Graph the line that passes through the points (8, -3) and (4, 1) and
determine the equation of the line.

Answer:

see explanation

Step-by-step explanation:

given the equation

a = [tex]\frac{k}{b}[/tex]

to find k use the given condition a = 8 when b = 6 , then

8 = [tex]\frac{k}{6}[/tex] ( multiply both sides by 6 to clear the fraction )

48 = k

a = [tex]\frac{48}{b}[/tex] ← equation of variation

2

if b = 3

a = [tex]\frac{48}{3}[/tex] = 16

3

if b = 4

a = [tex]\frac{48}{4}[/tex] = 12

4

if b = 12

a = [tex]\frac{48}{12}[/tex] = 4

5

if b = 1.5

a = [tex]\frac{48}{1.5}[/tex] = 32

6

if b = 3.6

a = [tex]\frac{48}{3.6}[/tex] = 13.3333.. = 13 [tex]\frac{1}{3}[/tex]

7

if b = 4.8

a = [tex]\frac{48}{4.8}[/tex] = 10

for the remaining questions, rearrange the equation with b as the subject

a = [tex]\frac{48}{b}[/tex] ( multiply both sides by b )

ab = 48 ( divide both sides by a )

b = [tex]\frac{48}{a}[/tex]

8

if a = 3

b = [tex]\frac{48}{3}[/tex] = 12

9

if a = 4

b = [tex]\frac{48}{4}[/tex] = 12

10

if a = 4.5

b = [tex]\frac{48}{4.5}[/tex] = 10.666... = 10 [tex]\frac{2}{3}[/tex]

11

if a = 4.8

b = [tex]\frac{48}{4.8}[/tex] = 10

12

if a = 3.6

b = [tex]\frac{48}{3.6}[/tex] = 13.333... = 13 [tex]\frac{1}{3}[/tex]

13

if a = 6

b = [tex]\frac{48}{6}[/tex] = 8

Negative Slope can be used to describe the line representing the relationship between the number of balloons remaining and the number of hats created.

In the given question, we have to find what phrases can be used to describe the line representing the relationship between the number of balloons remaining and the number of hats created.

As we know that,

(1) Negative Slope: A line with a negative slope is one that is moving from left to right in a downward direction. The rise to run ratio of the line, in other words, is negative.

(2) Decreasing Function: For a given function, y = F(x), the function is known as an increasing function if the value of y increases as the value of x increases, and the function is known as a decreasing function if the value of y decreases as the value of x increases.

(3) Constant Slope: Small slopes correspond to low speeds, negative slopes to high speeds, and constant slopes (straight lines) to steady speeds.

Hence, Negative Slope can be used to describe the line representing the relationship between the number of balloons remaining and the number of hats created.

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Step-by-step explanation:

credits are also on there

The function that describes the depth of the soil is h(x) = -(1/2)x + 8.

Where x is the number of bags of soil.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

Depth of the soil = 8 inches

One bag of soil increases by 1/2 of an inch.

Now,

The function denotes the depth of the soil.

h(x) = -(1/2)x + 8

Where x is the number of bags of soil

Thus,

The function is h(x) = -(1/2)x + 8.

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It is possible for a valid argument to have a false conclusion as long as at least one premise is false.

When the premises are genuine, validity guarantees a true conclusion; when the premises are wrong, validity provides no assurance. Even in a legitimate argument, faulty premises might lead to either a true or erroneous conclusion. In many cases, it was chance rather than reasoning that led to the correct conclusion.

Avoid including: Important evidence or analysis that was not provided in the main body for a stronger conclusion paragraph.Generic closing phrases (for example, “In conclusion…”)Weak remarks that undercut your argument (for example, “There are valid points on both sides of this debate.”)

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The inequality to discover the values of x for which the rectangle's perimeter is under 112 is x<  26.

An inequality in mathematics is a relationship between two expressions or values that is not equal. Thus, imbalance leads to inequality. An inequality creates the link between two values that are not equal in mathematics. Egality is distinct from inequality. When two values are not equal, most commonly use the not equal symbol (). Different inequalities are used to contrast values, no matter how small or large. Many simple inequalities can be resolved by modifying the two sides until the variables are all that remain. But a number of things contribute to inequality: Negative values on both sides are divided or added. Trade off the left and right.

given

perimeter of a rectangle = length + length + width + width

length + length + width + width = perimeter of a rectangle

(x +4) + (x+4) + x + x < 112

x + 4 + x + 4 + x + x < 112

4x + 8 < 112

4x < 104

x < 26

So ,The inequality to discover the values of x for which the rectangle's perimeter is under 112 is x<  26.

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The average monthly salary of all the staff is going to be 19,333.34 ₹.

Average is the value obtained by dividing the sum total of a set of figures by the number of figures. In this question, we have to find the average monthly salary of all the staff taken together,

So the sum total of the set of figures here will be (20,000 × no. of males + 18,000 × no. of males) ₹ and the number of figures here will be no. of males + no. of females. It's given that

No. of males=10

No. of females=5

So, the total no. of figures = 15

Sum total of  set of figures = (20,000 × 10 + 18,000 × 5 )₹ and the average will be

=(20,000 × 10 + 18,000 × 5) ₹/15

=(200,000+90,000)/15₹

=290,000/15 ₹

=19,333.34 ₹

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Answer:

It appears that the solution set of the inequality 5n + 1.5 ≥ 4 is the set of all real numbers greater than or equal to -0.3. This can be determined by looking at the graph and noting that the region to the right of the vertical line x = -0.3 is shaded, which indicates that all values of x in that region are included in the solution set.

To verify this, we can substitute -0.3 into the inequality in place of n to see if the inequality is satisfied:

5(-0.3) + 1.5 ≥ 4

This simplifies to:

-1.5 + 1.5 ≥ 4

Which further simplifies to:

0 ≥ 4

Since this is not true, -0.3 is not a solution of the inequality. However, all values of x that are greater than or equal to -0.3 are solutions, as indicated by the shaded region on the graph.

Step-by-step explanation:

The modulus increases by a factor of 10 and the argument increases by 5π/3.

Modulus of the complex number:

The modulus of a complex number is the square root of the sum of the squares of the complex number's real and imaginary parts. If z is complex, the absolute value of complex z is given by √{[Re(z)]2 + [Im(z)] and denoted by |z|. exclusive. The absolute value of a complex number z = a + ib is the distance between the origin (0, 0) of the complex plane and the point (a, b). The modulus of a complex number is a distance, so its value is always non-negative.

The absolute value of a complex number z = x + iy denoted by |z| is given by the formula |z|. Given = √(x2 + y2), where x is the real part of the complex number z and y is the imaginary part. The modulus of a complex number z can also be computed using the conjugate of z. Since

z. z = (x+ iy)(x −iy)

=x²+y² , we have

    z. z = |z|²

⇒ |zI =√z. z.

Then,

The modulus of the z will be =|z|= √p²+q²

We have,

z = 5 – 5i √3

So,

Now rewrite this given equation in the form of z = r(Cosθ + iSinθ),

For this first calculate the modulus,

|Z| = √((5√3)² + 5²)

|Z| = √(25×3 + 25)

|Z| = √(100) = 10

And,

Argument, θ = tan⁻¹ (b/a)

θ = tan⁻¹ (5√3/5)

θ = tan⁻¹ (√3)

θ = 71

Therefore, the modulus increases by a factor of 10, and the argument increase by 5π/3.

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Answer:

The modulus increases by a factor of ✔ 10.

The argument increases by ✔ 5π over 3

Step-by-step explanation:

correct on edge 2023

Answer:

x = 90

Step-by-step explanation:

The diagram shows that angles 1 and 4 correspond with each other. Given that the two lines should be parallel, corresponding angles have the same answer. When corresponding angles cross at the same relative location (known as the junction), they will have the same angle measure.

So, set the 1st and 4th angles equal to each other.

3x-160 = x+20

2x = 180

x=90

Answer:x=90

Step-by-step explanation:Angles 1 and 4 must be equal to each other, as they are corresponding angles, so you set 3x-160 equal to x+20 and after solving, you get x is equal to 90.

the distance it will cover before coming to rest is 75m. Solved using the concept of velocity.

Simply said, velocity is the rate of movement in a certain direction. such as the speed of a car driving north on a highway or the pace at which a rocket takes off.

Due to the fact that it includes both magnitude and direction, velocity is a vector quantity. Since acceleration is only the rate at which velocity changes, acceleration is likewise a vector quantity.

Given that,

initial velocity (u) = 30 m/s

acceleration (a) = - 6 m/s²

As we know,

v² = u² + 2as

or, 0 = (30)² + 2 × (-6) × s

or, s = 75 m

Hence, the distance it will cover before coming to rest is 75m

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Answer:

cant answer sorry i didnt realize it was an equation

Step-by-step explanation:

The polynomial which has a degree of  7 can be known as a polynomial of class 7.

Polynomials are expressions containing of variables and constants. The variable having the highest power forms the degree of the polynomial.

The degree of a polynomial with one variable is known as the highest exponent power of that variable in the mentioned polynomial.

Finding the degree of a polynomial with more than one variable is a simple task , as adding the exponents of each variable in the supplied terms and then determining which term has the highest degree. That is the polynomial's degree.

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Answer:

Use the following denomination (Ghana cedis 200,100,50 and 20)to find the quantities of notes

1.3584655000

2.85760000

3.146737000

4.5555627000

5.7777000

please help

Step-by-step explanation:

1. Eliminate any constant that is on the same side as the variable.

2. Use inverse operations to isolate the variable by itself.

3. Whatever you do to one side you do to the other.

Answer:

60 because their a 2 induivedinal in 1 sock.

Step-by-step explanation:

30 x 2 = 60

The general two steps to solve the two-step equations are:

Step 1: Addition and subtraction to isolate the variable.

Step 2: Multiplication or division to determine the value of the variable.

Now, According to the question:

Solving Two Step Equations:

Two step equations are very easy to solve. It includes just one extra step as compared to one-step equations to solve. We can solve a two-step equation by isolating the variable (usually represented by an alphabet or letter) on one side of the equation and all other values on the other side. The general two steps to solve the two-step equations are:

Step 1: Addition and subtraction to isolate the variable.

Step 2: Multiplication or division to determine the value of the variable.

Generally, two step equations are of the form ax + b = c, where a, b, c are real numbers. A few examples of two step equations are:

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to get the equation of any straight line, we simply need two points off of it, let's use those from the picture below.

[tex](\stackrel{x_1}{-10}~,~\stackrel{y_1}{-100})\qquad (\stackrel{x_2}{30}~,~\stackrel{y_2}{140}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{140}-\stackrel{y1}{(-100)}}}{\underset{\textit{\large run}} {\underset{x_2}{30}-\underset{x_1}{(-10)}}} \implies \cfrac{140 +100}{30 +10} \implies \cfrac{ 240 }{ 40 } \implies 6[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-100)}=\stackrel{m}{ 6}(x-\stackrel{x_1}{(-10)}) \\\\\\ y +100 = 6 ( x +10)\implies y+100=6x+60\implies {\Large \begin{array}{llll} y=6x-40 \end{array}}[/tex]

The value of x in the give trigonometrical question is 10.6 when hypotenuse is 13 in the right angled triangle.

Trigonometry is the branch of mathematics that deals with particular functions of angles and how to use them in calculations. There are six common trigonometric uses for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (csc) are their respective names and acronyms.

The figure illustrates these six trigonometric functions in relation to a right triangle. For instance, the triangle has an angle A, and the sine of A, or sin A, is defined as the ratio between the side opposite to A and the side opposite to the right angle (the hypotenuse).

Cos 35° = x/13

0.819152 = x/13

x = 0.819152 × 13

x = 10.6

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It will take a time of n/60m minutes for the jetski to cover n metres at the same speed.

Speed = distance/ time

Speed = m/s

For the distance of n meters.

distance = speed * time

n = m/s*time

n = m /s* time

Time = n(m/sec)

Time = n/m * sec

Time = n/60m min

Thus, it will take  n/60m minutes for the jetski to cover n metres at the same speed.

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Answer: $120

Step-by-step explanation:

So you find 1/3 of 180, basically, you multiply them which is 60.

So if he has a third of the money, he has $60, but he needs 180. So we subtract $180 (how much money he needs) from $60 (the money he has). Which is 120 dollars, so the boy needs $120.

Or 2/3 more.

The coordinate points of the point P is (-3.5, 2.3).

What is a coordinate plane?

Two number lines combine to form a two-dimensional surface known as a coordinate plane. It is created when the origin, a point where the X- and Y-axes coincide, is crossed by a horizontal line.

The ratio in which the point 'P' divides the line segment RQ is -

a:b = 5:1

The coordinates of the end-points of line segment RQ are -

R(4, -1)  and  Q(-5, 3).

The coordinates of the point H are obtained when a point H divides a line segment with end points (p, q) and (s, t) in the ratio a:b -

H = [(as + bp)/(a + b)], [(at + bq)/(a + b)]

H = [(5*-5 + 1*4)/(5 + 1)], [(5*3 + 1*-1)/(5 + 1)]

H = (-21/6, 14/6)

H = (-3.5, 2.3)

Therefore, the coordinate points are obtained as H = (-3.5, 2.3).

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So x = 2.1 is the only possible value of x that makes the equation true.

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.

An algebraic expression in mathematics is an expression created using variables, constant algebraic numbers, and algebraic operations. A good example of an algebraic expression is 3x2 2xy + c.

The equation is given as follows:

-3x + 6.3 = 0

To find the value of x, we need to isolate x on one side of the equation. We can do this by adding 3x to both sides:

-3x + 3x + 6.3 = 0 + 3x

6.3 = 3x

Now we can divide both sides by 3:

x = 6.3/3

x = 2.1

So x = 2.1 is the only possible value of x that makes the equation true.

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Answer:

50+100x=300x+75x

Step 1: Simplify both sides of the equation.

50+100x=300x+75x

100x+50=(300x+75x)(Combine Like Terms)

100x+50=375x

100x+50=375x

Step 2: Subtract 375x from both sides.

100x+50−375x=375x−375x

−275x+50=0

Step 3: Subtract 50 from both sides.

−275x+50−50=0−50

−275x=−50

Step 4: Divide both sides by -275.

[tex]\frac{-275x}{-275}[/tex] =  [tex]\frac{-50}{-275}[/tex]

x= [tex]\frac{2}{11}[/tex]

Answer:

C. 2%

Step-by-step explanation:

(6500-5000) / 15 / 5000 x 100% = 1500 / 15 / 5000 x 100% = 100 / 5000 x 100% = 0.02 x 100% = 2%

The coefficient of x² in 2 x² x³ is 2 n with number.

2 x² x³

= 2 x² (x³)

= 2 x² (x  x  x)

= 2 x² x  x  x

The coefficient of x² is 2.The expression 2 x² x³ can be written as 2 x² (x³). This can be further simplified to 2 x² (x  x  x). The coefficient of x² is 2, which means that the coefficient of x² in 2 x² x³ is 2. The coefficient of a term is the numerical factor of the term, or the number that is multiplied with the term. In this case, the coefficient of x² is 2, as it is the number multiplied with x².

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2x 11 is congruent to 13 mod 16, if 3x 7 is congruent to 2 mod 16.

If 3x 7 is congruent to 2 mod 16, then 2x 11 is congruent mod 16 to what integer between 0 and 15, is inclusive.

To find the solution of 2x 11 congruent mod 16, given 3x 7 congruent to 2 mod 16, we can first use the given equation to find the value of x and then substitute it into the second equation.

First, we can solve for x in the given equation:

3x 7 is congruent to 2 mod 16

3x is congruent to 2 mod 16

x is congruent to 6 mod 16

Now that we know that x is congruent to 6 mod 16, we can substitute it into the second equation:

2x 11 is congruent to 2(6) 11 which is congruent to 13 mod 16

So the solution is that 2x 11 is congruent to 13 mod 16.

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[tex]sin(A)+cos(A)=\sqrt{2}\hspace{10em}tan(A)+cot(A)=2 \\\\[-0.35em] ~\dotfill\\\\ tan(A)+cot(A)=2\implies \cfrac{sin(A)}{cos(A)}+\cfrac{cos(A)}{sin(A)}=2 \\\\\\ \cfrac{sin^2(A)+cos^2(A)}{cos(A)sin(A)}=2\implies \boxed{\cfrac{1}{cos(A)sin(A)}=2} \\\\[-0.35em] ~\dotfill[/tex]

[tex]sin(A)+cos(A)=\sqrt{2}\implies (~~sin(A)+cos(A)~~)^2=(\sqrt{2})^2 \\\\\\ sin^2(A)+2sin(A)cos(A)+cos^2(A)=2 \\\\\\ 2sin(A)cos(A)+sin^2(A)+cos^2(A)=2\implies 2sin(A)+1=2 \\\\\\ 2sin(A)cos(A)=1\implies \boxed{2=\cfrac{1}{cos(A)sin(A)}}[/tex]

now, another way to look at this identity will  be as a unified system of equations

[tex]\begin{cases} (~~sin(A)+cos(A)~~)^2=2\\\\ ~~ ~tan(A)+cot(A)=2 \end{cases}\implies (~~sin(A)+cos(A)~~)^2=tan(A)+cot(A)[/tex]

and we'd end up with the same rigamarole.

The plot for histogram is given below. Through digits distribution it can be seen that last digit of height of many students are same and the heights appear to be reported.

What is frequency distribution?

To make the information easier to understand, frequency distributions are visual displays that organise and present frequency counts. Absolute frequencies as well as relative frequencies, such as percentages or ratios, can be displayed in frequency distributions.

The table of data is given below.

According to the table the histogram is plotted.

The graphic representation of data points arranged into user-specified ranges is called a histogram. The histogram, which resembles a bar graph in appearance, condenses a data series into an intuitive visual by collecting numerous data points and organising them into logical ranges or bins.

The digits distribution show that the maximum number of students have a height whose last digit is 3.

The heights appears to be reported by the students and not actually measured as maximum of them are having same last digit which corresponds to the possibility that the first digit might be different. This is a possible example of a survey.

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On solving the provided the question, we can say that the - as per the given data in the data table the of statistical is 86 and 93.

Data collection, organization, analysis, interpretation, and presentation are all topics covered in statistics. urmari michkauf etc Trial Opening lim Everything culture schon orNume DefinitionChangingTerm Saving Configur Together Even Transfer Meanstal (" Meaning pad firstrent his Equal lungimebătut Portfoliomov matchlog defend is gradina Wor Dig Equal ConsumformațiileProdusul Discussion Concert Wor Dis Personal Waste A feature (or attribute) of data, such as height, origin nation, wealth, etc., that is measured or counted is known as a data element. Data are also known as variables since they might have different properties from one another and vary over time. Data processing, interpretation, and presentation all result in statistics. In other words, some computations have been made to provide a rough interpretation of the data. Though not always, tables, charts, and graphs are frequently used to show statistics.

From the statistical table,

we have observed value = 86

and the final value is 93

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