If two lines intersect and one of the angles formed has a measure of 67°, which of the following statements are true? Explain your answers.

We can count the number of zeros and ones to see how many bits are used to represent 255 in binary i.e. 11111111. Therefore, we have used 8 bits to represent 255 in binary.

Convert 255 to base 2?

       255  =  8 bits

      255 in Binary: 255₁₀ = 11111111₂

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To determine the width of the statue:

A local park has a length (L), width (W), and height (H) (all in feet)

Solve equation 1 and 2 simultaneously,

Solve equation 3 & 4 simultaneously, make W the subject of formular

Therefore the value of width of the statue = 12 feet

To determine in how many pices of 2/3ft can a 9ft long ribbon be cut, you have to divide 9 by 2/3:

To divide both fractions, first turn the 9 into a fraction by adding 1 as a denominator

Now you have to invert the fraction that is the denominator of the division

And multiply it by the first fraction

She can divide the ribbon in 13 pieces of 2/3ft each

Given:

For the given figure,

The surface area is calculated as,

Answer: surface area is 92 square ft.

Answer:

0.116

Step-by-step explanation:

[tex]\frac{0.232}{2}[/tex] = 0.116

Answer:

Step-by-step explanation:

Given:

Using a graphing calculator, we have the graph shown below:

The point of intersection of the equations represents the solution to the system.

Hence, the solution to the system is:

x = 0.216

y = 0.646

Given the expression:

You can factor it by following these steps:

1. Find the Greatest Common Factors (GCF) of the terms:

- The Greatest Common Factor (GCF) of the coefficients can be found by decomposing each coefficient into their Prime Factors:

Notice that all the coefficients have:

Therefore, that is the Greatest Common Factor (GCF) of the coefficients.

- The Greatest Common Factor (GCF) of the variables is the variable with the lowest exponent:

Hence:

2. Now you can factor it out:

Hence, the answer is:

8k + 3 +4k

________________

First, add the k

8k + 4k = (8+4) k = 12 k

________________

you add if there are other variables or numbers

3

________________

12k + 3

Do you have any questions regarding the solution?

Aye itz just me, this is the solution:

Initial balance = $ 37.99

Purchase 1 = ($ 26.29)

Purchase 2 = ($ 22.98)

Overdraft fee = ($ 25.00)

Deposit = $ 55.07

______________________

New balance = 37.99 - 26.29 - 22.98 - 25 + 55.07

New balance = $ 18.82

Part A

The dimensions of the shape shown are given as

length, l = 12 in

breadth (b) = width, w = 4 in

The area of the shape is given as;

Therefore, the area of the shape is 48 square inches.

Part B

The perimeter of a shape is the sum of all the outer sides enclosing the shape

From the above shape, we add all four sides together

Consequently, we can get the perimeter using formula method as well

Therefore, the perimeter of the shape is 32 inches.

Part C

From the dimension given in the question, since the shape has a length and width, and the length and width are not equal, then the shape is a rectangle.

The shape, therefore, is a rectangle.

Then x=36.

It can be observed that sppiner is spun 40 times. So proabaility for red colour must include 40 in denominator. The fraction 1/5 has 5 in denominator which be change to 40 by multiplication of 8 to numerator and denominator.

So, it is expected to land 8 times on the red colour.

So answer is,

and It would be expected to land on red 8 times.

The derivative of the function y = -1/x-2 is 1/(x-2)².

Given, the function is y = -1/x-2

Differentiate the function with respect to x.

dy/dx = d/dx (-1/x-2)

the function is in the form of :

d/dx [f(x)g(x)] = f(x)d/dx((x)) + g(x)d/dx(f(x))

here d/dx [f(x)g(x)]  = d/dx [(-1)(1/x-2)]

therefore, d/dx [(-1)(1/x-2)] = (-1)d/dx(1/x-2) +(1/x-2)d/dx(-1)

⇒ d/dx [(-1)(1/x-2)] = (-1)(-1)(x-2)⁻¹⁻¹ + (1/x-2)d/dx(0)

⇒ d/dx [(-1)(1/x-2)] = 1(x-2)⁻² + 0

⇒  d/dx [(-1)(1/x-2)] = 1/(x-2)²

Hence the derivative of the function is 1/(x-2)²

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Given:

Given the function

and a point x = 3.

Required: Equation of the line tangent to y at x = 3.

Explanation:

The derivative of a function is he slope of the tangent line of the function at a given point. So, finding the derivative gives the slope of the tangent line.

Substitute 3 for x into the derivative.

Therefore, the slope of the tangent line is -31/27.

Substitute 3 for x into y.

(3, 38/9) is the only point on the tangent line where it intersects the original graph.

Plug these coordinates along with slope into the general point-slope form to find the equation.

Solving for y will give the equation in slope-intercept form.

Final Answer: The equation of the tangent line is

The English Alphabet consist of 26 letters. The number of outcome of the experiment therefore is 26 which consist of the sample space.

S = {A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z}

Answer

Option C is correct.

AB = 6.3 units

Explanation

In a right angle triangle, the side opposite the right angle is the Hypotenuse, the side opposite the given angle that is non-right angle is the Opposite and the remaining side is the Adjacent.

Using trignometric relations, we can see that TOA wil work for this

Tan θ = (Opp/Adj)

θ = 40°

Opp = AB = ?

Adj = AC = 7.5 units

Tan 40° = (Opp/7.5)

Opp = AB = 7.5 (Tan 40°) = 6.3 units

Hope this Helps!!!

According to the given graph, we have the following:

1) The graph represents a plane descending.

2) The line is slanting downwards and therefore has a negative slope.

3) It takes the plane 15 seconds to touch the ground.

4) The plane starts at 3 kilometers in the sky.

5) Graph does not touch the origin (0,0).

The given graph shows a decreasing line, starting at y = 3, and reaching y = 0 when x = 15.

we have

C -----> total charge

b -----> number of buckets of balls

Remmeber that

the equation of the line in slope intercept form is equal to

y=mx+b

where

m is the slope and b is the initial value or y-intercept

In this problem

m=$1.50 per buckey

b=$5

therefore

y=1.50x+5

or

C=1.50b+5

Answer:

6/7

Step-by-step explanation:

24/28 they both are commonly divisible by 4,

making them 6/7

Using the Pythagorean theorem, the distance between two points (x1, y1) and (x2, y2) is gotten as follows:

Since we have the two coordinates: (2, 8) and (-8, 2)

where:

(x1, y1)= (2, 8)

(x2, y2) = (-8, 2)

Therefore, the distance between them is:

Therefore, the distance between the two p is: 11.7

Correct option is: Option D

Solution

A probability distribution in which all of the values of the random variable occur with equal probability is called a uniform probability distribution. Describe an example of an experiment that would produce a uniform distribution. Then find the theoretical probabilities that would result from this experiment. Include a table and graph of the distribution.

Answer:

The theoretical probability experiment of rolling a die would result in a uniform distribution because the probabilities of rolling a 1,2,3,4,5,6 are all equally likely to occur.

Therefore the sum of rolling two dice is an option

Hence the correct answer is

Option 1

The given equation is

The first step is to add 4x to both sides of the equation. We have

3 - 2x = 16x^2

Adding 2x to both sides of the equation, we have

3 - 2x + 2x = 16x^2 + 2x

3 = 16x^2 + 2x

Subtracting 3 from both sides of the equation, we have

3 - 3 = 16x^2 + 2x - 3

0 = 16x^2 + 2x - 3

16x^2 + 2x - 3 = 0

This is a quadratic equation. We would solve for x by applying the method of factorisation. The first step is to multiply the first and last terms. We have 16x^2 * - 3 = - 48x^2. We would find two terms such that their sum or difference is 2x and their product is - 48x^2. The terms are 8x and - 6x. By replacing 2x with with 8x - 6x in the equation, we have

16x^2 + 8x - 6x - 3 = 0

By factorising, we have

8x(2x + 1) - 3(2x + 1) = 0

Since 2x + 1 is common, we have

(2x + 1)(8x - 3) = 0

2x + 1 = 0 or 8x - 3 = 0

2x = - 1 or 8x = 3

x = - 1/2 or x = 3/8

We would substitute these values in the original equation to check. We have

The solution is x = 3/8

Answer:

[tex]y-6=-\dfrac{1}{8}(x-10)[/tex]

Step-by-step explanation:

To find the equation of a line that passes through two points, first find its slope by substituting the given points into the slope formula.

Define the points:

Substitute the points into the slope formula:

[tex]\implies m=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{7-6}{2-10}=\dfrac{1}{-8}=-\dfrac{1}{8}[/tex]

Therefore, the slope of the line is -¹/₈.

[tex]\boxed{\begin{minipage}{5.8 cm}\underline{Point-slope form of a linear equation}\\\\$y-y_1=m(x-x_1)$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $(x_1,y_1)$ is a point on the line.\\\end{minipage}}[/tex]

To find the equation in point-slope form, simply substitute the found slope and one of the given points into the point-slope formula:

[tex]\implies y-6=-\dfrac{1}{8}(x-10)[/tex]

If we have:

To solve for l we can start by inverting the sides and substracting 2w from both sides so that the term with l becomes alone in the left side:

Now, we can divide both sides by 2 so thay the 2 in 2l gets canceled:

So, the answer we would get is

There were 52 billiard balls in the set.

Assume that billiard balls are arranged in rows to form an equilateral triangle, then the first row consists of 1 ball, second row consists of 2 balls, and third row consists of 3 balls,  and so on. So there must be n balls in the nth row.

So, the total number of billiard balls that forms the equilateral triangle with n rows is:  

1 + 2 + 3 + ... + n = n(n + 1)/2

Let x1 and x2 be the total number of balls in the first and second arrangements respectively.  

Then,

x1 = n(n + 1)/2 + 7

It has been said that there were 3 lesser balls in the second arrangement:  

x2 = (1 + (n + 1))/2 × (n + 1) - 3

x2 = (n + 1) × (n + 2)/2 - 3

Since x1 = x2,

n(n + 1)/2 + 7 =  (n + 1) × (n + 2)/2 - 3

We solve above equation to find the value of n,

multiplying both the sides by 2

n(n + 1) + 14 = (n + 1)(n + 2) - 6

n² + n + 14 = n² + 3n + 2 - 6

n - 3n = -4 - 14

-2n = -18

n = 9

So, x1 = 9(9 + 1)/2 + 7

          = 9(5) + 7

          = 45 + 7

          = 52

Therefore, there were 52 billiard balls in the set.

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Given the function below:

Substituting each value of x in the table in the function above, we get

Note that:

The sum of the exterior angles of a polygon does not depend on the number of sides of the polygon

The sum of the exterior angles of a polygon is 360°

Therefore, the correct option is 360°

Prob 22

7 + | 6v + 7| ≤ 60

then

| 6v + 7| ≤ 53

now eliminate lines ||

6v + 7 ≤ 53

and

6v + 7 ≤ - 53,. 6v ≤ -60

Now solve for x

6v ≤ 47,. v≤ 46/6

also

6v ≥ -47,. v≥ -46/6

Then answer is

-10 ≤ v ≤ -46/6

Graph for problem 22