Given the area of triangle AEC=63cm^2, find the area of triangle ABC.

Step 2.

There are not restricted values because because it's possible to simplify the expression and there is not a denominator.

You have to determine the distance of the diagonals of the polygons.

Asuming each square of the grid corresponds to one unit, to determine said distances you have to count the squares.

For the second polygon the diagonals are HF= 6 and GE= 9

For the third polygon the diagonals are LJ=2 and KI= 3

Let's find the square root of all to find which is a whole number

√254 = 15.937

√255 =15.967

√256 =16

Hence √256 is a whole number

The correct option is C.

Given:

To Determine: The value of the given expression

Solution

Let us apply the logarithm rule below

Applying the rule below again

And finally applying the rule below

Hence, the solution of the given expression is 1, OPTION A

Answer:

32(x-1)²/33 +12(y-1/2)²/11 = 1

Explanation:

The equation of the ellipse is:

8x² + 9y² - 16x - 9y + 2 = 0

First, let's rewrite the expression as:

(8x² - 16x) + (9y² - 9y) + 2 = 0

(8x² - 16x) + (9y² - 9y) + 2 - 2 = 0 - 2

(8x² - 16x) + (9y² - 9y) = -2

Now, we need to complete the squares, so we will add 8 and 9/4 to both sides to get:

(8x² - 16x + 8) + (9y² - 9y + 9/4) = -2 + 8 + 9/4

8(x² - 2x + 1) + 9(y² - y + 1/4) = 33/4

8(x - 1)² + 9(y - 1/2)² = 33/4

Finally, multiply by 4 and divide by 33 to get:

4(8)(x-1)² + 4(9)(y - 1/2)² = 4(33/4)

32(x-1)² +36(y-1/2)² = 33

32(x-1)²/33 +36(y-1/2)²/33 = 33/33

32(x-1)²/33 +12(y-1/2)²/11 = 1

Therefore, the answer is:

32(x-1)²/33 +12(y-1/2)²/11 = 1

According to the given data we have the following:

In order to isolate F in the equation we would make the following:

First we would have the following property:

Therefore 9C=5f-160

9C+160=5f

So:

Answer

(4 ft/82 in) = (24/41)

Explanation

To answer this, we first need to note that

1 foot = 12 inches

So,

4 feet = 4 × 12 = 48 inches

So,

4 ft to 82 inches

= 48 inches to 82 inches

Dividing both sides by 2, we have

48 inches to 82 inches

= 24 inches to 41 inches.

In fraction form,

(4 ft/82 in) = (24/41)

Hope this Helps!!!

If after using the salt, 2/5 of the salt remains, it means that Anna used 3/5 of the salt in the bag.

A bag contains 6 1/2 pounds of salt, convert this to a fractional number:

To find how many pounds of salt she used, multiply 3/5 by the total amount of salt in the bag, this is:

She used 39/10 pounds of salt.

Recall that we are given the numbers 2*7 and 7*2. By a fact, we have that

Note that in both cases, we are multiplying numbers 2 and 7, but what is changed it the order in which we do so. On the expression on the left we are multiplying 7 times 2, and on the expression on the expression on the right we are multiplying 2 times 7. This two expressions are equal due to the conmutative property of the multiplication of integers.

Solution

Animals that are reptiles and endangered = 14

Total animals = 219

Remember that the formula for the volume of a cylinder is:

We know that:

Thereby,

Solving for D,

Using the data given,

We get that the diameter of the cylinder is 23"

Given:

We have the graph below:

To determine the correct ordered pairs, let's solve for each of them.

a) (x, y) ==> (0, -1)

From the equation, substitute 0 for x and -1 for y:

b) (x, y) ==> (3, -2)

Substitute 3 for x and -2 for y:

c) (x, y) ==> (3, -5)

Substitute 3 for x and -5 for y:

d) (0, -5)

Substitute 0 for x and -5 for y:

e) (x, y) ==> (-3, 0)

Substitute -3 for x and 0 for y:

ANSWER:

(0, -1)

(3, -2)

(-3, 0)

We can find the percent of increase by means of this formula:

Increase in percent = 100 * (new quantity - original quantity) /original quantity

By replacing the given values into the above formula, we get:

a.

Increase in percent = 100 * (106 - 100) / 100 = 100 * 6 / 100 = 600/100 = 6

Then, the percent of increase equals 6%

b.

Increase in percent = 100 * (16 - 10) / 100 = 100 * 6 / 10 = 600/10 = 60

Then, the percent of increase equals 60%

c.

Increase in percent = 100 * (56- 50) / 50 = 100 * 6 / 50 = 600/50 = 12

Then, the percent of increase equals 12%

It is given that the scale used in the map is,

For 9 inches,

Thus, a distance of 9 inches on the map corresponds to 150 miles in actual.

For 15 inches,

Thus, a distance of 15 inches on the map corresponds to 250 miles in actual.

For 21 inches,

Thus, a distance of 21 inches on the map corresponds to 350 miles in actual.

Let x be the original price then we can set up the following equation:

Answer: $460.

ANSWER:

B. $80

EXPLANATION:

We'll use the below function to determine how much is the bill for a person who uses 600 kWh in a month;

So the bill is $80

Solution

step 1

Step 2

X Intercepts = 3

or (3, 0)

Step 3

Vertical asymptote = 2

Final answer

C. The x-intercept 3, and the asymptote is located at x = 2.

Given the function f:

We want to find its output global maximum and global minimum values.

To do this, we need to find the deritative of the function first:

Now, we're going to set it equal to zero:

Finally, replace the values x=-5, x=0, and the solutions of the previous equation in the original function. The highest value will be the maximum and the lowest value will be the minimum:

The output global maximum at the interval -5,0 is 34.43.

3,628,800

1) Note that in these arrangements, according to the text the order of the blocks does not matter.

2) When this kind of thing happens we call this is a Permutation, in which the blocks may present in any order, that is not relevant

3) We can calculate it like this:

Thus, there are 3,628,800 different ways to arrange those 10 blocks

Given:

There are given that the Jotham needs 12 litters of 20% alcohol solution.

Explanation:

Let x be the volume of the 50% solution needed

Then,

The volume of the 10% solution to mix is:

Then,

The equation to find x is:

That means,

It say that the volume of the pure alcohol in ingredients is equal to the volume of pure alcohol.

Then,

From the above equation, calculate the value of x

So,

Final answer:

For the 50%, there are 3 litters solution and for the 10%,

Hence, 3 liters of the 50% solution and 9 liters of the 10% solution.

Graphs

The amount of money Sheryl makes is modeled in the graph shown.

A.

There are two points located on the graph.

The first point is at (0, 0) and represents the condition where Sheryl has not worked (0 hours) and has not earned a dollar ($0). This means she only gets paid per hour worked.

The other point at (1, 13) (approximately) represents the fact that Sheryl earned $13 for an hour worked.

B.

The graph does not show Shery's earnings for 9 hours, but we can use the result in part A to find that out.

If she makes $13 in an hour worked, then she should earn $13 * 9 = $117 for 9 hours of work.

Let be x the random variable

a)

If we need the probability of x when it is not more than a, we can write it using inequalities as below

Notice that x can be equal to a but no more than a

And the probability is then

So, the answer to question a) is the 4th option

b) 'x being at least a' can be written using inequalities in this way:

Notice that x can be equal to a, but not less than a

Therefore, the probability is given by the expression

So, the answer to question b) is the last option

The given figure is the combination of a triangle and rectangle.

In the given

The triangles are similar according to the question. Therefore, the following ratio can be formed

1) 2.4 2) 1/2

First, let's rewrite:

We would convert the fraction to decimal and add the outcome to the whole number:

Answer = 2.4

2) 0.5 = 5/10

In its simplest form, we need to divide with a number that is common to both the numerator and the denominator. The number is 5

0.5 as a fraction in its simplest form = 1/2

You have that the perimeter of the rectangle is given by the following formula:

l: length of the rectangle

w: width of the rectangle

Then, you replace the pevious expression for l and w in the formula for the perimeter, just as follow:

Hence, the perimeter of the rectangle is P = 4x2 - 8x + 6

Let Harris family used their sprinkler for x hours and Carter family used their sprinkler for y hours.

Then the equation for total time of sprinkler use is,

Determine the equation for total water output from both the sprinkler.

Substitute 55-x for y in the equation to eliminate the y terms.

Substitute 25 for x in the equation y=55-x to obtain the value of y.

So Harris family used sprinkler for 25 hours and Carter family used sprinkler for 30 hours.

The dataset consists on the points:

{22,25,50,58,28,24,25,51,43,32,49,38}

Sorting the numbers from lowest to highest:

{22,24,25,25,28,32,38,43,49,50,51,58}

There are 12 numbers, thus the median is the mean of the data 6 and 7:

M = (32+38)/2 = 35

The first point is 22, the last point is 58

The only box plot that follows all the conditions is A, where the median is at 35

Answer: A

The expression is given as

To determine the product of the expression.

Hence the product of the expression is