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fiasKO [112]
3 years ago
9

What are the zeros of the function g(x) = (x + 6) (x – 4)(x + 2) ?

Mathematics
1 answer:
vitfil [10]3 years ago
5 0

9514 1404 393

Answer:

  x in {-6, -2, 4}

Step-by-step explanation:

The zero product rule tells you that a product will be zero if and only if one of the factors is zero. These binomial factors are zero when x has a value that is opposite the constant of the binomial.

  x +6 = 0   ⇒   x = -6

  x -4 = 0   ⇒   x = 4

  x +2 = 0   ⇒   x = -2

The zeros of the function are the x-values -6, -2, and 4.

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The perimeter of the triangle shown are equal. Find the side lengths of each triangle.
Lunna [17]

Good morning ☕️

___________________

Step-by-step explanation:

Let p1 be the perimeter of triangle ABC

p2 be the perimeter of triangle PQR

p1=(2x+4)+(2x+3)+(2x) = 6x+7

p2=(2x)+(2x)+(3x+1) = 7x+1

p1=p2 ⇔ 6x+7=7x+1 ⇔ 7x-6x=7-1 ⇔x=6

Then :

AC=2(6)=12

AB=2(6)+4=16

BC=2(6)+3=15

PQ=12

QR=12

PR=3(6)+1=19.

_____

:)

6 0
3 years ago
Read 2 more answers
Equilateral triangle ABC has an area of \sqrt{3}√ ​3 ​ ​​ . If the shaded region has an area of \piπK − \sqrt{3}√ ​3 ​ ​​ , what
Liono4ka [1.6K]

Answer:

The value of k = 4/3

Step-by-step explanation:

* Lets explain how to solve the problem

- An equilateral triangle ABC is inscribed in a circle N

- The area of the triangle is √3

- The shaded area is the difference between the area of the circle

  and the area of the equilateral triangle ABC

- The shaded are = k π - √3

- We need to find the value of k

* <u><em>At first lets find the length of the side of the Δ ABC</em></u>

∵ Δ ABC is an equilateral triangle

∴ Its area = √3/4 s² , where s is the length of its sides

∵ The area of the triangle = √3

∴ √3/4 s² = √3

- divide both sides by √3

∴ 1/4 s² = 1

- Multiply both sides by 4

∴ s² = 4 ⇒ take √ for both sides

∴ s = 2

∴ The length of the side of the equilateral triangle is 2

* <u><em>Now lets find the radius of the circle</em></u>

- In the triangle whose vertices are A , B and N the center of the circle

∵ AN and BN are radii

∴ AN = BN = r , where r is the radius of the circle

∵ The sides of the equilateral angles divides the circle into 3 equal

   arcs in measure where each arc has measure 360°/3 = 120°

∵ The measure of the central angle in a circle equal the measure

  of the its subtended arc arc

∵ ∠ANB is an central angle subtended by arc AB

∵ The measure of arc AB is 120°

∴ m∠ANB = 120°

- By using the cosine rule in Δ ANB

∵ AB = 2 , AN = BN = r , m∠ANB = 120°

∴ (2)^{2}=r^{2}+r^{2}-2(r)(r)cos(120)

∴ 4=r^{2}+r^{2}-2(r)(r)(-0.5)

∴ 4=r^{2}+r^{2}-(-r^{2})

∴ 4=r^{2}+r^{2}+r^{2}

∴ 4=3r^{2}

- Divide both sides by 3

∴ r^{2}=\frac{4}{3}

- Take square root for both sides

∴ r = 2/√3

* <u><em>Lets find the value of k</em></u>

∵ Area circle = πr²

∵ r = 2/√3

∴ Area circle = π(2/√3)² = (4/3)π

∵ Area shaded = area circle - area triangle

∵ Area triangle = √3

∴ Area shaded = (4/3) π - √3

∵ Area of the shaded part is π k - √3

- Equate the two expressions

∴ π k - √3 = (4/3) π - √3

∴ k = 4/3

* The value of k = 4/3

7 0
2 years ago
Ms.Holmes decided to water her plants.She had 2 1/2 gallons of water.She gave each plant 1/4 gallon of water.Which expression co
Inessa [10]

Answer:

(1/4)x=2 1/2

Step-by-step explanation:

It is 2.5 gal. of water and 0.25 gal. of water per plant.

It could also be x=(1/4)/(2 1/2)

6 0
3 years ago
Which statement about g(x)=x^2-576 is true
goldenfox [79]
We can answer without the picture or answer options
5 0
3 years ago
Please Round 1.54 thank you
bearhunter [10]

Answer:

okay so it would be 2 or 1.5 i dont know if you want it whole number but i will explain

if the number is 5 or more like 5.1 or even 5 you round up

if the number is under 5 like 4,3,2,1 your round down

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
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