what is the solution for the following system of equations? -y + 3x = 6 and y = -6x + 12

Answer and Step-by-step explanation:

To graph the equation with a slope of -2 and a y-intercept of 6, we can use the slope-intercept form of the equation of a line, which is:

y = mx + b

where m is the slope and b is the y-intercept.

Substituting in the given values, we get:

y = -2x + 6

To graph this line, we can start by plotting the y-intercept, which is the point (0, 6). Then, we can use the slope to find additional points on the line. The slope of -2 means that for every increase of 1 in the x-direction, the y-value decreases by 2. So, we can plot another point by starting at the y-intercept and moving down 2 units and to the right 1 unit. This gives us the point (1, 4). We can continue this pattern to plot more points and draw the line.

Here's what the graph looks like:

Step-by-step explanation:

We are given the slope -2 and the y intercept -6. So we can create a linear equation using this data:

[tex]y=-2x+6[/tex]

Now all we have to do is graph it.

(graph below)

Sergio saved at a rate of change of 34.4% when he had $500 saved for a family vacation.

The component technique is a technique of troubles where you first calculate the worth of a single item, then multiply a certain value to get the answer. Simply defined, a single product value is extracted from either a specified multiple using the one method. For contrast, 40 pens will costs you 400 rs, or $1.01. The method used to execute this might be regulated. a solitary nation. anything seems to have a distinctive component.  (Classic Algebra, Quantitative Analysis, Math and science of Matrix or Operators).

given

1% of $500 = $5

Total Saving from $500 to $ 860

860 / 5 = 172

Now percentage of growth :-

172/500 *100

17200/500 = 34.4

Hence, the rate of change Sergio savings = 34.4%

Sergio saved at a rate of change of 34.4% when he had $500 saved for a family vacation.

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Answer:

50% smaller

Step-by-step explanation:

The value of weight of 64 kg when converted to pounds is   141.09568 pounds.

kilogram is the standard unit of mass in the International System of Units (SI), while pounds are a common unit of mass used in the United States and other countries.

To Know how to convert between different units of measurement is essential for accurate calculations and comparisons. convert 64kg to pounds, you can use the formula: 1 kilogram is equal to 2.20462 pounds.

Therefore, to convert 64kg to pounds, you would multiply 64 by 2.20462.

64 x 2.20462 =  141.09568 pounds

So, weight of 64kg is equivalent to  141.09568 pounds.

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Due to the exponential growth of bacteria it only took 10 minutes to fill 3 additional empty bottles.

What is an exponential function?

The formula for an exponential function is f(x) = a^x, where x is a variable and a is a constant that serves as the function's base and must be bigger than 0.

The bacteria took more time to double from 1 cell to a bottle full of cells. Once the bottle was full, each cell in the full bottle doubled, causing an additional bottle to be filled in 5 minutes.

Then the 2 full bottles doubled in the next 5 minutes, causing all 3 bottles to be full.

The answer needed is -

The full bottle doubled after 5 minutes.

The 2 full bottles doubled after 5 minutes.

Exponential growth is a multiplicative rate of change.

Therefore, due to exponential growth bacteria filled the bottle fast.

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Answer:

The bacteria took more time to double from 1 cell to a bottle full of cells. Once the bottle was full, each cell in the full bottle doubled, causing an additional bottle to be filled in 5 minutes. Then the 2 full bottles doubled in the next 5 minutes, causing all 3 bottles to be full.

So the length of the path along the longest side of the park would be 35 yds.

The three sides of a triangle, a three-sided polygon in geometry, are made up of three edges and three vertices. A triangle's most important property is that its internal angles can all be added up to 180 degrees.

The area of a right triangle is given by the formula A = (1/2) * b * h, where b and h are the lengths of the legs of the triangle. Since one of the legs of the park is 21 yds and the area is 294 yd², we can solve for the length of the other leg:

A = (1/2) * b * h

294 = (1/2) * 21 * h

h = (2 * 294) / 21

h = 28

So the length of the other leg of the triangle is 28 yds.

To find the length of the hypotenuse, we can use the Pythagorean theorem, which states that the sum of the squares of the legs of a right triangle is equal to the square of the length of the hypotenuse:

c² = a² + b²

Plugging in the values we have, we get:

c² = 21² + 28²

c² = 441 + 784

c² = 1225

c = 35

So the length of the path along the longest side of the park would be 35 yds.

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The number 41 is a prime number because it can be divided only by the number one and itself to yield remainder zero.

A prime number is defined as the number which is an integer, greater than one and has the ability to divide only by one and the number itself. The division here indicates that remainder should be zero.

Now, we see that 41 is an integer and it is greater than one. Additionally, it can not be divided by other numbers expect one and itself. These reasons make 41 a prime number.

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Answer: 5 minutes(not sure)

Step-by-step explanation:

She first left her house and went to the shops which approximately says in the graph that she went there at 2 time elapsed(minutes) and then left a 5 when you take that away it gives u 3 minutes

So to find out how long it took her to come out of the bank she arrived at 7 time elapsed (minutes) and then left at 12, you do 12-7=5

Therefore i think the answer is 5 minutes

Answer: -3

Step-by-step explanation:

for an equation [tex]ax^2+bx+c[/tex] to factor you need to figure out what numbers add to b and multiply to c. In this case b is -1 and c is -6. It is easier because one of the numbers has already been figured out for you so what number combined with 2 will add to -1 and multiply to -6? the answer would be -3 because 2+(-3) is -1 and 2*(-3) is -6.

The distance between the two points, we can use the trigonometric equation distance = altitude/tan(angle of depression). Using this equation, we can calculate the distance to be approximately  6,665.93 ft.

Pilot is at point A. The angles of depression to mileposts B and C are 32 degrees and 56 degrees, respectively. We are asked to find the distance between B and C.

Let AB = x, BC = y, and AD = CD = h = 25,000 ft.

tan(32°) = h/AB

tan(56°) = h/AC = h/(AB + BC)

We can use the first equation to solve for AB:

AB = h/tan(32°) = 25,000/tan(32°) ≈ 44,908.55 ft

We can use the second equation to solve for AC:

tan(56°) = h/(AB + BC)

tan(56°) = 25,000/(AB + BC)

AB + BC = 25,000/tan(56°)

BC = 25,000/tan(56°) - AB ≈ 38,242.62 ft

Therefore, the distance between the two mileposts is:

BC ≈ 38,242.62 - 44,908.55 ≈ 6,665.93 ft

So the distance between the two mileposts is approximately 6,665.93 ft.

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Here in the given diagram all the sides are equal and the diagonals are perpendicular. So the given parallelogram is a rhombus.

Here the data given are

ABCD is a parallelogram

∠BOC = 90°

So AOB = 180 - ∠BOC ( angle of a straight line is 180°)

∠ AOB = 180-90 = 90°

Also ∠ COD = ∠DOA = 90°

OA = OC, OB= OB ( Diagonals of a parallelogram bisect each other)

So the triangles are congruent. So AB = BC

Similarly ΔBOC and ΔCOD are congruent, BC= CD

Similarly ΔCOD and ΔDOA are congruent, CD= AD

So, AB = BC = CD= DA

Since all sides are equal and diagonals are perpendicular, the given parallelogram is a rhombus.

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The complete question is given as the image below.

When changing the sign of the constant a from positive to negative, the domain remains the same. But the range changes.

A function's range is the set of all values it can accept, whereas its domain is the set of all values for which it is defined.

Consider the given function f(x)=a|x|. Let us consider "a" takes positive values that is [tex]a\geq0[/tex]. Then, the given function is defined as follows,

[tex]f(x)=\begin{cases}a(x)=ax}\; &x\geq0\\{a(-x)=-ax\;&x < 0\end{cases}[/tex]

Then, the domain will be [tex]\text{domain}=\mathbb{R}\{(-\infty, \infty)[/tex] and the range will be given as [tex]\text{Range} = \text{only non-negative real numbers} = \mathbb{R}^++\{0\}[/tex].

Now let us consider "a" takes negative values that is a<0. Then, the given function is defined the same and the domain will remain the same. But the range will be given as [tex]\text{Range} = \text{only negative real numbers} = \mathbb{R}^-+\{0\}[/tex].

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The surface area of a square base pyramid is 696.96 cm².

The surface area of the cone is 353.43 mm².

The surface area of a square base pyramid is calculated by applying the following formula as shown below;

SA = 2bs + b²

where;

let the half of the base = x

Apply Pythagoras theorem to determine the value of x using the given heights of the right triangles

x = √ ( 17² - 15.4² )

x = 7.2 cm

The base of the pyramid = 2x = 2 (7.2 cm ) = 14.4 cm

SA = 2 x 14.4 x 17  +  ( 14.4)²

SA = 696.96 cm²

The surface area of the cone is calculated as follows;

SA = πrs + πr²

where;

The slant height of the cone is calculated as follows;

s = √ (4.5²  +  20² )

s = 20.5 mm

SA = π x 4.5 x 20.5   +   π(4.5²)

SA = 353.43 mm²

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Answer: r = 5.5%

Step-by-step explanation:

6/12 = 0.5 (years)

(I=Prt) || 1375 = 50000 * r * 0.5

1375 = 25000r

1375/25000 = 25000r/25000

0.055 = r

0.055 * 100% = r

5.5% = r

(Please correct me if I'm wrong)

Dallas and San Antonio, Texas are separated by approximately 240 miles (386 kilometres) by road. The predicted journey time is around 4 hours, although this may vary based on traffic and other conditions.

Dallas is located in Texas, in the country's southern central area. It is the ninth-largest city in the United States and the third-largest in Texas in terms of population. Dallas is part of the Dallas-Fort Worth metropolitan area, which is one of the largest in the United States. Dallas, in North Texas, is surrounded by a variety of suburban towns. Dallas and San Antonio are approximately 240 miles apart.

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Using proportions, we determined 24 out of every 36 households have a guest room.

Proportion, in general, is referred to as a part, share, or number considered in comparative relation to a whole. Proportion definition says that when two ratios are equivalent, they are in proportion. It is an equation or statement used to depict that two ratios or fractions are equal.

Given that, six out of every 9 households have a guest room.

So, the ratio is 6:9

Margaret asked x households in her neighborhood if they have a guest room, and 24 said yes

So, the ratio is 24:x

Now, the proportion is 6:9::24:x

6x=9×24

x=36

Hence, 24 out of every 36 households have a guest room.

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The value of the given expression 105 times 3 is equal to 315.

Calculation of the expression 105 times 3 is equal to :

  1

1 0 5

×    3

3 1 5

Therefore, the calculated value of the expression 105 times 3 is equal to 315.

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Answer: i think its 40

Step-by-step explanation: because triangles in general are supposed to have the angle 180 and 40 add 400 add 100 equals 180

It is not possible to get 8 aces from a standard 52 cards deck. The indicated degree of likelihood as a probability value is 0 (Zero).

The procedure for probability states that the possibility of an occurrence occurring, or P(E), equals the proportion of the number of favorable outcomes to the number of total outcomes.

Mathematically,

Possibility (E) = favorable outcomes/total outcomes.

We know that there are four aces in total in a 52-card deck.

Therefore the probability of getting 8 aces can be expressed by using the factorial of the number. This can result in a decrease of numbers by multiplying the previous number, this is called the factorial of a number.

P(8A) = 7/52 × 6/51 × 5/50 × 4/49 × 3/48 × 2/47 × 1/46 × 0/45

P(8A) = 0

The probability of getting is zero.

Therefore, it is not possible to get 8 aces from a standard 52 cards deck.

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Answer:

It is extremely important to protect ecosystems from human-induced change, as ecosystems provide vital services such as air and water purification, climate regulation, and nutrient cycling, which are essential for human well-being.

Preserving natural conditions at all costs may not always be feasible, as human populations continue to grow, and there may be competing demands for resources. On the other hand, prioritizing human needs over the needs of the ecosystem can have detrimental consequences in the long run.

Taking an approach that does not prioritize ecosystem protection can lead to the loss of biodiversity, the degradation of natural resources, and the loss of ecosystem services. These negative consequences can lead to reduced agricultural productivity, increased incidence of natural disasters, and negative impacts on human health.

Finding a balance between human needs and the needs of the ecosystem is therefore critical. This can be achieved through sustainable development practices that promote economic growth while preserving the environment, such as the use of renewable resources, ecosystem restoration, and sustainable agriculture practices.

The solution to the system of equations is x = 5 and y = -2, or (5,-2) in coordinate form.

An equation is a mathematical statement that shows that two expressions are equal. It is usually written as an expression on the left-hand side (LHS) and an expression on the right-hand side (RHS) separated by an equal sign (=).

The expressions on both sides of the equation can contain variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. The variables in an equation represent unknown values that can vary, while the constants are fixed values that do not change.

Equations are used to represent mathematical relationships or describe real-world situations. They can be used to solve problems, make predictions, and test hypotheses.

To solve an equation, one must find the value of the variable that makes the LHS equal to the RHS. This is done by performing mathematical operations on both sides of the equation to isolate the variable. The goal is to get the variable by itself on one side of the equation, with a specific value on the other side.

Equations can be simple or complex, linear or nonlinear, and can involve one or more variables. Examples of equations include:

2x + 5 = 13

y = 3x^2 - 2x + 7

4a + 2b - 3c = 10

Equations are used in many areas of mathematics and science, including physics, chemistry, and engineering, among others.

Substitute the value of y in the second equation with the expression for y from the first equation:

2x + 3(4x-22) = 4

Simplify and solve for x:

2x + 12x - 66 = 4

14x = 70

x = 5

Substitute the value of x in the first equation to solve for y:

y = 4(5) - 22

y = -2

Therefore, the solution to the system of equations is x = 5 and y = -2, or (5,-2) in coordinate form.

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Cost for each pound of almonds is $1.5 and cost for each pound of jelly beans is $2.5.

Linear equations involve one or more expressions including variables and constants and the highest exponent of the variable is 1.

System of linear equations involve two or more linear equations.

Let x be the cost of each pound of almond and y be the cost of each pound of jelly beans.

Then from the first purchase, we have the equation,

3x + 5y = 17

Similarly, from the second purchase, we have,

12x + 2y = 23

So the system of equations are

3x + 5y = 17 and 12x + 2y = 23

Solving these, we will get the values of x and y which is the cost of each pound of almond and jelly beans.

3x + 5y = 17

12x + 2y = 23

Multiplying the first equation with 4, we get,

12x + 20y = 68

Subtracting 12x + 2y = 23 from 12x + 20y = 68,

18y = 45

y = $2.5

Substituting y = 2.5 in any of the equation above, we get,

x = $1.5

Hence the cost for each pound of almond and jelly beans are $1.5 and $2.5 respectively.

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Answer: 20

Step-by-step explanation:

a + b = 60.

a - 6 = 5b - 30 or a = 5b - 24

a = 60 - b

60 - b = 5 b - 24

84 = 6b

b = 14

a = 46

Mother is 46 and daughter is 14 now. After 6 years, daughter will be 20.

Hope this helped you, And if possible, could I have brainliest?

I also answered first! :D (Please don't copy what I said for the people that are going to answer this question, thank you!) :D

All of the given expressions are functions, but the first three are quadratic functions, while the last one is a quadratic function with a negative constant term.

What is the function?

A function is a mathematical relationship between two variables, where each input value (independent variable) corresponds to exactly one output value (dependent variable). It is often represented using a formula or equation.

All of the given expressions are functions, but the first three are quadratic functions, while the last one is a quadratic function with a negative constant term.

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The magnitude and direction of the vector is 7.3 units and 15.9° north of east respectively.

option B.

To find the magnitude and direction of MN, we can use the distance formula and trigonometry.

The distance formula is:

d = √((x₂ - x₁)² + (y₂ - y₁)²)

Using the coordinates of M(-3,-2) and N(4,0), we get:

d = √((4 - (-3))² + (0 - (-2))²)

d = √(49 + 4)

d = √(53)

d ≈ 7.3 units

To find the direction, we can use trigonometry. We can first find the angle between the line and the positive x-axis using:

tan θ = (y₂ - y₁)/(x₂ - x₁)

tan θ = (0 - (-2))/(4 - (-3))

tan θ = 2/7

θ = arc tan (2/7) =  15.9°

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187 centimeter is approximately equal to 6.1351 feet

To convert 185cm to feet, we can use the following formula:

1 cm = 0.0328 feet

The conversion is the process of changing the unit of one quantity to another units  

The conversion factor is defined as the number that is used to change one unit to another units by multiplying or dividing

Therefore,

The distance in feet = conversion factor × The distance in centimeter

Substitute the values in the equation

187 cm = 187 x 0.0328

Multiply the numbers

= 6.1351 feet ( rounded to four decimal places )

Therefore, 187 cm is 6.13517 feet.

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She bought three movies and four CD,s and this can be found by doing sum.

we given that price for each movie= 3$.

price for each CD = 2.50$.

The total movies and CD,s bought= 7.

Total dollars spent by her = 19$.

Therefore, the number of movies bought= 3+3+3= 9. ( No. of movies= 3).

similarly, the number of CD,s bought= 2.5+2.5+2.5+2.5= 10.( No. of CD,s= 4).

Hence, out of 19$ , 10 dollars were spent to buy CD,s and the other 9 dollars were spent to buy movies.

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Complete question:- During a sale at the electronics store, movies sold for $3 and CDs sold for $2.50. Isla spent $19 and bought a total of 7 movies and CDs. How many of each did she buy?

Answer:

A + B must lie between 90 and 450 degrees.

Explanation:

Since sin A and cos B are both negative, A and B must lie in the third quadrant or the fourth quadrant. In the third quadrant, sin A and cos B are both negative, while in the fourth quadrant, sin A is negative and cos B is positive.

Let's consider the case where A and B are both in the third quadrant. In this case, both A and B are between 180 and 270 degrees. Since A + B is the sum of two angles in this range, it follows that A + B must be between 360 and 450 degrees.

Now let's consider the case where A is in the fourth quadrant and B is in the third quadrant. In this case, A is between 270 and 360 degrees, while B is between 180 and 270 degrees. Since sin A is negative and cos B is positive, it follows that cos A and sin B are both negative. Using the identities sin(180 - x) = sin x and cos(180 - x) = -cos x, we can write:

sin A + cos B = sin(180 - (180 - A) - B) + cos(180 - (180 - A) - B)

= sin(180 - A) - cos(180 - B)

= -sin A - cos B

Therefore, A + B is the difference of two angles in the third quadrant, and it must be between 90 and 180 degrees.

Putting the two cases together, we see that A + B must lie between 90 and 450 degrees.