1, 2, 6}

For a relation y = f(x), the range is defined as the set of the possible outputs of the function (the possible values of y).

Here we can see a graph of 3 points, such that the coordinates of these points (on the form (x, y)) is:

(3, 6), (5, 2) and (6, 1)

The range is the set of the second values of each of these pairs, so the range in this case is:

R: {1, 2, 6}

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The integer value of both values is 10 and -4.

Zero, a positive natural number, or a negative integer denoted by a minus sign are all examples of integers. The inverse additives of the equivalent positive numbers are the negative numbers.

A positive integer and a negative integer cannot be multiplied. A pair of positive integers have a positive product. Two negative integers add up to a positive number. A positive integer and a negative integer do not add up to a positive number.

Positive and negative numbers are used differently in everyday life. Although positive numbers are frequently employed everywhere, negative integers are also used to measure temperature because it is possible for a city's temperature to be either -4°C or -10°C.

(+6)-(-3) (+1)

⇒ 6 + 3 + 1        [using rules of integers, (-)(-) yields (+)]

⇒ 9 + 1

⇒ 10

(-3)-(-7)-(+8)

⇒ -3 + 7 - 8       [using rules of integers, (-)(+) yields (-)]
⇒ -3 - 8 + 7

⇒ -11 + 7        

⇒   -4   [As -11 is greater than 7]

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Answer:

The simplest form would be 5 1/8

Step-by-step explanation:

You don't have a common factor with 41 and 8, so the real reduced answer would just be mixed, as 5 1/8.

Answer:

B

Step-by-step explanation:

3x + 8 = 2(x + 4) ← distribute parenthesis

3x + 8 = 2x + 8 ( subtract 2x from both sides )

x + 8 = 8 ( subtract 8 from both sides )

x = 0

B is the correct answer

Step-by-step explanation:

B is the correct answer

The rational expression that simplifies to 5 square root of 3 is given as follows:

C. [tex]\sqrt{75}[/tex]

A rational expression is a term that involves a root in the expression.

The simplified rational expression for this problem is given as follows:

[tex]5\sqrt{3}[/tex]

The original expression, from which the simplified expression was obtained, can be obtained moving the number 5 back to the square root.

The number is moved back into the square root with an exponent of 2, hence the original expression is obtained as follows:

[tex]\sqrt{3 \times 5^2} = \sqrt{75}[/tex]

Which is the original expression, meaning that the correct option regarding which expression simplifies to five times the square root of three is given by option C.

The problem is given by the image presented at the end of the answer.

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Therefore , the solution of the given problem of slope intercept comes out to be  y = 0.66x +12.65.

The gradient intercept method can be used once you are satisfied that Y = mx + b holds true. The direction form can be used to illustrate a hypothesis for a line by focusing on a single point directly and its slope. The slope is determined by the increase across the run and is first represented by the point form (x,y). The slope can be determined using slope intercept method, which is y = mx + b. (0, b). The direct form is a method for formulating a prediction equation for a line by making just one precise declaration about a vector slope.

Here,

Given : slope = 2/3

and coordinates = (0 , 12.65)

Thus ,

the equation of the given line by using formula of slope intercept:

=> y- y1  = m(x-x1 ) + c

=> y - 12.65 = 2/3*x

=> y = 0.66x +12.65

Therefore , the solution of the given problem of slope intercept comes out to be  y = 0.66x +12.65.

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Answer:

x= 92 degrees

Y=44 degrees

Answer: prime

Step-by-step explanation:

there is no greatest common factor (GCF) of the coefficients: 8 and -27. And the variables: c and d, are different so the polynomial is in its prime form.

For a triangle with vertices L (1 , 8),, M (0 , 0) , and N (-8 , 1)  the plot is plotted and the slope and lengths are

slope of LM =  8

slope of MN = 8

slope of NL =  7/9

length of LM = √65

length of MN = √65

length of NL = √130

The slope, m of the lines is calculated the formula

m = (y₀ - y₁) / (x₀ - x₁)

where

m = slope

x₂ and x₁ = points in x coordinates

y₂ and y₁ = points in y coordinates

Slope of LM  L (1 , 8), M (0 , 0)

m = (8 - 0) / (1 - 0)

m = (8) / (1)

m = 8

Slope of LM  L (1 , 8), M (0 , 0)

m = (8 - 0) / (1 - 0)

m = (8) / (1)

m = 8

Slope of NL,  N (-8 , 1), L (1 , 8)

m = (1 - 8) / (-8 - 1)

m = (-7) / (-9)

m = 7/9

The length of line in an ordered pair is calculated using the formula

d = √{(x₂ - x₁)² + (y₂ - y₁)²}

where

d = distance between the points

x₂ and x₁ = points in x coordinates

y₂ and y₁ = points in y coordinates

For LM  L (1 , 8), M (0 , 0)

d = √{(1 - 0)² + (8 - 0)²}

d =√{1 + 64}

d = √65

For MN  M (0, 0) N (-8 , 1)

d = √{(0 + 8)² + (0 - 1)²}

d =√{64 + 1}

d = √65

For NL N (-8 , 1), L (1 , 8)

d = √{(-8 - 1)² + (1 - 8)²}

d =√{81 + 49}

d = √130

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Answer:

13.29x

Step-by-step explanation:

1.97x - 4.83x = -2.86x

-2.86x + 7.95x = 5.09x

5.09x + 11.83x = 16.92x

16.92x - 3.63x = 13.29x

D) 2, 3, 4 is not a pythagorean triplet.

Pythagoras theorem is in the form of;

a²+b²=c²

Applying this formula to the given options we get'

a) 3, 4, 5 is a Pythagorean triplet because 3^2 + 4^2 = 9 + 16 = 25 = 5^2

b) 6, 8, 10 is not a Pythagorean triplet because 6^2 + 8^2 = 36 + 64 = 100 = 10^2

c) 5, 12, 13 is a Pythagorean triplet because 5^2 + 12^2 = 25 + 144 = 169 = 13^2

d) 2, 3, 4 is not a Pythagorean triplet because 2^2 + 3^2 = 4 + 9 = 13 ≠ 4^2

In other words the pythagorean theorem states that in a right angled triangle, the square of the hypotenuse is the sum of the squares of the other 2 sides.

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The slope-intercept method is a way to graph a linear equation in the form of y = mx + b, where m is the slope and b is the y-intercept. This method allows you to find the slope and y-intercept of the line and use that information to graph the line.

An explanation graph is what?

A graph shows how two variables that are typically measured along one of a pair of axes at right angles relate to one another.

To graph a linear equation using the slope-intercept method, you can follow these steps:

Identify the y-intercept by looking for the constant term (b) in the equation. The y-intercept is the point where the line crosses the y-axis, so it will have an x-coordinate of 0.

Plot the y-intercept on the coordinate plane.

Identify the slope of the line by looking for the coefficient of the x-term (m) in the equation. The slope represents the steepness and direction of the line.

Using the slope and the y-intercept, pick a point on the x-axis and use the slope to find the corresponding point on the y-axis.

Plot the point found in step 4.

Plot the two spots and then draw a straight line through them.

Note that this method will work for any linear equation where y = mx + b, and can help you graph a line quickly.

Also note that there is another method to graph a linear equation, it's called the point-slope method which is starting from any point on the line and use the slope to locate the additional line points.

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Answer:

48 centimeters

Step-by-step explanation:

This deals with the midline theorem.

The midline is defined by a seg that is joined by the midpoints of 2 sides.

The midline is half of the base, so if it is 10, the base is 20 cm.

You see that 26 cm is 1/2 of the hypotenuse because it is bisected, sot he whole thing is 26(2) or 52.

Now you have to solve for x using the Pythagorean theorem.

20^2 (400) + x^2  = 52^2 (2704)

Subtracted 400 from both sides to get x^2 by itself.

x^2 = 2304

Take the square root of both sides to isolate x (take the principle root)

x= 48 centimeters.

Hope this helps!

On solving the provided question we can say that the equation will be -

37.79x + 39.71y = 0.69 = 75.4 +75.4 = 150.8

An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.

the equation will be -

37.79x + 39.71y = 0.69

x = 2

y = 2

75.4 +75.4 = 150.8

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The total length of the flowers that Judy measures will be the 1 3/4 inches.

A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.

From the information, Judy measured the lengths of her flowers, in inches. The total length of the flowers will be the sum. This will be:

= 1/4 + 1/2 + 3/4 + 1/4

= 1 3/4 inches.

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Complete question

Judy measured the lengths of her flowers, in inches. The lengths are shown below.

1/4

1/2

3/4

1/4

What is the total length of the measurement?

The height of the redwood has been calculated as 372 meters.

In  order to get the height of this tree, I would have to make use of the similar triangles method. The proportion is set as

tree height / tree shadow = Eric's height / Eric's shadow

Eric's height is 6 feet, his shadow is 8 feet

The proportion is 6 / 8

= 3 / 4

To get the height of the tree we have to multiply the proportion by the distance with which Eric is away from the tree

= 3 / 4 * 496

= 372 feet

The redwood is 372 feet

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Answer: m = -1/2

Step-by-step explanation:

Bing bang boomarang i have no idea

To find the perpendicular distance between two lines in 3D, you can use the dot product of the vector joining the two lines and the cross product of the direction vectors of the two lines, divided by the length of the cross product vector.

To find the perpendicular distance between two lines in 3D, you can use the following method:

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Answer:

Step-by-step explanation:

2y+7=3x

-3x+2y=-7

1/2x+4y=6

x+8y=12

A. Using the given information, y expressed in terms of x is y = x + 50

B. The table that shows the relationship between y and x is

x               y

10             60

20            70

30             80

40             90

50             100

From the question, we are to express y in terms of x

From the given information,

There are x sparrows in a tree and 50 sparrows on the ground beneath the tree

If y represent the total number of sparrows in the tree and on the ground,

Then,

We can write that

y = x + 50

B.

We are to make a table to show the relationship between y and x

Using the equation above

y = x + 50

When x = 10

y = 10 + 50

y = 60

When x = 20

y = 20 + 50

y = 70

When x = 30

y = 30 + 50

y = 80

When x = 40

y = 40 + 50

y = 90

When x = 50

y = 50 + 50

y = 100

Thus,

The table is:

x               y

10             60

20            70

30             80

40             90

50             100

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