given AD is congruent to AC and AB is congruent to AE, which could be used to prove?

Okay, here we have this:

Considering that a real number is said to be irrational if it cannot be expressed as a quotient of whole numbers. ✓2 is an irrational number, and as all the irrational number are real numbers ✓2 is also a real number.

We are given the dimensions of a parallelogram and are asked to estimate its area

Recall that the area of a parallelogram of base b and height h is given by the formula

So the area of the parallelogram would be

as 3 1/4 and 5 1/2 are mixed numbers, we need to transform them to fractions

Recall that given a mixed number of the form

we can transform it into a fraction by multiplying the whole number by the denominator and adding the result to the numerator while leaving the denominator fixed. In this case, that is

So, applying this formula to both numbers, we get

and

so the area of the parallelogram would be

so the area of the parallelogram is approximately 18 square yards

Answer:

100%

Step-by-step explanation:

All of the numbers are factors of 24. So, picking a factor of 24 is guaranteed, so the probability is 1.

This is equal to 100%.

Answer: The answer is no

Step-by-step explanation:

this is because the two short side lengths, which is 5 and 7, they have to be added together, which is 12, and 12 is smaller than 13 (the largest side)

Answer:

No, because 5 + 7 < 13

Step-by-step explanation:

we get that:

Solution

The final answer

Based on the fact that Home Liquidators marked up their merchandise by 35% on cost, the company equivalent markup on selling price is 26%.

The equivalent markup by Home Liquidators on the selling price can be found by the formula:
= Percentage markup / Percentage selling price x 100%

The percentage markup  = 35%

Percentage selling price = (100% + 35%) = 135%

The equivalent markup by Home Liquidators is therefore:

= 35% / 135% x 100%

= 26%

In conclusion, the Home Liquidators has an equivalent markup of 26% on selling price.

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Check to see whether the slope of both lines are the same (option A)

When two system of equations do not intersect, the lines are said to be parallel lines.

This means there is no solution.

To determine if the lines are trully parallel, the slope of each equation need to be determined.

For parallel lines, the slope will be the same

The best action to help her find out whether the two equations are inded parallel, Check to see whether the slope of both lines are the same (option A)

Given the Definite Integral:

You can identify that the interval is:

By definition, if the function is continuous and positive in a closed interval, then:

In this case, you can identify that the function is:

You can graph it using a graphic tool:

Since the closed interval goes from 0 to 1, you need to find this area:

You can identify that you have to find the area of a quarter circle. In order to do it, you can use this formula:

Where "r" is the radius of the circle.

In this case, you can identify that:

Therefore, you get:

Then:

Hence, the answer is: Option D.

Given:

it is given that the current population of a threatened animal species is 1.3 ​million, but it is declining with a​ half-life of 25 years.

Find:

we have to find that how many animals will be left in 35 years and in 80 years.

Explanation:

we know 1.3million = 1300000

The decay law is

where t is in years and p(t) is the population at time t.

Now, the number of animals left in 35 years is

Therefore, 492608 animals will be left in 30 years.

Now, the number of elements left in 80 years is

In this case you need to click the 7 which is in the hundred millions place

From the information provided, the storm is travelling at a speed of 30km/hr. In other words, its travelling 30 kilometers every hour. If the storm is 60 kilometers away, then we have the following ratio;

Answer:

The decimal form of 2/4 is;

Explanation:

We want to turn the fraction to decimal.

it can be obtained by;

Therefore, the decimal form of 2/4 is;

The hole appears in the rational function when the numerator and the denominator have the same zeroes

Since the rational function is

Factorize the denominator

The rational function h(x) is

Since (x + 7) is in both numerator and denominator

Then there is a hole at x + 7 = 0

Let us find the value of x

The whole is at x = -7

Then simplify the fraction to find the value of y at x = -7

Cancel the bracket (x+7) up by the same bracket down

Substitute x by -7

The hole is at (-7, -1/14)

Step 1

Given;

Required; To find the value of y that makes the equation true

Step 2

Find the value of y

Hence, the value of y that makes the equation true is 16/3

Answer: I believe it is representing the angular position of a vector

In short, it is a symbol to represent a measured angle.

Answer:

He started with at least 34 stamp collection

Explanation:

Let x represent Carlos' initial stamp collection.

From the question, we're told that he sold half of them, bought twelve more, and currently has at least 29, we can go ahead and set up an inequality as shown below;

We can go ahead and solve for x following the below steps;

Step 1: Subtract 12 from both sides of the equation;

Step 2: Multiply both sides by 2;

From the above, we can say that Carlos started with at least 34 stamp collection

x = number of 2 bedrooms units

y= number of 3 bedroom units

194 condominiums

x+y = 194 (a)

the total number of rooms in the entire complex is 494

2x + 3y = 494 (b)

We have the system of equations:

x+y = 194 (a)

2x + 3y = 494 (b)

Solve (a) for x

x = 194-y

Replace x on (b) and solve for y

2 (194-y ) + 3 y = 494

388 - 2y +3 y = 494

-2y+3y = 494-388

y= 106

Replace y on (a) and solve for x

x + 106 = 194

x = 194-106

x= 88

2-bedroom units = 88

3- bedrooms units = 106

Statement Problem: Solve for the missing sides of the triangle;

Solution:

The sum of angles in a triangle is 180degrees. Thus,

Since measure angle A and measure angle B are equal. Thus, the triangle is isosceles and the two sides are equal.

We would apply sine rule to find the missing side a.

Thus,

CORRECT ANSWERS:

Using the binomial distribution, the measures are given as follows:

a) Expected value: 28.

b) Variance of 16.8 and standard deviation of 4.099.

The formula for the probability of x successes is:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are given by:

Hence, in the context of this problem, the values of these parameters are given as follows:

p = 0.4, n = 70.

The expected value of the distribution is calculated as follows:

E(X) = np.

Hence:

E(X) = 70 x 0.4 = 28.

The variance of the distribution is calculated as follows:

V(X) = np(1 - p) = 70 x 0.4 x 0.6 = 16.8.

The standard deviation of the distribution is calculated as follows:

sqrt(V(X)) = sqrt(16.8) = 4.099.

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REmember that

A continuous function allows the x-values to be ANY points in the interval, including fractions, decimals, and irrational values

A discrete function allows the x-values to be only certain points in the interval, usually only integers or whole numbers.

Discrete functions have scatter plots as graphs and continuous functions have lines or curves as graphs

Answer

Option D is correct.

x = ±i√(5) OR ±i√(3)

Explanation

The question wants us to solve

x⁴ + 8x² + 15 = 0

To solve this, we first say that

Let x² = y

So that,

x⁴ = (x²)² = y²

So, the equation becomes

y² + 8y + 15 = 0

This is a simple quadratic equation, we then solve this

y² + 8y + 15 = 0

y² + 3y + 5y + 15 = 0

y (y + 3) + 5 (y + 3) = 0

(y + 5) (y + 3) = 0

y + 5 = 0 OR y + 3 = 0

y = -5 OR y = -3

But, Recall that x² = y

If y = -5

x² = y = -5

x² = -5

x = √(-5)

If y = -3

x² = y = -3

x² = -3

x = √(-3)

So,

x = √(-5) OR x = √(-3)

Note that

√(-1) = i

√(-5) = √(-1) × √(5)

= i√5

And

√(-3) = √(-1) × √(3)

= i√3

Hence

x = ±i√(5) OR ±i√(3)

Hope this Helps!!!

The values of the given polynomial are:-

f(0) = 12

f(2) = 28

f(-2) = 52

Given polynomial:-

[tex]f(x)=-x^3+7x^2-2x+12[/tex]

We have to find the values of f(0), f(2) and f(-2).

Putting x = 0 in f(x), we get,

[tex]f(0)=-(0)^3+7(0)^2-2(0)+12[/tex]

f(0) = 0 +0 - 0 + 12 = 12

Hence, the value of f(0) is 12.

Putting x = 2 in f(x), we get,

[tex]f(2)=-(2)^3+7(2)^2-2(2)+12[/tex]

f(2) = -8 + 28 - 4 + 12 = 28

Hence, the value of f(2) is 28.

Putting x = -2 in f(x), we get,

[tex]f(-2)=-(-2)^3+7(-2)^2-2(-2)+12[/tex]

f(-2) = 8 +28 + 4 +12 = 52

Hence, the value of f(-2) is 52.

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Supplementary angles are two angles whose sum is exactly 180, therefore:

162 + x = 180

Solving for x:

subtract 162 from both sides:

x = 180 - 162

x = 18

We will have the following:

2)

A(0, 7) : <7, -3>

B(1, 3) : <7, -3>

C(-1, -4) : <7, -3>

D(-5, 1) : <7, -3>

3)

From the graph we will have the following:

a.

b.

***Explanation***

For point 2, we will simply apply the vector to the corresponding coordinates, that is:

We have the coordinates:

and the vector:

So, in order to determine the final image we will have to follow the transformation rule:

*For point 3, we will simply count the number of units the image has moved to the left or rigth and that will be our transformation rule for the x-axis, and the number of units the image has moved up or down and that will be our transformation rule for the y-axis.

In the case of the problem, the images moved 7 units to the rigth (+7) and then moved 5 units up (+5), so the transformation rule in coordinate notation is given by:

And in order to write it in vector notation, we simply write the units the images move:

Answer:

A. (0, 3)

C. (1, 1.5)

Explanation:

A point is a solution to the system if it satisfies both inequalities.

So for each option, we get:

Replacing (x, y) = (0, 3)

y ≥ -2x + 3

3 ≥ -2(0) + 3

3 ≥ 3

y ≤ -x² - x + 4

3 ≤ -0² - 0 + 4

3 ≤ 4

Since both inequalities are satisfied, (0, 3) is a solution.

For (x, y) = (-1, 5)

y ≥ -2x + 3

5 ≥ -2(-1) + 3

5 ≥ 2 + 3

5 ≥ 5

y ≤ -x² - x + 4

5 ≤ -(-1)² - (-1) + 4

5 ≤ -1 + 1 + 4

5 ≤ 4

Since 5 is not lower than 4, (-1, 5) is not a solution

For (x, y) = (1, 1.5)

y ≥ -2x + 3

1.5 ≥ -2(1) + 3

1.5 ≥ -2 + 3

1.5 ≥ 1

y ≤ -x² - x + 4

1.5 ≤ -(1)² - (1) + 4

1.5 ≤ -1 - 1 + 4

1.5 ≤ 2

Since both inequalities are satisfied, (1, 1.5) is a solution.

Therefore, the answers are

A. (0, 3)

C. (1, 1.5)

Suppose that an item regularly costs $100.00 and is discounted 22%. If it is then marked up 22%, is the resulting price $100.00? If not, what is it? Choose the correct answer below and, if necessary, fill in the answer box to complete your choice.​

1)

we have

100%-22%=78%=78/100=0.78

so

If is discounted 22%

the new price is 100,000*0.78=$78,000

2) If it is then marked up 22%

the new price is

100%+22%=122%=122/100=1.22

78,000*1.22=$95,160

therefore

The new price is not $100,000

the new price is $95,160

The equation of the line is found as y + 2 = (-2/3)(x - 5).

For the given question.

The passing coordinates of the line is given as;

(x1, y1) = (-1, 7)

(x2, y2) = (5, -2)

Find the slope using the equation.

slope = m = (y2 - y1)/(x2 - x1)

Put the values.

m = (-2 - 7)/(5 + 1)

m = -9/6

m = -3/2

Use the point slope formula to find the equation of line in slope intercept form.

y - y1 = m(x - x1)

y + 2 = (-2/3)(x - 5)

Thus, the equation of the line is found as y + 2 = (-2/3)(x - 5).

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