Please help me with this math question! Thank you!

(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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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:

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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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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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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Answer:  The answer should be 43

Step-by-step explanation:

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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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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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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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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Answer:

  m∠D = m∠E = 80°

Step-by-step explanation:

You want the measures of the angle of elevation (∠E) from A to B and the angle of depression (∠D) from B to A when they are described by the expressions 7x-4 and 4(x+8), respectively.

The angle of elevation and the angle of depression between the same two points have the same measures.

  m∠E = m∠D

  7x -4 = 4(x +8)

  7x -4 = 4x +32

  3x = 36 . . . . . . . . add 4-4x to both sides

  x = 12 . . . . . . . . divide by 3

  4(x +8) = 4(20) = 80 . . . . . . . . find the angle measures

Each of the angles has a measure of 80°.

The value of the given expression at the given points is 52.

What is expression?

Mathematical expressions consist of at least two numbers or variables, at least one math operation, and a sentence. It's possible to multiply, divide, add, or subtract with this mathematical operation.

An expression, also known as a mathematical expression, is a finite combination of symbols that are well-formed in accordance with context-dependent rules.

Consider, the given expression  

y + (x^2 - 2)/2

We have to find the value of expression at x = 10 and y = 3

Plug x = 10 and y = 2 in the above equation.

3 + (10^2 - 2)/2

3 + (100 - 2)/2

3 + 98/2

3 + 49

52

Hence, the value of the given expression at the given points is 52.

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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 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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Measure of exterior angle = 139°

Exterior angles are angles that are parallel to the inner angles of a polygon but lie on the outside of it. The measure of an exterior angle is equal to the sum of the two internal opposite angles.

Given,

In the figure

Measure of exterior angle = 15x + 34

Measure of opposite interior angle = 12x + 26 and 29°

But, measure of exterior angle is equal to sum of opposite two angles

⇒ 15x + 34 = 12x + 26 + 29

⇒ 15x - 12x = -34 + 26 + 29

⇒ 3x = 21

⇒ x = 21/3

⇒ x = 7

Measure of exterior angle = 15x + 34

                                            = 15(7°) + 34°

                                            = 105° + 34°

                                            = 139°

Hence, 139° is the measure of exterior angle.

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Answer:

To calculate the involuntary withholdings in all, you need to add up the amounts withheld for federal taxes, state taxes, and FICA.

First, calculate the amount withheld for federal taxes. To do this, multiply your gross pay of $1,375 by 12%, which is the percentage withheld for federal taxes:

$1,375 x 12% = $165

Next, calculate the amount withheld for state taxes. To do this, multiply your gross pay of $1,375 by 7%, which is the percentage withheld for state taxes:

$1,375 x 7% = $96.25

Next, calculate the amount withheld for FICA. To do this, multiply your gross pay of $1,375 by 8%, which is the percentage withheld for FICA:

$1,375 x 8% = $110

Now add the three amounts withheld for federal taxes, state taxes, and FICA

$165 + $96.25 + $110 = $371.25

So, the involuntary withholdings in all if your gross pay was $1,375 is $371.25

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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Using percentage error, the measured weight is 0.5% less than the expected weight.

The percentage error serves as a gauge for how closely a computed or experimental result matches the true or accepted value. It is determined as the true or accepted value multiplied by 100% times the absolute difference between the experimental or calculated value and the true or acceptable value.

The formula for percentage error is:

Percentage Error = (|experimental value - true value| / true value) x 100%

The weight of the distilled water can be calculated by subtracting the weight of the graduate from the combined weight of the graduate and water:

weight of water = 100.28 g - 85.49 g = 14.79 g

To calculate the percentage error, you can use the formula:

(measured weight - actual weight) / actual weight * 100%

The actual weight of 15 mL of distilled water is 15 g, so the percentage error is:

(14.79 g - 15 g) / 15 g * 100% = -0.5%

So, the deviation from the expected weight of 5 g is -0.5%, which means the measured weight of the distilled water is 0.5% less than the expected weight.

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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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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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Answer:

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

Step-by-step explanation:

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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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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Answer:4

Step-by-step explanation:

First you need to find how many cups of milk is in one serving. So, you take 2 1/2 and divide it by 5 to get 1/2 then you multiply 1/2 by eight to get 8/2. Simplify to get your answer which is 4.

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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The value after the multiplication of the given expression gives 1.

Multiplication of two numbers is defined as the addition of one of the number repeatedly until the times of the other number.

a × b means that a is added to itself b times or b is added to itself a times.

Given expression is (m y⁻⁴) (m⁻¹ y⁴).

We have to multiply this.

We have some of the rule of exponents that,

xᵃ . xᵇ = xᵃ⁺ᵇ and x⁰ = 1

(m y⁻⁴) (m⁻¹ y⁴) = (m m⁻¹) (y⁻⁴ y⁴)

                        = (m¹⁺⁽⁻¹⁾) (y⁽⁻⁴⁾⁺⁴)

                        = m⁰ y⁰

                        = 1

Hence the value is 1.

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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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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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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]