3. The function f(x) has the coordinates below. State the changes made to f(x) which result in the function g(x). Write the (x,y) rule that would transform the coordinates of f(x) to the coordinates of g(x). g(x) = -2f(x + 1) - 4

Given:

The given deciaml number is 365.24.

Required:

We need to convert the given decimal number into a binary number.

Explanation:

Consider the integer part of the given number.

Divide the number 365.

Consider the fraction part of the given number.

Multiply the number 0.24 by 2.

The binary number of the decimal number is

Final answer:

Let us begin by illustrating the problem using a diagram:

Here we have represented the angle that the driveway makes with the horizontal to be x

Step 1: Label the sides as shown:

Step 2: Using the sides given, find the required angle

The formula that relates the angle, opposite side and hypothenuse side is:

Applying the formula:

Hence, it makes an angle of 7.3 degrees with the horizontal

ANSWER

EXPLANATION

The figure given is a square.

Each angle in a square is 90 degrees and the diagonals bisect each angle.

This means that :

That is the value of x.

The equation for number of books collected by Robert is given as;

n= 14 d + 21

where d is the number of days he spent collecting .

Answer A. represents the number of books per day that are collected

Answer: 4 committees

Step-by-step explanation:

12 divided by 3 =  4      (this equation represents the teachers)

2 x 4 = 8       (this equation represents the students)

There can only be 4 committees because there are only 12 teachers. There are some students that will not be in a committee. 24 students will be committee-less to be exact.

Given that 150 is increased to 861

The absolute change formula is

Where

The new value = 861

The old value = 150

The absolute change is

Hence, the absolute change is 711

The formula for percentage is

Substitute the values into the percentage change formula

Hence, the percentage change is 474% increase

the variables are

where

a -----> is the number of adults

b-------> is the number of children.

answer is option B

Answer:

10

Step-by-step explanation:

30 -2

28 -3

25 -4

21 -5

16 -6

= 10

Answer:

  10

Step-by-step explanation:

Given the sequence 30, 28, 25, 21, 16, you want to know the next number.

First differences between successive terms are ...

  28 -30 = -2

  25 -28 = -3

  21 -25 = -4

  16 -21 = -5

These are not constant, so this is not an arithmetic sequence. However, we notice the second differences are constant:

  -3 -(-2) = -1

  -4 -(-3) = -1

  -5 -(-4) = -1

This observation tells us the next second difference is ...

  -5 +(-1) = -6

And the next number in sequence is ...

  16 +(-6) = 10

The next number is 10.

__

Additional comment

When a sequence of numbers is described by a polynomial or exponential, looking at differences (and their differences) can help determine the degree of the polynomial, or the common ratio of the exponential.

Here, the second differences are constant, so a second-degree (quadratic) polynomial will describe the sequence. The polynomial describing this sequence is ...

  a(n) = 31 -(n)(n+1)/2

Hello!

First, let's analyze the figure and write each side:

Analyzing it, we don't have enough information yet to calculate the tangent (because we don't know the measurement of P).

So, let's calculate the opposite side (by Pithagoras):

As we know the opposite side, we can calculate the tangent of P, look:

Curiosity: using the trigonometric table, this value corresponds to approximately 13º.

The tangent of P is 0.225.

An ordered pair for the equation 5x + y = 1 is (0, 1)

The equation of the function is given as

5x + y = 1

To determine the ordered pair, we simply set the value of x to any value.

And then calculate the value of y

Using the above parameters as a guide, we can assume that

x = 0

Substitute x = 0 in 5x + y = 1

5(0) + y = 1

Evaluate the product

0 + y = 1

So, we have

y = 1

Express as ordered pairs

(x, y) = (0, 1)

Hence, the ordered pair in the solution is (0, 1)

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An ordered pair of the equation 5x + y = 1 is (1, - 4).

An ordered pair (a,b) is a set of values for x and y coordinates.

As the name suggests (a, b) and (b, a) are two different ordered pairs.

Given, 5x + y = 1.

Or,

y = 1 - 5x.

Now we can choose any arbitrary value of x that corresponds to a value

of y.

At x = 1,

y = 1 - 5(1).

y = 1 - 5,

y = - 4.

∴ An ordered pair o the given equation 5x + y = 1 is (1, - 4).

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There are a total of 4 outcomes that involve choosing a blue marble

Here, we want to write a sample space for the selection

For us to have the sample space, we will have to write out the possible outcomes

We shall be representing the blue marble by b, the green by g and the yellow by y

We have the sample space as follows;

{1B,1G,1Y,2B,2G,2Y,3B,3G,3Y,4B,4G,4Y}

From the sample space, we can see that there are actually 12 possible results

Now, to get the outcomes involving blue marbles, we simply select the members of the sample space having B at the back

We have these as 1B, 2B, 3B and 4B

This is a total of 4 outcomes

For this problem, we need to describe a real-life situation where trigonometric functions can be used to model the problem.

Let's assume that a certain vehicle's position is controlled by the speeds of the wheels on each side of the car. Whenever the speeds on the left wheels and right wheels are equal, then the car moves forward, if the speed on the left side is greater than the one on the right side the car goes right, and if the speed on the right side is greater, then the vehicle goes to the left side. This type of car is called a differential drive car, and it's very common on remote-controlled (RC) vehicles.

If we want to model the speed of the car in a two dimensional grid, such as below:

We need to assume that the vehicle will have two components of velocity, one that is parallel to the x-axis and one that is parallel to the y-axis. These will form the linear velocity for the vehicle. We also need an angular velocity, which is the rate at which the angle of the vehicle changes.

If we assume that the wheels of the vehicles are at a distance of "L" apart from each other, then we can model the angular velocity of the vehicle as:

Where "vr" is the speed on the right wheel, and "vl" is the speed on the left wheel. The movement will happen with the center of the car as the center of the movement, with this we can assume that the velocity of the vehicle on the two axes should be:

Therefore we can describe the vehicle speed with the following equations:

The input variables are "vr" and "vl" which are the speeds of each wheel and the angle of the vehicle "theta", the output is the speed at the x coordinate and the speed at the y coordinate, and the angular speed.

This works very well because if the vehicle is moving parallel to the x-axis, the angle will be 0, the cosine of 0 is 1, therefore the speed on the y axis will be 0 and the speed on the x-axis will be given by 0.5(vr+vl). The opposite happens when the vehicle is moving parallel to the y-axis.

Since we need to solve for r we have to leave that variable alone in one side of the equation. We notice that at is adding in the right side, then it goes to the left side substracting, that is:

Therefore:

in the last part we only switch the sides of the equation.

Answer:

80

Step-by-step explanation:

This is a ratio and we can set it up as follows and solve for x:

[tex]\frac{2}{3} = \frac{x}{120}[/tex]

Multiply both sides by 120

80 = x

Answer:

35 degrees.

Explanation:

The figure shown is an isosceles triangle. An isosceles triangle has two of its sides and base angles to be equal.

Since the sum of the angles in a triangle is 180 degrees, hence:

110 + (base angles) = 180

110 + (<1 + <1) = 180 (since base angles are the same)

110 + 2<1 = 180

2<1 = 180-110

2<1 = 70

Divide both sides by 2

2<1/2 = 70/2

<1 = 35 degrees

Hence the angle between an eave and the horizontal support beam is 35 degrees.

if there was no ratio they were in the middle (4,6)

but in this case we must multiply by the ratio

so

so the C point is

Subtract the second equation from the first,

Given:

All lines that cross the x-axis are vertical line.

Required:

To find whether the given statement is true or false.

Explanation:

A vertical line is one the goes straight up and down, parallel to the y-axis of the coordinate plane.

The x-intercept is the point at which the graph crosses the x-axis.

Here all lines are not vertical lines.

Therefore the given statement is false.

Final answer:

False.

0.4 liters or 2/5

Step-by-step explanation:

Dividing the soda equally, Each student would get 0.4 liters or 2/5

The five credit score tiers are listed in ascending order, starting with the lowest tier:

Deep Subprime < Subprime < near prime < prime < superprime

The ability of a consumer to get credit may be significantly influenced by their credit score. These interactive graphs demonstrate how lending behavior has changed for different credit score profiles of borrowers.

We concentrate on the following five commercially available credit score levels:

Subprime's credit scores is between 580 to 619.

Prime's credit score level is between 660 to 719.

The credit score level of deep subprime is below 580.

The credit score level of near prime is 620 - 659.

The credit score level of superprime is 720 or above.

Therefore, the five tires of credit scores from lowest to highest are:

Deep Subprime < Subprime < near prime < prime < superprime

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The ratio of width to height is :

If h = 18 inches, the value of w will be :

The answer is w = 29.12 inches

Answer:

Angle Reason

m∠ECD = 140 Given

m∠ECB = 40 Supplementary angles

m∠EBC = 70 Isosceles triangle

m∠ABE = 110 Supplementary angles

Explanation:

Angle ECB and CED are supplementary because they form a straight line and their sum is 180 degrees. So, we can calculate the measure of ∠ECB as

m∠ECB = 180 - 140

m∠ECB = 40

Then, the interior sum of the angles of a triangle is equal to 180 degrees, so

m∠ECB + m∠EBC + m∠BEC = 180

40 + m∠EBC + m∠BEC = 180

However, m∠EBC = m∠BEC because triangle ABC is an isosceles triangle where 2 sides have the same length BC and EC. So, we can find m∠EBC as follows

40 + m∠EBC + m∠EBC = 180

40 + 2m∠EBC = 180

40 + 2m∠EBC - 40 = 180 - 40

2m∠EBC = 140

m∠EBC = 140/2

m∠EBC = 70

Then, the measure of ∠ABE is equal to

∠ABE = 180 - m∠EBC

∠ABE = 180 - 70

∠ABE = 110

Therefore, we can answer it as follows

Angle Reason

m∠ECD = 140 Given

m∠ECB = 40 Supplementary angles

m∠EBC = 70 Isosceles triangle

m∠ABE = 110 Supplementary angles

Sum of the exterior angles of a polygon = 360°

For a regular polygon, all the angles are equal:

mn = 360

where n = the number of sides

m = the size of an exterior angle

For m = 15°

15n = 360

n = 360/15

n = 24

Therefore, the polygon

We determine the greatest common factor as follows:

So, we factor:

So, the greatest common factor is 2n^3.

Answer:

2 and 3

Explanation:

Given the equation:

Now, observe the following:

Taking the indices:

y represents the distance of the snail to the flower, in ft

x represents time, in hours

In the beginning, the distance of the snail to the flower is 7 feet. Then, the point (0, 7) is on the graph

After the first hour, the snail crawls 2 feet, then its distance to the flower is 7 - 2 = 5 ft. Then, the point (1, 5) is on the graph.

After the second hour, the snail crawls another 2 feet, then its distance to the flower is 5 - 2 = 3 ft. Then, the point (2, 3) is on the graph.

After the third hour, the snail crawls another 2 feet, then its distance to the flower is 3 - 2 = 1 ft. Then, the point (3, 1) is on the graph.

The graph is

Hello there. To solve this question, we'll have to remember which other formulas for area of triangles can be used.

Most specifically, it asks for a formula that works on an obtuse triangle, that is, a triangle that haves an angle that measures more than 90º.

Besides the formula BH/2, that refers to half of the product between the measurements of the base and the height of the triangle, of course, this height must be a projection perpendicular to the base, as in the following drawing:

Another formula that can be used is Heron's formula;

Knowing the measures of all the sides of the triangle (no matter if it is an obtuse, acute or right triangle), say a, b and c, Heron's formula states that the area S of the triangle is given by:

Where

is the semiperimeter of the triangle.

This is the answer we've been looking for.

12 loaves of pumpkin bread.

Each loave is cut into 1/8 pieces.

So, there are 8 pieces per loaf:

8 pieces per loaf x 12 loaves = 96 pieces

If she gives one piece to each friend she can give it to 96 friends:

96 pieces / x friends = 1 per friend

96/x =1

96 = x(1)

96= x

The most appropriate choice for congruency of triangles will be given by

[tex]\bar{IL} \cong \bar{JP}[/tex]

Third option is correct.

What are congruent triangles?

Two triangles are said to be congruent if their corrosponding sides and corrosponding angles are equal.

There are five axioms of congruency. They are

SSS axiom, SAS axiom, ASA axiom, AAS axiom, RHS axiom.

Here,

ΔIKL ≅ ΔJOP [Given]

[tex]\bar{IL} \cong \bar{JP}[/tex] [Corrosponding parts of congruent triangles are congruent]

Third option is correct.

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Complete Question

The diagram with the question has been attached below

Answer:

x = 3/2 = 1.5

Explanation:

The initial equation is:

To solve the equation, we need to multiply both sides by 250 as:

This fraction can be simplified as:

Therefore, the value of x is 3/2 as a fraction or it is 1.5 as a decimal.