which property of equality should you apply to keep the equation 22*a= 242in balance when solving?

To solve this question, follow the steps below.

Step 01: Solve the operation inside the parentheses.

Step 02: Solve the division.

Step 03: Solve the subtraction.

Answer: 5.

Let's fill a table with the first two years, we already know those

So, we need to complete the chart for years 3,4, and 5. We know that in year 3, will receive double the money than we get in year 2, this is 2*$2=$4. Now we write that result on our table.

In year 4 we'll get double the money than in year 3, this is 2*$4=$8

Similarly, in year 5 we get double the money than what we got in year 4: 2*$8=$16

And we have filled in the table!

Now, a bonus, the pattern here seems to be an equation, notice this:

year 1 -> $1 = $2^0

year 2 ->$2 = $2^1

year 3 -> $4 = $2^2

year 4 -> $8 = $2^3

year 5 -> $16 = $2^4

This means that the amount of money we'll receive each year is given by

Where t is the year! (year 1, year 2, etc)

Solution:

Step 1: Calculate 8% of the raw sheets of aluminum :

This is the weight that is lost in the production of the fuel tank.

Step 2: Calculate the weight of the tank :

200 pounds - 16 pounds = 184 pounds.

So that, we can conclude that the correct answer is:

184 pounds.

Answer

Option C is correct.

x = -0.26 + 2pn

OR

x = -2.88 + 2pn

Explanation

Using the calculator and inverse functions

Let the unknown angle be x

Sin x = -0.26

x = Sin⁻¹ (-0.26)

x = -0.26 or -2.88 (From the calculator)

In order to generalize it, we add 2pi to both of them.

x = -0.26 + 2pn

OR

x = -2.88 + 2pn

Hope this Helps!!!

SOLUTION:

Step 1:

In this question, we are given the following:

A circular pool with a radius of 3 m sits in a rectangular yard that is 14 m by 8 m. What area of the yard is NOT covered by the pool?

Step 2:

The area of the yard that is NOT covered by the pool is given as :

CONCLUSION:

The area of the yard NOT covered by the pool is:

we are given the following expression:

First, we will subtract 17 to both sides:

We get an expression of the form:

To complete the square we will add and subtract the following term:

Replacing the values:

Therefore, we will add and subtract 36:

Now we associate the first three terms:

Now we factor in the associated terms:

Solving the operations:

Now we solve for "x", first by adding 28 to both sides:

Now we take square root to both sides:

Now we subtract 6 to both sides:

Now we factor 28 as 7*4:

Given:

The grade distribution is tests = 30%, quizzes = 15%, homework=10%, labs=25%, and the final exam= 20%.

Averages for each category: Tests=80%; Quizzes=70%; Homework=80%; Labs=90%; Final exam=90%.

Required:

We need to find the final grade.

Explanation:

Let the total mark for each is 100,

The mark for the test is 80.

We need to find 30% of 80.

The mark for the quizzes is 70.

We need to find 15% of 70.

The mark for the homework is 80.

We need to find 10% of 80.

The mark for the labs is 90.

We need to find 25% of 90.

The mark for the final exam is 90.

We need to find 20% of 90.

Add grade values for all the categories.

The final grade was 83 out of 100.

Divide 83 by 10.

The final grade is 8.3 out of 10.

Final answer:

First, we need to calculate the value of the monthly payments. We can use the general ordinary anuity formula:

Where PV=$87000

n=20

i=0.06

Replace the given values and solve for PMT:

Now that you have the payment, you can construct the table of the amortization schedule with the know information:

To calculate the missing information, start by calculating the interest component of the payment (interest paid) by multiplying the periodic interest by the remaining principal.

The monthly interest is the yearly interest divided by 12, then:

And the interest paid is then:

Now, calculate the principal paid by subtracting the interest paid from the payment amount:

Then, by putting the values on the amortization schedule:

The remaining principal is 87000-7150.06 (principal paid).

Now for the second payment, calculate the interest paid with the new remaining principal:

And the principal paid is:

The remaining principal is:

Thus:

And for the third month, you apply the same calculations and the amortization schedule is:

Explanation

1 ticket =$12

2 ticket =$24

3 ticket =$36

The Solution:

Part (a)

Representing the problem fully in a diagram, we have:

Part (b)

We are required to find the length of QA= x.

We shall use Trigonometrical Ratio as below:

Making x the subject of the formula, we get

Thus, the distance from the control tower to point A is 80.0 meters.

Part (c)

We are required to find the length of AB= y.

Considering triangle PQB, we have:

Solving for y, we get

Thus, the distance moved by the plane from its initial position is 108.9 meters.

EXPLANATION:

When multiplying and/or dividing fractions, answer if each of the statements below are TRUE or FALSE.

1.The denominators MUST be the same. (FALSE);They can have different denominators for both multiplying and dividing fractions.

2.You must convert mixed numbers into improper fractions before multiplying or dividing.(TRUE) ; This procedure is important so that the operation between fractions is as easy and correct.

3.You can keep mixed numbers when performing multiplication or division.

(FALSE) ; These mixed fractions must be converted to improper fractions to later do the correct multiplication or division.

4.Numerators must be multiplied by numerators and denominators must be multiplied by denominators.​(FALSE); The numerator of the first fraction must be multiplied in a cross by the denominator of the second fraction; the denominators are multiplied by each other.

we have that

the value of a represent a vertical dilation

so

We stretch the graph in the vertical direction by a scale factor of

If the value of a> 1

then

we have stretching of the graph

If the value of 0 < a < 1

then

we have a compress of the graph

Okay, here we have this:

We need to solve the following expression:

Finally we obtain that the result is -11.25.

1) In this expression, we have

1.1 ) Terms: We have 6 terms in total.

2c -2b +c +3 + b -4 Combining like terms we can rewrite them as

c -b -1

1.2) Like terms are the ones that share the same variable

2c, c

-2b, b

1.3) Coefficients the numbers that multiply the variables

2c - 2b + c + 3 + b - 4

So we have:

2, -2, 1

1.4) The constants. Simply put in this case, the numbers that do not vary

-4 and 3

Multiply 3x11/12 and reduce to lowest terms Convert into a mix number ​

we have

3*(11/12)=11/4

convert to mixed number

11/4=8/4+3/4=2+3/4=2 3/4

Assuming that each snack pack has 1 juice box and 1 cheese cracker snack, then Holli can make as much as the lowest quantity of juice boxes or cheese cracker snacks.

Let the triangles represent cheese cracker snacks and squares represent juice boxes:

The smallest pack possible includes one cheese cracker snack and one juice box:

The red ovals represent snack packs. Since there are not enough cheese cracker packs to make 77 snack packs, the maximum amount of packs that can be made is 76.

From the drawing, we can see that each snack pack will have one juice box.

A.

Since both fractions have the same numerator, you can factorize 1/9 aout of the parentheses, because:

Then you can simplify the expression as:

Given:

Log6 21.

We are asked to use change of base formula to determine form the options which is equivalent.

let's apply the base change formula:

For C:

Log10 10

Log10 21

Log10 10

Log10 6

Apply power law of logarithm to simplify the expression:

1

LOg10 21

1

Log10 6

ivide fraction by multiplying its reciprocal:

1 x Log10 6

Log10 21

Write as a single fraction:

Log10 6

Log10 21

Apply the base chande formula: log21 6

Check its equivalency: False.

Option A is False

Notice that we have 12 people evenly distributed in a round table (360°).

This way, each person would be

30° from each other.

After the two passes, the soup would have moved 120°, meaning that

It would have moved 4 places.

Now, the person sitting 4 places away from Lacy, if the soup is passed counterclockwise, is Haifa

Therefore, the soup would be in front of Haifa.

Notice that triangles TUZ and WXV have an angle with the same measure; therefore, we need two additional corresponding similar angles, or two corresponding similar sides, or one side and an angle to prove similarity.

Options A is not possible since it would imply that triangle TUZ has two 90°-inner angles.

Option B states a relation between two sides of triangle TUZ, not between two sides (one of each triangle). Option B cannot be the answer.

According to the figure, angles TUZ and WXV have to be congruent; therefore, option C cannot be the answer.

The only valid alternative is option D, option D is the answer.

We have:

Applying properties of logarithms:

Given the cost of item =$ 100

If it is discounted 24%

So, the discount will be = 24% of 100 = 0.24 x 100 = $24

The cost after discount = 100 - 24 = $76

If it is marked up 24%

so, the rise will be = 24% of 76 = 0.24 x 76 = $18.24

The cost after marked up = 76 + 18.24 = $94.24

So, the answer is : No, and the cost will be = $94.24

ANSWER

KM = 17

EXPLANATION

We have that point L is on the line segment KM.

Let us draw a diagram to represent it:

From the diagram, we see that the length of KM is the sum of the lengths of KL and LM.

This means that:

KM = KL + LM

KM = 12 + 5

KM = 17

That is the value of the length of KM.

Remember that the constant rate of change refers to the change between the variable.

In this case, the constant rate of change is $7.50 per hour, in other words, it's 7.50. As an equation would be

Given that the line passes through the points;

And slope;

1 liter = 1000 milliliters.

thus, 75791 liters =

thus, 75791000 milliters.

Answer:

y= 10

Step-by-step explanation:

look at picture for explanation

Given the system of equations;

We shall first of all re-arrange the equations in the slope-intercept form;

Note that the second one has already been expressed in the slope-intercept form. For the first one we would now have;

To plot this equations on a graph we take two extreme points. We can do this by finding the value of y when x = 0, and y when x = 0.

For the first equation, we would have;

Hence, for the first equation we have the two points;

For the second equation;

For the second equation we now have the points;

We can now input both sets of coordinates and our graph would come out as shown below.

The point of intersection as we can see is at where x = -6 and y = 4. Therefore;

ANSWER:

The solution to the system of equations as shown on the graph is;

Answer:

The question is given below as

Concept:

The question will be solved using the linear pair theorem below

The Linear Pair Theorem states that two angles that form a linear pair are supplementary; that is, their measures add up to 180 degrees.

By applying the principle, we will have that

Hence,

The value of x= 92°

Step 2:

By applying the linear pair theorem, we will also have that

Hence,

The value of z= 92°

Step 3:

By applying the linear pair theorem also, we will have that

Hence,

The value of y= 88°

Given that the ratio of the sides of two smaller polygons is 4:5

To Determine: The ratio of the areas

Solution:

Note that if the ratio of the sides of two similar shapes is a : b, then the ratio of their areas would be a² : b²

It was given in the question that the ratio of the sides of two smaller polygons is 4:5. Then, their areas would be

Hence, the ratio of the areas is 16 : 25