Determine whether the function f(x) = 3x is even or odd.
The function is even because f(-x) = f(x).
The function is odd because f(-x) = f(x).
The function is even because f(-x) = -f(x).
The function is odd because f(-x) = -f(x).

52.94% of the viewers prefer videos on a mobile or laptop device

The given parameters are

Viewers that prefer videos on a mobile or laptop device = 18

Total number of viewers = 34

The percentage of voters in this category is then calculated as

Percentage = 18/34 * 100%

Evaluate the expression

Percentage = 52.94%

Hence, 52.94% of the viewers prefer videos on a mobile or laptop device

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Answer:

C. B=38.8, C=95.2, c=42.9

Step-by-step explanation:

Find B by using sine rule

sin 46/31=sin B/27

sin B= 27 sin 46/31

B=sin‐¹(0.627)

B=38.8

Find C

C= 180-(A+B)

C=180-(38.8+46)

C=95.2

Using sine rule, Find c

31/sin 46=c/sin 95.2

c=31 sin 95.2/sin 46

c=42.9

The expression that is not a rational expression is:

[tex]\frac{(x + 3)(2x - 1)}{x + 3}[/tex]

A rational expression is an expression that has a variable in the denominator.

For expression [tex]\frac{(x + 3)(2x - 1)}{x + 3}[/tex], x + 3 is a common term to the numerator and denominator, hence it is simplified to 2x - 1 and is not a rational expression.

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The option that is not a rational expression is [tex]\frac{3x + 4\sqrt{x} -7}{2x+2}[/tex]

Rational expression are fraction whose numerator and denominator are polynomials.

In other words, rational expression is the ratio of two polynomials.

Therefore, an example of a ration expression is as follows:

[tex]\frac{x^{2}+9 }{x + 1}[/tex]

Therefore, the option that is not a rational expression is as follows;

[tex]\frac{3x + 4\sqrt{x} -7}{2x+2}[/tex]

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Answer:

  (c)  25/4

Step-by-step explanation:

A perfect square trinomial is obtained by "completing the square." The constant in a perfect square trinomial is the square of half the x-coefficient.

A "perfect square trinomial" is the square of a binomial.

  (x +a)² = x² +2ax +a²

Of note here is that the constant (a²) is the square of half of the x-term coefficient:

  ((2a)/2)² = a²

The given expression (x² +5x) has an x-term coefficient of 5. The square of half that is ...

  (5/2)² = 25/4

The constant that must be added to make x² +5x into a perfect square trinomial is 25/4.

  (x² +5x) +25/4 = x² +5x +25/4 = (x +5/2)²

Answer:

∠ABE = 33°

Step-by-step explanation:

        Angle bisector is a straight line that divides the angle into two congruent (equal) angles.

So, BE bisects the ∠ABD into two equal angles.

⇒∠ABE will be half of ∠ABD

∠ABD = ∠ABE + ∠BED

66°     = ∠ABE + ∠ABE

66      = 2∠ABE

∠ABE = 66/2

∠ABE = 33°

20 years is the answer.

A= R(1+r)^ t

A-415    

R=230

r=3%

415=230 (1+3%)^ t

t=log1.03  315/230

t=19.89 (use calculator)

David will invest at least 20 years.

An investment is a dedication of an asset to achieve an increase in value over a period of time. Investing requires the sacrifice of current assets such as time, money and effort. In finance, the purpose of an investment is to generate a profit on the invested asset

The most common example of an investment type. Investment is generally what you want to use in the future with the aim of generating regular cash flow or increasing the value of something over time so that you can sell it at a higher price than you purchased.

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The equation of the perpendicular bisector of BC with B(-2, 1), and C(4, 2) is y = 7.6 - 6•x

The slope, m, of the line BC is calculated as follows;

The slope of the perpendicular line to BC is -1/(1/6) = -6

The midpoint of the line BC is found as follows;

[tex] \left( - 2 + \frac{4 - ( - 2)}{2}, \: 1 + \frac{2 - 1}{2} \right) = (1,\: 1.5)[/tex]

The perpendicular bisector is the perpendicular line constructed from the midpoint of BC.

The equation of the perpendicular bisector in point and slope form is therefore;

(y - 1.5) = -6•(x - 1)

y - 1.6 = -6•x + 6

y = -6•x + 6 + 1.6 = 7.6 - 6•x

Which gives;

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Using the monthly payment formula, it is found that her down payment should be of $1,419.

It is given by:

[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]

In which:

For this problem, the parameters are:

A = 250, r = 0.072, n = 72.

Hence:

r/12 = 0.072/12 = 0.006.

We solve for P to find the total amount of the monthly payments, hence:

[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]

[tex]P\frac{0.006(1.006)^{72}}{(1.006)^{72}-1} = 250[/tex]

0.0171452057P = 250

P = 250/0.0171452057

P = $14,581.

The total payment is of $16,000, hence her down payment should be of:

16000 - 14581 = $1,419.

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The slope of C'D' is equal to the slope of CD because dilation preserves shape which is 2

Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, translation, rotation and dilation.

Rigid transformation is a transformation that preserves the shape and size of a figure such as translation, reflection and rotation. Dilation preserves only the shape.

Polygon ABCD has vertex at A(1, 1), B(2, 3), C(5, 4), and D(4, 2).

Slope of CD = (2 - 4) / (4 - 5) = 2

Polygon ABCD is dilated by a scale factor of 8 with the origin resulting in the image A′B′C′D′.

Slope of C'D' = slope of CD (because preserves shape) = 2

The slope of C'D' is equal to the slope of CD because dilation preserves shape which is 2

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The slope of C'D' is equal to the slope of CD because dilation preserves shape which is 2

What is transformation?

Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, translation, rotation and dilation.

Rigid transformation is a transformation that preserves the shape and size of a figure such as translation, reflection and rotation. Dilation preserves only the shape.

Polygon ABCD has vertex at A(1, 1), B(2, 3), C(5, 4), and D(4, 2).

Slope of CD = (2 - 4) / (4 - 5) = 2

Polygon ABCD is dilated by a scale factor of 8 with the origin resulting in the image A′B′C′D′.

Slope of C'D' = slope of CD (because preserves shape) = 2

The slope of C'D' is equal to the slope of CD because dilation preserves shape which is 2

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Answer:

b. x^2+4x

Step-by-step explanation:

So since you don't know the width, you can just represent it as a variable, and in this case that variable will be "x". Now using this variable we can use it to represent the length since there is a relationship between the width and length which is given. Since the length is 4 feet greater than the width, we can represent the length as (x+4). Now to find the area, we simply multiply the length * width, which is x * (x+4) = x^2 + 4x

Answer:

2

Step-by-step explanation:

(-1,-4) (2,2)

To find the slope, use the equation y2-y1/x2-x1

2-(-4)/2-(-1) = 6/3

6/3=2

2 is the slope.

Answer:

-1,-3,-4 it is just subtracting the same amount.

Step-by-step explanation:

The height of the cylinder is 4 x units.

The area of the cylinder’s base is One-fourthπx2 square units .

What is the volume of cylinder?

We know the volume of a cylinder is given by the formula  π r2 h, where r is the radius of the cylinder and h is the height.

Formula for volume of the cylinder

V = r² π h

Volume of the cylinder= πx³

Diameter=x

Radius (r)=diameter/2

       r  =  x/2

     V = r² π h

   πx³=(x/2)² πh

πx³= (x²/4)πh

Divide both sides by π

x³ =(x²/4)h

Make h the subject of the formula

  h = x³ ÷ x²/4

     =x³ ×4 / x²

     =4x³ / x²

     =4 * x * x * x / x * x

  h=4x

Area of the base:

B = r² π

r=x/2

B=(x/2)² * π

 =(x²/4)π

=πx²/4

=1/4(πx²)

Therefore, The area of the cylinder’s base is One-fourthπx2 square units.

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The complete question is -

A cylinder with a base diameter of x units has a volume of πx3 cubic units. A cylinder with a base diameter of x units has a volume of pi x cubed cubic units. Which statements about the cylinder are true? Select two options. The radius of the cylinder is 2x units. The area of the cylinder’s base is One-fourthπx2 square units. The area of the cylinder’s base is One-halfπx2 square units. The height of the cylinder is 2x units. The height of the cylinder is 4x units.

The inverse function of [tex]A(b) = 12 \cdot \frac{b + 9}2[/tex] is b(a) = a/6 - 9

The function is given as:

[tex]A(b) = 12 \cdot \frac{b + 9}2[/tex]

Divide 12 by 2

[tex]A(b) = 6 \cdot (b + 9)[/tex]

Rewrite the function as

[tex]a = 6 \cdot (b + 9)[/tex]

Divide both sides by 6

a/6 = b + 9

Subtract 9 from both sides

b = a/6 - 9

Express as a function

b(a) = a/6 - 9

Hence, the inverse function of [tex]A(b) = 12 \cdot \frac{b + 9}2[/tex] is b(a) = a/6 - 9

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[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]

[tex]\qquad❖ \: \sf \: \angle1 \cong \angle2[/tex]

( by corresponding angle pair )

[tex]\qquad❖ \: \sf \: \angle2 \cong \angle3[/tex]

( given in the question )

[tex] \qquad \large \sf {Conclusion} : [/tex]

[tex]\qquad❖ \: \sf \: \angle1 \cong \angle3[/tex]

Answer:

[tex]\huge\boxed{\sf DE = 9}[/tex]

Step-by-step explanation:

From the figure,

AB = 2

BC = 3

AD = 6

Substitute in the given formula

[tex]\displaystyle \frac{AB}{BC} =\frac{AD}{DE} \\\\\frac{2}{3} = \frac{6}{DE} \\\\Cross \ Multiply \\\\2 \times DE = 6 \times 3\\\\2DE = 18\\\\Divide \ 2 \ to \ both \ sides\\\\DE = 18/2\\\\DE = 9\\\\\rule[225]{225}{2}[/tex]

Using the z-distribution, it is found that the 95% confidence interval for the proportion of college students who work to pay for tuition and living expenses is: (0.4239, 0.5161).

If we had increased the confidence level, the margin of error also would have increased.

A confidence interval of proportions is given by:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which:

In this problem, we have a 95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96. Increasing the confidence level, z also increases, hence the margin of error also would have increased.

The sample size and the estimate are given as follows:

[tex]n = 450, \pi = 0.47[/tex].

The lower and the upper bound of the interval are given, respectively, by:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.47 - 1.96\sqrt{\frac{0.47(0.53)}{450}} = 0.4239[/tex]

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.47 + 1.96\sqrt{\frac{0.47(0.53)}{450}} = 0.5161[/tex]

The 95% confidence interval for the proportion of college students who work to pay for tuition and living expenses is: (0.4239, 0.5161).

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The point F as described in the task content is at point; 0.6 on the number line.

Since it follows from.tge task content that; point D is at -3, and point E Is at 6, it follows that the length of segment, DE is; |-3-6| = 9.

Consequently, since the ratio of Df to FE ls 2:3

It follows that point F is at -3 + (2/5) × 9.

Point F is therefore at 0.6 on the number line.

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The correct statement comparing the theoretical and experimental probabilities is given as follows:

[tex]\frac{1}{4} < \frac{7}{25}[/tex].

A probability is given by the number of desired outcomes divided by the number of total outcomes.

The theoretical probability is taken before any experiment. Since the four sections are equal, the theoretical probability is:

T(H) = 1/4.

The experimental probability is taken considering previous experiments. Out of 100 tosses, 28 landed on H, hence:

E(H) = 28/100 = 7/25.

Hence the correct statement is:

[tex]\frac{1}{4} < \frac{7}{25}[/tex].

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Combining the like terms, the simplified polynomials are given as follows:

a) 4x² - 14x + 17

b) -5x² - 20x + 8

Polynomials are simplified combining the like terms, that is, adding these numbers with the same variable.

Item a:

4(x - 2)(x + 1) - 5(2x - 5)

Applying the distributive property:

4(x² - x - 2) - 10x + 25

4x² - 4x - 8 - 10x + 25

Combining the like terms:

4x² - 4x - 10x - 8 + 25

4x² - 14x + 17

Item b:

-5(x + 2)² + 28

-5(x² + 4x + 4) + 28

-5x² - 20x - 20 + 28

-5x² - 20x + 8

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The missing digit for the American Express Traveler's Check identification number is option (C) 6 is the correct answer.

In this question,

A Check Digit is a decimal (or alphanumeric) digit added to a number for the purpose of detecting the sorts of errors humans typically make on data entry.

A check digit is a digit added to a string of numbers for error detection purposes. Normally, the check digit is computed from the other digits in the string. A check digit helps digital systems detect changes when data is transferred from transmitter to receiver.

The last digit of a bar code number is a calculated check digit. The check digit is calculated from all the other numbers in the bar code and helps to confirm the integrity of your bar code number.

The American Express Traveler's Check identification number is 783920*814.

In Airline tickets, there are several digits plus a check digit.

Divide the ID number by 7. The check digit is the remainder.

Sum of digits = 7+8+3+9+2+0+8+1+4

⇒ 42

Now divide the sum by 7, the remainder is

⇒ 42 mod 7 = 42 - (5×7)

⇒ 42 mod 7 = 6

Hence we can conclude that the missing digit for the American Express Traveler's Check identification number is option (C) 6 is the correct answer.

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The length of ED is half the length of AB.

Reasons:

The given parameters are;

In ΔABC, point E is the midpoint of AC

The midpoint of BC is the point D

Segment ED = s

Segment CE = p

Segment EA = r

Segment CD = q

Segment DB = t

Segment ED = s

Segment AB = u

Required:

The expression that represents the value of [tex]s[/tex].

Solution:

CE = 0.5 × AC Definition of midpoint

CD = 0.5 × CB Definition of midpoint

Therefore, we have;

[tex]\frac{CE}{AC} =\frac{CD}{CB} =0.5[/tex]

Therefore, given that ∠C ≅ ∠C, by the reflexive property, we have;

ΔABC is similar to ΔCDE by Side-Angle-Side similarity

Which gives;

[tex]\frac{CE}{AC} = \frac{CD}{CB} = \frac{ED}{AB} =0.5=\frac{1}{2}[/tex]

ED = s and AB = u which gives;

[tex]\frac{ED}{AB}=\frac{s}{u} =0.5=\frac{1}{2}[/tex]

[tex]\frac{s}{u} =\frac{1}{2}[/tex]

Which gives:

[tex]s=\frac{1}{2} *u[/tex]

The expression that represents the value of s is; s = one-half u

Therefore, the length of ED is half the length of AB.

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The question you are looking for is here:

If point E is the midpoint of segment AC and point D is the midpoint of segment BC, which expression represents the value of s? triangle CAB, point E is on segment AC between points A and C and point D is on segment BC between points B and C, creating segment ED, CE equals p, EA equals r, CD equals q, DB equals t, ED equals s, and AB equals u s equals p over q s = one half s equals q over p s = 2u

The equation of the line is 3x + y = 1

The points are given as:

(5, −2) and (3, 4)

Start by calculating the slope (m)

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

This gives

m = (4 + 2)/(3 - 5)

Evaluate

m = -3

The equation is then calculated as:

y = m(x - x1) + y1

This gives

y = -3(x + 2) +5

So, we have:

y = -3x - 6 + 5

Evaluate the like terms

y = -3x - 1

Rewrite as:

3x + y = 1

Hence, the equation of the line is 3x + y = 1

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Applying the distance formula, to calculate the coordinates of B, use: 3 =√[(x-4)² + (y-2)²]  

The distance formula, [tex]d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex], is used to find the distance between two points on a coordinate plane.

We are given one point A(4, 2), let:

B (x, y) = (x2, y2)

A(4, 2) = (x1, y1)

d = 3 units

Plug in the values into the distance formula to find how to calculate the coordinates of B:

3 =√[(x-4)² + (y-2)²]  

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If the radius of sector is 12 centimeters and angle of 65 degrees then the arc's length is 13.6 cm.

Given a sector has a radius of 12 cm and an angle 65 degrees.

We have to calculate arc's length.

We know that arc's length is equal to Θr where Θ is in radians.

We have been given angle in degrees ,so we have to convert degrees in radians.

Angle=65*π/180=13π/36

length of arc =Θr

Putting the values in the formula above :

length =13π/36*12

=13*3.14/3

=40.82/3

=13.6

Hence if the radius of sphere is 12 cm and angle 65 degrees then the length of arc of sphere is 13.6 cm.

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Answer:

626.7 [tex]cm^{2}[/tex]

Step-by-step explanation:

Consider the figure as a circle with radius 7.5 and a rectangle with width 30 and length 15.

CIRCLE

A = pi*r*r = pi*7.5*7.5 = 56.25pi =176.7

RECTANGLE

A = l*w = 15*30 = 450

176.7 + 450 = 626.7 [tex]cm^{2}[/tex]

Answer: 626.7cm^2

Step-by-step explanation:

30 * 15 = 450

area of circle = πr^2

r = 15/2 = 7.5

[tex]7.5^2=56.25*pi=176.7[/tex]

450+176.7 = 626.7

Answer:

( x-3) ^2 + ( y-1) ^2 = 4

Step-by-step explanation:

The equation for a circle is given by

( x-h)^2 + ( y-k) ^2 = r^2  where (h,k) is the center and r is the radius

( x-3) ^2 + ( y-1) ^2 = 2^2

( x-3) ^2 + ( y-1) ^2 = 4