Mark says that an angle showing a turn through of a circle that is 10 inches across

• The same-side interior angles ∠A, and ∠B are congruent orderly to ∠D and ∠F.

And the Remote interior angle ∠C from ΔABC is congruent to the Remote Interior angle ∠D of triangle ΔDEF.

1) As congruent triangles have three congruent angles and sides in order, then we state that, using this specific vocabulary:

2) Δ ABC is congruent to ΔDEF, because

• The same-side interior angles ∠A, and ∠B are congruent orderly to ∠D and ∠F.

And the Remote interior angle ∠C from ΔABC is congruent to the Remote Interior angle ∠D of triangle ΔDEF.

3) Hence, that's the answer.

An order of magnitude is the class of scale of any amount in which each class contains values of a fixed ratio to the class preceding it. Usually, the amount scaled is 10, and the scale is the exponent applied to this amount.

Question 5

The weight of each car is 3,000 pounds. There are 5 cars in total. Therefore, the total weight is given to be:

Writing the calculated weight in standard form, scaling to 10, we have:

Therefore, the order of magnitude is 4.

Question 6

The number of people that voted per county is 20,000. There are 7 counties in total. Therefore, the total number of people that voted is:

Writing the calculated number in standard form, scaling to 10, we have:

Therefore, the order of magnitude is 5.

We are given the following operation

The result of this operation is the addition of one and another one that is by definition 2, we represent it like thio

First, calculate each velocity:

so:

Now calculate the average between the 3 velocities:

The answer is 126.67 m per minute.

Given:

The radius of cylinder is r = 2 yd.

The height of cylinder is h = 7.

Explanation:

The formula for the surface area of cylinder is,

Substitute the values in the formula to determine the surface area.

Answer: 113.04

In the given circle, The diameter of the circle is 8 in

Radius is the half of the diameter,

Radius = Diameter/2

Radius = 8/2

Radius = 4 in

Area of the circle with radius r is express as :

Substitute the value of radius = 4in

Area of the circle is 50.27 in²

Answer : Area of the circle is 50.27 in²

Looking at the Algorithm

We can see that

A) True

2 is one of the roots and the divisor of that Divison

B) False

When we plug into the function (x) the root the result is going to be zero

Since f(-2) = 5(-2)² -16(-2) +12 f(-2) = 20 +32 +12 f(-2) = 64 not equal to zero, then x = -2 is not the root

f(x) = -5x² -16x +12 has x_1= 2 and x_2= 6/5

C) False

Factoring f(x) = -5x² -16x +12 we'll have f(x) = (5x -6)(x-2)

D) True

For the previous explanation

E) True

Rewriting as a factored form we'll have f(x) = (5x -6)(x-2)/(x-2) = 5x -6

F) False

We can't find the same result as the previous one. by dividing by (x+2)

Given:

(a) The parent function of p(x) is the cubic function:

(b) To produce p(x) from y, we need to perform the following transformations in order:

* Shift to the left 3 units. This gives the function:

* Stretch vertically by a factor of 3. This gives the function:

* Shift upward 2 units. This gives the final function:

(c) The graphs of the parent function (in blue) and the transformed function (in red) are shown below:

You have the following information:

- Two-thirds (which means 2/3) of the people on a hike are adults.

- There are 36 adults

In order to calculate the number of people, you consider that 36 is 2/3 of the total people. If you name x as the total people, the number of adults is 2/3x. Thus, you can write the following algebriac expression:

2/3 x = 36

you solve the previoues equation for x. First, you multiply both sides by 3 and you divide both sides by 2.

x = 36(3/2) = 108/2 = 54

Hence, the number of people on the hike is 54

Using the given information, let's make a diagram

To find x, we just have to use the sine function which is equivalent to the ratio between the opposite leg and the hypotenuse.

We have the following:

solving by substitution:

now, for x

The solution is

Okay, here we have this:

Considering the provided figure and information, we are going to calculate the requested measure, so we obtain the following:

So to calculate the length of the base, we will solve in the formula for the area of the triangle, we have:

Triangle Area=(Base*height)/2

Triangle Area*2=Base*height

Base=(Triangle Area*2)/height

Let's replace:

Finally we obtain that the length of the base of triangle is 9 cm.

Given that :

We can prove that :

is it's inverse doing the following:

Step 1. Set y = f(x):

Step 2. Switch the variables:

Then we solve for y:

Step 3. The inverse of :

can be found in a similar way.

This tells us that f(x) and g(x) are one to one functions are f(x) is the mirror image of g(x)

Answer:

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

The mean is:

Simplify and solve for x:

Answer:

x = 45

Step-by-step explanation:

Formula we use,

→ (Sum of numbers/Total numbers) = 35

Now the value of x will be,

→ (Sum of numbers/Total numbers) = 35

→ (20 + 30 + 45 + x)/4 = 35

→ (95 + x)/4 = 35

→ 95 + x = 35 × 4

→ x = 140 - 95

→ [ x = 45 ]

Hence, the value of x is 45.

SOLUTION

The principle behind the Exterior Angle Theorem is that:

the sum of two interior angles is equal to one exterior angle.

In this question, we have that :

X + ( X - 48 ) = X + 50

Collecting like terms, we have that:

2 X - 48 = X + 50

2X - X = 50 + 48

X = 98 Degrees.

CONCLUSION: The value of X = 98 Degrees.

Explanation: There are different ways to solve this problem but let's focus on just one. When we have a division multiplied by a number we can always consider the following

Step 1: Once we understand that we can solve by models as follows

First, let's solve the numerator (our multiplication)

Step 2: Once our numerator 3 x 12 = 36 now we have

Now we can solve our division as follows

As we can see above, we have 36 blue boxes divided into 4 red larger boxes equally which gives us 9 blue boxes for each of the red boxes. It means 36/4 = 9.

Final answer: So our final answer is

.

Answer

Percentage of students that are freshman = 23%

Explanation

Total number of students in a club = 100

Number of freshman = 23

Percentage of students that are freshman = [(Number of freshman)/(Total number of students in a club)] x 100

Percentage of students that are freshman = (23/100) x 100

Percentage of students that are freshman = 23%

Step 1

Find the number of windows on each floor

In a large building, there are 10 floors, each floor has the following;

Step 2

Find the number of windows in a large building

Step 3

Find the cost the cleaning contractor will take to clean the windows in each building.

Step 4

Find the cost of cleaning all the windows in 22 large buildings

Hence, the cost of washing all windows in the 22 large buildings = $31,680

Distributive Property

The distributive property of the product with respect to the sum states that if a product and a sum are to be operated like follows:

x* ( y + z )

Then the result is the product of x by each term separately:

x* ( y + z ) = x*y + x*z

Now, we have the expression:

8 ( 2m + 1 )

Applying the distributive property:

8 * 2m + 8 * 1

16m + 8

Answer:

Step-by-step explanation:

1) Since the degree of the denominator is lower than the numerator's we can divide these expressions through long division that way:

As we can see in each step the aim is to cancel the leading coefficient.

2) Note that a Long Division, has a way to write its answer so we can tell that this is the answer:

Note that the remainder is written above the divisor on the final answer.

Answer:

[tex]\sqrt{122}\approx{11.05}[/tex]

Step-by-step explanation:

In any right triangle, the sum of the squares of the lengths of the legs equals the square of the length of the hypotenuse. This is commonly represented by the equation [tex]a^2+b^2=c^2[/tex].

In the triangle on the left:

[tex]a^2+b^2=c^2[/tex]

[tex]5^2+9^2=c^2[/tex]

[tex]25+81=c^2[/tex]

[tex]106=c^2[/tex]

[tex]\sqrt{106}=c[/tex]

The hypotenuse of the triangle on the left becomes a leg of the triangle on the right, so we repeat the process:

[tex]a^2+b^2=c^2[/tex]

[tex]4^2+(\sqrt{106})^2=c^2[/tex]

[tex]16+106=c^2[/tex]

[tex]122=c^2[/tex]

[tex]\sqrt{122}=c[/tex]

[tex]c\approx{11.05}[/tex]

Given:

Total number of candy in a bag is 15.

Number of orange flavored candy is 2

Number of cherry flavored candy is 6

Let A be the event of picking an orange or a cherry flavored candy from the bag.

ANSWER;

The fraction of the time she worked was 7/9 of the time the polls were opened

EXPLANATION;

Here, we want to get the fraction of the time in which Marlene worked

What we have to do here is to calculate the total time the pool was opened, then calculate the total time in which she went for break. Then we divide the break time by the total opening time

We proceed as follows;

From 7 : 30 am to 9pm

7:30 am to 9:30 pm is 14 hours

Kindly note that we are to subtract 30 minutes, so we have the total time as 13 hours and 30 minutes

For ease of calculations, we shall have all the time in minute

Recall, 60 minutes are in an hour

So, in 13 hours, we have 13(60) = 780 minutes

Added to the 30, we have a total of 780 minutes + 30 minutes = 810 minutes

Break Times

The first break is 10; 30 am to 12 pm; that is a total time of 1 hour 30 minutes

The second break is from 5:30 pm to 7 pm; that is another 1 hour 30 minutes

Total time spent on breaks is 3 hours

Converting to minutes, we simply multiply by 60 and that will give 3(60) = 180 minutes

Thus, we can now proceed to divide;

The above is the fraction spent on breaks. To get the farction worked, we simply subtract the above fraction from 1

We have this as;

This implies that

Combining them we have

-4.4

Now to the graph

Let's begin by identifying key information given to us:

x is lesser than or equal to plus or minus 2

We will proceed to plot the graph

The given function is expressed as

f(x) = 2^(x + 1)

The domain of a function is the set of all the possible values of x that would satisfy the function.

The range of a function is the set of all the possible values of y that would satisfy the function.

Since the fuction has no denominator or even root, the values of can be all real numbers. This means that the domain would be between - infinity and infinity

For the range, no matter how small the value of x that we input into the function, the value of f(x) or y would never be lesser than zero. Also, there is no limit to the value of f(x) even if we input very large values of x. Thus, the range is between 0 and infinity. Thus,

the correct option is the second one