The graph of a line passes through the two points below
(2,-4);(-3,1)
Which of these can be used to determine the slope of the line

The equation for a is   a=2A-b

Function, in mathematics, is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given here:  A=1/2(a+b)

                     a=2A-b

Hence, the equation for a is   a=2A-b

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The solution to the equation 3(4x-10) = 2(3x-30) is x = -5.

What is algebra?

Algebra is a branch of mathematics that deals with mathematical operations and symbols used to represent numbers and quantities in equations and formulas. It involves the study of variables, expressions, equations, and functions.

Let's solve for x:

3(4x - 10) = 2(3x - 30)

First, we can simplify both sides by distributing the coefficients:

12x - 30 = 6x - 60

Next, we'll move all the x terms to one side of the equation and the constants to the other side:

12x - 6x = -60 + 30

Simplifying further:

6x = -30

Finally, we can solve for x by dividing both sides by 6:

x = -5

Therefore, the solution to the equation 3(4x-10) = 2(3x-30) is x = -5.

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The simplest forms of the expressions are;

a) 1/4y^10

b) 1/243d^18q

We have to note that the simplest form is the form of the expression that we can not be able to break down further. We mean that when we get to the simplest form, there is no other way that we can be able to express it.

Let us now try to use the laws of the exponents to bring the expressions to the simplest forms.

a) 3(y^-4)^4/12y^-6

1/4y^-16/y^-6

1/4y^-10

1/4y^10

b) (3d^-2)^-4/3d^10q

3^-4 d^-8/3d^10q

1/243d^18q

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The value of x in the following parallelogram is 15

You should recall that a parallelogram is a quadrilateral whose opposite sides are equal and parallel

The given sides are

This means that

X + 10 = 2x -5

Collecting like terms we have

x-2x = -5-10

-x = -15

Dividing by -

We have x= 15

Therefore x is 15 in the parallelogram.

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Answer:fx

Step-by-step explanation:

The yards of thread that will take to make an entire sock will be 3 3/4 yards.

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.

In this case, 2 1/2 yards of thread to make 4 /6

of a sock.

The yards of thread that will take to make an entire sock will be:

= 2 1/2 ÷ 4 / 6

= 5 / 2 × 6/4

= 30 / 8

= 15 / 4

= 3 3/4 yards.

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Answer:

b < -30

Step-by-step explanation:

27 > B + 57   Subtract 57 from both sides

27 - 57 > b +57 - 57

-30 > b

or

b < -30

Answer: 225°

Step-by-step explanation:

The correct option is D)

Refer Figure

Given:

ABCD  is a square

ABP  is an equilateral triangle

AB=BP=BC  (△ABP is equilateral and AB and BC belong to a square, hence all are equal)

∠ABC=∠ABP+∠PBC=60°+∠PBC

90°−60°=∠PBC

∠PBC=30°

In △BPC

BP=BC

∠BPC=∠BCP= 2

180−∠PBC

​ ( angles opposite to equal sides of a triangle are equal)

∠APC=∠APB+∠BPC=(60+75)°=135°

Hence, Reflex ∠APC=(360−135)°=225°

The value of the x is 11.

What are vertically opposite angles?

Opposite angles are the angles directly opposite each other where two lines cross. The intersection point is called the vertex, which is where the lines connect to form the angle. Opposite angles are also called vertical angles. In this instance, the word vertical refers to the vertex as opposed to direction.

We have given,

Two opposite angles:

(6x + 1)°, and 67°

So, We need to determine the value of x.

We know that the property of opposites angles, which the opposite angles are equal to each other.

So, (6x + 1)° = 67°

By calculating further:

6x + 1 = 67

6x = 67 - 1

6x = 66

x = 66/6

x = 11

Hence, the value of the x is 11.

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Step-by-step explanation:

10x + 17 + 8X - 31 + 6x - 8 = 180

Use this equation and solve this equation and you will find the answer

When A point is (3, 1) and B point is (-1 , -1), the midpoint of AB is ( 2, 1) . The line segment's exact midway is where the midpoint is located.

The term "midpoint" describes a point along a line that connects two points. The midway is situated between the two reference locations, which are the line's ends. The line connecting these two places is split into two equally sized sections by the middle. A point that splits a line segment into two equal halves is known as the midway. In other words, the line segment's exact midway is where the midpoint is located. It is demonstrably true that the middle of a number line has the same value as the average of any two matching places on the line.

given

midpoint of AB is equal to (x2 - x1) / 2 (3 + 1) / 2 = 2.

the midpoint of AB is 1

the midpoint of AB is (y2 - y1)/2

= (1+1)/2.

= ( 2 ,1 )

When A point is (3, 1) and B point is (-1 , -1), the midpoint of AB is ( 2, 1) .

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The solution to the expression -11/14 x (-1/17) is 11/238

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

-11/14x(-1/17)

Express properly

So, we have the following representation

-11/14 x (-1/17)

Remove the brackets

This gives

-11/14 x (-1/17) = 11/14 * 1/17

So, we have

-11/14 x (-1/17) = 11/238

Hence, the solution is 11/238

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Answer:

The volume of wood in a tree varies directly with the height and the square of the length of the tree. This means that if we increase the height of the tree, the volume of wood in the tree will also increase, and if we increase the length of the tree, the volume of wood will increase by the square of that increase.

This relationship can be expressed mathematically as:

V = khl^2

Where V is the volume of wood in the tree, h is the height of the tree, l is the length of the tree, and k is a constant of proportionality.

This relationship is based on the assumption that the cross-sectional area of the tree remains constant, and that the volume of wood in the tree is directly proportional to the height and the square of the length of the tree.

Answer:

ST = 10

Step-by-step explanation:

Δ RSQ and Δ RTP are similar by the AA postulate , then

the ratios of corresponding sides are in proportion , that is

[tex]\frac{RS}{RT}[/tex] = [tex]\frac{RQ}{RP}[/tex] ( substitute values )

[tex]\frac{5}{RT}[/tex] = [tex]\frac{9}{9+18}[/tex] = [tex]\frac{9}{27}[/tex] = [tex]\frac{1}{3}[/tex] ( multiply both sides by 3 to clear the fraction )

RT = 3 × 5 = 15

Then

ST = RT - RS = 15 - 5 = 10

In 1663200 ways objects can be chosen if the order of the choices is relevant. The solution has been obtained using permutation.

What is permutation?

An arrangement of items in a specific manner or sequence is referred to as a permutation. It is important to think about both the selection and the arrangement when dealing with permutation. Briefly put, permutations depend much on ordering. In other words, a permutation is a combination that is ordered.

We want to choose 7 objects without replacement from 11 distinct objects

So, since the order of the choices is relevant, we will use permutation.

Therefore,

⇒nPr = n! ÷ (n - r)!

⇒11P7 = 11! ÷ (11 - 7)!

⇒11P7 = 11! / 4!

⇒11P7 = (11 * 10* 9 * 8 * 7* 6 * 5)

⇒11P7 = 1663200 ways

Hence, in 1663200 ways objects can be chosen if the order of the choices is relevant.

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Answer:

Below

Step-by-step explanation:

A)  Juan reads at   57 pages /hr

B)  Juan reads 9 pages more per hour (57-48) than Lexi

       in 7 hours this will be   7 hr * 9 p/hr = 63 pages

A vertical line in geometry is one that crosses the page from top to bottom.

A vertical line in geometry is one that crosses the page from top to bottom. Its cousin is the horizontal line that spans the page from left to right. A horizontal line and a vertical line are perpendicular.

Businesses utilize segmentation as a marketing strategy to focus on a certain market segment or type of customer. While vertical segmentation sharpens your marketing emphasis to target customers in a smaller demographic, horizontal segmentation entails offering a product to a broad range of consumers.

A horizontal object is one that is perpendicular to the horizon. Due to the fact that vertical is the polar opposite of horizontal, anything that forms a 90° (right angle) with either the horizontal or the horizon is referred to as vertical. This means that the horizontal line is one that crosses from left to right. Mathematical applications of the horizontal and vertical.

Therefore, the correct answer is option C. (5.-4) and (-2, 3).

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The correct option is B.

The Equation that represents the line that has a slope of 1/3 and an x-intercept of 5 is y-0 = 1/3(x-5)

The slope of a line is the measure of the steepness of a line and its direction. It can be used to predict whether the lines are parallel, perpendicular, or none.

The slope of any line can be calculated using any two distinct points lying on the line.

y -y1 = m(x-x1)

where y1 = 0

x1 = x-intercept = 5

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

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The simplest form of the given expression is px=-3x^3-2x²-6x-16,r(x)=-45, and q(x)=x-3.

What is polynomials?

Using variables and coefficients, polynomials are algebraic expressions. The term "indeterminates" is sometimes used to describe variables. The terms Poly and Nominal, which together signify "many" and "terms," make up the word polynomial. When exponents, constants, and variables are combined using mathematical operations like addition, subtraction, multiplication, and division, the result is a polynomial (No division operation by a variable). The expression is categorized as a monomial, binomial, or trinomial based on the number of terms it contains.

(-x^4+7x^3+2x+3)/ (x-3)

=-x² + 4x² + 12x + 38 + 117/(x - 3)

Hence the simplest form of the given expression is px=-3x^3-2x²-6x-16,r(x)=-45, and q(x)=x-3.

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The number of items is discrete and the total time is a continuous variable recorded by the pet store.

The two things recorded by the pet store;

first is the number of items purchased and another is the time between the given interval of 8 am to 11 am.

we know that

the number of items was counted so it will be discrete and the total time was measured so it will be a continuous variable.

Therefore, the types of variables recorded by the pet store are the number of items as a discrete variable and the total time as a continuous variable.

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Answer:

Step-by-step explanation:

1 radian is equal to 180^0/Pi

[tex]55=55*\frac{180}{\pi y} \\=54.97787[/tex]

If the sum of two digits t and u is t + u = 9, then the second equation is option 2: t = 1/2 u.

What is a digit?

In math, single integers called digits are used to represent values. To represent all mathematical values, the numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 are employed in various combinations and repetitions.

The first equation is as given t + u = 9

Second equation t = u/2 since the number in the tens position is one half of the one in the units. So if you divide u by two, you should have one t, as the equation states.

The second equation is t = (1/2)u => u = 2t

When we replace this in first equation we get -

t + 2t = 9  

3t = 9  

t = 9/3

t = 3

When we replace it again in the equation -

u = 2 t

= 2 · 3

= 6

The requested number is 36.

Therefore, the number is 36 and the second equation is t=u/2.

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Answer: c -2

Step-by-step explanation:

y=-2x+3

-2 is the slope because y= mx+b and m is the slope

Answer:

a) D [-2x +3] | b) D [-2]

Step-by-step explanation:

Get it into the form y=mx+b

To do this subtract 2x from 2x+y=3 to get y= -2x+3

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

Part B: Find the slope

The slope is the coefficient in front of the x in the slope-intercept form.

In this case, it is -2.

Therefore, -2 is the slope of the line.

Answers: [-2x + 3] and [-2]

Answer:

[tex]y=\frac{3}{4}x-\frac{7}{2}[/tex]

Step-by-step explanation:

[tex]m_{\parallel}=\frac{3}{4} \\ \\ y-1=\frac{3}{4}(x+6) \\ \\ y-1=\frac{3}{4}x-\frac{9}{2} \\ \\ y=\frac{3}{4}x-\frac{7}{2}[/tex]

Answer: 3/1. 6/2. 9/3. 12/4. 15/5. 18/6. 21/7. 24/8. 27/9 and many more

Step-by-step explanation:

Answer:

Step-by-step explanation:

1)  m∠1 = m∠2

4x - 1 = 2x + 7

2x = 8

x = 8/2 = 4

2)  m∠1 = (m∠YWX) / 2 = 62/2 = 31

3)  AB is 4 squares long.  Start at A, go over 2 squares, then draw a line straight up to point C.

4)  Altitude is the height of a triangle.  Find the midpoint of the bottom line, then draw a line straight up to the vertex (top of the triangle).  Your drawn line should form a right angle with the bottom line.

Therefore , the solution to the given problem of function comes out to be ss a result, Rolle's Theorem remains true.

Mathematics deals with numbers and their variants, formulae and associated structures, geometries and their areas, and locations where they might be found. The term "function" describes the connection between a group of input, of which each has a corresponding output. A function is an association among inputs and outputs where each input results in a single, unique output. A realm as well as a codomain, or scope, are assigned to each function. Functions are typically denoted by the letter f. (x). The input is an x. On activities, one-to-one activities, many-to-one functions, within operations, and on functions are the four main categories of functions that are available.

Here,

Consider

f(-1)=1-[tex](-1 )^{\frac {2}{3}}[/tex]=0

and f(1)=1-[tex](-1 )^{\frac {2}{3}}[/tex]=0

So, f(-1)= f(1) (1)

As a result of differentiating f(x) with regard to x, we now have

f'(x)= -2 / 3

Consequently, f'(0) is false.

So, at 0inleft (-1,1 ), f cannot be deduced.

Therefore, the given function in the range (-1,1) does not satisfy Rolle's theorem.

As a result, no c exists in (-1,1) for which f'(c )=0 even though f(-1)=f(1 ).

As a result, Rolle's Theorem remains true.

Therefore , the solution to the given problem of function comes out to be ss a result, Rolle's Theorem remains true.

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