Graph this line using the slope and y-intercept:
y=1/8x+6

The point (1,0) is a solution to the system of linear equations.

What is a linear system of equations?

A system of linear equations consists of two or further equations made up of two or further variables similar that all equations in the system are considered contemporaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.

We are given a system of linear equations i.e. y = -x + 1 and 3x - y = 3.

In order to check that which point is a solution to the system of linear equations, we need to put the values in the given system.

1. (3/2 , -1/2)

Here, x = 3/2 and y = -1/2

Putting these values in the equations, we get

y = -x + 1

1/2= -3/2+1

1/2=1/2

3x - y = 3

3(3/2)-(-1/2) ≠ 3

9/2+1/2 ≠ 3

5 ≠ 3

Thus, it is not a solution to the system of linear equations.

2. (1 , 0)

Here, x = 1 and y = 0

Putting these values in the equations, we get

y = -x + 1

0= -1+1

0=0

3x - y = 3

3(1)-(0) = 3

3=3

Thus, it is a solution to the system of linear equations.

3. (-1/2, 3/2)

Here, x = -1/2  and y = 3/2

Putting these values in the equations, we get

y = -x + 1

3/2= -(-1/2)+1

3/2=1/2+1

3/2=3/2

3x - y = 3

3(-1/2)-(3/2) ≠ 3

-3/2-3/2 ≠ 3

-3 ≠ 3

Thus, it is not a solution to the system of linear equations.

4. (0, 1)

Here, x = 0  and y = 1

Putting these values in the equations, we get

y = -x + 1

1= -0+1

1=1

3x - y = 3

3(0)-(1) ≠ 3

0-1 ≠ 3

-1 ≠ 3

Thus, it is not a solution to the system of linear equations.

Hence, the point (1,0) is a solution to the system of linear equations.

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A graph which shows a function whose inverse is also a function include the following: A. On a coordinate plane, 2 curves are shown. f (x) is a curve that starts at (0, 0) and opens down and to the right in quadrant 1. The curve goes through (4, 2). The inverse of f (x) starts at (0, 0) and curves up sharply and opens to the left in quadrant 1. The curve goes through (2, 4).

In Mathematics, a vertical line test can be defined as a technique which is typically used to determine whether or not a given relation is a function.

According to the vertical line test, a vertical line must cut through the x-coordinate (x-axis) on the graph of a function at only one (1) point, in order for it to represent a function. Else, the relation does not represent a function because it can only have one output value (y) for a unique input value (x).

In conclusion, we can reasonably infer and logically deduce that the relation graphed in graph 1 represents a function whose inverse is also a function because it passed the vertical line test, unlike the other graph.

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The slope of the line that passes through the points (0, -6) and (0, -5)is undefined.

Slope is line's inclination with regard to the horizontal is quantified numerically. In analytical geometry, a line, ray, or line segment's slope is the ratio of the vertical to horizontal distance between any two points on the line, ray, or line segment ("slope equals rise over run").

In differential calculus, the derivative of a function yields the slope of a line tangent to its graph, which represents the function's instantaneous rate of change with respect to changes in the independent variable.

Ok so slope is the change in y over change in x.

Your why changed from 6 to -5 so you can write this as -5 - 6

Your x didn’t change it went from 0 to 0

You can write this as 0-0

Now -11/0 is what you end up with as a slope.

Any number divided by 0 is undefined so your slope is undefined.

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The measure of ∠D is equal to 120°.

In Euclidean geometry, a parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure.

Given is a parallelogram as shown in the image attached.

We can write -

{8x}° + {4x}° + ∠B = 180°

∠B = 180° - {8x}° - {4x}°

∠B = 180 - 40 - 20

∠B = 120°.

∠B = ∠D = 120°      [Opposite angles of a ||gm are equal}

Therefore, the measure of ∠D is equal to 120°.

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Answer:  The answer should be 43

Step-by-step explanation:

The values of sine, cosine, tangent, cosecant, secant, and cotangent for the angle θ are 9/√97, -4/√97, 9/√97, -4/√97, -√97/4 and √97/9.

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

We have to find the values of sine, cosine, tangent, cosecant, secant, and cotangent for the angle θ in standard position on the coordinate plane with the point (−4,9) on its terminal side.

r = √(16 + 81) = √97

sinθ = y/r = 9/√97

cosθ = x/r = -4/√97

tanθ = y/x = 9/√97

cotθ = x/y = -4/√97

secθ = r/x = -√97/4

cscθ = r/y = √97/9

Hence, the values of sine, cosine, tangent, cosecant, secant, and cotangent for the angle θ are 9/√97, -4/√97, 9/√97, -4/√97, -√97/4 and √97/9.

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To evaluate (gof)(-4), we first need to find the result of f(-4) and then plug that value into g(x),where (gof)(-4) = 29.

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The experimental probability that a person selected at random is going to City C is 2/15

Probability is the likelihood of a desired event happening.

Experimental probability is a probability that relies mainly on a series of experiments.

Experimental probability (City C) = number of responses for City C / total responses

number of responses for City C = 12

Total responses = 28 + 38 + 12 + 18 + 4 = 90

Experimental probability (City C) = 12/90 = 2/15

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Answer:

6/8 is equivalent to 3/

Answer:

moving your shape left, right, up, or down a number of units

Step-by-step explanation:

The annual increase in the value of the comic book is 21.7%

If each year the increase is X (a percentage), the initial value is A, and we define "t" as the number of years, then the value is given by the exponential function.

f(t) = A*(1 + X/100%)^t

Here we know that the initial value is A = 0.05

And after 83 years, the new value is 609,000 dollars, then we can write the equation:

609,000 = 0.05*(1 + X/100%)^83

609,000/0.05 = (1 + X/100%)^83

12,180,000 =  (1 + X/100%)^83

Now we can apply the exponent 1/83 in both sides:

(12,180,000)^(1/83) =  1 + X/100%

1.217 = 1 + X/100%

1.217 - 1 = X/100%

0.217*100% = X

21.7% = X

That is the increase per year.

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(I) x+ y=5,2x+2y=10

(ii) x−y=8,3x−3y=16

Step 1

I) x +y=5   …(i)

2x+2y=10    …(ii)

⇒x +y=5

⇒y=5−x

x  0  3

y  5  2

Plot (0,5) and (3,5) on graph and join them to get equation x +y=5.

2x+2y=10

⇒2y=(10−2x)

⇒y=

2

10−2x

​ =5−x   …(iii)

x  5  2

y  0  3

So, the equation is consistent and has infinitely many solution

Step 2

ii) x−y=8   ….(i)

3x−3y=16   ….(ii)

⇒x−y=8

⇒−x +y=−8

⇒y=−8+x

⇒y=x−8

x  8  0

y  0  -8

3x−3y=16   …(ii)

⇒3x=16+3y

⇒3x−16=3y

⇒y= 3x−16/3

⇒y=x− 16/3

x 16/3  0

y  0  -16/3

Plotting both the equation in graph, we see that the lines are parallel , so inconsistent.

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Yes, the given relation is proportional and has a constant of proportionality = 0.3 or ratio of proportionality 3/10, thus option (A) is correct.

What are the ratio and proportion?

The ratio is the division of the two numbers.

For example, a/b, where a will be the numerator and b will be the denominator.

Proportion is the relation of a variable with another. It could be direct or inverse.

As  given,

A 12-ounce cup costs $3.60.

The ratio of cost to ounce = 3.60/12 = 0.3

A 16-ounce cup costs $4.80.

The ratio of cost to ounce = 4.80/16 = 0.3

So constant of proportionality is 3/10.

Hence "Yes, the given relation is proportional with a constant of proportionality is 0.3".

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We can use the complement rule to solve this problem, which states that the probability of an event happening is equal to 1 minus the probability of the event not happening.

The event we're trying to find the probability of is "at least 2 of the candies have a caramel center." The complement event is "fewer than 2 of the candies have a caramel center."

To find the probability of the complement event, we need to find the probability that exactly 0 candies have a caramel center, plus the probability that exactly 1 candy has a caramel center.

The probability that exactly 0 candies have a caramel center is (2/5)^0 * (3/5)^3 = (3/5)^3

The probability that exactly 1 candy has a caramel center is 3 * (2/5) * (3/5)^2 = (18/125)

The probability of the complement event is (3/5)^3 + (18/125)

Therefore, the probability of at least 2 of the candies having a caramel center is 1 - (3/5)^3 - (18/125)

I hope this helps :)

The ratio for Tan A is 9/40.

Trigonometric ratios are determined by the value of the ratio of sides of a right-angled triangle and contain the values of all trigonometric functions. The trigonometric ratios of a given acute angle are the ratios of the sides of a right-angled triangle with respect to that angle.

The six Trigonometric Ratios and their formulas are given below

Sin θ = Opposite Side/Hypotenuse

Cos θ = Adjacent Side /Hypotenuse

Tan θ = Opposite Side/Adjacent Side

Cot θ = Adjacent Side/Opposite Side

Sec θ = Hypotenuse/Adjacent Side

Cosec θ = Hypotenuse/Opposite Side

Here we have

Right-angled triangle ABC and the right angle at C

From angle A,  

Opposite side = BC and Adjacent side = AC

As we know tan θ = Opposite side /Adjacent side

=> Tan A = BC/AC = 9/40  

Therefore,

The ratio for Tan A is 9/40.

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Step-by-step explanation:

The distance between the two points (1, 2) and (-1, -7) is the square root of ((1 + 1)^2 + (2 + 7)^2), which is approximately 11.8. Rounding to the nearest tenth, the distance is 11.8.

Answer:

9.2

Step-by-step explanation:

In a two-dimensional plane, the distance between any two points (x₁, y₁) and (x₂, y₂) is given by the formula::

[tex]d = \sqrt {(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2}[/tex]

For:

(x₁, y₁) = (1, 2)
(x₂, y₂) = (-1, -7)

[tex]d = \sqrt {(-1 - 1)^2 + (-7 - 2)^2}[/tex]

==> [tex]d = \sqrt {(-2)^2 + (-9)^2}[/tex]

==>  [tex]d = \sqrt {{4} + {81}}[/tex]

[tex]d = \sqrt {85}[/tex]

[tex]d = 9.2195[/tex]

[tex]d = 9.2\;\; \textrm{rounded to the nearest thenth(one decimal place)}[/tex]

Answer:

2) If you spent a total of $1,200, you had the phone for 20 months.

Step-by-step explanation:

From the equation, the cost of the phone is 400 and the monthly data plan costs $30 per month

For 20 months, you would have paid:
30 x20 + 400 = 600 + 400 = $1000

and not $1200

So statement 2 is false

Answer:

Step-by-step explanation:

The function is described as f(x) = 1/2x, while the inverse is defined as f-1(x) = 2x.

The inverse function "undoes" the original function given a function. To get the inverse of a function, we must first swap the x and y variables before solving for y.

We may obtain the inverse function of f(x) = 1/2x by exchanging x and y: y = 1/2x.

then calculate x: x = 2y

As a result, the inverse function f-1(x) = 2x.

We may now employ these functions to solve issues by undoing the original function with the inverse function.

The function is defined as f(x) = 1/2x, and the inverse as f-1(x) = 2x.

The inverse function of a function "undoes" the original function. To get the inverse of a function, swap the x and y variables before solving for y.

By exchanging x and y, we may derive the inverse function of f(x) = 1/2x: y = 1/2x.

then compute x: x = 2y

The inverse function f-1(x) Equals 2x as a result.

By redoing the original function with the inverse function, we may now use these functions to solve problems.

Answer:

1,2,2 then -4,-2, -2 and for the last one is x

Step-by-step explanation:

engenuity

On solving the provided question, we can say that by equation we have = x*(x-9) = x^2 - 9x

A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.

let the 1st number be x

2ndd be x-9

then by equation we have = x*(x-9) = x^2 - 9x

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The differentiation of [tex]e\x^{x}[/tex] is [tex]e\x^{x}[/tex] proved using the first law of differentiation or limit law.

A technique for determining a function's derivative is differentiation. Mathematicians use a procedure called differentiation to determine a function's instantaneous rate of change based on one of its variables. The most typical illustration is velocity, which is the rate at which a distance changes in relation to time.

Differentiation is the ratio of a slight change in one quantity to a little change in another that depends on the first quantity. Calculus' major emphasis on the differentiation of a function makes it one of the subject's key ideas. Differentiation is the process of determining the maximum or lowest value of a function, the speed and acceleration of moving objects, and the tangent of a curve. If y = f(x) and f(x) is differentiable, then f'(x) or dy/dx is used to indicate the differentiation.

[tex]\frac{d}{dx}e\x^{x}[/tex] using first order or limits to differentiate we get

for [tex]\lim_{h \to0} \frac{f(x+h) - f(x)}{h} = \frac{d}{dx}f(x)[/tex]

therefore,

[tex]\lim_{h \to 0} \frac{e\x^{(x +h)}- e\x^{x} }{h} \\[/tex] = [tex]\lim_{h \to 0} \frac{e\x^{x}(e\x^{h}-1 ) }{h}[/tex] = [tex]\lim_{h \to 0} \frac{e\x^{x}*e\x^{h} }{1} \\[/tex] ( using L-Hospital)

[tex]\lim_{h \to 0} e\x^{x} * e\x^{h} = e\x^{x} (proved)[/tex]

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Therefore , the solution of the given problem of equation comes out to be s = 9/4 *t is the best equation.

The equal letter (=) is used to signify equivalence between the statements in a mathematical formula. Using mathematical equation, which are declarations of reality, it is shown that many mathematical variables are equivalent. For instance, the equal sign in the equation

y + 6 = 12 divides the values 12 or b + 6 into two halves. The number of words that each side of a symbol corresponds to can be measured. Typically, a symbol's meaning is at odds with itself.

Here,

Given :

s represents the number of hours sick leave

and number of weeks be represented by t.

So,

4 weeks and 9 hours of sick leave .

To find the best equation which satisfies the problem:

=> s = 9/4 *t

Putting s = 9

and t =4

=> 9 = 9/4 * 4

=> 9 =9

Therefore , the solution of the given problem of equation comes out to be s = 9/4 *t is the best equation.

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The value for which the rational expression is undefined is a = -9

A rational expression is an expression that is the ratio of two polynomials. It is also known as a fraction in which the numerator and denominator are both polynomials.

To determine the values for which a rational expression is undefined, you need to find the values that make the denominator of the expression equal to zero.

Since we have (9a-11)/(-a-9), equate the denominator to 0 and solve for a. That is:

-a-9 = 0

-a = 9

a = -9

Thus, a = -9 is the value for which the rational expression is undefined.

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Susan needs to buy 24 packages of hotdog buns to have one bun for each hot dog.

A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.

Given, Susan buys 16 packages of hot dogs and each package contains 12 hot dogs.

Therefore, The total number of hotdogs is,

= (16×12).

= 192 hotdogs.

Also given dog buns are sold in packages of 8.

Therefore, The number of packages of hotdog buns needed are,

(192/8).

= 24 packages of hotdog buns.

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Lucy owe $550 each month.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

The monthly total amount they owe includes $950 for rent, $100 for parking and $50 for utilities.

So, the total they have spend on all assets

= 950+ 100 + 50

= 1100

So, they will split the amount

= 1100/2

= $550

Hence, Lucy owe $550.

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An inequality to represent Malia's situation is 4x ≤ 40. The time for which Malia has been hiking is 10 minutes.

What is an inequality?

In Algebra, an inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa.

While hiking on a cliff Malia elevates at a distance = 8 feet

Then Malia descends at a distance = 4 feet

The bottom of the cliff is at the distance of -32 feet from Malia.

Let x represent the number of minutes Malia has been hiking.

The diagram is drawn for the situation.

A right-angled triangle ABC is formed -

Where the total measure of AB is 40 feet.

The time for which Malia has been hiking is AB' = 4x.

So, now the inequality becomes -

4x ≤ 40

On dividing both sides by 4 -

x  ≤ 40

Therefore, Malia has been hiking from 10 minutes.

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We can write the piecewise function as -

          {f(x) = x + 1 ,   x ∈ (- ∞, 1)}

f(x) →  {f(x) = 5 ,        x ∈ (1, 4)}

          {f(x) = x - 1 ,   x ∈ [5, ∞)}

In mathematics, a piecewise-defined function (also called a piecewise function, a hybrid function, or definition by cases) is a function defined by multiple sub-functions, where each sub-function applies to a different interval in the domain.

A piecewise function is continuous on a given interval in its domain if the following conditions are met:

For a piecewise function to be differentiable on a given interval in its domain, the following conditions have to fulfilled in addition to those for continuity above:

Give is a piecewise function in the graph.

We can write the piecewise function as follows.

For the interval (- ∞, 1) →

The line passes through the point -

(- 1, 0) and (0, 1)

We can write slope of the line -

{m} = (1 - 0)/(0 + 1) = 1

{m} = 1

and

{c} = 1

So, we can write f(x) as -

f(x) = x + 1

For the interval (1, 4) →

f(x) = 5

For the interval [5, ∞) →

The line passes through the point -

(4, 3) and (5, 4)

We can write slope of the line -

{m} = (4 - 3)/(5 - 4) = 1/1

{m} = 1

and

For the point (5, 4), we can write -

4 = 1 x 5 + c

c = 4 - 5

{c} = - 1

So, we can write f(x) as -

f(x) = x - 1

Combining all the parts, we can write piecewise function as -

          {f(x) = x + 1 ,   x ∈ (- ∞, 1)}

f(x) →   {f(x) = 5 ,        x ∈ (1, 4)}

          {f(x) = x - 1 ,   x ∈ [5, ∞)}

Therefore, we can write the piecewise function as -

          {f(x) = x + 1 ,   x ∈ (- ∞, 1)}

f(x) →  {f(x) = 5 ,        x ∈ (1, 4)}

          {f(x) = x - 1 ,   x ∈ [5, ∞)}

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The denominator is equal to zero when u = 11/12, then for that value the expression is undefined.

The expression is undefined if we have an undefined operation, like a logarithm of a negative number or a division by zero.

Here we have a rational expression, which is:

(-9u + 8)/(-12u + 11)

Notice that we have the variable on the denominator, then the values for which the expression is undefined are the values of u such that the denominator becomes equal to zero:

-12u + 11 = 0

11 = 12u

11/12 = u

The expression is undefined for u = 11/12.

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Congruent angles are frequently used in the world of architecture, construction, design, and art.

Alternate Interior Angles are congruent if a transversal cuts two parallel lines. Alternate Exterior Angles are congruent if a transversal cuts two parallel lines. When a transversal cuts two parallel lines, the resulting angles are congruent.

Angle measure is the same for congruent angles. An ordinary pentagon, for instance, has five sides and five angles, each of which is 108 degrees. The angles of a regular polygon will always be congruent, regardless of its size or scale.

Are situated on opposite sides of the transversal, but between the two parallel lines. The corresponding alternate internal angles for this example would be 2 and 6, and 7 and 3. 

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The value of x in the image above is equal to: C. 50.

In Mathematics, the Alternate Interior Angles Theorem states that when two (2) parallel lines are cut through by a transversal, the alternate interior angles that are formed are congruent.

The Linear Pair Postulate states that the measure of two (2) angles would add up to 180° provided that they both form a linear pair.

By applying the Linear Pair Postulate to the two (2) alternate interior angles, we have the following:

x + (x + 80) = 180

2x + 80 = 180

2x = 180 -80

2x = 100

x = 100/2

x = 50.

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Answer:

50

Step-by-step explanation: