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cestrela7 [59]
3 years ago
14

Select the polynomial that is a perfect square trinomial.

Mathematics
2 answers:
Sveta_85 [38]3 years ago
7 0

Answer:

The answer is 16x2 − 8x + 1

To be a perfect square trinomial, the rule must be used:

(a - b)² = a² - 2ab + b²

Let's check all choices

A. a = 7x, b = 4

(7x - 4)² = 49x² - 56x + 16

B. a = 2a, b = 5

(2a - 5)² = 4a² - 20a + 25

C. a = 5b, b = √10

(5b - √10)² = 25b² - 10√10 b + 10

D. a = 4x, b = 1

(4x - 1)² = 16x² - 8x + 1

CORRECT

Step-by-step explanation:

cestrela7 [59]3 years ago
3 0
The answer is <span>16x2 − 8x + 1
</span>
To be a perfect square trinomial, the rule must be used:
(a - b)² = a² - 2ab + b²

Let's check all choices
A. a = 7x, b = 4
(7x - 4)² = 49x² - 56x + 16

B. a = 2a, b = 5
(2a - 5)² = 4a² - 20a + 25

C. a = 5b, b = √10
(5b - √10)² = 25b² - 10√10 b + 10

D. a = 4x, b = 1
(4x - 1)² = 16x² - 8x + 1
CORRECT
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Find the length of each side of the triangle determined by the three points P1,P2, and P3. State whether the triangle is an isos
Tanya [424]

Answer:

The triangle is both an Isosceles triangle and a right triangle.

Step-by-step explanation:

Given the vertices of a triangle.

$ P_{1} = (- 1, 4) $

$ P_{2} = (6, 2) $    and

$ P_{3} = (4, - 5) $

We find the distance between all the points to determine the length of each side of the triangle.

Distance between any two points, say, $ (x_1, y_1) $ and $ (x_2, y_2) $ is:

                                 $ \sqrt{\bigg ( \textbf{x}_{\textbf{2}} \hspace{1mm} \textbf{- x}_{\textbf{1}} \bigg )^{\textbf{2}} \textbf{+}   \bigg( \textbf{y}_{\textbf{2}} \hspace{1mm} \textbf{- y}_{\textbf{1}} \bigg)^ {\textbf{2}} $

Length between $ P_1 $ and $ P_{2} $ , (Side 1) :

$ (x_1, y_1) = (- 1, 4) $     and

$ (x_2, y_2) = (6, 2) $

Distance = $ \sqrt{\bigg(6 - (-1) \bigg)^{2} \hspace{1mm} + \hspace{1mm} \bigg( 2 - 4 \bigg )^2 $

$ = \sqrt{7^2 + 2^2} $

$ = \sqrt{49 + 4} $

$ = \sqrt{\textbf{53}} $

Length of Side 1 = $  \sqrt{\textbf{53}} $ units.

Distance between $ P_1 $ and P_2 , (Side 2):

$ (x_1, y_1) = (-1, 4) $

$ (x_2, y_2) = (4, - 5) $

Distance = $ \sqrt{ \bigg( 4 + 1 \bigg)^2 \hspace{1mm} + \bigg( - 5 - 4 \bigg ) ^2 $

$ = \sqrt{ 25 + 81 } $

$ = \sqrt{\textbf{106}} $

Length of Side 2 = $ \sqrt{\textbf{106}} $ units.

Distance between $ P_2 $ and $ P_3 $ , Side 3 :

$ (x_1, y_1) = (4, 5) $

$ (x_2, y_2) = (6, 2) $

Distance = $ \sqrt{ 2^2 \hspace{1mm} + \hspace{1mm} 7^2} $

$ = \sqrt{49 + 4} $

$ = \sqrt{\textbf{53} $

Length of Side 3  = $ \sqrt{\textbf{53}} $ units.

Note that the length of Side 1 = Length of Side 3.

That means the triangle is Isosceles.

Also, For a triangle to be right angle triangle, using Pythagoras theorem we have:

(Side 1)² + (Side 3)² = (Side 2)²

$ \bigg( \sqrt{53} \bigg )^2 \hspace{1mm} + \hspace{1mm} \bigg( \sqrt{53} \bigg)^2 \hspace{1mm} = \hspace{1mm} \bigg ( \sqrt{106} \bigg ) ^2 $

i.e, 53 + 53  = 106

Hence, the triangle is a right - angled triangle as well.

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Answer:

a) The slope of the function is 3.

c) The equation is represented by n(t) = 3\cdot t + 35.

d) The y-intercept of the function is 35.

Step-by-step explanation:

a) According to the statement, we must assume that number of pieces of mail that must be hand-sorted (dependent variable) is represented by a linear function in terms of time (independent variable). That is:

n(t) = m\cdot t + n_{o} (1)

Where:

m - Slope, measured in number of pieces per minute.

t - Time, measured in minutes.

n_{o} - Initial number of pieces of mail that must be hand-sorted (y-intercept), measured in pieces.

n - Current number of pieces of mail that must be hand-sorted, measured in pieces.

From Geometry, we know that a line can be formed by know two distinct points. If we know that n(15\,min) = 80\,p and n(45\,min) = 170\,p, then the following system of linear equations is formed:

15\cdot m + n_{o} = 80 (2)

45\cdot m + n_{o} = 170 (3)

The solution of the system of equations is:

m = 3 and n_{o} = 35

The slope of the function is 3.

c) By (1) and using results from a) we conclude that the equation function is:

n(t) = 3\cdot t + 35 (4)

d) The y-intercept of the function is 35.

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