(Q1) Which of the following is true about the function y = 3 • 2x?

Answer:

1/4

-64

Step-by-step explanation:

QUESTION 1

The given logarithmic expression is

[tex]\log_4(\frac{1}{16})[/tex]

We rewrite [tex]\frac{1}{16}[/tex] in the index form to base 4.

This implies that;

[tex]\log_4(\frac{1}{16})=\log_4(4^{-2})[/tex]

We now apply the power rule: [tex]\log_a(m^n)=n\log_a(m^n)[/tex].

[tex]\log_4(\frac{1}{16})=-2\log_4(4)[/tex]

Recall that logarithm of the base is 1.

[tex]\log_4(\frac{1}{16})=-2(1)[/tex]

[tex]\log_4(\frac{1}{16})=-2[/tex]

QUESTION 2

The given logarithm is;

[tex]\log_2(\sqrt[5]{32})[/tex]

[tex]\log_2(\sqrt[5]{2^5})[/tex]

This is the same as;

[tex]\log_2(2^{5\times \frac{1}{5}})[/tex]

[tex]\log_2(2^{1})[/tex]

[tex]\log_2(2)=1[/tex]

Answer:

4√34

Step-by-step explanation:

the question asks for the value of the hypotenuse

Applying the Pythagorean equation

a²+b²=c² where a=12cm, b=20cm and c?

substituting values to equation

12²+20²=c²

144+400=c²

544=c²

√544=c

√16 × √34 =c

4×√34

4√34

ANSWER

[tex] 4 \sqrt{34} cm[/tex]

EXPLANATION

The missing side is the hypotenuse of the right triangle.

According to the Pythagoras Theorem, the length of the square of the hypotenuse is equal to the sum of the length of the squares of the two shorter legs.

Let the hypotenuse be x.

Then,

[tex] {x}^{2} = {20}^{2} + {12}^{2} [/tex]

[tex]{x}^{2} = 400 + 144[/tex]

[tex] {x}^{2} = 544[/tex]

Take positive square root of both sides.

[tex]x = \sqrt{544} [/tex]

[tex]x = 4 \sqrt{34} [/tex]

Answer:

Step-by-step explanation:

(x - 4)

What you are being asked to do is find the exact same binomial in the top as is in the bottom.

But there's a small catch. You must stipulate that x cannot equal 4. If it does, then you will get 0/0 which is undefined. You can't have that happening -- not at this level.

Any other value for x is fine.

you want to take 3×1/4 which would equal 0.75. but if you want to change it into a fraction it would be 3/4

The answer is: There are a total of 16 skits in the video.

From the statement, we know that the total length of the video is 101 minutes and it contains a 5-minute introduction, the rest of the minutes are short skits (which are 6 minutes long each one).

So, we need to write the following equations:

First equation:

[tex]TotalDuration=Introduction+n*Skit[/tex]

Second equation:

[tex]Skit=6Minutes[/tex]

Where,

[tex]TotalDuration=101Minutes\\Introduction=5Minutes\\n=NumberOfSkits\\Skit=6Minutes[/tex]

So, replacing and substituting the second equation into the first equation we have:

[tex]101Minutes=5Minutes+n*6Minutes\\n*6Minutes=101Minutes-5Minutes\\n*6Minutes=96Minutes\\n=\frac{96Minutes}{6Minutes}=16[/tex]

So, there are a total of 16 skits in the video.

Let's prove it substituting "n" into the first equation:

[tex]101Minutes=5Minutes+16*6minutes\\101Minutes=5Minutes+96Minutes\\101Minutes=101Minutes[/tex]

Have a nice day!

34

6ttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttt

Answer:

Option a. 1C, 2A, 3B, 4D.

Step-by-step explanation:

1) We know that tan(x)=sin(x)/cos(x). If x=0, sin(x)=0 and cos(x)=1 then tan(x)=0. For that reason, we know that the graph passes through the point (0,0).

If x=45, then sin(45)= [tex]\frac{\sqrt{2}}{2}[/tex] and cos(45)=[tex]\frac{\sqrt{2}}{2}[/tex]. Thus tan(45)=1. The only graph that passes through the point (0,0) and is possitive when x=45 is the graph C.

2) We know that cot(x)=cos(x)/sin(x). If x=0, sin(x)=0 and cos(x)=1 then tan(x)=+∞. For that reason, we know that the graph has an asymptote in y=0, in other words, it never crosses the y-axis.

If x=45, then sin(45)= [tex]\frac{\sqrt{2}}{2}[/tex] and cos(45)=[tex]\frac{\sqrt{2}}{2}[/tex]. Thus cot(45)=1. The only graph that has an asymptote in y=0 and is possitive when x=45 is the graph A.

3) We know that -tan(x)=-sin(x)/cos(x). If x=0, sin(x)=0 and cos(x)=1 then -tan(x)=0. For that reason, we know that the graph passes through the point (0,0).

If x=45, then sin(45)= [tex]\frac{\sqrt{2}}{2}[/tex] and cos(45)=[tex]\frac{\sqrt{2}}{2}[/tex]. Thus -tan(45)=-1. The only graph that passes through the point (0,0) and is negative when x=45 is the graph B.

) We know that -cot(x)=-cos(x)/sin(x). If x=0, sin(x)=0 and cos(x)=1 then tan(x)=-∞. For that reason, we know that the graph has an asymptote in y=0, in other words, it never crosses the y-axis.

If x=45, then sin(45)= [tex]\frac{\sqrt{2}}{2}[/tex] and cos(45)=[tex]\frac{\sqrt{2}}{2}[/tex]. Thus -cot(45)=-1. The only graph that has an asymptote in y=0 and is negative when x=45 is the graph D.

The correct matches of the functions with their graphs are as follows: 1) y = tan(x) matches with graph C, 2) y = cot(x) matches with graph A, 3) y = -tan(x) matches with graph B, and 4) y = -cot(x) matches with graph D.

1) y = tan(x) matches with graph C:

  - The tangent function has a period of π (180 degrees) and is undefined at odd multiples of π/2 (90 degrees). This is why it has vertical asymptotes at x = π/2, 3π/2, etc.

  - The graph of y = tan(x) passes through (0, 0) because tan(0) = 0.

  - It has a repeating pattern where it increases to positive infinity as it approaches the vertical asymptotes and decreases to negative infinity as it approaches the odd multiples of π/2.

2) y = cot(x) matches with graph A:

  - The cotangent function is the reciprocal of the tangent function: cot(x) = 1/tan(x). It is undefined at even multiples of π/2 (0, π, 2π, etc.), which is why it has vertical asymptotes at x = 0, π, 2π, etc.

  - The graph of y = cot(x) never crosses the y-axis, and it has an asymptote at y = 0.

  - It has a repeating pattern where it approaches 0 as it approaches the vertical asymptotes.

3) y = -tan(x) matches with graph B:

  - The negative tangent function, -tan(x), is the reflection of the positive tangent function y = tan(x) about the x-axis.

  - The graph of y = -tan(x) passes through (0, 0) because -tan(0) = 0.

  - It has a repeating pattern similar to the positive tangent but is reflected about the x-axis.

4) y = -cot(x) matches with graph D:

  - The negative cotangent function, -cot(x), is the reflection of the positive cotangent function y = cot(x) about the x-axis.

  - The graph of y = -cot(x) never crosses the y-axis, similar to the positive cotangent, and it has an asymptote at y = 0.

  - It has a repeating pattern similar to the positive cotangent but is reflected about the x-axis.

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⅔x+4≤14

⅔x≤10

2x≤30

x≤15

Max value of x is 15

7x-2≤?

7(15)-2=105-2=103

7x-2≤103

Greatest value for 7x-2 is 103

Answer:

House of representatives=h

United states senate= u

h=4u+35

If u=100:

h=4(100)+35

h=400+35

h=435

Hope this helps :}

Answer:

a:  sample mean: 130.2 pounds

This is not the population mean

Step-by-step explanation:

To find the mean weight of the sample, add up all the values and divide by the total number of values entered.  In this case, 10, so we have...

mean:  (136 + 99 + 118 + 129 + 125 + 170 + 130 + 128 + 120 + 147)/10 =

1302/10 = 130.2

This is not the population mean.  It is the mean of the sample.  We would have to know more information to make a conjecture about the population mean.

Final answer:

The population mean of the students' weights is determined by summing all the weights and dividing by the number of students, resulting in 130.2 pounds.

Explanation:

To find the population mean (denoted as μ), we add up all the weights of the ten students in the population and divide it by the total number of students. Let's do the calculation:

The weights of the students are 136, 99, 118, 129, 125, 170, 130, 128, 120, and 147 pounds.

The sum of these weights is 136 + 99 + 118 + 129 + 125 + 170 + 130 + 128 + 120 + 147 = 1302 pounds.

Since there are 10 students in the population, we divide the total weight by 10 to find the mean:

μ = ΣX / N = 1302 / 10 = 130.2 pounds

Therefore, the population mean (μ) is 130.2 pounds.

Answer:

C

Step-by-step explanation:

The formula we use here is:

Length of arc = [tex]\frac{\theta}{360}*2\pi r[/tex]

Where

[tex]\theta[/tex]  is the central angle

r is the radius

Putting the given information into the formula we can solve for the central angle:

[tex]LengthOfArc=\frac{\theta}{360}*2\pi r\\4=\frac{\theta}{360}*2\pi(5)\\4=\frac{\theta}{360}*10\pi\\\frac{4}{10\pi}=\frac{\theta}{360}\\\theta=\frac{4*360}{10\pi}\\\theta=45.84[/tex]

rounded to nearest degree, we have 46 degree

C is the right answer.

Answer: OPTION C

Step-by-step explanation:

To solve this problem you must apply the proccedure shown below:

- Use the following formula for calculate the measure fo the central angle:

[tex]\theta=\frac{s}{r}[/tex]

Where s is the arc length and r is the radius.

- Know the lenght of the arc and the radius, you can substitute values.

Therefore, you obtain;

[tex]\theta=\frac{4}{5}=0.8\ radians[/tex]

Convert to degrees:

[tex]\frac{(0.8)(180\°)}{\pi}=45.83\°[/tex]≈46°

Answer:

12 miles per (1/3) hour equals

36 miles per hour

Step-by-step explanation:

Answer:

The answer is ellipse; 3x² + y² + 6x - 6y + 3 = 0

Step-by-step explanation:

* At first lets talk about the general form of the conic equation

- Ax² + Bxy + Cy²  + Dx + Ey + F = 0

∵ B² - 4AC < 0 , if a conic exists, it will be either a circle or an ellipse.

∵ B² - 4AC = 0 , if a conic exists, it will be a parabola.

∵ B² - 4AC > 0 , if a conic exists, it will be a hyperbola.

* Now we will study our equation:

* 3x² + y² = 9

∵ A = 3 , B = 0 , C = 1

∴ B² - 4 AC = (0)² - 4(3)(1) = -12

∴ B² - 4AC < 0

∴ The graph is ellipse or circle

* If A and C are nonzero, have the same sign, and are not

 equal to each other, then the graph is an ellipse.

* If A and C are equal and nonzero and have the same

 sign, then the graph is a circle.

∵ A and C have same signs with different values

∴ It is an ellipse

* Now lets study T(-1 , 3), that means the graph will translate

 1 unit to the left and 3 units up

∴ x will be (x - -1) = (x + 1) and y will be (y - 3)

* Lets substitute the x by ( x + 1) and y by (y - 3) in the equation

∴ 3(x + 1)² + (y - 3)² = 9

* Use the foil method

∴ 3(x² + 2x + 1) + (y² - 6y + 9) = 9

* Open the brackets

∴ 3x² + 6x + 3 + y² - 6y + 9 = 9

* Collect the like terms

∴ 3x² + y² + 6x - 6y + 12 = 9

∴ 3x² + y² + 6x - 6y + 12 - 9 = 0

∴ 3x² + y² + 6x - 6y + 3 = 0

* The answer is ellipse of equation 3x² + y² + 6x - 6y + 3 = 0

Sure.  To make an equilateral triangle we make any segment AB, which is already done, then we draw one circle (or an arc from the circle) with center A and radius AB, and one circle with center B and radius AB.  The two circles intersect at two points; we call either one of them C and ABC is equilateral.

Answer: C

Answer:

V=64

Step-by-step explanation:

What you do is go based off the volume formula of a cube which is V=a^3.

You have a side length of 4.

V=4^3.

V=64.

Answer:

C 294

Step-by-step explanation:

We can use proportions to solve.  Put number of miles over gallons

202 miles          x miles

--------------- = ----------------

11 gallons           16 gallons

Using cross products

202*16 = 11 x

Divide by 11 on each side

202*16/11 = 11x/11

293.81818181818 =x

To the nearest whole number

294 miles =x

Answer:

  a.  sec(x) = √2

Step-by-step explanation:

csc(x)/cot(x) = (1/sin(x))/(cos(x)/sin(x)) = 1/cos(x) = sec(x) = √2

Answer:

The correct answer is a) [tex] \sec(x) = \sqrt{2}[/tex].

Step-by-step explanation:

Here we need to use some trigonometric identities:

Then, substituting the above identities in the given formula we have:

[tex] \frac{\csc(x)}{\cot(x)} = \frac{\frac{1}{\sin(x)}}{\frac{\cos(x)}{\sin(x)}} = \frac{1}{\sin(x)}\frac{\sin(x)}{\cos(x)} [/tex]

Notice that we can simplify the sinus in both fractions. Thus,

[tex]\frac{\csc(x)}{\cot(x)} = \frac{1}{\cos(x)} = \sec{x}[/tex].

From here, the solutions is pretty straightforward.

Answer:

[tex]x\ge3[/tex]

Step-by-step explanation:

The given function is [tex]f(x)=\sqrt{x-3}[/tex].

The domain of this function refers to all values of x, for which the function is defined.

This square root function is defined when the expression under the radical sign is greater or equal to zero.

That is; the domain of the function is [tex]x-3\ge0[/tex]

This implies that [tex]x\ge3[/tex]

Answer:

Step-by-step explanation:

You need to multiply .75 and 9 you'll get 6.75 .. then you need to take 20 and subtract 6.75 and you'll get 13.25

Answer:

C is the correct choice.

Answer:

1. f(-1)

2.f(1)

3.f(0)

4.f(8)

5.f(5)

6.f(2)

Step-by-step explanation:

[tex]f(-1)-------------\ \ \ \ -6\\\\f(0)-------------\ \ \ \ \ \ \ -5\\\\f(1)-------------\ \ \ \ \ \ \ -4\\\\f(2)-------------\ \ \ \ \ \ \ -3\\\\f(5)-------------\ \ \ \ \ \ \ \ \ 0\\\\f(8)-------------\ \ \ \ \ \ \ \ \ 3[/tex]

We are given a function f(x) by:

          [tex]f(x)=x-5[/tex]

It is a linear function with positive slope i.e. 1.

Also, now we will calculate the value of the function at different values of x and match the function to it's corresponding value.

a)

[tex]f(-1)[/tex]

[tex]f(-1)=-1-5\\\\i.e.\\\\f(-1)=-6[/tex]

b)

[tex]f(0)[/tex]

Now when x=0 we have:

[tex]f(0)=0-5\\\\i.e.\\\\f(0)=-5[/tex]

c)

[tex]f(1)[/tex]

when x=1

[tex]f(1)=1-5\\\\i.e.\\\\f(1)=-4[/tex]

d)

[tex]f(2)\\\\f(2)=2-5\\\\i.e.\\\\f(2)=-3[/tex]

e)

[tex]f(5)[/tex]

when x=5 we have:

[tex]f(5)=5-5\\\\i.e.\\\\f(5)=0[/tex]

f)

[tex]f(8)[/tex]

Put x=8

[tex]f(8)=8-5\\\\i.e.\\\\f(8)=3[/tex]

Answer:

The correct option is D) [tex]\frac{2}{3}[/tex]

Step-by-step explanation:

Consider the provided figure.  

We need to find the probability that a random leaf that lands on the rectangle lands within the section shaped like a trapezoid.

For this first find the total area as shown:

The given figure is a rectangle.

The area of rectangle is [tex]l\times b[/tex]

Where, l = 6 cm + 3 cm = 9 cm and b = 5cm

Therefore the area of the rectangle is;

Area of rectangle = [tex]9cm\times 5cm=45cm[/tex]

Now find the area of trapezoid.

The area of trapezoid is: [tex]\frac{a+b}{2}h[/tex]

Where h is the height and a and b are the parallel sides.

Area of trapezoid = [tex]\frac{9+3}{2}\times 5=30[/tex]

Thus, the area of trapezoid is 30 cm.

Therefore, the probability that a random leaf that lands on the rectangle lands within the section shaped like a trapezoid is:

[tex]Probability=\frac{\text{Area of trapezoid}}{\text{Area of rectangle}}[/tex]

[tex]Probability=\frac{30}{45}=\frac{2}{3}[/tex]

Hence, the correct option is D) [tex]\frac{2}{3}[/tex]

Answer:

2/3

Step-by-step explanation:

I got it right

Answer:

Ben drove faster

Step-by-step explanation:

350 miles / 6.5 hours = 53.84 miles per hour

520 miles / 12.25 hours = 42.44 miles per hour

53.84 is faster than 42.44 therefore Ben is faster.

The equation is y =(4/5)x -6

Answer:

[tex]\large\boxed{y=\dfrac{4}{5}x-6}[/tex]

Step-by-step explanation:

The slope-intercept form of the equation of a line:

[tex]y=mx+b[/tex]

m - slope

b - y-intercept

We have the slope [tex]m=\dfrac{4}{5}[/tex] and the y-intercept [tex]b=-6[/tex].

Substitute:

[tex]y=\dfrac{4}{5}x-6[/tex]

Answer:

The length is 10 inches and the width is 7 inches.

Step-by-step explanation:

A rectangle is shape with 4 sides where 2 pairs of sides are equal and form 4 perpendicular angles. 1 pair of sides is the width and is distance w. 1 pair of sides id the length and is 3 inches more than the width or 3 + w. The total distance around the shape is the perimeter. We know the perimeter is 34 inches. Add each side together and set it equal to 34. Then solve for w.

P = l + l + w + w

34 = 3 + w + 3 + w + w + w

34 = 6 + 4w

28 = 4w

7 = w

This means its length which is 3 inches longer is 7 + 3 = 10.

The mathematical representation of the expression 'Four less than the quotient of a number x and 5' is 'x/5 - 4'. This involves division and subtraction of the number x.

The subject of this question is Mathematics, particularly algebraic expressions. In this case, you are being asked to express the phrase 'Four less than the quotient of a number x and 5' as an algebraic expression. The 'quotient of a number x and 5' implies division of the number x by 5, which is represented as 'x/5'. 'Four less than' signifies a subtraction of four from the preceding expression. Therefore, the whole expression can be written as 'x/5 - 4'.

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Answer:

The problem that is getting solved is 40 divided by zero

Answer:

Step-by-step explanation:

This is a faulty way of showing it. What you are solving here is

40 - 10*4 which is 0. What is transcribed is not equivalent to any division that I can see.

Perhaps 0/40

If you have answers, please list them.

Answer: option d.

Step-by-step explanation:

Based on the information given in the problem, you know that:

[tex]tan^2x=\frac{1}{2}[/tex]

You also know that:

[tex]sec^2(x)=tan^2(x)+1[/tex]

Substitute values. Then, you obtain:

[tex]sec^2(x)=\frac{1}{2}+1\\\\sec^2(x)=\frac{3}{2}[/tex]

Apply square root to both sides. Therefore, you obtain:

[tex]\sqrt{sec^2(x)}=\±\sqrt{\frac{3}{2}}\\\\sec(x)=\±\frac{\sqrt{3}}{\sqrt{2}}\\\\sec(x)=\±\frac{\sqrt{3}}{\sqrt{2}}\frac{\sqrt{2}}{\sqrt{2}}\\\\sec(x)=\±\frac{\sqrt{3(2)}}{2}\\\\sec(x)=\±\frac{\sqrt{6}}{2}[/tex]

Answer:

D

Step-by-step explanation:

Answer:

B is the answer because the other equations have real numbers

Step-by-step explanation:

Answer:

B is the correct answer

Step-by-step explanation:

Final answer:

The system of equations has infinitely many solutions because they represent the same line. The solution can be written in terms of the parameter t as (x, y) = ((3 + 6t)/5, t).

Explanation:

The student's question involves determining the type of solution a system of two linear equations has and finding the solution if it exists. The given system of equations is:

5x - 6y = 3

10x - 12y = 6

Notice that the second equation is just the first equation multiplied by 2. This means the system has infinitely many solutions because the two equations are actually the same line. To find these solutions in terms of a parameter t, we can solve the first equation for x as follows:

Choose t to represent y (i.e., let y = t).

Substitute y = t into the first equation to get 5x - 6t = 3.

Solve for x to find x = (3 + 6t)/5.

Therefore, the solutions to the system can be expressed as (x, y) = ((3 + 6t)/5, t), where t is any real number.