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MAXImum [283]
2 years ago
12

The degree of the polynomial function f(x) is 4.

Mathematics
1 answer:
Lyrx [107]2 years ago
3 0

Answer:

Option A

Step-by-step explanation:

Degree of the polynomial function = 4

That means highest degree term of the given polynomial has power = 4

If the roots of a quadratic polynomial are a, b, c, d then the polynomial function will be,

f(x) = (x - a)(x - b)(x - c)(x - d)

It's given in the question that roots are x = -2, -1, 1 and 3

Therefore, polynomial function will be,

f(x) = (x + 2)(x + 1)(x - 1)(x - 3)

From the given options, graph A shows that the graph intersects the x-axis at x = -2, -1, 1 and 3

Therefore, Option A will be the answer.

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In triangle abc, the perimeter is 36, and ab=ac. line ad is perpendicular to bc at the point d, and triangle abd's perimeter is
Musya8 [376]
Let x=ab=ac, and y=bc, and z=ad.

Since the perimeter of the triangle abc is 36, you have:

Perimeter of abc = 36
ab + ac + bc = 36
x + x + y = 36
(eq. 1) 2x + y = 36

The triangle is isosceles (it has two sides with equal length: ab and ac). The line perpendicular to the third side (bc) from the opposite vertex (a), divides that third side into two equal halves: the point d is the middle point of bc. This is a property of isosceles triangles, which is easily shown by similarity.

Hence, we have that bd = dc = bc/2 = y/2 (remember we called bc = y).

The perimeter of the triangle abd is 30:

Permiter of abd = 30
ab + bd + ad = 30
x + y/2 + z =30
(eq. 2) 2x + y + 2z = 60

So, we have two equations on x, y and z:

(eq.1) 2x + y = 36
(eq.2) 2x + y + 2z = 60

Substitute 2x + y by 36 from (eq.1) in (eq.2):

(eq.2') 36 + 2z = 60

And solve for z:

36 + 2z = 60 => 2z = 60 - 36 => 2z = 24 => z = 12

The measure of ad is 12.

If you prefer a less algebraic reasoning:

- The perimeter of abd is half the perimeter of abc plus the length of ad (since you have "cut" the triangle abc in two halves to obtain the triangle abd).

- Then, ad is the difference between the perimeter of abd and half the perimeter of abc:

ad = 30 - (36/2) = 30 - 18 = 12
4 0
3 years ago
Read 2 more answers
32.8g of sugar is needed to make 4 cakes. How much sugar is needed for 7 cakes?
allochka39001 [22]

Answer:

57.4g

Step-by-step explanation:

32.8g of sugar is needed to make 4 cakes. How much sugar is needed for 7 cakes?

From the above questions, we know that:

4 cakes = 32.8g

7 cakes = x g

Cross Multiply

4 × xg = 7 × 32.8g

x = 7 × 32.8g/4

x = 57.4 g

Therefore, 57.4g is needed for 7 cakes

6 0
2 years ago
The sum of two numbers is 15.
Blizzard [7]

Answer:

7

Step-by-step explanation:

15-8=7 this is how you answer it

3 0
3 years ago
Read 2 more answers
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Oliga [24]
Slope = (2+6)/(2+2) = 8/4 = 2

answer:

slope = 2
8 0
3 years ago
Jesse and Amir were assigned the same book to read for class. Jesse started reading on Saturday, and he is reading 30 pages a da
barxatty [35]

Answer:

whats the question?

Step-by-step explanation:

8 0
3 years ago
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