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Cloud [144]
3 years ago
14

Use algebra to explain how you know that a rectangle with side lengths one less and one more than a square will always be 1 squa

re unit smaller than the square. 2. What is the difference in the areas of a square and rectangle if the rectangle has side lengths 2 less and 2 more than a square? Use algebra or a geometric model to compare the areas and justify your answer. 3. Explain why the method for factoring shown in this lesson is called the product-sum method.
Mathematics
1 answer:
My name is Ann [436]3 years ago
4 0

Answer:

Step-by-step explanation:

1. If a is the length of the side of the square, then a 2 is the area of the square. The rectangle’s side lengths will be (a − 1) and      (a + 1). That product, which represents the area of the rectangle, is a 2 − 1, or 1 square unit less than the area of the square.

2. Using the same logic as for Problem 1, the rectangle dimensions will be     (a + 2) and (a − 2) with an area of a 2 − 4. Therefore, the area of the rectangle is 4 square units less than the area of the original square

3. It is called the product-sum method because you look for the two numbers with a product equal to the constant term of the quadratic expression and a sum equal to the coefficient of the linear term

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LA and B are vertical angles. If m_A = (5x + 5) and m_B = (4x + 29), then find the measure of_A.​
OverLord2011 [107]

Answer:

If A and B are vertical angles, then they are congruent, so their measures are equal.

This means

(5x + 5)º = (4x + 29)º

5x + 5 = 4x + 29

x = 24

Then angle A has measure (5*24 + 5)º = 125º.

Step-by-step explanation:

5 0
3 years ago
Is The polar form of a complex number is unique?
Pie

Answer:

  no

Step-by-step explanation:

The angle in the polar form of a complex number can have any multiple of 2π radians added to it, and the number will be the same number. That is, there are an infinite number of representations of a complex number in polar form.

6 0
3 years ago
Angle 3 and angle 4 form a linear pair. The measure of Angle 3 is four more than three
mel-nik [20]

Answer:

angle 3. ( x ) is 136°

angle 4 ( y ) is 44° !!

Step-by-step explanation:

Let angle 3 be x and angle 4 be y

Given, Angle 3 and angle 4 form a linear pair

x + y = 180 [ sum of linear pair angle is 180 ] ... ( i )

Also, The measure of Angle 3 is four more than three

The measure of Angle 3 is four more than threetimes the measure of angle 4.

x = 4 + 3y .... ( ii )

Putting value of x from ( ii ) in ( i )

4 + 3y + y = 180

4y = 176

y = 44

Also, x + y = 180 => x = 180 - 44 = 136

7 0
3 years ago
Which of the following probabilities is equal to approximately 0. 2957? Use the portion of the standard normal table below to he
Travka [436]

Probability of an event is the measure of its chance of occurrence. The event out of the listed events whose probability is 0.2957 is given by : Option C: P(0.25 \leq Z \leq 1.25)

<h3>How to get the z scores?</h3>

If we've got a normal distribution, then we can convert it to standard normal distribution and its values will give us the z-score.

If we have

X \sim N(\mu, \sigma)

(X is following normal distribution with mean \mu and standard deviation \sigma )

then it can be converted to standard normal distribution as

Z = \dfrac{X - \mu}{\sigma}, \\\\Z \sim N(0,1)

(Know the fact that in continuous distribution, probability of a single point is 0, so we can write

P(Z \leq z) = P(Z < z) )

Also, know that if we look for Z = z in z tables, the p-value we get is

P(Z \leq z) = \rm p \: value

Using the z-table, we get the needed probabilities as:

Case 1:

P(-1.25 \leq Z \leq 0.25) = P(Z \leq 0.25) - P(Z \leq -1.25) \approx 0.5987 - 0.1056 = 0.4931

Case 2:

P(-1.25 \leq Z \leq 0.75) = P(Z \leq 0.75) - P(Z \leq -1.25) \approx 0.7734- 0.1056=0.6678

Case 3:

P(0.25 \leq Z \leq 1.25) = P(Z \leq 1.25) - P(Z \leq 0.25) \approx 0.8944 - 0.5987=0.2957

Case 4:

P(0.75 \leq Z \leq 1.25) = P(Z \leq 1.25) - P(Z \leq 0.75) \approx 0.8944 - 0.7734 =0.1210

Thus, the event out of the listed events whose probability is 0.2957 is given by : Option C: P(0.25 \leq Z \leq 1.25)

Learn more about z-scores here:

brainly.com/question/13299273

5 0
2 years ago
What is the common denominator of -1/y and 2/5y
Anarel [89]
-1/y = 2/5y. The change from -1 to 2 would be -2, so we now that the change from y to 5y would also have to be -2. -2 = -10 so you multiply by 5. After doing the same to the top you would come to the conclusion that the LCD would be 5y.  Hope this helps!
4 0
3 years ago
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