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1) f(x)-3

Therefore, f(x)-3=2x-4-3

2) f(x-3)

Thus, f(x-3)=2(x-3)-4

3) f(-3x)

Then, f(-3x)=2(-3x)-4

4) -3f(x)

Hence, -3f(x)=-3(2x-4)

Answer:

  150 km

Step-by-step explanation:

You want to know the number of kilometers each train has traveled when they meet. The first goes 60 km/h and has a half-hour head start. The second goes 75 km/h.

At t hours after 10 am, the distance of the first train from Kanpur will be ...

  distance = speed × time

  distance = 60t

At t hours after 10 am, the distance of the second train from Kanpur will be ...

  distance = 75(t -1/2) . . . . . . the distance is 0 at 10:30 am, 1/2 after 10 am

These distances will be equal when ...

  60t = 75(t -1/2)

The time at which the trains meet will be the solution to the above equation.

  60t = 75t -37.5 . . . . eliminate parentheses

  0 = 15t -37.5 . . . . . . subtract 60t

  0 = t -2.5 . . . . . . . . . divide by 15

  2.5 = t . . . . . . . . . the trains meet 2.5 hours after the first one leaves

The distance traveled by each of the trains is the same at that time. It will be the distance traveled by the first train:

  60t = 60(2.5) = 150 . . . . km

The two trains will be together 150 km from Kanpur.

Given the two functions:

We need to find (RoS)(4). THis is the functional composition. We take S(x) and put it into R(x) and then put "4" into that composed function. Shown below is the process:

When we plug in "4", into "x", we have:

Answer:

124

Step-by-step explanation:

Since the amount of time is being multiplied by 4, the number of parts will also be multiplied by 4.

[tex]31(4)=124[/tex]

The value of expression ( – 5q–1)–( – 2q–8) is -3q + 7.

As per the known fact, the similar signs are consequently takes as positive for calculation. So, the two negative signs will be takes as positive. So, rewriting the expression to solve and find its value.

Value of expression = (-5q - 1) + 2q + 8

Rearrange the expression

Value of expression = - 5q + 2q - 1 + 8

Performing addition of numerals written with q and subtraction of constant values

Value of expression = - 3q + 7

Thus, the value of expression mentioned in question is -3q + 7.

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Answer:

C

Step-by-step explanation:

HOPE IT HELPS MARK BRAINLEIST PLS

The radius of this exoplanet's orbit is equal to 4.71 × 10¹¹ meters.

In order to calculate the radius of the exoplanet's orbit, we would apply  Kepler's Third Law of planetary motion.

Mathematically, Kepler's third law of planetary motion can be calculated by using this formula:

T² = 2π√(r³/GM)

Where:

Making radius (r) the subject of formula, we have:

Radius, r = ∛(GMT²/2π)

Note: Universal gravitational constant is equal to 6.67 × 10⁻¹¹ m³kg⁻¹s⁻².

Orbital period, T = 3.95 × 365 × 24 × 60 × 60 = 341,280 seconds

Substituting the given parameters into the formula, we have;

Radius, r = ∛(6.67 × 10⁻¹¹ × 3.97×10³⁰ × (341,280)²/2 × 3.142)

Radius, r = 4.71 × 10¹¹ meters.

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Answer:

Step-Congruent angles are frequently used in the world of architecture, construction, design, and art. Congruent angles have the same angle measure. For example, a regular pentagon has five sides and five angles, and each angle is 108 degrees. Regardless of the size or scale of a regular polygon, the angles will always be congruent.

Given:

a) The radius is​ doubled.

b) The radius is​ tripled.

To find:

The changes to the surface area of a sphere

Explanation:

Let us take the original radius as r.

The surface area of the original sphere is,

a) The new radius will be,

So, the surface area of the sphere with the new radius is,

Therefore, the surface area of a sphere becomes four times the original surface area if the radius is​ doubled.

b) The new radius will be,

So, the surface area of the sphere with the new radius is,

Therefore, the surface area of a sphere becomes nine times the original surface area if the radius is​ tripled.

1. The decrease in dollars in Tammy's investment account, based on a 7.5 percent decrease, is $615.

2. The balance in Tammy's investment account at the end of last year was $7,585.

The percentage is the proportion of a value in relation to another.

Percentages show how much a variable is contained in another.

The percentage gives the fractional value of the decrease in the investment account.

Initial investment = $8,200

Decrease in investment = 7.5%

Decrease in dollars = $615 ($8,200 x 7.5%)

Balance = $7,585 ($8,200 - $615)

Thus, we can conclude that Tammy's investment account decreased by $615, representing a 7.5% decrease.

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A lowest denominator to solve the given equation is 10.

What are fractions?

Fraction are ratios in which numerator and denominator are both integers and denominator is not zero.

We are given a equation

[tex]\frac{74}{5}+1\frac{9}{10}[/tex]

Upon solving we get the following

[tex]\frac{74}{5}+\frac{19}{10}[/tex]

If we multiply both numerator and denominator of the first term by 2 we get

[tex]\frac{148}{10}+\frac{19}{10}[/tex]

Hence after this we can add

Hence A lowest denominator to solve the given equation is 10

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Answer:

78.59$

Step-by-step explanation:

Answer:

h = 9 cm

Explanation:

The volume of the solid can be calculated as:

So, we can replace the value of the Volume by 1323 cm³ and B by 147 cm² as:

Then, dividing by 147 into both sides, we get:

Therefore, the height h of the solid is 9 cm.

The greater triangle and the smaller ones (the two triangles inside the original one, that share the side y) are similar triangles, then we can formulate the following expressions:

• For the larger triangle and the triangle on the left

From this equation, we can solve for z, to get:

Then, z equals 3√5

• Similarly, with the larger triangle and the one on the right:

From this expression, we can solve for x, like this:

Then, x equals 6

• With the triangles on the right and on the left:

Solving for y, we get:

Then, y equals 2√5

The numbers that Linda should put on her number line are 5,10,15,20...1000 .

Integers are frequently represented as specifically labelled dots evenly spaced on a line. Despite the fact that the graphic only depicts the integers from -3 to 3, the product contains all real numbers, which continue indefinitely in each direction, as well as numbers that lie between the integers. It is frequently used to help teach simple numerals, particularly with negative numbers.

The numbers are skip counted. so each number differs from the preceding number by 5.

let us take the number counting starts from 0. so the second number will be 5+5=10

The third number 10+5 = 15 and so on and so forth.

Hence it forms an arithmetic sequence of numbers whose first term is 5 and common difference is 5.

A number line is really a picture of a stepped straight line as serves as a visual representation of real numbers in primary mathematics. Every point of a x axis is assumed to coincide to a true figure, and every decimal digits to a point.

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The correct option is True, there is enough information given to say that both line are parallel.

For the given question.

The two lines are given with angles measure from 1 to 8.

Where,

As, the sum of the angles is;

∠4 + ∠3 = 91° + 89°

∠4 + ∠3  = 180° (supplementary angles)

Thus, we can say that both lines are parallel to each other.

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From the given expression, it is found that:

a) When x = 7 and y = 11, the numeric values are given as follows:

b) They will only have the same numeric value when x = y.

To find the numeric value of a function or of an expression, we replace each instance of the variable in the function by the desired value.

The same is true for multi-variable expressions, as each variable will have a numeric value that we will replace in the function.

In the context of this problem, the expressions are given as follows:

When x = 7 and y = 11, the numeric values are given as follows:

The notable product of the square of the sum is different of the sum of the squares, and the same holds true for the subtraction, hence both expressions will only have the same value when x = y, as factors (x - y)² and (x² - y²) will both be of 0, resulting in a multiplication of 0 in each expression and a value of 0.

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Answer:

P(X = 2) = 43.2%

Step-by-step explanation:

P(X = 2) = 3 * 0.6^2 * (1 - 0.6)^(3 - 2)

P(X = 2) = 54/125

P(X = 2) = 0.432

P(X = 2) = 43.2%

Answer: Correct! The answer is 12.

Step-by-step explanation:

1) Draw the triangle.

Drawing a triangle usually helps you see the problem better!
|    \

|        \  13 cm

|           \

|______\

  5 cm

2) Solve the other leg

To find the other leg, we need to use the Pythagorean theorem. Which goes like this

[tex]a^2+b^2=c^2[/tex]

We will then substitute the numbers into the equation

[tex]5^2+b^2=13^2[/tex]

Simplify

[tex]25+b^2=169[/tex]

Set the variable on one side

[tex]b^2=144[/tex]

Get rid of the squared in the b by square rooting both sides.

[tex]b=12[/tex]

The answer is 12.

Okay, here we have this:

Considering the provided set of numbers we are going to organize the numbers from smallest to largest, so we obtain the following:

Remember that 5/6 is approximately 0.83 and 4/5 is 0.8, then:

Considering the number line and that the smaller numbers are further to the left and the larger numbers are further to the right, we are left with the following order from least to greatest: 4/5, 0.82, 5/6.

Answer: 17x - 39

Step-by-step explanation:

1) Find all sides of the hallway.

P = 4x-9 + x-2 + x+2 + 3x - 11 + x-2 + 3x - 11 + x+4 + 2x-9 + x-1

2) Add it together

P= 17x - 39

To be able to determine if the figure is a right triangle.

The given length must satifies the given conditions,

a.) The sum of the two sides must always be lesser than the other side. We get,

Given: a = 14 ; b = 16 ; c = 18

Let's check,

a + b > c ; 14 + 16 > 18 = 30 > 18 Satisfies the criteria

b + c > a ; 16 + 18 > 14 = 34 > 14 Satisfies the criteria

a + c > b ; 14 + 18 > 16 = 32 > 16 Satisfies the criteria

b.) The square of the longest side is equal to the sum of the squares of the other two sides (Pythagorean Theorem). We get,

Therefore, checking the relationships of the given the following lengths, the figure is not a right tiangle.

The linear equation that passes through the two points (0, 360) and (10, 560) is:

y = 20*x + 360

Remember that the slope-intercept form of a linear equation is:

y = a*x + b

Where b is the y-intercept and a is the slope or rate of change.

If we know that the line passes through the points (x₁, y₁) and (x₂, y₂) then the slope is:

[tex]a = \frac{y_2 -y_1}{x_2 - x_1}[/tex]

Here the line must pass through (0, 360) and (10, 560), so the slope is:

[tex]a = \frac{560 - 360}{10 - 0} = 20[/tex]

And because of the point (0, 360) we can see that the y-intercept is 360, then the linear equation is:

y = 20*x + 360

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Recall that to complete the table we have to evaluate the given function at every value of x:

Answer:

Table:

Graph:

The solution of equation as ordered pairs can be given as {0, 3/2, 3, 6, 15/2}.

Domain may be defined as the input variable x for any of the given function which gives a suitable set of output variables y. The input variable is called the independent variable whereas the output variable is called the dependent variable. The equation given in the question 3x - 2y = -6 can also be expressed as y = (3x + 6)/2. The ordered pairs of Domain are {-2, -1, 0, 2, 3}. Now if we put these values as values of x we get the values of y as,

At x = -2, y = 0, at x = -1, y = 3/2, at x = 0, y = 3, at x = 2, y = 6 and at x = 3, y = 15/2.

These are the values of outputs, and the ordered pair will be expressed as

{0, 3/2, 3, 6, 15/2}.

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B. 2/10 = 20%

The total number of weeks shown in the simulation = 10

By observing the simulation, we would see that there is no 0 or 1 in group 2 and group 3. This means that Juan was late everyday of week 2 and week 3

The number of weeks that Juan was late everyday = 2

The estimated probability that Juan will be late evryday of next week = 2/10 = 20%

First, lets perform each transformation and then take a look at its graph:

1.

The only etiquette that matches this plot is: Function decreases as x increases

2.

The only etiquette that matches this plot is: x-intercept at (1.5 , 0)

3.

The only etiquette that matches this plot is: Asymptote of x = 0