Which choice is a term in this expression? -3x − 7(x + 4)

The linear speed based on the information is 1326 km/h.

The radius will be:

= 6378 + 252

= 6630 km

The angular speed is 0.2. The linear speed will be:

= 6630 × 0.2

= 1326 km/h.

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Answer: B

Step-by-step explanation: Trust me bro

The true statements are:

B. N⊂R

C. S⊂N

D. ∅⊂N

F. {10.11.12,...}⊆S

Note that:

Following the points highlighted above, the true statements in the given options re:

B. N⊂R

C. S⊂N

D. ∅⊂N

F. {10.11.12,...}⊆S

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Answer:

Absolute value parent function

Explanation:

What is an Absolute value function?

It is a function in Algebra in where the variable is inside the absolute value bars (| |)

f(x)=|x|

y=x on the right side and y=-x on the left side of the graph

Hope it helps!

The two characteristics that makes the median a better choice are: A. The data are skewed and there are outliers.

In a data distribution, the median is a better choice to use to describe the data over the mean when an outlier exist and the data is skewed.

IN the dot plot given below, the data has an outlier of 10 while the data distribution is also screwed, this makes the median a better choice.

Therefore, the answer is: A. The data are skewed and there are outliers.

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Answer:

A

Step-by-step explanation:

It is the quadratic parent function

Considering the definition of an inequality, the inequality that can be used to determine x is 20x + 10≤ 80

An inequality is the existing inequality between two algebraic expressions, connected through the signs:

An inequality contains one or more unknown values ​​called unknowns, in addition to certain known data.

Solving an inequality consists of finding all the values ​​of the unknown for which the inequality relation holds.

A rental car company charges $20 per day to rent a car and $0.10 for every mile driven.

Addison wants to rent a car, knowing that:

On the other hand, x represents the maximum number of days Alyssa can afford to rent for while staying within her budget.

Then, the inequality that can be used to determine x is:

20x + 0.1×100≤ 80

So:

20x + 10≤ 80

In summary, the inequality that can be used to determine x is 20x + 10≤ 80

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The number of people who can go to the game only on Sunday by applying the concept of set theory is equal to 5.

Total number of people for a trip to a baseball game = 15

Number of people planning to go on Saturday = 10

Number of people planning to go Sunday = 12

Let x be the number of people who can go on both Saturday and Sunday.

Then, the number of people who can go only on Saturday is 10 - x.

And the number of people who can go only on Sunday is 12 - x.

Total of 15 people are going to the baseball game.

Using set theory we have,

Number of people going on Saturday only + number of people going on Sunday only + number of people going on both = 15

Substitute the value we have,

⇒(10 - x) + (12 - x) + x = 15

Simplifying the above equation, we get,

⇒22 - x = 15

⇒ x = 7

The number of people who can only go to the game on Sunday is

= 12 - x

= 12 - 7

= 5

Therefore, using set theory number of people can only go to the game on Sunday is equal to 5 .

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Answer:

5) y = 1x + 2

6) y = -0.5x + 6

Explanation:

5)

Given points are (-3, -1), (2, 4)

[tex]\sf slope \:formula: \dfrac{y_2 - y_1}{x_2- x_1} = \dfrac{\triangle y}{\triangle x} \ \ \ where \ (x_1 , \ y_1), ( x_2 , \ y_2) \ are \ points[/tex]

Here, find slope:

[tex]\rightarrow \sf slope \ (a) = \dfrac{4-(-1)}{2-(-3)} = \dfrac{5}{5} = 1[/tex]

Find Equation:

y = ax + q

Here found that a = 1, take (x, y) = (-3, -1)

[tex]\sf -1 = 1(-3) + q[/tex]

[tex]\sf q - 3 = -1[/tex]

[tex]\sf q = -1 + 3[/tex]

[tex]\sf q = 2[/tex]

So, in total equation:

y = 1x + 2

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

6)

Given points are (-2, 7), (2, 5)

[tex]\sf slope \:formula: \dfrac{y_2 - y_1}{x_2- x_1} = \dfrac{\triangle y}{\triangle x} \ \ \ where \ (x_1 , \ y_1), ( x_2 , \ y_2) \ are \ points[/tex]

Here, find slope:

[tex]\rightarrow \sf slope \ (a) = \dfrac{5-7}{2-(-2)} = -0.5[/tex]

Find Equation:

y = ax + q

Here found that a = -0.5, (x, y) = (-2, 7)

[tex]\sf 7 = -0.5(-2) + q[/tex]

[tex]\sf 7 = 1 + q[/tex]

[tex]\sf q = 7-1[/tex]

[tex]\sf q = 6[/tex]

So, in total equation:

y = -0.5x + 6

Answer:

Answer:

C

Step-by-step explanation:

y = (x - 2)² = x² - 4x + 4 → (1)

x + y - 2 = 0 → (2)

substitute y = x² - 4x + 4 into (2)

x + x² - 4x + 4 - 2 = 0

x² - 3x + 2 = 0

(x - 1)(x - 2) = 0

equate each factor to zero and solve for x

x - 1 = 0 ⇒ x = 1

x - 2 = 0 ⇒ x = 2

substitute these values into (2) and solve for y

x = 1 : 1 + y - 2 = 0 ⇒ y - 1 = 0 ⇒ y = 1 ⇒ (1, 1 )

x = 2 : 2 + y - 2 = 0 ⇒ y + 0 = 0 ⇒ y = 0 ⇒ (2, 0 )

the line intersects curve C at 2 points (1, 1 ) and (2, 0 )

The domain of the rational function is:

{x ∈ ℝ| x ≠ –2, 2}

Here we have the rational function:

[tex]f(x) = \frac{x^2 - x - 12}{x^3 - 4x^2 - 4x + 16}[/tex]

We want to get the domain of that function. First, we can rewrite the numerator and denominator as:

[tex]x^2 -x - 12 = (x + 3)*(x - 4)[/tex]

[tex]x^3 - 4x^2 - 4x + 16 = (x - 4)*(x + 2)*(x - 2)[/tex]

Then we can rewrite the rational function as:

[tex]f(x) = \frac{(x + 3)*(x - 4)}{(x - 4)*(x + 2)*(x - 2)}[/tex]

This can be simplified to:

[tex]f(x) = \frac{(x + 3)}{(x + 2)*(x - 2)}[/tex]

Now, the domain will be the set of all real numbers, minus the values of x that generate problems.

In this case, the values:

x = -2 and x = 2 make the denominator to be zero, and we can't divide by zero, so  we conclue that the domain is:

{x ∈ ℝ| x ≠ –2, 2}

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The simple annual interest rate for the $ 525 loan is equal to 46.35 %.

In this situation we assume that the loan does not accumulate interests continuously in time. Hence, the interest rate for paying the loan back 75 days later is:

575 = 525 · (1 + r/100)

50 = 525 · r /100

5000 = 525 · r

r = 9.524

The loan has an interest rate of 9.524 % for 75 days. Simple annual interest rate is determine by rule of three:

r' = 9.524 × 365/75

r' = 46.350

The simple annual interest rate for the $ 525 loan is equal to 46.35 %.

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Answer: A = JIH

B = GJH

C = GH

D = 300

E = 60

Step-by-step explanation:

A) <JIH is a inscribed angle

B) GJH is a major arc

C) GH is a minor arc

D) m GH = m<GFh = 60

The terms that completes the sentence are zeros; vertical. Option A

The functions of a sign chart include;

From the mentioned functions, we can se that the terms that completes the sentence are zeros and vertical asymptotes.

Thus, the terms that completes the sentence are zeros; vertical. Option A

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The parabola vertex is (1,5), the focus of the parabola is (1,6), and the directrix y = 4.

The graph of a parabolic equation is a U-shape curve graph that is established from a quadratic equation.

From the given information:

[tex]\mathbf{y=\dfrac{1}{4}(x-1)^2+5}[/tex]

The vertex of an up-down facing parabolic equation takes the form:

y = ax² + bx + c  is [tex]\mathbf{x_v = -\dfrac{b}{2a}}[/tex]

Rewriting the given equation:

[tex]\mathbf{y = \dfrac{x^2}{4}-\dfrac{x}{2}+\dfrac{21}{4}}[/tex]

[tex]\mathbf{x_v = -\dfrac{b}{2a}}[/tex]

[tex]\mathbf{x_v = -\dfrac{(-\dfrac{1}{2})}{2(\dfrac{1}{4})}}[/tex]

[tex]\mathbf{x_v =1}[/tex]

Replacing the value of x into the equation, y becomes:

[tex]\mathbf{y_v = 5}[/tex]

Thus, the parabola vertex is (1,5)

From the vertex, the focus of the parabola is (1,6), and the directrix y = 4.

The graphical representation of the parabola is seen in the image attached below.

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The quantity of rainfall that fell in the second half of the month is; ¹/₆ of an inch.

We are given;

Rainfall during first half of the month = 1/2 inch

Total rainfall for the month = 2/3 inch

Now, to find the rainfall for the second half of the month, we just subtract the one for the first half from the one for the month to get;

Rainfall in second half of the month = ²/₃ - ¹/₂ = ¹/₆ inches

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The rise is the difference in y-coordinates:

The run is the difference in x-coordinates:

The slope is the quotient of rise over run:

========================

If two points on a line are A(10, −3) and B(12, 9), the rise is 12, and the run is 2, so the slope of the line is 6.

Bearing is a topic that can be used to locate the position of an object at a given time. Therefore, the blimp is 80 m far away from its starting point. And in the North-East direction.

The speed of an object relates the distance it covers to the time taken to cover the said distance.

i.e speed = [tex]\frac{distance}{time taken}[/tex]

⇒ distance = speed x time taken

In the given question, the initial distance covered can be determined as;

distance = 40 mph x 3 h

              = 120 m

The final distance covered can be determined as;

distance = 40 mph x 1 h

              = 40 m

Let the distance from its starting point to its final location be represented by x.

Thus applying the Cosine rule, we have:

[tex]c^{2}[/tex] = [tex]a^{2}[/tex] + [tex]b^{2}[/tex] - 2abCos C

[tex]x^{2}[/tex] = [tex]120^{2}[/tex] + [tex]40^{2}[/tex] - 2(120 x 40) Cos 90

   = 14400 + 1600 - 9600

[tex]x^{2}[/tex] = 16000 - 9600

   = 6400

x = [tex]\sqrt{6400}[/tex]

 = 80

x = 80 m

Therefore, the distance of the blimp from its starting point to its final destination is 80 m.

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This is a simple harmonic motion exercise. The proof that the resultant force on the particle, at time t, is -225 Newtons is indicated below.

Note that we have been given the following:

Mass = 9kg,

Y = 45 N

ζ = 0.4 m

Then, Y/ζ  = 45N/0.4m

= 112.5 N/m

Hence, the spring constant =

K = 112. 5N/m

From this point we can resolve the Amplitude (A):
Amplitude is given as:

A = CB - PB

= 0.6 - 0.5

A = 0.1m

I) So because one spring is elongated by x and the other is compressed by x, Hence, the spring force is:

F[tex]_{net}[/tex] = - Kₓ - Kₓ

= - 2Kₓ
= -2 x 112.5 x* X

F[tex]_{net}[/tex] = -225x Newton ..........Lets call this expression 1

From equation 1 above, we know that

Ma = -225x

a = (-225/m) x

⇒ a ∝ - x,

Hence, the motion is is simple harmonic in nature.

The time period, T = 2 π√m/K[tex]_{eq}[/tex]

Where, K[tex]_{eq}[/tex] = 2K

= 2π√(9/225)

= 2π * 3/15

= 2(22/7) * (3/15)

= 1.25714285714; thus

T ≈ 1.26 secs...............lets call this expression 2

Note that Angular Frequency is = 2π/T

= 2π/1.26

= 4.9866550057

ω = 4.99 rad/s

Since the velocity at any point x from the mean position is given by

V = ω √ (A² - x²); hence

V = 4.99 √[(0.1)² - (0.05)²

V = 4.99 x 0.0866
V = 0.432134

V ≈ 0.432..........Lets call this expression 3

Along the x-axis, A simple harmonic motion can be depicted as:

x = A sin (ωt + Ф) ..........lets call this expression 4

where, Ф = Phase constant

At t = 0; x = A

A = A sinФ

⇒ SinФ = 1

⇒ Ф = π/2

Expression 4 becomes:

x = A sin (ωt + π/2)

Inserting the values of ω and A, we have

x = 0.1 sin (4.99t + π/2).........Lets call this expression 5a

or  x  = 0.1 cos (4.99t).......Lets call this expression 5b

Hence,

Sin(π/2  + Ф) = CosФ

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Step-by-step explanation:

The formula for the angle between vectors

[tex] \alpha = \cos {}^{ - 1} ( \frac{uv}{ |u| |v| } ) [/tex]

To multiply vectors, multiply the first component and multiply the second component and add them.

(-4*-1) + (-3*5)= 4-15=-11.

To find magnitude of vectors, use the Pythagorean theorem

[tex]u = \sqrt{ { - 4}^{2} + { - 3}^{2} } = 5[/tex]

[tex]v = \sqrt{ - 1 {}^{2} + 5 {}^{2} } = \sqrt{26} [/tex]

so

[tex] |u| |v| = 5 \sqrt{26} [/tex]

Know we have,

[tex] \alpha = \cos {}^{ - 1} ( \frac{7}{5 \sqrt{26} } ) [/tex]

[tex] \alpha = 105.94[/tex]

in degrees,

[tex] \alpha = 1.849[/tex]

in radians

Answer:

115.6° (1 d.p.)

Step-by-step explanation:

To find the angle between two vectors:

**Please see attached for the triangle diagram**

Given vectors:

[tex]\textbf{u}=-4\textbf{i}-3\textbf{j}[/tex]

[tex]\textbf{v}=-\textbf{i}+5\textbf{j}[/tex]

Use Pythagoras Theorem to find the magnitude of each vector:

[tex]\implies |\textbf{u}|=\sqrt{(-4)^2+(-3)^2}=5[/tex]

[tex]\implies |\textbf{v}|=\sqrt{(-1)^2+5^2}=\sqrt{26}[/tex]

[tex]\overrightarrow{\text{UV}}=\textbf{v}-\textbf{u}=(-\textbf{i}+5\textbf{j})-(-4\textbf{i}-3\textbf{j})=3\textbf{i}+8\textbf{j}[/tex]

[tex]|\overrightarrow{\text{UV}}|=\sqrt{3^2+8^2}=\sqrt{73}[/tex]

Cosine Rule (for finding angles)

[tex]\sf \cos(C)=\dfrac{a^2+b^2-c^2}{2ab}[/tex]

where:

Find angle θ using the cosine rule:

[tex]\implies \cos(\theta)=\dfrac{|\textbf{u}|^2+|\textbf{v}|^2-|\overrightarrow{\text{UV}}|^2}{2|\textbf{u}||\textbf{v}|}[/tex]

[tex]\implies \cos(\theta)=\dfrac{5^2+\left(\sqrt{26}\right)^2-\left(\sqrt{73}\right)^2}{2(5)\left(\sqrt{26}\right)}[/tex]

[tex]\implies \cos(\theta)=\dfrac{-22}{10\sqrt{26}}[/tex]

[tex]\implies \theta=\cos^{-1}\left(\dfrac{-22}{10\sqrt{26}}\right)[/tex]

[tex]\implies \theta=115.5599652...^{\circ}[/tex]

Therefore, the angle between the vectors is 115.6° (1 d.p.).

Answer: (-2,2)

Step-by-step explanation:

The solution to a system of equations represented graphically is the point where the graphs intersect.

14.11 is the price of one share in the company TYK.

Given:

Find:

Solution:

The dividend is the amount paid to the shareholders for their investment in the company.

Dividend at end of 7th year = $1 per share (given)

dividend expected growth rate = 6%  (given)

the dividend will be paid from the end of seven years.

So find the price of the share at the end of the 6th year.

price at the end of the 6th year

= Dividend at the 7th year/discount rate growth rate

= 1/(10%-6%) = 1/4% = 25

price of the share at the end of the 6th year is $25

discount price 10% (given)

current price share = 25/(1+10%)^6

                              = 25/(1.1)^6

                              = 25/1.77

                             = 14.11

The current price of the share is $ 14.11

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The interest rate needed to double the investment in 18 years is  6%.

Interest earned is a function of the amount invested, interest rate and time. The future value of the investment is to be $6000 (3000 x 2). Interest earned would be $3000 (6000 - 3000)

Interest rate = interest earned / (amount invested x time )

$3000 / ($3000 x 18) = 6%

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Answer:

The three planes of motion are the sagittal, coronal (or frontal) and transverse planes.

Sagittal Plane: Cuts the body into left and right halves. Forward and backward movements.

Coronal (or Frontal Plane): Cuts the body into front and back halves. ...

Transverse Plane: Cuts the body into top and bottom halves.

We make use of [tex]y = \log_x(z)[/tex] to solve for y, when you know x and z

The expression is given as:

x^y = z

The above expression is an exponential expression.

Start by taking the logarithm of both sides

y log(x) = log(z)

Divide both sides by log(x)

[tex]y = \log_x(z)[/tex]

Hence, we make use of [tex]y = \log_x(z)[/tex] to solve for y, when you know x and z

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The slope of restaurant B is twice that of restaurant A

The tables of values are given as

           X(Bill)     Y(Tip)                          X(Bill)        Y(Tip)

Rest A     10           1                  Rest B      25            5    

Rest A     20          2                 Rest B      50            10

Rest A     30          3                 Rest B      75             15

The slopes are calculated using

Slope = (y2 - y1)/(x2 - x1)

Using the table of values, we have:

Rest A = (2 - 1)/(20 - 10)

Rest A = 0.1

Rest B = (10 - 5)/(50 - 25)

Rest B = 0.2

By comparing the slopes, we have:

Rest B = 2 * Rest A

This implies that the slope of restaurant B is twice that of restaurant A

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Option b) is correct

In statistics, a histogram is a graphical representation of the distribution of data. A histogram is represented by a set of rectangles, adjacent to each other, where each column represents a certain type of data. Statistics is a stream of mathematics that is used in various fields. When figures are repeated in statistical data, this repetition is known as frequency and can be written in the form of a table, called a frequency distribution. Frequency distributions can be displayed graphically using different types of graphs and one of them is a histogram.

A histogram chart is used under certain conditions. They are:

Data should be numeric.

A histogram is used to check the shape of the data distribution.

It is used to check if the process changes from one period to another.

It is used to determine whether the output differs when it involves two or more processes.

It is used to analyze whether the given process meets the customer's requirements.

The data 1,2,12,14,15,16,18 is given

We need to find the histogram which best fits to the given data

Total number that falls between 0-9 is 2

Total Number that falls between 10-19 is 5

Total Number that falls between 20-29 is 1

Total Number that falls between 30-39 is 5

Total Number that falls between 40-49 is 3

Total Number that falls between 50-59 is 1

Hence the histogram is obtained

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Answer:

7

Step-by-step explanation:

7x11=77

The area of the triangle will be 14.9835cm².

Your information is incomplete and the complete question wasn't found. An overview will be given.

The area of a triangle is defined as the total region that is enclosed by the three sides of any particular triangle.

Basically, it is equal to half of the base times height, i.e. A = 1/2 × b × h. Hence, to find the area of a tri-sided polygon, we have to know the base (b) and height (h) of it.

In this case, let the assumed base be 4.82cm and the height is given as 6.2172cm.

The area will be:

= 1/2 × 4.82 × 6.2172

= 14.9835cm²

In conclusion, the area is 14.9835cm².

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The function which compares the growth of both functions is; The function y = 3x is growing slower than y = 3^x.

The graphs in the task content are given as y=3x which is a linear graph, and y=3^x which is the exponential graph.

Hence, it follows that although both graphs are growing, the graph of function y = 3x is growing slower than y = 3^x.

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