What does a simple machine do when it makes your effort less?
makes work go faster

makes your power more

makes the amount of work you do less

makes resistance force greater than applied force

Answer:

For two linear equations : a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0;

To determine if two such straight lines are parallel, then you should check for the following conditions :

a₁/a₂ = b₁/b₂ ≠ c₁/c₂ , where a,b are coefficients of x and y for each line.

if this condition is true for the coefficients of x,y, and the intercept of lines (c₁ and c₂) then they are parallel.

for instance,

let's say we have two lines :

x + 2y - 4 = 0,

2x + 4y - 12 = 0;

Now to check if they are parallel you simply check if the condition for parallel lines is met or not.

for these two lines :

a₁ = 1 , b₁ = 2, and c₁ = -4;

a₂ = 2, b₂ = 4, and c₂ = -12;

evaluating the values in the condition we have :

[tex]\frac{1}{2}[/tex] = [tex]\frac{2}{4}[/tex] ≠[tex]\frac{-4}{-12}[/tex] ;

since the condition for parallel is true for these two lines, we can conclude they are parallel.

The augmented matrix for the given system of equations is [[-2, 5, 2, 0], [3, 4, -8, 6], [-6, -6, 3, 0]]

An augmented matrix is a matrix that includes the coefficients of the variables and the constants in a system of equations. Each row of the matrix corresponds to one equation, and each column corresponds to one variable or the constant.

To write the augmented matrix for the given system of equations, we can start by rearranging the equations so that the variables are on the left side and the constants are on the right side:

5x + 2z = 2
3x + 4y - 8z = -6
-6x + 6y - 3z = 0

Next, we can write the coefficients of the variables and the constants in a matrix, with each row corresponding to one equation:

[5, 0, 2, 2]
[3, 4, -8, -6]
[-6, 6, -3, 0]

Finally, we can combine these rows into a single matrix to get the augmented matrix:

[[-2, 5, 2, 0], [3, 4, -8, 6], [-6, -6, 3, 0]]

This is the augmented matrix for the given system of equations.

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Answer: 137.8 cm

Step-by-step explanation:

Using Pythagorean's Theorem, a² + b² = c², we can find the length of one of the braces.

Plug in your values:

115² + 76² = c²

13225 + 5776 = c²

19001 = c²

√19001 = c

c ≈ 137.8 cm

The braces are 137.8 cm long.

Hope this helps!

Answer:

Step-by-step explanation:

1 ticket costs 1 × $4.50 = $4.50

2 tickets cost 2 × $4.50 = $9.00

3 tickets cost 3 × $4.50 = $13.50

4 tickets cost 4 × $4.50 = $18.00

The first table is the only one that matches these values.

Step-by-step explanation:

the perimeter of a rectangle is

2×length + 2×width

simply because the perimeter means to go along every side the shape has.

I don't see any answer options. you did not provide any. I can only give you the approach of how to solve this.

so, that means for us

2(6x + 5) + 2×3x = 100

12x + 10 + 6x = 100

18x = 90

x = 90/18 = 5

it definitely should be (-2,3)

The function to represent the total charges for your hotel and car rental is C,) p(x) = 45 + 214x

In other terms, an equation is a mathematical statement stating that "this is equivalent to that." It appears to be a mathematical expression on the left, an equal sign in the center, and a mathematical expression on the right.

Given that hotel, you are going to stay at charge $135 per night. It can be represented by the function p(x) = 135x.

Also, car rental company charges a $45 insurance fee plus $79 per day.

It can be represented by the function p(x) = 45 + 79x.

Daily rental fee = $135 per night,

Write the equation for the total fees

p(x) = 45 + 214x

Thus, x represents the number of days.

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Answer:

kindly update the question

Answer:

If applying the 20% off coupon and the 10% coupon it would be separate. This would be different than a 30% coupon

Step-by-step explanation:

Let's say you are taking 20% off of $100, doing that would reduce the price to $80 because you took off $20, after this you would apply the 10% off coupon to the $80, your total would be 72 now because 10% of 80 is 8. The 20% Coupon and the 10% coupon stacked would bring your total to $72. If you flat out took 30% out of 100 dollars you would be left with $70 compared to the $72 that you got with the 20% coupon and the 10% coupon.

20% + 10% would remove less than a 30% coupon because after applying the 20% coupon, your 10% coupon would remove less because of the lower number being subtracted. Hope this helps

The solution set in interval notation, 19(7 − x) ≥ 88 − 14x, is (-∞, 9]

To solve the inequality 19(7 - x) ≥ 88 - 14x, we will first distribute the 19 on the left side of the inequality and then combine like terms to isolate the variable x.

19(7 - x) ≥ 88 - 14x
133 - 19x ≥ 88 - 14x
-5x ≥ -45
x ≤ 9

Now, we can write the solution set in interval notation. Interval notation uses brackets or parentheses to indicate the endpoints of an interval. Brackets indicate that the endpoint is included in the interval, while parentheses indicate that the endpoint is not included.

Since x is less than or equal to 9, the solution set in interval notation is (-∞, 9]. This means that any value of x less than or equal to 9 will satisfy the inequality.

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The scientific notation or representation of expression (2.5 X 1/10²)(4.2 X 10⁶) is equal to 10.5×10⁴.

Scientific notation is a way of writing very large or very small numbers. Numbers are written in scientific notation as a number from 1 to 10 multiplied by a power of 10.For example, 650,000,000 can be written in scientific notation as 6.5 ✕ 10⁸. 

Scientific notation is utilized by scientists, mathematicians, and engineers whilst they may be operating with very huge or very small numbers

Solution for scientific notation according to the information given:

(2.5 X 10^-2)(4.2 X 10⁶) = 2.5 ×(1/10²) × 4.2 × 10⁶

                                        = 2.5 × 4.2 × 10⁴

                                        = 10.5 × 10⁴

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The formula for the nth term of the arithmetic sequence is 3(3n-1) or -3+9n(option B)

An arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference from any succeeding term to its preceding term remains constant throughout the sequence. The constant difference is called common difference of that arithmetic progression.

The nth term of a n arithmetic sequence is given as:

a(n) = a+(n-1)d

where a is the first term and d is the common difference

a = 6

d = 15-6 = 9

a(n) = 6+( n-1) 9

= 6+9n -9

a(n) = 9n-3

a(n) = 3(3n-1)

therefore the formula for the nth term of the sequence is 3(3n-1)

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Answer:

Step-by-step explanation:

I can't see anything.

The area of the figure composed of a rectnagle and a triangle is 128in².

The figure in the the image is composed of rectangle and a triangle.

The area of a rectangle = length × width

Area of a triangle = 1/2 × base × height

Hence;

Area of the composite figure will be;

A = area of a rectangle + area of a triangle

From the image;

Now, we solve for thr area of the composite figure.

A = area of a rectangle + area of a triangle

A = ( 12in × 9in ) + ( 1/2 × 5in × 8in )

A = ( 108in² ) + ( 20in² )

A = 128in²

Therefore, the total area of the figure id 128 squared inch.

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Answer:

1286.3934 kg

Step-by-step explanation:

Convert 153% to a decimal:

153 / 100 = 1.53

Multiply 840.78 by 1.53:

840.78 * 1.53 = 1286.3934

Answer:

[tex]y=\frac{2}{3}x+1[/tex]

Step-by-step explanation:

Slope-Intercept Line Equation:

[tex]y=mx+b[/tex]

Where [tex]m[/tex] is the slope and [tex]b[/tex] is the y-intercept.

From the graph, we can see that the y-intercept is (0, 1). This means that the equation is currently:

[tex]y=mx+1[/tex]

To find the slope, we can use a point on the line to replace the x and y variables. The point that we use cannot have x equal to zero. If we use the x-intercept [tex](-1.5, 0)[/tex], the new equation will be:

[tex]0=m(-1.5)+1[/tex]

Then, we must find m:

[tex]0=m(-1.5)+1[/tex]

[tex]-1=m(-1.5)[/tex]

[tex]\frac{-1}{-1.5}=m[/tex]

[tex]m=\frac{2}{3}[/tex]

Now we can find the equation of the line:

[tex]y=\frac{2}{3}x+1[/tex]

Answer: there 28/29 days

Step-by-step explanation:

Answer: 28/29

Step-by-step explanation:

28 Days

29 Days for a leap year

Answer:

x to the power of 67000 to the 5th power.

Step-by-step explanation:

The shortest distance Jose can ride to park is 5 miles.

The Pythagoras theorem which is also referred to as the Pythagorean theorem explains the relationship between the three sides of a right-angled triangle. According to the Pythagoras theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides of a triangle.

Given that, Jose can follow the roads getting to the park- first heading south 3 miles, then heading west 4 miles.

Let the shortest root Jose can choose be x miles.

By using Pythagoras theorem, we get

x²=3²+4²

x²=9+16

x²=25

x= 5 miles

Therefore, the shortest distance is 5 miles.

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Answer:4/5 and y = 9/5.

Step-by-step explanation:We can start by substituting the second equation into the first equation, replacing y with 1/2x+8:

3x + 4(1/2x+8) = 36

Simplifying, we get:

3x + 2x + 32 = 36

Combining like terms, we get:

5x + 32 = 36

Subtracting 32 from both sides, we get:

5x = 4

Dividing both sides by 5, we get:

x = 4/5

Now that we have found x, we can substitute it back into the second equation to find y:

y = 1/2x + 8 = 1/2(4/5) + 8 = 9/5

Therefore, the solution to the system of equations is x = 4/5 and y = 9/5.

Answer:

Traduction:

Ann and Barbara are comparing their ages. They find that Barbara is the age that Ann was when Barbara was the age that Ann was when Barbara was half the age that Ann is today. If the sum of their current ages is 44 years, what is Ann's age today?

Soit x l'âge d'Ann aujourd'hui.

On sait que l'âge de Barbara est x - (x/2) = x/2 (car Barbara avait la moitié de l'âge d'Ann lorsque l'écart d'âge entre elles était de x/2).

On sait également que l'âge d'Ann lorsque Barbara avait x/2 ans est (x/2 - x) = -x/2 ans de moins que son âge actuel.

Donc, l'âge d'Ann lorsque Barbara avait l'âge qu'avait Ann à ce moment-là est x - (x/2) - (-x/2) = 2x/2 = x ans.

Ainsi, l'âge de Barbara aujourd'hui est également x ans.

La somme de leurs âges actuels est 44 ans, donc :

x + x = 44

2x = 44

x = 22

Donc, l'âge d'Ann aujourd'hui est 22 ans.

|x| + 2 is always greater than |x| because |x| is always positive or zero.

Absolute value of a number is defined as the positive value of the number. even the number is negative, the absolute value is the positive value of that number.

Consider |x| for any number x.

The possibilities of x are positive number, zero or negative number.

If x is a positive number, |x| is also the same positive number.

2 adding to |x| is also positive number.

So |x| + 2 > |x|

If x is a negative number, |x| is the positive value of that negative number.

So |x| + 2 > |x|.

If x is 0, the |x| = 0

|x| + 2 = 0 + 2 = 2 > |x| = 0

Hence in all cases, |x| + 2 > |x|.

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The mean of the values will be 9.4, the median will be 3 points and the mode will be 4

It should be noted that mean in mathematics simply means the total added values of all the data in a set of divided by the number of days in a set.

The mean of the values will be:

= (10 + 8 + 11 + 12 + 6) / 5

= 47 / 5

= 9.4

The median of the set of numbers is the number on the middle when arranged ascending or in a descending manner. This is 3 points. The mode is 4.

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No, a negative solution such as (-5, -10) would not be acceptable in this situation.

Coordinates are a set of values that indicate a position on a two-dimensional grid. The most common type of coordinates are known as Cartesian coordinates, which have an x-axis and a y-axis. Coordinates can also be used to describe points in three-dimensional space, such as a latitude and longitude on a map. Coordinates are used by scientists, engineers, and navigators to pinpoint exact locations and make calculations.

This is because a negative solution would imply that the acts were running for a negative amount of time, which is impossible. Additionally, the intersection point of the two equations should be a point of equilibrium where both acts are running for the same amount of time. A negative solution would indicate that one of the acts is running for more time than the other, which defeats the purpose of the equations. Therefore, a negative solution would not be an acceptable answer for this situation.

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The answer to this question is C) 0.8. This can be determined using the Pythagorean Theorem.

What is Pythagorean theorem?

The Pythagorean Theorem is one of the most important theorems in mathematics, and it has been used for centuries to solve various mathematical problems. It is a fundamental tool for measuring distances and calculating angles in Euclidean geometry.

The theorem can be expressed as an equation, a^2 + b^2 = c^2, where a and b are the lengths of the sides of the triangle, and c is the length of the hypotenuse. This equation can be used to calculate the lengths of the sides of a right-angled triangle if two of the sides are known.

The theorem states that the sum of the squares of the lengths of the two legs of the triangle is equal to the square of the length of the hypotenuse. In this case, the legs of the triangle are AB and BC, each of which is 10 units long. Therefore, the formula for this triangle is 10² + 10² = 12², or 100 + 100 = 144. Solving this equation shows that the length of the hypotenuse, AC, is equal to 12 units, which is a ratio of 0.8 compared to the lengths of the two legs. Therefore, the correct answer is C) 0.8.

The value of sin can then be determined using the sine formula, which states that the ratio of the length of the side opposite the angle to the length of the hypotenuse is equal to the sine of the angle. In this case, the side opposite the angle is AB, which is 10 units long. The hypotenuse is AC, which is 12 units long. Therefore, the sine of the angle is equal to 10/12, or 0.8. Therefore, the value of sin is 0.8.

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The correct answer is c. Failed to reject the null hypothesis.

Failed to reject the null hypothesis.

Explanation:

In this problem, we are given the price of drugs for human doses and animal doses from different pharmacies. We are asked to form a statistical decision using the p-value method. The null hypothesis is that the prices for the animal doses are equal to the prices for the human doses, while the alternative hypothesis is that the prices for the animal doses are significantly less than the prices for the human doses.


To form a statistical decision, we need to compare the p-value with the level of significance (α). If the p-value is less than or equal to α, we reject the null hypothesis. If the p-value is greater than α, we fail to reject the null hypothesis.


In this case, the level of significance is 1% (α=0.01). Since the p-value is not given in the problem, we cannot make a decision. Therefore, the correct answer is c. Failed to reject the null hypothesis.

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If the stone dropped by Maria falls 2 meter in 1st second, then the stone would have fallen 30 meter after 10 seconds.

The distance that the stone falls in the first second is = 2 meters;

The distance that the stone falls in the 50th second is = 149 meters;

So, the rate of fall of the stone can be calculated as:

⇒ (149 - 2)/(50 - 1);

⇒ 147/49;

⇒ 3.

So , the stone is falling at the rate of 3 meter per second,

The distance fall by the stone after 10 second can be calculated as :

⇒ 10×3

⇒ 30 meter.

Therefore, After 10 seconds the stone would have fallen 30 meter.

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The value for the quadratic equation is C(t) = t² + 3.

When two lines or rays intersect and cross at one endpoint or vertex, a vertex angle is created. This angle, which is expressed in degrees, is occasionally confused with face angle. Two intersecting lines at the corner of a 2D object, such a polygon, generate a vertex angle. In 3D forms, however, multiple angles are conceivable since there are more than two lines.

The standard form of the quadratic function is given as:

C(t) = at² + bt + c

Using different values of t from the table we have:

a(-2)² + b(-2) + c = 7

a(-1)² + b(-1) + c = 4

a(0)² + b(0) + c = 3

Simplifying the equations we have:

4a - 2b + c = 7

a - b + c = 4

c = 3

Substituting the value of c = 3 in equation 2:

a - b = 1

Further solving the equation for a and b we have:

a = 1

b = 0

Hence, the equation for the quadratic equation is C(t) = t² + 3.

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The response to the given question would be that Hence, 2 is the proportionality constant between y and x.

Partnerships that have the same ratio across time are said to be proportional. For instance, how many trees there are in an orchard and how many apples there are in a harvest of apples are determined by the average number of apples per tree. Proportional in mathematics refers to a linear connection between two numbers or variables. As the first quantity doubles, so does the other. When one of the variables drops to 1/100th of its previous value, the other also decreases. When two quantities are proportional, it means that as one rises, the other rises as well, and the ratio between the two quantities stays the same at all levels. As an example, consider the diameter and circumference of a circle.  

We must calculate the ratio of the change in y to the change in x in order to discover the constant of proportionality between two variables, x and y. The slope of the line that depicts the connection between x and y is another name for this.

The slope of the line, which is the change in y divided by the change in x, is therefore equal to the constant of proportionality between y and x. As we can see from the graph, y grows by 2 units for every unit rise in x. Hence, the line's slope is 2/1, or only 2.

Hence, 2 is the proportionality constant between y and x.

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Austin would have approximately $2,108 more than Josiah.

Approximately means "nearly" or "close to" an exact amount or number. It is often used to describe a quantity that is not exact, but can be estimated or rounded off. For example, "There were approximately 25 people in the room" means that the number was close to 25, but not necessarily exactly 25.

Using the formula A = P(1 + r/n)^nt, where P is the principal amount, r is the interest rate, n is the number of times compounded, and t is the number of years, we can calculate the amount of money Austin and Josiah would have in 17 years.
For Austin: A = $92,000(1 + 5.875/365)^365*17 = $120,308.05
For Josiah: A = $92,000(1 + 0.0575)^17 = $118,200.43
Therefore, Austin would have approximately $2,108 more than Josiah.

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