How do you use substitution with the system of equations x+2y=14 and y=3x-14

The equation for a circle with center (2,8) and radius 3 is written as (x - 2)^2 + (y - 8)^2 = 9.

The question provided describes the properties of a circle and is asking for its equation.

A circle with a center (2,8) and radius 3 can be represented by the equation (x - 2)^2 + (y - 8)^2 = 3^2.

This is derived from the general equation of a circle (x - h)^2 + (y - k)^2 = r^2, where (h,k) is the center and r is the radius.

Domain: [tex](-\infty, \infty)[/tex]

Range: [tex](-\infty, \infty)[/tex]

Explanation:

The function is [tex]y=-\frac{1}{4} x[/tex]

The domain of a function is the set of all input values for which the function is well defined. Generally, domain consists of all x-values of the function. Hence, the function [tex]y=-\frac{1}{4} x[/tex] is defined in the interval [tex](-\infty, \infty)[/tex].

The range of a function is the set of output values obtained by substituting the value of x in the function. Hence, the function [tex]y=-\frac{1}{4} x[/tex] is defined in the interval [tex](-\infty, \infty)[/tex].

Answer:

Explanation:

You can set a system of equation using the following steps:

1. Name the variables:

2. Set the equations that relate the variables:

        equation (1): x = 2y - 46

         equation (2): x + y = 122

3. Solve the system:

Substitute equation (1) into equation (2)

Solve for y:

Subsitute the value on y in equation 1, to find the value of x:

Thus, the average yearly salary of a person with a masters degree is $ 66 thousand.

Final answer:

Using a system of equations with the variables B (the average salary for a bachelor's degree) and M (the average salary for a master's degree), we solved to find that the average yearly salary for an individual with a bachelor's degree is $56,000 and with a master's degree is $66,000.

Explanation:

The problem at hand involves creating two algebraic equations to solve for the average yearly salaries of individuals with a bachelor's degree and a master's degree based on the provided information. Let the average yearly salary for an individual with a bachelor's degree be represented by B, and the salary for an individual with a master's degree be represented by M.

According to the problem, the average yearly salary of an individual with a master's degree is $46 thousand less than twice the salary of an individual with a bachelor's degree, so we can write the first equation as: M = 2B - 46.

The second equation comes from the fact that combined, their earnings amount to $122 thousand, so: B + M = 122.

Now, we can substitute the first equation into the second to solve for B: B + (2B - 46) = 122. Simplifying, we get 3B - 46 = 122. Adding 46 to both sides gives 3B = 168, and dividing by 3 yields B = 56. So, the average salary for someone with a bachelor's degree is $56,000.

To find the salary for a master's degree holder, we substitute B = 56 into the first equation: M = 2(56) - 46. That simplifies to M = 112 - 46, giving us M = 66. Hence, the average salary for someone with a master's degree is $66,000.

Answer:

the melting point of water is 0

Answer:

-2

Step-by-step explanation:

-6x=5x+22

-6x-5x=22

-11x=22

x=22/-11

x=-2

Answer:

y = -2x -7

Step-by-step explanation:

y + 5 = -2 (x +1)

y + 5 = -2x -2 . move 5 to the other side by subtracting from both sides.

y = -2x -7

Step-by-step explanation:

We have,

[tex]6h^5+0h^4-12h^3+0h^3+0h=0[/tex]

To find, the value of h = ?

∴ [tex]6h^5+0h^4-12h^3+0h^3+0h=0[/tex]

⇒ [tex]6h^5[/tex] + (0)[tex]h^4[/tex] - 12[tex]h^3[/tex] + (0)[tex]h^3[/tex] + (0)h = 0

⇒ [tex]6h^5[/tex] + 0 - 12[tex]h^3[/tex] + 0 + 0 = 0

⇒ [tex]6h^5[/tex]  - 12[tex]h^3[/tex] = 0

Taking 6 [tex]h^3[/tex] as common, we get

[tex]6h^3(h^2-2)[/tex] = 0

⇒6[tex]h^3[/tex] = 0 or,   [tex]h^2[/tex] - 2 = 0

⇒ 6[tex]h^3[/tex] = 0 ⇒ h = 0

⇒ [tex]h^2[/tex] = 2  

⇒ h = ± [tex]\sqrt{2}[/tex]

Hence, the value of h = 0,  ± [tex]\sqrt{2}[/tex]

The terms that are called means are 2 and 36

Solution:

A proportion is simply a statement that two ratios are equal

Proportion is written as:

[tex]\frac{a}{b} = \frac{c}{d}[/tex]

In ratios, we can write as,

a : b = c : d

To find the cross products of a proportion, we multiply the outer terms, called the extremes, and the middle terms, called the means.

[tex]\frac{a}{b} = \frac{c}{d}\\\\a \times d = b \times c[/tex]

Here, a and d are extremes

b and c are means

In the given proportion,

[tex]\frac{12}{36} = \frac{2}{6}[/tex]

[tex]12 \times 6 = 2 \times 36[/tex]

Here, 12 and 6 are extremes

2 and 36 are means

In the given proportion 12/36=2/6, the mean terms are 12 and 6. To verify the proportion, one can use the cross-products method, which confirms its correctness since the multiplication of means and extremes produces equal results.

In the proportion 12/36=2/6, the terms that are known as the means are the two numbers that are on the inside of the proportion, which are 12 and 6 in this case. Proportions are made up of four terms, with the first and last terms called the extremes, and the two terms in the middle called the means. To solve a proportion and check if it is true, you can use the cross-products method, which involves multiplying the means and the extremes. If the cross-products are equal, then the proportion is true. In this example, 12 (the mean) multiplied by 2 (an extreme) is equal to 24, and 36 (the other extreme) multiplied by 6 (the mean) also gives 24, confirming that this proportion is correct.

Answer:

Ur answer

Step-by-step explanation:

If A4 paper has width 21cm and length of 30cm

Then,

A5 paper has a length of 21cm

So find the width,

A4 has width 30cm

so,

A5 must have half the answer

15cm

The width of A5 paper is 21cm, which is derived from the length of A4 paper, based on the standard ratio of the A series paper sizes.

The width of A5 paper can be determined using the properties of the standardized A series paper sizes. As A4 paper has dimensions of 21cm by 30cm and the A series has a height to width ratio of the square root of 2, when an A4 sheet is cut in half, it results in two A5 sheets.

Thus the length of A4 becomes the width of A5. To find the width of A5, we simply take the length of A4, which is 21cm in this case.

Therefore, the width of an A5 sheet is also 21cm, making the dimensions of A5 paper 21cm by 14.85cm (since half of 30cm is 14.85cm).

Three equivalent expressions to 24k + 12k are 36k, 12k(2 + 1), and 6k(4 + 2). To calculate Cammie's total spending on x pounds of plums and y pounds of oranges, the expression 3x + 2y is used.

Equivalent expressions for 24k + 12k can be found by combining like terms or using the distributive property. Here are three equivalent expressions:

For the second part of the question, an expression to determine the total amount Cammie will spend on x pounds of plums at $3 per pound and y pounds of oranges at $2 per pound is given by:

3x + 2y

This expression represents the total cost by multiplying the quantity of each fruit by its price and then adding the results together.

Answer:

Step-by-step explanation:

you put the equation in slope and intercept form by making y the subject of the formula

i.e

y = -2x + 2

-2 is the slope and 2 is the intercept

Answer:

Step-by-step explanation:

2x + y = 2

Making y as subject

y = - 2x + 2

And the equation is y = mx + c

Where m is slope = -2

Y intercept = 2

Answer:

160 good luck tho on whatever

Step-by-step explanation:

450-290

The question is about determining the initial elevation of a hiker's journey given the increase in elevation and the current elevation. The hiker started at an elevation of 160 feet before the hike.

The student is asking a question related to change in elevation during a hike. If a hiker increased their elevation by 290 feet and is currently at 450 feet, they must have started at an elevation of 160 feet that morning. This is calculated by subtracting the increase from the current elevation: 450 feet - 290 feet = 160 feet.

Answer:

Option A) [tex]-6r^2s^4t^3[/tex] is correct

Therefore the result is [tex]\frac{18r^4s^5t^6}{-3r^2st^3}=-6r^2s^4t^3[/tex]

Step-by-step explanation:

Given expression is [tex]\frac{18r^4s^5t^6}{-3r^2st^3}[/tex]

To find the result of the given expression:

That is solve the fractional expression as below:

[tex]\frac{18r^4s^5t^6}{-3r^2st^3}[/tex]

[tex]\frac{18r^4s^5t^6}{-3r^2st^3}=\frac{-6r^4s^5t^6}{r^2st^3}[/tex]

[tex]=-6r^4s^5t^6.r^{-2}s^{-1}t^{-3}[/tex]  ( using the properties [tex]\frac{1}{a^m}=a^{-m}[/tex] and [tex]a^m.a^n=a^{m+n}[/tex])

[tex]=-6r^{4-2}s^{5-1}t^{6-3}[/tex]

[tex]=-6r^2s^4t^3[/tex]

Therefore [tex]\frac{18r^4s^5t^6}{-3r^2st^3}=-6r^2s^4t^3[/tex]

Therefore the result is [tex]-6r^2s^4t^3[/tex]

Therefore option A) [tex]-6r^2s^4t^3[/tex] is correct

Answer:

$1.29

Step-by-step explanation:

5.16 divided by 4

Answer:

12

Step-by-step explanation:

Answer:

46 hours

Step-by-step explanation:

We are given the information;

Required to determine the number of hours;

We need to know that;

Number of hours = Amount earned ÷ rate per hour

Therefore;

First week;

Number of hours = $192 ÷ $8 per hour

                             = 24 hours

Next week

Number of hours = $176 ÷ $8 per hour

                             = 22 hours

Thus, number of hours she worked = 22 + 24

                                                           = 46 hours

Therefore, in the two weeks Molly baby-sited for 46 hours

Answer:

I'm Going With A.) Hope It Helps

Answer:

we need the picture or answer choices

Step-by-step explanation:

Answer:

a) A=π(r×r)

Where π=constant pie of 3.143

           r= half of diameter

b) 31420 square units

Step-by-step explanation:

The Atlanta Traffic Commission needs to know how much space the Ferris Wheel takes up.  

A)What is the AREA formula for a circle?

A=π(r×r)

Where π=constant pie of 3.143

           r= half of diameter

B)Show your work to find the AREA of the Ferris Wheel. Don't forget to add your square units

A=π(r×r)

   =3.142×100×100

   =31420 square units

The formula for the area of a circle is A=πr². To find the area of a circular object, like a Ferris Wheel, you need to know the radius. If the radius is 10 units, then A=π(10)² = 314 square units.

The subject of this question is Mathematics and it's a Middle School level question. It's about calculating the area of a circle, which in this case is the Ferris Wheel.

A) The formula for the area of a circle is Pi times the radius squared (A=πr²). Pi (π) is approximately 3.14 and the radius (r) is the distance from the center of the circle to the outside of the circle.

B) To find the area of the Ferris Wheel, you'll need to know the radius. Let's assume the radius of our Ferris Wheel is 10 units. Plugging these values into the formula we have: A=π(10)² = π * 100 = 314 square units. The unit of measurement for the area depends on the unit used for the radius. If the radius was in meters, then the area is in square meters, if the radius was in feet, then the area is in square feet, and so on. If no units is given, we just call it 'square units'.

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For this case we have that by definition, the perimeter of a rectangle is given by:

[tex]P = 2l + 2w[/tex]

Where:

l: It is the length of the rectangle

w: It is the width of the rectangle

According to the statement we have to:

[tex]l = w + 3 \frac {1} {6} = w + \frac {19} {6}\\P = 15 \frac {1} {3} = \frac {46} {3}[/tex]

The length and perimeter are expressed in centimeters.

Substituting we have:

[tex]\frac {46} {3} = 2 (w + \frac {19} {6}) + 2w\\\frac {46} {3} = 2w + \frac {38} {6} + 2w\\\frac {46} {3} = 2w + \frac {19} {3} + 2w\\\frac {46} {3} = 4w + \frac {19} {3}\\\frac {46} {3} - \frac {19} {3} = 4w\\\frac {27} {3} = 4w\\[/tex]

[tex]9 = 4w\\w = \frac {9} {4}[/tex]

Thus, the width of the rectangle is [tex]\frac {9} {4}[/tex] centimeters.

The length is:

[tex]l = w + \frac {19} {6} = \frac {9} {4} + \frac {19} {6} = \frac {54 + 76} {24} = \frac {130} {24} = \frac {65} {12}[/tex] centimeters.

Answer:

[tex]l=\frac{65}{12}[/tex] centimeters

[tex]w=\frac{9}{4}[/tex] centimeters

Answer:

The length of the triangle is [tex]\frac{65}{12} cm[/tex] and the width is [tex]\frac{9}{4} cm[/tex]

Step-by-step explanation:

Given

Length of the Rectangle = [tex]3\frac{1}{6}[/tex] longer than the width

Perimeter of the Rectangle = [tex]15\frac{1}{3}[/tex]

Required

What are the width and length of the rectangle.

Let L represent the length of the rectangle, W represent the width of the rectangle and P represent the Perimeter.

So, we have that

L = [tex]3\frac{1}{6}[/tex] + W

P = [tex]15\frac{1}{3}[/tex]

Perimeter of a rectangle is calculated by 2( L + W)

So,

P = 2( L + W) becomes

[tex]15\frac{1}{3} = 2(3\frac{1}{6} + W + W)[/tex]

[tex]15\frac{1}{3} = 2(3\frac{1}{6} + 2W)[/tex]

Convert fractions to improper fractions

[tex]\frac{46}{3} = 2(\frac{19}{6} + 2W)[/tex]

Open Bracket

[tex]\frac{46}{3} = 2 * \frac{19}{6} + 2 * 2W[/tex]

[tex]\frac{46}{3} = \frac{19}{3} + 4W[/tex]

Make 4W the subject of of formula

[tex]4W = \frac{46}{3} - \frac{19}{3}[/tex]

[tex]4W = \frac{46 - 19}{3}[/tex]

[tex]4W = \frac{27}{3}[/tex]

[tex]4W = 9[/tex]

Make W the subject of of formula

[tex]W = \frac{9}{4}[/tex]

Recall that

L = [tex]3\frac{1}{6}[/tex] + W

So, [tex]L = 3\frac{1}{6} + \frac{9}{4}[/tex]

[tex]L = \frac{19}{6} + \frac{9}{4}[/tex]

[tex]L = \frac{38 + 27}{12}[/tex]

[tex]L = \frac{65}{12}[/tex]

Hence, the length of the triangle is [tex]\frac{65}{12} cm[/tex] and the width is [tex]\frac{9}{4} cm[/tex]

Answer:

27:72

Step-by-step explanation:

First I would convert three days to hours. 24×3=72

Answer: 27:72

The ratio of the two times will be 3 / 8.

A ratio in mathematics shows how many times one number is contained in another. For instance, if a dish of fruit contains eight oranges and six lemons.

The ratio of oranges to lemons is eight to six. The ratio of oranges to the overall amount of fruit is 8:14, and the ratio of lemons to oranges is 6:8.

Given that compare in hours: 27 hours to 3 days. The ratio will be calculated as:-

In 3 days there are 72 hours.

Ratio = 27 / 72 = 3 / 8

Therefore, the ratio of the two times will be 3 / 8.

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Answer:596

Step-by-step explanation:

There are a total of  216 boys in the college.

The ratio can be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects.

Given,  there is an introductory engineering course if 396 students are enrolled and there are 6 boys to every five girls.

Given that the ratio of boys to girls = 6/5

Since there are a total of 396 students in the college

so.

6x + 5x = 396

11x = 396

x = 36

Thus, the number of boys in College = 36 * 6

Number of boys in college = 216

therefore, There are a total of  216 boys in the college.

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Answer:

(5)(2)+(7)(3)−3(2+3)+4

=20

The height of wall of play structure is 8.48 feet

Solution:

A climbing wall leaning against the top of a play structure forms a right triangle with the ground

The figure is attached below

ABC is a right angled triangle

AB is the height of wall of play structure

Let "x" be the height of wall of play structure

AB = x

BC is distance from the bottom of the climbing wall to the base of the play structure

BC = 7 feet

AC is the length of climbing wall

AC = 11 feet

We can apply pythogoras theorem for right angled triangle

Pythagorean theorem, states that the square of the length of the hypotenuse is equal to the sum of squares of the lengths of other two sides of the right-angled triangle.

Therefore, by above definition for right angled triangle ABC,

[tex]AC^2 = AB^2+BC^2[/tex]

Substituting the values we get,

[tex]11^2 = x^2 + 7^2\\\\121 = x^2 + 49\\\\x^2 = 121-49\\\\x^2 = 72\\\\\text{Take square root on both sides }\\\\x = \sqrt{72}\\\\x = 8.48[/tex]

Thus the height of wall of play structure is 8.48 feet

Answer:

8ft

Step-by-step explanation:

i did the test on T4L

Answer:

y = 9/10

Step-by-step explanation:

Hope this helps also if you download photomath it really helps. :)

1 - 2/3y = 6/15   Isolate/get y by itself, first subtract 1 on both sides

-2/3y = 6/15 - 1       [to combine fractions, they need to have the same denominator]

-2/3y = 6/15 - 15/15

-2/3y = -9/15        Multiply the inverse of -2/3, which is -3/2 on both sides to get y by itself

y = 27/30      Simplify

y = 9/10

Answer: 22

Step-by-step explanation:

3x + 5y = 2 .......................... equation 1

2x - 6y = 20 ........................... equation 2

solving the system of linear equation by elimination method. Multiply equation 1 by 2 and equation 2 by 3 , then we have

6x + 10y = 4 ............................. equation 3

6x - 18y = 60 ........................... equation 4

subtract equation 3 from equation 4 , then we have

-28y = 56

divide through by -28

y = -2

substitute y = 2 into equation 1 to find the value of x , then we have

3x + 5 (-2) = 2

3x - 10    = 2

3x = 2 + 10

3x = 12

x = 4

Therefore :

5x - y = 5 (4) - (-2)

          = 20 + 2

          = 22

Answer:

Part A)

The unit price for the 12-cupcake option is $

2.42

The unit price for the 24-cupcake option is $

2.33

The unit price for the 50-cupcake option is $2.58

Part B) The 24-cupcake option has the lowest unit price

Part C) see the explanation

Part D) see the explanation

Step-by-step explanation:

Part A) Find each unit price to the nearest cent

we know that

To find out the unit rate divide the cost by the number of cupcakes

so

Part 1) 12 cupcakes for $29

[tex]\frac{29}{12}=\$2.42\ per\ cupcake[/tex]

Part 2) 24 cupcakes for $56

[tex]\frac{56}{24}=\$2.33\ per\ cupcake[/tex]

Part 3) 50 cupcakes for $129

[tex]\frac{129}{50}=\$2.58\ per\ cupcake[/tex]

Par B) Which option gives the lowest unit price?

The 24-cupcake option has the lowest unit price

Part C) One way to convert from inches to centimeters is to multiply the number of inches by 2.54. How many centimeters are in 1/4 inch?

Multiply 1/4 inches by 2.54

(1/4)(2.54)=0.635 cm

Part D) A stack of 500 pieces of paper is 1.875 inches tall.

Find the thick of each piece of paper

Divide 1.875 inches tall. by 500 pieces

[tex]\frac{1.875}{500}=0.00375\ in/piece[/tex]

therefore

Diego is incorrect

The unit price for the 12-cupcake is $2.42.

The unit price for the 24-cupcake is $2.32.

The unit price for the 50-cupcake is $2.58.

The 24-cupcake option has the lowest unit price.

It is 0.636cm centimeters are in 1/4 inch.

The thick of each piece of paper is 0.00375cm per paper.

Given that,

A sign in a bakery gives these options:

12 cupcakes for $29

24 cupcakes for $56

50 cupcakes for $129

We have to determine,

Find each unit price to the nearest cent.

According to the question,

Price for 12 cupcakes for $29.

Unit price of 12-cupcakes = [tex]\rm\frac{29}{12} = 2.42[/tex]

The unit price for the 12-cupcake is $2.42.

Price for 24 cupcakes for $56.

Unit price of 24-cupcakes = [tex]\rm\frac{56}{24} = 2.33[/tex]

The unit price for the 24-cupcake is $2.32.

Price for 50 cupcakes for $129.

Unit price of 50-cupcakes = [tex]\rm\frac{129}{50} = 2.58[/tex]

The unit price for the 50-cupcake is $2.58.

To centimeters are in 1/4 inch.

Multiply 1/4 inches by 2.54,

[tex](\frac{1}{4} )(2.54)=0.635 cm[/tex]

It is 0.636cm centimeters are in 1/4 inch.

The thick of each piece of paper,

Divide 1.875 inches tall. by 500 pieces for thick of each piece of paper,

[tex]= \frac{1.875}{500} \\\\= 0.00375cm[/tex]

The thick of each piece of paper is 0.00375cm per paper.

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Answer:

Therefore, the resulting expression for the price Genevieve will pay

will be:  [tex]p-100-\frac{3}{20}p[/tex]

Step-by-step Explanation:

Let the original cost of a laptop = p dollars

So, subtract the $100 and 15% off coupon (15% off on original 'p' cost)

The resulting expression for the price Genevieve will pay can be computed as:

[tex]p-100-15\%\:p[/tex]

[tex]=p-100-15\frac{p}{100}[/tex]

[tex]=p-100-\frac{3}{20}p[/tex]        ∵ [tex]15\%\mathrm{\:in\:fractions}:\quad \frac{3}{20}[/tex]

Therefore, the resulting expression for the price Genevieve will pay

will be:  [tex]p-100-\frac{3}{20}p[/tex]

Keywords: price, algebraic expression

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Answer:

I have to guess c.) 10 I am not positive though

Step-by-step explanation:

Answer:

The correct answer is B. 144°

Step-by-step explanation:

Let's recall that in a trapezium the bases are parallel and one of its properties is that  the two angles on the same side are supplementary, that is the sum of the angles of two adjacent sides is equal to 180°.

Upon saying that, we can find out the value of a and b, this way:

∠a = 180 - 36

∠a = 144

∠b = 180 - 113

∠b = 67

But the question is regarding ∠a. Then the correct answer is B. 144°