Two mechanics worked on a car. The first mechanic worked for 10 hours, and the second mechanic worked for 15 hours. Together they charged a total of 1650 . What was the rate charged per hour by each mechanic if the sum of the two rates was 135 per hour?

Using simple mathematical operations we can conclude that Adriel will earn $2,10,000 after 29 years working at the job.

The order of operations is a rule that outlines the proper steps to take when analyzing a mathematical equation.

The steps that we can memorize using PEMDAS include parentheses, exponents, multiplication and division (from left to right), addition and subtraction (from left to right), and so on.

So, we know that:

Adriel will earn $65,000 this year.

She will get a raise of $5,000 each year.

Then, her salary after 29 years would be:

= (5000 * 29) + 65,000

= 1,45,000 + 65,000

= $2,10,000

Therefore, using simple mathematical operations we can conclude that Adriel will earn $2,10,000 after 29 years working at the job.

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a polynomial of degree 5 with integer coefficients that has zeros -2, √3i, √2i, and y-intercept of 36 is

[tex]f(x) = x^{5} + 5x^{4} + 13x^{3} + 21x^{2} - 6x + 84[/tex]

Let us begin by writing the polynomial factors using the supplied zeros:

Because -2 is a zero, the polynomial has a component of (x + 2).

Because [tex]\sqrt{ 3i }[/tex] is a zero, its conjugate -[tex]\sqrt{ 3i }[/tex] is likewise a zero, implying that the polynomial has a component of (x - [tex]\sqrt{3i}[/tex])(x + [tex]\sqrt{3i}[/tex]) = (x2 + 3).

Similarly, because [tex]\sqrt{2i}[/tex] is a zero, its conjugate -[tex]\sqrt{ 2i }[/tex] is also a zero, implying that the polynomial has a component of (x - [tex]\sqrt{ 2i }[/tex])(x + [tex]\sqrt{ 2i }[/tex]) = (x2 + 2).

Finally, we know that the y-intercept is 36, which means that the polynomial's constant term is 36 when x=0.

When we add these components together, we get:

[tex]f(x) = (x + 2)(x^2 + 3)(x^2 + 2) + 36[/tex]

Extending on this, we get:

[tex]f(x) = x^{5} + 5x^{4} + 13x^{3} + 21x^{2} - 6x + 84[/tex]

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The image of the point (-1, 2) after a rotation of 270° counterclockwise about the origin is (2, 1).

To rotate a point counterclockwise about the origin, we can use the following formulas:

(x', y') = (y,-x)

where (x, y) are the coordinates of the original point, (x', y') are the coordinates of the rotated point

In this case, we want to rotate the point (-1, 2) by 270° counterclockwise about the origin.

So, we have

(x', y') = (2,1)

Therefore, the image of the point (-1, 2) after a rotation of 270° counterclockwise about the origin is (2, 1).

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Answer:

9 : 7

Step-by-step explanation:

4.5 : 3.5 are decimals so we can multiply them both by 2 to get whole numbers. 4.5 doubled is 9 and 3.5 doubles is 7. Therefore the ratio becomes 9:7

The width of the rectangle is 5.

The area of a rectangle is given by the formula:

Area = Length x Width

where Length and Width are the measurements of the two adjacent sides of the rectangle.

For example, if a rectangle has a length of 6 units and a width of 4 units, then its area would be:

Area = Length x Width

Let's start by using the formula for the area of a rectangle:

Area = Length x Width

We are given that the area of the rectangle is 30xF²y and that one of its sides (length) is 6xy. Substituting these values into the formula, we get:

30x²y = (6xy) x Width

Simplifying the right-hand side by multiplying 6xy by Width, we get:

30x²y = 6x²y x Width

Dividing both sides by 6x²y, we get:

Width = 30x²y / 6x²y

Simplifying the right-hand side by canceling out the common factors of 6, x², and y, we get:

Width = 5

Therefore, the width of the rectangle is 5.

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Using percentages we know that the bucket which is of 460 grams is made up of 92 grams of recyclable plastic.

A% is a mathematical figure or ratio that denotes a percentage of 100.

Ratios, fractions, and decimals are some of the numerous ways to represent a dimensionless connection between two numbers.

The symbol "%" is generally written after the integer to denote percentages.

A figure or ratio that is stated as a fraction of 100 is referred to as a percentage in mathematics.

So, in the given situation we will use percentages to get what % of recyclable plastic is used as follows:

= 460/100 * 20

= 4.60 * 20

= 92 grams

Therefore, using percentages we know that the bucket which is of 460 grams is made up of 92 grams of recyclable plastic.

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Answer:

The equation of function g after horizontal compression by a factor of 3 is:

g(x) = 7(3x) + 1 = 21x + 1

To substitute a numerical value for k into the function equation, we need to know the value of k. It is not given in the question, so we cannot provide a numerical answer.

Step-by-step explanation:

When a function is horizontally compressed by a factor of k, we divide the input (x) by k to obtain the new input for the transformed function.

The equation for the horizontally compressed function is:

g(x) = f(x/k)

Substituting f(x) = 7x + 1, we get:

g(x) = 7(x/k) + 1

Simplifying, we get:

g(x) = (7/k)x + 1

Thus, the equation for the transformed function g is obtained by replacing k with the given compression factor.

For example, if the compression factor is 3, then:

g(x) = (7/3)x + 1

And to substitute a numerical value for k, we need to know the value of k. If k = 2, for example, then:

g(x) = (7/2)x + 1

Answer:

A

Step-by-step explanation:

Answer:

2) [tex](3x+2)^{2}[/tex]

3) [tex](2x+5)(2x-5)[/tex]

4) [tex](x^{2} +8)(x^{2} -8)[/tex]

Step-by-step explanation:

A method I was taught was the snowflake method whenever there were numbers in front of [tex]x^{2}[/tex] (ex [tex]4x^{2} and 9x^{2}[/tex]) picture shown below (you can search up some videos if you would like)

The snowflake method is really efficient and helps factor polynomials faster

For 3 and 4, you basically have to find the square root of the number without the [tex]x^{2}[/tex] and make sure (for example 25) one parenthesis had -5 and the other had +5. Number 4 had [tex]x^{4}[/tex], [tex]x^{2}*x^{2}[/tex] is  [tex]x^{4}[/tex] so you would include that in the equation. To double check, use foil.

The area of circle is represented by quadratic expression A = π · x², for a radius x = 5 units, the area of circle equals 25π square units.

In this question we need to derive the area formula for a circle as a function of radius and compute the value of the figure for a given radius. According to geometry, the area of a circle (A), in square units, is described by following quadratic equation:

A = π · x²

Where x is the radius of the circle, in units.

If we know that x = 5, then the area of the circle is now computed:

A = π · 5²

A = 25π

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The values of t for which the height of the ball is of 26 feet are given as follows:

t = 0.57 s and t = 2.18 s.

The quadratic function that models the height of the ball after t seconds is given as follows:

h(t) = -16t² + 44t + 6.

The height of the ball is of 26 feet when:

h(t) = 26

Hence:

-16t² + 44t + 6 = 26

16t² - 44t + 20 = 0.

The coefficients are given as follows:

a = 16, b = -44, c = 20.

Using a quadratic function calculator, the solutions to the quadratic equation are given as follows:

t = 0.57 s and t = 2.18 s.

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The phrase represents that the expression is the cost of a product that is priced at $25.75 per unit with an additional fixed cost of $10.

The expression 25.75x + 10 represents a phrase that involves a numerical value that is dependent on a variable x.

We can think of this expression as a linear function, where x is the independent variable and 25.75x is the dependent variable that is multiplied by a coefficient of 25.75.

The constant term of 10 represents a fixed value that is added to the result of the multiplication.

One possible phrase that can be represented by this expression is the cost of a product that is priced at $25.75 per unit with an additional fixed cost of $10.

The variable x in this case would represent the number of units of the product being purchased.

Multiplying the price per unit by the number of units purchased (25.75x) gives us the variable component of the cost, and adding the fixed cost of $10 to this gives us the total cost of the purchase.

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The number of days it will take 5 workers to create 20 products, found using the work rate for 1 worker is 80 days

Work rate is the rate at which a specified work is completed.

The number of days it will take 10 workers to create 20 products = 40 days

Therefore;

The number of days it will take 1 worker to create 20 products = 40 × 10 days = 400 days

Where 1 worker can create 20 products in 400 days, then;

The work rate for one worker indicates;

The number of days it will take 5 workers to create 20 products can be found by dividing the number of days it will take 1 worker to create the 20 products by 5

5 workers will take = 400 days ÷ 5 = 80 days

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Answer:300

Step-by-step explanation:

We can find the answer the simple way.

There are 10 triangles in a regular pentagon

We used pythagorean theorm to find side b, 12

12*5*0.5 is 30

30*10 is 300

The transformation in words for picture 6 is a rotation of 90° counterclockwise or 90° counterclockwise rotation.

The algebraic rule for the above transformation is (x, y) → (-y, x).

The transformation in words for picture 7 is a reflection across the line x = -3.

The algebraic rule for the above transformation is [tex]Ref_{x=-3} \triangle ABC[/tex].

The transformation in words for picture 8 is a reflection across the x-axis.

The algebraic rule for the above transformation is (x, y) → (x, -y).

In Mathematics and Geometry, the rotation of a point 90° about the center (origin) in a counterclockwise (anticlockwise) direction would produce a point that has these coordinates (-y, x).

By applying a rotation of 90° counterclockwise to the vertices of quadrilateral RSTUVW, the coordinates of W of the image is as follows:

(x, y)                               →            (-y, x)

Ordered pair W  = (-1, 3) → Ordered pair R' = (-(3), -1) = (-3, -1).

In Mathematics and Geometry, a reflection over the x-axis is modeled by this transformation rule (x, y) → (x, -y). Therefore, a reflection over the x-axis would maintain the same x-coordinate while the sign of the x-coordinate changes from positive to negative or negative to positive.

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Answer:[tex]18\frac{3}{8}[/tex] yards

Step-by-step explanation:

Formula:

Base x Height ---> [tex]3\frac{1}{2}[/tex] x [tex]5\frac{1}{4}[/tex] = [tex]18\frac{3}{8}[/tex]

Answer: (3, -2.333) or (3, -7/3)

Step-by-step explanation:

We're given an x value (x=3) when looking at the coordinate, so we're trying to find what y is equal to given the equation. We can plug in x=3 into 5x+3y=8 and isolate for y.

[tex]5(3)+3y=8\\15 + 3y=8\\3y=-7\\y=-\frac{7}{3}[/tex]

Answer:

y= -2 1/3

Step-by-step explanation:

Since you have x, you put x into the equation and work through the problem.

5(3)+3y=8

15+3y=8, then subtract 15 from both sides

3y=(-7), then divide both sides by 3

y=(-7)/3 or (-2 1/3)

Answer:

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

'At most' means less than or equal, therefore the quotient of p and q is:

The matching choice is D.

'At least' means more than or equal, therefore the reciprocal of w is:

The matching choice is A.

Answer:

g) The correct option is: p/q ≤ 6

The phrase "the quotient of p and q" means p divided by q, which is expressed as p/q. The statement "the quotient of p and q is at most 6" means that the value of p/q cannot exceed 6, but it can be less than or equal to 6. Therefore, we use the less than or equal to a symbol (≤) to represent this statement.

here is an explanation of each option:

Here's how to express each statement as an inequality in terms of 8a^2:

p/q ≤ 6:

p ≤ 6q

8a^2p ≤ 48a^2q

8a^2p ≤ 48a^2q

h) The correct option is: 1/w ≤ 9

The reciprocal of a number w is 1/w. The phrase "the reciprocal of w is at least 9" means that the value of 1/w cannot be less than 9, but it can be greater than or equal to 9. Therefore, we use the less than or equal to symbol (≤) to represent this statement.

Here's an explanation of each option:

Here's how to express each statement as an inequality in terms of 8a^2:

1/w ≤ 9:

1 ≤ 9w

0 ≤ 9w - 1

0 ≤ 72a^2w - 8a^2

0 ≤ 72a^2w - 8a^2

Note that the inequality for 1/w ≤ 9 involves a quadratic term with respect to "w," whereas the inequality for p/q ≤ 6 only involves linear terms with respect to "p" and "q."

Answer:

380

Step-by-step explanation:

The formula for the area of a circle is A = pi r^2

radius is half the diameter so you would do 11 (half of diameter) to the second power, which is 121. Now you would do 121 times pi, which would be 380.132711084. When rounded to the nearest whole, it is 380.

SORRY IF THIS DIDN'T MAKE SENSE!

The scale factor of the dilation is 48.

The scale factor is a mathematical concept that describes the ratio of the lengths, areas, or volumes of two similar geometric figures. Similar figures have the same shape but may have different sizes.

When one figure is a dilation (a type of transformation that changes the size of a figure without changing its shape) of another figure, the scale factor is the ratio of the corresponding side lengths or dimensions of the two figures.

The scale factor of the dilation is the ratio of the length of the image to the length of the original object. In this case, the length of the image is 12 millimeters and the length of the original object is 0.25 millimeters. Therefore, the scale factor is:

scale factor = length of image/length of the original object

scale factor = 12 mm / 0.25 mm

scale factor = 48

So the scale factor of the dilation is 48.

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Answer:

A. m∠X = 50°, AC = 3 cm

Step-by-step explanation:

If ABC is congruent to XYZ then the corresponding angle and sides are congruent so:

∠A = ∠X

∠B = ∠Y

∠C = ∠Z

and

AB = XY

BC = YZ

AC = XZ

Because we know m∠A is 50° and ∠A and ∠X are congruent then m∠X is also 50°

And because we know XZ is equal to 3 cm and XZ and AC are congruent  then AC is also 3 cm

The probability that either event will occur is 0.68

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

The Venn diagram

On the Venn diagram, we have

Total = 15 + 12 + 18 + 12 - 12 + 21

Evaluate

Total = 66

This means that

P(A) = (15 + 12)/66

P(A) = 27/66

Also, we have

P(B) = (18 + 12)/66

P(B) = 30/66

Using the formula of the OR rule of probability:

P(A or B)=P(A) + P(B) - P(A and B)

Substitute the known values in the above equation, so, we have the following representation

P(A or B) = 27/66 + 30/66 - 12/66

Evaluate

P(A or B) = 45/66

This gives

P(A or B) = 0.68

Hence, the solution is 0.68

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Answer: Box plot:    |       o

19 |          

18 |          

17 |          

16 |          

15 |       o  

14 |     o      

13 |          

12 |   o     o

11 | o  o  o  

10 |          

9 | o  o      

8 |   o      

7 |  o        

  |___________

Line plot: 19|

18|

17|

16|

15|     o

14|   o

13|

12| o   o

11|o o o

10|

9|o o

8|  o

7|o

 |___________

   1 2 3 4 5 6 7 8 9 10  (data index)

Step-by-step explanation:

The correct answer as a trinomial in descending degree order is -2x^2 + 6x + 4

Here's the step-by-step solution with the figures:

(5x^2 + 10x - 5) - (7x^2 + 4x - 9)

= 5x^2 + 10x - 5 - 7x^2 - 4x + 9 (distribute the negative sign)

= (5x^2 - 7x^2) + (10x - 4x) + ( -5 + 9) (collect like terms)

= -2x^2 + 6x + 4 (simplify and arrange in descending degree order)

Therefore, the simplified expression in descending degree order is -2x^2 + 6x + 4.

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After answering the presented question, we may conclude that  the solution of the expressions are as follows.

In mathematics, you can multiply, divide, add, or subtract. An expression is constructed as follows: Number, expression, and mathematical operator A mathematical expression (such as addition, subtraction, multiplication, or division) is made up of numbers, variables, and functions. It is possible to contrast expressions and phrases. An expression or algebraic expression is any mathematical statement that has variables, integers, and an arithmetic operation between them. For example, the phrase 4m + 5 has the terms 4m and 5, as well as the provided expression's variable m, all separated by the arithmetic sign +.

the solution of the expressions are as follows -

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Answer:

Answer:

12 ounces

Step-by-step explanation:

Let x = Small Mug

& y = Large Mug

Then we write the given statement in an equation form as below:

2x + 1y = 20 ounces of coffee ---------------> EQUATION 1

3y - 1x = 32 ounces of coffee ----------------> EQUATION 2

Let us solve the above equation for y;

Multiply Equation 2 by '2', we get;

-2x + 6y = 64 ----------------------> Equation 3

Add Equation 1 and Equation 3, we get;

(2x + y) + (-2x + 6y) = 64 + 20

7y = 84

Divide the above equation by 7, we get;

y = 84 / 7

or, y = 12

Hence, One Large mug can hold 12 ounces of coffee.

Step-by-step explanation:

Answer: 7 [tex]\frac{1}{7}[/tex] lbs

Step-by-step explanation:

    We will divide the 50 lbs bag by 7, to represent te 7 dogs.

50 lbs food / 7 dogs = 7 [tex]\frac{1}{7}[/tex] lbs