1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
guajiro [1.7K]
3 years ago
10

Identify the intervals on which each quadratic function is positive Part 1

Mathematics
1 answer:
Gemiola [76]3 years ago
4 0

Answer:  1) (-∞, -6) U (-3, ∞)

               2) (-∞, -4) U (2, ∞)

               3) (-∞, -3) U (8, ∞)

<u>Step-by-step explanation:</u>

Find the zeros. Since the a-value is positive, the curve will be positive to the left of the leftmost zero and to the right of the rightmost zero.  +   -   +

                                                                                                     ←---|----|--→

1) y = x² + 9x + 18

  y = (x + 3)(x + 6)

 0 = (x + 3)(x + 6)

 0 = x + 3       0 = x + 6             +         --           +

 x = -3             x = -6              ←------|-----------|--------→

                                                     -6           -3

Positive Interval: (-∞, -6) U (-3, ∞)    

2) y = x² + 2x - 8

  y = (x + 4)(x - 2)

 0 = (x + 4)(x - 2)

 0 = x + 4       0 = x - 2              +         --          +

 x = -4             x = 2               ←------|-----------|--------→

                                                     -4            2

Positive Interval: (-∞, -4) U (2, ∞)    

3) y = x² - 5x - 24

  y = (x + 3)(x - 8)

 0 =  (x + 3)(x - 8)

 0 = x + 3       0 = x - 8               +        --           +

 x = -3             x = 8               ←------|-----------|--------→

                                                     -3            8

Positive Interval: (-∞, -3) U (8, ∞)    

   

You might be interested in
Triangle A B C is shown. Angle A B C is 95 degrees and angle B C A is 45 degrees. The length of A B is c and the length of B C i
NARA [144]

Answer:

(B)c = StartFraction (3) sine (45 degrees) Over sine (40 degrees) EndFraction

c=\dfrac{3 * \sin 45}{sin 40}

Step-by-step explanation:

In Triangle ABC is shown.

\angle A B C= 95 degrees

\angle B C A = 45 degrees.

|AB|=c

|BC|=3.0 cm

\angle A+\angle B+\angle C=180^\circ\\\angle A+95+45=180\\\angle A=180-140=40^\circ

Using the Law of Sines

\dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}

\dfrac{3}{\sin 40}=\dfrac{c}{\sin 45}\\\\$Cross multiply\\c*\sin 40 =3 * \sin 45\\\\c=\dfrac{3 * \sin 45}{sin 40}

The correct option is B.

6 0
3 years ago
Read 2 more answers
What is 5/15 written in simplest form?
jeka57 [31]
Divide the numerator and denominator by 5

This should give you 1/3
Hopes this helps!
8 0
3 years ago
Read 2 more answers
hbjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjlllllllllllllllllllllllllllllk
V125BC [204]
JE BAD WBDONEODVDIWBDIWBDOVDKEBDOEBEKDVIEEJLEBEIDBDIVDKEHDOEHKDBEIEUWPWOEJHDOEBDKWKWOHEHDBEIDHEBEBRH
4 0
3 years ago
A glass jar has a height of 5 inches and a radius of 2. 5 inches. vanessa wants to fill the jar with beads that cost $0. 12 per
Shalnov [3]
Answer:
height(h)= 5in
radius(r) =2.5in
Volume(V)= pi ×r^2 ×h
V=(22/7)2.5^2×5=98.21in^3
$0.12=1 in^3
Amount to be paid= 0.12×98.21
=$11.79

Step-by-step explanation:
Firstly, find the volume of the jar. When the filled with the beads to the brim, it will assume the shape of the jar, hence their volume will be equal. We assume that the jar is a cylinder. After you find the volume, multiply the volume by the amount per cubic inches.
6 0
2 years ago
Law of sines: How many distinct triangles can be formed for which m∠A = 75°, a = 2, and b = 3?
butalik [34]
According to the law of sines:

\frac{a}{sin(A)} = \frac{b}{sin(B)}

Using the given values, we can find the angle B and find the number of possible triangles that can be formed.

\frac{2}{sin(75)}= \frac{3}{sin(B)} \\  \\ &#10;sin(B)=3* \frac{sin75}{2}  \\  \\ &#10;sin(B)=1.45 \\  \\ &#10;B=sin^{-1} (1.45)

The range of sin is from -1 to 1. The above expression does not yield any possible value of B, as sin of no angle can be equal to 1.45.

Therefore, we can conclude that no triangle exists with the given conditions.
5 0
3 years ago
Other questions:
  • Six people are sitting around a circular table, and each person has either blue eyes or green eyes. Let x be the number of peopl
    7·1 answer
  • Quadrilateral WXYZ has vertices W(-3, 4), X(1, 8), Y(8, 7) and Z(-2, -3). The quadrilateral is an isosceles trapezoid.
    15·1 answer
  • A meat market has 68 pounds of meat to divide into 6 packs. He must use all the meat. How many pounds of meat will be in each pa
    9·2 answers
  • PLLLLLLLLLLLLLLLLLLLLEEEEEEEEEESSSSSSSSSSSSSSSWWWWWWWWWWW<br> help me
    8·1 answer
  • What does<br> non-proportional and<br> proportional
    13·2 answers
  • Need help thanksssss
    6·1 answer
  • True or false?<br> please help me out
    12·2 answers
  • ASAP PLZTo estimate 103% of 63 rich rounded 103% down to 100% 63 down to 60 and multiplied 60 by 1 to get 60 which of these stat
    14·1 answer
  • 7 Lanza is a gardener.
    5·1 answer
  • Data : Peraturan kedisiplinan kerja atas dasar kesepakatan kerja bersam dengan serikat pekerja. Hasil Pemantauan atas Absensi Ta
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!