Solve the following system of equations by substitution method. x+2y=5 2x+y=4​

Answer:

\(6x^4y^8\sqrt{5x}\)

Step-by-step explanation:

\(\textsf{When $x > 0$ and $y > 0$, we want to find the expression that is equivalent to}\) \(\sqrt{180x^9y^{16}}.\)

\(\textsf{First, apply the radical rule:} \quad \sqrt{ab}=\sqrt{a}\sqrt{b}\)

\(\sqrt{180}\sqrt{x^9}\sqrt{y^{16}}\)

\(\textsf{Rewrite $x^9$ as $x^{8+1}$:}\)

\(\sqrt{180}\sqrt{x^{(8+1)}}\sqrt{y^{16}}\)

\(\textsf{Apply the exponent rule:} \quad a^{b+c}=a^b \cdot a^c\)

\(\sqrt{180}\sqrt{x^{8}\cdot x^1}\sqrt{y^{16}}\)

\(\sqrt{180}\sqrt{x^{8}}\sqrt{x}\sqrt{y^{16}}\)

\(\textsf{Apply\:the\:radical\:rule:\:}\sqrt[n]{a^m}=a^{\frac{m}{n}},\:\quad a\geq 0\)

\(\sqrt{180}\;x^{\frac{8}{2}}\sqrt{x}\;y^{\frac{16}{2}}\)

\(\sqrt{180}\;x^4\sqrt{x}\;y^8\)

\(\sqrt{180}\sqrt{x}\;x^4\;y^8\)

\(\textsf{Rewrite $180$ as $(6^2 \cdot 5)$:}\)

\(\sqrt{6^2 \cdot 5}\sqrt{x}\;x^4\;y^8\)

\(\textsf{Apply the radical rule:} \quad \sqrt{ab}=\sqrt{a}\sqrt{b}\)

\(\sqrt{6^2} \sqrt{5}\sqrt{x}\;x^4\;y^8\)

\(\textsf{Apply the radical rule:} \quad \sqrt{a^2}=a, \quad a \geq 0\)

\(6 \sqrt{5}\sqrt{x}\;x^4\;y^8\)

\(\textsf{Apply the radical rule:} \quad \sqrt{a}\sqrt{b}=\sqrt{ab}\)

\(6 \sqrt{5x}\;x^4\;y^8\)

\(\textsf{Rearrange:}\)

\(6x^4y^8\sqrt{5x}\)

\(\textsf{Therefore, when $x > 0$ and $y > 0$, the expression that is equivalent to}\)

\(\sqrt{180x^9y^{16}}\;\textsf{is}\;\;\boxed{6x^4y^8\sqrt{5x}}\:.\)

Therefore, the value of the expression -2f(-6) - 7g(-7) is equal to -99.

In mathematics, a function is a rule that assigns a unique output value to each input value. Functions are often represented as equations or graphs that relate the input (also known as the independent variable) to the output (also known as the dependent variable). The input is usually denoted by the variable x, and the output is usually denoted by the variable y. Functions can be used to model relationships between different quantities, such as time and distance, or temperature and pressure. They are a fundamental concept in mathematics and are used in many fields, including physics, engineering, economics, and computer science.

Here,

Using the function notations given in the problem, the statement can be read as follows:

-2 times the value of the function f evaluated at x = -6, minus 7 times the value of the function g evaluated at x = -7, is equal to:

-2f(-6) - 7g(-7) =

Substituting the expressions for f(x) and g(x) given in the problem, we get:

-2*(3*(-6)+1) - 7*(-2*(-7)+5) =

Simplifying this expression, we get:

-2*(-17) - 7*(19) = 34 - 133 = -99

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Answer:

look it up hahahahah

Step-by-step explanation:

The population of Kentucky is nearly 5.9 times that of North Dakota.

To determine how many times larger Kentucky's population is than North Dakota's population, divide Kentucky's population by North Dakota's population:

4.47 x 10^6 / 7.62 x 10^5

We can simplify the fraction by dividing both the numerator and denominator by 7.62 x 10: 4.47 x 106 / 7.62 x 105 = 5.87

5.9, rounded to the closest tenth.

As a result, the population of Kentucky is nearly 5.9 times that of North Dakota.

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Answer:

24

Step-by-step explanation:

becuse 6+6+6+6=24

The most appropriate chart to depict US energy consumption would be a pie chart since a pie chart helps to see the composition of different proportions representing total consumption.

Chart A is not appropriate because a line graph is used to depict information to analyze changes over time or over a period. However, to show the energy consumption, the line graph is not an accurate depiction since the type of energy source is a categorical variable.

Chart B is also appropriate because it is a column graph and such type of graphs are used to represent categorical variables. The US energy consumption can be represented well through a column graph as it well depicts the highest consumption source and the lowest consumption source.

Yes more than one kind of display would therefore be acceptable as we can use to show the information through both a pie chart and a column graph.

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Answer:

Step-by-step explanation:

Solution

Object A

Object B

Object C

Step-by-step explanation:

To differentiate the function f(x) = 1/x^3, we can use the power rule of differentiation. Here's the step-by-step process:

Write the function: f(x) = 1/x^3.

Apply the power rule: For a function of the form f(x) = x^n, the derivative is given by f'(x) = nx^(n-1).

Differentiate the function: In our case, n = -3, so the derivative is:

f'(x) = -3 * x^(-3-1) = -3 * x^(-4) = -3/x^4.

Therefore, the derivative of the function f(x) = 1/x^3 is f'(x) = -3/x^4.

The algebraic expression represents the result of adding 19 to twice a number is 19 + 2n.

What is an algebraic expression?

An algebraic expression is a combination of numbers, variables, and mathematical operations that can be simplified or evaluated. It is a fundamental concept in algebra, which is the branch of mathematics that deals with the study of symbols and the rules for manipulating them.

To translate the phrase "19 increased by twice a number" into an algebraic expression, we can use the following steps:

Identify the operation being performed: In this case, the phrase "increased by" indicates that we need to use the addition operator (+).

Identify the constants and variables: The constant in this expression is 19, and the variable is "a number", which we will represent with the variable n.

Write the expression: Using the information from steps 1 and 2, we can write the expression as follows:

19 + 2n

Hence, the expression represents the result of adding 19 to twice a number is 19 + 2n.

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The algebraic expression represents the result of adding 19 to twice a number is 19 + 2n.

What is an algebraic expression?

An algebraic expression is a combination of numbers, variables, and mathematical operations that can be simplified or evaluated. It is a fundamental concept in algebra, which is the branch of mathematics that deals with the study of symbols and the rules for manipulating them.

To translate the phrase "19 increased by twice a number" into an algebraic expression, we can use the following steps:

Identify the operation being performed: In this case, the phrase "increased by" indicates that we need to use the addition operator (+).

Identify the constants and variables: The constant in this expression is 19, and the variable is "a number", which we will represent with the variable n.

Write the expression: Using the information from steps 1 and 2, we can write the expression as follows:

19 + 2n

Hence, the algebraic expression represents the result of adding 19 to twice a number is 19 + 2n.

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Answer:

8/9. 5/9+1/3 L.C.M =9 ANS= 8/9.

Hi there!

Matching Vocabulary...

I would be doing from up to down so you don’t mess up...

1. millimeters

2. mass

3. kilogram

4. capacity

5. liter

6. gram

put the instrument at x and u will b ab, to find

Step-by-step explanation:

u need an instrument and it is known as D innsimplemwords then use at,point to find its andswer

Answer:

3+17=p

p= 20p

Step-by-step explanation:

Answer:

216

Step-by-step explanation:

Answer:

\(f(x)=\dfrac{1}{x+4}\)

Step-by-step explanation:

Asymptote: a line which the curve gets infinitely close to, but never touches.

From inspection of the graph, we can see that there is an asymptote at \(x=-4\), since the curve gets infinitely close to this line, but never touches it.

Therefore, the function is undefined at \(x=-4\)

For a rational function to be undefined, the denominator must equal zero at that point.  Therefore, we are looking for a rational function with a denominator that equals zero when \(x=-4\).

Therefore, option D is the correct solution, since:

\(f(-4)=\dfrac{1}{-4+4}=\dfrac{1}{0} \implies \sf und efined\)

Answer:

3/4

Explanation:

The ratio of 150 to 200 as a fraction is

Now, to write it in its lowest term, we need to divide the numerator and denominator by 50, so

Then, the answer is 3/4

Answer;

Explanation;

Here, we want to get the solution a pair of linear equation which we are to solve simultaneously by the graphical method

We need to plot the graphs of these two lines; The point at which the lines meet will represent the solution to the system of linear equations

The general equation of a straight line is;

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

To plot the lines, we need the x-intercepts and the y-intercepts

This refer to the point at which the line touches the x and y axes respectively

Let us take the lines one after the other;

The y-intercept here is -4; so the point is (0,-4)

To get the x-intercept value, we simply set y to zero and get the value of x

So the x-intercept is (-4/3,0)

To plot the line; we simply join (0,-4) and (-4/3,0)

For the second line;

We have the y-intercept as -2

So the point is (0,-2)

To get the x-intercept, we simply set y to 0 and solve for x

So, the x-intercept point is (-2,0)

We can now join (0,-2) and (-2,0) to represent the second line

Proceeding, we get the lines on the cartesian grid

This is shown in the attachment below;

As we can see from the plot, the lines touch at the point (-1,-1) and that represents the solution to the equation

A ray from the vertex of the angle through the point where the two arcs intersect. This ray is a copy of the original angle.

The steps for constructing a copy of an angle:

Step 1: Draw the angle.

Step 2: Place the center of the protractor on the vertex of the angle.

Step 3: Line up the baseline of the protractor with one of the angle's rays.

Step 4: Read the degree measure where the other ray crosses the protractor.

Step 5: Draw a ray from the vertex of the angle to the right.

Step 6: Use a ruler to mark the same distance on the ray that was just drawn.

Step 7: Draw a ray from the vertex through the point just marked on the ray.

This is the copy of the angle's second ray.

Step 8: Use a compass to draw an arc centered at the vertex of the original angle that passes through one of the angle's rays.

Step 9: Without adjusting the compass, draw another arc that intersects the previous arc at a point.

Step 10: Draw a ray from the vertex through the point where the two arcs intersect.

This is the copy of the original angle.

Using a compass, draw an arc centered on the vertex of the original angle passing through one of the angle rays. Place the tip of the

compass on the vertex of the original angle and draw an arc that intersects one of the angle rays.

Draws another arc that intersects the previous arc at a point without adjusting the compass.

Draw a second arc that intersects the first arc at another point, keeping the compass latitude.

Using a ruler or ruler, draw a ray from the vertex of the angle through the point where the two arcs intersect. This ray is a copy of the original angle.

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The cosine function for a specific angle in a triangle is defined by the ratio of the triangle's adjacent side and hypotenuse.

This is further explained below.

Generally, trigonometric functions are a set of real functions that link the ratios of the lengths of two sides of a right-angled triangle to an angle in the triangle.

They find widespread use in all fields of study that are in some way connected to geometry, including geodesy, solid mechanics, celestial mechanics, navigation, and a great many more.

In conclusion, The ratio of a triangle's adjacent side to its hypotenuse is used to determine the cosine function for a certain angle in the triangle.

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Answer:

50

Step-by-step explanation:

Answer:

Population = 75,342 households

Sample = 400 randomly selected households

The percentage who live in a single household unit = Parameter

The average of 2.9 person per household of all households in the city = parameter

The $65,000 median family income of all the households in the city = Parameter

Step-by-step explanation:

The population refers to all the entire elements, observations or subject which fits into a particular study. In the scenario above, the entire household in the city of study. That is, the 75,342 households.

The sample is the subset of the population which is a smaller set of observation meant to be representative of the larger population. The sample here is the 400 randomly selected households.

Parameter differs from statistics in that numerical estimates or calculations obtained from the population is called the parameter while the numerical characteristics derived from the sample is called statistic.

In this exercise we have to use the knowledge of probability to calculate the chances of choosing a TV approved by the quality control, so:

400  randomly selected households

So, based on the information given in the statement, we have:

Some parameters for this equation are:

The inhabitants of a place refers to all the complete essential feature, attention or subject that fits into the study. In the sequence of events above, the complete household fashionable the city of study. That is, the 75,342 households.

The sample exist the subset of the inhabitants of a place that exist a tinier set of comment on something scrutinized intend expected representative of the best inhabitants of a place. The sample in this place happen the 400 carelessly picked households.

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The rate (in km/h) at which the distance from the plane to the radar station is increasing a minute later is 0 km/h (rounded to the nearest whole number).

To solve this problem, we can use the concepts of trigonometry and related rates.

Let's denote the distance from the plane to the radar station as D(t), where t represents time. We want to find the rate at which D is changing with respect to time (dD/dt) one minute later.

Given:

The plane is flying with a constant speed of 360 km/h.

The plane passes over the radar station at an altitude of 1 km.

The plane is climbing at an angle of 30°.

We can visualize the situation as a right triangle, with the ground radar station at one vertex, the plane at another vertex, and the distance between them (D) as the hypotenuse. The altitude of the plane forms a vertical side, and the horizontal distance between the plane and the radar station forms the other side.

We can use the trigonometric relationship of sine to relate the altitude, angle, and hypotenuse:

sin(30°) = 1/D.

To find dD/dt, we can differentiate both sides of this equation with respect to time:

cos(30°) * d(30°)/dt = -1/D^2 * dD/dt.

Since the plane is flying with a constant speed, the rate of change of the angle (d(30°)/dt) is zero. Thus, the equation simplifies to:

cos(30°) * 0 = -1/D^2 * dD/dt.

We can substitute the known values:

cos(30°) = √3/2,

D = 1 km.

Therefore, we have:

√3/2 * 0 = -1/(1^2) * dD/dt.

Simplifying further:

0 = -1 * dD/dt.

This implies that the rate at which the distance from the plane to the radar station is changing is zero. In other words, the distance remains constant.

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Answer:

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

If the system of linear equations has infinitely many solutions, it means the two lines overlap.

In other words, each point of one of the lines also belongs to the second line.

Choices a, b, c  give us one or no solutions and therefore not the answer.

Choice d is reflecting the infinitely many solutions and hence is the correct one.

The value of the equation that defines the function is f(x) = 3(5/3)ˣ

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

(0, 3) and (1, 5)

An exponential function is represented s

y = abˣ

Where,

a = y when x = 0

So, we have

y = 3bˣ

Using the other point, we have

3b = 5

This gives

b = 5/3

So, we have

f(x) = 3(5/3)ˣ

Hence, the equation defining f is f(x) = 3(5/3)ˣ

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\(h(x) = x + 1\)

\(k(x) = x - 2\)

_________________________________

\((h + k)(x) = h(x) + k(x)\)

\((h + k)(x) = (x + 1) + (x - 2) \\ \)

\((h + k)(x) = x + 1 + x - 2\)

\((h + k)(x) = 2x - 1\)

\((h + k)(2) = 2(2) - 1\)

\((h + k)(2) = 4 - 1\)

\((h + k)(2) = 3\)

_________________________________

And we're done.....♥️♥️♥️♥️♥️

Answer:it’s 5

Step-by-step explanation:

because it is