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Dmitry_Shevchenko [17]
3 years ago
6

A polynomial has x-intercepts of 3, 0, and –1, and passes through the point (1, –8). Which of the following functions could repr

esent this graph? 1. x3 – 2x2 – 3x 2. x2 – 2x – 3 3. 2x2 – 4x – 6 4. 2x3 – 4x2 – 6x
Mathematics
1 answer:
Brilliant_brown [7]3 years ago
3 0

Answer:

option 4

Step-by-step explanation:

Given the x- intercepts say x = a, x = b, x - c then the corresponding factors are

(x - a), (x - b), (x - c) and the polynomial is the product of the factors

Here the x- intercepts are x = 3, x = 0, x = - 1, thus the factors are

(x - 3), (x - 0), (x - (- 1) , that is

(x - 3), x and (x + 1) , then

y = ax(x - 3)(x + 1) ← where a is a multiplier

To find a substitute (1, - 8) into the equation

- 8 = a(1 - 3)(1 + 1) = - 4a ( divide both sides by - 4 )

a = 2, thus

y = 2x(x - 3)(x + 1) ← expand factors using FOIL

   = 2x(x² - 2x - 3) ← distribute by 2x

    = 2x³ - 4x² - 6x

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Line m is parallel to line p. m ∠ HEF = 39º and m ∠ IGF = 13º. Find the m ∠ EFG. Explain in detail how you know you are correct.
svetlana [45]

Answer:

The measure of ∠EFG is 52°

Step-by-step explanation:

Given line m is parallel to line p. m∠HEF = 39º and m∠IGF = 13º.we have to find m∠EFG.

In ΔJFG,

By angle sum property of triangle, which states that sum of all angles of triangle is 180°

m∠FJG+m∠JGF+m∠JFG=180°

⇒ 39°+13°+m∠JFG=180°

⇒ m∠JFG=180°-39°-13°=128°

As JFE is a straight line ∴ ∠JFG and ∠EFG forms linear pair

⇒ m∠JFG+m∠EFG=180°

⇒ 128°+m∠EFG=180°

⇒ m∠EFG=52°

The measure of ∠EFG is 52°

6 0
3 years ago
Find the volume of a pyramid with a square base, where the perimeter of the base is 8.2\text{ cm}8.2 cm and the height of the py
7nadin3 [17]

Answer:

V=18.2cm^3

Step-by-step explanation:

The volume of the pyramid is given by:

V=\frac{A_{b}h}{3}

where A_{b} is the area of the base and h is the height.

We know that the height is:

h=13cm

Thus we need to find the area of the square at the base.

The perimeter of the square is:

p=8.2cm

this means that the length of the sides of the square is :

l=\frac{p}{4}\\ \\l=\frac{8.2cm}{4}\\ \\l=2.05cm

Now we can find the area of the base which the area of the square:

A_{b}=l^2\\A_b=(2.05cm)^2\\A_b=4.2025cm^2

and finally we find the volume:

V=\frac{A_{b}h}{3}

V=\frac{(4.2025cm^2)(13cm)}{3}\\ \\V=\frac{54.6325cm^3}{3}\\ \\V=18.2108cm^3

Which rounded to the nearest tenth of a cubic centimeter is: V=18.2cm^3

3 0
3 years ago
Adele opens an account with $100 and deposits $35 a month. Kent opens an account with $50 and also deposits $35 a month. Will th
Svetach [21]
Equations:

100 + 35m
50 + 35m

Steps:
100 + 35m = 50 + 35m <span>

<em>Set the equations equal to each other.</em>
</span>   <span />
<span>
100 + 35m = 50 + 35m <span>
-50              - 50
</span>
<em>Subtract 50 from both sides of equation to isolate the variable on one side</em>.

50+35m=35m
     -35m  -35m

<em>Subtract 35m from both sides of equation.</em>

50=m

In fifty months, they will have the same amount of money. They will each contain $1850 dollars.

Hope this helps.
</span>                      

7 0
3 years ago
72 greater than r is less than −432
pshichka [43]

its Greater than

Step-by-step explanation:

the 72 is a positive and -432 is a negative cause it has a minus

6 0
3 years ago
Find the distance between the points (4.5,-1.5), (4.5,7.25)<br> The distance is ____.
poizon [28]

Answer:

8.75

Step-by-step explanation:

5 0
3 years ago
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