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
WARRIOR [948]
3 years ago
9

In quadrilateral $ABCD$, we have $AB=3,$ $BC=6,$ $CD=4,$ and $DA=4$.

Mathematics
1 answer:
vampirchik [111]3 years ago
8 0
The triangle inequality applies.

In order for ACD to be a triangle, the length of AC must lie between CD-DA=0 and CD+DA=8.

In order for ABD to be a triangle, the length of AC must lie between BC-AB=3 and BC+AB=9.

The values common to both these restrictions are numbers between 3 and 8. Assuming we don't want the diagonal to be coincident with any sides, its integer length will be one of ...
{4, 5, 6, 7}
You might be interested in
Parabolas. Please help me
olganol [36]
  1. x² = 16 y
  2. x = 0
  3. (x + 4)² = 2/3 (y - 2)
  4. Gayle identifies that the vertex of the parabola is <u>(3, -1)</u> . The parabola opens <u>right</u>, and the focus is <u>3 </u>units away from the vertex. The directrix is <u>6 </u>units from the focus. The focus is the point <u>(6, -1)</u>. The directrix of the equation is <u>x = 0.</u>
  5. (y - 6)² = 4p (x - 3)

Step-by-step explanation:

1. First figure

We plot the parabola as given in the attached diagram.

As it is facing upwards, the equation goes as x² = 4py

where, p = 4 (refer the attached diagram)

x² = 4py

x² = 4 (4) y

∴, standard form of parabola is x² = 16 y

2. Second figure

(y + 3)² = 4 (x - 1)

Comparing the given equation with the standard form

(y - k)² = 4p (x - h)

Now from this equation we get to know that

h = 1

p = 1

Directrix is x = (h - p)

So, x = 0

3. Third figure

3x² + 24x - 2y + 52 = 0

3x² + 24x = 2y - 52

3 (x² + 8x) = 2 (y - 26)

(x² + 8x) = 2 (y - 26) / 3

Adding 16 on both sides,

x² + 8x + 16 = 2 (y - 26) / 3 + 16

(x + 4)² = 2/3 y - 52/3 + 16

(x + 4)² = 2/3 y - 4/3

(x + 4)² = 2/3 (y - 2)

4. Fourth figure

(y + 1)² = 12 (x - 3)

Comparing the given equation with the standard form

(y - k)² = 4p (x - h)

Now from this equation we get to know that

k = -1

h = 3

p = 3

Gayle identifies that the vertex of the parabola is <u>(3, -1)</u> . The parabola opens <u>right</u>, and the focus is <u>3 </u>units away from the vertex. The directrix is <u>6 </u>units from the focus. The focus is the point <u>(6, -1)</u>. The directrix of the equation is <u>x = 0.</u>

5. Fifth figure

Focus = (2, 6)

Directrix is x = 4

Therefore, it follows the standard form

(y - k)² = 4p (x - h)

Directrix is given by x = h-p = 4

Focus is given by (h + p, k) = (2, 6)

Solving for (h - p) = 4, (h + p) = 2

2 - p - p = 4

-2p = 2

p = -1

Hence, h = 3

Therefore, the standard form can be written as

(y - 6)² = 4p (x - 3)

7 0
3 years ago
Find an equation for the nth term of the arithmetic sequence.<br> -20, -16, -12, -8, ...
liq [111]
Common difference = -16-(-20) = 4
nth term = -20+(n-1)4
5 0
3 years ago
Read 2 more answers
Presence of the activity in this illustration is an example of how a country’s government can be shaped by
katen-ka-za [31]

Answer:

c or d but i think d

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
6) Aisha uses 2 meters of thread for every three squares that she se
Serggg [28]

Answer:

57 squares

Step-by-step explanation:

38/2=19

19*3=57

3 0
3 years ago
Read 2 more answers
The radius of a circle is 35 centimeters.
dem82 [27]

Answer:

3864.5

Step-by-step explanation:

I used 3.14 for pie, since its more common than 22/7.

To find the area of a circle: pir^2.

r=35

pi=3.14

35 times 35=1225

1225 times 3.14=3846.5

6 0
3 years ago
Other questions:
  • !!50 POINTS!! You have six $1 bills, eight $5 bills, two $10 bills, and four $20 bills in your wallet. You select a bill at rand
    8·2 answers
  • Rewrite the equation below so that it does not have fractions.
    5·2 answers
  • How many liters are in 13 quarts
    5·1 answer
  • A culture started with 6,000 bacteria. After 4
    15·1 answer
  • The original price of a set lunch was 30 dollars. It is now sold at a 20%
    7·2 answers
  • Which equation has a slope of –52 and a y-intercept of –2?
    13·1 answer
  • Other question.........
    6·2 answers
  • Select the correct answer.
    14·1 answer
  • What is the solution to the linear equation? 6k 10. 5 = 3k 12 k = 0. 5 k = 2 k = 7. 3 k = 9.
    13·1 answer
  • On Wednesday 28% of the customers who bought gas at a gas station made additional purchases. There were 300 customers who bought
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!