Using the distributive property to write an equivalent expression that has no grouping symbols2(n+3)

Answer:

The solution of the equation is;

Explanation:

Given the equation;

Applying Distributive property of multiplication, we have;

Therefore, the solution of the equation is;

The box is 2.25 cubic feet (option D)

length of the box = 36 inches

width = 18 inches

depth = height = 6 inches

To get the volume of the box in cubic feet, we need to first convert the dimensions from iches to feet to make it easy to solve.

conversion from iches to ft:

12 inches = 1 ft

36 inches = 36/12

= 3 ft

18 inches = 18/12

width = 18 inches = 3/2 ft

6 inches = 6/12

height = 6 inches = 1/2 ft

The box is a rectangular prism

Volume of rectangular prism = length × width × height

Given:

A circular piece of stock be to mill a hexagonal shape with a side length of 2.7 ​in.

Required:

We need to find the diameter of hexagon.

Explanation:

now use the sin function

so by r

Final answer:

Diameter of hexagon is 5.4 in

The area of the sector is 31.8m^2 ( nearest tenth)

Given the following sequence

We want to know if this sequence is arithmetic. The general term of an arithmetic sequence is given by

Where d represents the common ratio. An arithmetic sequence increases by the same value every term(this value is the common ratio). If the difference between neighbor terms is the same for all of our terms, this sequence can be written as an arithmetic sequence.

Let's calculate the difference between the terms

Since the difference is the same, this sequence is Arithmetic.

1) The equation we used today to represent a line is called :

The slope-intercept form

In this form, y=mx +b

2) For the equation y=mx+b, m is the slope

It measures how steep is the line.

3) For the equation y=mx+b, b is the line coefficient

This is the point where the line intercepts the y coordinate.

Substituting x=-9 in the given equation we get:

Simplifying the above result, we get:

Adding 2 to both sides of the equation, we get:

Therefore, the coordinates of the point with x=-9 are:

Answer:

We can eliminate some of these choices , knowing that if we dilate a triangle they are the same shape but not necessarily the same size. Thus , they are not congruent. Therefore, the last two choices are false since it denotes congruency.

It is also stated from the problem that the triangle is rotated by 180 degrees therefore the congurent pair of angle can be found on the opposite side in the figure. Therefore , we can eliminate the first choice since it states that the congruency among angles are at the same side.

Thus, CHOICE 2 is true.

The general form of a equation of a circle is:

Where:

r is the radius of the circle

(h,k) are the coordinates of the center of the circle

Then, the given equation:

The radius and the coordinates of the center are:

Then, the graph for this circle is: Photo number 2

The distance between two points is the length of the path connecting them. The shortest path distance is a straight line. In a 2 dimensional plane, the distance between points (X1, Y1) and (X2, Y2) is given by the Pythagorean theorem:

The answer would be d = 11.31

The first step is draw line segment AB.

EXPLANATION

We can represent the states in the following picture:

We can apply a Trigonometric ratio in order to get the value of the third side, assuming that it is called x:

Multiplying both sides by 8:

Switching sides:

Multiplying terms:

In conclusion, the measure of the third side is approximately equivalent to 4√2 or 5.65

For this problem, we are given the expression for a circle and we need to determine which graph represents it.

The expression for the circle is:

We can rewrite it as:

This means that the radius is equal to 7. So we need to find the circle that has a center in the origin and a radius equal to 7. The correct option is the bottom right option.

Robert chops 40% of the pile of firewood in 3/4 of an hour.

Then, we would chop 80% of the pile of firewood in 2*(3/4)=3/2 hours.

where 3/2 = 1.5 hours

Also, he would chop the missing 20% in (3/4)/2=3/8.

The full work is for 3/8+3/2 =15/8 hours

Now, if one hour is paid $12.00, we can use the rule of three to know how much is paid for 15/8 hours:

1h-----------$12.00

15/8 h -------- $x

where x=(12.00*5/8)/1

x=22.50

Hence, Robert will be paid $22.50 to chop the entire pile of firewood.

Given

Graph of the function y = f(x)

Find

domain of f(x)

Explanation

As we know domain of a function is all the values of x that makes the function defined.

here in the graph , the function is defines for x values 0 to 5

since , the point 0 and 5 is in open interval , so , the graph does not include the points 0 and 5

hence , the domain is (0 , 5)

Final Answer

Therefore , the domain of the given function is (0 , 5)

We are asked to find the probability to find a student that has a cat when we know he/she has a dog. Then, we need to know how many students have a dog, and how many have a dog and a cat.

We already know that 12 students have a dog. However we do not know how many students have a cat and a dog.

Let's calculate that.

We know we have 30 students.

We know 6 do not have dogs nor cats.

The sum of students having dogs, the students having cats and the students having none is 37, but we know that there are only 30 students. Then, we can say that 7 students have both a dog and a cat. That is just the information we needed.

Then, we can calculate the probability that a student has a cat given that they have a dog as follows:

Let's say P is that probability:

In general, given a function g(x)

Angle 2 is 45 degrees. because DB bisects angle ABC

Angle 1 is 90 degrees. because DB bisects

Recall

f(x)=y

Given

f(2)= 21 and f(-4) = -15

f(x) =

Step 1

Step 2

Let's solve equation (i) and Equation (ii) simultaneously

Step 3

using Equation (ii)

Step 4

M= 6 and b= 9

The linear equation is

Step 1

2n = 70

divide both sides by 2

Step 2

Make a conclusion based on step 1

If n = 3.5

Then substituting for n = 3.5 in the equation

Therefore n = 3.5 is not a solution of the equation 2n = 70

So, to solve this we will have to Test by substituting the 4 into the equations given

E) 11b + 187 -2756/13

11(4) + 187 - 212

44+187 - 212 = 19

19 is not equivalent to 180

A regular 9 sided building is 814 ft along one side what is the distance from a Vertex to the center of the building ​

we know that

A regular 9 sided polygon, can be divided into 9 isosceles triangle

The equal distances of the isosceles triangle is equal to the radius or the distance from a Vertex to the center of the building ​

the base of the isosceles triangle is given and is equal to 814 ft

The measure of the interior angle of the vertex is equal to

360/9=40 degrees

that means

we have

Applying the law of sines

814/sin(40)=r/sin(70)

solve for r

r=(814/sin(40))*sin(70)

r=1,190 ft

therefore

1) Let's prove this identity

Since tan (θ) = sin(θ)/cos((θ)

And cot((θ) = cos ((θ)/sin((θ)

2) Let's plug it into:

Simplifying (dividing) sin(θ) on the numerator, with sin (θ) on the denominator and similarly cos (θ) with cos(θ) we'll get to 1 over 1 time 1 over 1 = 1

Then 1=1

Answer:

Step-by-step explanation:

If you have one apple and you buy another one, you will have 2 apples. Therefore,

SOLUTION:

We are told that;

Rewriting, we have;

Subtracting the first and second equations, we have;

and;

Thus, the first four terms of the sequence are;

We are told that jose is 35 years old and makes 40.000 per year. Also, we are told that they can get by 75% of his income. So, in the table, we look for the age column for 35 years and in the gross earnings we look for the 40000 row.

Inside the 35 years column, we take a look at the inner column that says 75%. Crossing all this information, we get that the table shows a multiplier of 8.0

This means that their beneficiaries would earn 8 times the salary of jose. That is

From the statement, we know that:

• P(A) = 0.4,

• P(A and B) = 0.2.

Because A and B are independent events, the probability of A and B is the product of the individual probabilities:

Replacing the data of the problem, we get:

P(B) = 0.5

Solution

Using cosine rule to solve for the length of the tunnel:

c=length of side c

a=length of side a

b=length of side b

A=angle opposite c

Therefore the length of the tunnel = 250.1m



Trigonometry and Triangles

To solve the problem, we need to recall the following:

* The sum of the interior angles in a triangle is 180°

* The sum of two supplementary angles is 180°

* The tangent of an acute angle in a right triangle is defined as:

We included a new variable z to help solve the problem. Details below:

Angle 59° and angle z° are supplementary because they are a linear pair, thus:

z + 59 = 180

Solving for z:

z = 121

Now we focus on the left triangle with interior angles of 45°, z°, and x°. The sum of all three must be 180°, thus:

45 + 121 + x = 180

Solving for x:

x = 180 - 45 - 121

x = 14

Now focus on the bigger triangle (the one that contains two smaller triangles).

This triangle is right (it has one interior angle of 90°) and it's also an isosceles triangle because it also has one interior angle of 45°.

Any right triangle